Answer all


1) 4x*3x


2) 2/3+ 1/4

Answer:

[tex]4.\\\text{E. }x=5, x=-6,\\\\5.\\\text{A. }x=7, x=-3\\\\\text{18.}\\\text{D. No mistakes.}[/tex]

Step-by-step explanation:

For [tex]a=|b|[/tex], there are two cases:

[tex]\begin{cases}a=b,\\a=-b\end{cases}[/tex]

Question 4:

Given [tex]5|2x+1|=55[/tex],

Divide both sides by 5:

[tex]|2x+1|=11[/tex]

Divide into two cases and solve:

[tex]\begin{cases}2x+1=11,2x=10, x=\boxed{5}\\-(2x+1)=11,2x+1=-11, 2x=-12, x=\boxed{-6}\end{cases}[/tex]

Therefore, the solutions to this equation are [tex]\boxed{\text{E. }x=5, x=-6}[/tex].

Question 5:

Given [tex]\frac{1}{2}|4x-8|-7=3[/tex],

Add 7 to both sides:

[tex]\frac{1}{2}|4x-8|=10[/tex]

Multiply both sides by 2:

[tex]|4x-8|=20[/tex]

Divide into two cases and solve:

[tex]\begin{cases}4x-8=20,4x=28, x=\boxed{7}\\-(4x-8)=20, 4x-8=-20, 4x=-12, x=\boxed{-3}\end{cases}[/tex]

Therefore, the solutions to this equation are [tex]\boxed{\text{A. }x=7, x=-3}[/tex]

Question 18:

There are no mistakes in the solution shown. The answer properly isolates the term with absolute value with no algebraic mistakes. Following that, the answer divides the equation into both absolute value cases and solves algebraically correctly. Therefore, the correct answer is [tex]\boxed{\text{D. No mistakes.}}[/tex]

Answer:

divide both sides by -9.

because of the negative sign of this multiplication factor the inequality changes from "greater than" to "less than".

x < -3

that is the solution to this inequality.

we have to find the value of the x°=<GHC

In the triangle BDH,

<D=31°

<B=47°

we know that,

Sum of three angle of a triangle is 180°

According to the question,

<D+<B+<BHD=180°

31°+47°+<BHD=180°

78°+<BHD=180°

<BHD=180°-78°

<BHD=102°

But,

<GHC and <BHD forms a straight line

so,

<GHC+<BHD=180°

102°+x=180°

x=180°-102°

x=78°

Therefore,

The value of x is 78°

Answer:

at x = 11

0 =-4.5X +49.5

x = 49.5/4.5

x = 11

Step-by-step explanation:

x1 y1  x2 y2

1 45  3 36

(Y2-Y1) (36)-(45)=   -9  ΔY -9

(X2-X1) (3)-(1)=    2  ΔX 2

slope= -4  1/2    

B= 49  1/2    

Y =-4.5X +49.5    

Answer:

symmetric property

Step-by-step explanation:

Multiplication property would require multiplication

Subtraction property would require subtraction

Reflexive property  says x=x

The symmetric property  says if a=b then b=a

OD = DO

OF = FO

Convenience sampling.

Answer:

[tex]8x^{4}[/tex]

3n-10

(a÷5)+12

Step-by-step explanation:

Numbers listed as in the picture.

70) 8 * [tex]x^{4}[/tex]= [tex]8x^{4}[/tex]

71) 3 * n -10= 3n-10

72) 12+ a/5= (a÷5)-12

Answer:

B For each x increase of 1, the y increases by a common factor of 3

Step-by-step explanation:

so it means that y is adding 3 every time x adds 1

Answer:D

The last one explanation of that graphic line is correct answer.

