Find the area of triangle whose base is 10 cm and height is 12
cm.

The answer choice which represents the image of the line given as in the task content; y = x - 1 under the translation; (x,y) -> (-x, y) is; y = -x -1.

It follows that the image of the line; y = x -1 according to the task content is to be determined under the transformation; (x,y) -> (-x, y).

Since, the transformation in discuss involves; a chance in the polarity of x values, it follows that the transformation indicated is a reflection over the y-axis.

Hence, the resulting image of the line given; y = x-1 is; y = -x -1.

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The probability that the proportion of overweight or obese children in the sample will be greater than 0.57 is less than 50%.

The first paragraph summarizes the answer, stating that the probability is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

In the second paragraph, we can explain the reasoning behind this conclusion. The Central Limit Theorem states that for a large sample size, the sampling distribution of the sample proportion will be approximately normal, regardless of the shape of the population distribution. In this case, the sample was taken in a way that meets the conditions for using the Central Limit Theorem.

Since the population proportion of overweight or obese children is 0.60, any sample proportion below this value is more likely to occur. Therefore, the probability of obtaining a sample proportion greater than 0.57 would be less than 50%. This is because the resulting z-score, which measures how many standard deviations the sample proportion is away from the population proportion, would be negative.

To summarize, the probability of the proportion of overweight or obese children in the sample being greater than 0.57 is less than 50% because 0.57 is less than the population proportion of 0.60, and the sampling distribution is approximately normal.

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Using a system of equations, the numbers of each machine made are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The factory needs to make 54 tables each day, hence:

x + y + z = 54.

The number of dining tables made per day should equal the number of coffee tables, hence:

x = y.

Then, on the first equation:

2y + z = 54.

The number of coffee tables should be three more than the number of end tables, hence:

y = z + 3.

Replacing in the equation 2y + z = 54:

2(z + 3) + z = 54

3z = 48

z = 16.

Then:

The numbers of each machine made are given as follows:

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Answer:

The third triangle is the answer

Step-by-step explanation:

Answer:

answer is c

Step-by-step explanation:

did it

Based on these observations, option (d) 30 seems to be the most reasonable choice for a longer distance down the fairway.

To determine how far down the fairway the ball hits the ground, we need to consider the horizontal range of the golf ball. The range is the horizontal distance traveled by the ball before it hits the ground.

The range can be calculated using the formula:

Range = (Initial Velocity)² * sin(2 * Launch Angle) / g

Where:

Initial Velocity is the initial velocity of the golf ball (180 ft/sec).

Launch Angle is the angle at which the ball is hit off the tee.

g is the acceleration due to gravity (approximately 32.2 ft/sec²).

Since you haven't provided the launch angle for each club, we cannot determine the exact range for each one. However, we can make some general observations based on the given answer choices:

(a) 15: This option implies a lower launch angle, which would likely result in a shorter range.

(b) 20: Similar to option (a), a lower launch angle would generally result in a shorter range.

(c) 25: This option suggests a moderate launch angle, which could correspond to a reasonable range.

(d) 30: A higher launch angle typically leads to a longer range, so this option may result in a greater distance.

Based on these observations, option (d) 30 seems to be the most reasonable choice for a longer distance down the fairway.

However, without specific launch angles for each club, we cannot determine the exact answer.

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Answer:

Replacing x = 1 in the equation above, we have: (4x1) + 22 = 13

=> 5 +22 = 13 => 27 \(\neq\) 13

So 27 is not equal to 13 => x=1 is not a solution to 4x+22 = 13.

Step-by-step explanation:

Answer:

x=-9/4

Step-by-step explanation:

The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is y = 3x + 2

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Line has slope, m = 3, a new parallel line of slope 3 passing through point  (-1, 3)

(y - y₁) = m  (x - x₁)

y - 3 = 3 (x - -1)

y = 3x + 1 + 3

y = 3x +  4

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now, we're assuming the interest is compound interest with a 7.5 APR or namely 7.5% compounding annually, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$7600\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years \end{cases}\)

\(7600=600\left(1+\frac{0.075}{1}\right)^{1\cdot t}\implies \cfrac{7600}{600}=1.075^t\implies \cfrac{38}{3}= 1.075^t \\\\\\ \log\left( \cfrac{38}{3} \right)=\log(1.075^t)\implies \log\left( \cfrac{38}{3} \right)=t\log(1.075) \\\\\\ \cfrac{\log\left( \frac{38}{3} \right)}{\log(1.075)}=t\implies {\LARGE \begin{array}{llll} 35.11\approx t \end{array}}\qquad \textit{about 35 years and 40 days}\)

We can conclude that they form a right triangle

So GF = FH

OF^2 = GF^2 + OG^2

OF^2 = 8.4^2 + 8^2

OF^2 = 70.56 + 64

OF^2 = 134.56

OF = 11.6

Answer: D. Population: all the first-year students at the university

Sample: a group of 185 incoming first-year students

Conclusion: The reason for the majority of the students to choose the university was affordability.

