Complete the statement.
The slope of this line is [?]
2.
+1(
2
-4-3-2-1
1 2 3
2
-1
432
d

The side lengths are given as follows:

The side lengths for this problem are obtained considering the triangle midsegment theorem, which states that the midsegment of the triangle divided the laterals of the triangle into two segments of equal length.

The congruent segments(segments of equal length) are given as follows:

Hence the lengths are given as follows:

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Answer:

first find the length of trangel using

h^2=p^2+b^2

Equivalent expression for the missing side length of a rectangle is \(\sqrt{60} x\)

The missing side length when x =3 is 23.2 inch

In a rectangle , opposite sides are equal . The vertex of rectangle is right angle . The diagonal of rectangle forms a right angle triangle.

Given the width of the triangle is 2x. The diagonal of triangle is 8x inches

Let 'L' be the length of the rectangle

To find out the expression for the length of the triangle use pythagorean theorem

hypotenuse ^2=length ^2 + width ^2

\((8x)^2=L^2+(2x)^2\\64x^2+4x^2+L^2\\64x^2-4x^2=L^2\\60x^2=L^2\\L =\sqrt{60x^2}\\ L=\sqrt{60}x\)

An equivalent expression for the missing side length of a rectangle

\(\sqrt{60} x\)

find the missing side length when x=3

Substitute 3 for x

\(L= \sqrt{60} x\\L =\sqrt{60}(3)\\L= 23.2 inch\)

Equivalent expression for the missing side length of a rectangle is \(\sqrt{60} x\)

The missing side length when x =3 is 23.2 inch

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Step-by-step explanation:

the key is to understand that

12 in = 1 ft

1 ft³ (= a cube of 1 ft × 1ft × 1ft or 12in × 12 in × 12 in = 1728 in³) weighs 40 lbs.

her truck can only carry 1,700 lbs without breaking down.

but it would have space for 66×60×24 = 95040 in³ =

95040/1728 = 55 ft³ of soil, which would weigh

55 × 40 = 2200 lbs (too much for the truck).

the same ratio as for the weight her truck can carry applies for the filled volume of the truck bed with that weight :

1700/2200 = 17/22

so, she can only fill 17/22 of her truck bed volume with soil.

i)

percents are calculated by multiplying the ratio by 100 :

17/22 × 100 = 77.27272727... % ≈ 77%

she can fill about 77% of her truck bed with soil without going over the weight limit.

ii)

since she can transport only 1700 lbs in one trip, and 1 ft³ of soil weighs 40 lbs, she can transport

1700/40 = 42.5 ft³ of soil per trip.

she would then earn

42.5 × 1.5 = $63.75 per trip.

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

The equation of the plane that contains the two lines is:3x + 9y − 12z + 6 = 0.

Given two lines r1 and r2 such that,  r1 = [x,y,z] = [1+3t,-3t,2+t] r2 = [x,y,z] = [4,s,-3s+2]The point of intersection of these two lines is (x, y, z) which is common to both lines. We can use the equation of two lines to find the values of t and s, and then the point of intersection. As given, the equation of the line r1 is: r1 = 1, 3, 0 + t 3, −3, 2 And the equation of line r2 is: r2 = 4, 0, 2 + s −3, 3, 0 To find the point of intersection, we set the x, y, and z components of the two lines equal to each other and solve for t and s. Then we substitute the values of t and s back into either equation to get the point of intersection, (x, y, z). Equating the x coordinates, we get:1 + 3t = 4 + s Equating the y coordinates, we get:−3t = 3 Solving for t, we get: t = −1 Substituting this value of t into either equation of the lines, we get: r1 = 1, 0, 1 r2 = 4, −1, 5 Therefore, the point of intersection is (1, 0, 1).

Given two lines r1 and r2 such that,  r1 = [x,y,z] = [1+3t,-3t,2+t] r2 = [x,y,z] = [4,s,-3s+2]Let's find the equation of the plane that contains these two lines. The normal vector of the plane is perpendicular to both of the lines and can be found using the cross product of the direction vectors of the two lines: n = r1 × r2= [3,9,-12]Therefore, the equation of the plane is:3(x−1) + 9(y−0) − 12(z−1) = 0Simplifying this expression, we get:3x + 9y − 12z = −6Therefore, the equation of the plane that contains the two lines is:3x + 9y − 12z + 6 = 0.

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Answer:

Hello! answer: 308 HOPE THAT HELPS!

Answer:

1. 942.48

Step-by-step explanation:

Input the numbers in the formula.

Answer:

The marks lost by Aaron in the final examination is 147.35

To answer this question, we will follow the following steps:

As given in the question, we have,

The total marks of the final examination = 600

The marks scored by Aaron = 452.65

So,

The marks that Aaron lose

= total marks - scored marks

= 600 - 452.65

= 147.35

Hence, Aaron lost 147.35 marks in the final examination.

