The following system of equations has only one solution, which is (2,0), because you can use the method of substitution to find the value of x and if it has multiple solutions.
y = x - 2
y = - x + 2
x - 2 = - x + 2
2x = 4
x = 2 (substituting this back into the equation)
y = 2 - 2
y = 0
volume of this prism
The volume is (area of cross-section) x (length) .
-- The cross-section is a triangle. The area of a triangle is
Area = (1/2) (base) (height) .
In this one, the base is 9/4 m and the height is 3-1/3 m .
Area = (1/2) (9/4 m) (3-1/3 m)
Area = (1/2) (9/4) (10/3)
Area = 90/24 m² .
-- Volume = (area of cross-section) x (length)
Volume = (90/24 m²) x (7-1/3 m)
Volume = (90/24) x (22/3) m³
Volume = (1,980 / 72) m³
Volume = 27.5 m³
In how many different, distinguishable orders can the letters of the word mathematics be arranged?
A)39,916,800
B)4,989,600
C)6,652,800
Answer:
B)4,989,600
Step-by-step explanation:
The letters of 'MATHEMATICS' contains 11 letters.
The following letters repeats twice, TT,MM,AA.
When we talk of distinguishable wasy, we are referring to arrangement without repetition.
Therefore the letters of "MATHEMATICS" can be arranged in [tex]\frac{11!}{2!2!2!}=4,989,600[/tex] distinguishable ways.
The correct answer is B.
Mr. Cooper is building a playset in his backyard for his kids. He has a made a scale drawing of the playset to help him estimate the amounts of building materials he needs to purchase. Part of the playset includes a rectangular sandbox, which has a length of 5 feet and a width of 7 feet. On the scale drawing, the length of the sandbox is 2 A. The scale used in the drawing is = 1 foot. B. On the scale drawing, the width of the sandbox is inches. C. If Mr. Cooper decides to make a new scale drawing of the playset, in which he uses a scale of inch = 1 foot, all of the dimensions in the old drawing will be multiplied by a factor of .
Answer:
If Mr. Cooper decides to make a new scale drawing of the play set, in which he uses a scale of inch = 1 foot, all of the dimensions in the old drawing will be multiplied by a factor of ⇒ the last answer
Step-by-step explanation:
* Lets study what is the meaning of the scale factor
- To find a scale factor between two similar figures
# Find two corresponding sides and write the ratio of the two sides.
# If you begin with the smaller figure, your scale factor will be less
than one.
# If you begin with the larger figure, your scale factor will be greater
than one
* Now lets solve the problem
- The rectangular sandbox, has a length of 5 feet and a width of
7 feet
- On the scale drawing, the length of the sandbox is 2 inches
- The actual sandbox and the drawing sandbox are similar
∵ The length of the actual sandbox is 5 feet
∵ The drawing length is 2 inches
∵ 1 foot = 12 inches
∴ The scale factor is 2/(5 × 12) = 1/30
* That means each actual dimensions will multiply by 1/30 to find
the drawing dimensions
∴ The drawing length of the sandbox = 5 × 12 × 1/30 = 2 inches
∴ The drawing width of the sandbox = 7 × 12 × 1/30 = 2.8 inches
* All of the dimensions in the old drawing will be multiplied by
a factor of 1/30
1/2 inch
3 3/4
2
i know im 2 years late but hopefully this helps someone else
help fast I am not sure about this question.
Use the following data and graph the best-fit quadratic curve. What is a good approximation for the value of c?
1 ) 2
2) 3
3) 1
4) -2
Answer:
3
Step-by-step explanation:
Graphing the best-fit quadratic curve for the data-set can be done using Ms. Excel Application.
The first basic step is to enter the data into any two adjacent columns of the excel workbook. Highlight the two columns where the values have been entered, click on the insert tab and then select the x,y scatter-plot feature. This will create an x,y scatter-plot for the data.
Next, click on the Add Chart Element feature and add a polynomial trend-line of order 2 which is basically a quadratic curve. Finally, check the display equation on chart box. This step will plot the quadratic curve as well as give the equation of the best-fit quadratic curve.
The attachment below shows the best-fit quadratic curve to the data-set and its corresponding equation.