Answer:

D. Population: all the first-year students at the university

Sample: a group of 185 incoming first-year students

Conclusion: The reason for the majority of the students to choose the university was affordability..

We can calculate the future cost of sneakers by taking the present cost as the initial value and applying a 5.1% increase every year for 25 years.

If the cost of a pair of sneakers increases by approximately 5.1% every year, we can estimate the cost of a pair of sneakers 25 years from now. To calculate this, we can use the compound interest formula.

The compound interest formula can be used to calculate the future value of an investment or in this case, the cost of sneakers after a certain number of years. The formula is given by: A = P(1 + r)^n, where A is the future value, P is the present value, r is the annual interest rate (as a decimal), and n is the number of years.

Using this formula, we can calculate the future cost of sneakers by taking the present cost as the initial value and applying a 5.1% increase every year for 25 years.

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Answer:

17

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school

Let's assume that the total number of students in the school is "x".

40 percentage  of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.

We also know that the number of students who play at least one sport is 102. Therefore, we can write:

0.4x = 102

Move 0.4 to the right hand side of the equation

x = 102 / 0.4

Divide the numbers

x = 255

Therefore, there are 255 students at the school.

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The total cost of Cole's breakfast, including an 18% tip, was $94.40. If the bill came to $80, and Cole left an 18% tip, then the tip amount would be calculated by multiplying the bill amount by 0.18 (or 18%).

Tip = $80 x 0.18 = $14.40

To calculate the total cost of Cole's breakfast, we need to add the tip amount to the bill amount:

Total cost = $80 + $14.40 = $94.40

Therefore, the total cost of Cole's breakfast, including an 18% tip, was $94.40. It is customary to leave a tip in the United States, and the amount typically ranges from 15-20% of the bill. The tip is a way to show appreciation for good service and is an important part of the restaurant industry's compensation model. While the exact amount of the tip can vary depending on the level of service and the customer's satisfaction, leaving an appropriate tip is a way to support the workers in the restaurant industry and help ensure that they are paid fairly for their work.

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The correct answer is d. As viscosity increased, the flow rate decreased and the graph was linear.

Viscosity is a measure of a fluid's resistance to flow. The higher the viscosity of a fluid, the more resistant it is to flow. Flow rate, on the other hand, is a measure of how much fluid flows through a particular point in a given amount of time.

When viscosity increases, the flow rate decreases, and this relationship is linear. This means that as viscosity increases, the flow rate decreases at a constant rate, resulting in a straight-line graph. The slope of this graph represents the degree of change in flow rate with respect to viscosity.

In contrast, if the flow rate were to increase as viscosity increased, the graph would be curved, indicating a nonlinear relationship between the two variables. Therefore, option d is the correct answer, and the other options do not accurately describe the relationship between flow rate and viscosity.

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Answer:

Option (1).

Step-by-step explanation:

Given  functions are f(x) = \(\frac{1}{x}\) and g(x) = x - 2

(fog)(x) = f[g(x)]

By substituting g(x) in place of x in the function f(x),

f[g(x)] = \(\frac{1}{(x-2)}\)

Graph of the function f[g(x)] will have,

Vertical asymptotes : x = 2

Horizontal asymptotes : y = 0

And no oblique asymptotes.

Out of four options graph number (1) matches the given characteristics of the function.

Therefore, graph (1) will be the answer.

Answer:

9/4

Step-by-step explanation:

= -3a

= -3(-3)

= 9

=B^2

= (2)^2

=4

therefore answer: 9/4

Answer:

D is the correct answer

Step-by-step explanation:

Trust

For the first differential equation:

y' + 5y' + 2y = 0, y(0) = 1, y'(0) = 2

We can apply the Laplace transform to both sides of the equation:

L{y'} + 5L{y'} + 2L{y} = 0

Using the linearity property of the Laplace transform, we can write:

L{y'} = sY(s) - y(0)

L{y''} = s^2 Y(s) - sy(0) - y'(0)

L{y} = Y(s)

Substituting these expressions into the differential equation, we get:

sY(s) - y(0) + 5(sY(s) - y(0)) + 2Y(s) = 0

Simplifying and solving for Y(s), we get:

Y(s) = (y(0) s + y'(0)) / (s^2 + 5s + 2)

    = (1s + 2) / (s^2 + 5s + 2)

To solve for y(t), we can apply partial fraction decomposition to express Y(s) in terms of simpler fractions:

Y(s) = (1s + 2) / (s^2 + 5s + 2)

    = A / (s + α) + B / (s + β)

where α and β are the roots of the quadratic denominator, and A and B are constants to be determined.

