In some? country's Congress, the number of Representatives is 20 less than five times the number of Senators. There are a total of 520 members. Find the number of Senators and the number of Representatives.

Answer:

  A. 17 1/2 . . . cubic feet

Step-by-step explanation:

The volume is the product of the length, width, and height. If your calculator doesn't deal with mixed numbers, it can be convenient to use one that does.

  (4 ft)(2 1/2 ft)(1 3/4 ft) = 17 1/2 ft³

The volume of the box is 17 1/2 cubic feet.

____

You can also convert the numbers to decimal to use on your calculator:

  4 × 2.5 × 1.75 = 17.500

Or convert them to improper fractions:

  4 × 5/2 × 7/4 = 35/2 = 17 1/2

Final answer:

The volume of the box is 17 1/2 cubic feet, making the correct answer A. 17 1/2.

Explanation:

To find the volume of the box, we need to multiply its length, width, and height together.

The formula for volume is Volume = length × width × height.

Given that the box has a length of 4 feet, a width of 2 1/2 feet, and a height of 1 3/4 feet, we first need to convert these measurements into improper fractions or decimals to make the multiplication easier.

Width: 2 1/2 feet = 5/2 feet
Height: 1 3/4 feet = 7/4 feet

Volume = 4 feet × (5/2 feet) × (7/4 feet) = 20/2 × 7/4 = 10 × 7/4 = 70/4 = 17 1/2 cubic feet.

Therefore, the correct answer is A. 17 1/2 cubic feet.

Answer:

  No, the clay will not pour out easily. I know this because the angle of the truck bed is less than 50°, which is the minimum angle for easy pouring.

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

If α represents the angle of the truck bed, this means ...

  sin(α) = 9/15

We can find α using the inverse sine function:

  α = arcsin(9/15) ≈ 36.87°

We note this angle is less than 50° so we expect the clay will not pour out easily.

Using the tangent function of trigonometry, we find that the angle of the raised dump truck is approximately 30.96°. Since this is less than the necessary 50°, the clay will not pour out easily when the dump truck is raised to 9 feet.

In order to solve this problem, we need to use trigonometry, specifically the tangent function. We form a right triangle, using the truck's bed length (15 feet) as the hypotenuse, the height it's been lifted (9 feet) as the opposite, and we want to find the angle this makes with the ground.

We use the relationship in trigonometry: Tan(angle) = Opposite/Hypotenuse. Converting the values to this equation, Tan(angle) = 9/15. Solving this gives us the angle as the inverse tan of 9/15.

Using a calculator to find the Inverse tan (also known as arctan or tan^-1) of 9/15 gives us an angle, which is approximately 30.96°.

No, The clay will not pour out easily when the body of the dump truck is raised to 9 feet. I know this because the body angle of the dump truck (approximately 30.96°) is less than the necessary 50° for the clay to pour out easily.

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Answer:

13/27

Step-by-step explanation:

1/3 ÷ 9/13

Copy dot flip

1/3 * 13/9

13/27

[tex]AB=\sqrt{(10-1)^2+(3-7)^2}=\sqrt{81+16}=\sqrt{97}\approx9.85[/tex]

Answer:

B.  z = 2

Step-by-step explanation:

Set up the matrix like this.  I multiplied the last row by a 2 to get rid of the fractions so that's what you will see:

[tex]\left[\begin{array}{ccc}2&1&-1\\0&2&3\\-1&2&2\end{array}\right][/tex]

I used Cramer's Rule to solve for the value of y.  In order to do that you need to find the determinant of the matrix, then you need to find the determinant of the matrix after you sub the solution set into the column representing z.

Find the determinant requires that I "pick up" the first 2 columns and then drop them at the end of the matrix and do the multiplication of the majors minus the minors.  The matrix looks like this:

2    1    -1    2    1

0    2    3    0    2

-1    2    2    -1    2

The multiplication of the majors:

[(2×2×2)+(1×3×-1)+(-1×0×2)] = (8-3+0)=5

The multiplication of the minors:

[(-1×2×-1)+(2×3×2)+(2×0×1)] = (2+12+0) = 14

So the determinant of the matrix is I A I = 5 - 14 = -9

Now for the determinant of z, noted as I [tex]A_{z}[/tex] I.  Notice that I am replacing the laast column with the solution set this time:

2    1    -8    2    1

0    2    -6    0    2

-1    2    -8    -1    2

The multiplication of the majors:

[(2×2×-8)+(1×-6×-1)+(-8×0×2)] = (-32+6+0) = -26

The multiplication of the minors:

[(-1×2×-8)+(2×-6×2)+(-8×0×1)] = (16 - 24 + 0) = -8

So the determinant of I [tex]A_{z}[/tex] I = -18

Cramer's Rule is to divide I [tex]A_{z}[/tex] I by I A I:

[tex]\frac{-18}{-9}= 2[/tex]

So the value you need for z to solve for y is 2

The value of z is 2.

