4. Solve for x ONLY *
Find the value of each variable.

The triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

We have,

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given that YO = NZ.

Consider YO = NZ

Now Add OZ on both sides

YO + OZ = NZ + OZ

YZ = NO

Consider triangles Δ MNO and ΔXYZ.

M ≅ X

N ≅ Y

YO ≅ NZ

Δ MNO ≅ ΔXYZ by AAS postulate.

Therefore, the triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

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complete question:

The congruency of △MNO and △XYZ can be proven using a reflection across the line bisecting OZ. However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Given: M ≅ X

N ≅ Y

YO ≅ NZ

Prove: △MNO ≅ △XYZ

We need 4608 cubes to fill the rectangular prism.

We have,

The rectangular prism has a volume of:

Volume = length x width x height

Volume = 8 in. x 4 in. x 2 1/4 in.

Volume = 72 in³

Each cube has a volume of:

Volume of cube = edge length³

Volume of cube = (1/4 in.)³

Volume of cube = 1/64 in³

To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of each cube:

Number of cubes = Volume of prism / Volume of a cube

Number of cubes = 72 in³ / (1/64 in³)

Number of cubes = 72 in³ x 64 / 1

Number of cubes = 4608 cubes

Therefore,

We need 4608 cubes to fill the rectangular prism.

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The length of the shorter side of the room is 3.2 inches

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

A rectangular room is 28 feet by 32 feet.

So, the perimeter is

P = 2 * (28 + 32)

Evaluate

P = 120

So, the scale factor from the room to the drawing is

Scale factor = 12/120 i.e. division of perimeters

So, we have

Scale factor = 1/10

The small length of the room is 32 feet

So, we have

Smaller length = 1/10 * 32

Smaller length = 3.2 inches

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The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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The Explanation of decimal place value is like place value with whole numbers is shown below.

We know,

Each place value to the left of a whole number is multiplied by ten, but a place value to the right of a decimal number is divided by ten.

For example,

We take whole number 254 where place values are

2- Hundred, 5- Tens and 4- Ones

and, take the decimal 2.369 where the place values are

3- Tenth, 6- hundredth and 9- thousandth

So, both decimal and whole number have similar concept of place value but one is multiplied by 10 and other is divided by 10.

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The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the volume of the sphere is 10000 m³, we can set up the equation:

Volume =  (4/3)πr³

r³ = Volume / (4/3)π

r = ∛( Volume / (4/3)π )

r = ∛( 10000/ ( (4/3) × 3.14) )

r = 13.4 m

Therefore, the radius is 13.4 m.

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The correct statements about the circle equation are:

Remember that the general circle equation is:

(x - a)² + (y - b)² = R²

Where (a, b) is the center and R is the radius.

Here the given equation is.

x² + y² - 2x - 8 = 0

We can complete squares in x to get:

(x - 1)² - 1 + y² - 8 = 0

(x - 1)² + y² = 9

(x - 1)² + y² = 3

So, the center is (1, 0) and the radius is 3.

The correct statements are:

The radius of the circle is 3 units.

The standard form of the equation is (x – 1)² + y² = 3.

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The x-coordinate of A” is 2

Here, we want to know;

the x-coordinate of the rotation about the origin of a point 90 degrees clockwise.

A rotation of 90 degrees clockwise about the origin will turn the coordinates (x, y) to (-y, x)

Here, The coordinates of A is (3,-2)

So, upon the assigned rotation, it becomes;

A'' = (2,-3)

So, the x-coordinate of A” is 2

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Result:

The number of children having an age of 6 1/2 years more than 7 1/4 years = 3/4.

To do this, we would subtract the number of children who are 7 1/4 years old from the number of children who are 6 1/2 years old: x - y

Let x = number of children 6 1/2 years old

Let y = number of children 7 1/4 years old

x = 6 1/2 years or 13/2 years

y= 7 1/4 years or 29/4 years

= 13/2 - 29/4

= (26/4) - (29/4)

= -3/4

Coverting to the absolute value, we get:

|-3/4| = 3/4

Thus, 3/4 more children are 6 1/2 years old than 7 1/4 years old.

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The numerical value of the algebraic expression 1.5 × 6 + 8.3 is 17.3; The factors are 1.5 and 6 & the terms: 1.5 * 6 and 8.3

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

1.5 × 6 + 8.3

The above expression is an algebraic expression and as such the parts of the expressions are

When the expression is evaluated, we have

1.5 × 6 + 8.3 = 17.3

This means that the result of evaluating the expression 1.5 × 6 + 8.3 is 17.3

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The product of the expression is given as  1/4x²y²

Remember that an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). It can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient

The given expression is  (3x⁵y²)/(xy)  * (6xy²) / (9x³y)

Multiply through to have

{(3x⁵y²)(6xy²)} / {(xy)(xy)}

⇒( 18x⁶y⁴) / (72x⁴y²)

Simplify to get

Therefore the value of the expression is 1/4x²y²

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Answer: f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Step-by-step explanation: Using the given recursive formula:

f(1) = 0

f(n) = f(n-1) + 2

We can find the values of f(n) for different values of n:

f(1) = 0

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

f(5) = f(4) + 2 = 6 + 2 = 8

And so on.

