Last week Jovanna ran 30 miles
more than Rachel. Jovanna ran
47 miles. How many miles did
Rachel run?

The two beaches will be approximately the same width in 15 years. The two beaches will have approximately the same width in 11.5 years.

The Western Beach is losing sand at a rate of 10 feet per 5 years, while the Dunes Beach is gaining sand at a rate of 25 feet per 5 years. This means that the two beaches are getting closer together at a rate of 15 feet per 5 years.

In 15 years, the Western Beach will be 70 feet wide, and the Dunes Beach will be 95 feet wide.

If we assume that the rates of erosion and accretion remain constant, we can get a better approximation of when the two beaches will have the same width by using a linear equation. The equation for the Western Beach is y = -2x + 100, where y is the width of the beach in feet and x is the number of years since 1995. The equation for the Dunes Beach is y = 5x + 20, where y is the width of the beach in feet and x is the number of years since 1995.

To find the year when the two beaches have the same width, we can set the two equations equal to each other and solve for x. This gives us the equation -2x + 100 = 5x + 20. Solving for x, we get x = 11.5.

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For each statement for triangle SQP and SQR, Q is the midpoint of PR: No, ∠P ≅ ∠R: No, ∠PSQ ≅ ∠RSQ: Yes, m∠P = 33°, m∠RSQ = 57°: No, ∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes.

What is triangle?

A triangle is a geometric shape that consists of three line segments connected end-to-end to form a closed shape. Triangles are one of the basic shapes studied in geometry and are used in a wide range of applications, from construction to computer graphics.

Here are the answers to whether each statement provides enough information to prove that △SQP ≅ △SQR:

Q is the midpoint of PR: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the angles or sides.

∠P ≅ ∠R: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠SQP is a right angle, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-side (AAS) congruence criterion.

∠SQP is a right angle, m∠P = 33°, m∠RSQ = 57°: No, this information alone is not sufficient to prove the triangles are congruent. We need additional information about the sides or other angles.

∠P ≅ ∠R, ∠PSQ ≅ ∠RSQ: Yes, this information is sufficient to prove that the triangles are congruent by the angle-angle-angle (AAA) congruence criterion.

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Answer:

6

Step-by-step explanation:

Step-by-step explanation:

To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:

9^2 + 3(9) - 5 = 81 + 27 - 5 = 103

Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.

rate my answer, please.

verified and e-x/2 function is defined in the interval (-∞,+∞)

We need to verify, whether, (2y' + y = 0) , when y = e-x/2

From y = e−x/2 ,

we obtain,

→y′ = − (1/2)e−x/2

→2y′ + y = −2(1/2)e−x/2 + e−x/2

= −e−x/2 + e−x/2

= 0 →hence verified and e-x/2 function is defined in the interval (-∞,+∞)

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Answer:

t = 41

Step-by-step explanation:

The figure shows a polygon with one exterior angle at each vertex.  In any polygon, the sum of those angle measures is 360 degrees.

Setup the sum and set it equal to 360.

3t + 2t + 61 + 52 + 42 = 360

Combine like terms.

5t + 155 = 360

Subtract 155.

5t = 205

Divide by 5.

t = 41

Answer:

the grocery store

Step-by-step explanation:

its .85 miles which is farther than any other answer

We can use the logarithmic identity log_a(b) + log_a(c) = log_a(bc) to simplify the left side of the equation:

log_2(x) + log_4(x+1) = log_2(x) + log_2((x+1)^(1/2))

Using the rule log_a(b^c) = c*log_a(b), we can simplify further:

log_2(x) + log_2((x+1)^(1/2)) = log_2(x(x+1)^(1/2))

Now we can rewrite the equation as:

log_2(x(x+1)^(1/2)) = 3

Using the rule log_a(b^c) = c*log_a(b), we can rewrite this as:

x(x+1)^(1/2) = 2^3

Squaring both sides, we get:

x^2 + x - 8 = 0

This is a quadratic equation that can be solved using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 1, and c = -8. Plugging in these values, we get:

x = (-1 ± sqrt(1^2 - 4(1)(-8))) / 2(1)

x = (-1 ± sqrt(33)) / 2

x ≈ -2.54 or x ≈ 3.54

However, we must check our solutions to make sure they are valid. Plugging in x = -2.54 to the original equation results in an invalid logarithm, so this solution is extraneous. Plugging in x = 3.54 yields:

log_2(3.54) + log_4(4.54) = 3

0.847 + 0.847 = 3

So x = 3.54 is the valid solution to the equation.

Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

Answer:

1/2

Step-by-step explanation:

slope is 3/6 simplified is 1/2

Answer:

the slope is 1/2 simplified

Step-by-step explanation:

Formula: M=rise/run

rise=3

run=6

3/6= 1/2

Answer:

y'=|x-5|-1

Step-by-step explanation:

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Answer:

Yes

Step-by-step explanation:

The FIFO  method of process costing assumes that the opening work in process is the first group of units to be processed and completed during the current period. The opening work in progress is charged separately to completed production and the cost per unit is based only on the current period costs and the production for the current period. The closing work in process is assumed to come from the new units started during the period.

Answer:

2x+3=11

2x=11-3

x=8/2

x=4........

Answer: \(x = 4\)

Step-by-step explanation:

Okay, so we start with our equation.

\(2x + 3 = 11\).

Then we need to get x alone. To do that we subtract the 3 on the side with the x.

But what we do to one side, we do to the other. So we subtract 3 from the 11 as well

2x + 3 = 11    

      -3    -3

2x = 8

Then we divide by 2 on both sides to get X.

\(\frac{2x}{2} =\frac{8}{2}\)

\(\frac{2x}{2} = x\)

\(\frac{8}{2} = 4\)

\(x = 4\).

Answer:

j = 9.65

Step-by-step explanation:

\(\frac{8}{cos(34)}\) = j

j = 9.649743588... (round as needed)

ANSWER

y = -2x + 4

EXPLANATION

a. We want to find the equation of the line that is parallel to the given equation and passes through (5, -6):

2x + y = 12

Let us put the equation in the slope-intercept form:

y = -2x + 12

When two lines are parallel, their slopes are equal.

The general form of a linear equation is:

y = mx + c

where m = slope

c = intercept

This means that the slope of the given equation is -2. Therefore, the slope of the equation we need is also -2.

Now, we can apply the point-slope method to find the equation of the line.

We have:

y - y1 = m(x - x1)

where (x1, y1) is a point that lies on the line

m = slope

(x1, y1) => (5, -6).

Therefore:

y - (-6) = -2(x - 5)

y + 6 = -2x + 10

=> y = -2x + 10 - 6

y = -2x + 4

That is the equation of the line that passes through (5, -6) and is parallel to the given equation.

Answer:

7 laps

Step-by-step explanation:

Answer:

17/2 pi

Step-by-step explanation:

Area of the whole circle is pi r², which is 9 pi

9 pi x 17/9 pi / 2 pi = 17/2 pi

The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm

The sector area

The area of the sector is calculated as

Area = x/360 * πr²

Where

r² = 8² + 6²

So, we have

r² = 100

This means that

Area = 82/360 * π * 100

Evaluate

Area = 71.55

The triangle area

This is calculated as

Area = 0.5bh

So, we have

Area = 0.5 * 8 * 6

Evaluate

Area = 24

So, the area of the figure is

Figure = 24 + 71.55

Figure = 95.55

Hence, the area is 95.55

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The centre and the radius of the circle is (-7, -1) and 6 units

The equation of the circle in standard from is expressed as:

x^2+y^2+2gx+2fy+C = 0

where;

(-g, -f) is the centre

r= √g²+f²-C

Given the equation below

x^2+y^2+14x+2y+14 = 0

2g = 14

g = 7

2f = 2

f =1

Hence the centre of the circle is (-7, -1)

Radius = √49+1-14

Radius = √36 = 6 units

Hence the centre and the radius of the circle is (-7, -1) and 6 units

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The zeros and the multiplicities are

from the question, we have the following parameters that can be used in our computation:

f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³

The power of each factor are the multiplicities

So, we have

Zero(s) of multiplicity one:

x - 6 = 0

Zero(s) of multiplicity two:

x - 11 = 0

Zero(s) of multiplicity three:

x + 6 = 0 and x + 5 = 0

When evaluated, we have

Zero(s) of multiplicity one:

x = 6

Zero(s) of multiplicity two:

x = 11

Zero(s) of multiplicity three:

x = -6 and x = -5

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Answer:

2/10ths?