The correct answer is an option (B) z = 2

"It is a set of numbers arranged in rows and columns so as to form a rectangular array."

"An inverse of matrix 'B' is  a matrix such that [tex]B\times B'=I[/tex] where [tex]I[/tex] is an identity matrix."

"It is a set of equations for which we find a common solution."

For given question,

We have been given a system of equations.

2x + y - z = -8

2y + 3z = -6

-1/2x + y + z = -4

We can write the third equation as, -x + 2y + 2z = -8

So, we have system of equations,

2x + y - z = -8

2y + 3z = -6

-x + 2y + 2z = -8

We write above system of equations in matrix form as,

[tex]\Rightarrow \begin{bmatrix}2 & 1 & -1 \\0 & 2 & 3 \\-1 & 2 & 2\end{bmatrix}[/tex] [tex]\begin{bmatrix}x \\y \\z\end{bmatrix}[/tex] [tex]=\begin{bmatrix}-8 \\-6 \\-8\end{bmatrix}[/tex]

⇒ AX = B

We use inverse matrix to find the solution of given system of equations.

Pre-multiply both the sides of above equation by [tex]A^{-1}[/tex]

[tex]\Rightarrow A^{-1} AX = A^{-1}B\\\\\Rightarrow IX=A^{-1}B\\\\\Rightarrow X=A^{-1}B[/tex]

The inverse of matrix A is,

[tex]A^{-1}=\begin{bmatrix}\frac{2}{9} & \frac{4}{9} & \frac{-5}{9} \\\\\frac{1}{3} & \frac{-1}{3} & \frac{2}{3} \\\\\frac{-2}{9} & \frac{5}{9} & \frac{-4}{9}\end{bmatrix}[/tex]

So, the solution of given system of equations would be,

[tex]\Rightarrow \begin{bmatrix}x \\y \\z\end{bmatrix}=\begin{bmatrix}\frac{2}{9} & \frac{4}{9} & \frac{-5}{9} \\\\\frac{1}{3} & \frac{-1}{3} & \frac{2}{3} \\\\\frac{-2}{9} & \frac{5}{9} & \frac{-4}{9}\end{bmatrix} . \begin{bmatrix}-8 \\-6 \\-8\end{bmatrix}[/tex]

[tex]\Rightarrow \begin{bmatrix}x \\y \\z\end{bmatrix}= \begin{bmatrix}0 \\-6 \\2\end{bmatrix}[/tex]

Therefore, the value of z is 2.

The correct answer is an option (B) z = 2

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Answer:

A.  (8, 7), B (19, −12), C (−21, 14)

Step-by-step explanation:

You swap the X and Y coordinate for reflections over y=x

Answer:

Its the first choice.

Step-by-step explanation:

You flip the coordinates so the point (a, b) shifts to (b, a). So point A (7, 8) shifts to (8.7).

Answer: [tex](gof)(-7) =495[/tex]

Step-by-step explanation:

Given the functions f(x) and g(x), to find [tex](gof)(x)[/tex] you need to substitute [tex]x=f(x)=x^2 + 6[/tex] into the function g(x):

[tex](gof)(x) = ( x^2 + 6)+ 8( x^2 + 6)\\\\(gof)(x)=x^2 + 6+ 8x^2 + 48\\\\(gof)(x)=9x^2 + 54[/tex]

Now, to find  [tex](gof)(-7)[/tex] you must substitute [tex]x=-7[/tex] into [tex](gof)(x)[/tex], then you get:

[tex](gof)(-7) = 9(-7)^2 + 54\\\\(gof)(-7) =9(49)+54\\\\(gof)(-7) =441+54\\\\(gof)(-7) =495[/tex]

Answer:

  rotation

Step-by-step explanation:

"Isometric" means all measures stay the same.

Rotations that describe the isometric transformation.

