The Sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the numbers.

Answer:

[tex]m\angle B\approx 80.27^\circ\text{ and } m\angle C\approx 59.73^\circ[/tex]

Side AB measures approximately 20.15 units.

Step-by-step explanation:

We can use the Law of Sines, given by:

[tex]\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}[/tex]

Since we already know ∠A and a, we can use it to determine our other measures.

We know that b is 23. Substitute:

[tex]\displaystyle \frac{\sin 40^\circ}{15}=\frac{\sin B}{23}[/tex]

Solve for ∠B:

[tex]\displaystyle \sin B=\frac{23\sin 40^\circ}{15}[/tex]

We can take the inverse sine of both sides:

[tex]\displaystyle m\angle B=\sin^{-1}\frac{23\sin 40^\circ}{15}[/tex]

Use a calculator (make sure you're in Degrees mode!):

[tex]m\angle B\approx 80.27^\circ[/tex]

The interior angles of a triangle must total 180°. Hence:

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]

Substitute in known values:

[tex](40^\circ)+(80.27^\circ)+m\angle C=180^\circ[/tex]

Therefore:

[tex]m\angle C\approx 59.73^\circ[/tex]

Lastly, to find AB or c, we can use the Law of Cosines:

[tex]c^2=a^2+b^2-2ab\cos(C)[/tex]

a = 15, b = 23, and to prevent rounding errors, we will use the exact value for C. Recall that we know that:

[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex]

Using the exact value for ∠B, we acquire:

[tex]40^\circ+\displaystyle \sin^{-1}\frac{23\sin40^\circ}{15}+m\angle C=180^\circ[/tex]

Therefore:

[tex]\displaystyle m\angle C=\left(140-\sin^{-1}\frac{23\sin40}{15}\right)^\circ[/tex]

Substitute:

[tex]\displaystyle c^2=(15)^2+(23)^2-2(15)(23)\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)[/tex]

Simplify and take the square root of both sides.

[tex]\displaystyle c=\sqrt{754-690\cos\left(140-\sin^{-1}\frac{23\sin40^\circ}{15}\right)}[/tex]

And use a calculator:

[tex]c\approx 20.15[/tex]

Answer:

Hi! The person above is actually correct, just that it needed to be rounded to the nearest tenth. Check the picture for confirmation. Hope this helped <3

Step-by-step explanation:

The measure of angle B is approximately

80.3

The measure of angle C is approximately

59.7

The length of side AB is approximately

20.2

I got it correct on Edmentum/Plato

Answer: 43

Step-by-step explanation:

Lets start with the result. First add the number you subtracted with 73

= 73+13=86

Now they had doubled it, now we instead divide it as it was multiplied. Division is the opposite of Multiplication.

86/2= 43

Hence the Answer or the First Number was 43

HOPE IT HELPS AND PLS MARK BRAINLIEST

Step-by-step explanation:

Feel free to ask for more help. I love Linear Algebra

Answer:

x = 41°

Step-by-step explanation:

Using the cofunction identity

sinx = cos(90 - x) , then

sin49° = cos(90 - 49)° = cos49°

with x = 41°

Answer:

to find y you have to do trigonometry

Reason: Any two perpendicular lines will have their slopes multiply to -1, where neither line is vertical.

The given line has slope -1/4 and the perpendicular slope is 4

(-1/4)*4 = -1

Put another way: the answer is 4 because it's the negative reciprocal of -1/4.

Answer:

B

Tasha's investment will yield more over many years because the amount invested at 8% causes the overall total to increase faster.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i got a 100%

Answer:

I think it's 7.93725

I'm not sure if I did this correctly

Answer:

a is the answer because I just did that question and got 100 percent.

Answer:

d

Step-by-step explanation:

Answer:

I think it is B

Step-by-step explanation:

Answer:

1: 5

2: 67

3: 65

4:  30

5: 210

6: 210

Step-by-step explanation:

Answer:

all real numbers

Step-by-step explanation:

The domain is the values that x can take

x can be any real number

Answer:

Temperature after 10 minute = 27.9 degree Celsius

Step-by-step explanation:

Current temperature, P = 100 degree Celsius

% rate in temperature loses = 12% per minute = 0.12

Time,  t = 10 minutes

Temperature after t minutes ,

                                           [tex]= P ( 1 - r )^t\\\\=100( 1 - 0.12)^10\\\\=100(0.278500976)\\\\=27.85[/tex]

                                           = 27.9 degree Celsius

Answer:

2.64 km

Step-by-step explanation:

The first step is to calculate the distance in meters

= 24×110

= 2640 meters

1km= 1000 meter

2640 meters to kilometer

= 2640/1000

= 2.64 kilometers

Hence the distance is 2.64 km

Answer:

O = 29

P = 61

Step-by-step explanation:

90 = (x+3) + (2x+9)

90 = 3x + 12

90 - 12 = 3x

78 = 3x

x = 26

26 + 3 = O = 29

(26 * 2) + 9 = P = 61

61 + 29  = 90 = Complementary Angles

Answer:

23 poudsfgghhhhhhhxcvbnmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm

(a) [tex]a+b-c\\-2+-3-4\\-5-4\\-9[/tex]

(b) [tex]b+c^3\\-3+4^3\\-3+64\\61[/tex]

(c)[tex]\frac{3b^2-c^2+a^2}{-3abc} \\\frac{3(-3)^2-(4)^2+(-2)^2}{-3(-2)(-3)(4)} \\\frac{3(9)-16+4}{6(-3)(4)} \\\frac{27-16+4}{-18(4)} \\\frac{11+4}{-72} \\\frac{15}{-72} \\-\frac{5}{24}[/tex]

Answer:

The answer to (A) is -9.

The answer to (B) is 61.

The answer to (C) is [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.

Step-by-step explanation:

For problem (A), which is [tex]a+b-c[/tex], in order to solve for this problem, plug in the information given from the question. The problem will look like [tex](-2)+(-3)-(4)[/tex]. Solve the problem by first adding (-2) + (-3), which equals (-5), and then, solve for (-5) -(4), which equals -9. The final answer for problem (A) will be -9.

For problem (B), which is [tex]b+c^{3}[/tex], start by plugging in the information given from the question. The problem will look like [tex](-3)+(4)^{3}[/tex]. Solve the problem by cubing 4, which equals 64, and then, solve for (-3)+(64), which equals 61. The final answer for problem (B) will be 61.

For problem (C), which is [tex]\frac{3b^{2}-c^{2}+a^{2} }{-3abc}[/tex],  start by plugging in the information given from the question. The problem will look like [tex]\frac{3(-3)^{2}-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Solve the problem by first simplifying the numerator.

To simplify the numerator, raise -3 to the power of 2, which will equal 9, and multiplying 3 by 9, which will look like [tex]\frac{27-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Next, raise 4 to the power of 2, which equals 16, and multiply -1 by 16, which will look like [tex]\frac{27-16+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. The next step is to raise -2 to the power of 2, which will look like [tex]\frac{27-16+4 }{-3(-2)(-3)(4)}[/tex]. Then, subtract 16 from 27, which equals 11, and add (11) + (4), which equals 15. The numerator equals 15.

Next, simplify the denominator. First, multiply -3 by -2, which equals 6, and the problem will look like [tex]\frac{27-16+4 }{6(-3)(4)}[/tex]. Then, multiply 6 by -3, which equals -18, and the problem will look like [tex]\frac{27-16+4 }{-18(4)}[/tex]. The next step is to multiply -18 by 4, which equals -72, and the denominator will equal -72.

Then, reduce the expression by cancelling the common factor, and the common factor is 3. The final answer will be [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.

Answer:

B

Step-by-step explanation:

y = k/(x + 3)

Let x = 2

Let y = 8

k = ?

8 = k/(2 + 3)      Combine the terms on the right

8 = k/(5)            Multiply both sides by 5

8*5 = k

k = 40

Let x = 7

y = 40/(7 + 3)

y = 40/10

y = 4

Answer:

The prices are equal when it's 12 pages. For 12 pages, she'd be charged $57

Step-by-step explanation:

x = PER page

y = total

Online scrapbooking equation:

y = 45 + x

Family friend equation:

y = 9 + 4x

Where prices (y) would be equal:

y = 45 + x     (Multiply this by -4)

y = 9 + 4x

y = 9 + 4x

-4y = -180 - 4x

-3y = -171

y = 57

y = 45 + x

-y = -9 - 4x

0 = 36 - 3x

3x = 36

x = 12

Answer:

Step-by-step explanation:

For the data collected by Martin from students about whether they played a musical instrument, the relative frequency of a boy playing an instrument is 0.348.

Relative frequency of an event is the measure of something happens relative to the total outcomes of that event.

The relative frequency can be given as,

[tex]f_r=\dfrac{f}{n}[/tex]

Here, (f) is the frequency of the number of times data occurred in an event and (n) is the total number of outcomes.

The relative frequency can also be defined as, it is the ratio of subgroup frequency to the total frequency of any event.

Martin collected data from students about whether they played a musical instrument.

The table shows his results.

Here, the total number of boys are 92 and the total number of boys who play instrument is 32. Thus, the relative frequency is,

[tex]f_r=\dfrac{32}{92}\\f_r=0.348[/tex]

Thus, for the data collected by Martin from students about whether they played a musical instrument, the relative frequency of a boy playing an instrument is 0.348.

Learn more about the relative frequency here;

https://brainly.com/question/3857836

#SPJ2

Answer:

3

Step-by-step explanation:

The equation for finding a slope is (y2-y1)/(x2-x1), where (x1, y1) is a set and (x2,  

y2) is another set. (2-(-7))/(-5-(-8) = (2+7)/(-5+8) = 9/3 = 3. Hope this makes sense and helps!

