mr adams installed a gate shown. line c is parallel to line d. if m /_4 =40° , find m/_6 and m/_7. justify your answer

Answer:

Both triangles are similar by SAS

Step-by-step explanation:

See attachment for triangles

\(\triangle OKJ\) and \(\triangle ONM\)

From the attachment:

\(OK = 3; OJ = 30; KN = 1; JM = 3\)

Calculate the lengths of ON and OM

\(ON=OK+KN=3+1= 4\)

\(OM = OJ + JM = 30 + 10 = 40\)

To determine if both triangles are similar or not, we make use of the following equivalent ratios

\(OK : OJ = ON : OM\)

\(3 : 30 = 4 : 40\)

Divide the first ratio by 3 and the second by 4

\(1:10 = 1 : 10\) --- This implies that both triangles have 2 similar sides

From the attachment,

\(\angle KOJ = \angle NOM\) ---- similar angles

Since the two triangles have 2 similar sides and a similar angle, then both triangles are similar by SAS

Answer:

72.54

Step-by-step explanation:

Use formula for trapezoid: a+b/2 * h

Since the number of dimes is x and the number of nickels is y, then the total number of coins is x+y. Since Matthew has at least 15 coins, then:

Since a dime has a value of 0.1 and a nickel has a value of 0.05, the total value of x dimes is 0.1x and the total value of y nickels is 0.05y. Furthermore, since Matthew's coins have a maximum value of $1 combined, then:

Then, the system of inequalities is:

Plot the system to solve it graphically:

The green region is the solution for both inequalities simultaneously.

Since the number of coins must be positive, then the solution must lie on the first quadrant of the coordinate plane:

Pick any point inside the green region. That is a possible solution:

Then, a possible solution is x=2 and y=15.

This way, the total number of coins is 17 and the total value of those coins is:

By rearranging the equation, we get the equation of the line parallel to 5x + 4y = 24 that passes through the point (8, -5) as y = (-5/4)x + 5.To find the equation of a line parallel to another line, we need to determine the slope of the given line.

The equation of a line can be written in slope-intercept form as y = mx + b, where m represents the slope.

To determine the slope of the given line 5x + 4y = 24, we need to rearrange the equation in slope-intercept form. First, subtract 5x from both sides: 4y = -5x + 24. Next, divide all terms by 4: y = (-5/4)x + 6. Therefore, the slope of the given line is -5/4.

Since the line we are looking for is parallel to this line, it will also have a slope of -5/4. Now we can use the point-slope form of a line to find the equation. The point-slope form is given as y - y1 = m(x - x1), where (x1, y1) represents the given point (8, -5) and m is the slope.

Substituting the values into the equation, we have y - (-5) = (-5/4)(x - 8). Simplifying further, y + 5 = (-5/4)x + 10.

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Answer:

Length: 10

Width: 9

Explanation:

Perimeter Formula:

2(length + width)

So 2(length + width)=38

length + width=19

length + 9=19

length=10

Answer:

\(A=\left[\begin{array}{ccc}1&1&0\\0&0&0\\\end{array}\right]\)

Step-by-step explanation:

We have a linear transformation L mapping R3 into R2 ⇒

\(L:\) \(IR^{3}\) ⇒ \(IR^{2}\)

We need to find a matrix A such that \(L(x)=Ax\) for every \(x\) in R3

We have the formula of \(L(x)\) ⇒

\(L(x)=L(\left[\begin{array}{c}x1&x2&x3\end{array}\right])=\left[\begin{array}{c}x1+x2&0\end{array}\right]\)

We must notice that \(x\) is a vector in R3 and the image of L is a vector in R2.

Given that L is define as \(L:\) \(IR^{3}\) ⇒ \(IR^{2}\) , the matrix that defines the linear transformation L will be a matrix A ∈ \(IR^{2x3}\)

How can we find this matrix A? One way is to apply L to a base from the domain of L (R3) and putting that result as the columns of the matrix A.