A good approximation for the value of c from the equation is thus 3. This is simply the y-intercept of the curve. 3.21 is closer to 3.
Please help I’m very confused I will mark brainliest
Divide the total weight of granola by the weight of each bar.
768 ounces / 4 ounces per bar = 192
They can make 192 bars.
PLEASE HELP ME ILL GIVE YOU POINTS
Answer: I think the answer is the second box.
Step-by-step explanation: It says 20 males have watched the show. I hope I helped you. If I am wrong, tell me in a polite way. :D
Hello there! The answer is the second chart, or B.
To find the answer, look at the parts of the question.
Let's start in the beginning. Note how it says "Of the 80 participants, 30 were male and 50 were female". This means that, looking at the options, in the "total" row, there should be a value for "30" by male, "50" by female and 80 at the bottom. This means that it cannot be A since this option says that there were 80 females and 80 males and 160 total, or C since it says there are 80 males and 55 females with a total of 135.
Next, it says that 45 have watched the show and 35 have not. If you look at the options left B and D, the only one the has these numbers for have and have not watched is B, making this the correct answer.
I hope this helps and have a great rest of your day! :)
I need help with this question
3rd one for the answer all the other ones are wrong. It shifted down
ANSWER
[tex]y = \sqrt[3]{x + 4} - 1[/tex]
EXPLANATION
The given function is
[tex]y = \sqrt[3]{x} [/tex]
The transformation
[tex]y = \sqrt[3]{x + k} - c[/tex]
shifts the graph of the base function k units left and c units down.
Since the graph is shifted 4 units left, k= 4
Also, the graph is shifted 1 unit down.
This implies that c=1
The new equation is
[tex]y = \sqrt[3]{x + 4} - 1[/tex]
The last option is correct.
Which statement below is ALWAYS TRUE?
(A) Complementary angles are both acute angles.
(B) Any two acute angles are complementary angles.
(C) Supplementary and Complementary angles are always adjacent angles.
(D) Supplementary angles are both obtuse angles
The statement that is always true is that supplementary and complementary angles are always adjacent angles.
Explanation:The statement that is ALWAYS TRUE is (C) Supplementary and Complementary angles are always adjacent angles. Supplementary angles are two angles that add up to 180 degrees, while complementary angles are two angles that add up to 90 degrees. Adjacent angles are two angles that have a common vertex and a common side between them. So, it is always true that supplementary and complementary angles are adjacent angles because they share a common side.
what is the simplest form of Q40
Answer:
-10√5 + 30
Step-by-step explanation:
This is a product of two monomials, so we would kind of like FOIL this.
F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT.
O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT.
I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT.
L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT.
Doing this will give 5 - 10√5 + 25. Combine like-terms to end up with -10√5 + 30 [or 30 - 10√5].
I am joyous to assist you anytime.
You randomly select one card from a 52-card deck. Find the probability of selecting the four of spades or the six of diamonds.
Answer:
1/26
Step-by-step explanation:
There's only 1 four of spades and only 1 six of diamonds. So the probability is:
P = P(4 of spades) + P(six of diamonds)
P = 1/52 + 1/52
P = 1/26
The probability of selecting the four of spades or the six of diamonds from a standard 52-card deck is 1/26. This is determined by adding the probabilities of each individual card being drawn since they are mutually exclusive events.
Explanation:The question asks about the probability of selecting a specific card from a standard 52-card deck. To find the probability of selecting either the four of spades or the six of diamonds, we recognize that these are two distinct events. Since there is one four of spades and one six of diamonds in a deck, and there are 52 cards in total, the probability of drawing the four of spades is 1/52 and similarly the probability of drawing the six of diamonds is also 1/52. These events are mutually exclusive, meaning they cannot happen at the same time, so we can simply add the two probabilities together to find the total probability:
Probability(four of spades or six of diamonds) = Probability(four of spades) + Probability(six of diamonds) = 1/52 + 1/52 = 2/52.
Therefore, the probability is 2/52, which can be simplified to 1/26.
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In a class there are 15 students. 8 of them like playing soccer , 6 of them like swimming , and 2 like both and swimming and playing soccer. How many students do not like either playing soccer or swimming?
