The similarity statement relating the three triangles in the diagram is 'YHB ~ YDH ~ HDB'. This is because they are all similar triangles, sharing the same shape but differing in sizes due to scale.
Explanation:In this case, the answer would be 'YHB ~ YDH ~ HDB'. We are looking for a similarity statement, which states that all three triangles are similar. Similar triangles are triangles that have the same shape, but can be different sizes, i.e. they are scaled versions of each other. Since HD is a perpendicular drawn from right angle H in triangle YHB, this creates two triangles (YDH, HDB) that are respectively similar to the original triangle YHB as each of the two triangles include one of the acute angles of triangle YHB and their own right angles. Therefore, YHB ~ YDH ~ HDB.
Learn more about Similar Triangles here:https://brainly.com/question/34830045
#SPJ12
Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets slod. How many children’s ticket and how many adult tickets did he sell?
Answer:
615 children tickets
195 adults tickets
Step-by-step explanation:
Let the number of children’s tickets be c and the number of adult tickets be a.
Children’s ticket is $3 and adult’s is $5 for a total of $2,820. This means:
3c + 5a = 2,280
This is the first equation.
The number of children’s tickets sold is 30 more than 3 times that of the adults. This means
c = 3a + 30.
This is equation ii. We now substitute ii into I to yield:
3(3a+ 30) + 5a = 2,820
9a + 90 + 5a = 2,820
14a + 90 = 2,820
14a = 2820 - 90
14a = 2730
a = 2730/14 = 195 tickets
c = 3a + 30
c = 3(195) + 30 = 615
Final answer:
By setting up a system of equations based on the total sales and the relationship between the number of adult and children's tickets sold, we can solve to find that Galen sold 130 adult tickets and 420 children's tickets for the church's carnival which is 195.
Explanation:
The question involves finding the number of children's and adult tickets sold by Galen for a church's carnival, given the total sale amount and the price of each ticket type. To solve this, we can set up a system of equations based on the information provided:
The total amount from ticket sales is $2,820.Children's tickets are $3 each, and adult tickets are $5 each.The number of children's tickets sold was 30 more than 3 times the number of adult tickets sold.Let x be the number of adult tickets sold and y be the number of children's tickets sold. The problem statements can be translated into two equations:
3y + 5x = 2820 (total sales equation)y = 3x + 30 (relationship between tickets sold)Substituting the second equation into the first gives us:
3(3x + 30) + 5x = 2820
Solving for x, we find that Galen sold 130 adult tickets. Using the relationship between x and y, we then find that 420 children's tickets were sold.
14x= 2730
x=195.
If two triangles are congruent, which of the following statements must be true? Check all that apply.
Answer:
All statements are correct for two congruent triangles
Step-by-step explanation:
If two triangles are congruent than the rules states that
Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
As the fig shows two triangle
Δ PQR
Δ LMN
All three corresponding sides of triangle are congruent
all three corresponding angles are congruent
Both triangle are of same size
Both are of same shape
hence all the statements are CORRECT
Keywords:Geometry
Learn more about Geometry at:
mathopenref.com/congruenttriangles.htmlbrainly.com/question/3617539#learnwithBrainly
Find the vertex of the graph of the function. f(x) = (x + 4)2 - 1
a) (0,4)
b) (-1, 0)
c) (-4,-1)
d) (-1,-4)
Answer:
The vertex of the function is at point (-4,-1).
Step-by-step explanation:
Given function:
[tex]f(x)=(x+4)^2-1[/tex]
Solution:
The vertex form of a function is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
where [tex](h,k)[/tex] is the vertex of the function. At this point the function has the maximum or minimum value.
Writing the given function in the vertex form.
[tex]f(x)=(x-(-4))^2+(-1)[/tex]
On comparing the above function with the standard form we find that:
[tex]a=1\\h=-4\\k=-1[/tex]
Thus, the vertex of the function is at point (-4,-1)
The vertex of the function f(x)= (x + 4)² - 1 is at the point (-4,-1) by comparing it with the vertex form of a quadratic function f(x) = a(x - h)² + k.
