Right triangles MNP and QRS are congruent. Right triangles M N P and Q R S are shown. The length of side Q S is 8 meters. The length of M N is 17 meters and the length of P N is 15 meters. What is the area of △MNP? 40 m2 60 m2 68 m2 127.5 m2

Answer:

B.  x + 10 ≥ 70;  x ≥ $60

Step-by-step explanation:

Given:

The equation that models the given parameters is:

To solve for x, subtract 10 from both sides of the equation:

\(\implies x+10-10 \geq 70-10\)

\(\implies x \geq 60\)

Therefore, Kelvin needs to withdraw at least $60 from the bank.

The total amount it costs Jeff and Valerie to fill up their vehicles.

The correct option is D.

bx is most likely the amount it costs Jeff and Valerie to fill up their cars because they both pay x dollars per gallon.

Ay = Megan Bx

= Valerie and Jeff

Ay + Bx = Megan + Valerie and Jeff

Algebra is a field of mathematics that assists in the depiction of problems or situations using mathematical expressions. To produce a meaningful mathematical expression, variables like as x, y, and z are used, as well as mathematical operations such as addition, subtraction, multiplication, and division.

Working from left to right, first complete multiplication and division, then addition and subtraction.

The principles of algebra include numbers, variables, constants, expressions, equations, linear equations, as well as quadratic equations.. It also includes basic mathematical operations such as addition, subtraction, multiplication, and division within algebraic equations.

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Answer:

p = - 115

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

px - 5y = 60 ( subtract px from both sides )

- 5y = - px + 60 ( divide all terms by - 5 )

y = \(\frac{1}{5}\) px - 12 ← in slope- intercept form

with slope m = \(\frac{1}{5}\) p , thus

\(\frac{1}{5}\) p = - 23 ( multiply both sides by 5 to clear the fraction )

p = - 115

Answer:

257.8

Step-by-step explanation:

The angle of 4.5 radians is approximately equal to 257.8 degrees.

The formula to convert radians to degrees is written as follows:

degrees = radians x (180/π)

where π (pi) is approximately 3.14159.

To convert 4.5 radians to degrees, we can use the conversion factor 180/π, which is the number of degrees in one radian.

degrees = 4.5 x (180/π)

degrees ≈ 257.87 degrees (rounded to the nearest 10th).

Therefore, the angle of 4.5 radians is approximately equal to 257.8 degrees.

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Step-by-step explanation:

Here in the given figure b and 30° are alternate to each other so it can be name as alternative angle....

b = 30°

Now...

a + 30° = 180° ( being supplementary angle )

a = 180° - 30°

a = 150°

Now the value of c will be 150° being corresponding

angle with a

c = 150°

z = 60° ( being alternative angle )

Now let's find the value of x.....

here ,

60° + 50° + x = 180° ( the sum of interior angle of triangle is 180°

x = 180° - 110°

x = 70°

Now...

y = 70° ( alternative angle )

\(....\)

Answer:

2x radius I believe

Tell me if im wrong and I will remove this

Answer:

\(m=-7\)

\(n=3\)

Step-by-step explanation:

A parallelogram has two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.

Therefore we can say that

\(9m+21=15m-21\)

\(3n+38=11n+14\)

Lets solve the first equation for \(m\).

Subtract \(15m\) from both sides.

\(9m+21-15m=-21\)

Subtract \(15m\) from \(9m\).

\(-6m+21=-21\)

Subtract \(21\) from both sides.

\(-6m=-42\)

Divide both sides by \(-6\).

\(m=\frac{-42}{6}\)

\(m=-7\)

Lets solve the second equation for \(n\).

Subtract \(3n\) from both sides.

\(38=8n+14\)

Subtract \(14\) from both sides.

\(24=8n\)

Divide both sides by \(8\).

\(n=3\)

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Answer:

19/5

Step-by-step explanation:

Aquí, queremos escribir el número total de millas que Hans corrió en forma de una fracción impropia.

Para hacer esto, agregamos todas las millas recorridas.

Matemáticamente, eso sería 3 + 4/5 = 3 4/5 Esta es la forma de fracción mixta.

La fracción impropia es así (5 * 3) + 4/5 = 19/5

Answer:

\(32\frac{1}{2}\)

Step-by-step explanation:

Typically, to find the slope of the line we use the formula \(\frac{y2-y1}{x2-x1}\) where y2, y1, x2, and x1 are the point's coordinates. Since the expression is already written for us, we just have to evaluate.

