Solve the equation 7b-27=8(6+4b)

Answers

Answer 1

Answer:

b = -3

Step-by-step explanation:

7b-27=8(6+4b)

Distribute

7b -27 = 48 + 32b

Subtract 7b from each side

7b-7b-27=48+32b-7b

-27 = 48+25b

Subtract 48 from each side

-27-48 = 48+25b -47

-75 = 25b

Divide each side by 25

-75/-25 =25b/25

-3 =b

Answer 2

Answer: b= -3

Step-by-step explanation:

[tex]7b-27=8\left(6+4b\right)[/tex]

distribute

[tex]7b-27=48+32b[/tex]

add 27 to both sides

[tex]7b-27+27=48+32b+27[/tex]

[tex]7b=32b+75[/tex]

subtract 32b on both sides

[tex]7b-32b=32b+75-32b[/tex]

divide -25 on both sides

[tex]-25b=75[/tex]

[tex]b=-3[/tex]


Related Questions

A ship travels a distance of 700 km. On the return trip it averages 10km/hr faster and 8 hours less, tp travel the 700km back. Determine how long the original part of the trip took in hours

Answers

Answer:

The total duration of the trip is 48 hours.

Step-by-step explanation:

Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:

[tex]v =\frac{\Delta s}{\Delta t}[/tex]

Where:

[tex]\Delta s[/tex] - Travelled distance, measured in kilometers.

[tex]\Delta t[/tex] - Time, measured in hours.

[tex]v[/tex] - Speed, measured in kilometers per hour.

Now, each stage is represented by the following expressions:

Outbound trip

[tex]v = \frac{700\,km}{\Delta t}[/tex]

Return trip

[tex]v + 10\,\frac{km}{h} = \frac{700\,kh}{\Delta t - 8\,h}[/tex]

By eliminating [tex]v[/tex] and simplifying the resulting expression algebraically:

[tex]\frac{700\,km}{\Delta t} + 10\,\frac{km}{h} = \frac{700\,km}{\Delta t -8\,h}[/tex]

[tex](700\,km)\cdot \left(\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} \right) = 10\,\frac{km}{h}[/tex]

[tex]\frac{1}{\Delta t - 8\,h}-\frac{1}{\Delta t} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]\frac{8\,h}{\Delta t \cdot (\Delta t-8\,h)} = \frac{1}{70}\,\frac{1}{h}[/tex]

[tex]560\,h^{2} = \Delta t\cdot (\Delta t - 8\,h)[/tex]

[tex](\Delta t )^{2}-8\cdot \Delta t - 560 = 0[/tex]

This equation can be solved by means of the Quadratic Formula, whose roots are presented below:

[tex]\Delta t_{1} = 28\,h[/tex] and [tex]\Delta t_{2} = -20\,h[/tex]

Only the first roots offers a physically resonable solution. Then, total duration of the trip is:

[tex]t_{T} = 28\,h +20\,h[/tex]

[tex]t_{T} = 48\,h[/tex]

The total duration of the trip is 48 hours.

Find the vertex of the parabola.
f (x) = x squared minus 6 x + 13
a.
( 4, 0)
c.
( 3, 4)
b.
(0, 3)
d.
( 4, 3)

Answers

Answer:

The vertex is (3,4)

Step-by-step explanation:

f (x) = x^2 - 6 x + 13

Completing the square

-6/2 = -3 and squaring it = 9

    = x^2 -6x +9 +4

   = ( x-3) ^2 +4

The equation is now in vertex form

a( x-h) ^2 +k

where the vertex is ( h,k)

The vertex is (3,4)

Answer:

C on edge

Step-by-step explanation:

In the expression 3x^2+y+-5 which of the following choices is the exponent in the term 3x^2?

A. 3

B. 2

C. X

D. None of these choices

Answers

Answer:

2

Step-by-step explanation:

3x^2

The coefficient is 3

The variable is x

The exponent is 2

Which of the following best represents the average rate at which the human hair grows (1 point)
a
0.25 inches per second
b
0.25 meters per hour
с
0.25 meter per month
d
0.25 inches per month

Answers

Answer:

D.0.25 inches per months

Step-by-step explanation:

The average rate or speed of human hair growth is about 0.25inches per month.

4x-8+9-6x=3x+6 cual es el valor de la x?

Answers

Answer:

El valor de x en esta ecuación es -1.

