write each number from the box and the correct category shown in the table

True statements are:

Step-by-step explanation:

We have the following statements to check on whether it's right or wrong:

1. It has a directrix of x = -4:

According to figure , parabola directrix is at -4 i.e. at x = -4 , Therefore this statement is true!

2. It opens to the left:

In figure, Parabola opens to right not left , Therefore this statement is wrong!

3. It has a vertex at the origin:

Vertex of Parabola is at what points not shown in figure. Therefore this statement cannot be confirmed as true.

4. The axis of symmetry is the y-axis:

Axis of symmetry for above parabola is x-axis as it cuts parabola into two equal halves , y-axis doesn't do this ! Therefore this statement is wrong!

5. It has a focus at (4, 0):

Parabola focus is at [tex]F(4,0)[/tex] on x-axis . And so, Therefore this statement is true!

1. True it has a directrix of x = -4; 2. False it opens to the left; 3. False it has a vertex at the origin; 4. True the axis of symmetry is the y-axis; 5. True it has a focus at (4, 0).

In this parabola, the given statements can be evaluated as follows:

1. Directrix : The given directrix is x = -4. The directrix of a parabola is a vertical line that is equidistant from all points on the parabola. In this case, the directrix is to the left of the origin, so it's possible that the parabola opens to the right.

2. Direction of Opening : The parabola cannot open to the left because the given directrix is to the left of the origin. Parabolas open towards their focus or away from their directrix. Since the directrix is to the left, the parabola opens to the right.

3. Vertex : The vertex is the point where the parabola changes direction. The origin (0, 0) is not the vertex in this case, as the parabola opens to the right.

4. Axis of Symmetry: The axis of symmetry is a vertical line that passes through the vertex and divides the parabola into two equal halves. Since the parabola opens to the right, its axis of symmetry is the y-axis.

5. Focus : The focus is a point inside the parabola that is equidistant to the vertex and the directrix. The focus should indeed be to the right of the vertex, and at a distance of 4 units, based on the given directrix

x = -4.

Mathematically, the equation of a parabola that opens to the right, with its vertex at the origin, is of the form:

[tex]\[x^2 = 4py\][/tex]

Given that the directrix is x = -4, the distance from the origin to the directrix is 4 units. So, the equation becomes:

[tex]\[x^2 = 16y\][/tex]

The focus is at a distance of p units from the vertex, where [tex]\(p = 4\)[/tex], so the focus is at (4, 0).

In summary, the given parabola opens to the right, has a vertex at the origin, its axis of symmetry is the y-axis, and its focus is at (4, 0), with a directrix of x = -4.

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Answer:

2y + 3x = 8

Step-by-step explanation:

Step 1:  Add 3/2x to both sides

y + 3/2x = -3/2x + 4 + 3/2x

y + 3/2x = 4

Step 2:  Multiply both sides by 2

(y + 3/2x)*2 = 4*2

2y + 3x = 8

Answer:  2y + 3x = 8

Answer:

0.155

Step-by-step explanation:

Answer:

$0.15 per ounce

Step-by-step explanation:

2.48/16 = 0.155

The coordinates of P are (12, 2).

Solution:

Given data:

[tex](x_1, y_1)= A (4, 2)[/tex]  and [tex](x_2, y_2)=B(22, 2)[/tex]

P(x, y) is the point on the line segment AB.

AP : PB = m : n = 4 : 5.

That is m = 4 and n = 5.

Section formula:

[tex]$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)[/tex]

[tex]$P(x, y)=\left(\frac{4\times 22 + 5\times 4}{4+5}, \frac{4\times 2 + 5\times 2}{4+5}\right)[/tex]

[tex]$P(x, y)=\left(\frac{88 + 20}{9}, \frac{8+10}{9}\right)[/tex]

[tex]$P(x, y)=\left(\frac{108}{9}, \frac{18}{9}\right)[/tex]

P(x, y) = (12, 2)

Hence the coordinates of P are (12, 2).

