Answer: The value of a is 2 and the value of b is 3.
Step-by-step explanation:
Given : △CDE maps to △STU with the transformations (x, y) → (x − 2, y − 2) →(3x, 3y)
The first transformation is a translation ,so there will be no change in the length of the sides ∵ translation is a rigid motion.
The second transformation is a dilation ,so there will be a change in the length of the sides by scale factor of 3. ∵ dilation is not a rigid motion.
Basically , by combining both transformation:
Length of Side in △STU = 3 x (Corresponding side in △CDE )
⇒ ST = 3CD and TU = 3 DE
If CD = a + 1, DE = 2a − 1, ST = 2b + 3 and TU = b + 6 , then
2b + 3=3(a + 1) and b + 6 = 3(2a − 1)
⇒ 2b + 3=3a+3 and b + 6 = 6a-3
⇒ 3a-2b=0 (i) and b = 6a-9 (ii)
Put value of b from (ii) in (i) , we get
3a-2(6a-9)=0
⇒ 3a-12a+18=0
⇒ -9a=-18
⇒ a= 2
Put value of a in (ii) , we get
b= 6(2)-9
=12-9=3
Hence, the value of a is 2 and the value of b is 3.
Answer:
a = 4 , b = 6
Step-by-step explanation: I did the same question
Multiply or divide as indicated.
y -9 • y -8 • y 10
.
Answer:
-16y -10
Step-by-step explanation:
So basically, since there are no parentheses, we can use PEMDAS:
y - 9 * y - 8 * y - 10
y - 9y - 8y - 10
-8y -8y - 10
-16y -10
The answer is y^-7 I had this in my lesson
HELP ASAP!!! will give brainliest to best answer!!
What proportional segment lengths verify that XZ¯¯¯¯¯∥PQ¯¯¯¯¯ ?
Fill in the boxes to correctly complete the proportion.
Answer:
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
or
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
Step-by-step explanation:
we know that
If two figures are similar then the ratio of its corresponding sides is proportional
In this problem
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
so
[tex]\frac{YP}{YX}=\frac{YQ}{YZ}[/tex]
substitute the given values
[tex]\frac{16}{21}=\frac{8}{10.5}[/tex]
Rewrite
[tex]\frac{16}{8}=\frac{21}{10.5}[/tex]
The boxes should be filled with [tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
The calculation is as follows:As we know that
In the case when two figures are similar so the ratio of its corresponding sides is proportional
In this given situation
triangle YPQ and triangle YXZ are similar by AA Similarity Theorem
So,
[tex]\frac{YP}{YX} = \frac{YQ}{YZ}[/tex]
[tex]\frac{16}{21} = \frac{8}{10.5}\\\\\frac{16}{8} = \frac{21}{10.5}[/tex]
It can be any of the both.
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Write a formula that describes the value of an initial investment of $1,200, growing an interest rate of 4% compounded continuously.
Continuous compound is e^rate x time
The formula would be D. 1200e^0.04t
Answer: OPTION D A = 1200.e(0.04)(t)
Step-by-step explanation:
If the interest is compounded continuously for t years at a rate of r per year, then the compounded amount is given by:
A = P. e rt
P =$1200, r = 4% , t = t years
A = 1200.e(0.04)(t)
Which of the following represents a direct variation?
y=2/x
y = -3x
y = x2 – 2x + 5
y=square root x
Answer:
Direct variation is constantly proportional (constant multiple)
Answer:
a) y = - 1/2 x
Step-by-step explanation:
The equation that represents a direct variation is y = -3x. So, correct option is B.
A direct variation is a relationship between two variables where one is a constant multiple of the other. In other words, as one variable increases or decreases, the other also increases or decreases in a consistent manner. The equation for direct variation is typically of the form y = kx, where k is the constant of variation.
Let's analyze each given equation:
y = 2/x - This equation does not represent a direct variation because y is not a constant multiple of x.
y = -3x - This equation does represent a direct variation because y is a constant multiple of x. Here, k (the constant of variation) is -3.
y = x² - 2x + 5 - This equation is a quadratic equation, not a direct variation, as it involves x raised to a power greater than 1.
y = √x - This equation does not represent a direct variation as y is not a constant multiple of x.