Step-by-step explanation:

4x - 8 + 9 - 6x = 3x + 6

En primer lugar, combinar términos similares en cada lado de la ecuación.

-2x + 1 = 3x + 6

A continuación, resta 3 veces en ambos lados de la ecuación.

-5x + 1 = 6

Ahora, resta 1 de ambos lados de la ecuación.

-5x = 5

Por último, divida por -5 en ambos lados de la ecuación.

x = -1

X(X + 8) = 9
Algebra 2

Answers

Answer:

x = -9, 1

Step-by-step explanation:

x (x + 8 )= 9

x^2 + 8x = 9

x^2 + 8x - 9 = 0

(x + 9)(x - 1) = 0

x = -9, 1

Hope this helps!

Answer:

x = 3 and x = 0

Step-by-step explanation:

A way to solve is simplifying the given equation:

X^2 + 8x = 9

So

x = 3 and x = 0

3^2 + 8(0) = 9

9 + 0 = 9

9 = 9

What is the rate of change of the function? On a coordinate plane, a line with negative slope goes through points (0, 1) and (1, negative 1). –2 Negative one-half One-half 2 Mark this and return

Answers

Answer:

-2

Step-by-step explanation:

slope: (y² - y¹) / (x² - x¹)

(-1 - 1) / (1 - 0) = -2 / 1 = -2

y = -2x + b

plug in an (x, y) value to find b

1 = -2(0) + b

1 = -2 + b

b = 3

y = -2x + 3

rate of change is -2

Answer:

-2

Step-by-step explanation:

solve 2<2x+4<10 for x

Answers

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Let's solve your inequality step-by-step.

[tex]2<2x+4<10[/tex]

[tex]2 + -4 < 2x + 4 + -4 < 10 + -4[/tex] (Add -4 to all parts)

[tex]-2 < 2x < 6[/tex]

[tex]\frac{-2}{2} < \frac{2x}{2} < \frac{6}{2}[/tex] (Divide all parts by 2)

[tex]-1 < x < 3[/tex]

So the answer is : [tex]-1 < x < 3[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Need Help Trigonometry

Answers

Answer:

tan(<G) = [tex] \frac{HI}{GI} [/tex]

Step-by-step explanation:

Given:

Right triangle ∆GHI,

Required:

Equivalent of tan(<G)

SOLUTION:

Recall the acronym for trigonometric ratios of angles in a right triangle: SOHCAHTOA.

Thus, the TOA in the acronym above stands for:

Tan(θ) = side opposite to θ ÷ side adjacent to θ

Where,

θ is the angle of interest = <G

Opposite side = HI

Adjacent side = GI

The equivalent of tan(<G) = [tex] \frac{HI}{GI} [/tex]

Create a box plot for either the girls or boys data. Give 2 valid conclusions based on the data collected? (4 points)

Answers

Answer:

1) Please find attached the box and whiskers chart created with Excel

2) The conclusions are;

a) The measure of central tendency (the mean and the median) are approximately equal,

b) The standard deviation for the first five data points is 14.17 while the standard deviation for the whole ten data points is 23.99 as such the data values appeared more clustered at the center and show wider spread towards right ends of the chart

Due to the lack of correlation between the standard deviation and the five data values, the data is not uniformly distributed

Step-by-step explanation:

The given data is as follows;

1,    2,    3,    4,   5,    6,    7,    8,    9,    10

15, 18,   22,  32, 50, 50,  55, 56,  81,    81

The first quartile Q₁ = 22

The second quartile, Q₂ (Median) = 50

The third quartile, Q₃ = 56

The interquartile range IQR = 56 - 22 = 34

The minimum value = 15

The maximum value = 81

The mean = 46

The standard deviation = 23.99

Therefore, the measure of central tendency (the mean and the median) are approximately equal,

The data values appeared more clustered at the center and show wider spread towards the left and right ends of the chart

The standard deviation for the first five data points is 14.17 while the standard deviation for the last five data points is

Due to the lack of correlation between the standard deviation and the five data values, the data is not uniformly distributed.

Teenagers tend to ride skateboards and bicycles is order to get around the town.the probability of a teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is 0.36. If a teenager is chosen at random, the probability that the teenager owns a skateboard or a bicycle is

Answers

Answer:  0.82

Step-by-step explanation:

Given : P(own skateboard) =0.37

P( own bicycle) =0.81

P(own skateboard and bicycle) = 0.36

Since, P(A or B) =P(A)+P(B)-P(A and B)

So, P(own skateboard or  bicycle) = P(own skateboard) + P( own bicycle)-P(own skateboard and bicycle)

= 0.37 + 0.81 -  0.36

= 0.82

Hence, the probability that the teenager owns a skateboard or a bicycle is  0.82.

In an examination ,80%examines passed in english,70%In mathematics and 60% in both subjects.if 45 examines failed in both subject.
1.draw a venn-diagram to represent the above information .
2.find the number of examines who passed only one subject.
3.find the number of student who failed in mathematics.​

Answers

Answer:

1. Please refer to attached diagram.

2. 135

3. 135

Step-by-step explanation:

Given that

80%examines passed in English, n(E) = 80%

70%In mathematics, n(M) = 70%

and 60% in both subjects, n(E [tex]\cap[/tex] M)  = 60%

45 examines failed in both subject.

1. Venn Diagram is attached in the answer area.

One circle represents the pass examines in Maths and

Other circle represents the pass examines in English.

Rectangle represents the total number of examines that appeared for the exam.

Rectangle minus the area of union of circles represent the number of students who failed in both subjects.

2. To find the number of examines who passed in only one subject.

i.e. n(E) - n(E [tex]\cap[/tex] M) + n(M) - n(E [tex]\cap[/tex] M) = (80 - 60 + 70 - 60)% = 30%

Let us find the number of students who passed in atleast one subject:

[tex]n(E\cup M) = n(E) +n(M)-n(E \cap M)\\\Rightarrow n(E\cup M) = (80 +70-60)\% = \bold{90\%}[/tex]

So, number of students who failed in both subjects = 100 - 90% = 10% of total students = 45

So, total number of students appeared = 450

So, number of examines who passed in only one subject = 450 [tex]\times[/tex] 30% = 135

3. Number of students who failed in mathematics.

100% - Passed in Mathematics = 100% - 70% = 30% of 450 = 135

An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?

Answers

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

Answer:

octagonal: 8 faces, 16 edges, 9 verticestriangular pyramid: 3 faces, 6 edges, 4 verticestriangular prism: 3 faces, 9 edges, 6 vertices

Step-by-step explanation:

A pyramid has twice as many edges as faces, and 1 more vertex than faces.

Octa- means 8.

Tri- means 3.

a) An octagonal pyramid has 8 faces, 16 edges, and 9 vertices.

b) A triangular pyramid has 3 faces, 6 edges, and 4 vertices.

__

A triangular prism will have 3 additional edges for the second "base", and 2 additional vertices.

c) A triangular prism has 3 faces, 9 edges, and 6 vertices.

__

Additional comments

We have not counted the base as a "face." We have only counted those that meet at the point of the pyramid.

There are as many vertices on the base as there are faces, and there is one more vertex where all the faces meet.

There is one edge at the base for each face, and there is one edge from the base vertex to the point of the pyramid for each face--a total of two edges per face.

__

A triangular pyramid is shown in the attachment.

London answered 20 questions correctly on her multiple choice history final that had a total of 80 problems. What percentage of questions did London answer correctly on the final exam?

Answers

Answer:

25%

Step-by-step explanation:

correct/total

20/80

1/4

Changing to a decimal

.25

.25*100%

25%

Answer:

1/4 or 25%

Step-by-step explanation:

1). 20 / 80 = 1 / 4 = 25 %

Hope this helps

What is the distance, in units, between the points [tex](2, -6)[/tex]and (-4, 3)? Express your answer in simplest radical form.

Answers

Answer: [tex]3\sqrt{13}[/tex]

Step-by-step explanation:

[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]\sqrt{\left(-4-2\right)^2+\left(3-\left(-6\right)\right)^2}[/tex]

[tex]=3\sqrt{13}[/tex]

68) Volume of a Bucket: Determine the volume of a cylindrical bucket in cubic inches if the bucket's radius is 5 in.
and the height is 12 in. The formula for the volume of a cylinder is V = yrah. Use the Te key on your calculator.

Answers

Answer:

V = 300[tex]\pi[/tex] in³ or 942.48 in³

Step-by-step explanation:

Use the cylinder volume formula, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height.

Plug in the values and solve:

V = [tex]\pi[/tex](5²)(12)

V = 300[tex]\pi[/tex] in³ or 942.48 in³

BELL RINGER #2
A consultant charges $45 for each hour she works on a consultation, plus a flat $30
consulting fee. How many hours of work are included in a $210 bill for a consultation?
A. 2 4/5
B. 4
c. 4 2/3
D. 5 1 / 2
E. 7

Answers

Answer:

A. 2 4/5

Step-by-step explanation:

To find how many hours she worked for $210, you must get the amount of money she gets in 1 hour.

Because she charges $43 dollars every hour, and fines a fee of $30 flat, we must add both of the amount to get how many she earns in 1 hour.

So:

$45 + $30= $75

She earn $75 in 1 hour.

Next, divide $210 dollars that she earned for working for hour(s) to the amount of money she earned in 1 hour to find how many hours she worked.

So:

$210 ÷ $75= 2.8 hours

The answer is 2.8 hours

Because the given answers is in fraction, we must change the decimal into a fraction.

To change a decimal into a fraction, you must place the decimal over its place value.

Because 8 in the decimal 2.8 is in the tenths place, you must place it over 10

So:

2.8 into a decimal is 2 8/10

Simplify (only simplify if possible):

Divide 8 and 10 to their GCF which is 2.

So:

8 ÷ 2= 4

10 ÷ 2= 5

So the fraction and the answer is now:

2 4/5

I hope this helps! I'm sorry if it's wrong and too complicated.

Flying against the wind, a jet travels 1650 miles in 3 hours. Flying with the wind, the same jet travels 3480 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the wind?

Answers

Step-by-step explanation:

Let the rate of the plane be x

The rate of the wind be y

Against the wind

Resultant velocity = x-y

1650/3 = x - y

550 = x - y

With the wind

Resultant velocity = x + y

3480/4 = x + y

870 = x + y

Solve equation simultaneously

Add both equations

870+550 = x+y+x-y

1420 = 2x

x = 710

x + y = 870

y=870 - 710

y = 160

The rate of jet in still air = 710 mph

The rate of wind = 160 mph

HOPE IT HELPS!

PRETTY PLEASE MARK ME BRAINLIEST :-)

Howard is designing a chair swing ride. The swing ropes are 5 meters long, and in full swing they tilt in an angle of 29 degrees. Howard wants the chairs to be 2.75 meters above the ground in full swing. How tall should the pole of the swing ride be?

Answers

Answer:

Step-by-step explanation:7.12 meters tall

Express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression.

-7.5 and 5.4

Answers

Answer:

Step-by-step explanation:

m

Solve each system of equations 4x+6y=3 and -10x-15y=-4

Answers

Answer:

There is no solution

Step-by-step explanation:

they all subtract eachother out

Please answer this question now

Answers

Answer:

Approximately 439.6 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cone is the following:

[tex]A=\pi r^2+\pi r l[/tex]

Where, r is the radius and l is the slant height.

The radius is 7 and the slant height is 13. We also use 3.14 for π Thus:

[tex]A=(3.14)(7)^2+(3.14)(7)(13)\\\text{Use a Calculator}\\A\approx 439.6[/tex]

Answer:

292.77

Step-by-step explanation:

πr(r+[tex]\sqrt{h2+r2}[/tex])

13 x 2 = 26

7 x 2 = 14

26 + 14 = 40

[tex]\sqrt{40}[/tex] = 6.32

7 + 6.32 = 13.32

3.14 x 7 = 21.98

21.98 x 13.32 =

292.77

3
4
x
+
6
=
1
+
1
3
x

Answers

Answer:

[tex]\boxed{x = -5/21}[/tex]

Step-by-step explanation:

Hey there!

To simplify we need to combine like terms and use the communicative property,

34x + 6 = 1 + 13x

-13x to both sides

21x + 6 = 1

-6 to both sides

21x = -5

Divide both sides by 21

x = -5/21

Hope this helps :)

Answer: I'm guessing you need me to solve this for you.

I interpreted the equation this way: 34x + 6 = 1 + 13x

The solution is -5/21.

Step-by-step explanation:

34x + 6 = 1 + 13x

Step 1: Simplify both sides of the equation.

34x + 6 = 13x + 1

Step 2: Subtract 13x from both sides.

