PLEASE HELP IM SO STUCK

Part A

[tex]4x^2 -7x-15=0\\\\(4x+5)(x-3)=0\\\\x=-\frac{5}{4}, 3[/tex]

So, the x-intercepts are [tex]\boxed{\left(-\frac{5}{4}, 0 \right), (3,0)}[/tex]

Part B

The vertex will be a minimum because the coefficient of [tex]x^2[/tex] is positive.

The x-coordinate of the vertex is [tex]x=-\frac{-7}{2(4)}=\frac{7}{8}[/tex]

Substituting this back into the function, we get [tex]f\left(\frac{7}{8} \right)=4\left(\frac{7}{8} \right)^2 -7\left(\frac{7}{8} \right)^2 -15=-\frac{289}{16}[/tex]

So, the coordinates of the vertex are [tex]\boxed{\left(\frac{7}{8}, -\frac{289}{16} \right)}[/tex]

Part C

Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.

The graph is shown in the attached image.

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:

f(x) = a · x² + b · x + c

f(x) = a · [x² + (b / a) · x + (c / a)]

f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]

f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²

If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.

The y-intercept is found by evaluating the quadratic equation at x = 0:

f(0) = a · 0² + b · 0 + c

f(0) = c

And the zeros are determined by the quadratic formula:

x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)

The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).

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u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1). This can be obtained by simplifying the equation and taking w to one side of the equation with other constants.

Simplifying an equation can be done by using the following steps:

Here it is given that the equation is,

⇒ u - 5= - 4(w - 1)

We have to find an equation in which w is taken to one side of the equation with other constants.

First by adding both side of the equation with 5 we get,

⇒ u - 5 + 5 = - 4(w - 1) + 5

By opening the bracket we get,

⇒ u = - 4w + 4 + 5

Finally by adding the constants we get,

⇒ u = - 4w + 9

Hence u = - 4w + 9 is the rearranged equation so that w is the independent variable given that the equation is u - 5= - 4(w - 1).

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Answer:

22°

Step-by-step explanation:

Since IJ is a diameter, arc LJ measures 68 degrees.

Therefore, the measure of angle JKL is (112-68)/2=22°

Answer:

x = 99°

y = 91°

Step-by-step explanation:

For Cyclic quadrilateral, the sum of the opposite angles = 180°

Let's find x :-

x + 81° = 180°

x = 180 - 81

x = 99°

Let's find y :-

y + 89° = 180°

y = 180 - 89

y = 91°

Hope this helps you !

The coordinates of the missing points G. and H are G(a, y) and H(a,0) respectively

A right angled triangle is a triangle that has 3 sides and angle with one of its angles to be 90 degrees.

From the given triangle, the measure of the x-coordinate point of G and H will be equal.

Since the line GH intersects the x-axis and the point where the line intersects the x-axis is where y = 0, hence the coordinate H is (a, 0) and the measure of G is (a, +y)

The y-value of G can be any positive value on the y-axis

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Answer:

put four balls in each been

Step-by-step explanation:

Answer:

it can be use in equation

An irrational number is a number that cannot be expressed as a fraction for any integers and. . Irrational numbers have decimal expansions that neither terminate nor become periodic.

The following numbers are rounded up as follows:

8.6134

5.5218

Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.

Thousandth, hundredth and tenth are used after the decimal point.

8.6134

5.5218

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Answer:

109x

Step-by-step explanation:

We know that there are 109 students in the fourth grade, who each have x cupcakes. In order to find the total amount of cupcakes, we could add all of the cupcakes together to get:

x + x + x + x + .... x

109 times because there are 109 students.

This can be simplified to become 109x.

Answer: Y = 4x + 2

(It would be either the third or fourth choice since they are the same, one of them must be mistaken)

Step-by-step explanation:

Given information

(x₁, y₁) = (1, 6)

(x₂, y₂) = (0, 2)

Find the slope through the formula

[tex]Slope~=~\frac{y_2~-~y_1}{x_2~-~x_1}[/tex]

[tex]\Large Slope~=~\frac{2~-~6}{0~-~1}[/tex]

[tex]\Large Slope~=~\frac{-4}{-1}[/tex]

[tex]\Large Slope~=~4[/tex]

Substitute values into the linear form

Equation: y = mx + b

Point (0, 2)

y = mx + b

(2) = (4) (0) + b

2 = 0 + b

b = 2 - 0

b = 2

Therefore, the equation is [tex]\Large\boxed{y=4x+2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

y = 4x+2

Step-by-step explanation:

The first step is to find the slope

m = ( y2-y1)/(x2-x1)

m = ( 2-6)/(0-1)

    = -4/-1

   = 4

The slope intercept form of the equation is

y = mx+b  where m is the slope and b is the y intercept

y = 4x+b

The y intercept is where x is equal to 0

The y intercept is 2

y = 4x+2

Answer:

A) the fraction of the week that Jamaar spent in this garden.

Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

volume of pyramid = 1/3(5.2)h cm3

Prism is a three dimensional figure. A prism is a 3-dimensional shape with two identical shapes (bases) facing each other.

we know that,

The volume of the pyramid is equal to

volume = (1/3) × base area × height

we have height = h cm

area of base = 5.2 cm^2

substitute in the formula

                       v = 1/3 × 5.2 × h

                        volume = 1.73h cm^3

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The component form of the vector that translates the top triangle to the bottom triangle is (3, -5). This is further explained below.

Generally, a number with both direction and magnitude, especially when used to map out where one point in space is in relation to another.

In conclusion, The vector that converts the top triangle to the bottom triangle has the following component form: (3, -5).

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The total cost of the glass for your window now  $174.8

The complete question is added as an attachment

From the attached figure, we have the following parameters:

The area of region 1 is calculated using:

Region 1 = Area of square - Area of circle B

This is calculated as

Region 1 = L^2 - π(d/2)^2

So, we have:

Region 1 = 24^2 - 3.14 * (20/2)^2

Evaluate the quotient

Region 1 = 24^2 - 3.14 * 10^2

Evaluate the exponent

Region 1 = 576 - 3.14 * 100

Evaluate the product

Region 1 = 576 - 314

Evaluate the difference

Region 1 = 262

The cost per square inch of this region is $0.10.

So, we have:

Total cost of region 1 = 262 * $0.10

Total cost of region 1 = $26.10

The area of region 2 is calculated using:

Region 2 = Area of circle B - Area of circle A

This is calculated as

Region 2 = π(D/2)^2 - π(d/2)^2

So, we have:

Region 2 = 3.14 * (20/2)^2 - 3.14 * (18/2)^2

Evaluate the quotient

Region 2 = 3.14 * 10^2 - 3.14 * 9^2

Evaluate the exponent

Region 2 = 3.14 * 100 - 3.14 * 81

Evaluate the product

Region 2 = 314 - 254.34

Evaluate the difference

Region 2 =  $59.66

The cost per square inch of this region is $0.15.

So, we have:

Total cost of region 2 = 59.66 * $0.15

Total cost of region 2 = $8.949

The circle B is divided into sectors.

And the angles of the sectors are 90 and 270 degrees

The area of each sector is

Area = ∅/360 * π(d/2)^2

So, we have:

Circle B = ∅/360 * π(d/2)^2 + ⊕/360 * π(d/2)^2

So, we have:

Circle B = 90/360 * 3.14 * (18/2)^2 + 270/360 * 3.14 * (18/2)^2

Evaluate the quotient

Circle B = 0.25 * 3.14 * 9^2 + 0.75 * 3.14 * 9^2

Evaluate the exponent

Circle B = 0.25 * 3.14 * 81 + 0.75 * 3.14 * 81

Evaluate the product

Circle B = 63.585 + 190.755

The cost per square inch of this region is $0.80 for 1 sector and $0.20 for the rest

So, we have:

