y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.

The solutions to the quadratic equation (x - 4)² = 36 are

x = 10 and x = -2.

We have,

To solve the quadratic equation (x - 4)² = 36, we can start by taking the square root of both sides of the equation.

However, we need to consider both the positive and negative square roots because squaring a number eliminates the sign.

Taking the square root of both sides, we have:

√[(x - 4)²] = √36

Simplifying further:

|x - 4| = 6

Now, we can set up two separate equations to consider both the positive and negative square roots:

x - 4 = 6 or x - 4 = -6

Solving the first equation:

x - 4 = 6

Adding 4 to both sides:

x = 10

Solving the second equation:

x - 4 = -6

Adding 4 to both sides:

x = -2

Therefore,

The solutions to the quadratic equation (x - 4)² = 36 are

x = 10 and x = -2.

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Answer:

it's c

Step-by-step explanation:

because for .087  you move the decimal 3 times

                  so the decimal is going to end up 08.7

                                                                                here

We can write 0.87 as 87 / 100.

Option D is the correct answer

Given,

0.087

We have to see the other form it can be written.

The numbers which have a decimal point.

Example: 23.4

It can be written in fractions aswell.

23.4 = 234/10

We have,

0.87

Since there are two numbers after the decimal point we can write it as:

= 0.87
= 087 / 100

= 87 / 100

Thus we can write 0.87 as 87 / 100.

Option D is the correct answer.

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Answer: y =  9, z = 8

Step-by-step explanation:

Here, the given equations are,

150x + 80y + 12z = 2,466 ---------(1)

380x + 95y + 48z = 5,419 ---------(2)

210x + 130y + 60z = 3,960 --------(3)

4 × equation (1) - Equation (2),

220x + 225y = 4,445  ------------(4)

5 × equation (1) - equation (3),

540x + 270y = 8,370

⇒ 270 y = 8370 - 540 x

⇒ y = 31 - 2 x

Substituting the value in equation (4),

220 x + 225 ( 31 - 2 x ) = 4445

220 x + 6975 - 450 x = 4445

- 230 x = - 2530

x = 11

By putting this value in equation (5),

we get, y = 31 - 22

y = 9

By putting the value of x and y in equation (1),

1650 + 720 + 12 z = 2466

2370 + 12 z = 2466

12 z = 96

z = 8

Answer:

Y=9

Z=8

For the next one, the solution can be expressed as 11,9, and 8

Step-by-step explanation:

Just did it on edg!

Answer:3/4 i think

Step-by-step explanation:

The fruit salad requires 32 cups of grapes.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Bradley is making fruit salad for each bowl of fruit salad he needs 3/4 cup of grapes.

He makes 24 bowls of fruit salad.

Number of cups of grapes = Total number of bowls ÷ Number of cups of grapes in each bowl

= 24 ÷ 3/4

= 24 × 4/3

= 32

Therefore, the fruit salad requires 32 cups of grapes.

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Answer:

s=3

Step-by-step explanation:

The number that corresponds to the prime factorization '2 to the 3rd power times 3 times 5 to the 2nd power' is 600. Calculate this by resolving each component then multiply the results.

The question revolves around finding the result of a number given its prime factorization, specifically when the prime factorization is '2 to the 3rd power times 3 times 5 to the 2nd power'. Let's start by resolving each of those components:

So, with these resolved components, we only have to multiply the results, which is 8 (from 2 cubed) times 3 times 25 (from 5 squared).

This would give us the answer: 8 * 3 * 25 = 600.

Therefore, the number that corresponds to the prime factorization '2 to the 3rd power times 3 times 5 to the 2nd power' is 600.

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20 is 25% of 80. so the number is 80.

percentage, a relative value indicating hundredth parts of any quantity.

We need to find 20 is 25% of what number

Let x be the number which we have to find.

Convert 25% to decimal number.

25/100=0.25

Now multiply 0.25 with x which results 20

0.25x=20

Divide both sides by 0.25

x=20/0.25

x=80

Hence, 20 is 25% of 80. So 80 is the required number.

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Answer: The graph is represented by the inequality y>3x+2

Step-by-step explanation:

Linear inequality is like linear equation just we have inequality signs (<,>,≤,≥) instead of equal sign(=).

In the given question we have the linear inequality represented by graph

We can see the line in the graph passing through the point (-3,-7)

Let's check which option satisfy the point

1) y<3x+2 for this the line should be y=3x+2

⇒ -7=3(-3)+2

⇒-7= -9+2⇒-7=-7,which is true.