So, the equation that represents a direct variation is option 2) y = -3x. It has a direct relationship between y and x with a constant of variation of -3.
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A plane travels 240 miles on a bearing of N 10° E and then changes its course to N 67° E and travels another 180 miles. Find the total distance traveled north and the total distance traveled east. (Round each answer to the nearest whole number.)
Answer:
Step-by-step explanation:
Given
Plane travels 240 miles [tex]10^{\circ}[/tex] East of North
Position vector [tex]\vec{r_1}=240(\cos(10)\hat{j}+\sin (10)\hat{i})[/tex]
Then the plane travels 180 miles [tex]67^{\circ}[/tex] East of North
[tex]\vec{r_{21}}=180(\cos(67)\hat{j}+\sin (67)\hat{i})[/tex]
[tex]\vec{r_2}=\vec{r_{21}}+\vec{r_1}[/tex]
[tex]\vec{r_2}=\left ( 240\sin (10)+180\sin (67)\right )\hat{i}+\left ( 240\cos (10)+180\cos (67)\right )\hat{j}[/tex]
[tex]\vec{r_2}=\left ( 207.36\right )\hat{i}+\left ( 306.68\right )\hat{j}[/tex]
Total distance traveled in North direction is given by coefficient of \hat{j}
i.e. North[tex]=306.68\ miles\approx 307\ miles[/tex]
Total distance traveled in East direction is given by coefficient of \hat{i}
East [tex]=207.36\ miles\approx 207\ miles[/tex]
A garden supply store sells two types of lawn mowers. Total ales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Write and solve a system of equations to find the number sold of each type of mower.
Answer:
The number of small mowers are 19 and the large mowers are 11.
Step-by-step explanation:
Given:
A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold the 30. The small mower cost $249.99 and the large mower costs $329.99.
Now, to find the number of each type of mower sold.
Let the number of small mower be [tex]x.[/tex]
And the number of large mower be [tex]y.[/tex]
So, total number of mowers are:
[tex]x+y=30[/tex]
[tex]x=30-y\ \ \ ....(1)[/tex]
Now, the total sales of mowers are:
[tex]249.99(x)+329.99(y)=8379.70[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]249.99(30-y)+329.99y=8379.70[/tex]
[tex]7499.7-249.99y+329.99y=8379.70[/tex]
[tex]7499.7+80y=8379.70[/tex]
Subtracting both sides by 7499.7 we get:
[tex]80y=880[/tex]
Dividing both sides by 80 we get:
[tex]y=11.[/tex]
The number of large mower = 11.
Now, to get the number of small mowers we substitute the value of [tex]y[/tex] in equation ( 1 ):
[tex]x=30-y\\x=30-11\\x=19.[/tex]
The number of small mower = 19.
Therefore, the number of small mowers are 19 and the large mowers are 11.
Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can't recall the brand name and does not wish to return home to find the old can of paint. So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy. So he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband's selections independent of his wife's selections
The probability that both the woman and her husband fail to get the correct brand of paint is 4/9.
Explanation:To determine the probability that both the woman and her husband fail to get the correct brand of paint, we need to consider the probability of each event happening independently. Since the woman selects two brands at random out of the three available, the probability of her not getting the correct brand is 2/3. Similarly, the husband also selects two brands at random out of the three, so his probability of not getting the correct brand is also 2/3. Since the events are independent, we can multiply the probabilities together to get the probability that both fail to get the correct brand. Therefore, the probability is (2/3) * (2/3) = 4/9.
The husband's selections are independent of his wife's selections because each brand he chooses is not influenced by the brands his wife chooses. Regardless of what she selects, he still has three brands to choose from and selects two at random. This means that his probability of not getting the correct brand is the same regardless of his wife's choices.
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The sketch shows the floor plan of a bathroom. The shower tray is 2'6" square and is
fixed to the floor. The toilet and washbasin are both wall mounted.
14) Allowing for 15% wastage, approximately how many square yards of floor tiles should
be ordered?
