Select the correct answer.
Which statement is true?

Answer:

D) [tex]x^{2} =8y[/tex]

Step-by-step explanation:

Because the receiver of the parabolic dish antenna is 2 feet above the vertex, the parabola must be vertical. Therefore, we will use the equation [tex](x-h)^2=4p(y-k)[/tex] where [tex](h,k)[/tex] is the vertex of the parabola and [tex](h,k+p)[/tex] is the focus point. Since we are given that the receiver is 2 feet above the vertex which is located at the focus point and the vertex is [tex](0,0)[/tex] at the origin, then the focus point is [tex](0,0+p)[/tex] where [tex]p=2[/tex]. Therefore, the equation that models a cross section of the dish is [tex]x^{2} = 8y[/tex].

Answer:

229.459 rounded

Step-by-step explanation:

V=πr2h

1441 = [tex]\pi[/tex] r 2 (1)

divide 1441 by 2 and then divide by 3.14 (pi)

r = 229.459 rounded

Answer:

Aiden will have $17878 more than autumn

Step-by-step explanation:

For Aiden;

Formula for continuous compounding is;

FV = Pe^(rt)

P = 98000

r = 2⅜% = 0.02375

t = 11

Thus;

FV = 98000 × e^(0.02375 × 11)

FV = 127258.1218

For Autumn;

Formula for regular compounding;

FV = PV(1 + (r/n))^(nt)

Where;

PV is present value = 98000

r is rate = 2¾% = 0.0275

n is number of times amount is compounding = quarterly = 4

t is time in years = 11

Thus;

FV = 98000 + (1 + (0.0275/4))^(4 × 11)

FV = 98001.3518

Difference in their compounded amounts after 11 years is;

127258.1218 - 98001.3518 = 29256.77 ≈ $17878

Answer:

No

Step-by-step explanation:

2x-3 = 0 so x = 3/2

3x+2 = 0 so x = - 2/3

x+2 = 0 so x=-2 (twice)

x-7/8 = 0 so x=7

By using Pythagorean's theorem we will find that the measure of AC = 5.66 units.

Remember that for any right triangle with an hypotenuse H and two legs A and B, the Pythagorean theorem says that:

A^2 + B^2 = H^2

Here we know that:

AB = 4

BC = 4

Because these two have the same length, we know that these two must be the legs, then AC (the side we want to find) is the hypotenuse.

Then we can write:

4^2 + 4^2 = AC^2

16 + 16 = AC^2

√(16 + 16) = AC

√32 = AC

5.65 = AC

The measure of the hypotenuse of the right triangle is 5.66 units.

Learn more about right triangles:

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Answer:

45

Step-by-step explanation:

5*60=300 minutes

300/300=1

means he makes 1 in one minute

so 45 for 45

Answer:

[tex]\frac{6x^3+40xy^2-45x^2y+30y^3}{60}[/tex]

Step-by-step explanation:

Primero que todo reescribiremos el problema como una ecuacion:

[tex]\frac{6}{5}x^{3}-x^{3}+\frac{4}{3}xy^{2}-\frac{3}{2}x^{2} y+y^{3}[/tex]

Ahora rompemos el parentesis cambiando el signo:

[tex]\frac{3}{5}x^{3}-\frac{1}{2}x^{3}+\frac{2}{3}xy^{2}-\frac{3}{4}x^{2} y+\frac{1}{2}y^{3}[/tex]

Ahora simplificamos los terminos con variables iguales:

[tex]\frac{1}{10}x^{3}+\frac{2}{3}xy^{2}-\frac{3}{4}x^{2} y+\frac{1}{2}y^{3}[/tex]

Ahora restamos los primeros dos terminos y los ultimos dos terminos:

[tex]\frac{3x^{3}+20xy^{2}}{30}-\frac{6x^2y+4y^3}{8}[/tex]

Y realizamos la ultima suma de fracciones:

[tex]\frac{24x^3+160xy^2-180x^2y+120y^3}{240}[/tex]

Y por ultimo podemos simplificar la espresion dividiento doto por 4:

[tex]\frac{6x^3+40xy^2-45x^2y+30y^3}{60}[/tex]

Answer:

[tex]x=\frac{3}{5}[/tex]

x = - 1

Step-by-step explanation:

5x² + 2x - 3 = 0

5x² + 2x - 3x = 0

(5x² + 5x) + (- 3x - 3) = 0

5x(x + 1) - 3(x + 1) = 0

(5x - 3)(x + 1) = 0

Create separate equations.

5x - 3 = 0

x + 1 = 0

5x - 3 = 0

5x - 3 + 3 = 0 + 3

5x = 3

5x ÷ 5 = 3 ÷ 5

[tex]x=\frac{3}{5}[/tex]

x + 1 = 0

x + 1 - 1 = 0 - 1

x = - 1

Answer:

5.7

Step-by-step explanation:

Answer:

y is 8/5 when x = -4.

Step-by-step explanation:

If the value of "Y" varies directly with "X", we can write y = kx, where k is the constant of proportionality.

If "y=-8,when x=20," then we can find k:    -8 = 20k, or k = -2/5.

Then y = (-2/5)x.

If x = -4, then y = (-2/5)(-4) = 8/5

y is 8/5 when x = -4.

