2) What is the slope of the line from the following table? (Please show your work)

The solution to the system of equations y = x − 5 and y = 5x − 17 is x = 3 and y = -2

The system of equations is given as

y = x − 5

y = 5x − 17

Substitute y = x − 5 in the equation y = 5x − 17

So, we have

x - 5 = 5x − 17

Evaluate the like terms

4x = 12

Divide both sides by 4

x = 3

Substitute x = 3 in y = x − 5

y = 3 − 5

So, we have

y = -2

Hence, the solution is x = 3 and y = -2

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Using the velocity, the rocket reaches its maximum height at 3.25 seconds.

In the given question we have to find the maximum height at the rocket reaches.

From the question; a toy rocket is shot vertically into the air from a launching pad 5 feet above the ground with an initial velocity of 104 feet per second.

The height h in feet of the rocket above the ground at t seconds after launch is given by the function h(t)= -16t^2+104t+5.

As we know that at the maximum height, the velocity will be zero.

So the given function of the heigth is

h(t)= -16t^2+104t+5

Velocity(v) = dh(t)/dt = -32t+104

As the maximum height v=0

-32t+104 = 0

Subtract 104 on both side, we get

-32t= -104

Divide by -32 on both side

t= 3.25 seconds

Hence, the rocket reaches its maximum height at 3.25 seconds.

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The value of missing number is 8.

Integers come in three types:

Given:

6(-?)+1=-47

let the unknown value be x.

6(-x ) + 1= -47

Now, Subtract 1 from both side

-6x + 1 - 1= -47 - 1

-6x = -48

x= -48/(-6)

x = 8

Hence, -6(8) + 1 = -47.

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Answer:

Step-by-step explanation:

To find the slope, subtract the y values, and divide it by subtracting the x values. The order matters!

(9-6)/(1-6)=-3/5

Option A is the correct choice (0.04)

The incidence rate of disease x among persons exposed to factor a is 0.04

The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.

Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.

The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.

Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04

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COMPLETE QUESTION:

6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880

Select one:

a. 0.04

b. 0.19

c. 0.25

d. 4.00

e. 5.17

The radius of each of the smaller balls is R = 2r.

You can use a tape measure, for instance, to directly measure the distance around the sphere's widest point. The radius of this circle, which serves as the sphere's circumference, is one. A circle's circumference is computed as 2 x x radius. Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.

Given,

A steel ball is melted down to make eight smaller identical balls. If the radius of the original steel ball was 20 cm:

Let the spherical ball's radius be R.

And with r being the radius of 8 similar balls,

According to the inquiry,

Volume of 8 similar balls = the volume of a larger sphere

3/4πR³ = 8 × 3/4πr³

R³ = 8r³

R = 2r

The radius of each of the smaller balls is R = 2r.

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Answer:

t =2.45s

Step-by-step explanation:

H=-16t2+96t

then, -16t2= -96t

divide both sides by 16

-16t2/16 = -96t/16

-t2 = -6

t2=6

t=√6

t=2.45

The largest area of the rectangle is 6502.5 square feet.

Given that,

Using fence parallel to one of the rectangle's sides, a cattle rancher wants to surround a rectangular area and divide it into four pens (see the figure below). To finish the task, 510 feet of fencing are available.

We have to find what could the four pens' combined total area be.

We know that,

The rectangular shape's length is l and its width is b.

Total fencing= 2l + 5b=510 feet

2l +5b =510 feet

We can write as,

l=1/2(510-5b)

Total area of the rectangle is length into breath

A(b) = l × b

A(b) = 1/2(510-5b)×b

A(b)= 1/2(510b -5b²)

For maximum area

A'(b)=0

1/2(510b -5(2b))=0

b=51

We get l as

l = 1/2(510-5b)

l = 1/2(510-5(51))

l = 127.5

Total area of the rectangle is 127.5 × 51

Total area of the rectangle is 6502.5 square feet.

Therefore, The largest area of the rectangle is 6502.5 square feet.

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Answer:

XY = 12.4 cm

Step-by-step explanation:

a² + b² = c²

(4 cm)² + (XY)² = (13 cm)²

16 cm² + XY² = 169 cm²

XY² = 153 cm²

XY = √(153 cm²)

XY = 12.4 cm

Answer:7

Step-by-step explanation:

yabba dabba doo

With the help of angles we can say that ∠HJI=∠FJG.

Acc to our question-

Hence, ∠HJI≅∠FJG are equal and congruent.

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The price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

Let the price of 1 kilogram of jelly bean cost be x

and the price of 1 kilograms of gummy worms be y

Dean bought 2 kilograms of jelly beans and 3 kilograms of gummy worms

for $38

2x + 3y = 38......equation 1

Sue bought 3 kilograms of jelly beans and 3 kilograms of gummy worms

for $45

3x + 3y = 45........equation 2

Subtracting equation 2 from equation 1

2x + 3y - (3x + 3y) = 38 - 45

2x - 3x + 3y - 3y = -7

-x = -7

x = 7

2(7) + 3y = 38

14 + 3y = 38

3y = 24

y = 8

Therefore, the price of one kilogram of jelly bean and gummy worms is $7 and $8 respectively.

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An applicant needs 84.04 minutes to finish the test in order for 97 percent of them to pass.

An aptitude test is required of job candidates. Let's assume that the test's completion time has a mean of 69 minutes and a standard deviation of 8 minutes.

To get how much time an applicant should be given so that 97 percent of them will be able to complete the test.

Mean (μ) = 69

standard deviation (σ) =8

Hence, due to population standard deviation (σ) is known to use the normal distribution.

x_ Norm (μ,σ)

x_ Norm (69,8)

Therefore, x_ random variable that represents the time of applicant;

P(X<x) = 0.97

Corresponding to the left tail area of 0.97 lies in the z-table of z row of 1.8 and column 0.08.

P(z < 1.88) = 0.97

z < 1.88

(X - μ)/σ < 1.88

X < 1.88 (8) + 69

X < 84.04

The time taken by an applicant so that 97 percent of them will be able to complete the test is 84.04 minutes.

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Answer:

Step-by-step explanation:

663.98

Answer: 663.98

Step-by-step explanation:

(8.42*109)=917.78

(2.35*108)=253.8

917.78-253.8=663.98

That aint no question

Answer:

Step-by-step explanation:

from the area we find the side by taking the square root, having found the side we multiply it by 4 and we have the perimeter, we can solve it with a simple expression that summarizes what I wrote

4√81 =

4 × 9 =

36 mm

Answer: No

Step-by-step explanation: You want to find the unit rate for each bagel. 6/3 is 2 dollars, so each bagel is going to cost 2 dollars. If your getting 24 bagels for 9 dollars, 24/9 is 2 2/3 dollars for each bagel. 2 ≠ 2 2/3 so therefore, they're not the same.

Answer:

143.75

Step-by-step explanation:

11/4+110+15+16 1/2=143.75

The other leg has its length to be 11.49 units

To calculate the length of the other leg distance, we make use of the Pythagoras theorem

Mathematically, this theorem is represented by:

w² = y² + z²

Such that x = hypotenuse, y = leg and  z = other leg

From the question, we have the following parameters

w = 14, y = 8 and z = the other leg

Substituting these values in w² = y² + z²

14² = 8² + y²

Evaluate the exponents

196 = 64 + y²

Evaluate the like terms

y² = 132

Take the square roots of both sides

y = 11.49

Hence, the length of the other leg is 11.49 units

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Answer: 11 units

Step-by-step explanation: i took the test and got it right

The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest.

To begin, change R from a percentage to a decimal, using the formula:

r = R/100 r = 14/100

r = 0.14 rate per year;

Next, find A by solving

A = P(1 + r/n)nt A = 12,000.00(1 + 0.14/12)(12). (5)

A = 12,000.00(1 + 0.011666666666667)(60) (60)

A = $24,067.32

Summary: The total amount accrued, principal plus interest, with compound interest on a principal of $12,000.00 at a rate of 14% per year compounded 12 times per year over 5 years is $24,067.32.

The amount of the initial loan, or principal, is multiplied by one plus the annual interest rate raised to the number of compound periods minus one to determine compound interest. You will then be left with the loan balance plus compound interest.

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The positive slope is tilted towards the right on a coordinate plane and the negative slope is tilted towards the left on the coordinate plane.

When two variables have a positive slope, it means that they are positively correlated; that is, when x rises, y rises as well, and when x falls, y falls as well. A line on a line graph that has a positive slope rises as the line advances from left to right.

A line that slopes downward from left to right is said to have a negative slope. In other words, the rise-to-run ratio of the line is negative.

The graph of the two real-life situations is attached with the answer below. In which the equation y = 4x means that the value of y is increasing by 4. Similarly, the equation for negative slope is y = -4x means that the value of y is increasing in opposite direction by factor 4.

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The function has a maximum value of 30 at x = 3.

Given Function:

f(x) = -3+18x+3

here a = -3 , b = 18 , c = 3

a is negative so it has maximum value

x = -b/2a

= -18/2*(-3)

= -18/-6

= 18/6

= 3

f(x) = -3* + 18*3 + 3

= -3*9+54+3

= -27+54+3

= 27+3

= 30

Therefore the function has a maximum value of 30 at x = 3.

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1. The pairs of polygons are similar.

2. The pairs of polygons are not similar.

3. The missing measure is of x = 5.2.

4. The missing measure is of x = 16.

5. The value is AB = 6.

6. The perimeter of the yellow tile is of 240 cm.

7. The value is DF = 0.75.

Similar polygons are polygons that share these two following features:

Hence, for itens 1 and 2, we have that:

For item 3, the side lengths are proportional, hence:

x/2.6 = 8/4

x/2.6 = 2

x = 2 x 2.6

x = 5.2.

Same as item 4, hence:

x/10 = 9.6/6

x/10 = 1.6

x = 16.

For item 5, considering the equivalent side lengths, we have that:

AB/8 = 12/16

AB/8 = 3/4

AB = 24/4

AB = 6.

The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:

3 x 80 cm = 240 cm.

For item 7, we have that:

DF/3.4 = 2.25/9

DF = 3 x 2.25/9

DF = 0.75.

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Answer:

∠T

Step-by-step explanation:

∠T is the common angle found in both triangles.

In ΔPTS, ∠PTS represents ∠T.

In ΔQTR, ∠T is represented by ∠QTR.

Answer:

The angle T is common side.

Step-by-step explanation:

Given triangles,

→ ∆PTS & ∆QTR

Now we have to,

→ fInd common angle of both triangles.

The common angle is,

→ <T (angle T)

→ As it is present in both triangles.

Hence, the common part is angle T.

The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15

General equation of quadratic is

f(x) = a[tex]x^{2}[/tex] + bx + c

and Standard form is

f(x) =a [tex](x-h)^{2}[/tex] + k

where h , k are coordinates of vertex

and x , y represent some point on the graph.

By replacing f(x) with y in standard equation we get

y = a[tex](x-h)^{2}[/tex] + k

Put value of x , y , h , k from the graph.

h = -2

k = 7

x = 0

y = 9

9 = a (4) + 7

a = 2

Now put value of a in standard equation

f(x) = 2 [tex](x + 2)^{2}[/tex] + 7

f(x) = 2[tex]x^{2}[/tex] + 4x + 15

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The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.

In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.

The given system of equations is

x + y = -1          ......(1)

3x - y = 21       ......(2)

Rewrite equation (1)

y = - x - 1        ......(3)

Put equation (4) in equation (3)

3x -(-x -1) = 21

3x + x + 1 = 21

4x = 20

x = 20/4

x = 5

Put x= 5 in equation (3)

y = - 5 - 1

y = - 6

So, both the options are correct, (5, -6) is the solution of both equations.

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The Answers is 90

Step-by-step explanation: Imagion taking 4 DE and make a square out of it. All sides of a square is 90 degress so De is 90 degress