\(\frac{325-162.5}{10-5}\)

Evaluate

\(\frac{162.5}{5}\)

We cannot use decimals for our slope so we need to convert 162.5 into a fraction.

\(\frac{162\frac{1}{2}}{5}\)

Evaluate further

\(32\frac{1}{2}\)

The slope is \(32\frac{1}{2}\)

The angle in degrees south of east, is a line connecting your starting point to your final position is 144.46°.

The displacement vector represents the displaced distance along with the direction of displacement. The initial point of the displacement is represented by a tail of a vector arrow whereas, the final point is represented by the arrowhead. Assume i walk 17.5 m straight west and then 24.0 m straight north. Let vectors A and B denotes the displacement. The total displacement, R is determined by adding both vector and direction is θ. So, \( \vec R = \vec A + \vec B\)

\( \vec R = −17.5 \hat{i} + 24 \hat j\)

The magnitude of the displacement vector is denoted by,

\(| \vec R |= \sqrt{{ (- 17.5)}^{2} + {24}^{2} } = \sqrt{882.25} = 29.70 \\ \)

The angle of displacement is given by,

\(θ={tan}^{- 1} ( \frac{24}{ - 17.5}) \)

From the above diagram, the displacement is at − 54.46° , which is in the west-north direction in the compass. Let the south of east angle be φ. Now, the angle south of east is φ = 180° - 90° - θ Hence required angle is 90° + 54.46° = 144.46°.

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Complete question:

Suppose you walk 17.5 m straight west and then 24.0 m straight north. At what angle, in degrees south of east, is a line connecting your starting point to your final.

The distance between the shores A and B is 250 meters.

Width of the river= D

Distance covered by boat A and B= a and b

Distance covered by A and B =Width of the river for the first meet.

D = a + b..............(1)

Hence:

b = 100 meters.............(2)

Sum of the distances traveled is 3times with width of the river  as  they both went 3 times after they first passed.

Second time= 50 meters

Hence:

3a = D+ 50...........(3)

Put the value of equation 2 into equation 1

3 ×100 = D+ 50

D=300-50

D =250 meters

Therefore the distance between the shores A and B is 250 meters.

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Answer:

It is C

Step-by-step explanation:

Got it right in edg

Answer:

A piece of charcoal was unearthed at an archeological site and found to contain 10% of its original carbon-14. The half-life of carbon-14 is 5,730 years. This means that after 5,730 years, only half of the original amount of carbon-14 will remain.  Which equation can be solved to determine the age of the charcoal?

C on edg

Step-by-step explanation:

The sampling distribution of the sample mean would have a mean of 112 pounds and a standard deviation of 1.4142 pounds.

The sampling distribution of the sample mean would follow a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Given that the population mean weight is claimed to be 112 pounds and the population standard deviation for the mean weight is claimed to be 20 pounds, the sampling distribution of the sample mean would be:

Mean of the sampling distribution = Population mean = 112 pounds

Standard deviation of the sampling distribution = Population standard deviation / Square root of sample size

= 20 pounds / sqrt(200)

= 1.4142 pounds

Therefore, standard deviation of the sampling distribution is 1.4142

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The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

it takes about 2.79 seconds for the object to hit the ground

Step-by-step explanation:

t√h/4

h=125 feet

t=√125/4=√25×√5/4

t=5√5/4=11.18/4

t=2.79 secs

it takes the object 2.79 seconds to

hit theground

hope this helps. kindly give a feedback if you need more help..

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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Answer: We can use the Pythagorean theorem to solve this problem, which states that in a right 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.

In this case, we have:

a = -10

b = 24

c = ?

Using the Pythagorean theorem, we can solve for c:

c^2 = a^2 + b^2

c^2 = (-10)^2 + 24^2

c^2 = 676

c = sqrt(676)

c = 26

Therefore, the length of the missing side of the right triangle is 26 units.

The length of the missing side of the right triangle is 26.  To find the length of the missing side of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).

The formula is:

\(c² = a² + b²\)

In this problem, a = 10 and b = 24. To find the length of the missing side (the hypotenuse, c), we can plug these values into the formula:

c² = 10² + 24²
c² = 100 + 576
c² = 676

Now, we take the square root of both sides to find the length of the missing side:

c = √676
c = 26

So, the length of the missing side (the hypotenuse) of the right triangle is 26.