Answer: 1
Step-by-step explanation:
8 likes playing soccer
6 likes swimming
2 likes both
So in other words, because the 2 students likes swimming and playing soccer, they must be coming from the combined number of students (8+6=14) leaving only 1 who doesn't like to play either swimming/soccer.
There are 3 students who do not like either playing soccer or swimming and it can be determined by using set operation.
Given that,
In a class, there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playing soccer.
We have to determine,
How many students do not like either playing soccer or swimming?
According to the question,
Let x be the number of students who do not like either playing soccer or swimming.
Total number of students = n(U) = 15
Number of students who like playing soccer = n(A) = 8
Number of students who like swimming = n(B) = 6
Then,
The number of students like both = 2
Number of students who like swimming = Total number of students who like swimming - number of students like both
Number of students who like swimming = 6 -2 = 4
And Number of students who like playing soccer = Total number of students who like playing soccer - number of students like both
Number of students who like swimming = 8 -2 = 6
Therefore,
The total number of students = Number of students who like swimming + Number of students who like swimming + Number of students who do not like either playing soccer or swimming.
[tex]\rm 15 = (8-2) + (6-2) + x +2\\\\15 = 6+4+x+2\\\\15 = 12+x\\\\x = 15-12\\\\x=3[/tex]
Hence, there are 3 students who do not like either playing soccer or swimming.
To know more about Sets click the link given below.
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Which is the simplified form of x^-12
For this case we must simplify the following expression:
[tex]x ^ {12}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then we can rewrite the expression as:
[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]
ANswer:
[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]
Answer:
[tex]\frac{1}{x^{12}}[/tex]
Step-by-step explanation:
The given expression is [tex]x^{-12}[/tex]
We never leave the final expression having a negative exponent.
So, we must change this negative exponent to a positive exponent.
In order to do that, we use the below property of exponent:-
[tex]x^{-m}=\frac{1}{x^m}[/tex]
Here m = 12
Therefore, by using this property, we get
[tex]x^{-12}\\\\=\frac{1}{x^{12}}[/tex]
Thus, the simplified form is
[tex]\frac{1}{x^{12}}[/tex]
NEED ANSWER NOW. WILL MARK BRAINLIEST
For which distributions is the median the best measure of center?
Select each correct answer.
A bar graph with most of the values hovering around 25 y.
A bar graph with values that climb up past 18 y then descend down to just above 2 y.
A bar graph with bars that gradually rises up to over 20 y then drops off down below 2 y.
A bar graph with bars that gradually rises up to over 24 y then drops off down below 2 y.
Answer:
it would be c beacuse i did the test so ya
Answer:
b
Step-by-step explanation:
choose the standard form of the equation of the circle with radius 5 √ 3 centered at( -6, 2) please help
Answer:
(x + 6)² + (y - 2)² = 75
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 6, 2) and r = 5[tex]\sqrt{3}[/tex], hence
(x - (- 6))² + (y - 2)² = (5[tex]\sqrt{3}[/tex] )², that is
(x + 6)² + (y - 2)² = 75
Which of the following is equivalent to 5x+2/x = -12/x-1
A) 6x - 1 = -12x
B) - 12(5x + 2) = x(x-1)
C) - 12(x - 1) = x(5x + 2)
D) (5x + 2) (x - 1) = -12
Answer:
[tex] \frac{5x + 2}{x} = \frac{ - 12}{x - 1} [/tex]
[tex]equivalent \: to \\ \: (5x + 2)(x - 1) = - 12x[/tex]
For this case we must find an expression equivalent to:
[tex]\frac {5x+2} {x} = \frac {-12} {x-1}[/tex]
We multiply both sides of the equation by "x":
[tex]5x+2 = \frac {-12x} {x-1}[/tex]
We multiply both sides of the equation by "x-1":[tex](5x+2) (x-1) = - 12x[/tex]
ANswer:[tex](5x+2) (x-1) = - 12x[/tex]
Which of these ordered pairs is a solution to the linear inequality y> 3x + 2? (-2,-7)
(-1,-5)
(2,8)
(2,9)
Answer:
(2, 9)Step-by-step explanation:
Put the coordinates of the points to the inequality and check:
y > 3x + 2
for (-2, -7) → x = -2, y = -7
-7 > 3(-2) + 2
-7 > -6 + 2
-7 > -4 FALSE
==========================
for (-1, -5) → x = -1, y = -5
-5 > 3(-1) + 2
-5 > -3 + 2
-5 > -1 FALSE
==========================
for (2, 8) → x = 2, y = 8
8 > 3(2) + 2
8 > 6 + 2
8 > 8 FALSE
===========================
for (2, 9) → x = 2, y = 9
9 > 3(2) + 2
9 > 6 + 2
9 > 8 TRUE
what is an equation of the line that is perpendicular to y-3=4(x+2) and passes through the point (-5, 7)
Answer: [tex]y-7=-\frac{1}{4}(x+5)[/tex]
Step-by-step explanation:
The equation of the line in Point-Slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope and ([tex]x_1,y_1[/tex]) is a point on the line.