Answer:

48

Step-by-step explanation:

Answer:

b)48

Step-by-step explanation:

Answer:

x = -2 , y = 1

Step-by-step explanation:

Solve the following system:

{-2 x - y = 3 | (equation 1)

-9 x - y = 17 | (equation 2)

Swap equation 1 with equation 2:

{-(9 x) - y = 17 | (equation 1)

-(2 x) - y = 3 | (equation 2)

Subtract 2/9 × (equation 1) from equation 2:

{-(9 x) - y = 17 | (equation 1)

0 x - (7 y)/9 = -7/9 | (equation 2)

Multiply equation 2 by -9/7:

{-(9 x) - y = 17 | (equation 1)

0 x+y = 1 | (equation 2)

Add equation 2 to equation 1:

{-(9 x)+0 y = 18 | (equation 1)

0 x+y = 1 | (equation 2)

Divide equation 1 by -9:

{x+0 y = -2 | (equation 1)

0 x+y = 1 | (equation 2)

Collect results:

Answer: {x = -2 , y = 1

Answer:

C) (−2, 1)

Step-by-step explanation:

hey bro, what do you mean by this question?

do you want to convert 9.60 dollars into pounds? if so then right now the exchange rate for dollars to pounds is 0.80. So you will do this (0.80)(9.60)=7.68

If you mean pounds like how much something weighs then all you need to do is just divide 9.60 by 4 = 2.4 which means $2.4 per pound.

10

Step-by-step explanation:

first what is 10 take away 2 is 8 then 10 take away 2 is 8 + 2 equals 10 8 + 2 equals 10 so that's how I got the answer 10

Answer:

0+7-4=3

Step-by-step explanation:

They started with none, hence the 0. "Gained" typically means addition, so you add seven. "Lost" is a signal word for subtraction, so subtract zero. It comes out to 4.

Answer:

1,350 cm^2

Step-by-step explanation:

It's a cube so all faces/bases are the same.

15 × 15 = 225

225 × 6 = 1,350

Answer:

[tex]\frac{(12)}{2} +2\\6+2=8\\8[/tex]

Hope this helped

Answer:

4

Step-by-step explanation:

 n/6 + 2 when n = 12

n/6 + 2

Replace n with 12

Therefore,

n/6 + 2 = 12/6 + 2

= 2+2

=4

I hope this was helpful, please rate as brainliest

The volume of the prism = 14 ft³

Solution:

Number of cubes in the prism = 1750

Edge length of each cube (a) = [tex]\frac{1}{5}[/tex] ft

To find the volume of each cube:

Volume of each cube = a³

                                    [tex]$=\left(\frac{1}{5} \right)^3[/tex]

Volume of each cube [tex]$=\frac{1}{125} \ \text{ft}^3[/tex]

To find the volume of the prism:

Volume of the prism = Volume of each cube × Number of cubes

                                  [tex]$=\frac{1}{125} \ \text{ft}^3\times 1750[/tex]

                                  = 14 ft³

The volume of the prism = 14 ft³

Answer:

m=2/3

Step by Step Explanation:

x1,y1= 3,-6

x2,y2=3,-3

m={-3-3}           (Fraction Form)

    {-6-3}

Refine:

m={2}{3}

Answer:

Slope = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Step 1:  Identify x1, x2, y1, y2

Slope Formula:  [tex]\frac{y2-y1}{x2-x1}[/tex]

(x1, y1) -> (3, 3)

(x2, y2) -> (-6, -3)

Step 2:  Plug into the formula

Slope = [tex]\frac{-3 - 3}{-6 - 3}[/tex]

Slope = [tex]\frac{-6}{-9}[/tex]

The top negative sign and the bottom negative sign cancel to make a positive number.

Slope = [tex]\frac{-6}{-9}[/tex]

Slope = [tex]\frac{6}{9}[/tex]

The top and bottom can be simplified by a factor of 3.