A
7.25
B
6.25
C
9.25
D
5.50
E
8.50
Lea sold 2 cherry pies and 4 pumpkin pies for a total of $116. Kali sold 7 cherry pies and 8 pumpkins pies for a total of $286. What is the cost of one cherry pie and of one pumpkin pie
Answer: the cost of one cherry pie is $18 and the cost of one pumpkin pie is $20
Step-by-step explanation:
Let x represent the cost of one cherry pie.
Let y represent the cost of one pumpkin pie.
Lea sold 2 cherry pies and 4 pumpkin pies for a total of $116. This means that
2x + 4y = 116 - - - - - - - - - - - - - -1
Kali sold 7 cherry pies and 8 pumpkins pies for a total of $286. This means that
7x + 8y = 286 - - - - - - - - - - - - 2
Multiplying equation 1 by 7 and equation 2 by 2, it becomes
14x + 28y = 812
14x + 16y = 572
Subtracting, it becomes
12y = 240
y = 240/12 = 20
Substituting y = 20 into equation 1, it becomes
2x + 4 × 20 = 116
2x + 80 = 116
2x = 116 - 80 = 36
x = 36/2 = 18
How does the Pythagorean Theorem relate to trigonometric ratios? What is important to remember about coterminal angles and their trigonometric function values?
Answer:
How Pythagoras theorem relates to Trigonometry ratios
For a right angled triangle ∆ABC,
Let a = hypothenus
b = opposite
c = adjacent
Sin²θ + Cos²θ = 1
Provided that a² + b² = c²
To prove this divide through by c²
Tongive
a²/c² + b²/c² = c²/c²
Sinθ = a/c , Cosθ = b/c
So, the above equation becomes
(Sinθ)² + (Cosθ)² = 1
Sin²θ + Cos²θ = 1
Coterminal Angles
Coterminal Angles are angles who share the same initial side and terminal sides.
Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.
Final answer:
The Pythagorean Theorem and trigonometric ratios are related through the relationships between the sides of a right triangle. The theorem helps to calculate the sides involved in defining the sine, cosine, and tangent functions. Coterminal angles share the same trigonometric values despite having different measurements.
Explanation:
The Pythagorean Theorem is intimately related to trigonometric ratios, as it provides the fundamental relationship between the sides of a right-angled triangle. In trigonometry, the ratios of these sides define sine, cosine, and tangent functions. The Pythagorean theorem states that a² + b² = c², where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse of a right triangle. For example, given an angle θ within the right triangle, the cosine of θ is the adjacent side over the hypotenuse (cos(θ) = a/c), which implicitly uses the Pythagorean relationship when solving for the hypotenuse 'c'.
It's also important to remember coterminal angles in trigonometry, which are angles that share the same terminal side. Coterminal angles can be found by adding or subtracting whole multiples of 360° (or 2π radians). Although coterminal angles are different in measure, they have the same sine, cosine, and tangent values because these trigonometric functions are based on the position of the terminal side, not the actual angle measurement. Hence, coterminal angles have identical trigonometric function values.
After production, an electrical circuit is given a quality score of A, B. C, or D. Over a certain period of time, 77% of the circuits were given a quality score A. 11% were given a quality score B, 7% were given a quality score C, and 5% were given a quality score D. Furthermore, it was found that 2% of the circuits given a quality score A eventually failed, and the failure rate was 10% for circuits given a quality score B. 14% for circuits given a quality given a quality score C, and 25% for circuits given a quality score D. Show all your work and circle your final answers. Use four decimal places for your calculations. a) Find the probability of a circuit failing. b) If a circuit failed, what is the probability that it had received a quality score either C or D?
Answer:
a) 0.0125
b) 0.4579
Step-by-step explanation:
For this question use tree diagram method to solve the question or by simply listing down the probabilities as I have done in the attached picture. Firstly, we need to convert all percentages in to decimal and those decimals will represent probability of each event. For example if we consider probability of quality score A it can be found by diving 77 with 100:
77/100 = 0.77
Similarly all probabilities can be found by simply dividing percentages with 100.
Part (b) is a conditional probability question. Given that a circuit failed is the condition. So we need to use conditional probability method to solve it.
Final answer:
The probability of a circuit failing is 4.87%. If a circuit failed, there is a 45.77% chance that it received a quality score of C or D.