You can identify that in the equation of the line [tex]y-3=4(x+2)[/tex], the slope is:
[tex]m=4[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:
[tex]m=-\frac{1}{4}[/tex]
Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation [tex]y-y_1=m(x-x_1)[/tex] to get the equation of this line:
[tex]y-7=-\frac{1}{4}(x-(-5))[/tex]
[tex]y-7=-\frac{1}{4}(x+5)[/tex]
What can you tell about the mean of each distribution?
Answer:
there is a SMALL DIFFERENCE in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week
Step-by-step explanation:
i got it right lol
There is a small difference in the mean number of stray cats placed in homes.
We have given the mean of each distribution
What is the mean?
The mean is the mathematical average of a set of two or more numbers that can be computed with the arithmetic mean method or the geometric mean method.
Therefore we can say that,
There is a small difference in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week.
Therefore there is a small difference in the mean of each distribution.
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Which of the following comparisons is FALSE?
a. 4 liters < 1 gallon b. 1 foot < 1 meter c. 25 grams < 1 ounce d. 10 kilometers < 9 miles
Answer:
A
Step-by-step explanation:
Let's check each one-by-one.
a.
we know 3.79 liters is 1 gallon, so 4 liters IS NOT LESS THAN 1 gallon
THis is false.
b.
We know 1 feet is 0.30 meters, so definitely 1 foot is less than 1 meter.
This is true.
c.
we know around 28.35 grams is 1 ounce, so definitely 25 grams is less than 1 ounce.
THis is true.
d.
We know 1 km is approximately 0.62 miles so 10 km would be around 0.62*10 = 6.2 miles
So definitely 9 miles IS GREATER than 10 km.
THis is true.
So answer choice A is false, only.
Match each expression with an equivalent expression.
Question 4 options:
6x−4y
6−4x
6x−4x
6x−4
1. 2x
2. 2(3x−2)
3. 2(3−2x)
4. 2(3x−2y)
Answer:
[tex]6x-4y[/tex] → 4. [tex]2(3x-2y)[/tex]
[tex]6-4x[/tex] → 3. [tex]2(3-2x)[/tex]
[tex]6x-4x[/tex] → 1. [tex]2x[/tex]
[tex]6x-4[/tex] → 2. [tex]2(3x-2)[/tex]
Step-by-step explanation:
You need to:
Factor out 2 from [tex]6x-4y[/tex], then you get the equivalent expression:
[tex]=2(3x-2y)[/tex] this matches with OPTION 4
Factor out 2 from [tex]6-4y[/tex], then you get the equivalent expression:
[tex]=2(3-2x)[/tex] this matches with OPTION 3
Make the subtraction for [tex]6x-4x[/tex], then you get the equivalent expression:
[tex]=2x[/tex] this matches with OPTION 1
Factor out 2 from [tex]6x-4[/tex], then you get the equivalent expression:
[tex]=2(3x-2)[/tex] this matches with OPTION 2
Answer:
6x-4y=2(3x-2y),
6-4x=2(3-2x),
6x-4x=2x,
6x-4=2(3x-2)
Step-by-step explanation:
We have been given 4 expressions
6x−4y, 6−4x, 6x−4x, 6x−4
Now we need to simplify or factor so that we can match each expression with an equivalent expression.
6x-4y=2(3x-2y)
6-4x=2(3-2x)
6x-4x=2x
6x-4=2(3x-2)
Now we can easily see that right side is unique for each of the given expression which can be easily matched with given choices.