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Answer:

y = -5/6 x - 7

Step-by-step explanation:

A line is shown with points (0, -7) and (-2, -6).

y = mx + b

m = -5/6; b = -7

y = -5/6 x - 7

The type I error for the hypothesis test in this scenario would be rejecting the null hypothesis, which states that the average attendance at games is not over 67,000, when it is actually true.

In hypothesis testing, a type I error, also known as a false positive, occurs when the null hypothesis is incorrectly rejected, and a significant result is obtained even though the null hypothesis is actually true. In this case, the null hypothesis would state that the average attendance at games is not over 67,000, meaning the owner's claim is not supported.

However, if the null hypothesis is rejected based on the sample data, and the owner decides to move the team to a city with a larger stadium based on this result, it would be a type I error if the actual average attendance is indeed not over 67,000. This would mean that the owner made a decision to move the team based on an incorrect rejection of the null hypothesis, leading to an erroneous conclusion.

Therefore, the type I error in this hypothesis test would be rejecting the null hypothesis and moving the team based on the claim of an average attendance over 67,000, when in fact the null hypothesis is true and the average attendance is not over 67,000

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The value of n in the given congruent triangle is 6.

Congruent triangles have the same corresponding angle measures and side lengths.

Given that two congruent triangles, Δ ABC ≅ Δ XYZ,

Since, we know that, corresponding parts of congruent triangle are equal,

Therefore,

AB = XY

5n+8 = 38

5n = 30

n = 6

Hence, the value of n in the given congruent triangle is 6.

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Answer:

50

Step-by-step explanation:

Answer:

23.6 degrees

Step-by-step explanation:

The expression is evaluated to 1/9. Option D

We need to know that index forms are described as mathematical forms used in the representation of number or variables that are too large or too small in more convenient forms.

Also, other names for these index forms are scientific notation and standard forms.

From the information given, we have that;

\(3^-^\sqrt[3]{8}\)

Now, find the cube root of the exponent with value of 8, we have;

∛8 = 2

Substitute the value, we have;

3⁻²

Express as a fraction, we get;

1/3²

Find the square of the denominator

1/9

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Answer:

2(8 x 4) + 2(4 x 10) + 2(8 x 10)

Step-by-step explanation:

the expression represents the surface area, because it is finding the area of the three different sizes of sides, doubling them, then adding them together

The empty squares in the addition chain can be completed thus:

1. 3 + 0 + 11 = 14

2. -1 + 5 = 4

3. -9 + 1 + 2 = -6

For the middle part;

1. 14 + 4 = 18

2. 4 + (-6) = -2

For the last part;

18 + (-2) = 16

In order to complete the empty squares, a knowledge of the additive inverse will be required. This states that + x - x = 0. In that vein, we can calculate the negative and positive figures aright.

For instance, in the third square, we have an equation of this sort:

-9 + 1 + x = -6

Now, we know that -9 + 1 is equal to -8

The expression becomes;

-8 + x = -6

Make x the subject of the formula:

x = -6 + 8

x = 2.

Now we can fill in the missing box with the figure 2.

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Answer:

division

you divide 3 into 12 getting you 4=y

According to the solving the value of a and b of the X² - 4X - 21 equation are:

a = -2

b= -25

A quadratic problem is a sort of problem in mathematics that deals with either a variable multiplied by itself – a process known as squares. The area of a square is defined as its side length multiplied by double itself in this language.

 In everyday life, we employ quadratic formulas to calculate areas, determine the profit of a product, or calculate the velocity of an object. Furthermore, quadratic equations are defined as equations with at least one squared variable.

X² - 4X - 21

Expand to check:

For a.

(X - 2)² - 4 - 21 = (X - 2)² - 25

                       = X² - 4X + 4 - 25

                       = X² - 4x -21

                       =  (X - 2)² - 25

a = -2 , b = -25

For b.

X² - 4X - 21 = (X - 2)² - 25 due to part a we can say that:

(X - 2)² - 25 = 0

X - 2 = ± 25

x  = 7 , X = -3

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Step-by-step explanation:

if

c = 3 + 6 = 9

and

n = 4 + 5 = 9

then it could be true