Total cost of circle B = 63.585 * 0.80 + 190.755 * 0.20

Total cost of circle B = 89.019

Add the total costs

Total cost of the glass for your window = Region 1 + Region 2 + Circle B

Total cost of the glass for your window = $26.10 + $59.66 + $89.019

Evaluate the sum

Total cost of the glass for your window = $174.779

Approximate

Total cost of the glass for your window = $174.8

Hence, the total cost of the glass for your window now  $174.8

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Answer:

the number is 2

Step-by-step explanation:

5x = x + 8

5x - x = 8

4x = 8

x = 8/4

x = 2

Answer:

D

Step-by-step explanation:

1=5 ( being corresonding angle)

Answer:

[tex] {x}^{x} (1 + log(x)) [/tex]

I hope this helps you.

The midpoint of PQ is (1, -0.5)

The coordinates of the point 2/3 of the way from p to q are (-0.2, 0.4)

What is the midpoint of a line segment?

the midpoint is the middle point of a line segment. It is equidistant from both endpoints.

The midpoint of PQ

To calculate this, we use the midpoint formula;

(x,y) = {(x1 + x2)/2 , (y1 + y2)/2}

From the question; (x1,y1) = (-5,4) and (x2,y2) = (7,-5)

So (x,y) = (-5+7)/2 , (4-5)/2 = 2/2, -1/2 = (1,-0.5)

The coordinates of the midpoint of PQ are (1,-0.5)

What is the internal division of the line segment?

we will use here the internal division formula of the section formula;

Mathematically the coordinates can be calculated using the formula;

(x,y) = (mx2 + nx1)/m+ n , (my2 + ny1)/m + n

in this case, m = 2 and n = 3

(x1,y1) = (-5,4)

(x2,y2) = (7,-5)

So substituting these values, we have;

(x,y) = (2(7)+ 3(-5))/(2+3) , 2(-5) + 3(4)/(2+3)

(x,y) = (14 -15)/5 , (-10 + 12)/5

= (-1/5, 2/5) = (-0.2, 0.4)

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Answer: 1.71, 1 3/4, 16/9, pie

Step-by-step explanation: We convert all the numbers to improper fractions. 1.71 = 171/100. 1 3/4 = 175/100 because 3/4 is 0.75. pi is 3.14... which is larger than all of the other numbers. So, pi is the largest. For 16/9, we can just divide to find the solution. Once you divide, you will notice that the answer is 1.77777777... This means that it is larger than 1.71 and 1.75 so 16/9 is the second largest. 1.71 is smaller than 1.75 so the order is 1.71, 1 3/4, pie, 16/9

Step-by-step explanation:

I think the above picture should help

Answer:

f(-4)= 3

f(3) = 4

Step-by-step explanation:

y= f(x)

which means y is a function of x

or, in simpler words what is the value of y w.r.t to x

On obseving the graph carefully, you'll see the for the x= -4 the value of y is 3

similarly, for x= 3 , y - coordinate is 4

At 22nd percentile in the distribution of ages of homeless Floridians, an 18 year old would be considered.

Given that 78% of the ages are greater than or equal to 18 years. Hence.

18 years will be (100 - 78)th percentile

i.e. 22nd percentile.

Historically, policymakers and practitioners at every level of government have focused special attention on specific subpopulations.

Decision-makers are often concerned about children and young people due to their vulnerability. People in families with children make up 30 percent of the homeless population. Unaccompanied youth (under age 25) account for six percent of the larger group.

Finally, due to their service to our country, veterans are often analyzed separately from the larger group. They represent only six percent of people experiencing homelessness.

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Answer: x < -2

Step-by-step explanation:

[tex]\frac{1}{2} x-7 < -8[/tex]

First add 7 to both sides

[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]

[tex]\frac{1}{2} x < -1[/tex]

Now multiply by 2 to cancel out 1/2 and leave you with x

[tex]2*\frac{1}{2} x < -1(2)[/tex]

[tex]x < -2[/tex]

Answer:

assuming it's a perfect world and that the fish lives in a 1 cubic meter fish tank 1*1.4422 will increase the volume my a factor of 3