Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

Answer:

B and C

Step-by-step explanation:

Use the Pythagorean Theorem a^2+b^2=c^2.

We can see in B that 8^2 is 64 and 15^2 is 225 which adds to 17^2 which is 289.

In C, the sqrt of 2 squared is just 2 and adding that by another sqrt 2^2 results in 4 which is also the value of 2^2.

Answer:(use the Pythagorean formula)

Step-by-step explanation:

Find the two smaller sides. Square each one them add them together. Then square the third side (the biggest side). If your two answers match, it's a right triangle!

Make sure that you don't make the mistake of adding the two smaller sides together before squaring.

Answer:

210

Step-by-step explanation:

The general formula for picking k items from a total of n is

[tex]_{n}C_{k} = \frac{n! }{(n-k)!k! }[/tex]

Thus, if we want to select a committee of six people from a club with 10 members, the number of combinations is

[tex]_{10}C_{6} = \frac{10! }{(10-6)!6! }[/tex]

[tex]= \frac{10! }{4!6! }[/tex]

[tex]= \frac{10\times9\times8\times7}{4\times3\times2\times1 }[/tex]

[tex]= \frac{5040 }{24 }[/tex]

= 210

The committee can be selected in 210 separate ways.

Answer:

4 1/4 × 3 × 1 1/4

Step-by-step explanation:

To find volume you need to do length×width×height

The expression which can be used to find the volume of the rectangular prism is, Volume = l × w × h

If a three dimensional prism has 6 rectangular faces such that all 3 pair of opposite faces are congruent.

The three dimensions of a rectangular prism are length, width and height.

Let, length of rectangular prism = l unit

Width of rectangular prism = w unit

And the height of rectangular prism = h unit

Then, Volume of rectangular prism = Length × Width × Height

                                                           = l × w × h  cubic unit

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Answer:

Step-by-step explanation:

The perimeter of the given figure is equal to the circumference of whole circle.

The formula of a circumference of a circle:

[tex]C=\pi d[/tex]

d - diameter

We have d = 70 cm. Substitute:

[tex]C=70\pi\ cm[/tex]

The area of given figure is equal to the area of rectangle 70cm × 35cm.

(look at the picture).

The area of a rectangle:

[tex]A=(70)(35)=2,450\ cm^2[/tex]

The area of a circle is given by the formula A = πr², where π represents pi, and r the radius. The area can be left in terms of pi to avoid rounding errors, with the example of a circle with 1.2-meter radius having an area of approximately 4.5 m² when considering significant figures.

The area of a circle is expressed as A = πr², where π (pi) is approximately 3.14159265, and r is the radius of the circle. In terms of pi, this formula is often left in the form of πr² to retain the exact value without rounding. For example, if we have a circle with a radius of 1.2 meters, the area would be calculated as A = π(1.2 m)² = 4.5238934 m² using a calculator with eight-digit precision. However, since the radius is given with two significant figures, the appropriate representation of the area would be A=4.5 m².

It is important to note that when expressing the area in terms of pi, you may encounter different contexts such as finding the area of a semicircle using the definite integral that results in r²/2 for the semicircle's area, or understanding proportionalities in a circle divided into slices.

Answer:  104°

Step-by-step explanation:

Since ∠JKL and ∠LKM are supplementary, then their sum is 180°.

∠JKL + ∠LKM = 180

2x + 4 + x + 26 = 180

            3x + 30 = 180

            3x         = 150

              x         =  50

∠JKL = 2x + 4

        = 2(50) + 4

        = 100 + 4

        = 104

Answer:

[tex]\$25.60[/tex]

Step-by-step explanation:

step 1

Find the volume of the container

The volume is equal to

[tex]V=8^{3}=512\ cm^{3}[/tex]

step 2

Find the volume of the crystal cube

The volume is equal to

[tex]V=1^{3}=1\ cm^{3}[/tex]

step 3

Find the total number of crystal cubes in the container

Divide the volume of the container by the volume of the crystal cube

so

[tex]512/1=512\ crystal\ cubes[/tex]

step 4

Find the cost

Multiply the number of crystal cubes by $0.05

[tex]512*0.05=\$25.60[/tex]

