7)
3)
5)
Determine if the two triangles are congruent. If they are, state how you know.
2)
1)
A
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The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.

A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.

Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.

Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.

If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:

7 : (23 + 7) = 7 : 30

You can simplify the ratio to 7/30 or approximately 0.23 or 23%.

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The answer to our inquiry is that 180 grams of zinc contain a particular compound.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare another data item (A) to this other data point (B).

The zinc to copper ratio in a particular compound is 4: 11.

Copper weighs 495 grammes in the chemical.

How much zinc does it chemically contain in grammes.

Assume that y is the scalar multiple of zinc and copper.

as stated

The proportion of zinc over copper in a certain compound is 4 to 11.

Copper weighs 495 g in the chemical.

Equation is than

11y = 495

11y = 495

y = 495/11

y = 45

Zinc in a particular chemical = 4y

= 4x45

= 180 grams

Therefore 180 grams of zinc contain in a certain chemical .

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Step 1: Calculate the length of one platter. To calculate the length of one platter, multiply 0.4 meters by 4 sides, which gives us a total of 1.6 meters.

Step 2: Calculate the length of the row of platters. To calculate the length of the row of platters, multiply the length of one platter (1.6 meters) by the number of platters (7), which gives us a total of 11.2 meters.

Therefore, the row of platters is 11.2 meters long.

What exactly are algebraic word issues? The process of converting phrases into equations and then solving those equations is known as solving algebraic word problems. a single variable, and. In a real-world situation, the variable typically stands for an unknowable quantity.

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Answer:

3x+5y = -13

Step-by-step explanation:

Since there are two variables, you must solve for one of them first. One way we can do that is through elimination.

X seems the easiest to eliminate.

We can subtract the two equations.

 x - 4y = -10
- 2x+9y = -3

If we subtract it like this, it wouldn't eliminate any variables. So, let's multiply the first equation by 2 so both equations have 2x.

 2x - 8y = -20
- 2x+9y = -3
Now, subtract the equations.

-17y = -17

We can solve for y now.

y = 1

Since we have y's value, we can solve for x. Plug y back into one of the equations.

x - 4(1) = -10

x - 4 = -10

x = -6

Now that we have both the x and y values, simply plug it into 3x+5y.

3(-6) + 5(1)

-18 + 5
-13

So the answer is -13

The domain of the function is all real numbers , except x = 0

The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.

The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.

Given data ,

Let the domain of the function be represented as D

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

When the value of the x of function approaches zero from the positive direction , the function f ( x ) gets larger

And , when the value of the x of function approaches zero from the negative direction , the function f ( x ) gets larger in the negative direction

Now , the domain of the function will be all the real numbers except 0

Hence , the domain of the function is all real numbers except 0

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When data are positively skewed, the mean will be greater than the median.

This is because the mean will be pulled in the direction of the higher values in the data set, while the median will ignore the higher values and be more affected by the lower values in the data set.

Positively skewed data is characterized by a long tail on the right side of the distribution graph. This means that the data set contains more values that are higher than the mean and median. As a result, the mean will be a higher value than the median, as the mean will be pulled in the direction of the higher values. The median, however, will remain unaffected by the higher values and will be more affected by the values at the lower end of the distribution.

the complete question is :

When data are positively skewed, the mean will usually be:

a. greater than the median

b. smaller than the median

c. equal to the median

d. positive or negative depending on the data set

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The mean (expected value) of X is 3.48, and the standard deviation of X is 1.27.

The mean or expected value of X, representing the number of games the team might win, can be calculated using the formula:

E(X) = n * p

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, E(X) = 6 * 0.58 = 3.48

The standard deviation of X, representing the spread of the distribution, can be calculated using the formula:

SD(X) = √(n * p * (1 - p))

where:

n = number of games (6)

p = probability of winning each game (0.58)

So, SD(X) = √(6 * 0.58 * (1 - 0.58)) = 1.27

Therefore, the mean of X is 3.48, and the standard deviation of X is 1.27.