Answer:

x = 17/4

Step-by-step explanation:

Let x = the number

8x-14 = 4x+3

Subtract 4x from each side

8x -14-4x = 4x+3-4x

4x-14 = 3

Add 14 to each side

4x-14+14 = 3+14

4x = 17

Divide by 4

4x/4 = 17/4

x = 17/4

Step-by-step explanation:

-5x - 4y= -117x + 3y = 18

-5x +117x = 3y + 4y = 18

112x = 7y = 18

Answer:

Two functions f(x) and g(x) are inverses if and only if:

f( g(x) ) = x

and

g( f(x) ) = x

In this case, we have:

f(x) = 1*x - 6

g(x) = 6*x + 1

Let's check if the functions are inverses.

f( g(x) ) = 1*g(x) - 6 = 1*(6x + 1) - 6 = 6x + 1 - 6 = 6x - 5

and

g( f(x) ) = 6*f(x) + 1 = 6*(1x - 6) + 1 = 6x - 36 + 1 = 6x - 35

So we can see that:

f( g(x) ) ≠ x

g( f(x) ) ≠ x

Thus, f(x) and g(x) are not inverses.

Particularly, the two compositions are:

f( g(x) ) =  6x - 5

g( f(x) ) =  6x - 35

Both of these are linear functions, thus the domain in both cases is the set of all real numbers, that can be written as:

domain = (-∞, ∞)

Answer:

Solutions given:

Velocity ratio V.R =5

effort =500N

efficiency =80%

magnitude of load=?

mechanical advantage [M.A ]

we have

efficiency =M.A/V.R*100%

80=M.A./5*100

80/100*5=M.A

M.A.=4

again

we have

M.A =load/effort

4=load/500

load=500*4

load=2000N

Answer:

-1

Step-by-step explanation:

Increasing the x-value by one results in the y-value decreasing by 1. Therefore, the average rate of change is -1.

Answer: -1

Step-by-step explanation: ;)

Answer

Slope-intercept form: y=5x-2

Standard form: 5x-y=2

Explanation

Slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. You can just plug in the numbers to go y=5x-2.

Standard form is Ax+By=C. This form is usually used to find the x-intercept and y=intercept. You can rearrange the numbers to get standard form; 5x-y=2.

Answer:

Step-by-step explanation:

If AD is an altitude, then by definition it drops from the vertex angle (the top angle) and meets the base at a right angle, which measures 90 degrees. That means that 17x + 73 is a right angle:

17x + 73 = 90 and

17x = 17 so

x = 1

Answer:

119.95 years

Step-by-step explanation:

The general equation is given by:

[tex]P = A*(1 + \frac{r}{n} )^{n*t}[/tex]

Where:

A is the initial amount, we know that the first deposit is of $150, then:

A = $150

t is the variable, in this case, is the number of years.

n =  number of times that the interest is compounded in one unit of t, because the interest is compounded monthly, we have n = 12.

r = interest rate in decimal form.

r = 2.5%/100% = 0.025

Replacing these in our equation, we get that:

[tex]P = 150*(1 + \frac{0.025}{12} )^{12*t}[/tex]

Now we want to find the time such that his savings, P, are equal to $3000.

Then we need to solve the equation:

[tex]P = 150*(1 + \frac{0.025}{12} )^{12*t} = 3000[/tex]

[tex](1 + \frac{0.025}{12} )^{12*t} = 3000/150 = 20\\[/tex]

Now, remember that:

Ln(a^x) = x*ln(a)

So if we apply the natural logarithm to bot sides, we get:

[tex]Ln((1 + \frac{0.025}{12} )^{12*t}) = Ln( 20)\\\\(12*t)*Ln(1 + \frac{0.025}{12}) = Ln(20)\\\\t = \frac{Ln(20)}{12*Ln(1 + \frac{0.025}{12})} = 119.95[/tex]

So after 119.95 years you will have the $3000.