Answer:

11.7

Step-by-step explanation:

Using the cosine ratio, then

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{9}{h}[/tex]

Multiply both sides by h , the hypotenuse

h × cos40° = 9 ( divide both sides by cos40° )

h = [tex]\frac{9}{cos40}[/tex] ≈ 11.7 ( to the nearest tenth )

Answer: B 312

Step-by-step explanation:i did this before in k12 yep its 312

hope this helps

Answer:

[tex]6^{\frac{7}{3} }[/tex]

Step-by-step explanation:

Using the rules of exponents

• [tex]\sqrt[n]{a^{m} }[/tex] ⇔ [tex]a^{\frac{m}{n} }[/tex]

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]

Hence

[tex]\sqrt[3]{6}[/tex] = [tex]6^{\frac{1}{3} }[/tex] and

6² × [tex]6^{\frac{1}{3} }[/tex] = [tex]6^{\frac{7}{3} }[/tex]

$16 / $80 * 100% = 20%.

$16/$80 *100= 20%

answer is 20%

Answer:

Step-by-step explanation:

The formual fo ana area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

b - base

h - height

We have A = 50 cm² and h = 2b. Substitute:

[tex]\dfrac{(b)(2b)}{2}=50\\\\b^2=50\to b=\sqrt{50}\ m\to b\approx7.1\ m\\\\h=2b\to h=2(7.1)=14.2\ m[/tex]

To find the height and base of the triangle with an area of [tex]50 m^2[/tex]and the height being twice the base, we use the area formula[tex]A = (base imes height) / 2,[/tex] solve for the base, and double it to find the height. The base is approximately 7.1 m, and the height is approximately 14.1 m.

The question seeks the height and base of a triangle whose area is 50 [tex]m^{2}[/tex] and the height is twice the length of its base. The area of a triangle can be calculated using the formula A = [tex](base imes height) / 2.[/tex] Since the height is twice the base, we can say the height is 2b, where b is the base.

Plugging into the formula for the area of a triangle, we get:

Area, A = 50 m2

[tex]A = (b imes 2b) / 2[/tex]

50 = b2

b = \/50

b \/= 7.1 m (to the nearest tenth)

[tex]Height (h) = 2 imes b = 2 imes 7.1 m[/tex]

h = 14.1 m (to the nearest tenth)

Therefore, the base of the triangle is approximately 7.1 m and the height is approximately 14.1 m.

Answer:

24-q

Step by Step Explanation :

24 decreased by q is basically saying 24 minus q which is 24-q

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

step 1

Find the ratio of the height of shape A to the height of shape B

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area shape A

y----> surface area shape B

so

[tex]z^{2} =\frac{x}{y}[/tex]

substitute

[tex]z^{2} =\frac{4}{25}[/tex]

[tex]z =\frac{2}{5}[/tex]

therefore

the ratio of the height of shape A to the height of shape B is equal to

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

step 2

Find the ratio of the height of shape B to the height of shape C

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> volume shape B

y----> volume shape C

so

[tex]z^{3} =\frac{x}{y}[/tex]

substitute

[tex]z^{3} =\frac{27}{64}[/tex]

[tex]z =\frac{3}{4}[/tex]

therefore

the ratio of the height of shape B to the height of shape C is equal to

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

step 3

Find the ratio of the height of shape A to the height of shape C

we have

[tex]\frac{hA}{hB}=\frac{2}{5}[/tex]

[tex]\frac{hB}{hC}=\frac{3}{4}[/tex]

Multiply

[tex](\frac{hA}{hB})(\frac{hB}{hC})=\frac{hA}{hC}[/tex]

so

[tex](\frac{2}{5})(\frac{3}{4})=\frac{6}{20}=\frac{3}{10}[/tex]

In this problem, we're working with the geometric property of similarity to compare the heights and volumes of different shapes. Using the ratios of their surface areas and volumes, we found that the ratio of the height of Shape A to Shape C is 15:8.

In order to solve this problem, it is necessary to first know that, for similar shapes, the ratio of the areas is actually the square of the ratio of the corresponding length measurements (this includes dimensions such as the height). In this particular case, since shapes A and B are similar, the ratio of their surface areas will give the square of the ratio of the heights:

√(25/4) : 1 => 5 : 2

Now, for shapes B and C, we have the volume ratio given as 27 : 64. Since, for similar shapes, the ratio of the volumes is the cube of the ratio of the corresponding length measurements, the cube root of the volume ratio will give the ratio of the heights:

∛(27/64 : 1) => 3 : 4

Using these two ratios, we can find the ratio of height from shape A to shape C by multiplying together the heights of shape A to B and shape B to C: (5/2) * (3/4) => 15 : 8.

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The answer is -3, let me know if you want me to give you the steps

The answer would be -3

[tex] - 7 {v}^{2} - 25v - 12 \\ = - 7 {v}^{2} - 21v - 4v - 12 \\ = - 7 v (v + 3) - 4(v + 3) \\ = ( - 7v - 4)(v + 3) \\ = - (7v + 4)(v + 3)[/tex]

Answer: -2x²-11x-35

Step-by-step explanation:

-2(p+4)²-3+5p

-2(x²+8x+16)-3+5x

-2x²-11x-35

To simplify the expression -2(p+4)^2-3+5p, it's important to distribute, multiply, and combine like terms. The simplified expression is -2p^2 -11p -35.

To simplify the expression -2(p+4)^2-3+5p, it's easier to break it down step by step:

This is the simplest form of the original expression.

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Answer:D)78

Step-by-step explanation:70+71+75+75+88+89/6

Answer:

See attached picture

Step-by-step explanation:

This is a linear equation. To graph it, use the model y = mx + b where m is the slope and b is the y-intercept. Here m = 2 and b = 4. Start at the point (0,4) on the y-axis. Mark this point because it is the y-intercept. Then move up 2 units and over 1 to the point (1, 6). Mark this point. And connect. This is the correct graph. See attached picture.

Answer:

I think the answer would be to divide the inches by 4.  So Length would be 3.5 inches and width would be 1.25 inches . I might be wrong but if you have no hope I would go with my answer.

Step-by-step explanation:

Answer:

lenght: 3.5 inches.

width: 1.25 inches.

Step-by-step explanation:

You have the following information:

- The drawing must be 1/4  the size of the original drawing.

- The tree in the original drawing is 14 inches tall and 5 inches wide.

Therefore, keeping the above on mind, you can find the length and width of the tree in Barry's drawing by multiplying the original dimensions by 1/4.

Then, you obtain the result shown below:

[tex]lenght=\frac{1}{4}*14in=3.5in\\\\width=\frac{1}{4}*5in=1.25in[/tex]

Answer:

b

Step-by-step explanation:

Answer:

a. [tex]8^{8}\sqrt{8}[/tex]

Step-by-step explanation:

The given expression is

[tex]\sqrt{8^{17}}[/tex]

We rewrite the radicand to obtain;

[tex]\sqrt{8^{16}\times 8}[/tex]

Split the radicand;

[tex]\sqrt{8^{16}}\times \sqrt{8}[/tex]

[tex]\sqrt{(8^{8})^2}\times \sqrt{8}[/tex]

[tex]8^{8}\sqrt{8}[/tex]

➷ Substitute it into the equation:

3 = 2x + 5

Subtract 5 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

The other coordinate is -1

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

-1

Step-by-step explanation:

1.We know that the equation of the line is y=2x+5 ( with a gradient of 2 and a

y-intercept of 5) and the y coordinate is 3 so we must work out x (x,3).

2.We know y=3 so

3 = 2x+5

3. Solve the equation

3=2x+5

(-5 from both sides)

-2=2x

(Divide both sides by 2 to isolate x)

-1 = x so x = 1

Hope this helps:)

5INGH

Answer:

The answer is A. [-4/3]

For the second part the answer is a rotation 90 CCW about origin

Hope this helped!