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Answer:

(x - 2) is not a factor of f(x)

Step-by-step explanation:

We can use the Remainder Theorem to check if (x - 2) is a factor of f(x) = x^3 - 2x^2 + 2x + 3.

The Remainder Theorem states that if we evaluate a polynomial at a specific value and the result is zero, then that value must be a root of the polynomial and therefore the polynomial can be divided by the corresponding linear factor.

So, if we plug in x = 2 into f(x), we get:

f(2) = 2^3 - 2 * 2^2 + 2 * 2 + 3

= 8 - 8 + 4 + 3

= 7

Since f(2) is not equal to zero, it follows that (x - 2) is not a factor of f(x).

Alternatively, we could use the Factor Theorem, which states that a polynomial is divisible by (x - a) if and only if f(a) = 0. Since f(2) is not equal to zero, (x - 2) is not a factor of f(x).

Based on the given time; the number the second hand points at are;

There are a total of 12 numbers on a clock starting from 1 and ending at 12

There are 60 strokes or lines with equal spaces on a clock

Each stroke or line represents a second

60 seconds = 1 minutes

1. 15 seconds after 1:00.

= The seconds hand points at 3

2. 30 seconds after 1:00.

The seconds hand points at 6

3. 1 minute after 1:00.

1 minutes = 60 seconds

The seconds hand points at 12

4. 5 minutes after 1:00

5 minutes = 300 seconds

The seconds hand points at 12

Therefore, the seconds hand of the given time points at 3, 6, 12 and 12 respectively.

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The exponential function of the family f(x) = 2^x with a vertical shrink and a translation down 5 units is given as follows:

A. f(x) = 0.5(2)^x - 5.

The parent function is defined as follows:

f(x) = 2^x.

For the vertical shrink, the function is multiplied by a constant that has an absolute value less than one, hence:

f(x) = 0.5(2)^x.

For the translation down 5 units, the number 5 is subtracted from the definition of the function, hence:

A. f(x) = 0.5(2)^x - 5.

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The toddler crawled a total of 24 feet (2 yards = 6 feet and 8 more feet).

The question asks how many feet the toddler traveled. To answer this question you need to convert yards to feet then add the measurements together. One yard is equivalent to three feet, so the toddler traveled two yards which is six feet. The toddler then stopped and continued to crawl eight more feet. To figure out the total distance the toddler traveled, you need to add the two measurements together. Six feet plus eight feet is equal to fourteen feet. Therefore, the toddler traveled a total of twenty-four feet.

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Answer: No Solution

Step-by-step explanation: When you use the elimination method on second equation by multiplying it by 2 you get two equations that add up to a different solution. Since the variable coefficients are the same on both, there will be no solution.

The average rate of change of the function over the interval -2 ≤ x ≤ 4 is given as follows:

4.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The two points in this problem are given as follows:

(-2, -3) and (4,21).

Hence the change in the output is of:

21 - (-3) = 24.

The change in the input is of:

4 - (-2) = 6.

Hence the rate is of:

24/6 = 4.

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Answer: How can you tell whether X and Y are proportional?

Step-by-step explanation: How can you tell whether X and Y are proportional?

To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional. please select brainiest if right

Yes, Ernesto has enough oil to make both recipes. Each recipe calls for 1/3 cup of oil, and he has one cup of oil. Therefore, he has enough oil to make both recipes with some oil left over.

The statement that best describes the area of the triangle is:

It is one-half the area of a square of side length 4 units.

Option B is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle:

The base is 4 units, and the height is 4 units.

Area of the triangle.

= 1/2 x base x height

= 1/2 x 4 x 4

= 8 units²

Now,

a)

It is one-half the area of a rectangle of length 4 units and width 2 units.

This is not possible since we do not have 2 units.

b)

It is one-half the area of a square of side length 4 units.