Answer:

y=2x+1

Step-by-step explanation:

y= mx + c

c= 1

m= slope which is -2

y=2x+1

Answer:

0.75

Step-by-step explanation:

you said it was 0.75

1/√2

Step-by-step explanation:

Imagine a right-angled triangle, for e.g. Triangle ABC,

Where

B = 90°

Remember your Toa Cah Soh.

sin 45° = opposite / hypotenuse

If theta = 45°

Angles A and C = 45° (Sum of angles in a triangle equal = 180°)

Since theta are the same, we can also deduce that the length AB and BC are the same.

Take for example AB = BC = 1 = opposite

By the Pythagorean theorem,

AB² + BC² = AC²

1² + 1² = AC²

2 = AC²

AC = √2 = hypotenuse

Therefore:

sin 45° = opposite / hypotenuse

sin 45° = 1/√2

Answer: The perimeter is about 20.26 units

Step-by-step explanation:

To calculate the distance between the points, we use the formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where,

d = distance

[tex]x_2\text{ and }x_1[/tex] are the coordinates of the points on x-axis

[tex]y_2\text{ and }y_1[/tex] are the coordinates of the points on y-axis

For the given points:

B(0,3), C(4,-1), E(2,-3) and F(-2,1)

[tex]x_2=4\\x_1=0\\y_2=-1\\y_1=3[/tex]

Putting values in above equation, we get:

[tex]BC=\sqrt{(4-(0))^2+(-1-3)^2}\\\\d=\sqrt{16+16}=5.66units[/tex]

[tex]x_2=2\\x_1=4\\y_2=-3\\y_1=-1[/tex]

Putting values in above equation, we get:

[tex]CE=\sqrt{(2-(4))^2+(-3-(-1))^2}\\\\d=\sqrt{36+4}=4.47units[/tex]

To calculate the perimeter of a rectangle, we use the equation:

[tex]Perimeter=2(l+b)[/tex] ....(1)

where,

l = length of the rectangle = BC = 5.66 units

b = breadth of the rectangle = CE = 4.47 units

Putting values in equation 1, we get:

[tex]Perimeter=2(5.66+4.47)\\\\Perimeter=20.26 units[/tex]

Hence, the perimeter is about 20.26 units

Answer:

$117,351 JMD

Step-by-step explanation:

It is simple. 1 US dollar is 150.45 JMD, so 780 US dollars should be:

780 * 150.45 = 117,351

Step-by-step explanation:

$1US dollar=$150.45JMD

$780US dollars=?

=$150.45×$780

=$117,351

Answer:

The number 1 and 47

or 13 and 59

Answer:

16 and 62

Step-by-step explanation:

Two variables x and y. x < y.

y - x = 46

y = 46 + x

4x = y + 2

y = 46 + x in 4x = y + 2

4x + y = x + y + 46 + 2

4x + y - y = x + y - y + 46 + 2

4x = x + 48

4x - x = x - x + 48

3x = 48

3x ÷ 3 = 48 ÷ 3

x = 16

y = x + 46

y = 16 + 46

y = 62

Answer: 98.1

Step-by-step explanation:

Given: mass= 970 gm

Time = 14 min

rate of decay= 15.1% per minute.

Now, computing to get amount of element remaining after 14 minutes.

Formula; Element remaining=

Element remaining=

⇒ Element remaining=

⇒ Element remaining= ≅ 98.1 (nearest 10th of a gram)

∴ 98.1 element is still remaining after 14 minutes.

Answer:

98.1

Step-by-step explanation:

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credit: jitushashi120

Step-by-step explanation:

3(−3x2+5x)

=(−3)(−3x2+5x)

=(−3)(−3x2)+(−3)(5x)

=9x2−15x

Step-by-step explanation:

1.(first second or third)

Answer:

it should be 50 100 150 200 250 300....

Answer:

12 apple pies

Step-by-step explanation:

If he uses 6 apples for each pie and he has 12 bags of apples with 6 apples in each bag, then we can infer that each bag is one pie.

So, 1x12 = 12 apple pies

Hope this helped :)

Step-by-step explanation:

29/8= 3.625

It lies between 3 and 4

Hope this helped!

Answer:

Between 3 and 4 pieces of fabric.

Step-by-step explanation:

29/8 is equal to 3.625, which you can round up to 4 or round down to 3, since they are both the nearest whole numbers to 3.625.

The length of each side of the square is (3x-2) units

The dimensions of the rectangle are (5x + 4y) and (5x -4y) units

From the question, we are to factor out the given expression for the area of the square

The expression is

9x² − 12x + 4

Factoring

9x² − 12x + 4

9x² −6x -6x + 4

3x(3x -2) -2(3x-2)

(3x -2)(3x -2)

Hence, the length of each side of the square is (3x-2) units

Part B:

The given expression is

25x² − 16y²

Factoring

25x² − 16y²

By difference of two squares, we get

(5x + 4y)(5x -4y)

Hence, the dimensions of the rectangle are (5x + 4y) and (5x -4y) units

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Step-by-step explanation:

Hey there!

Please see your required answer in pictures.

Hope it helps!

Answer:

Step-by-step explanation:

??

Answer:

0

Step-by-step explanation:

Just add up the numbers and divide by 7

-3-2-1+1+2+3

-6+6=0

0/7 is 0

Answer:

(-4,3)

Step-by-step explanation:

G is plotted 4 units left and 3 units up

:) ur welcome