The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
2^1/3
2^1/2
2^2/3
2^3/2
Thank you!
Answer:
2^3/2
Step-by-step explanation:
The question is on formulae variation
Given T²=A³.....................the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A
Making T subject of the formulae
T²=A³.............................square root both sides
T= √A³ OR (A³)^1/2
if the orbital period of planet Y is twice the orbital period of planet X then,
Y=2T
Y=2× √A³
Y=2×(A³)^1/2
Applying the laws of indices
Y=2×(A)^(3×1/2)
Y=2×(A)^3/2
Compare
A^3/2 and 2A^3/2
The mean distance increased by 2^3/2
(16+5i) + (6-7i)
How do I solve this?
Answer:
[tex]\large\boxed{(16+5i)+(6-7i)=22-2i}[/tex]
Step-by-step explanation:
[tex](16+5i)+(6-7i)=16+5i+6+7i\qquad\text{combine like terms}\\\\=(16+6)+(5i-7i)=22-2i[/tex]
Answer:
22-2i
Explanation:
16+6=22
5i-7i=-2i
Which algebraic expression is equivalent to the expression below? 2(9x+11)+3
A: 18x + 28
B: 18x + 25
C: 9x + 17
D: 11x + 22
Answer:
B: 18x + 25
Step-by-step explanation:
2(9x+11)+3
Distribute the 2
2*9x + 2*11 +3
18x +22 +3
Combine like terms
18x +25
Convert 192 cups to gallons. Enter your answers in the boxes. There are cups in 1 gallon. Therefore, 192 cups is equal to gallons.
The answer is 12 because there are 16 cups in 1 gallon. 192/16 is 12! Hope this helps! :)
Answer:
Convert 192 cups to gallons. Enter your answers in the boxes. There are (16) cups in 1 gallon. Therefore, 192 cups is equal to (12) gallons.
If the ratio of side lengths of similar polygons is 6:11, what is the ratio of perimeters
Answer:
6 : 11
Step-by-step explanation:
the ratio 6 : 11 applies to all linear measure in the similar polygons
Both side lengths and perimeter are linear, hence
ratio of both is 6 : 11
Work out the value of a and b in the identity.
3ax + 6 - 4(x + b)= 11x + 14
Answer:
a=5, b=-2
Step-by-step explanation:
If you simplify the equation, you get:
3ax +6 -4x -4b - 11x - 14 = 0 =>
3ax - 15x -4b -8 = 0
group together x's and constants:
(3a-15)x -8 -4b = 0
To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2
You are standing 16 ft. from the center of a circular swimming pool. The distance from you to a point of tangency is 25 ft. What is the approximate DIAMETER of the pool?
Check the picture below.
recall the diameter is twice as long as the radius, thus d = 2r = 38.42 or rounded up to 38.
40 POINTS!!
Q: Evaluate. 9^2+2x4−5
A.21
B.75
C.84
D.327
No false answers, no spamming to get points, no saying "Why don't you just try"
The answer is C 84. Your welcome
in the function y-1=1/2(x-6)^2 what effect does the number 6 have on the graph, as compared to the graph y=x^2
Answer: The graph is shifted 6 units to the right.
Step-by-step explanation:
It is important to remember that:
When [tex]f(x-k)[/tex], then the function is shifted "k" units to the right.
Knowing this and given the quadratic parent function [tex]y=x^2[/tex] and the function [tex]y-1=\frac{1}{2}(x-6)^2[/tex], you can observe that one of the transformations is the following:
[tex]f(x-k)[/tex]
Where:
[tex]k=6[/tex]
Therefore, you can notice that the effect is:
The graph is shifted 6 units to the right.
Can someone answer this please :)
Answer:
32
Step-by-step explanation:
The face closest to us has 4 by 4 unit cubes which is 16 cubes.
There are 2 faces deep in the cubiod so the total is 32 unit cubes.
Answer:
The size of the cuboid is 32, or approximately 5.66 squared.
Step-by-step explanation:
First, find the dimensions of the cuboid.
(4)(4)(2)
Next, multiply the numerics (the values).
(4x4)x2 = 16x2 = 32
The cuboid's volume is 32, or about 5.66 squared.