34x + 6 − 13x = 13x + 1 − 13x

21x + 6 = 1

Step 3: Subtract 6 from both sides.

21x + 6 − 6 = 1 − 6

21x = − 5

Step 4: Divide both sides by 21.

21x/21 = -5/21

x = -5/21

Hope this helped you!

+
If the
sides of a triangles are
6, 8 and n. how
many integer values of n
could be the
measure of the
third side of the triangle?

Answers

Answer:

11

Step-by-step explanation:

The sum of the shortest two sides must be greater than the longest side.

If n is the longest side:

6 + 8 > n

14 > n

If 8 is the longest side:

6 + n > 8

n > 2

So n must be an integer greater than 2 and less than 14.

n can be 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, or 13.

There are 11 possible integers.

[tex] \LARGE{ \boxed{ \rm{ \purple{Answer}}}}[/tex]

We know,

Sum of two sides of a triangle > Third side

Then,

⇛ 6 + 8 > n

⇛ 14 > n

Nextly,

Difference of two sides of a triangle < Third side

Then,

⇛ 8 - 6 < n

⇛ 2 < n

Then, Range of third side:

☃️ 2 < n < 14

Possible measures of 3rd sides = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 or 13.

There are 11 possible values of 3rd side. Out of them, any measure is the length of 3rd side.

━━━━━━━━━━━━━━━━━━━━

If g(x) = (-2x²) - 3. Find g(0).


Answers

Answer:

-3

Step-by-step explanation:

When g(0), it means that x=0.

So, if we use 0 instead of x, the answer becomes:

-3

Answer:

-3

Step-by-step explanation:

g(0) = (-2(0)^2) -3

as anything multiplied with 0 is 0,

g(0) = 0 - 3

= - 3

Let f(x) = x2 − 8x + 5. Find f(−1)

Answers

Answer:

14

Step-by-step explanation:

[tex]f(x)=x^2-8x+5[/tex]

now substitute x for -1

[tex]f(-1)=(-1)^2-8(-1)+5[/tex]

now solve

[tex]f(-1)=1+8+5[/tex]

[tex]f(-1)=14[/tex]

there is your answer! hope this helps! :)

Answer: 14

Explanation:

f(-1) = (-1)^2 - 8(-1) + 5
f(-1) = 1 + 8 + 5
f(-1) = 14

(a²b²-c²)(a²b²+c²)
simplify​

Answers

Answer:

a⁴b⁴ - c⁴

Step-by-step explanation:

The difference of squares formula states that (a - b)(a + b) = a² - b². In this case, a = a²b² and b = c² so a² - b² = (a²b²)² - (c²)² = a⁴b⁴ - c⁴.

Answer:

a^4b^4 - c^4.

Step-by-step explanation:

(a²b²-c²)(a²b²+c²)

Difference of 2 squares:

= (a²b²)^2 - (c²)^2

= a^4b^4 - c^4.

Type the correct answer in the box. Use numerals instead of words. The height of a baseball, in feet, is represented by this expression, where t is time in seconds. -16t squared+64t+3 The height of the baseball after 3.5 seconds is BLANK feet.

Answers

Answer:

31 Feets

Step-by-step explanation:

Given the expression for the height of a baseball:

Height(t) = -16t^2 +64t +3

Height in Feets ; time (t) in seconds

Height of baseball after 3.5 seconds :

Height(3.5) = -16(3.5)^2 + 64(3.5) + 3

Height = - 16(12.25) + 64(3.5) + 3

Height = - 196 + 224 + 3

Height = 31 Feets

Height after 3.5 seconds = 31 feets

Determine the value of x. 30° 45° 20° 60°

Answers

Answer:

x=30

Step-by-step explanation:

x+2x+3x=180

6x=180

x=180/6=30

a line is perpendicular to y=4x-2 and intersects the point (4,-11). what is the equation of this perpendicular line?

Answers

Answer:

y = -1/4x - 10

Step-by-step explanation:

Hey there!

Well to the slopes of 2 perpendicular lines are reciprocals of each other meaning if the line has a slope of 4 then it’s perpendicular line has a slope of -1/4.

Now to find the y intercept we need to graph,

y = -1/4x and point (4, -11)

Look at the image below.

By looking at the image below we can tell that in order for the perpendicular line to go through point (4,-11) it would be -10.

The equation is y = -1/4x - 10

Hope this helps :)

Other Questions
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