The dimensions of a 7-cm by 2-cm rectangle are
multiplied by 3. How is the area affected?

Answer:

x = -1

y = -1

Step-by-step explanation:

3x - y = -2

2x + y = -3

Multiply equation 1 by 2 and equation 2 by 3

We have

2x3x - 2xy = 2x-2

3x2x + 3xy = -3x3

Equation 1 6x - 2y =-4

Equation 2 6x + 3y = -9

Subtract equation 2 from 1

We have -5y = 5

Divide both sides by -5

y = 5/-5 = -1

Now Substitute y = -1 into any of the equations to get x

Using equation 1 , we have

3x - (-1) = -2

3x +1 = -2

Collect like terms

3x = -2 -1

3x = -3

Divide both sides by 3

x = -3/3 = -1

Answer

First of all, we need to identify the type of equation this is...

Since we are solving two at a go, it means it's a simultaneous equation.

Now, we need to solve them differently.

Taking the first one which says...

3x -y = -2

Then we say

When x is 0, y =?

So in the equation above , we replace x with 0

Meaning- 3x-y = -2

3(0) -y= -2

0 -y= 2

-y =-2

Y =2

Also, when y =0.

3x- 0 =-2

3x=-2

X=-2/3.

Also for the other equation

2x+ y =-3

When x= 0 in the above equation

2(0) + y= -3

0 +y=-3

Y=-3

When y = 0

2x+ 0= -3

2x = -3

X=-3/2

The above is what well plot on the graph.

t

Step-by-step explanation:

Answer:

No, the cone will not hold all of the ice cream.

Step-by-step explanation:

Given:

" According to the Joy Cone Company, their waffle cones have a diameter of 2 5/8 inches and a  height of 6 inches.

If you place one scoops of ice cream (in the shape of a sphere) with a diameter of 2 7/8 inches would let  it melt.

Now, to explain mathematically will the cone hold all of the ice cream.

Taking the value of π = 3.14.

So, to get the volume of waffle cone we put formula:

Height (h) = 6 inches.

Diameter = [tex]2\frac{5}{8}=\frac{21}{8}\ inches.[/tex]

Thus radius (r) = Diameter ÷ 2 = [tex]\frac{\frac{21}{8}}{2} =\frac{21}{16} \ inches.[/tex]

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

[tex]Volume=3.14\times \frac{21}{16} \times \frac{21}{16} \times \frac{6}{3}[/tex]

[tex]Volume=3.14\times 1.31\times 1.31\times 2[/tex]

[tex]Volume=10.78\ inches^3.[/tex]

The volume of waffle cone = 10.78 inches³.

Now, to get the volume of scoop which is in the shape of sphere we put formula:

Diameter = [tex]2\frac{7}{8} =\frac{23}{8} \ inches.[/tex]

Thus radius (r) = Diameter ÷ 2 [tex]=\frac{\frac{23}{8}}{2} =\frac{23}{16} \ inches.[/tex]

[tex]Volume = \frac{4}{3} \pi r^3[/tex]

[tex]Volume = \frac{4}{3} \times 3.14\times \frac{23}{16} \times \frac{23}{16} \times \frac{23}{16}[/tex]

[tex]Volume=1.33\times 3.14\times 1.44\times 1.44\times 1.44[/tex]

[tex]Volume=12.47\ inches^3.[/tex]

The volume of one scoop of ice cream = 12.47 inches³.

So, as the volume of scoop of ice cream is more than the volume of cone.

Thus, if placing one scoop of ice cream in the cone and let it melt, the cone will not hold all of the ice cream.

Therefore, no the cone will not hold all of the ice cream.

The ice cream scoop will not fit into the cone due to volume differences.

The ice cream scoop will not fit into the cone. To determine this mathematically, we need to compare the volume of the cone to the volume of the ice cream scoop.

The volume of the cone can be calculated using the formula for the volume of a cone: V = 1/3 × π × r² × h.

Similarly, the volume of the sphere (ice cream scoop) can be calculated using the formula for the volume of a sphere: V = 4/3 × π × r³.

By plugging in the given measurements, we can determine that the volume of the ice cream scoop will be greater than the volume of the cone, indicating that the ice cream scoop will not fit into the cone.

The function h(x) = x^2 - 1 has a negative average rate of change over the interval from x = -∞ to x = 0, which is where the parabola is decreasing toward its vertex at the origin.

