Referring to the Fig. in Question #3, evaluate the expression shown when a = 3, b = 8, c = 4 Please help.

Answer:

[tex]-\frac{16.7}{13.3}[/tex]

Step-by-step explanation:

Step 1: Collect the like terms

8.8 + 7.9 = -5.5x - 7.8x

Step 2: Simplify

16.7 = -13.3x

Step 3: Divide both sides by -13.3

[tex]\frac{16.7}{-13.3} =\frac{-13.3}{-13.3}x[/tex]

[tex]x =- \frac{16.7}{13.3}[/tex]

Therefore the answer is [tex]-\frac{16.7}{13.3}[/tex]

Answer:

  x = -1 34/133

Step-by-step explanation:

Given

  8.8 +7.8x = -7.9 -5.5x

  13.3x = -16.7 . . . . . . . . . . . add 5.5x -8.8

  x = -16.7/13.3 = -167/133 . . . . divide by 13.3 and simplify

  x = -1 34/133 ≈ -1.25564

Answer:

280-17=273

Step-by-step explanation:

because 80-17 equals 73 sooooooo add 200

Answer:

B. 1995

Step-by-step explanation:

As per the graph the lowest production was in 1995, the production figure was around 203 billion dollars

So the answer choice is B. 1995

Answer:

Option D. m<A = 43, m<B = 55, a = 20

Step-by-step explanation:

1. Determination of angle B.

Angle C = 82

Opposite C (c) = 29

Opposite B (b) = 24

Angle B =?

Using Sine rule, we can obtain the value of angle B as follow:

b/Sine B= c/Sine C

24/Sine B = 29/Sine 82

Cross multiply

29 × Sine B = 24 × Sine 82

Divide both side by 29

Sine B = (24 × Sine 82) /29

Sine B = 0.8195

Take the inverse of Sine.

B = Sine¯¹ (0.8195)

B = 55

2. Determination of angle A.

Angle C = 82

Angle B = 55

Angle A =?

The value of angle A can be obtained as follow:

A + B + C = 180 (sum of angle in a triangle)

A + 55 + 82 = 180

A + 137 = 180

Collect like terms

A = 180 – 137

A = 43

3. Determination of side a (Opposite A)

Angle C = 82

Opposite C (c) = 29

Angle A = 43

Opposite A (a) =?

The value 'a' can be obtained as by using sine rule as illustrated below:

a/Sine A = c/Sine C

a/Sine 43 = 29/Sine 82

Cross multiply

a × Sine 82 = 29 × Sine 43

Divide both side by Sine 82

a = (29 × Sine 43) /Sine 82

a = 20

Therefore,

m<A = 43, m<B = 55, a = 20

Answer:

0

Step-by-step explanation:

0 · |-6|

Absolute value means take the non negative number

0* 6

0

The value of the given absolute value equation 0 · |-6| is 0.

Given that an absolute value equation 0 · |-6|, we need to evaluate this.

To evaluate the expression 0 · |-6|, let's break it down step by step:

First, calculate the absolute value of -6:

|-6| = 6

Now, multiply the result from step 1 by 0:

0 · 6 = 0

When you multiply any number by 0, the result is always 0.

In this case, even though |-6| equals 6, multiplying it by 0 will make the overall result 0.

This is a fundamental property of multiplication with zero.

So, the final answer is 0.

Learn more about absolute value click;

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Answer:

r=1

Step-by-step explanation:

-5r+2r=-3r

-3r=-3

Divide by -3 on both sides

r=1

Answer:

2b - 8z - 6

Step-by-step explanation:

Rearrange the equation, so like terms are near each other

-2b+4b-3z-5z-6

Now we add the b's and z's to get,

2b - 8z - 6

Answer:

2b -8z -6

Step-by-step explanation:

−2b−5z−6+4b−3z​

Combine like terms

−2b+4b−5z−3z​−6

2b -8z -6

Answer:

Step-by-step explanation:

Call T the top

call G the bottom

T G B is a right triangle

37 at B, 90 at G, thus 53 at BTG

TGA is a right triangle

25 at A, 90 at G, thus 65 at ATG

thus 122 at ABT

law of sines:

sin 25 / BT = sin 12/ 57

so BT = 156 meters (first answer)

now angle ABT = 180 - 12 - 25

= 143

so

sin 143 /AT = sin12/57

AT = 164 meters, second answer

Answer: He run 7 high-speed intervals and 8 low-speed intervals.

Step-by-step explanation:

Let x = Number of high-speed intervals.

y= Number of low-speed intervals .

He runs high-speed intervals in 16 seconds, and low-speed intervals in 23 seconds, and he runs a combined total of 15 intervals in 4 minutes and 56 seconds.

4 min 56 sec = (4(60)+56) sec = 296  sec   [ 1 minute = 60 seconds]

According to the question , we have the following linear equations :

[tex]x+y=15\ ...(i)\\\\ 16x+23y=296\ ...(ii)[/tex]

Multiply (i)by 16 , we get

[tex]16x+16y=240\ ...(iii)[/tex]

Subtract (iii) from (ii)

[tex]7y=56\\\\\Rightarrow\ y=8[/tex]

Put value of y in (i) , we get

[tex]x+8=15\Rightarrow\ x=7[/tex]

Hence, he run 7 high-speed intervals and 8 low-speed intervals.