Let's work with the cannonic base of R3  :

\(B_{IR^{3}}=\) { \(\left[\begin{array}{c}1&0&0\end{array}\right],\left[\begin{array}{c}0&1&0\end{array}\right],\left[\begin{array}{c}0&0&1\end{array}\right]\)}

Now if we transform each vector of the base :

\(L(\left[\begin{array}{c}1&0&0\end{array}\right])=\left[\begin{array}{c}1&0\end{array}\right]\)

\(L(\left[\begin{array}{c}0&1&0\end{array}\right])=\left[\begin{array}{c}1&0\end{array}\right]\)

\(L(\left[\begin{array}{c}0&0&1\end{array}\right])=\left[\begin{array}{c}0&0\end{array}\right]\)

The final step is to put the result of each vector as the columns of the matrix A :

\(A=\left[\begin{array}{ccc}1&1&0\\0&0&0\\\end{array}\right]\) ⇒

\(L(x)=Ax\) being A the matrix calculated. It is important to remark that the transformation L is defined in the cannonic base.

We can verify the matrix A by performing the transformation into any vector of R3. For example, let's calculate :

\(L(\left[\begin{array}{c}1&2&3\\\end{array}\right])=\left[\begin{array}{c}3&0\end{array}\right]\)

If we use the equation and :

\(A\left[\begin{array}{c}1&2&3\end{array}\right]=\left[\begin{array}{ccc}1&1&0\\0&0&0\end{array}\right]\left[\begin{array}{c}1&2&3\end{array}\right]=\left[\begin{array}{c}3&0\end{array}\right]\)  

If we use the matrix A calculated.

The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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Answer:

6

Step-by-step explanation:

im not sure but I think 6 is the answer

Answer:

Therefore the distance between the points is 9 units.

__________________________________________________________

Hello! In this question, we will find the distance between the two given points.

__________________________________________________________

Explanation:

In this problem, we were given the points:

In order to find the distance between the two points, we will use our given information and plug it into the distance formula:

\(d = \sqrt{(x2-x1)^2+(y2-y1)^2}\)
In this case, our values would be:

__________________________________________________________

Solve:

Plug in the values into the formula above and solve:
\(d = \sqrt{(-5-4)^2+(-7-(-7))^2}\\\\d=\sqrt{(-9^)^2+(0)^2}\\\\d=\sqrt{81}\\\\\boxed{d=9}\)
__________________________________________________________

Answer:

The distance between the two points would be \(\boxed{\text{9 units}}\)

__________________________________________________________

Additional info:

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Answer: 18- 3t

Step-by-step explanation:

Answer:

Angle ACB = 44°

There are two ways to solve it. Both are right

Solution number 1

From triangle ABC

angle BAC = 180°-(102° +44°) = 36°

Because BG is parallel with AC

Another solution

The sum of angles in the shape AGBC = 360°

Answer:

wwww

Step-by-step explanation:

The factor form of -9x³ - 12x² - 4x is -x(3x + 2)²

Polynomial factors are the expressions that divide a polynomial evenly, leaving no remainder.

In other words, if one polynomial is a factor of another polynomial, then when the second polynomial is divided by the first, the result is another polynomial with no remainder.

Here we have

-9x³ - 12x² - 4x

To find the factored form of this expression to simplify the given expression as follows

A. x(3x - 2)(3x + 2)

=> x[ (3x)² - (2)²]

=> x[ (9x² - 4 ]

=> 9x³ - 4x

Hence, A. x(3x - 2)(3x + 2) = 9x³ - 4x

B. -x(3x + 2)²

=> -x [9x² + 4 + 12x]

=> -9x³ - 4x - 12x

Hence, B. -x(3x + 2)² = -9x³ - 4x - 12x

C. x(3x - 2)²

=> x [9x² + 4 - 12x ]

=> 9x³ + 4x - 12x²

Hence, C. x(3x - 2)² = 9x³ + 4x - 12x²

D. -x(3x - 2)(3x + 2)

=> -x[ 9x² - 4]