Answer:

The correct option is B.

Step-by-step explanation:

From the given graph it is clear the x-coordinate of the vector is 3 and y-coordinate of the vector is 4 in the coordinate plane.

The given vector can be defined as

[tex]A=\begin{bmatrix}3 & 4\end{bmatrix}[/tex]

Translation vector is

[tex]B=\begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

We need to find the resulting vector,

[tex]AB=\begin{bmatrix}3 & 4\end{bmatrix}\cdot \begin{bmatrix}0 & -1\\ 1 & 0\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}3(0)+4(1) & 3(-1)+4(0)\end{bmatrix}[/tex]

[tex]AB=\begin{bmatrix}4& -3\end{bmatrix}[/tex]

Therefore the correct option is B.

The true statement is the side lengths will form a triangle because 6+7>4. So option (d) is correct.

To determine if the given side lengths can form a triangle, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the side lengths as follows:

a = 4  meters

b = 6  meters

c = 7  meters

We'll check each possible combination:

1. \( a + b > c \): \( 4 + 6 > 7 \) (True)

2. \( a + c > b \): \( 4 + 7 > 6 \) (True)

3. \( b + c > a \): \( 6 + 7 > 4 \) (True)

Since all three conditions are true, the given side lengths (4, 6, 7 meters) can indeed form a triangle.

Thus, the correct option is D. The side lengths will form a triangle because 6 + 7 > 4.

Complete Question:

A triangular garden is being formed with stones. The three sides measure 4 meters by 6 meters by 7 meters. Which of the following is a true statement about the side lengths of the triangle?

A. The side lengths will not form a triangle because 6+4>7.

B. The side lengths will form a triangle because 4+6<7.

C. The side lengths will not form a triangle because 7+4<6.

D. The side lengths will form a triangle because 6+7>4.

Answer:

Yes different signs leads to a negative product.

Step-by-step explanation:

So I don't know if this was helpful, but I hope you find it very helpful!

Answer: 132%

Step-by-step explanation:

Answer:

Step-by-step explanation:

The general equation for a circle of radius r with center at (h, k) is

(x - h)² + (y - k)² = r²

Here, this equation becomes:

(x - 1)² + (y - 2)² = 3²

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius. The equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

The center point of the given circle is (1,2).

The length of the radius of the circle is 3 units.

Equation of the circle way to represent the circle in the coordinate plane using its center points and the radius.

The standard form of the equation of the circle is,

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Here,

(h,k) is the center of the circle.

[tex]r[/tex] is the radius of the circle.

Put the values given in the problem in the standard form of the equation of the circle. Thus,

[tex](x-1)^2+(y-2)^2=3^2[/tex]

[tex]x^2+1-2x+y^2+4-4y=9[/tex]

[tex]x^2+y^2-2x-4y+5-9=0[/tex]

[tex]x^2+y^2-2x-4y-4=0[/tex]

Thus the equation of the circle centered at the point (1,2) and has a radius of length 3 can be given as,

[tex]x^2+y^2-2x-4y-4=0[/tex]

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Answer:

-40

Step-by-step explanation:

Try rearranging and factoring -8y-2c-2b-8x-2a:

This is equal to -8(x + y) -2(a + b + c).

Since x + y = 7, we have:

                            -8(7) -2(a + b + c)

and since a + b + c = 8, we end up with:

                             -56 - 2(8), or

                               -56 - 16    = -40

Answer:

v = -2.5

Step-by-step explanation:

9(9-2v) = -12(v-8)

81−18v= −12v+96

So move -18v to the other side and change the sign. Same to 96.

81-96 = -12v + 18v

-15 = 6v

v = -2.5

Answer:

44=y

Step-by-step explanation:

27+x=y

We know x = 17, so we can substitute x=17 into the equation

27 + 17 = y

44=y

Answer:

[tex]y=44[/tex]

Step-by-step explanation:

Substitute 17 for x in the equation since [tex]x=17[/tex]

[tex]27+(17)=y[/tex]

[tex]44=y[/tex]