Step-by-step explanation:

distanceSolution:

Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have

It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:

Thus, the velocity-time graph for the toy car is as shown below:

The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,

Hence, the

The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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Given:

The matrix is:

\(A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}\)

To show:

\((A^{-1})^{-1}=A\)

Solution:

If a matrix is:

\(M=\begin{bmatrix}a&b\\c&d\end{bmatrix}\)

Then,

\(M^{-1}=\dfrac{1}{ad-bc}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}\)

We have,

\(A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}\)

Using the above formula, we get

\(A^{-1}=\dfrac{1}{(\cos x)(\cos x)-(-\sin x)(\sin x)}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}\)

\(A^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}\)

\(A^{-1}=\dfrac{1}{1}\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}\)

\(A^{-1}=\begin{bmatrix}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix}\)

Now, the inverse of \(A^{-1}\) is:

\((A^{-1})^{-1}=\dfrac{1}{(\cos x)(\cos x)-(\sin x)(-\sin x)}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}\)

\((A^{-1})^{-1}=\dfrac{1}{\cos^2x+\sin^2x}\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}\)

\((A^{-1})^{-1}=\dfrac{1}{1}A\)

\((A^{-1})^{-1}=A\)

Hence proved.

Answer:

1 term-38. ,2nd term-36. ,3rd tern is34

With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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The product in standard form that is the area as sum of the generic rectangle is given by 6x² - 5x - 4.

Given the expression is:

(3x - 4)(2x + 1)

Multiplying the algebraic terms we get,

(3x - 4)(2x + 1)

= (3x)*(2x) - 4*(2x) + 1*(3x) - 4*1

= 6x² - 8x + 3x - 4

= 6x² + (3 - 8)x - 4

= 6x² + (-5)x - 4

= 6x² - 5x - 4

Hence the product of the algebraic expressions that is the area as sum of the generic rectangle is given by 6x² - 5x - 4.

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Answer:

Slope is 20 (rise/run)

y = 20x

(no y-intercept)

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

Slope is 20

Step-by-step explanation:

The formula for slope is Y2-Y1 divided by X2-X1

Hope this helped :)

The range of the function g(x) is [300, ∞)

In this question, we have been given that we have deposited $300 into a savings account that earns interest annually.

The function g(x) = 300(1.04)^x used to find the amount of money in the savings account, g(x), after x years.

We need to find the range of the function.

Since a savings account earns interest annually, x can have take values from 0 to infinity.

For x = 0 year,

g(0) = 300(1.04)^0

g = 300 * 1

g = 300

For x tends to ∞, the value of function would be ∞

Therefore, the range of the function g(x) is [300, ∞)

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Answer:

1/2 .

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation:

The equation that shows the relationship between the number of minutes and total number of ladles of broth is y = 2x + 5

Let x represent the number of minutes and y represent the total number of ladies.

Since he adds 2 ladles of broth each minute and he has 5 ladies initially, hence:

y = 2x + 5

The equation that shows the relationship between the number of minutes and total number of ladles of broth is y = 2x + 5

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Answer:

2x+5

Step-by-step explanation:

I did it on IXL:

$0.38×192=$72.96

So the answer is $72.96

Answer:

consider x as the number of hours you work

so, the function that would satisfy this equation is

10x

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

Do you see the negative sign in front of the parentheses? That is -1.

Multiply each term inside the parentheses by -1.

Doing so, we get -8 -b.

Answer:

9x7ym+b=83

Step-by-step explanation:

For a data set of relationship between the type of college and management level, the marginal distribution with frequencies of management level high, medium and low in percents are 5.6%, 53.8% and 40.6% respectively..

The marginal relative frequency of a data set is determined by dividing the sum of a row or the sum of a column by the total number of values in a dataset. The relationship between the type of college attended (public or private).

Numbers of people = 3265

See the above table represents the different management levels ( high, medium and low) for different types of colleges. We have to calculate the marginal distribution of management level in percents. See the above figure 2 which contains all total or sum values of each row and columns.

Total frequency in this case = 3265

Number of high management level = 182

Marginal frequency Percent for high management level = \( ( \frac{182}{3265})100\)

= 5.6%

Number of medium management level

= 1756

Marginal frequency Percent for medium management = \( ( \frac{1756}{3265})100\)

= 53.8%

Number of low management level

= 1327

Marginal frequency Percent for low management = \( ( \frac{1327}{3265})100\) = 40.6%

Hence, required value is 40.6%.

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Complete question:

The above figure complete the question.

Researchers looking at the relationship between the type of college attended (public or private) and achievement gather the following data on 3265 people who graduated from college in the same year. The variable "management level" describes their job description 20 years after graduating from college. Type of College Public Private High 75 107 Medium 962 794 Low 732 595

Management level Calculate the marginal distribution of management level in percents.

Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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