Explanation:The function given is in the vertex form of a quadratic function, which is f(x) = a(x - h)² + k. In this form, the vertex of the graph of the function is at the point (h, k). For f(x)=(x + 4)² - 1, you can see that h is -4 and k is -1. Therefore, the vertex of the graph of the function is at the point (-4,-1).
Learn more about Vertex of a Quadratic Function here:https://brainly.com/question/32309965
#SPJ3
Find the exact values for sin theta, cos θ, and tan θ. A right triangle has a vertical side of length 12, a horizontal side of length 35, and a hypotenuse of length 37. The angle formed by the sides of lengths 35 and 37 is labeled θ.
Answer:
SinƟ = 12/37
CosƟ =35/37
TanƟ = 12/35
Step-by-step explanation:
The diagram of the triangle is attached
Using SOH CAH TOA
SinƟ = Opposite/Hypotenuse
SinƟ = 12/37
CosƟ= adjacent/Hypo tenuse
CosƟ =35/37
TanƟ=Opposite/Adjacent
TanƟ = 12/35
PLEASEEE HELP ME ASAP!!
Answer:
Hence,
The measure of ∠A is 60.065°
[tex]\m\angle A= 60.065[/tex]
Step-by-step explanation:
Given:
ΔABC is a Right Angle Triangle at ∠ B = 90°
BC = Opposite side to ∠A = 13 unit
AC = Hypotenuse = 15 unit
To Find:
m∠A = ?
Solution:
In Right Angle Triangle ABC ,Sine Identity,
[tex]\sin A= \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin A= \dfrac{BC}{AC}=\dfrac{13}{15}=0.8666\\\angle A=\sin^{-1}(0.8666)\\m\angle A= 60.065\°[/tex]
Hence,
The measure of ∠A is 60.065°
[tex]\m\angle A= 60.065[/tex]
If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30. If the person gets a 7, he wins $10. Otherwise he wins nothing. If the cost to play the game is $3, what does a player expect to get out of this game every time he/she plays?
If they were to win $30 they would expect to get $27 in profit.
If they were to win $10 they would expect $7.
If they were to win $0 they would expect $-3 in profit, so technically if they win nothing they lose money.
Hope I could help! :D
If player expect to get out of this game every time he/she plays then they would loose money.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30.
and, If they were to win $30, they would anticipate making a profit of $27.
Also, if they would anticipate $7 if they were to win $10.
So, if they were to win nothing, they would lose money because they would expect to make $-3 in profit.
Learn more about Probability here:
https://brainly.com/question/11234923
#SPJ5
Weinstein, McDermott, and Roediger (2010) con- ducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a se tion, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers. a. Identify the dependent variable for this study. b. Is the dependent variable discrete or continuous? c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable? or h ctudy reports that alcohol consumption is ta university why or why not. pidor inexperiment?
Answer:
Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies.
One part of the study asked students to prepare for a test by reading a passage.
In one condition, students generated and answered questions after reading the passage.
In a second condition, students simply read the passage a second time.
All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a. Identify the dependent variable for this study:
The dependent variable for this study is effectiveness.
b. Is the dependent variable discrete or continuous?
The dependent variable is discrete.
c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
The scale of measurement is ratio scale.
Step-by-step explanation:
a) To identify the dependent variable you need to find the item, circumstance, concept, sense, time frame, or any category in an specific scientific research, that is going to be measured. In this particular case, the dependent variable measured is the effectiveness of the different study strategies used based by the number of correct answers on a test. This variable could be influenced by independent variables also.
b) The method by which we obtain the resulting values make the difference between a discrete variable and a continuous variable. If measuring is the used method, then it is a continuous variable, but if counting is the utilized method to get the correct number of correct answers, as it is stated in this case, then it is a discrete, finite and countable.
c) The measurements´ accuracy are given by the different scales or levels and they are classified as:
- Nominal
- Ordinal
- Interval
- Ratio
Interval and ratio scales data are similiar is also known as called metric, sharing units, and represent quantiy., therefore the scale of measurement used in this study is ratio scale.
In accordance with 14 CFR Part 107, at what maximum altitude can you operate an sUAS when inspecting a tower with a top at 1,000 ft AGL at close proximity (within 100 feet)?