The roots of s^2 + 5s + 2 = 0 can be found using the quadratic formula:

s = (-5 ± √(5^2 - 4(1)(2))) / (2(1))

 = (-5 ± √17) / 2

Therefore, we have:

α = (-5 + √17) / 2

β = (-5 - √17) / 2

Using partial fraction decomposition, we can write:

Y(s) = A / (s + α) + B / (s + β)

    = [A(s + β) + B(s + α)] / [(s + α)(s + β)]

Equating the numerators, we get:

1s + 2 = A(s + β) + B(s + α)

Substituting s = -α, we get:

-αA + βB = 1α + 2

Substituting s = -β, we get:

-βA + αB = 1β + 2

Solving for A and B by solving the system of linear equations:

A = (2 + α) / (√17)

B = (2 + β) / (-√17)

Substituting the values of A and B, we get:

Y(s) = [(2 + α) / (√17)] / (s + α) - [(2 + β) / (√17)] / (s + β)

Using the inverse Laplace transform, we can find y(t):

y(t) = [(2 + α) / (√17)] e^(-αt) - [(2 + β) / (√17)] e^(-βt)

For the second differential equation:

y''' + y = A8(t - 3.), y(0) = 1, y'(0) = 0

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Answer:

-40

Step-by-step explanation:

Use PEMDAS

3 – 7 • 5 + 2 • 4

Multiply first:

3-35+8

3-43

-40

Hope this helps! Please mark brainliest :)

Answer:

Step-by-step explanation:

3-7 times 5 + 2

3-35+2

-32+2

-30

To draw the image of quadrilateral ABCD under a translation by 1 unit to the right and 4 units up, we will move each point of the quadrilateral in the specified direction.

Let's assume the coordinates of the original quadrilateral ABCD are as follows:

A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), D(x₄, y₄)

To perform the translation, we will add the given values to the x-coordinates and y-coordinates of each point:

A'(x₁ + 1, y₁ + 4), B'(x₂ + 1, y₂ + 4), C'(x₃ + 1, y₃ + 4), D'(x₄ + 1, y₄ + 4)

Now, plot the original quadrilateral ABCD and then move each point to its corresponding new position.

For example, if point A had coordinates (2, 3), after the translation, it will move to (2 + 1, 3 + 4) = (3, 7). Similarly, you can calculate the new coordinates for points B, C, and D using the same process.

Once you have the new coordinates for each point, connect them to form the image of the quadrilateral ABCD under the translation.

The new quadrilateral A'B'C'D' will be a shifted version of the original quadrilateral, 1 unit to the right and 4 units up.

It's important to note that the scale and proportions of the quadrilateral will remain the same after the translation. Only its position in the coordinate plane will change.

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Answer:

(-2, 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

6x - y = -14

-2x + y = 6

Step 2: Solve for x

Elimination

Step 3: Solve for y

Answer:

Domain: (-∞,∞), Range: [2,∞)

Answer:

9th grade student=33.3%, unit 7=45%

Step-by-step explanation:

The length of the wire is given as follows:

21 ft.

Similar triangles are triangles that share these two features presented as follows:

From the similar triangles, the proportional relationship to obtain the height of the tower is given as follows:

4/5 = 13/h

4h = 13 x 5

h = 13 x 5/4

h = 16.25.

Applying the Pythagorean Theorem, the length of the wire is given as follows:

l² = 16.25² + 13²

l = sqrt(16.25² + 13²)

l = 21 ft.

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Answer:

9(4a minus 3) is equivalent to 36a minus 27.

The researcher's multiple linear regression model is statistically significant, indicating that the predictors collectively have a significant influence on the patients' scores in the fitness test.

The model explains approximately 66.1% of the variance in the patients' scores. However, it is not appropriate to state that the predictors account for 112% of the variance in the fitness test scores.

The given information provides the following details about the multiple linear regression model:

R-squared (R2) value: The R2 value of 0.665 indicates that approximately 66.5% of the variance in the patients' scores in the fitness test can be explained by the predictors included in the model.

Adjusted R-squared (adjusted R2) value: The adjusted R2 value of 0.661 takes into account the number of predictors and sample size, providing a more conservative estimate of the model's goodness of fit. In this case, it suggests that approximately 66.1% of the variance in the patients' scores can be explained by the predictors.

F-statistic: The F-statistic of 112.56 is used to test the overall significance of the regression model. It indicates whether there is a significant relationship between the predictors and the dependent variable (fitness test scores). The associated p-value is stated as 0.00, which means the model is statistically significant.

Based on these findings, we can conclude that the researcher's multiple linear regression model is statistically significant, meaning that there is evidence to support the notion that the predictors collectively have a significant influence on the patients' scores in the fitness test.

The model explains approximately 66.1% of the variance in the fitness test scores, as indicated by the adjusted R2 value.

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