The student asked over which interval the function h(x) = x^2 - 1 has a negative average rate of change. The average rate of change is negative when the function is decreasing. In the case of h(x) = x^2 - 1, which is a parabola opening upwards, the function decreases as x moves from the left to the right towards the vertex. Therefore, the interval in which the function has a negative average rate of change is from x = -∞ to x = 0, because this is where the function values are falling. To find the average rate of change between two points x1 and x2, we can use the formula: (h(x2) - h(x1)) / (x2 - x1). If x1 is to the left of the y-axis (x1 < 0) and x2 is the y-axis (x2 = 0), we will get a negative result since h(x2) < h(x1) in that interval, showing a negative average rate of change.

The function h(x) = x^2 - 1 has a negative average rate of change over the interval − 3 ≤ x ≤ 1. This interval includes the vertex of the parabola at x = 0, where the function is decreasing, resulting in a negative rate of change.

The function h(x) = x2 - 1 has different average rates of change depending on the interval we are considering. To find an interval where the average rate of change is negative, we need to look at intervals where the function is decreasing. The function h(x) will be decreasing on any interval that includes the value x = 0 since this is where the vertex of the parabola represented by h(x) is located, and it is a parabola opening upwards.

Analyze intervals around x = 0 to find where the function decreases. Looking at Choice C (−3 ≤ x ≤ 1), we can calculate the average rate of change as:

Since the average rate of change is negative (-2), Option C is the interval over which h(x) has a negative average rate of change.

the complete Question is given below:

h(x)=x 2 −1h, left parenthesis, x, right parenthesis, equals, x, squared, minus, 1 Over which interval does h hh have a negative average rate of change? Choose 1 answer: Choose 1 answer: (Choice A) A − 3 ≤ x ≤ 5 −3≤x≤5minus, 3, is less than or equal to, x, is less than or equal to, 5 (Choice B) B 1 ≤ x ≤ 4 1≤x≤41, is less than or equal to, x, is less than or equal to, 4 (Choice C) C − 3 ≤ x ≤ 1 −3≤x≤1minus, 3, is less than or equal to, x, is less than or equal to, 1 (Choice D) D − 1 ≤ x ≤ 5 −1≤x≤5minus, 1, is less than or equal to, x, is less than or equal to, 5 Show Calculator

1. [tex]\frac{x^3}{x^8}=x^{-5}[/tex]

2. [tex]\frac{6x}{2x^8} = 3x^{-7}[/tex]

3. [tex]\frac{28x^6}{21x^2} = \frac{4}{3}x^4[/tex]

Step-by-step explanation:

1. x^3/x^8

Given fraction is:

[tex]\frac{x^3}{x^8}[/tex]

When the bases are same in both numerator and denominator then the exponents can be added

i.e.

[tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

So,

[tex]\frac{x^3}{x^8} = x^{3-8} = x^{-5}[/tex]

Part b:

[tex]\frac{6x}{2x^8}\\= \frac{3.2.x}{2.x^8}\\=\frac{3x}{x^8}\\=3x{1-8}\\=3x^{-7}[/tex]

Part c:

Given

[tex]\frac{28x^6}{21x^2}\\= \frac{7.4.x^6}{7.3.x^2}\\=\frac{4}{3} x^{6-2}\\=\frac{4}{3}x^4[/tex]

Keywords: Fractions, exponents

Learn more about fractions at:

#LearnwithBrainly

Answer:

45°

Step-by-step explanation:

90-45=45°

a. Perimeter

b. Volume

c.Suface Area

Answer:

Option C

Step-by-step explanation:

We want to select the expression that can be used to find the slope of the line going through the points (–7, 3) and (1, –9)

Recall that the slope is given by:

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

We substitute the points into the formula to get:

[tex] \frac{ - 9 - 3}{1 - - 7} [/tex]

Therefore the third choice is correct.

Answer:

C

Step-by-step explanation:

Answer:

(B) Parameters

(A) Statistics

Step-by-step explanation:

edg 2020

The mean and the standard deviation of a normal population are called parameters, and of a random sample from a population are called statistic

The steps are as follow:

Therefore, the mean and the standard deviation of a normal population are called parameters, and of a random sample from a population are called statistic

Learn more about Normally distributed data here:

https://brainly.com/question/1407349

#SPJ2

Answer:

The answer is y = x

The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The equation for the line of reflection for the given points (6, 3.7) and (3.7, 6) is y = -x + 9.7.