18.1

Answer:

18.1 miles

Step-by-step explanation:

TOTAL distance= sum of individual distance

[tex]3 \times \frac{1}{2} + 5 \times \frac{3}{5} + 2 \times \frac{1}{3} + 6 \times \frac{2}{3} [/tex]

[tex] = 18.1miles[/tex]

Answer:

18 1/10

Step-by-step explanation:

Add the total distances

Get a common denominator of 30

3 15/30 + 5 18/30  + 2 10/30 + 6 20/30

16 63/30

16 + 60/30 +3/30

18+3/30

18 1/10

Answer: [tex]56\ kmph,\quad 50\ kmph[/tex]

Step-by-step explanation:

Given

Two cars are 600 km apart moving towards each other

Difference in their speed is 6 kmph

After 4.5 hr, they are 123 km apart that is, they covered a distance of [tex]600-123=477\ km[/tex] in 4.5 hours

Suppose their speeds is [tex]v_1\ \text{and}\ v_2[/tex]

[tex]\therefore v_1-v_2=6\quad \ldots(i)[/tex]

Also, distance traveled is given by

[tex]\Rightarrow 477=[v_1+v_2]4.5\\\Rightarrow v_1+v_2=106\quad \ldots(ii)[/tex]

Solve, (i) and (ii) , we get [tex]v_1=56\ kmph\ \text{and}\ v_2=50\ kmph[/tex]

Answer:

Check out the answer. Hope it helps!!

Answer:

y = 100,000 (1 + 0.04) ²⁰

Step-by-step explanation:

Here:

100,000 = original amount.

0.04 = rate (a percent)

and

20 = number of times you need to run the simulation.

Answer:

irrelevant is the answer for it doesn't belong

Answer:

xsqrt(2)

Step-by-step explanation:

sqrt(14x^3) / sqrt(7x)

We know sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt(14x^3/7x)

sqrt(2x^2)

sqrt(ab) = sqrt(a) sqrt(b)

sqrt(2) sqrt(x^2)

sqrt(2) x

xsqrt(2)

Answer:

B

Step-by-step explanation:

first you can cross out choices C and D because the equation that they gave you has a positive y-intercept

so it has to be shifting 10 units up

now you're left with choices A and B

the answer is choice B because the slope is 5 which is also 5/1 (rise over run)

that would mean that it's gradually growing slimmer (the function)

you can also check by graphing it and it indeed is slimmer than y=x^2

so that concludes that it is being stretched vertically

Answer:

d)

Step-by-step explanation:

c/d - 2c/5d = 5c/5d - 2c/5d = 3c/5d = x

3c/d = 5x

c/d = 5x/3 = 5/3 × x

Answer:

1/2

slope = Δy/Δx

start at (-1,3)  to get to the line from there you can go down 1 ( Δy = -1)

and left 2 (Δx = -2)

-1/-2 = 1/2

Step-by-step explanation:

Answer:

20 < L < 24

Step-by-step explanation:

We know that in any given triangle, the length of two sides is always greater than the length of the third side.

Since the sail is a triangle having length of one side as 22 feet and the length of another side as 2 feet, and let L be the length of the third side.

It follows from our triangle rule of sides above that

22 + 2 > L  (1)

22 + L > 2   (2)and

L + 2 > 22   (3)

It follows that from (1)

22 + 2 > L  

⇒  24 > L (4)

It follows that from (2)

22 + L > 2

⇒ L > 2 - 22

⇒ L > - 44  (5) and

It follows that from (3)

L + 2 > 22

⇒ L > 22 - 2

⇒ L > 20  (6)

Since from (5) and (6),

L > -44 and L > 20

and 20 > -44 ⇒ L > 20

⇒ 20 < L (7)

From (4) 24 > L ⇒ L < 24 (8)

Combining (7) and (8), we have

20 < L < 24

So, the possible range of values of the third side are 20 < L < 24

Answer:

Numbers greater than or equal to 0.

Step-by-step explanation:

The domain of this function is {x∈R | x≥0}, meaning that x can be anything greater than or equal to 0.

Answer:

11. 40.5

12. 84

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

= 3200 ÷ 35

= 91.43

round up to nearest whole number

= 92 km