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Answer:

.15 kilometers or 150 meters

Step-by-step explanation:

Answer:

Since both equations are equal to y, we can set them equal to each other.

y =-3x +8

y = -5x -2

-3x +8 = -5x -2

Solve for x.To do this, we need to get x by itself. First, move all the numbers to one side of the equation, and all the variables to the other.

-3x +8 = -5x -2

Add 5x to both sides

-3x+5x +8=-5x+5x -2

2x+8=-2

Subtract 8 from both sides

2x+8-8 = -2-8

2x=-10

Now, all the numbers are on one side, with the variables on the other. x is not by itself, it is being multiplied by 2. To undo this, divide both sides by 2

2x/2= -10/2

x= -5

Now, to find y, substitute -5 in for x in one of the equations.

y = -5x -2

y= -5(-5) -2

y=25-2

y=23

Put the solution into (x,y)

The solution is (-5, 23)

Answer:

35.36 cm

Step-by-step explanation:

The diagonal of a square will be given by

[tex]D=\sqrt {a^{2}+b^{2}}[/tex]

Where a is the length of one side and b is the length of another side. For a square, botj sides are equal hence the diagonal calculations will be as follows

Given that a is 25 then

[tex]D=\sqrt {25^{2}+25^{2}}[/tex]

D=35.3553390593274

Rounding off the nearest two decimal place

D=35.36 cm

The length of the diagonal (c) of the square paper that measures 25 cm on a side can be found using the Pythagorean Theorem (a² + b² = c²). In this case, a = 25cm, b = 25cm, and by solving for c we get c = √(25² + 25²) ≈ 35.36 cm.

In order to answer your question about the length of the diagonal of a square, you would need to use the Pythagorean Theorem. The Pythagorean Theorem is a mathematical principle which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as: a² + b² = c².

In a square, all sides are equal, so we can consider the given measurement of 25 cm for both 'a' and 'b'. Hence, a = 25cm and b = 25cm. That would make our equation: 25² + 25² = c². When you calculate it, we get 625 + 625 = c², summing them up you get 1250 = c². To find 'c', you will take the square root of 1250 which equals approximately 35.36 cm. So, the length of the diagonal of the square paper is around 35.36 cm.

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Answer:

$R = $500 + $15(t)

Step-by-step explanation:

in this question, we are told to give a mathematical expression that would model the amount of money that is made by Hillel.

from the question, we were made to understand that the amount of money he makes is a front of his time t. that is noted.

and also, he has a base cost of $500.

now, let’s write an equation;

R = $500 + 15(t)

where t represents the length of the performance as suggested by women

Answer:

9 inches

Step-by-step explanation:

Volume is the product of cross sectional area and height.

V=Ah

Where A is area of base and h is height

Given that the base is square, the area of square is given by A=b*b

Xonsidering that the area is given as 81 square inches then

b*b=81

b is the square root of 81 which is +9 or -9

Since base must be positive interger, then base is 9 inches

Answer:

3.4 miles

Step-by-step explanation:

60 × 3 = 180

she has to drive 180 miles

180 ÷ 50 = 3.4

3.4 miles

In this problem, we need to understand the relationship between rate, time and distance. Here, we establish that Maria's aunt's house is 180 miles away. When Maria drives at a rate of 50 miles per hour, it takes her 3.6 hours to reach her aunt's house.

This is a problem of rate, time, and distance, specifically about understanding how changes in rate (or speed) affect time. Here, Maria drives to her aunt's house at a rate of 60 miles per hour, which takes 3 hours. The distance to her aunt's house, then, is 60 miles/hour times 3 hours, or 180 miles. We know that distance = rate times time (D = rt).

Now, when Maria drives at a rate of 50 miles per hour, the time will change. To find the new time, we rearrange the formula to t = D/r. Plugging the values in, t = 180 miles / 50 miles/hour, we get 3.6 hours. So, it would take Maria 3.6 hours to reach her aunt's house if she drives at a rate of 50 miles per hour.

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I don’t know about the first one the second one if it starts from the origin the point represents that it an proportional 3 is when they start together by seeing if it is x and y I don’t know if it is right

The zeros of the function [tex]G(r) = r^2 - 6r - 5[/tex]5 are r = 11 and r = -5.

To find the zeros of the function [tex]G(r) = r^2 - 6r - 55[/tex], we set G(r) equal to zero and solve for r:

Now, we can use the quadratic formula to solve for r:

r = [-b ± √[tex](b^2 - 4ac)[/tex]] / 2a

where a, b, and c are the coefficients of the quadratic equation [tex](r^2 - 6r - 55 = 0)[/tex].