Answer:
The max altitude you can operate an sUAS on these given conditions is 1400ft AGL.
Step-by-step explanation:
Final answer:
The sUAS can fly at a maximum altitude of 1,100 feet AGL when inspecting a tower with a top at 1,000 feet AGL, assuming it stays within 100 feet of the tower as per 14 CFR Part 107.
Explanation:
In accordance with 14 CFR Part 107, specifically considering sUAS (small Unmanned Aircraft Systems) operations around structures, there are specific altitude regulations. When a drone operator is inspecting a tower, and the drone is within 100 feet laterally of the structure, the drone can operate above the standard 400 feet above ground level (AGL) limit. For a tower with a top at 1,000 feet AGL, the sUAS can fly at a maximum altitude of 1,100 feet AGL, assuming it stays within 100 feet of the structure. This is possible because the regulations allow the sUAS to fly 400 feet above the structure's uppermost limit when it is within a close radius of the structure.
Is −8c an even integer? Yes, because −8c = 2(−4c) + 1 and −4c is an integer. Yes, because −8c = 2(−4c) and −4c is an integer. No, because −8c = 2(−4c) and −4c is an integer. No, because −8c = 2(−4c) + 1 and −4c is an integer.
Answer:
Yes, because −8c = 2(−4c) and −4c is an integer
Step-by-step explanation:
We want to determine whether [tex]-8c[/tex] is an even integer.
Recall that even integers are of the form: [tex]2n[/tex]
Let us see if we can rewrite the given expression in the form 2n, where n is an integer.
Let us factor 2 to get:
[tex]-8c=2(-4c)[/tex]
If -4c is an integer and we let m=-4c,then
[tex]-8c=2(m)=2m[/tex], where m is an integer.
Therefore the answer is Yes, because −8c = 2(−4c) and −4c is an integer
Solve the inequality 1 2p + 7 ) 1 39
Answer: p=11
Step-by-step explanation:
12p+7)139
-7 -7
12p)132
÷12 ÷12
P)11
Answer:
p= 11
Step-by-step explanation:
1 2p + 7 > 1 39
collection of like term
12p > 139 - 7
12p > 132
Divide both side by the coefficient of p
12p/12 > 132/12
p = 11
If you run around the house randomly and then end up back where you started moving a total of 44 meters what is distance and what is change in position
Answer:
Distance = 44 m
Change in position = 0 m
Step-by-step explanation:
Given:
Running around the house covering a total length of 44 m and reaching the same position where you started.
So, initial position is same as final position.
Change in position is given as:
Change = Final position - Initial position
Now, since, final position = Initial position.
So, Change in position = 0 m
Now, distance is the total length of the path covered. So, you started from your initial position and ran around the house covering a path length of 44 m before reaching the same starting position.
Therefore, the distance is equal to the path length and hence is equal to 44 meters
On Monday, Lou drives his ford escort with 28-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his car to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou’s tires make per second?(A) Decrease by 14.3%
(B) Decrease by 12.5%
(C) Increase by 14.3%
(D) Increase by 12.5%
(E) Cannot be determined with the given information.
Answer:
[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]
(B) Decrease by 12.5%
Step-by-step explanation:
For this case we know that the revolution is proportional to the circumference.
And we know that the average number of revolutions of 32 inch tires for Tuesday is higher than the original value of 28 inch tires for Monday.
We know that we have x mi/hr, so we can select a value fo x in order to find the average revolutions with the following formula:
[tex] Avg = \frac{x}{mi}[/tex]
Let's say that we select a value for x for example x= 28*32 = 896, since this value is divisible by 32 and 28.
If we find the average revolutions per each case we got:
Tuesday:
[tex] Avg = \frac{896}{32}=28[/tex]
Monday:
[tex] Avg = \frac{896}{28}=32[/tex]
And then we can find the % of change like this:
[tex] \% Change= \frac{|Final-Initial|}{Initial} *100[/tex]
And if we replace we got:
[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]
Because we are assuming that the initial amount is the value for Monday and the final value for Tuesday.