An isometric transformation (or isometry) exists as a shape-preserving transformation (movement) in the plane or space. The isometric transformations are reflection, rotation, and translation, and varieties of them such as the glide, which exists as the mixture of a translation and a reflection. Therefore, the correct answer is rotation.

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ANSWER

[tex]y = 3x - 17[/tex]

EXPLANATION

The given line has equation;

[tex]y - 3x = 2[/tex]

We solve for y to get;

[tex]y = 3x + 2[/tex]

The slope of this line is 3.

Since tyheline is parallel to this line, it also has slope 3.

The line passes through (6,1), we can use the slope intercept form,

[tex]y-y_1=m(x-x_1)[/tex]

We substitute the point and the slope to get;

[tex]y - 1 = 3(x - 6)[/tex]

[tex]y = 3x - 18 + 1[/tex]

[tex]y = 3x - 17[/tex]

Answer: First Option

[tex]y = 3x - 17[/tex]

Step-by-step explanation:

For a linear equation of the form

[tex]y = mx + b[/tex] the slope of the line is the constant m.

In this case we have the line

[tex]y-3x=2\\y=3x +2[/tex]

Then the slope is [tex]m=3[/tex]

If the equation of the line sought is parallel to the line [tex]y=3x +2[/tex] then by definition both lines have the same slope m = 3

Therefore the equation of the line sought is:

[tex]y = 3x + b[/tex]

Where b is a constant that represents the intersection of the line with the y axis.

[tex]b = y_0 -3(x_0)[/tex]

Where [tex](x_0, y_0)[/tex] is a point belonging to the line sought.

In this case the point is (6, 1)

So

[tex]b =1 -3(6)[/tex]

[tex]b =-17[/tex]

Finally the equation is:

[tex]y = 3x - 17[/tex]

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

x=56.7

Step-by-step explanation:

From the given triangle, the opposite side of angle x is 66 mm

79 mm is opposite to the right angle, so hypotenuse = 79 mm

we know the opposite side and the hypotenuse

To find the angle we use sin

[tex]sin(x)= \frac{opposite side}{hypotenuse}[/tex]

opposite side = 66

hypotenuse = 79

[tex]sin(x)= \frac{66}{79}[/tex]

[tex]x=sin^{-1}(\frac{66}{79})[/tex]

x=56.66199855

Round the answer to nearest tenth

x=56.7

Answer:

b. 2002

Step-by-step explanation:

divide the geometry kids by total kids to take calculus.

The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts.

The The experimental probability of a freshman studying geometry taking a calculus class before graduation is obtained by dividing the  number of students taking calculus to the number of students of student taking statics.

Referred to the excel table in the attachment for the probability.

The experimental probability of a freshman studying geometry taking a calculus class before graduation in 2002 is found at;

[tex]\rm P_{2002}(\%) = \frac{512}{822} \times 100 \\\\ P_{2002}(\%) =62.29[/tex]

The experimental probability of a freshman studying geometry taking a calculus class before graduation was greatest in 2002.Option B is correct.

Hence,Option B is correct.

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Answer:

  x² +4x +4

Step-by-step explanation:

Matching the expressions, you see you have y=2. Put 2 where y is and simplify.

  (x +2)² = x² +2x(2) +(2)² = x² +4x +4

ANSWER

[tex] {x}^{2} + 4x + 4[/tex]

EXPLANATION

We want to expand:

[tex](x { + 2)}^{2} [/tex]

Using the identity:

[tex] {( x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} [/tex]

We put y=2 into the identity to obtain;

[tex] {( x + 2)}^{2} = {x}^{2} + 2x(2) + {2}^{2} [/tex]

This simplifies to:

[tex]{( x + 2)}^{2} = {x}^{2} +4x + 4[/tex]

Answer:

≈ 5.4m

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + 2^2 = c^2

29 = c^2

c ≈ 5.3852m

Answer:

12.4 meters

Step-by-step explanation:

We do have to use Pythagorean Theorem to get the diagonal part... But we are not done after that.  It wants to know how far we have walked after going down the length, the width, and the diagonal. We are going to have to add 3 numbers at the end (3 measurements for the things I just mentioned)

5^2+2^2=c^2

25+4=c^2

29=c^2

c=sqrt(29) approx 5.4

So now we do 5+2+5.4 which is 12.4 meters

Step-by-step explanation & answer:

Let

x = "one number", then

4x+2 = "the other number"

If the sum is decreased by two, that gives

sum decreased by two = (x+4x+2) - 2 = 5x

The sum decreased by two = 25 (given)

therefore

5x = 25

x = 5

So

"one number" = 5

"another number" = 4x+2 = 4*5+2 = 22

Answer:

Easy its D

Step-by-step explanation:

remember he does not want to pass 2,000

1,400 - 400 = 1,000

1,000 + 1,200 = 2,200

Answer:

No; 1,200 will cause him to exceed 2,000.

Step-by-step explanation:

Given that Brett wants to stay within his daily calorie limit of 2,000 calories, and he has already consumed 1,400 calories and burned 400 calories at the gym, the maximum additional calories he can consume without exceeding his limit is:

2,000 (daily limit) - 1,400 (already consumed) - 400 (burned at the gym) = 1,000 calories

So, Brett can consume a maximum of 1000 more calories to stay within his daily limit of 2,000 calories. Therefore, 1,200 calories is not a viable solution because it exceeds his limit by 200 calories.

The correct answer is:

No; 1,200 will cause him to exceed 2,000 calories.

Hope this helps :))

Answer:

2x+5=3x-3

Step-by-step explanation:

The larger number is represented by X=5, and that number plus x would be 2x+5. The sum of those is 3 less than 3 times x, which is shown by 3x-3. So, 2x+5=3x-3

Answer:

The numbers are 8 and 13. Hopefully that can help with the equation.

Step-by-step explanation:

Answer:

  -x^8y^2 -2y^7 -2xy^4 -6xy

Step-by-step explanation:

Eliminate parentheses.

  xy^4 + 5y^7 - 6xy - 7y^7 - x^8y^2 -3xy^4

Arrange in descending degree order, group like terms.

  -x^8y^2 +(5y^7 -7y^7) +(xy^4 -3xy^4) -6xy

Combine like terms.

  -x^8y^2 -2y^7 -2xy^4 -6xy

Answer:

  D(-7, 2)

Step-by-step explanation:

The midpoint of diagonal AC is the same as the midpoint of diagonal BD, so ...

  (A+C)/2 = (B+D)/2

We can solve for D by multiplying by 2 and subtracting B:

  D = A + C - B

  D = (-2, 4) +(-4, 1) -(1, 3) = (-2-4-1, 4+1-3)

  D = (-7, 2)

Answer:

(-) $29.26 per thousand for a 3-year 3.4% loan

(a) $5,240

(b) $153.32

(c) $279.52

Step-by-step explanation:

• Payment per thousand

The payment amount can be computed from the formula ...

A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual rate, n is the number of payments per year, and t is the number of years.

For a $1000 3-year loan at 3.4%, this evaluates to ...

A = 1000(0.034/12)/(1 -(1 +0.034/12)^(-12·3)) ≈ $29.26

The monthly car payment per $1000 borrowed is $29.26.

__

• Rudy's trade-in allowance and down payment will reduce the amount he finances to ...

$10,240 -3000 -2000 = $5,240

__

• $5,240 = 5.24 × $1000, so Rudy's payment will be ...

5.24 × $29.26 = $153.32

__

• The amount of interest Rudy pays is the difference between the amount paid back and the amount of the loan.

(36 mo)×($153.32/mo) - 5240 = $279.52

Monthly Car Loan Payment Per $1000 Borrowed is $29.26

(a) money he will borrow for loan = $ 5240

(b) monthly auto payment = $ 153.32

(c) the total amount of interest he will pay is $279.52

(d) Total payment for car= $ 10,519.52

Given Information :

We find out the monthly car loan payment for every $1000 borrowed.

Lets use monthly payment formula

[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }[/tex]

Where P is the loan amount.

r is the rate of interest and t is the number of years

n is the period

P=1000

Given that  3-year auto loan at 3.4% APR.

t=3, r= 3.4%= 0.034, n=12

Substitute all the values and calculate the monthly loan

[tex]A=\frac{P\cdot \frac{r}{n} }{1-(1+\frac{r}{n})^{-nt} }\\A=\frac{1000\cdot \frac{0.034}{12} }{1-(1+\frac{0.034}{12})^{-12\cdot 3} }\\A=\frac{1000\cdot \frac{0.034}{12}}{1-\left(\frac{0.034}{12}+1\right)^{-36}}\\A=\frac{2.83333\dots }{1-1.00283\dots ^{-36}}\\A=29.25782[/tex]

Monthly Car Loan Payment Per $1000 Borrowed is $29.26

The cost of car is  $10,240. Allowance = 3000 and down payment = 2000

(a) Auto loan = cost of car - allowance - down payment

[tex]Auto \; loan = 10240 - 3000 -2000=5240[/tex]

(b) Monthly Car Loan Payment Per $1000 Borrowed is $29.26

Monthly car loan payment for $5240 is

[tex]\frac{5240}{1000} * 29.26=153.32[/tex]

(c) first we find out the total loan amount paid in 3 years (36 months)

[tex]36 \cdot 153.3224=5,519.52[/tex]

To find the amount of interest he pay , we subtract the loan amount

[tex]5,519.52-5240=279.52[/tex]

the total amount of interest he will pay is $279.52

(d) Total payment for car = down payment +total loan amount paid

Total payment for car =[tex]5000+5519.52=10,519.52[/tex]

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Answer:

The coordinates of H′ are (-2,0).

Step-by-step explanation:

It is given that square EFGH stretches vertically by a factor of 2.5 with respect to the x-axis to create rectangle E′F′G′H′.

If a figure stretches vertically by a factor of 2.5 with respect to the x-axis, then the x-coordinates remains same and the points which lie on the axis are also remains the same after stretch.

It is given that the coordinates of H are (-2,0). This point lie on the x-axis, therefore it will remains the same after stretch.

Therefore the coordinates of H′ are (-2,0).

Answer: 5 triangle STU is similar to triangle SYU

11 sub traction property.

Step-by-step explanation:

i got it right on edgnuity if its the question with the triangle and the proof chart with 11 statements

Answer:

5: triangle STU is similar to triangle XYU

11: subtraction property

Step-by-step explanation:

Final answer:

To solve the given system of linear equations, we use substitution to find y = 1/9 and then find x = 7/9 as the values that satisfy both equations.

Explanation:

The student is attempting to solve a system of linear equations. To find the values of x and y that satisfy this system, we need to use a method such as substitution or elimination. Given the system:

x = −2y + 1

13x + 8y = 11

We can substitute the expression for x from the first equation into the second equation:

13(−2y + 1) + 8y = 11

−26y + 13 + 8y = 11

−18y + 13 = 11

−18y = −2

y = −2/−18

y = 1/9

Now we can substitute this value of y back into the first equation to find x:

x = −2(1/9) + 1

x = −2/9 + 1

x = −2/9 + 9/9

x = 7/9

Therefore, the solution to the system is x = 7/9 and y = 1/9.

A

The first equation has slope 6 and y intercept -4.  I'd plot y intercept (0,-4) and (1,2), and connect the dots and extend for the first line.

The second equation has slope 5 and y intercept -3.  I'd plot y intercept (0,-3) and (1,2), and connect the dots and extend for the second line.

We stumbled on the solution, both lines contain (1,2)

B

I don't like the graphing.  This is algebra, not connect the dots.

We have two equations for y, we equate them to find the x where they meet.

6x - 4 = 5x - 3

6x - 5x = -3 + 4

x = 1

y = 6(1) - 4 = 2

Check:  y = 5(1) - 3 = 2, good

Answer: (1, 2)

Answer:

its the mean for the data, its showing you the average studying time

Answer:

10"

Step-by-step explanation:

The volume for a cube is V = l × w × h

But since this is a cube, all the sides aree the same length, so we could rewrite this in terms of x as:

V = [tex]x^3[/tex]

If we know the volume to be 1000, we sub it in for V:

[tex]1000=x^3[/tex]

We "undo" a cube by taking the cubed root of both sides.  The cubd root of x cubed is just x, and the cubed root of 1000 is 10.  Therefore, x = 10

Answer:

45 units

Step-by-step explanation:

The perimeter is equal to 2(width+length)

Let the longer side be the length of the rectangle

2(2x+3x+3)=146

Divide both sides by 2

2x+3x+3=73

5x+3=73

5x=70

x=14

The longer side = 3x+3

substitdude x into the equation

3(14)+3

= 45 units

X=33/17

Here is how it works

By the way what you are working with is called improper factions, which is when the big number is placed over the smaller number.

Now 33/17 is also 1 16/17

35/17 is also 2 1/17

Now we can the proper fractions which are 1 16/17 and 2 1/17

1+2=3 and 16/17 + 1/17 equals 1

3+1=4

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