In this case, a = 1, b = -6, and c = -55. Let's substitute these values into the formula:

r = [-( -6) ± √[tex]((-6)^2 - 4 * 1 * (-55))[/tex]] / 2 * 1

r = [6 ± √(36 + 220)] / 2

r = [6 ± √256] / 2

Now, let's consider the two possible solutions:

1) r = [6 + √256] / 2

r = [6 + 16] / 2

r = 22 / 2

r = 11

2) r = [6 - √256] / 2

r = [6 - 16] / 2

r = -10 / 2

r = -5

So, the zeros of the function  are r = 11 and r = -5.

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Answer:

Answer is below

Step-by-step explanation:

Charles is wrong because 3 doesn't represent exponential decay. This is because 3 is greater than 1, so it represents exponential growth. If the number was less than 1, then it would represent exponential decay.

If this answer is correct, please make me Brainliest!

The correct answer is Charles should represent as  Exponential growth instead of exponential decay

Here f(x) = 3 where 3 is greater than 1

so, It is exponential growth instead of exponential decay

Hence , Charles made an error of exponential decay instead of exponential growth.

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Answer:

log5(125)=3 The 5 should be smaller and a little lower.

Step-by-step explanation:

Answer:

he started fishing by 5:10pm

Step-by-step explanation:

just subtract 1:30 from 6:40

If I had to guess that it mean -4x + 6y = -18 and y = -2x+21:

Since we have a y =, we can plug that in.

-4x + 6(-2x + 21) = -18

-4x  -12x + 126 = -18

-16x = -18 -126

-16x = -144

-16x/-16 = -144/-16

x = 9

The value of x is equal to 9 and the value of y is equal to 3

Data given;

To solve the linear equations above, we have to use substitution method.

from equation 1

[tex]-4x + 6y = -18[/tex]

Make x the subject of formula

[tex]-4x + 6y = -18\\x = \frac{9 + 3y}{2}[/tex][tex]-4x + 6y = -18\\-4x = -18 - 6y \\\frac{-4x}{-4} = \frac{-18-6y}{-4}\\ x = \frac{9 + 3y}{2}[/tex]

substitute the value of x into equation 2

[tex]y = -2x + 21\\y = -2(\frac{9+3y}{2})+ 21\\ y = {-9-3y} + 21\\y = -3y + 12\\4y = 12\\4y/4 = 12/4\\y = 3[/tex]

substitute the value of y into either equation 1 or 2

[tex]y = -2x + 21\\3 = -2x + 21\\2x = 21 - 3\\2x = 18\\2x/2 = 18/2\\x = 9[/tex]

From the calculations above, the value of x is 9 and y is 3

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Answer:

  y +3 = -6(x +9)

Step-by-step explanation:

The point-slope form of the equation of a line is ...

  y -k = m(x -h)

for a line with slope m through point (h, k).

You want the line with slope -6 through point (-9, -3), so its equation is ...

  y -(-3) = -6(x -(-9))

  y +3 = -6(x +9) . . . . . matches the last choice

Answer:

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Step-by-step explanation:

Mean SAT scores = 1026

Standard Deviation = 209

Mean ACT score = 20.8

Standard Deviation = 4.8

We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.

The formula to calculate the z-score is:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.

z-score for junior scoring 860 in SAT exam will be:

[tex]z=\frac{860-1026}{209}=-7.59[/tex]

z-score for junior scoring 16 in ACT exam will be:

[tex]z=\frac{16-20.8}{4.8}=-1[/tex]

The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.

Answer:

C 84.2-79.2/SQRoot(10.2^2/50  + of of 6.8^2/30)

​

Step-by-step explanation:

Final answer:

To determine if there is a significant difference in lifespan between men who are distance runners and those who are not, a two-sample t-test test statistic is calculated as approximately 1.051 using the provided sample means, standard deviations, and sample sizes.

Explanation:

To determine if men who are distance runners live significantly longer, on average, than men who are not distance runners, we would use a two-sample t-test statistic. The test statistic formula for a two-sample t-test is:

t = (x1 - x2) / [tex]\sqrt{(s1^2/n1 + s2^2/n2)[/tex]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes of the two groups.

In this case, the mean age at death for men who are distance runners is 84.2, the standard deviation is 10.2, and the sample size is 50 (n1 = 50). The mean age at death for men who are not distance runners is 79.2, the standard deviation is 6.8, and the sample size is 30 (n2 = 30).