We can see that each term in the sequence is 2 more than the previous term. So, we can write the general formula for f(n) as:

f(n) = 2n - 2

Therefore, we can use this formula to find the value of f(n) for any positive integer n.

Answer:

  $264

Step-by-step explanation:

You want to know Jenny's annual finance charges if her credit card balance averages $1100 and her interest rate is 24%.

The annual interest charge will be the product of the annual interest rate and the average balance over the course of the year.

  24% × $1100 = $264

Jenny spends about $264 per year on credit card interest.

Answer:

May is 52 inches tall

Step-by-step explanation:

stephan=46in

sister=6+stephan(in inches)=6+46=52

The volume of a rectangular prism would be 100 cubic cm.

Since we know that rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

We are given that base of a rectangular prism is 20 cm sq. . If the height of the prism is 5 cm, then;

Base area = 20 cm sq.

Height = 5 cm

Volume of a rectangular prism=Length X Width X Height

Volume of a rectangular prism= Base area  X Height

Volume of a rectangular prism= 20 x 5

= 100

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Answer: 2 2/3+ 8

Step-by-step explanation: it goes 2 under the ten

Answer:

See provided explanation

Step-by-step explanation:

Slope=change in y/change in x

General equation for a line: y=mx+b

You know that the slope(m) is 8/3, and the y-intercept is 8. So your graph will intersect the y axis at the point (0,8). from there, use slope=rise/run to graph the remaining points. Starting at (0,8), move 8 up and 3 right, this is your next point. Do the same in the other direction, starting at (0,8) move down 8 and left 3 points. Doing this will get you the points (-3,0) and (3,16). repeat this process until you have enough points to form a line. I attatched a picture of what the graph should look like.

The expected number of lefties top ranked baseball players in a sample of 15 top ranked baseball players, obtained from the 1 to 3 ratio of lefties to righties top ranked baseball players is 5 top ranked baseball players

A ratio is a quantitative comparison between two values that indicates the number of times one quantity is contained in or can contain the other value or quantity.

The ratio or proportion of left handed top ranked baseball players = 1 in 3

Therefore, the ratio of lefties to righties top ranked baseball players = 1 : 3

The number of top ranked baseball players in the sample = 15

The number of the top ranked baseball players in the sample that are left handed is therefore;

Number of left handed baseball players in the sample = (1/3) × 15 = 5

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Answer:  B. 78

Step-by-step explanation:

Given:

BC=CD

all the other sides of each triangle are radii, so they are all equal the 2 triangles are congruent.

>Both angles A =78

An angle from the radius is the same as the arc angle it creates.

The arc angle is double only if the angle touches the end of the circle not the radius.  that's why it's not 156

So, <BAC =78   so arc angle BC=78

The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

We have,

To construct a 96% confidence interval about the population mean(μ) with a sample size of n = 57,

we can use the following formula:

CI = x ± z (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, z is the z-score associated with the desired confidence level (96% in this case), and √n is the square root of the sample size.

The z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or calculator.

For a two-tailed test, the z-score is 1.96.

Substituting the given values, we have:

CI = 19.3 ± 1.96 (4.8/√57)

Calculating the standard error of the mean (s/√n):

s/√n = 4.8/√57 ≈ 0.634

Substituting this value into the formula:

CI = 19.3 ± 1.96*0.634

Calculating the upper and lower bounds of the confidence interval:

lower bound = 19.3 - 1.96*0.634 ≈ 18.06

upper bound = 19.3 + 1.96*0.634 ≈ 20.54

Therefore,

The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

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To construct a 96% confidence interval for the population mean, use the formula x ± z*(s/√n) with z being the z-score for the 96% level, x being the sample mean, s being the sample standard deviation, and n being the sample size. Substituting the given values will give the lower and upper bound of the confidence interval.

The question is asking for the construction of a 96% confidence interval for a population mean u, given a sample size (n) of 57, a sample mean (x) of 19.3 and a sample standard deviation (s) of 4.8.

To find the confidence interval, we need to use the formula: x ± z*(s/√n) where z is the z-score associated with our confidence level. For a 96% confidence interval, the z-score is approximately 2.05 (you can find this from a standard z-table).

Substituting the given values into the formula gives: 19.3 ± 2.05*(4.8/√57)

Calculating the above expression will give the lower and upper bound of the 96% confidence interval.