Answer:

3

Step-by-step explanation:

To find the slope given two points, we use the slope formula

m = ( y2-y1)/(x2-x1)

m = ( 2 - -7)/(-5 - -8)

   = (2+7)/( -5+8)

  9/3

  3

Answer:

Step-by-step explanation:

The pic doesnt wrk comment question and ill answer

Answer:

B

Step-by-step explanation:

The equation of Nolan's line is  

The slope-intercept form of a line is given by:

Here

m is the slope of the line

and b is the y-intercept.

Given

y-intercept = b = 3

slope = m = 2

The values of m and b can be put into the equation to find the line's equation

So,

Putting the value

Hence,

The equation of Nolan's line is

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]A)\text{ } y-4=3(x+2)[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻  

[tex]\boxed{\text{Point-Slope Form Is...}}\\\\y-y_1=m(x-x_1)\\------------\\m - \text{slope}\\\\(x_1,y_1)- \text{point}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{\underline{Information Given:}}}\\\\\rightarrow \text{The point of } (-2,4)\\\\\rightarrow \text{The slope of 3}\\\\\\\text{\underline{This means the following:}}\\\\\rightarrow m = 3\\\\\rightarrow(x_1,y_1) = (-2,4)[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Replace the variables with the respective values:}}\\\\y-y_1=m(x-x_1)\\\\------------\\\rightarrow y-4=3(x-(-2))\\\\\rightarrow \boxed{y-4=3(x+2)}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

5-2y (the last option)

hope this helps!

please give brainiest<3

Answer:

2y-5

Step-by-step explanation:

Answer:

$1.1

Step-by-step explanation:

In a state with a sales tax rate of 6%,

Alex bought paper for his printer for

$17.99.

The amount of his sales tax to the nearest penny is calculated as:

Sales tax rate × Cost of Paper for his printer

Sales tax = 6% × $17.99

= 6/100 × $17.99

=$ 1.0794

Approximately≈ $1.1

Answer:

3p³ + 2p² – 3p – 11

Step-by-step explanation:

From the question given above, the following data were obtained:

Side 1 (S₁) = –1(p + 5)

Side 2 (S₂) = 2(p² – 3)

Side 3 (S₃) = 3p³ – 2p

Perimeter (P) =?

The perimeter of the triangle can be obtained as follow

P = S₁ + S₂ + S₃

P = –1(p + 5) + 2(p² – 3) + 3p³ – 2p

Clear bracket

P = –p – 5 + 2p² – 6 + 3p³ – 2p

Rearrange

P = 3p³ + 2p² – 2p – p – 6 – 5

P = 3p³ + 2p² – 3p – 11

Therefore, the perimeter of the triangle is 3p³ + 2p² – 3p – 11

Answer:

Step-by-step explanation:

shipping container is in the shape of a Right rectangular prism with the length of the 12 feet away the 8.5 feet and the height of 4 feet. The container is completely filled with contents that weigh on average 0.25 pounds per cubic foot what is the weight in pounds of the contents in the container

Right rectangular prism is a cuboid

Volume of Right rectangular prism = 12 * 8.5 * 4  = 408 cubic feet

Content Density = 0.25 pounds per cubic foot

Density = Mass / Volume

=>  0.25  = Weight of contents in container / Volume of container

=> 0.25 = Weight of contents in container / 408

=> Weight of contents in container  = 0.25 * 408

=> Weight of contents in container  = 102 pounds

Answer:

(3, 6)

1/3

y = -3x +15

Step-by-step explanation:

you do this step by step.

just think what you need. and then you get all of that one after the other.

so, we need the middle point between D and O.

for this we need to know the length of DO.

and we need the slope of DO, so that we can then calculate the perpendicular slope. with that slope we then build the line going through the middle point as well but with the perpendicular slope.

so, length of DO.

Pythagoras for the triangle of the differences between the individual coordinates.

DO² = (9- -3)² + (8-4)² = (9+3)² + 4² = 144 + 16 = 160

DO = sqrt(16×10) = 4×sqrt(10)

the distance D-middle is half of DO = 2×sqrt(10)

DO/2 => DO²/4 = 144/4 + 16/4 = 36 + 4 = 6² + 2²

=> we have to add to the coordinates of D 6 in x and 2 in y direction to get the middle point :

(-3 + 6, 4 + 2) = (3, 6)

the slope of DO

the slope of a line is the ratio of y/x representing the change of y with the change of x. it is the factor of x in the line equation.

for DO we know that when x changes by 12 (difference of the x values of D and O), then y changes by 4.

so, the slope is 4/12 = 1/3.

perpendicular slope of 1/3

we flip x and y and also change the sign, as when the original line goes up, then the y line goes down. and vice versa.

so, the perpendicular slope is -3/1 = -3

the equation of the perpendicular line through the middle point is

y = -3x + c

for c we need to use the coordinates of the middle point (3, 6)

6 = -3×3 + c

6 = -9 + c

c = 15

so our line is

y = -3x + 15