The equation for the line of reflection can be found by using the midpoint formula and the slope formula. The midpoint of each corresponding pair of points can be calculated to find the coordinates of the image points. Then, the slope of the original line and the slope of the reflected line can be calculated. Using the midpoint and slope, the equation of the line of reflection can be determined.

For example, to find the equation for the line of reflection for points (6, 3.7) and (3.7, 6), we can calculate the midpoint: ( (6 + 3.7) / 2, (3.7 + 6) / 2 ) = (4.85, 4.85).

Next, we can calculate the slope of the original line using the points (6, 3.7) and (5.4, 2) using the slope formula: (2 - 3.7) / (5.4 - 6) = -1.7 / -0.6 = 2.83.

Finally, we can calculate the slope of the reflected line using the points (4.85, 4.85) and (3.7, 6) using the slope formula: (6 - 4.85) / (3.7 - 4.85) = 1.15 / -1.15 = -1.

So, the equation for the line of reflection is y = -x + b. To find b, we can use the point (4.85, 4.85). Substituting the values into the equation, we get 4.85 = -(4.85) + b, which simplifies to b = 9.7.

Therefore, the equation for the line of reflection is y = -x + 9.7.

Answer:

Yes, it is.

Step-by-step explanation:

The second 8 in 8.8 is greater than the 0 in 8.01.

Answer:

im stuck on a similar problem right now

Answer:

8.2

Step-by-step explanation:

Use cosine law:

BC² = 7² + 9² - 2(7)(9)cos(60)

BC² = 67

BC = sqrt (67)

BC = 8.1853

BC = 8.2 (nearest tenth)

Claire will pay $309.01 for the bike.

Answer:

[tex]P(t)=4(1.019)^t[/tex]

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

[tex]P=a(1+r)^t[/tex]

where

P ---> is the world's population

t ---> is the number of years since 1945

a ---> is the initial population in 1945

r ---> is the percent rate of growth

we have

[tex]r=1.9\%=1.9/100=0.019[/tex]

substitute

[tex]P=a(1+0.019)^t[/tex]

[tex]P=a(1.019)^t[/tex]

Remember that

There were  approximately 4 billion people in the world in 1975

That means

Since year 1975 the initial value a=4 billion people

substitute

[tex]P(t)=4(1.019)^t[/tex]

Answer:

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.                                  

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4000 gallons

Standard Deviation, σ = 125 gallons

Sample size, n = 40

We are given that the distribution of amount of fuel is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Central limit theorem:

As the sample size increases, the distribution of sample mean has a similar popular distribution shape.

P(sample of 40 jumbo jets will be less than 3950 gallons)

P(x < 3950)

[tex]P( x < 3950) = P( z < \displaystyle\frac{3950 - 4000}{125}) = P(z < -0.4)[/tex]

Calculation the value from standard normal z table, we have,  

[tex]P(x < 3950) = 0.6554 = 65.54\%[/tex]

0.6554 is the probability that the mean number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons.

The probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.

it is given that

Mean μ= 4000 gallons

Standard deviation σ = 125 gallons

Number of trials x = 3950 gallons

Z-score = (x-μ)/σ

Z-score = (3950-4000)/125

Z-score = -0.4

So probbaility P(x<3950) = P(z<-0.4)

From the standard normal table,

P(x<3950) = 0.66

Therefore, the probability that the number of gallons of fuel needed to take off for a randomly selected sample of 40 jumbo jets will be less than 3950 gallons is 0.66.

To get more about normal distribution visit:

https://brainly.com/question/4079902

Using the formula for compound interest, the balance of a $15,000 investment at a 6% interest rate compounded annually after 9 years is approximately $25,342.19.

To calculate the balance of an investment of $15,000 at 6% interest compounded annually after 9 years, we can use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

Where:

In this case:

Plugging these values into the formula gives us:

A = $15,000(1 + 0.06/1)^(1\*9)

A = $15,000(1 + 0.06)^9

A = $15,000(1.06)^9

A = $15,000\*1.689479

A = $25,342.19 approximately

So, after 9 years, the balance will be $25,342.19, rounding to the nearest cent.