Answer:

[tex](-\frac{3}{22},\frac{185}{22} )[/tex]

Step-by-step explanation:

Step 1: Find out what the question is asking

Because we want the point to be equidistant to all the vertices of the triangle formed we want the circumcenter of the triangle as it is equidistant from all of the vertices, a circumcenter is made from the perpendicular bisectors of the triangle

Step 2: Give the vertices variables

A = (-4,8)

B = (-1,-1)

C = (3,7)

Step 2: Find the Circumcenter

Find the mid point of side AB

MAB

[tex]=(\frac{-4+(-1)}{2} ,\frac{8+(-1)}{2} )\\=(\frac{3}{2},\frac{7}{2} )[/tex]

Find the slope of side AB

mAB

[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-(-1)}{-4-(-1)} \\=\frac{9}{-3}\\ =-3[/tex]

Solve for 'b'

[tex](\frac{7}{2})=(-3)(\frac{3}{2} ) +b\\\frac{7}{2}=-\frac{9}{2}+b\\\frac{7}{2}+ \frac{9}{2}=b\\b = 8[/tex]

Therefore the equation for line AB is:

y = -3x + 8

Find the midpoint of side AC

MAC

[tex]=(\frac{-4+(3)}{2} ,\frac{8+(7)}{2} )\\=(-\frac{1}{2},\frac{15}{2} )[/tex]

Find slope of AC

mAC

[tex]=\frac{y2-y1}{x2-x1} \\=\frac{8-7}{-4-3} \\=\frac{1}{-7}\\ =-\frac{1}{7}[/tex]

Solve for 'b'

[tex]y=mx+b\\\frac{15}{2} =-\frac{1}{7} (-\frac{1}{2} )+b\\\frac{15}{2} =-\frac{1}{14} +b\\\frac{1}{14}+\frac{15}{2} = b\\b=\frac{53}{7}[/tex]

Therefore the equation for line AC is:

y = [tex]-\frac{1}{7}[/tex]x+[tex]\frac{53}{7}[/tex]

Step 3: Find the P.O.I of the 2 lines

Set both of the equation equal to each other

[tex]3x + 8=-\frac{1}{7} x+\frac{53}{7} \\3x +\frac{1}{7} x=\frac{53}{7}-8\\\frac{22}{7} x=-\frac{3}{7} \\x=-\frac{3}{22}[/tex]

We now know 'x' and we substitute x into any equation to find 'y'

[tex]y = -3(-\frac{3}{22} ) + 8\\y = \frac{9}{22} + 8\\y = \frac{185}{22}[/tex]

Therefore the new firehouse should be built at [tex](-\frac{3}{22},\frac{185}{22} )[/tex]

Answer:

b = sqrt(39)

Step-by-step explanation:

Since this is a  right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2

5^2 + b^2 = 8^2

25+b^2 =64

b^2 =64-25

b^2 =39

Take the square root of each side

b = sqrt(39)

Answer:

[tex]\sqrt{39}[/tex]

Step-by-step explanation:

Step 1: Find the unknown wide using Pythagorean Theorem

[tex]a^{2}+ b^{2} = c^{2}[/tex]

[tex]a^{2}+ 5^{2} = 8^{2}[/tex]

[tex]a^{2}+ 25 = 64[/tex]

[tex]a^{2}= 64-25[/tex]

[tex]a^{2=39[/tex]

[tex]\sqrt{a^{2}} = \sqrt{39}[/tex]

[tex]a=\sqrt{39}[/tex]

[tex]\sqrt{39}[/tex] cannot be simplified and more

Therefore the unknown side is [tex]\sqrt{39}[/tex]

Answer:

An action performed without any concious thoughts

The simple definition of reflex is the sudden movement that occurs when it responds to a stimulus in the body. This movement is without any conscious thought beforehand.

For example, you are facing one way and a ball gets thrown toward you from behind. If you have fast enough reflexes, you will sense the ball coming from behind and turn around to catch it.

Best of Luck!

Answer:

The triangle ABC is not a right triangle

Step-by-step explanation:

For a right angle triangle, we have;

The square of the longest side or leg of the triangle is equal to the  sum of the squares of the other two legs

The parameters given from the question, are;

The square of of the length of side A = 7 inch²

The square of of the length of side B = 18 inch²

The square of of the length of side C = 27 inch²

Therefore, the the longest side is side C and the inch² sum of the squares of the other two sides are 7 + 18 = 25 inch² which is less than the square of the  length of side C = 27  inch², therefore, the triangle ABC is not a right triangle.