Plugging the values into the formula, we calculate the test statistic as follows:

t = (84.2 - 79.2) / [tex]\sqrt{(10.2^2/50 + 6.8^2/30)[/tex]

t = 2.0 / [tex]\sqrt{((104.04/50) + (46.24/30))[/tex]

t = 2.0 / [tex]\sqrt{(2.0808 + 1.5413)[/tex]

t = 2.0 / √3.6221

t ≈ 2.0 / 1.9032

t ≈ 1.051

This is the test statistic that you would use to determine whether there is a significant difference in lifespan between the two groups.

Answer:

2.9 radians.

Step-by-step explanation:

Please kindly check the attached file for explanation.

The radian measure of a central angle intercepting an arc length of 5.8 units in a circle with a radius of 2 units is 2.9 radians when rounded to the nearest tenth.

The question deals with finding the radian measure of a central angle in a circle with a given radius and arc length. The formula for this calculation is theta = arc length / radius. Given that the circle's radius (r) is 2 units and the arc length (l) is 5.8 units, we substitute these values into the formula to find the radian measure of the central angle.

theta = l / r = 5.8 units / 2 units

This gives us theta = 2.9 radians. However, we need to round this to the nearest tenth, resulting in theta = 2.9 radians as the final answer.

To find the span of the bridge, or the length of its minor axis, we use the equation for an ellipse with the given dimensions and solve for 'b'. Then, we multiply 'b' by 2 to find the total span.

To determine the span of the bridge, or the length of its minor axis, we know that the top of the arch (which coincides with the semi-major axis) is 35 feet above the ground and the height is 15 feet above the ground at a distance of 27 feet from the center. The equation for an ellipse with a vertical major axis is:

where 'a' is the semi-major axis and 'b' is the semi-minor axis. Since the total height is 35 feet, the semi-major axis, 'a', is 35/2 = 17.5 feet. The distance of 27 feet from the center to the point where the height is 15 feet can be plugged into the equation with 'y' being the remaining height from that point to the top of the arch:

Upon calculating and rearranging the terms, we have:

Rounding 'b', the semi-minor axis, to two decimal places will give us the span of the bridge which is twice 'b' because it's a complete minor axis.

To find the span of the bridge (the length of its minor axis), we first need to determine the equation of the ellipse.

The standard equation of an ellipse with the center at the origin and the major axis along the x-axis is:

[tex]\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \][/tex]

Where \( a \) is the semi-major axis (half of the major axis) and [tex]\( b \)[/tex] is the semi-minor axis (half of the minor axis).

Given that the top of the arch is 35 feet above the ground (the major axis) and the height 27 feet from the center is to be 15 feet above the ground, we can set up the following system of equations:

1. When [tex]\( y = 0 \)[/tex] (ground level), [tex]\( x = a \)[/tex]

2. When [tex]\( y = 27 \)[/tex] (height above the center), [tex]\( x = 15 \)[/tex]

Using these conditions, we can solve for [tex]\( a \) and \( b \):[/tex]

[tex]1. \( \frac{a^2}{a^2} + \frac{0}{b^2} = 1 \)2. \( \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \)[/tex]

Solving equation 1 for[tex]\( a \):[/tex]

[tex]\[ \frac{a^2}{a^2} = 1 \]\[ a = a \][/tex]

Solving equation 2 for [tex]\( b \):[/tex]

[tex]\[ \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \]\[ \frac{225}{a^2} + \frac{729}{b^2} = 1 \]\[ \frac{729}{b^2} = 1 - \frac{225}{a^2} \]\[ b^2 = \frac{729a^2}{a^2 - 225} \]\[ b = \sqrt{\frac{729a^2}{a^2 - 225}} \][/tex]

We already know that [tex]\( a = 35 \)[/tex](since it's the distance from the center to the top of the arch).

[tex]\[ b = \sqrt{\frac{729 \times 35^2}{35^2 - 225}} \][/tex]

Now we can calculate [tex]\( b \):[/tex]

[tex]\[ b = \sqrt{\frac{729 \times 1225}{1225 - 225}} \]\[ b = \sqrt{\frac{893025}{1000}} \]\[ b ≈ \sqrt{893.025} \]\[ b ≈ 29.88 \][/tex]

So, the span of the bridge (the length of its minor axis) should be approximately 29.88 feet, rounded to two decimal places.

