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3 years ago

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Mathematics

1 answer:

Sindrei [870]3 years ago

8 0

Answer:

x=5

Step-by-step explanation:

We know that the angels in a triangle are equal to 180.

(6x+20)+(7x-10)+105=180

We open the prentices and simplify.

13x+115=180

Now we can subtract 115 on both sides.

13x=65

At last, we can divide by 13 on both sides to get the result of x.

x=5

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Three students wrote expressions on their dry-erase boards.

OlgaM077 [116]

Answer:

Student 2 and Student 3

Step-by-step explanation:

Student 2

-(5r - 3s + 1)

= - 5r +3s - 1

Student 3

= - 5r +3s - 1

3 0

3 years ago

A pink mixture uses 4 cups of white paint for every 3 cups of red paint

Viefleur [7K]

Answer:

its a 4:3 ratio, you couldve got pink paint at first

Step-by-step explanation:

what else did you want to know,

3 0

3 years ago

Find the 57th derivative of y = cos(7x).

mel-nik [20]

y = cos(7x)

First derivative = -7sin(7x)

Second derivative = - (7^2)cos(7x)

3rd derivative = (7^3)sin(7x)

4th derivative = (7^4) cos(7x)

5th derivative = -(7^5) sin (7x)

6th derivative = -(7^6) cos(7x)

nth derivative ?

Analysis and conclusion

If n is multiple of 4 or a number before a multiple of 8 the sign is positive

If n is one or two numbers after a multiple of 4 the sign is negative.

7 is raised to exponent n

if n is odd the function is sin(7x), if n is even the function is cos(7x)

n = 57 => odd, and it is a number after 56 which is a multiple of 4 => negative sign

Therefore, the 57th derivative = - (7^57)sin(7x)

6 0

3 years ago

quadrilateral WXYZ is reflected across the line y=x to create quadrilateral W’X’Y’Z'. What are the coordinates of quadrilateral

rosijanka [135]

Explanation

We are required to determine the coordinates of W’X’Y’Z' when WXYZ is reflected across the line y = x.

This is achieved thus:

From the image, we can deduce the following:

$\begin{gathered} W(-7,3) \\ X(-5,6) \\ Y(-3,7) \\ Z(-2,3) \end{gathered}$

We know that the following reflection rules exist:

Therefore, we have:

$\begin{gathered} (x,y)\to(y,x) \\ W(-7,3)\to W^{\prime}(3,-7) \\ X(-5,6)\to X^{\prime}(6,-5) \\ Y(-3,7)\to Y^{\prime}(7,-3) \\ Z(-2,3)\to Z^{\prime}(3,-2) \end{gathered}$

Hence, the answers are:

$\begin{gathered} \begin{equation*} W^{\prime}(3,-7) \end{equation*} \\ \begin{equation*} X^{\prime}(6,-5) \end{equation*} \\ \begin{equation*} Y^{\prime}(7,-3) \end{equation*} \\ \begin{equation*} Z^{\prime}(3,-2) \end{equation*} \end{gathered}$

This is shown in the graph bwlow for further undertanding:

3 0

1 year ago

A random sample of a specific brand of snack bar is tested for calorie count, with the following results: Assume the population

LenKa [72]

Answer:

The 95% confidence interval for the population mean (calorie count of the snacks bars) is (130.32, 161.68).

Step-by-step explanation:

The question is incomplete:

"A random sample of a specific brand of snack bar is tested for calorie count, with the following results: 149, 145,140,160,149,153,131,134,153. Assume the population standard deviation is σ=24 and that the population is approximately normal. Construct a 95% confidence interval for the calorie count of the snack bars."

We start by calculating the mean of the sample:

$M=\dfrac{1}{9}\sum_{i=1}^{9}(149+145+140+160+149+153+131+134+153)\\\\\\ M=\dfrac{1314}{9}=146$