Solve each system by substitution.
6) y = 2x - 3
y=-8x + 17​

Final answer:

The student needs to find the missing number 'b' in a data set, given that the range is 25. Since we know the smallest value is 1, adding the range to that value gives us the largest possible number, which in this case is 26. Therefore, 'b' must be 26 to achieve the specified range.

Explanation:

The student is asking about finding a missing value in a set of numbers given the range of the data set. To find the value of b, we must remember the definition of range: Range is the difference between the largest and smallest values in a set.

With the knowledge that the range is 25, and having the numbers 14, 14, 16, and 1, we identify 1 as the smallest value.

If we add the range to the smallest number (1 + 25), we get the largest number the set could contain, which is 26.

Since the other numbers in the set are all smaller than 26, b must equal 26 for the range to be 25.

Answer:

x = 9.25

y = 13.5

Step-by-step explanation:

area = 33

let length be y and width be x

2x - 5 = y

area of rectangle = length * breadth

(2x-5)(x)=33

2x²-5x=33

2x²-5x-33=0

solving quadratic equation

x = 9.25

y = 13.5

Answer:

[tex]2\pi \times \: r = 150 \\ 6.2831r = 150 \\ \frac{6.2831r}{6.2831} = \frac{150}{6.2831} \\ r = 23.87cm[/tex]

Answer:

23.9

Step-by-step explanation:

circumference = Diameter · Pie

150 = X · pie

divide both sides by pie(use the accrual symbol on a calc) and you get 47.7 as the diameter then divide 47.7 by 2 and you get 23.9 as you radius

The value of b is 5.4

Explanation:

Given that ABC is a triangle.

It is also given that [tex]a=12[/tex] , [tex]\angle B=25^{\circ}[/tex] and [tex]\angle C=45^{\circ[/tex]

We need to find the value of b.

The value of b can be determined using the law of sine formula, which is given by

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

First, we shall find the angle of A.

Since, ABC is a triangle and all the angles in a triangle add up to 180°

Thus, we have,

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

  [tex]\angle A+25+45=180[/tex]

          [tex]\angle A+70=180[/tex]

                  [tex]\angle A=110^{\circ}[/tex]

Thus, the value of angle A is 110°

Let us substitute these values in the law of sine formula.

Hence, we get,

[tex]\frac{12}{sin \ 110^{\circ}} =\frac{b}{sin \ 25^{\circ}}[/tex]

Simplifying, we get,

[tex]\frac{12}{0.9397} =\frac{b}{0.423}[/tex]

Multiplying both sides of the equation by 0.423, we get,

[tex]\frac{12\times 0.423}{0.9397} =b[/tex]

Simplifying, we get,

[tex]\frac{0.5076}{0.9397} =b[/tex]

Dividing, we have,

[tex]5.4=b[/tex]

Thus, the value of b is 5.4

Answer: she is jogging 2.25 i think

Step-by-step explanation:

im sorry im not sure i just divided 135 by 60 but i dont think its right:(

Answer:

31/30 gallons

Step-by-step explanation:

finding the lowest common denominator for all three numbers. so 1/3 becomes 10/30, 1/5 becomes 6/30, and 1/2 becomes 15/30. 10/30+6/30+15/30=31/30

Answer:31/30

Step-by-step explanation:

you have to first find a common denominator. Which in this case is 30 so then you have to multiply by the same number for both bottom and top number of the fraction. 1/3 = 10/30 1/5=6/30 1/2=15/30. Then, you just have to add JUST THE TOP NUMBERS. You get 31/30 then divide that and i will leave that last part to you. Hope this helps!

First, subtract 24 from 31.

31 - 24 = 7

Now divide 7 by 2.

7 ÷ 2 = 3.5

Plug 3.5 into the equation to check.

24 + (3.5 × 2) = 31

x = 3.5

Answer:

5 days

Step-by-step explanation:

First subtract the flat fee so that you know you just have the price of the days

225-75

150       Then divide by 30, the day rate so you know how many days it was

150/30= 5

Selena had the car for 5 days

Answer:

warmer

Step-by-step explanation:

-11 is closer to zero the -15

Answer:

warmer

Step-by-step explanation:

-15 is colder.