Explanation:
Calculating the Probability of Circuit Failure
To find the probability of a circuit failing, we multiply the probability of receiving each quality score by the probability of failure for that score, then add these together:
A score: 0.77 * 0.02 = 0.0154 (1.54%)
B score: 0.11 * 0.10 = 0.0110 (1.10%)
C score: 0.07 * 0.14 = 0.0098 (0.98%)
D score: 0.05 * 0.25 = 0.0125 (1.25%)
The total probability of failure is the sum of these values: 0.0154 + 0.0110 + 0.0098 + 0.0125 = 0.0487 or 4.87%.
Probability of a Failed Circuit Having a C or D Score
If a circuit failed, to find the probability that it had a quality score of C or D, we divide the sum of the probabilities of failure for C and D by the total probability of failure:
(Probability of C failure + Probability of D failure) / Total probability of failure
= (0.0098 + 0.0125) / 0.0487
= 0.0223 / 0.0487
= 0.4577 or 45.77%.
A 2016 Pew Research poll estimated the proportion of people supporting each presidential candidate in the fall election. They based their estimates on telephone interviews of 2, 010 adults living in all 50 U.S. states They asked each participant which presidential and vice presidential candidate they support, and used that data to calculate the proportions. What is the statistic in this experiment? Select the correct answer below: a.The candidate each participant supports. b.The number of people Pew Research interviews. c.The number of people in the United States. d.The proportions of participants who support each presidential candidate. e.The proportions of U.S. adults who support each presidential candidate.
Answer:
option A- The candidate each participant supports.
Step-by-step explanation: the question asks about the 'statistics in the experiment', meaning the major factor or say the most important data to be considered to achieve the desired aim/result of the experiment.
From the question, the aim/result of the Research poll was to get 'the PROPORTION of people supporting each presidential candidate in the fall election'. Note that to find 'PROPORTION', you must first find the individual values and then compare them. That's what 'PROPORTION' is all about - comparing number of things or people.
So to achieve this, the most important data-'statistics' in this experiment is knowing the candidate each participant supports.
For example, if there are 5 presidential candidates: Mr A, B, C, D & E and after interviewing 2,010 adults, you find out that:
134 people supports Mr A;
268 people supports Mr B;
402 people supports Mr C;
536 people supports Mr D and
670 people supports Mr E.
Now because you know the candidate each participant supports, you can now derive the 'PROPORTION' of people supporting each candidate which is 134:268:402:536:670. NB: you have to always leave your answer in its lowest term, so the proprtion here is 1:2:3:4:5.
Answer:
The proportions of participants who support each presidential candidate.
Step-by-step explanation
Six less than the product of 11 and a number
Use the variable n to represent the unknown number.
11n - 6 is the algebraic expression for six less than the product of 11 and a number
Solution:
Given that,
Six less than the product of 11 and a number
Let "n" be the unknown number
Let us understand and break the given sentence
Six less than the product of 11 and a number
Which means,
six less than product of 11 and "n"
Which can be written as,
[tex]11n-6[/tex]
Thus the given sentence is translated into algebraic expression
The algebraic expression which represents 'six less than the product of 11 and a number' is 11n - 6, where n is the unknown number.
Explanation:The question is asking for an algebraic expression representing 'six less than the product of 11 and a number'. To translate this to mathematical terms, first, the 'product of 11 and a number' indicates multiplication between 11 and the unknown number, which we represent with the variable n. The 'six less than' part indicates that we subtract 6 from this product.
So, the algebraic expression that represents 'six less than the product of 11 and a number' is 11n - 6.
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A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli's bar?
Answer:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the - 1468665…
Step-by-step explanation:A large Ghirardelli's bar is 28 cm long and 8 cm wide. A smaller Ghirardelli's bar is 7 cm long. If the bars are similar, what is the perimeter of the smaller Ghirardelli's bar?
The point P(21,35) is on the terminal side of an angle in standard position. What is the distance from P to the origin?
Answer:
The distance from P to origin is approximately 40.82 units.
Step-by-step explanation:
We are given the following in the data:
The point P(21,35)
We have to find the distance of point P from the origin.