=> - 9x³ - 4x  

By the above calculations

The factor form of -9x³ - 12x² - 4x is -x(3x + 2)²

Complete Question:

What is the factored form of this expression? -9x^3 - 12x^2 - 4x

A. x(3x - 2)(3x + 2)

B. -x(3x + 2)^2

C. x(3x - 2)^2

D. -x(3x - 2)(3x + 2)

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Answer:

The answer is

\(y = dx - e \\ y + e = dx \\ d = \frac{y + e}{x} \)

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

B. The product of 5 and a number.

Product means multiplication is taking place. In this case, 5 is being multiplied with n.

Hope this helps!

Answer:

85100

Step-by-step explanation:

the decimal 0.85 can be converted to the fraction 85100 , by defintion of a decmial.

Answer:

Step-by-step explanation:

Answer:

(D)

Step-by-step explanation:

Sedimentary rock formation begins with igneous, metamorphic, or other sedimentary rocks. When these rocks are exposed at the earth’s surface they begin the long slow but relentless process of becoming sedimentary rock.All rocks are subject to weathering. Weathering is anything that breaks the rocks into smaller pieces or sediments. This can happen by the forces of like wind, rain, and freezing water.The sediments that form from these actions are often carried to other places by the wind, running water, and gravity. As these forces lose energy the sediments settle out of the air or water. As the settling takes place the rock fragments are graded by size. The larger heavier pieces settle out first. The smallest fragments travel farther and settle out last. This process of settling out is called deposition.The combination of weathering and movement of the resulting sediments is called erosion.Lithification is the changing of sediments into rock. There are two processes involved in this change. They are compaction and cementation.Compaction occurs after the sediments have been deposited. The weight of the sediments squeezes the particles together. As more and more sediments are deposited the weight on the sediments below increases. Waterborne sediments become so tightly squeezed together that most of the water is pushed out. Cementation happens as dissolved minerals become deposited in the spaces between the sediments. These minerals act as glue or cement to bind the sediments together.

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

You have for uncooked eggs left.

Step-by-step explanation:

9 (total amount of eggs) - 5 (eggs left after she cooks) = 4 eggs cooked.

Answer: 64

Step-by-step explanation:

Answer:64

Step-by-step explanation:

Answer:

\( \to 5 \times \dfrac{3}{4} \\ \\ \to \dfrac{5 \times 3}{4} \\ \\ \to \dfrac{15}{4} \\ \\ \to \pmb{ 3 \dfrac{3}{4}}\)

\( \to 2 \times 1 \dfrac{1}{2} \\ \\ \to 2 \times\dfrac{3}{2} \\ \\ \to \dfrac{2 \times 3}{2} \\ \\ \to \dfrac{6}{2} \\ \\ \to \pmb{3}\)

From the resulting solution, the correct linear inequality graph is Graph C.

Given the inequality equation below:

2(2x-1)+7< 13 or -2x+5 ≤ -10.​

Simplify the expression

2(2x-1)+7< 13

Expand

4x - 2 + 7 < 13

4x + 5 < 13

4x < 13 - 5

4x < 8

x < 2

For the inequality -2x+5 ≤ -10.

-2x+5 ≤ -10

-2x  ≤ -15

x  ≥ 7.5

Hence the solution to the given system of inequalities are x < 2 and x  ≥ 7.5

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Answer:

20% of the Congress is made of Senators.

Step-by-step explanation:

Our whole here is 500, since the House of Representatives and Senate combined would have 500 members in this case. So, we now need to find out how many senators there are.

\(2\) x \(50\) = \(100\)

Now, since we know the fact that there are 100 senators in Congress, we will find out what percent of 500 is 100.

100 = 20% of 500. To check, we will multiply 5 by 100. We get 500.

Therefore, the answer is 20%.

Answer: 24 problems done before dinner

Step-by-step explanation:

Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner

Answer:

160

Step-by-step explanation:

4x5=20.

20×8=160

l×w×h.

Answer:

c

Step-by-step explanation: