Write the equation of the line that is perpendicular to 5x + 3y = -21 and
passes through the point (-5, 1).

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

Answer:

-60...make me brainlistt

Step-by-step explanation:

Answer:

m= 2 43/63

Step-by-step explanation:

steps

6 1/9 = 3 3/7 + m

convert mixed numbers into improper fractions 6 1/9 = 55/9

55/9 = 3 3/7 + m

convert mixed numbers into improper fractions 3 3/7 = 24/7

55/9 = 24/7 + m

switch sides

24/7 + m = 55/9

subtract 24/7 from both sides

24/7 + m - 24/7 = 55/9 - 24/7

simplify

m = 169/63

convert improper fraction to mixed number

169/63 = 2 43/63

so your final answer is 2 43/63

Hope that helps!

Answer:670000

Step-by-step explanation:

Rounding 673738 to the nearest ten thousand is 670000

The place value of the number 673738 from the right is given below:

8 stands for unit

3 represents tens

7 represents hundreds

3 represents tens thousands

7 represents ten thousands

6 represents hundred thousands

Since the number beside the 7 is 3 and it isn't up to 5, then the number to the nearest ten thousand will be 670000.

In conclusion, rounding 673738 to the nearest ten thousand is 670000.

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Answer:

11

Step-by-step explanation:

The positive difference between 19 and 8 is 11.

It is the value which is obtained when the smaller number is subtracted from the bigger number.

For given example,

We need to find the positive difference between 19 and 8.

here, 19 > 8

So, the smaller number = 8

the bigger number = 19

So, the positive difference would be,

19 - 8 = 11

Therefore, the positive difference between 19 and 8 is 11.

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Answer:

the answer is -7x^2- 14x

Step-by-step explanation:

Answer:

9x^2 - 6x

Step-by-step explanation:

6x^3 - 6x^3 = 0

x^2 - (-8x^2) = x^2 + 8x^2 = 9x^2

-10x - (-4x) = -10x + 4x = -6x

Answer: 9x^2 - 6x

Step-by-step explanation:

I think the wording on this problem is incorrect. is one of the insides supposed to be outside

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Answer:

\(l=56m\)

Step-by-step explanation:

From the question we are told that:

Angle from vertical \(\theta =5.6\)

Horizontal Distance \(d=107m\)

Angle of elevation \(\gamma=28.6\)

Generally the Trigonometric equation for exterior angles is mathematically given by

\(Exterior\ angles=\sum of\ two\ interior\ angles\)

Where

\(Exterior angles=90 \textdegree +5.6 \textdegree\)

Therefore

\(90 \textdegree +\theta \textdegree=\omega+\gamma\)

\(90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree\)

\(\omega=67 \textdegree\)

Generally the equation for The Sine rule is mathematically given by

\(\frac{sin \omega }{d}=\frac{sin \gamma}{l}\)

\(l=\frac{107 sin 28.6}{sin 67 \textdegree }\)

\(l=56m\)

Answer:B

Step-by-step explanation:

I think it should be B u= -1

Answer:

31.4

Step-by-step explanation:

diameter (d) = 10

circumference = (3.14)d

                        = (3.14)10 = 31.4

circumference = 31.4

Answer:

True I think.

Step-by-step explanation:

True, An expression to represent this is, 1.12S

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

In honors math increased by 12% in this year students.

Now, if S represents students.

Then, An expression to represent this situation is,

⇒ S + 12% of S

⇒ S + 0.12S

⇒ S (1 + 0.12)

⇒ 1.12S

Thus, The expression is true.

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Answer:

2878045.500 cubed metres

Step-by-step explanation:

volume = 1/3* pie* r*r*h

= 1/3 *3.14*165*165*101

=2878045.5 cubed metres

i hope it's helpful

Answer:

15.

The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.

So, the answer to the question "what is 5 divided by 1/3?" is
15!

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The time Ann finished playing in the backyard is 12 : 15 pm

Total time = 9:38 + 41 minutes + 1 hour 56 minutes

= 10:19 + 1 hour 56 minutes

= 12 : 15 pm

Therefore, the time Ann finished playing in the backyard is 12 : 15 pm

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Answer:

y = 7

Step-by-step explanation:

The equation of the line is y = 7 because since it's a horizontal line the y value will always stay the same, and the x value will always be changing. Therefore you could draw a line straight across the y-axis at 7

Answer:

\(\bold{4\sqrt3 + i4}\)

Step-by-step explanation:

Given complex number is:

\([2(cos10^\circ + i sin10^\circ)]^3\)

To find:

Answer in rectangular form after using De Moivre's theorem = ?

i.e. the form \(a+ib\) (not in forms of angles)

Solution:

De Moivre's theorem provides us a way of solving the powers of complex numbers written in polar form.

As per De Moivre's theorem:

\((cos\theta+isin\theta)^n = cos(n\theta)+i(sin(n\theta))\)

So, the given complex number can be written as:

\([2(cos10^\circ + i sin10^\circ)]^3\\\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\)

Now, using De Moivre's theorem:

\(\Rightarrow 2^3 \times (cos10^\circ + i sin10^\circ)^3\\\Rightarrow 8 \times [cos(3 \times10)^\circ + i sin(3 \times10^\circ)]\\\Rightarrow 8 \times (cos30^\circ + i sin30^\circ)\\\Rightarrow 8 \times (\dfrac{\sqrt3}2 + i \dfrac{1}{2})\\\Rightarrow \dfrac{\sqrt3}2\times 8 + i \dfrac{1}{2}\times 8\\\Rightarrow \bold{4\sqrt3 + i4}\)

So, the answer in rectangular form is:

\(\bold{4\sqrt3 + i4}\)

The statements supported by the data in the table are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

To determine which statements are supported by the data in the table, let's analyze the given information:

The mean number of cars sold in a month is the same at both dealerships.