Coordinates of origin: (0,0)
Distance formula:
[tex](x_1,y_1),(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Putting the values, we get,
[tex](21,35), (0,0)\\\\d = \sqrt{(0-21)^2 + (0-35)^2} = \sqrt{1666} = 7\sqrt{34} \approx 40.82\text{ units}[/tex]
The distance from P to origin is approximately 40.82 units.
A graduated cylinder with 10.0 mL of water ha mass of 25.0 g. 51 paper clips are added to the graduated cylinder . The total mass is 28 and the total volume is 14.7. What is the density of the paper clips? (Calculate your answer to 2 decimal places)
Answer: The density of the paper clips is 0.64 g/ml.
Step-by-step explanation:
Given : Volume of water = 10.0 mL
mass of water = 25.0 g
After 51 clips added to water , the total mass = 28 g
Total volume = 14.7
Mass of clips = total mass - mass of water
= 28 g-25g = 3g
Volume of clips = Total volume- Volume of water
= 14.7- 10.0 = 4.7 ml
Density of paper clips =[tex]\dfrac{\text{Mass of paper clips}}{\text{Volume of paper clips}}[/tex]
[tex]=\dfrac{3}{4.7}=0.638297\approx0.64\ g/ml[/tex]
Hence, the density of the paper clips is 0.64 g/ml.
Answer:
The density of the paper clips is 0.64 g/m
Step-by-step explanation:
hope this helps :)
If 6 is added to twice a number and this sum is multiplied by 5, the result is the same as if the number is multiplied by negative 3 and 4 is added to the product
Answer:
-2
Step-by-step explanation:
We assume you want to find the number. Let it be represented by x.
(6+2x)·5 = -3x +4 . . . . . the meaning of the problem statement
30 +10x = -3x +4 . . . . . eliminate parentheses
26 +13x = 0 . . . . . . . . . add 3x-4 to both sides
2 + x = 0 . . . . . . . . . . . . divide by 13
x = -2 . . . . . . . . . . . . . . subtract 2
The number is -2.
1.
A 0.40 kg football is thrown with a velocity of 15 m/s to the right. A stationary receiver
catches the ball and brings it to rest in 0.20 s. What is the force exerted on the ball by
the receiver?
Yo sup??
From Newton's 2nd law of motion
F*t=Δp
=mv-mu
mu=0.4*15
=6
t=0.2
mv=0
Therefore
F*0.2=6
F=30 N
Hope this helps.
the recommended daily intake rdi a nutrients supplement for a certain age group is 800 mg per day actully supplements needs vary from person to person which absolute value inequality expresses the rdi plus or minus 50 mg
a. |x-800|≥50
b. |50-x|≤800
c. |x-800|≤50
d. |x-50|≤800
Answer:
C
Step-by-step explanation:
The recommended daily intake of a nutrients supplement for a certain age group is 800 mg per day.
Actully supplements needs vary from person to person plus or minus 50 mg.
This means the minimum value is 800 - 50 = 750 mg per day and the maximum value is 800 + 50 = 850 mg per day.
Let x mg be a possible daily amount of nutrients supplement. Then
[tex]750\le x\le 850[/tex]
Subtract 800:
[tex]750-800\le x-800\le 850-800\\ \\-50\le x-800\le 50[/tex]
This inequality can be rewritten using absolute value notation as
[tex]|x-800|\le 50[/tex]
Based on their standard deviations, compare the tomatoes produced by the two varieties. Choose the correct answer below. A. Both varieties of tomatoes have similar consistency in their weights. B. The old tomatoes are more consistent in their weights than the new tomatoes. C. The new tomatoes are more consistent in their weights than the old tomatoes. D. While the new tomatoes are more consistent in their weights than the old tomatoes, the distribution of weights of the new tomatoes is left skewed.
Answer:
C. The new tomatoes are more consistent in their weights than the old tomatoes.
Context:
Agricultural scientists are working on developing an improved variety of Roma tomatoes. Marketing research indicates that customers are likely to bypass Romas that weigh less than 70 grams. The current variety of Roma plants produces fruit that averages 74 grams, but 11% of the tomatoes are too small. It is reasonable to assume that a Normal model applies.
The question is asking to compare the consistency of weights in two types of tomatoes based on their standard deviation. Select the option that best fits the standard deviation calculated for each group.