Slope = [tex]\frac{6}{9}[/tex]

Slope = [tex]\frac{6/3}{9/3}[/tex]

Slope = [tex]\frac{2}{3}[/tex]

Answer:  Slope = [tex]\frac{2}{3}[/tex]

Answer:

The correct answer is B. 1 in 12.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Percentage of the U.S. population that catches the flu each season = 8%

8% = 8/100

2. Assuming everyone has equal probability of catching the flu, about what are the odds of catching the flu in a given season?

Let's review together each of the possible answers given:

A. 1 in 8  = 1/2 = 0.125 = 12.5%, this is not the percentage given.

B. 1 in 12  = 1/12 = 0.083 = 8.3%, if we round to 8%, this is the percentage given.

C. 1 in 18  = 1/18 = 0.056 = 5.6%, this is not the percentage given.

D. 1 in 80 = 1/80 = 0.0125 = 1.25%, this is not the percentage given.

The correct answer is B. 1 in 12.

Answer:

24+8 square root 3

Step-by-step explanation:

The ratio is x : x radical 3 : 2x

hypotenuse= 2x= 16

x =8

x square root 3 = 8 square root 3

16+8=24

Answer: Period: 4. Amplitude: 3

Step-by-step explanation: The period is how long it takes for one cycle of the function (one up and down). In this graph, one cycle ends at 4.

The amplitude is how far away the extremes of the graph are from the midline. This graph is a total of 6 units tall, making the amplitude 3. (I usually find total graph height and divide by 2.)

Answer:

C. $34

Step-by-step explanation:

$58 is added every 2 hours so you just subtract that from $92 since $92 is the price of 2 hours and a full tank of gas.

Answer: x=0, x²=0

Step-by-step explanation:

Answer:

x=3 and x=5/2

Step-by-step explanation:

Answer:

3/4, 75% chance

Step-by-step explanation:

you have four in total, three of which are not c, so you have a three out of four chance of NOT picking c. 3/4 as a percentage is 75%

Answer:

25%

Step-by-step explanation:

On MobyMax its 25%

Answer:

Step-by-step explanation:

B is correct.  This choice accurately describes the sample.

The Elijah have been on the soccer team for 8 years.

Step-by-step explanation:

Let,

Given that,

The boys have been on the soccer team for 10 years.

Number of years of Deaundre + Number of years of Eliijah = 10 years.

x + (5x-2) = 10

Keep x terms on one side and constants on another side to solve for x value :

6x = 10+2

6x = 12

x = 12/6

x = 2

The Deaundre have been on the soccer team for 2 years.

Substitute x=2 in (5x-2) to find the number of years of Elijah,

5(2)-2 = 8 years.

Therefore, the Elijah have been on the soccer team for 8 years.

Answer:

25.5

Step-by-step explanation:

[tex]A_{t} = \frac{1}{2} * (6 + 3) * (5 + 2) = 31.5\\\\A_{r} = 2 * 3 = 6\\\\A = A_{t} - A_{r} = 31.5 - 6 = 25.5[/tex]

Final answer:

The point (1, 10) satisfies both given equations when substituting x with 1 and y with 10, therefore it is a solution to the system of equations.

Explanation:

To determine if the point (1, 10) is a solution to the given system of equations, we must substitute x with 1 and y with 10 into each equation and see if the equations hold true.

For the first equation y = 9x + 1, substituting gives us:

10 = 9(1) + 1
10 = 9 + 1
10 = 10

This is true, so (1, 10) satisfies the first equation.

For the second equation y = x + 9, substituting gives us:

10 = 1 + 9
10 = 10

This is also true, so (1, 10) satisfies the second equation as well.

Since (1, 10) satisfies both equations, it is indeed a solution to the system of equations.