Shailyn solved 69 more math problems than Karla by subtracting the number of problems Karla solved (549) from the number of problems Shailyn solved (618).

To find out how many more math problems Shailyn solved than Karla, we need to subtract the number of problems Karla solved from the number Shailyn solved. The calculation is as follows:

Therefore, Shailyn solved 69 more math problems than Karla.

Answer:

Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87

Step-by-step explanation:

i.) Let the side of the equilateral triangle base be a

ii.) the area of the base = 3.9 square feet

iii.) the area of equilateral triangle is = [tex]\frac{\sqrt{3} }{4} a^{2}[/tex] = 3.9

iv.) Base area  = 3.9 square feet

v.) The area that is not covered is the base.

vi.) The total area that is not covered  = 3.9 [tex]\times[/tex] 2  since there are two pyramids

    therefore the total area not covered = 7.8 square feet

vii.) therefore Kwame's team will save = 7.8 [tex]\times[/tex] $0.24 = $1.87

Answer:3.2%

Step-by-step explanation:

Answer:

t=100-2x

Step-by-step explanation:

The amount of water in the cup after t seconds can be represented by the linear function Y = 100 - 2t. This equation is derived from the initial amount of water in the cup and the rate at which water is being poured out.

The function that shows the amount of water in the cup after t seconds is a linear function. It can be represented as Y = 100 - 2t. In this equation, Y represents the amount of water left in the cup and t represents time in seconds.

This equation comes from the initial amount of water (100 milliliters) minus the rate of water being poured out of the cup (2 milliliters per second times the number of seconds). For example, after 3 seconds, the amount of water left would be 100 - 2*3 = 94 milliliters.

https://brainly.com/question/31353350

#SPJ3

Answer:

198 cm²

Step-by-step explanation:

We are given the dimensions of a rectangular prism;

3cm 9cm and 6cm

We are required to determine its surface area;

We need to know that;

Surface area of a rectangular prism is given by;

A = 2(WL+HL+WH)

Where L, W and H are length , width and height respectively;

Assuming;

Width is 3 cm

Length is 9 cm, and

Height is 6 cm

Then;

Area = 2 ( (3×9) + (6×9) + (3×6))

        = 2(99)

       = 198 cm²

Therefore, the area of the rectangular prism is 198 cm²

Final answer:

The surface area of a rectangular prism with dimensions 3 cm by 9 cm by 6 cm is 198 square centimeters.

Explanation:

To find the surface area of a rectangular prism with dimensions of 3 cm, 9 cm, and 6 cm, we need to calculate the area of all six faces of the prism and then sum those areas. The formula to find the surface area (SA) of a rectangular prism is:

SA = 2lw + 2lh + 2wh

where l is the length, w is the width, and h is the height.

Substituting our given dimensions into the formula gives us:

SA = 2(3 cm)(9 cm) + 2(3 cm)(6 cm) + 2(9 cm)(6 cm)

SA = 2(27 cm²) + 2(18 cm²) + 2(54 cm²)

SA = 54 cm² + 36 cm² + 108 cm²

SA = 198 cm²

So, the total surface area of the rectangular prism is 198 square centimeters.

Answer:

The costs of the ski packages will be the same if you set them equal to each other. The cost will be the same after 5 hours. The cost will be $35 for both packages.

Step-by-step explanation:

5 + 5x = 20 + 2x                     Set the equations equal

-5            -5                             Subtract 5 from both sides

5x = 15 + 2x

-2x          -2x                           Subtract 2x from both sides

3x = 15                                    Divide both sides by 3

x = 5

Answer:2

Step-by-step explanation:

Answer:

350 is your answer

Step-by-step explanation:

anything lower than five you wouldn't round up you'd round down so basically the 1 is pointless

Rounding 351 to the nearest 10 gives us 350, as per the rule of place value while rounding.

When rounding a number to the nearest 10, we consider the digit in the tens place. If the digit in the unit's place is 5 or greater, we round up; otherwise, we round down.

In the case of 351, the digit in the tens place is 5, and the digit in the units place is 1. Since the digit in the unit's place is less than 5, we round down. Therefore, when rounding 351 to the nearest 10, we get 350.