Explanation:In statistics, standard deviation is a measure of the amount of variation or dispersion in a set of values. A lower standard deviation means that the values tend to be close to the mean (average) value of the set, while a higher standard deviation implies that the values are spread out over a wider range. The question asks you to compare the consistency in weight between two types of tomatoes, determined by their standard deviations.
If the standard deviation of the old tomatoes' weight is lower than that of the new ones', option B ('The old tomatoes are more consistent in their weights than the new tomatoes') would be accurate. On the other hand, if the opposite is true, option C ('The new tomatoes are more consistent in their weights than the old tomatoes') would be correct. Option A would be right if the standard deviations are similar, indicating similar consistency, and option D would apply if along with the new tomato weights being more consistent, their weight distribution is left skewed.
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Please help!!! I will mark you brainliast
Answer:5 sqrt(2)
Step-by-step explanation:
All the sides of the square are congruent by the markings. Therefore they all measure 5 and because all 4 sides are congruent it is a square. Because it is a square the corners are right angles and you can use the Pythagorean Theorem. a^2 +b^2 = c^2.
5^2 + 5^2 = x^2
25 + 25 = x^2
50= x^2
X = square root of 50
X= square root of 25 Times Square root of 2
X= 5square root of 2
Answer: 5 sqrt (2)
Step-by-step explanation:
ABCD is a square
BCD is a triangle
BC=DC=5
To find DB
Let BC= a, DC=b, BD=c.
using Pythagoras Theorem in Triangle BCD
c2 = a2+b2
c2 = 52+52
c2= 25+25
c= √(50)
c2= √(25)×√ (2)
c= √(5× 5) √(2)
c= 5√(2) or c=5sqrt(2)
Rmbr, Let BC= a, DC=b, BD=c.
PLZ HELP, GIVING BRAINLIEST, LOOK AT THE PIC FOR GRAPH!!
Which of the following is the equation of the circle seen in the graph below?
A. (x + 2)^2 + (y - 1)^2 = 16
B. (x + 2)^2 + (y + 1)^2 = 4
C. (x - 2)^2 + (y + 1)^2 = 16
D. (x + 2)^2 + (y - 1)^2 = 4
Answer:
The answer to your question is letter C
Step-by-step explanation:
From the graph, we get the center and the radius
- The center is the point shown in the graph and its coordinates are (2, -1).
- The length of the radius is 4 units, from the center we count horizontally the number of squares (4)
Substitution
(x - 2)² + (y + 1)² = 4²
or (x - 2)² + (y + 1)² = 16
Answer:
A or B
Step-by-step explanation:
Because of the negtive 1
Hello! I'm afraid I don't know which equation to use to solve this problem.
I am familiar with solving for x and other stuff, but I have a problem with finding and using the right formula. I was wondering if anyone could help me out with that? :D (Will mark brainliest too!)
Find the value of x. Show all your work for full credit.
Yo sup??
This question can be solved by applying the properties of similar triangles
the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 35
The similarity property used here is called AAA ie angle angle angle property as all the three angles of the 2 triangles are equal.
therefore we can say
5x/45=20/36
x=5 units
Hope this helps
A certain solution of salt water is 10% salt and weighs 50 pounds. more salt must be added to produce a solution that is 25% salt. if x represents the pounds of salt to be added, which of the following expressions represents the number of pounds of salt in the 25% solution?
a) 0.25 (x+50)
b) 0.25x
c) 1.25 (x+50)
Answer
7.5 pounds
Step-by-step explanation:
Since adding x grams of salt will bring th percentage of the salt to 25
Hence. 10% of the 50 gram gives. 5 gram initial salt before it is added.
5+ x/ 50 * 100= 25/
5+x /50 = 0.25
5+x = 12.5
X= 12.5- 5
X= 7.5pounds
A snail starts at the bottom of a well 20 feet deep and crawls up 4 feet each day. However, each night as it sleeps, the poor snail slips back 3 feet. How long will it take the snail to get out of the well?
Answer:
20days
Step-by-step explanation:
The daily progress is 4ft - 3ft = 1ft
20ft/1ft = 20days
The snail will take 20 days to get out of the well.