2) y>3x+2 which similar as first.

3) y<x+2 for this the line should be y=x+2

⇒ -7= -3+2

⇒-7=-1 which is not true.

4) y > x + 2 is similar to third.

Option 3) and 4) cannot be the required linear inequality.

Now from 1) and 2) , 2) should be the required linear inequality as the graph is shaded above the line and that must be for y (>) greater than inequality. [ for y (<) less than inequality the graph must be shaded below the line]

Therefore, 2)  y > 3x + 2 is the required linear inequality which is represented by the graph.

The linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex] .

Further explanation:

It is given that a line passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex]  as shown below in Figure 1.

The slope of a line passes through points [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left( {{x_2},{y_2}}\right)[/tex]is calculated as follows:

[tex]m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}[/tex]                    ........(1)

Here, the slope of a line is denoted as [tex]m[/tex] and points are [tex]\left({{x_1},{y_1}}\right)[/tex] and [tex]\left({{x_2},{y_2}}\right)[/tex].

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] , [tex]2[/tex]  for [tex]{y_1}[/tex] , [tex]-3[/tex]  for [tex]{x_2}[/tex]  and [tex]-7[/tex]  for [tex]{y_2}[/tex]  in equation (1) to obtain the slope of a line that passes through points [tex]\left({0,2}\right)[/tex] and [tex]\left({-3,-7}\right)[/tex] .

[tex]\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}[/tex]

Therefore, the slope is [tex]3[/tex] .

The point-slope form of the equation of a line with slope [tex]m[/tex]  passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:

[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex]                                 .......(2)

Substitute [tex]0[/tex]  for [tex]{x_1}[/tex] ,  [tex]2[/tex] for [tex]{y_1}[/tex]  and [tex]3[/tex]  for [tex]m[/tex]  in equation (2) to obtain the equation of line.

[tex]\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}[/tex]

Therefore, the value of [tex]y[/tex]  is [tex]3x+2[/tex] .

Since the shaded part in Figure 1 is above the equation of line [tex]y=3x+2[/tex], therefore, greater than sign is used instead of is equal to.

Thus, the linear inequality is [tex]y>3x+2[/tex]  as shown below in Figure 2.

Now, the four options are given below.

[tex]\begin{aligned}{\text{OPTION A}}\to &y<3x+2\hfill\\{\text{OPTION B}}\to &y>3x+2\hfill\\{\text{OPTION C}}\to &y<x+2\hfill\\{\text{OPTION D}}\to &y>x+2\hfill\\\end{aligned}[/tex]

Since OPTION B matches the obtained equation that is [tex]y>3x+2[/tex] .

Thus, the linear equality represented by the graph is [tex]\boxed{{\mathbf{y>3x+2}}}[/tex]  and it matches with [tex]\boxed{{\mathbf{OPTION B}}}[/tex].

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Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality

the answer is 68

if you like at the other persons answer, they explain

but all i know is that its 68

thxs: to the person that answered this question first

Answer:

Please see the attachment for graph.

Step-by-step explanation:

We are a given a equation and need to graph it.

It is square root function. We make table of x and y and then plot the points on graph and join the points.

We will take some random values of x and then find the value of y corresponding to the value of x.

For x=1, Put x=1 into equation

[tex]y=-4\sqrt{1}=-4[/tex]

For x=4, Put x=4 into equation

[tex]y=-4\sqrt{4}=-8[/tex]

For x=9, Put x=9 into equation

[tex]y=-4\sqrt{9}=-12[/tex]

Table of x and y

     x          y

     1         -4

    4         -8

    9         -12

Now we plot the points on graph and join the points.

Please see the attachment for graph.

Final answer:

Catrina used 25 tiles to create a square, which means she made 5 rows with 5 tiles in each row, as the square root of 25 is 5.

Explanation:

Catrina used 25 square green tiles to form a square in the middle of her floor.

To find out how many rows she made and how many tiles she put in each row, we need to think about the properties of a square.

A square has equal sides, so the number of tiles in each row must be the same as the number of rows. Since the total number of tiles is a perfect square (25), we find the square root of 25 to determine the size of each side of the square.

The square root of 25 is 5, so Catrina created 5 rows with 5 tiles in each row. This forms a perfectly square area on her floor with green tiles.