Rounding 351 to the nearest 10 essentially means approximating it to the nearest multiple of 10. In this case, 351 is closer to 350 than to 360, which is the next multiple of 10.

So, rounding 351 to the nearest 10 gives us 350.

To learn more about the place value;

https://brainly.com/question/27734142

#SPJ6

Answer:

The value of k is 0.8

Step-by-step explanation:

we have

[tex]y=kx[/tex]

This linear equation represent a direct variation

we have

y=1.2, x=1.5

substitute in the equation

[tex]1.2=1.5k[/tex]

solve for k

divided by 1.5 both sides

[tex]k=1.2/1.5=0.8[/tex]

The linear equation is

[tex]y=0.8x[/tex]

Final answer:

To find the height of a cylinder with a known radius and surface area, subtract the area of the bases from the total surface area to get the lateral surface area, and then solve for the height. Using the surface area formula SA = 2πr² + 2πrh, the height is computed to be approximately 9.4 cm.

Explanation:

To calculate the height of a cylinder when you know its surface area and radius, you use the surface area formula for a cylinder, SA = 2πr² + 2πrh, where SA is the surface area, r is the radius, and h is the height of the cylinder. Given that the surface area (SA) is 1,220 cm² and the radius (r) is 10 cm, the formula can be rearranged to solve for h (height). The first step is to calculate the area of the circular bases, which is 2πr², then subtract this value from the total surface area to get the lateral surface area (2πrh), and finally divide by (2πr) to solve for h.

First, calculate the area of the circular bases:

Area of one base = πr² = 3.14159 × 10² cm² = 314.159 cm²

Total area of both bases = 2 × 314.159 cm² = 628.318 cm²

Subtract this from the total surface area to find the lateral surface area:

Lateral surface area = SA - area of bases = 1,220 cm² - 628.318 cm² = 591.682 cm²

Finally, solve for the height:

2πrh = 591.682 cm²

h = 591.682 cm² / (2 × 3.14159 × 10 cm)

h ≈ 9.4 cm

Thus, the height of the cylinder is approximately 9.4 cm.

The height is approximately 9.42 cm.

To find the height of a cylinder when given the radius and the surface area, use the formula for the surface area of a cylinder: [tex]SA = 2\pi r^2+2\pi rh[/tex]. Here, we know the surface area (SA) is 1220 [tex]cm^2[/tex], and the radius (r) is 10 cm.

First, let's write down the formula with the given values:

[tex]1220 = 2\pi (10)^2 + 2\pi (10)h[/tex]

We can simplify the equation step by step:

Therefore, the height of the cylinder is approximately 9.42 cm.

Answer:

Since there is a 50-50 chance of a person at the party choosing a gift card, and since there can only be 1 of 2 outcomes, we can assume that there will either be more people choosing a gift card than not, or there will be more people not choosing a gift card than are. So, that means that there would be 23 people (more or less) choosing a gift card and 22 people (more or less) not choosing a gift card or vice-versa.

Answer:

(3  x 40) - 85

120 - 85

35 video games

Answer:

She lands on 92.

Step-by-step explanation:

92=58+2+30+2

where she lands = 58+34

92 = 58 + 2x + y   where x=2 and y=32

Final answer:

Sally started on square 58 and used three cards with values of +2, +30, and +2, respectively. The equation for her moves is 58 + 2 + 30 + 2, which equals 92. Hence, she landed on square 92.

Explanation:

Sally's game piece was initially on square 58. To find out where she landed after using her cards, we can write an equation that adds the values on the cards to her starting position. Sally played three cards with the following values: +2, +30, and +2.

The equation to show Sally's moves is:

Starting position + first card + second card + third card = new position

58 + 2 + 30 + 2 = new position

Now, let's calculate the total:

58 + 2 = 60
60 + 30 = 90
90 + 2 = 92

Therefore, Sally's new position after using all her cards is on square 92.

Answer:

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

Step-by-step explanation:

Note the [tex]\sqrt[3]{8}[/tex] = 2 and [tex]\sqrt[3]{125}[/tex] = 5

Thus

[tex]\sqrt[3]{\frac{8}{125} }[/tex] = [tex]\frac{\sqrt[3]{8} }{\sqrt[3]{125} }[/tex] = [tex]\frac{2}{5}[/tex]

Answer:

2/5

Step-by-step explanation:

8 = 2^3

125 = 5^3