To calculate the mean, we need to find the average number of cars sold each month at each dealership.

For Admiral Autos:

(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13

For Countywide Cars:

(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13

Since both dealerships have an average of 13 cars sold per month, the statement is supported.

The median number of cars sold in a month is the same at both dealerships.

To find the median, we arrange the numbers in ascending order and select the middle value.

For Admiral Autos: 4, 10, 15, 17, 19

Median = 15

For Countywide Cars: 9, 10, 14, 15, 17

Median = 14

Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.

The total number of cars sold is the same at both dealerships.

To find the total number of cars sold, we sum up the values for each dealership.

For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65

For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65

Since both dealerships sold a total of 65 cars, the statement is supported.

The range of the number of cars sold is the same for both dealerships.

The range is determined by subtracting the lowest value from the highest value.

For Admiral Autos: 19 - 4 = 15

For Countywide Cars: 17 - 9 = 8

Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.

The data for Admiral Autos shows greater variability.

To determine the variability, we can look at the range or consider the differences between each data point and the mean.

As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.

Based on the analysis, the statements supported by the data are:

The mean number of cars sold in a month is the same at both dealerships.

The total number of cars sold is the same at both dealerships.

The data for Admiral Autos shows greater variability.

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The image below shows the graph f(x) = |x| – 4

Hope this helps! :)

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

According the question,

The tourist's investment function can be expressed as follows:

f(x) = 720 + 35x

Where x represents the quantity of additional tours that the tourist wants to add to their travel package.

The function f(x) represents the total cost of the travel package plus the additional cost of the extra tours.

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Answer:

the area of the rectangle is 35.25 square meters.

Step-by-step explanation:

To find the area of a rectangle, we multiply the length by the width.

First, we need to convert the mixed numbers to improper fractions to make the multiplication easier:

4 and 2/4 = 4 + 2/4 = 16/4 + 2/4 = 18/4

7 and 5/6 = 7 + 5/6 = 42/6 + 5/6 = 47/6

Now we can multiply the length and width:

Area = (18/4) * (47/6)

Area = (9/2) * (47/6) (canceling the common factor of 2 between 18/4 and 6 in 47/6)

Area = (9 * 47) / (2 * 6)

Area = 423/12

Area = 35.25

Therefore, the area of the rectangle is 35.25 square meters.

Answer:

the problem is like that or is showing u how are the equations ?

Answer:

It will take Sophia 1 hour to run 6 miles.

And 1 1/2 hours for 9 miles.

Step-by-step explanation:

The graph of the function y = 1/3x - 2 is added as an attachment

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

So, the equation is

y = 1/3x - 2

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations rules

The graph of the function is added as an attachment

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The area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1) coordinates is 6 square units

We first need to plot all the given points A  (2,-2), B (2,1), C (4,2), D (6,2)and E (4,-1) which is coordinate geometry

After joining the Points which is a pentagon and it can be divided in two shapes one is triangle CDE and a quadrilateral ABCE

Using the distance formula

BC = \(\sqrt{(y2-y1)^{2}+(x2-x1)^{2} }\) = \(\sqrt{(2-1)^{2} + (4-2^{2} }\) = √5

Since BC = AE and BC ll AE , we can say ABCE is a parallelogram

area of a parallelogram = base × Altitude

                                      = 2 × 2= 4

Area of triangle CDE where CD is perpendicular and CE is the base

                        = 1/2 ( 2×2)

                        = 1/2 (4)

                         = 2 square units

So the area of ABCDE = Area of ABCE + area of CDE

                                     = 4 square units + 2 square units

                                      = 6 square units

Hence, the area of the composite figure whose vertices have the  (2,-2), (2,1), (4,2), (6,2), (4,-1)coordinates is 6 square units

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Answer:

SA = 208 in²

Step-by-step explanation:

SA = 2(2)(7) + 2(2)(10) + 2(10)(7) = 208 in²

Answer:

208 in^2

Step-by-step explanation:

SA: 2(w · l + h · l + h · w)       formula

SA: 2(2 · 7 + 10 · 7 + 10 · 2)      plug the numbers in- w: width, l: length, h: height

SA: 2(14 + 70 + 20)          find area of 3 sides with different areas

SA: 28 + 140 + 40       doubling

SA: 208       final answer

Answer:

The minimum guaranteed mileage is  \(x = 71489.55\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 67900\)

     The standard deviation is  \(\sigma = 2050\)

Generally for the probability to be 4% the minimum guaranteed mileage is evaluated as

    \(P( X \ge x ) =1- P( \frac{X - \mu }{\sigma } < \frac{ x - 67900 }{ 2050} ) = 0.04\)

\(\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )\)

     \(P( X \ge x ) =1- P( Z<z) = 0.04\)

=>  \(P( X \ge x ) = P( Z<z) = 0.96\)

=>    \(z = \frac{ x - 67900 }{ 2050}\)

From the z table, the critical value corresponding to 0.96 to the left of the curve is  

         \(z = 1.751\)

So

        \(1.751 = \frac{ x - 67900 }{ 2050}\)

=>     \(x = 71489.55\)