Answer:

1900 ft

Step-by-step explanation:

To find the area where roses will be planted, find the area of the 2 triangles. 60×38 divided by 2 = 1140ft. 40×38 divided by 2 = 760. 760+1140=1900

Answer:

19.998

Step-by-step explanation:

Take the number and decrease (subtract)  by 9.1% of the original number

22 - 22*9.1%

Change the percent to decimal form

22 - 22*.091

22 -2.002

19.998

Final answer:

The result when the number 22 is decreased by 9.1% is 20.0, after calculating 9.1% of 22, which is 2.002, and subtracting it from 22 and rounding to the nearest tenths place.

Explanation:

To find the result when the number 22 is decreased by 9.1%, you can use the following steps:

Calculate the decrease amount by finding 9.1% of 22: (9.1/100) × 22.

Subtract the decrease amount from the original number: 22 - (9.1% of 22).

Using a calculator, the decrease amount is:
(0.091) × 22 = 2.002.

Then subtract this from the original number:
22 - 2.002 = 19.998.

However, we need to report our final answer to the nearest tenths place since that is the precision of the number 9.1%. Therefore, we round 19.998 to 20.0 to reflect the proper significant figures.

So, the result when the number 22 is decreased by 9.1% is 20.0.

Answer:

I don't know but I have the equations. (also Im going to assume you know a bit of trig)

Step-by-step explanation:

You have to use law of cosines.

a=11

b=15

take these equations and plug in the variables

a^2=b^2+c^2-2bc cos(a)

b^2=a^2+c^2-2ac cos (b)

c^2=a^2+b^2-2ab cos(c)

you will get something along the lines of

something=cos a

something=cos b

something=cos c

then in a calculator you push inverse cos or cos-1(x) and input the "something" into as x and that answer should be one angle, and repeat it for the rest of the three values.

Answer:   x + 4

                5x

Step-by-step explanation:

The first one is "x + 4" because you are adding 4 to the 1st number

The second one is "5x" because you are multiplying 5 to the 2nd number.

Yo sup??

by the property of log we can say that

laga+logb=logab

log4+log5=log4*5

=log20

Hope this helps

grusi lob ze cruz?masi pa koi foitaitua leo leone fatua fatui?

Answer:

1/4 and 2/12

Step-by-step explanation:

If you mulitply both the numerater and denominator by 2 (or any number) it will be equivelent.

1/6 is equivelient to 2/12, 3/18, etc.

However, if you divide 3/12, you get 0.25, which is equivelent to 1/4

The answer is n= -4. It shows the work to get -4

Answer:

900

Step-by-step explanation:

ANSWER: y

=

125

+

900

50

=

$

20.5

Step-by-step explanation: Cost of each puppet =  

$

20.5

Explanation:

The number of puppets :  

50

-------(given)

Let cost of each puppet be  

y

So, total cost will be  

50

y

He brought all string needed for  

$

125

He needs to invest  

$

18

for EACH puppet for the remaining material, i.e.

18

×

50

=

$

900

is the total extra investment to be done.

So total cost will be :  

125

+

900

=

50

y

#therefore cost of each puppet will be :

Answer:

11%

Step-by-step explanation:

The margin of error is the standard error times the critical value.

For a proportion, the standard error is:

σ = √(pq / n)

σ = √(0.132 × 0.868 / 1105)

σ = 0.0102

Since n is large, we can approximate the critical value using a normal distribution.  For 99% confidence, the critical value is 2.576.

The margin of error is:

ME = 0.0102 × 2.576

ME = 0.026

The confidence interval is 0.132 ± 0.026.  So the lower limit is 0.106, or 10.6%.  Rounded to the nearest whole number, that's 11%.

Answer:

center(8x,12y) radius 3

Step-by-step explanation:

If i am doing this correct

Answer:

assume an approximate value for the variable that will simplify the equation.

solve for the variable.

use the answer as the second approximate value and solve the equation again.

repeat this process until a constant value for the variable is obtained.

Answer:

the answer is 1/4

Step-by-step explanation:

1/2 *3/6=1/4

Answer:

Note from question, Let K be any integer.  Integer = 1

θ = πk

  θ = 3.142 * 1

  θ = 3.142 in three decimal places

θ = sin⁻¹ (2/3) + 2kπ

   θ = sin⁻¹0.667 + 2*1*3.142

   θ = 0.718 + 6.284

   θ = 7.002 in three decimal places

∴ 7.002 , 3.142

Step-by-step explanation:

Considering the equation

3 tan(θ) sin(θ) − 2 tan(θ) = 0

The objective is to solve the equation.

First solve the equation in one period.

3 tan(θ) sin(θ) − 2 tan(θ) = 0

( 3sinθ − 2 ) tanθ = 0

Therefore, 3sinθ − 2 = 0    also   tanθ = 0

            =>  sinθ = 2/3        ,        tanθ = 0

Pick the right equation.

tanθ = 0

    θ = tan⁻¹ 0

    θ = 0

Using the unit circle, the period of tangent functions is π

Then the general solution of the equation is θ = 0 + πk ==> θ = πk

Pick the left equation.

3sinθ − 2 = 0

3sinθ = 2

sinθ = 2/3

    θ = sin⁻¹ (2/3)

As the sine function has period 2π

Then the general solution is θ = sin⁻¹ (2/3) + 2kπ

Answer:

90⁰

Step-by-step explanation:

The diagonal of the rectangles forms two angles with the sides, about 32 degrees and 58 degrees respectively. These are found using the Pythagorean theorem to find the length of the diagonal, and then the arctan function to find the angles.

To find the angle that the diagonal makes with the sides of the rectangle, first calculate the length of the diagonal which can be found using the Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can write this as: c² = a² + b². In this case, the length and width of the rectangle are the two sides (a and b) and the diagonal is the hypotenuse (c).

So a = 68 inches, b = 42 inches. Plugging these into our formula gives: c² = 68² + 42², so c = √[(68²) + (42²)] which approximates to 80 inches.

Next, calculate the angles using the inverse tangent (or arctan) function: θ = arctan(opposite/adjacent). In this case, the angles are = arctan(42/68) and arctan(68/42). This gives us angles of approximately 32 degrees and 58 degrees.

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Answer:

D) 27

Step-by-step explanation:

1. add 4 on both sides to leave 4/3x by itself

2. subtract x on both sides to cancel x on the right side

3. multiply 3 ton both sides to cancel out fraction

Answer:

d(27)

Step-by-step explanation:

Answer:

66.25

Step-by-step explanation:

30.50 times 2 is 61 that’s for two caps

61 times 1.086 (1 is for the amount you are actually going to pay .086 is what percent is because you have to move the decimal over two when you are changing percent to decimal) and that comes out to 66.246. you round the 4 to 5 to get to nearest cent and comes out to be 66.25

Answer: $66.25

Step-by-step explanation:

Two baseball cap at $30.5 each is $30.5 ×2 = $61

Sales tax at 8.6% = 8.6/ 100= 0.086

Sales tax = 0.086 × 61

= 5.246

Total amount to be paid = $66. 25

Answer:

A-0.5777miles

B-0.7223miles

Step-by-step explanation:

Let A be truck with 58°, B be truck with 52° elevation and C be the position of the fire. We know that the AB is 1.3 miles apart.

-Using sine rule, we find the length of AB and BC as:

[tex]\angle C=180-(58+52)=70\textdegree\\\\\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.3}{sin \ 70}=\frac{b}{sin \ 52}\\\\b=\frac{1.3 sin \ 52}{sin 70}=1.0902mi\\\\\\c=\frac{1.3 sin \ 58}{sin 70}=1.1732[/tex]

#Bisect angle C, and use sine rule again to find the lengths of bisected AB:

[tex]\frac{a}{sin \ A}=\frac{b}{sin \ B}=\frac{c}{sin \ C}\\\\\frac{1.0902}{sin \ 90}=\frac{x}{sin \ (90-58)}\\\\x=\frac{1.0902\ sin \ 32}{sin \ 90}=0.5777mi[/tex]

Truck B's position is calculated as 1.3mi-0.5777miles=0.7223miles

Hence, truck one is 0.5777miles and truck two is 0.7223 miles from the fire.

Answer: i think the answer is -22 which is A

Step-by-step explanation:

Answer:

-22

Step-by-step explanation:

I put it in decimal form so it would be like this.2.20 dived by -.10 and got -22

The  arc MPN is a major arc, and the length of arc MPN is 79/9π

The given parameters are:

Ф = 360 - 44

Radius, r = 5

The arc length is then calculated using:

[tex]L = \frac{\theta}{360} * 2\pi r[/tex]

So, we have:

[tex]L = \frac{360 - 44}{360} * 2\pi * 5[/tex]

[tex]L = \frac{316}{360} * 2\pi * 5[/tex]

Evaluate the product

[tex]L = \frac{3160}{360} \pi[/tex]

Divide

[tex]L = \frac{79}9 \pi[/tex]

Hence, the length of arc MPN is 79/9π

Read more about arc lengths at:

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