Step-by-step explanation:

then it would be 1/5th

9514 1404 393

Answer:

  k = 4.5

  y = 4.5x . . . y bracelets in x hours

Step-by-step explanation:

The constant of proportionality is the "unit rate", the number of bracelets per hour.

  k = bracelets/hours = 36/8 = 4.5

The constant of proportionality is 4.5 (bracelets per hour).

__

The equation of a proportional relationship is ...

  y = kx

For this relationship, ...

  y = 4.5x . . . . . . y bracelets in x hours

Edith made about 97/70 cups of trail mix. The solution has been obtained by using ratios.

What is a ratio?

A ratio is produced by comparing or compressing two related bits of data. By counting the reciprocity of the relationship, we can determine the frequency with which one quantity equals another. A ratio is a number that can be used to show how much one thing is in comparison to another, to put it simply.

We are given that Edith made a bag of trail mix with 1/2 cup of ​pecans, 3/5 cup of apple slices, and 2/7 cup of pumpkin seeds.

So, the total amount of trail mix is:

⇒1/2 cup of pecans + 3/5 cup of apple slices + 2/7 cup of pumpkin seeds

⇒1/2 + 3/5 + 2/7

⇒(35 + 42 + 20)/70

⇒97/70

Hence, Edith made about 97/70 cups of trail mix.

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Answer:

Step-by-step explanation:

The problem specifies that you may use a calculator. The formula, as reference, is:

You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).

So the answers:

25th percentile is 34.

80th percentile is 48.4.

Answer:

ok

Step-by-step explanation:

ok fjFjxggkgclclcchlclcullcucuclcvuullulj

Answer:

where is x

Step-by-step explanation:

Answer:

If it is (3x+12) then the answer is 19.5

Step-by-step explanation:

The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.

We have,

Cylinder and prism.

Here we have to find the equivalent ratio to 8/2.

First simplifying the given ratio as

8/2

= (4 x 2)/2

= 4 /1

Now, some more ratios equivalent to 8/2.

1. 8/2 x 3/3 = 24/ 6

2. 8/2 x 4/4 = 32/8

3. 8/2 x 6/6= 48/12

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Answer:

Step-by-step explanation:

Given the functions f(x) = x² -3x -10 and g(x) = x +2, you want the values of ...

Using the values from the attached table, we find ...

  (f+g)(2) = f(2) +g(2) = 0 +4 = 4

  (f-g)(-1) = f(-1) -g(-1) = -12 -1 = -13

  (f×g)(1) = f(1)×g(1) = (-6)×(3) = -18

  (f/g)(4) = f(4)/g(4) = 18/6 = 3

The Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively.

If the spinner is fair, then each color must have the same probability,

this means that the probability for each color is the number of times that the color (in this case blue) is in the spinner divided by the total amount of colors in the spinner, then the theoretical probability for each color is:

Pt = 1/5 = 0.20

The experimental probability can be found by dividing the number of times that the spinner landed on a given color (in this case for blue we have 15 times) divided by the total number of spins ( 50)

Pe = 15/50 = 0.30

Therefore, the Experimental probability and the theoretical probabilities are 0.2 and 0.3 respectively

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Complete question:

A spinner has 5 equal-sized sections with different colors. You spin the spinner 50 times. The results are shown in the table. Find the theoretical and experimental probabilities of spinning blue.

Red Green Blue Yellow Orange

8           11      15       9          7

The theoretical probability is

The experimental probability is