So then the best answer for this case would be:
(B) Decrease by 12.5%
The function f(x) = Negative Startroot x EndRoot is shown on the graph.
On a coordinate plane, an absolute value graph starts at (0, 0) and goes down and to the left through (4, negative 2).
Which statement is correct?
The domain of the function is all real numbers less than or equal to −1.
The range of the function is all real numbers greater than or equal to 0.
The range of the function is all real numbers less than or equal to 0.
The domain of the function is all real numbers less than or equal to 0.
Answer:
the answer is c
Step-by-step explanation:
i took the test and got a 100
The range of the function is all real numbers less than or equal to 0.
A function is an expression that shows the relationship between two or more variables or numbers.
The domain of a function is the set of input values while the range is the set of output values.
From the graph, The range of the function is all real numbers less than or equal to 0.
Find out more on function at: https://brainly.com/question/10439235
Refer to the following breakdown of responses to a survey of room service in a hotel: Response - Frequency Not satisfied - 20 Satisfied - 40 Highly satisfied - 60 What percentage of the responses indicated that customers were satisfied?A. 40%B. 33%C. 50%D. 100%
Answer: B. 33%
Step-by-step explanation:
Given : Response - Frequency
Not satisfied - 20
Satisfied - 40
Highly satisfied - 60
Total customers = (Number of customers Not satisfied) + (Number of customers satisfied) + ( (Number of customers Highly satisfied) )
= 20+40+60=120
Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]
[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]
Hence, the percentage of the responses indicated that customers were satisfied = 33%
Thus , the correct answer is B. 33%
To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.
Explanation:To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.
Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.
To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.
Learn more about Percentage Calculation here:https://brainly.com/question/329987
#SPJ3
describe the long-term behavior
Answer:
a. Slant asymptote with a slope of 5
Step-by-step explanation:
Dividing out the polynomials, you get ...
[tex]\dfrac{5x^2-x+13}{x+10}=5x-51+\dfrac{523}{x+10}[/tex]
As the magnitude of x gets large, the fraction goes to zero, and the behavior matches the line ...
y = 5x -51
This is a slant asymptote with a slope of 5 and a non-zero y-intercept.
PLEASE HELPPPP Which value is equivalent to cos10∘?
Answer:
sin 80
Step-by-step explanation:
8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?
The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).
To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).
Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.
Using the combination formula, C(27, 8) is calculated as:
27! / (8! * (27-8)!)
= 27! / (8! * 19!)
Factor out the common terms from the numerator and denominator
The remaining terms give us the total number of combinations
The probability is therefore: 1 / C(27, 8).
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
To figure this out, use the acronym SOHCAHTOA to determine which trigonometric function to use.
8 is opposite to <R and 3 is adjacent to <R so we use tangent.
Set up the following equation: tan(x)=8/3
Find the inverse (aka. tan^-1): x=69.44
So your answer is <R=69.4 degrees
Hope this helped!
Solve the equation and check the solution . X-13.8=-20.4 the solution set is ?
Answer:
The answer is x = -6.6
Step-by-step explanation:
Answer:
X= -6.6
Step-by-step explanation:
Just do 13.8 - 20.4. It will equal -6.6.
A 63 liter mixture contains milk and water in a ratio of 4:5. then x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5. finally , 60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8. what is the value of x+y ?
Answer:
X+y=237Litres
Step-by-step explanation:
Let a be mixture of milk and water.
Let x =milk
Let y= water
z = x+y
Final volume of mixture =63litres + z
5/12(3+z))+60=8/15(63-z)
z =x+y= 237litres
The value of [tex]x+y[/tex] is 237 liters.
Given information:
A 63 liter mixture contains milk and water in a ratio of 4:5.
Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].
The initial mixture can be written as,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]
The initial amount of water and milk will be,
[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]
x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.
The mixture, now, can be written as,
[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]
60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.
Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.
The final mixture can be written as,
[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]
Solve for x and y as,
[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]
So, the value of [tex]x+y[/tex] will be,
[tex]x+y=147+90\\=237[/tex]
Therefore, the value of [tex]x+y[/tex] is 237 liters.