Answer:

Not a right angle

Step-by-step explanation:

Khan academy is never wrong :3

Answer:

1320

Step-by-step explanation:

as

SI=(P×T×R)/100

SI=(2000×12×11/2)/100

SI=132000/100

:.SI=1320

Answer:1320

Step-by-step explanation:2000×12×11/2/100

Two divide by twelve=6

2000÷100=20

20×6×11=1320

Answer:

The difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Step-by-step explanation:

We know that the area of a triangle A = 1/2bh where b = base and h = height.

Let A be the area of triangle 1 with base (3x + 7) and height (5x - 1).

So its area A = (3x + 7)(5x - 1)/2.

Now for the second triangle, the base is tripled, so its base is 3(3x + 7) and its height is doubled, so its height is 2(5x - 1)

So its area is A' = 3(3x + 7) × 2(5x - 1)/2 = 3(3x + 7)(5x - 1)

So the difference between the area of the original triangle and the new triangle is

A' - A = 3(3x + 7)(5x - 1) - (3x + 7)(5x - 1)/2

= (3x + 7)(5x - 1)(3 - 1/2)

= 5(3x + 7)(5x - 1)/2

So the difference between the area of the original triangle and the area of the new triangle is 5(3x + 7)(5x - 1)/2

Answer: A.  [tex]h(x)=16x^2-50x+38[/tex]

Step-by-step explanation:

Given: Francesca graphs the function  [tex]f(x) =2x - 3[/tex], George graphs the function [tex]g(x) = 4x^2 -x - 1[/tex].

Harold graphs the function [tex]h(x) = g(f(x))[/tex].

i.e. [tex]h(x)=g(2x - 3)[/tex]  [put value of f(x)]

[tex]=4(2x-3)^2-(2x-3)-1\\\\= 4((2x)^2-2(2x)(3)+3^2)-2x+3-1\ \ [(a-b)^2=a^2-2ab+b^2]\\\\= 4(4x^2-12x+9)-2x+2\\\\=16x^2-48x+36-2x+2\\\\=16x^2-50x+38[/tex]

So, Harold graph [tex]h(x)=16x^2-50x+38[/tex]

Hence, the correct option is A.  [tex]h(x)=16x^2-50x+38[/tex]

Answer:

8

Step-by-step explanation:

3 - (-5)

This can be rewitten to

3 + 5

Why?

2 negatives cancel each other out to make a positive, therefore:

3 + 5 = 8 or 3 - (-5) = 8

Answer:

8

3-(-5)=8 because two negatives make a positive so it is like adding 3 and 5 together to get the answer of 8.

Step-by-step explanation:

so the answer must be 2025 km.

The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be 2025 km.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

A plane is flying at a cruising speed of 900 km/h.

The distance of the plane travel from 11:15 a.m. to 1:30 p.m. on the same day will be

From 11:15 a.m. to 1:30 p.m., there are 2.25 hours.

Then the distance will be

D = 900 x 2.25

D = 2025 km

More about the speed link is given below.

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Answer:

a = 29/46

b= - 9/46

Step-by-step explanation:

Given:

Rationalizing the left side:

Comparing the left and right sides:

Answer:

  y +2 = 4(x -3)

Step-by-step explanation:

Point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

For m = 4 and (h, k) = (3, -2), the equation is ...

  y +2 = 4(x -3) . . . . . matches the first choice

Answer:

1.5%

Step-by-step explanation:

To find Rate in Simple Interest:

R = 100 S.I / T × P

R = 100 × 90/10 × 600

R = 9/6

R = 1.5%

1.5% is the rate.

Answer:

D. 13.

Step-by-step explanation:

f(x)=2x+1/x-4

let y = 2x + 1 / x - 4

xy - 4y = 2x + 1

xy - 2x = 4y + 1

x(y - 2) = 4y + 1

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

So f^-1(x) = (4x + 1)/(x - 2)

and f^-1(3) = (4(3) + 1) / (3 - 2)

= 13/1

= 13.

Answer:

Step-by-step explanation:

If we have triangle of sides: a, b, c, and a < b < c (or b<a<c) then:

for triangle to exist:

                                  a + b > c

So:

if  a=11, b=16  then 11 + 16 > c     ⇒   c < 27

if a=11, c = 16 then  11 + b > 16    ⇒   b > 5

We don't know if the unknown side (x) is the longest or not, so it has to be greater than 5 and less than 27

5 < x < 27

Answer:

D

Step-by-step explanation:

Insert 3 in place of x in the inverse function.

Your answer would be D, the equation is a function because it is a polynomial and all polynomials are functions.

Step-by-step explanation: I like to remember that polynomials have no negative , fraction exponents and no division. In this case everything is positive so I knew it was a polynomial , and like the answer says all polynomials are functions ! Hope this helped

Answer:

Elena has 6 and fran has 8

Step-by-step explanation:

Answer:

v = 18

Step-by-step explanation:

Given

79 = 61 + v ( subtract 61 from both sides )

18 = v

Explanation:

There are n = 8 sides in a regular octagon. The smallest angle of rotational symmetry is 360/n = 360/8 = 45 degrees. Rotating this amount will not change the regular octagon. The before and after will look identical.

ANSWER:

Your answer is 45 Degrees