Area of a square.

= Side²

= 4²

= 16 units²

So,

1/2x 16 = 8 units²

This is true.

c)

It is twice the area of a rectangle of length 4 units and width 2 units.

This is not possible since we do not have 2 units.

d)

It is twice the area of a square of the side length of 4 units.

This is not possible.

Thus,

It is one-half the area of a square of side length 4 units.

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Answer:

CD = 6.3

Step-by-step explanation:

triangles CFG and CDE are similar, so their side lengths are proportional

this means CD/CF = CE/CG

since we don't know CF, we need to first solve for CF in order to find CD

luckily, we know CD = CF + FD, and FD is given:

CD/CF = CE/CG -> (CF + FD) / (CF) = CE/CG

multiply both sides by CF to get CF + FD = CE * CF / CG

move the terms with CF to one side, and the constants to the other side:

CF - CF(CE/CG) = -FD

solve for CF:

CF(1-(CE/CG)) = -FD, CF = FD / ((CE/CG) - 1) = (1.8)/(((2.4+6)/(6)) - 1) = 4.5

Since CD = CF+FD, CD = 4.5 + 1.8 = 6.3

Alex will not be able to complete his job. According to the measurement given for the coil, the electrician will not be able to complete the job.

The circumference of the coil of wiring can be calculated with

C= 2πr

where r is the radius and π= 3.14

The radius can be calculated by dividing the diameter by 2. Then:

r= 18 inches ÷ 2

r= 9 inches

Convert 9 inches to yards (1 yard= 36 inches)

(9 inches)(1 yard ÷ 36 inches) = 0.25 yard

Substitute this radius into the formula:

C= 2(3.14)(0.25 Yard)

C= 1.57 Yard

Since there are 21 circles of wire, we need to multiply C= 1.57 yards by 21

C = (1.57 Yard)(21) = 32.97 Yard

The coil has 32.97 yards of wire and Alex needs 34 yards, therefore, this coil will not be enough to complete the job.

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The system is inconsistent.

The two lines are parallel and never intersect.

====================================================

Work Shown:

Solving the 1st equation for y.

3x-y=18

-y=18-3x

y = -(18-3x)

y = -18+3x

y = 3x-18

Plugging that into the other equation to solve for x.

-2y=-6x-120

-2(y)=-6x-120

-2(3x-18)=-6x-120

-6x+36=-6x-120

-6x+6x=-120-36

0x = -156

0 = -156

We arrive at a false statement.

Therefore, this system has no solutions

The system is inconsistent.

If you were to use a graphing tool like Desmos or GeoGebra, then you'll see the two lines are parallel. They never intersect to form a solution.

Answer & Step-by-step explanation:

To find the total rental cost, we need to add the flat fee to the mileage charge. Here are the steps:

1. Multiply the number of rental days by the flat fee: 3 days x $25/day = $75

2. Multiply the total miles driven by the mileage rate: 150 miles x $0.20/mile = $30

3. Add the flat fee and the mileage charge to get the total cost: $75 + $30 = $105

Therefore, the customer's total rental cost is $105.

Answer:

105$

Step-by-step explanation:

The correct option regarding the number of solutions of the sustem of equations is given as follows:

No solution.

We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.

The line going through points (0,4) and (3,3) is given as follows:

y = -0.33x + 4.

The line going through points (0,-1) and (3,-2) is given as follows:

y = -0.33x - 1.

The two functions have the same slope, hence they are parallel lines, and thus the number of solutions is of zero.

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Common theorems, properties, or strategies to the proof of the Triangle Proportionality Theorem and its converse include using similarity and congruence, angle-angle criterion, and transitive property of equality.

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the ratio of the lengths of the intersecting lines is equal to the ratio of the lengths of the corresponding sides of the triangle.

The converse of the Triangle Proportionality Theorem states that if two pairs of corresponding sides in two triangles are proportional, then the two triangles are similar.