Explanation:To find out how long it will take the snail to get out of the well, we need to determine how many days it takes for the snail to climb a distance of 20 feet. Each day, the snail climbs 4 feet but slips back 3 feet at night. So, the net distance the snail covers each day is 4 - 3 = 1 foot.
Dividing the total distance of 20 feet by the net distance covered each day (1 foot), we find that it will take the snail 20 days to get out of the well.
Hence, the snail will take 20 days to get out of the well.
Learn more about Snail's journey out of a well here:https://brainly.com/question/14683201
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Ethan went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 35 grams of sugar. Ethan purchased a total of 19 bottles of juice and soda which collectively contain 755 grams of sugar. Determine the number of bottles of soda purchased and the number of bottles of juice purchased.
9 bottles of soda and 10 juice bottles are purchased
Solution:
Given that,
Sugar contained by each soda bottle = 45 grams
Sugar contained by each juice bottle = 35 grams
Let,
x be the number of soda bottles
y be the number of juice bottles
Given that,
Ethan purchased a total of 19 bottles of juice
Therefore, we get,
x + y = 19 ---------- eqn 1
Ethan purchased a total of 19 bottles of juice and soda which collectively contain 755 grams of sugar
Therefore, we frame a equation as:
[tex]45 \times x + 35 \times y = 755[/tex]
45x + 35y = 755 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
x = 19 - y --------- eqn 3
Substitute eqn 3 in eqn 2
45(19 - y) + 35y = 755
855 - 45y + 35y = 755
10y = 100
y = 10
Substitute y = 10 in eqn 3
x = 19 - 10
x = 9
Thus 9 bottles of soda and 10 juice bottles are purchased
The area of a triangle is given by the formula A = 1 2bh, where A is the area, b is the length of the base, and h is the triangle's height. Of a triangle has a base 5 meters long and a height twice the length of the base, find its area.
Answer: The area of triangle is 25 sq. meters.
Step-by-step explanation:
Given : Area of a triangle = [tex]\dfrac{1}{2}bh[/tex] m, where b= base of triangle
h= height of triangle.
If a triangle has 5 meters long base and a height twice the length of the base,
that means b = 5 meters and h= 2(5) = 19=0 meters
Then the area of triangle becomes [tex]A=\dfrac{1}{2}(5)(10)=25 m^2[/tex] [Put alll values in the given formula]
Hence, the area of triangle is 25 sq. meters.
Need help with this
Answer:
2nd option
Step-by-step explanation:
given
BD = 4x
CE = 2x + 2
test each answer option by substituting the given values of x into each of the above equations and see if it is consistent with the given values for BD and CD in the answer options.
1st option, when x = 5,
BD = 4x = 4(5) = 20 (Consistent)
CE = 2x + 2 = 2(5) + 2 = 10 + 2 = 12 ( not consistent with CE=8)
2nd option, when x = 3/7,
BD = 4x = 4(3/7) = 12/7 (Consistent)
CE = 2x + 2 = 2(3/7) + 2 = 6/7 + 2 = 20/7 ( consistent with CE=20/7) (ANSWER)
3rd option, when x = 3,
BD = 4x = 4(3) = 12 (Consistent)
CE = 2x + 2 = 2(3) + 2 = 6 + 2 = 8 ( not consistent with CE=20)
Study Island: Gina has 24 more barrettes than Holly. The equation g = 24 + h, where g represents the number of barrettes Gina has, and h represents the number of barrettes Holly has, shows this relationship. If Gina has 51 barrettes, how many barrettes does Holly have?
See picture for solution and answer.
What is the area of this figure? Enter your answer in the box. units² points on graph are (-2,3) (-4,5) (-5,3) (-3,-3) (4,-3) (3,4) (4,3) WILL MARK BRAINLIEST 50 POINTs
Answer:
A: -4,3 The x coordinate of the vertex is given by x = -b/2a and the y coordinate of the vertex is given by y= f( -b/2a), we need to transform the equation to the form ax^2 + bx + c We have: 5(x+4)^2+3 = 5x^2+ 20x + 23 Then we substitute x= -20/2*5 y= f(-20/2*5) = -4 = f(-4) =3 So V(-4,3)
Step-by-step explanation:
Answer:
I still dont get what the answer is
Step-by-step explanation: