Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true? Math item stem image CLEAR CHECK The height of the red prism is one-third the height of the blue prism. The height of the red prism is the same as the height of the blue prism. The height of the red prism is six times the height of the blue prism. The height of the red prism is three times the height of the blue prism.

Answer:

Value of y = 3

Step-by-step explanation:

Given:

y-2<2 ........Eq1

3y+10>16.........Eq2

Find:

Value of y

Computation:

y-2<2

Add 2 both side,

y-2+2<2+2

y < 4

So y = (0,1,2,3)

Put y = 3 in both equation:

y-2<2

3-2<2

1<2

3y+10>16

3(3) + 10 >16

19>16

Both equation get satisfies by y = 3

So, Value of y is 3

9514 1404 393

Answer:

  33.9 m

Step-by-step explanation:

The relationship between the building height (h), the shadow length (s), and the angle of elevation of the sun (α) is ...

  tan(α) = h/s

  h = s·tan(α) = (18 m)tan(62°) ≈ 33.853 m

The building is about 33.9 meters tall.

Answer:

There are no choices, but [tex]\frac{10}{10.75}[/tex] can be changes in the following ways: multiplying the numerator and the denominator by the same amount, or dividing the numerator and denominator by the same amount.

Hope it helps <3

Answer:

40/43

Step-by-step explanation:

  The fraction

       10

-----------------

   10 3/4

can be simplified by converting 10 3/4 to the improper fraction 43/4:

       10                    10            40

-----------------  =  _______ = ----------

   10 3/4               43/4            43

Next time, please share any answer choices that are given to you.  Thank you.

Answer:

Hello!

__________________

4x+8=2x+2 = x =5

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x-8-2*x-(2)=0

2.1      Solve :    2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

2.2      Solve  :    x-5 = 0

Add  5  to both sides of the equation :

                     x = 5

Hope this helped you!

:D

Answer:

Option D is correct.

A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population.

Step-by-step explanation:

When humans are given the choice whether to participate in a survey like in this question, most often than not, the survey becomes biased.

This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the survey. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.

Discontent is more visibly and strongly expressed in humans.

In order to remove this bias, people should have been chosen at random and their responses recorded.

Hope this Helps!!!

Answer:

  (x, y, z) = (3, -2, 2)

Step-by-step explanation:

The augmented matrix for this set of equations is ...

  [tex]\left[\begin{array}{ccc|c}1&3&2&1\\2&-2&-5&0\\-1&2&4&1\end{array}\right][/tex]

Using your calculator or any of a number of web sites, you can find the reduced row-echelon form to be ...

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

This tells you the solution is (x, y, z) = (3, -2, 2).

Answer:

The zeroes of a quadratic equation are the points on the graph where it lies on the x-axis.

The vertex is the point where it is the maximum or minimum value of x or y depending on the symmetry.

The symmetry is the line where it cuts the graph through the vertex of the graph dividing it into two equal parts that mirror each other.

The quadratic formula, factoring, and completing the square are the methods used to solve a quadratic equation.

f(x) + 7 shifts the graph 7 units up, f(x +7) shifts the graph 7 units to the left

Step-by-step explanation:

Answer:

Step-by-step explanation:

8.  B is the midpoint of AD

A (x,y)

D( -1,3)      B (  (x-1)/2, (y+3)/2)  and B ( 1,1)

then (x-1)/2=1, x-1=2   ( +1)  ,  x= 2+1,  x=3

        (y+3)/2=1, y+3=2 ( -3)     y=2-3,  y= -1

then A (3, -1)

9. (-8,3)

    (s,3)      the midpoint  (0,u)

then    (s-8)/2=0,   s=8

           (3+3)/2=u,   u=6/2,   u= 3

10.  a=1   ( the y coordinate is  the same as the midpoint

  A(3,1)

   B(x,y)    the midpoint (5,1)

   (3+x)/2=5,   3+x=10 ,   x=10-3,  x=7

    (y+1)/2=1,  y+1=2,y=2-1,     y=1

B(7,1)

Answer:

f(x) = x³ - 4x² - 25x + 28

Step-by-step explanation:

Given the zeros x = 1, x = 7 and x = - 4 , then the corresponding factors are

(x - 1), (x - 7), (x + 4)

The polynomial is then the product of the factors, that is

f(x) = a(x - 1)(x - 7)(x + 4) , a is a multiplier

let a = 1 and expand the first pair of factors using FOIL

f(x) = (x² - 8x + 7)(x + 4) ← distribute

      = x³ - 8x² + 7x + 4x² - 32x + 28 ← collect like terms

      = x³ - 4x² - 25x + 28

Step-by-step explanation:

D. Graph D the answer is D

Answer:

D. Graph D the answer is D

Step-by-step explanation:

Answer:

The SAS Postulate.

Step-by-step explanation:

In the diagram, the two triangles are congruent. This is because there are two pairs of congruent sides, with a congruent angle in between. The two angles between the sides are congruent because of the Vertical Angle Theorem.

Hope this helps!

Answer:

P = 5.4641b cm.

Step-by-step explanation:

If the triangle ABC is isosceles and m∠BAC = 120°, we have that:

[tex]mACB = mABC = (180-120)/2 = 30\°[/tex]

Then, in triangle ABH, we have:

[tex]mABH + mBHA + mHAB = 180\°[/tex]

[tex]30\° + 90\° + mHAB = 180\°[/tex]

[tex]mHAB = 60\°[/tex]

If m∠BAC is 120°, we have:

[tex]mHAB + mHAC = 120\°[/tex]

[tex]m∠HAC = 60\°[/tex]

Now we can find the length of AH using the sine relation of angle m∠HAC:

[tex]sin(mHAC) = DH / AH[/tex]

[tex]0.866 = b / AH[/tex]

[tex]AH = b / 0.866 = 1.1547b[/tex]

Now, to find the length of HB and AB, we can use the tangent and cosine relation of the angle m∠HAB:

[tex]tan(mHAB) = HB / AH[/tex]

[tex]1.7321 = HB / 1.1547b[/tex]

[tex]HB = 1.7321 * 1.1547b = 2b[/tex]

[tex]cos(mHAB) = AH / AB[/tex]

[tex]0.5 = 1.1547b / AB[/tex]

[tex]AB = 1.1547b / 0.5 = 2.3094b[/tex]

So the perimeter of triangle ABH is:

[tex]P(ABH) = AB + HB + AH[/tex]

[tex]P(ABH) = 2.3094b + 2b + 1.1547b[/tex]

[tex]P(ABH) = 5.4641b[/tex]

The relation of a and b can be calculated using the tangent relation of the angle m∠HAC:

[tex]tan(mHAC) = DH / AD[/tex]

[tex]1.7321 = b / a[/tex]

[tex]b = 1.7321a[/tex]

Answer:

[tex]\boxed{20(r + 3t)}[/tex]

Step-by-step explanation:

[tex]20r + 60t[/tex]

Factor out 20 from the expression.

[tex]20(r) + 20(3t)[/tex]

Take 20 as common.

[tex]20(r + 3t)[/tex]

Answer:

Hello!

~~~~~~~~~~~~~~~~

Your answer would be (D) 60

~~~~~~~~~~~~~~~`~

Hope this helped you!

Answer:

49π or 153.938 mm²

Step-by-step explanation:

Area of a Circle Formula: A = πr²

Since we are given radius r, simply plug it into the formula:

A = π(7)²

A = 49π

A = 153.938

Answer:

Step-by-step explanation:

Pleased to help u....

Answer:

volume-24 cm³

total surface area-12 cm²

Step-by-step explanation:

Answer:

x =- 6, x = 7

Step-by-step explanation:

Given

g(x) = (x - 7)x + 6)

To find the zeros let g(x) = 0, that is

(x - 7)(x + 6) = 0

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 7 = 0 ⇒ x = 7

Answer:

1/8, 2/5 , 1/2, 3/4

Step-by-step explanation:

1/2= 0.5

1/8= 0.1

3/4= 0.8

2/5= 0.4

just arrange them in the order from smallest to largest......

Answer:

⅛ < ⅖ <  ½ < ¾

Step-by-step explanation:

First, rewrite the fractions so that they all have the same denominator.

The new denominator should be the lowest common multiple of the original denominators.

The L.C.M. of 2, 8, 4, and 5 is 40.

When multiplying the denominator to 40, make sure you multiply the numerator with the same value you use to multiply the denominator.

1/2 = 1x20 / 2 x 20 = 20/40

1/8 = 1x5 / 8x5 = 5/40

3/4 = 3x10 / 4x10 = 30/40

2/5 = 2x8 / 5x8 = 16/40

When all the denominators are the same, we can compare the numerator. The greater the numerator, the greater the fraction is.

Between 20, 5, 30, and 16, the smallest is 5, then 16, 20 and greatest is 30.

Since ascending order means listing them out from smallest to greatest, the order should be:

⅛ < ⅖ <  ½ < ¾

Answer:

0.75

Step-by-step explanation:

Since we use the base 10 decimal system, first convert 3/4 to out of 100:

3/4 = 75/100

We divide 75 by 100 to get 0.75

Answer:

least value of n =4

Step-by-step explanation:

i hope the screenshot of my work broken down step by step helps

Hey there! :)

Answer:

a = 1

b = -5

c = 6.

Step-by-step explanation:

Recall that in standard form, the coefficients of a quadratic equation are:

f(x)= ax² + bx + c

In the given equation, we can identity the coefficients:

f(x) = (1)x² - 5x + 6

a = 1

b = -5

c = 6.

Answer:

I hope it is correct.....

Answer:

I believe it is 84.825

Step-by-step explanation:

First find the area of the circle (A= πr^2)

Then divided the area by 4

Multiply the quotient by 3 to get the answer of 84.825

Answer:

5,318 millions of barrels

Step-by-step explanation:

Subtract Japan's number of barrels from the US' to find the difference:

7,297.4 - 1,979.4 = 5,318 millions of barrels

Answer: choice B

Step-by-step explanation:

just took the quiz

omm its B. G(x)=(x+8)^2

just took the test

Answer:

Step-by-step explanation:

1.The prime factorization of 54 is: 2 x 3 x 3 x 3.

2.The prime factorization of 24 is: 2 x 2 x 2 x 3.

3.The prime factors and multiplicities 54 and 24 have in common are: 2 x 3.

4.2 x 3 is the GCF of 54 and 24.

Answer: GCF(54,24) = 6.

Answer:

6 × 13

Step-by-step explanation:

To find the greatest common factor (GCF), write the prime factorization of each term.

54 = 2×3³

24 = 2³×3

The greatest common factor is the product of each prime number at its lowest exponent.

GCF = 2×3

GCF = 6

Factor:

54 + 24

6 (9 + 4)

6 × 13

Answer:

A

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

PQ is equal to QR, therefore QR=3

Draw a perpendicular line down from R to line TS to form a triangle and since PT=6, the height of the right angle triangle would be 3.

The base of the right triangle would be 7-3=4. Using pytag. theorem [tex]\sqrt{4^{2}+3^2 }=5[/tex]

Therefore RS=5.

So now we can sum up everything: PQ+PT+TS+RS+QR= 3+6+7+5+3=24

Answer:

y = 7x

Step-by-step explanation:

Given that;

You run 9.1 miles in 1.3 hours at a steady rate

Distance y = 9.1 miles

Time x = 1.3 hours

The relationship between the distance y and the time x is the speed v;

Distance = speed × time

y = v×x ......1

v = y/x

Substituting the given values;

v = 9.1/1.3

v = 7 miles/hour

To derive the equation that represents the proportional relationship between the x hours you run and the distance y in miles that you travel. We substitute v = 7 into equation 1;

y = 7x