Overall, these theorems, properties, and strategies form the basis for proving both the Triangle Proportionality Theorem and its converse, and they are used to establish the relationships between the lengths of sides and angles in triangles.

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Step-by-step explanation:

The difference in elevation between the bottom of the canyon and the bird's nest is 504 1/2 - (-62 2/5) = 504 1/2 + 62 2/5 = 566 5/5 = 566 feet

Answer:

Step-by-step explanation:

Say sea level is 0.

Bottom of the canyon is -62.4ft and bird's nest is 504.5ft

Subtract.

504.5 - 62.4 = 442.1ft

Answer:

The Value of R is 20%.

Step-by-step explanation:

Let R be the interest rate (in percentage) per year. The interest earned after one year would be R% of £8,500, which is (R/100) * £8,500 = £(R * 85)/100.

After paying tax, the amount Nick receives would be (R * 85)/100 * (100 - 30)/100 = £(R * 85 * 70)/10000.

Since Nick receives £166.60 after paying tax, we have:

£(R * 85 * 70)/10000 = 166.60

Solving for R, we get:

R = (10000 * 166.60) / (85 * 70) = 20.0.

Therefore, the interest rate R is 20%.

Answer:

  12/37

Step-by-step explanation:

Given right triangle ABC with sides AB=37, BC=12, and CA=35, you want the cosine of angle B.

The cosine of an angle in a right triangle is ...

  Cos = Adjacent/Hypotenuse

The leg adjacent to angle B is BC=12. The hypotenuse is AB=37.

Using these values, the cosine of B is ...

  cos(B) = BC/BA

  cos(B) = 12/37

Answer:

The minimum value of C is 14

Step-by-step explanation:

Sketch the graph of the constraints using

2x + y = 20

with intercepts (0, 20) and (10, 0)

2x + 3y = 36

with intercepts (0, 12) and (18, 0)

The solution to both are above the lines

Solve 2x + y = 20 and 2x + 3y = 36 to find the point of intersection at (6, 8)

Then the coordinates of the vertices of the region formed are

(0, 20), (6, 8) and (18, 0)

Evaluate the objective function at each vertex to determine minimum value

C = 0 + 20 = 20

C = 6 + 8 = 14

C = 18 + 0 = 18

Thus the minimum value of C is 14 when x = 6 and y = 8

Hope this helped to get you answer!

The playground's length and breadth are 12 yards and 17 yards, respectively.

The playground's area is 204 square yards, according to the statistics provided in the inquiry.

204 square yards is the area.

The playground's breadth is 5 yards more than its length.

Let the playground be 'l' yards long.

The playground's width will then be (l + 5) yards.

The formula for the playground area is Length × Width.

A =  Length x width

204 = l (l + 5)

204 = + 5l

+ 5l - 204 = 0

+ 17l - 12l - 204 = 0

l (l + 17) -12 (l + 17) = 0

(l + 17) (l - 12) = 0

(l + 17) = 0 or (l - 12) = 0

l = -17 or l = 12

The length value cannot be negative.

As a result, the length is 12 yards.

The breadth is thus equal to l + 5.

Width = 12 + 5

17 yards wide

As a result, the length is 12 yards and the breadth is 17 yards.

Option (b) is the right answer.

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A playground has a surface area of 204 yd2. The playground's breadth is 5 yards greater than its length. Determine the playground's length and breadth.

a.) 17 yards in length, 22 yards in breadth

b.) 12 yard length, 17 yard breadth

c.) 22 yard length, 17 yard breadth

d.) 17 yard length, 12 yard breadth

The quotient to the expression is 1/64

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: The expression 4⁻⁵ / 4⁻²

When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

Thus simplifying the expression we get

4⁻⁵ / 4⁻²

4⁻⁵× 4²

4⁻⁵ ⁺ ²

4⁻³

1/64

Thus the quotient is 4⁻³

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