If 30 cents out of every 1 dollar go to taxes, the remaining 70 cents is the net income. Therefore, the ratio of taxes to net income is 3:7.

The question asks for the ratio of taxes to net income if 30 cents out of every 1 dollar go to taxes. This question is asking for a mathematical comparison between the amount of money that goes to taxes and the remaining amount of money, which is the net income.

If 30 cents go to taxes out of 1 dollar, that means 70 cents (or $0.70) is the net income because 1 dollar minus 30 cents equals 70 cents. To arrive at the ratio, we compare the amount that goes into taxes to the net income. This would be 0.30 (taxes) to 0.70 (net income).

When we express this as a ratio in simplest form, we do not usually use decimals. Instead, we can convert the decimal into a whole number. Think of the 0.30 and the 0.70 as 30 and 70. The greatest common divisor of 30 and 70 is 10. If we divide both numbers by 10, we get 3 and 7. So, the ratio of taxes to net income is 3:7. Thus, the correct option is C. 3 : 7.

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Answer:

Rita made a sign error.

Step-by-step explanation:

Let x be the selling price of each necklace.

We are told that the materials to make each necklace cost $2.75.

Since profit is the difference between selling price and cost.

[tex]\text{Profit}=\text{Selling price- Cost}[/tex]  

So profit of Rita from selling one necklace will be:

[tex]\text{Profit of Rita from 1 necklace}=x-2.75[/tex]

To find the profit of Rita from selling 8 necklace we will multiply 8 by profit of 1 necklace.

[tex]\text{Profit of Rita from 8 necklaces}=8(x-2.75)[/tex]

As Rita wants to make a total profit of $78 from selling 8 necklaces, so we will substitute 78 as profit of 8 necklaces.

[tex]78=8(x-2.75)[/tex]  

Upon comparing our equation with the given equation we can see that Rita made a sign error as she added the cost with the selling price instead of subtracting the cost from selling price.

Let us find the selling price.

[tex]78=8x-22[/tex]  

[tex]78+22=8x[/tex]

[tex]100=8x[/tex]  

[tex]\frac{100}{8}=x[/tex]

[tex]12.5=x[/tex]  

We can see that the selling price of each necklace will be 12.5, therefore, Rita made a sign error.

Answer: 84yd

Step-by-step explanation:

Vcylinder=πr2h

=π(2)2(6)

=24π

≈24(3.14)

≈75.36 yd

_____________________

The height of the cone is the height of the figure minus the height of the cylinder:

8 yd−6 yd=2 yd

Vcone=13πr2h

=13π(2)22

=223π

≈223(3.14)

≈8.37 yd3

Add the volumes.

75.36 yd3+8.37 yd3=83.73 yd3

To the nearest cubic yard, the volume is 84 yd3.

Final answer:

Ana's conjecture that Raul lost 2/5 of his teeth is correct, as it simplifies from Raul's stated 4/10 after losing 8 out of the total 20 baby teeth.

Explanation:

Raul has said he lost 4/10 of his baby teeth, while Ana said Raul lost 2/5 of his teeth. To figure out which conjecture is true, we must consider Raul's claim first. Since a human usually has 20 baby teeth and Raul has lost 8 of those, we calculate the fraction of teeth he has lost by dividing the number of lost teeth by the total number of baby teeth: 8 ÷ 20 = 2/5. This simplifies to the fraction 2/5, which means Ana's conjecture is indeed the correct one. Both fractions actually represent the same value, because when you simplify 4/10 by dividing the numerator and the denominator by 2, you get 2/5.

Answer: For the second part it is B on edgu

Step-by-step explanation:

The solution is P ( 4 , 3 )

The vertex of the function is given by the coordinates P ( 4 , 3 )

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the equation be represented as A

Now , the parabola is

f ( x ) = | x − 4 | + 3   be equation (1)

Now ,

The vertex of f ( x ) = | x | is located at the origin, (0,0)

So , in the form f ( x ) = a | x - h | + k, the h-value translates the graph left/right and the k-value translates the graph up/down

And ,

In the function, f(x) = | x - 4 ) | + 3 , the h-value is 4, and the k-value is 3

So , the vertex of the function moves from the origin, (0,0) and translates 4 units right and 3 units up.

Therefore , the vertex is located at P ( 4,3 )

Hence , the vertex of equation is at P ( 4 , 3 )

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