Answer:

38

Step-by-step explanation:

Answer:

38 packs

Step-by-step explanation:

Answer:

  10

Step-by-step explanation:

Ground level is where h = 0, so solve the equation ...

  h(x) = 0

  -5(x -4)^2 +180 = 0 . . . . substitute for h(x)

  (x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36

  x -4 = 6 . . . . . . . . . . . . . . positive square root*

  x = 10 . . . . . . add 4

The object will hit the ground 10 seconds after launch.

_____

* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.

The object modeled by the quadratic equation h(x)=-5(x-4)²+180 will hit the ground 10 seconds after being launched.

The equation given is a quadratic equation which models the height of an object after being launched from a platform. To find out when the object will hit the ground, we need to determine when the height h(x) is equal to zero. The equation can be written as h(x) = -5(x - 4)² + 180.

To find the time when the object hits the ground, we set the height equal to zero and solve for x:
0 = -5(x - 4)² + 180
Solving the quadratic equation, we divide both sides by -5:
(x - 4)² = 36
Taking the square root of both sides gives two solutions: x - 4 = [tex]\pm6[/tex]. The positive root gives us the time after launch when the object hits the ground:
x - 4 = 6
x = 10

Therefore, the object will hit the ground 10 seconds after being launched.

Bonita have 12 dimes and 7 quarters in her pocket.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Bonita have with dimes and quarters in pocket = $2.95

Bonita have 5 more dimes than quarters.

Now,

Let number of dimes = x

Let number of quarters = y

Since, Bonita have 5 more dimes than quarters.

x = y + 5

Here,

Bonita have with dimes and quarters in pocket = $2.95

So, we can formulate;

0.1x + 0.25y = =$2.95

Substitute the value of x in above equation, we get;

0.1 (y + 5) + 0.25y = $2.95

0.1y + 0.5 + 0.25y = $2.95

0.35y + 0.5 = $2.95

Subtract 0.5 we get;

0.35y + 0.5 - 0.5 = $2.95 - 0.5

0.35y = 2.45

Divide by 0.35 we get;

y = 7

And, x = y + 5 = 7 + 5 = 12

Thus, Bonita have 12 dimes and 7 quarters in her pocket.

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We have been given that square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. We are asked to find the side length of square A'B'C'D'.

We know that when scale factor is greater than 1, then the resulting figure would be an enlargement.

To find the side length of new square after dilation, we will multiply the original side by scale factor.

[tex]\text{New side length}=\text{Original side}\times \text{Scale factor}[/tex]

[tex]\text{New side length}=\text{4 inches}\times 4[/tex]

[tex]\text{New side length}=16\text{ inches}[/tex]

Therefore, the side length of square A'B'C'D' would be 16 inches.

Answer: what trapezoid?

Answer:

5.64

Step-by-step explanation:

set up a ratio problem

5 ounces/2.35 = 12 ounces/x

5x = 28.2

x = 5.64

Answer:

5.64

Step-by-step explanation:

5x2.4=12

SO,

2.35x2.4=5.64

Answer:

To find the radius diameter circumference and area, The area of a circle =  π x radius^2, Circumference of a circle = π x diameter, Remember that the diameter = 2 x radius.

Step-by-step explanation:

Steps to solve:

f(x) = 3x+5/x; x = 2

~Substitute

f(2) = 3(2)+5/2

~Simplify

f(2) = 6+5/2

~Add

f(2) = 11/2

~Simplify

f(2) = 5.5

Best of Luck!

Answer:

69

Step-by-step explanation:

The solution is,  138 divided by 2 is 69.

Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

138 divided by 2

i.e. 138/2

= 69

Hence, The solution is,  138 divided by 2 is 69.

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Answer:

Measure of <N = 60°

(angles in an equilateral triangle are all equall 60°)

the measure of ∠M= 60°

(angles in an equilateral triangle are all equall 60°)

Step-by-step explanation:

Sum of angles in a triangle is equall to 180....

And in equilateral triangle of all sides equall...all angles are equal to 60° because all sides are equal.

So <m= <n=<o=60°

Answer:

36 minutes when both pipes are working together

Step-by-step explanation:

capacity of tank = 5400 liters

Pipe A flow per mint. = 5400/90 = 60 liters per mint.

Pipe B flow per mint. = 5400/60 = 90 liters per mint.

Flow of A + B per mint. 60 + 90 = 150 liter per mint.

Therefore, 5400 / 150 = 36 minutes to fill the tank