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The interpretation of the slope and y-intercept of this equation is that: C. The slope predicts a temperature increases of about 1/6 for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x = 0), the temperature is 60 degrees.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Since Ronnie determined that the association between the number of chirps per minute (x) that crickets make at different temperatures (y) in degrees Fahrenheit is linear and that the line of best fit is given by;

y = 1/6(x) + 60

By comparison, we have the following:

Slope, m = 1/6.

y-intercept = 60.

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The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.

Let's expect that the round and hollow drum includes a stature of h and a span of r.

The volume of a barrel is given by: V = πr^2h.

We know that the drum includes a capacity of 806 cubic yards, so able to compose:

πr^2h = 806

We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.

The zone of the beat and foot of the drum is given by: A = πr^2.

The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:

C_topbottom = 2A = 2πr^2

The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:

A_side = 2πrh

The whole fetched of building the drum is in this manner:

C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh

Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:

h = 806/(πr^2)

Substituting this expression for h into the taken a toll condition, we get:

C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r

To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:

dC/dr = 4πr - 27404/r^2 =

Fathoming for r, we get:

r = (27404/(4π))^(1/3) ≈ 10.19 yards

Substituting this esteem of r back into the expression for h, we get:

h = 806/(π(10.19)^2) ≈ 2.46 yards

Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:

Span: 10.19 yards

Stature: 2.46 yards

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The requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

There are three ways to write a ratio:

Thus, the requried it's true, that there are 3 ways to write a ratio the word to a colon and a fraction bar.

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Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

The diameter of Earth is about 2.7 times greater than the diameter of Mercury.

We have,

to determine the scale factor

Given the following values

Diameter of Mercury = 4.9×10^3km

Diameter of Earth = 1.3×10^4km

Taking the ratio of the diameters:

Ratio =  1.3×10^3/4.9×10^4

Ratio = 2.7

This shows that the diameter of Earth is about 2.7 times greater than the diameter of Mercury.

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complete question:

The diameter of Mercury is approximately 4.9×103 kilometers. The diameter of Earth is approximately 1.3×104 kilometers. About how many times greater is the diameter of Earth than the diameter of Mercury? 2.7 27 270 2700

Answer:

A. The blue line has the slope with the greatest value. The blue line is the steepest of the lines.

C. The function that describes the area A, in square feet, in terms of x is A(x) = 2x^2 + 9x + 4

To find the area A of a rectangle, you multiply its length by its width. In this case, the side lengths of the rectangle are (x+4) feet and (2x+1) feet. So, we can write the area function A(x) as follows:

A(x) = (x+4)(2x+1)

Now, we'll expand the expression:

A(x) = x(2x+1) + 4(2x+1)

A(x) = 2x2 + x + 8x + 4

Now, combine like terms:

A(x) = 2x^2 + 9x + 4

So, the correct answer is:

C.) A(x) = 2x^2 + 9x + 4

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Answer:

[tex]\huge\boxed{\sf Mean = 11.1 \ hours}[/tex]

Step-by-step explanation:

18, 7, 6, 13, 8, 17, 9

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{18+7+6+13+8+17+9}{7} \\\\Mean = \frac{78}{7} \\\\Mean = 11.1 \ hours\\\\\rule[225]{225}{2}[/tex]

Answer:

11.1

Step-by-step explanation:

The mean is simply the average of a given set of numbers

To find the mean we find the sum of the given numbers and divide that by the number of given values.

Given set of values:

Mean:

The mean of the number of hours the students watched of tv is 11.1 hours

Answer:

-13

Step-by-step explanation:

-6 + 28 ÷ (-4)​

= -6 - 7

= -13

So, the answer is -13

For 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

To find how much sauce and oregano will be needed to make 6 servings, we can use the ratio of sauce to oregano in the recipe.

For 4 servings, the recipe calls for 8 cups of sauce and 1/2 teaspoon of oregano. To find how much sauce and oregano are needed for 6 servings, we can set up a proportion:

sauce : oregano = 8 cups : 1/2 teaspoon = 16 cups : 1 teaspoon

So, for 6 servings, we need:

sauce : oregano = 16 cups : 1 teaspoon

To convert this to cups and tablespoons, we can multiply both sides of the proportion by 3/4:

sauce : oregano = (16 x 3/4) cups : (1 x 3/4) teaspoons

sauce : oregano = 12 cups : 3/4 teaspoon

sauce : oregano = 48 cups : 3 teaspoons

Therefore, for 6 servings, the recipe will need 12 cups of sauce and 3/4 teaspoon of oregano. So, the answer is option A: The recipe will need 12 cups of sauce and three-fourths teaspoons of oregano for 8 servings.

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