For more details, refer to the link:
https://brainly.com/question/11897796
Which expression represents the area of triangle ABC in square meters?
Triangle A B C has a base of 57 meters and a height of 14 meters.
One-half times 14 times 57
One-half times 14 times 64
One-half times 24 times 40
One-half times 24 times 57
Answer:
Answer is (A) One-half times 14 times 57
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Two Neighbors in a rural area want to know the distance between their homes in miles. What should the Neighbors use as a conversion factor to covert 4,224 to miles
Answer:
x = 0.8 Mi
Step-by-step explanation:
for x = 4224 ft we can use the factor (1 Mi/5280 ft)
then
x = 4224 ft (1 Mi/5280 ft) = 0.8 Mi
Please Help Me With My Algebra Homework
Answer:
The maximum of the sinusoidal function is 5.
Step-by-step explanation:
The maximum of the sinusoidal function is 5.
PLLLLLEEASSEE HELLPP
Which transformations have been performed on the graph of f(x)=\sqrt[3]{x} to obtain the graph of g(x)= -\frac{1}{2} \sqrt[3]{x-9}
Select EACH correct answer
A. reflect the graph over the x-axis
B. translate the graph down
C. translate the graph to the right
D. translate the graph up
E. stretch the graph away from the x-axis
F. translate the graph to the left
G. compress the graph closer to the x-axis
Answer:
The correct answer is compress the graph closer to the x axis
reflect the graph over the x axis
translate the graph to the right
Step-by-step explanation:
I just took the test
The correct answer is (A)(C)(G) because to transform the graph, we first reflect it over the x-axis, then translate it to the right, and finally compress it closer to the x-axis.
To determine the transformations applied to the graph of [tex]\( f(x) = \sqrt[3]{x} \)[/tex] to obtain the graph of [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], let's analyze each component of the transformation step-by-step.
Given [tex]\( f(x) = \sqrt[3]{x} \)[/tex] and [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], the transformations are as follows:
1. Horizontal Shift:
The term [tex]\( x-9 \)[/tex] inside the function indicates a horizontal shift.
Specifically, it shifts the graph to the right by 9 units.
2. Vertical Compression and Reflection:
The coefficient [tex]\( -\frac{1}{2} \)[/tex] outside the cube root function indicates a vertical transformation.
The negative sign reflects the graph over the x-axis.
The factor [tex]\( \frac{1}{2} \)[/tex] compresses the graph closer to the x-axis.
The complete question is:
Which transformations have been performed on the graph of [tex]f(x)=\sqrt[3]{x}[/tex] to obtain the graph of [tex]g(x)= -\frac{1}{2} \sqrt[3]{x-9}[/tex] ?
A. reflect the graph over the x-axis.
B. translate the graph down.
C. translate the graph to the right.
D. translate the graph up.
E. stretch the graph away from the x-axis.
F. translate the graph to the left.
G. compress the graph closer to the x-axis.
The graph shows the distance y, in centimeters, a pendulum moves to the right (positive displacement) and to the left (negative displacement), for a given number of seconds x.
How many seconds are required for the pendulum to swing from its position furthest to the right to its position furthest to the left?
It's 1.25 seconds, I just took the test and got 100% Good Luck!!! :)
The longer diagonal of a rhombus is three times the length of the shorter diagonal is x, what expression gives the perimeter of the rhombus? The perimeter of the rhombus is__.
Answer:
4(√2.5)x
Step-by-step explanation:
Let each side of the dragonal be P
Bringing out a Triangle out of the rhombus we have a right angle triangle with the base of x/2 and height of 3/2x.
And the hypothenus is P.
Applying Pythagoras theorem we have
p ^2= (1.5x)^2+(0.5X)^2
p ^2= 2.25X^2 +0.25X^2
P = (√2.5) X
Since the Rhombus consist of 4 triangles . The perimeter can best be expressed as 4 x the perimeter of the triangle.
P= 4(√2.5)x.
The longer diagonal of a rhombus is three times the length of the shorter diagonal. The expression that gives the perimeter of the rhombus cannot be determined with the information provided.