Let's determine if the point (1, 10) is a solution to the given system of equations by substituting the x and y values from the point into both equations.
The system of equations is:
1. \( y = 9x + 1 \)
2. \( y = x + 9 \)
We are given the point (1, 10), where x = 1 and y = 10.
We'll substitute these values into each equation to check for equality.
First, let's substitute x = 1 and y = 10 into the first equation:
\( y = 9x + 1 \) becomes \( 10 = 9(1) + 1 \), simplifying to \( 10 = 9 + 1 \), which further simplifies to \( 10 = 10 \).
The first equation is satisfied with x = 1 and y = 10.
Next, we'll substitute x = 1 and y = 10 into the second equation:
\( y = x + 9 \) becomes \( 10 = 1 + 9 \), simplifying to \( 10 = 10 \).
The second equation is also satisfied with x = 1 and y = 10.
Since the point (1, 10) satisfies both equations, we can conclude that (1, 10) is indeed a solution to the given system of equations.

For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0}):[/tex]It is a point through which the line passes

m: It is the slope of the line

According to the graph we have that the line goes through the following points:

[tex](x_ {1}, y_ {1}) :( 4,2)\\(x_ {2}, y_ {2}): (- 2, -2)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-2} {- 2-4} = \frac {-4} {- 6} = \frac {2} {3}[/tex]

We choose a point:

[tex](x_ {0}, y_ {0}): (-2, -2)[/tex]

The equation of the line is:

[tex]y - (- 2) = \frac {2} {3} (x - (- 2))\\y + 2 = \frac {2} {3} (x + 2)[/tex]

ANswer:

[tex]y + 2 = \frac {2} {3} (x + 2)[/tex]

Option A

The wall is 18.79 feet high from the ground.

Data;

To solve this problem, we need to use trigonometric ratio SOHCAHTOA in which we can find the missing side.

if we draw an illustration of this question, we would get

Using the sine angle ratio,

[tex]sin\theta=\frac{opposite}{hypothenuse}\\sin71=\frac{x}{20}\\ x=20sin71\\x=18.79ft[/tex]

The wall is 18.79ft high

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To calculate the height the ladder reaches on the wall, we use sine function and find it to be approximately 19 feet.

To find out how high up the wall the ladder touches the building when a 20-foot ladder forms an angle of 71° with the level ground, we can use trigonometry. Specifically, the sine function relates the opposite side to the hypotenuse in a right triangle. The ladder represents the hypotenuse, and the height reached on the wall is the opposite side.

Using the formula:

sin(angle) = opposite/hypotenuse

For this problem:
sin(71°) = height / 20 feet

Now we solve for height:
height = 20 feet × sin(71°)

We can calculate this using a calculator:
height ≈ 20 feet × 0.945
height ≈ 18.9 feet

To the nearest foot, the ladder reaches approximately 19 feet up the wall.

Answer:

1800ft tall

Step-by-step explanation:

The question is about calculating a tip which is 25% of a meal cost of $12.00. The tip is calculated by multiplying the total cost of the meal by the tip percentage, converted into decimal form. The answer is $3.00.

Percentage is a mathematical concept used to express a portion of a whole as a fraction of 100. It is a versatile tool in various fields, including finance, statistics, and everyday calculations. To calculate a percentage, you divide a part by the whole and then multiply by 100. Percentages are commonly used to represent proportions, express changes, and compare values, making them vital for analyzing data, understanding discounts, and determining growth rates. In essence, percentages simplify the representation of relative quantities and are fundamental in both practical and academic mathematics.

The subject of the question is Mathematics, specifically Percentage. The student is being asked to calculate 25% of $12.00, which is the cost of Eliza's meal. To calculate the tip, multiply the total meal cost by the percentage of the tip. Here's how we can do it:

So the tip Eliza left for the waiter was $3.00.

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Step-by-step explanation:

volume of a cone is given by

[tex] \frac{\pi {r}^{2}h }{3} [/tex]

1st cone,

B= 25π cm²

πr²=25π

r²=25

r=5

Here, volume = π(5)²×3.5/3

=29.1π cm³

2nd cone,

r=3cm

Here, volume = π(3)²×6.5/3

= 19.5π cm³

3rd cone,

r= 4cm

Volume = π(4)²×4.5/3

=24π cm³

4th cone,

B=4π cm²

r²=4

r=2

volume = π(2)²×7.5/3

= 10π cm³

So, the third cone has vol 24π cm³