Explanation:The perimeter of a rhombus can be found by adding the lengths of all four sides. In this case, the longer diagonal of the rhombus is three times the length of the shorter diagonal, which is represented by x. So, the shorter diagonal is x and the longer diagonal is 3x.
Since the longer diagonal of a rhombus creates two congruent right triangles, we can use the Pythagorean theorem to find the length of its sides. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, for one of the right triangles, the hypotenuse is 3x and the two sides are x. Using the Pythagorean theorem, we have:
x² + x² = (3x)²
2x² = 9x²
2 = 9
This equation is not true, which means that x cannot be the length of the shorter diagonal.
Therefore, since the given information is incorrect, we cannot find the expression that gives the perimeter of the rhombus.
Ella finished a bike race in 37.6 minutes. Miranda finished the race 9 1/10minutes sooner than Ella finished it. How many minutes did it take Miranda to finish the race
Answer:
x = 28.5 minutes
Step-by-step explanation:
Let x be the time taken for finishing the bike race.
Given:
Ella finished a bike race = 37.6 minutes
Miranda finished the race sooner than Ella = [tex]9\frac{1}{10} = \frac{91}{10} = 9.1\ minutes[/tex]
We need to find the minutes did it take Miranda to finish the race.
Solution:
From the statement, Miranda finished the race 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.
So, time taken by Miranda to finish the race:
[tex]Mirianda\ finshed\ a\ bike\ race = (Ella\ finshed\ a\ bike\ race) - 9.1[/tex]
[tex]x=37.6-9.1[/tex]
x = 28.5 minutes
Therefore, Miranda finished the bike race in 28.5 minutes.
The cost for a cell phone service is $75 per month plus $0.17 per minute. Which expression shows the monthly cost for the phone if x represents the number of minutes?
Answer:
we can use the variable c to represent the monthly cost
75+0.17x=c
Step-by-step explanation:
The expression shows the monthly cost for the phone if x represents the number of minutes if The cost for a cell phone service is $75 per month plus $0.17 per minute, is y = 75 + 0.17x.
What is equation?An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.
Given:
The cost for a cell phone service is $75 per month plus $0.17 per minute,
Write the equation as shown below,
Total cost = Cost for a month + per minute charge × total use in minutes,
Assume the total cost is y, and the use of minute is x then,
y = 75 + 0.17 × x
y = 75 + 0.17x
Thus, the monthly cost for the phone is 75 + 0.17x.
To know more about equation:
https://brainly.com/question/12788590
#SPJ5
10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and is not replaced. Another card is then randomly selected. What is the probability of selecting two numbers that are less than 6?
A. 2/9
B. 5/18
C. 1/5
D. 1/4
Answer:
Option A: [tex]$ \frac{\textbf{2}}{\textbf{9}} $[/tex]
Step-by-step explanation:
Given there are 10 cards viz: 1, 2, 3, 4, . . . , 10
We find the probability of drawing two cards less than six, without replacing the first card.
Draw 1:
There are 5 cards with value less than 6. 1, 2, 3, 4, 5
The total number of cards is 10.
The probability of the number being less than 6 = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} cards \hspace{1mm} less \hspace{1mm} than \hspace{1mm} 6}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $[/tex]
[tex]$ = \frac{5}{10} $[/tex]
Draw 2:
We are again drawing a card without replacing the card that was drawn earlier. This makes the total number of cards 9.
Also, the number of cards less than 6 will now be: 4.
Therefore, probability of drawing a number less than 6 without replacing
[tex]$ = \frac{4}{9} $[/tex]
Since, both draw 1 and draw 2 are happening we multiply the two probabilities. We get
[tex]$ \textbf{P} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{10}} \hspace{1mm} \times \hspace{1mm} \frac{\textbf{4}}{\textbf{9}} $[/tex]
[tex]$ \therefore P = \frac{\textbf{2}}{\textbf{9}} $[/tex]
Hence, OPTION A is the required answer.
which quadrilateral does not always have perpendicular diagonals
A. Square
B. Rhombus
C.kite
D. Isosceles trapezoid
Answer:
D. Isosceles trapezoid
Step-by-step explanation:
Answer: The answer is D. Isosceles trapezoid