4. Find the solution for the following problem. Explain your reasoning."
What is the solution to the equation below?
2(x - 3) = 2x + 5

Answer :

Brian has $49 left.

Step by step explanation :

Step 1 : Find how much money Brian spends on rent and food.

First question we should be asking is what is 3/5 of 735?

Let's find that.

[tex]\frac{3}{5}[/tex] * [tex]\frac{735}{1}[/tex]

= [tex]\frac{(3)(735)}{(5)(1)}[/tex]

= [tex]\frac{2205}{5}[/tex]

= 441

We know Brian spends $441 on rent. Now we find how much he spends on food.

[tex]\frac{1}{3} * \frac{735}{1}[/tex]

= [tex]\frac{(1)(735)}{(3)(1)}[/tex]

= [tex]\frac{735}{3}[/tex]

= 245

Brian spends $245 on food.

Step 2 : Add what he spends on rent and food together.

$441 + $245 = $686

Step 3 : To find out how much money Brian has left, we subtract $686 from $735.

$735 - $686 = $49

Conclusion : Brian has $49 left.

Hope this helps, please mark brainliest if possible. Have a nice day.

Answer:

f(x) = x² - 3x - 10

Step-by-step explanation:

Given zeros x = - 2 and x = 5, then the corresponding factors are

(x + 2) and (x - 5) , so

f(x) = (x + 2)(x - 5) ← expand using FOIL

     = X² - 3X - 10

Answer:

f(x) = x² - 3x - 10

(option D)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

if you divide both sides by ax+b you get 1=1 which is not a solution for x.

Answer:

Step-by-step explanation:

Reflection of (-8 , -1) over y = -x is (-1 , 8)

Image of (x , y) over the line y = -x is (y, -x)

Answer:

reflection on the y axis (x,y)=(-x,y)

(-8,-1)=(8,-1)

Step-by-step explanation:

hope this is helpful

Answer:

a = 18

Step-by-step explanation:

3(x+6)-x = 2x + a

Distribute

3x +18 -x = 2x+a

2x +18 = 2x+a

Subtract 2x from each side

18 = a

Answer:

0.8

Step-by-step explanation:   6  22  6  06

I plotted both sides of the equation using DEMOS graphing calculator and located the intersection at (0.779, 2.135)  I found that easier than finding the delta difference of both sides of the equation for the table or solving for x.

Answer:

61.6 dollars

Step-by-step explanation:

So, lets go over what we know:

The shows orginally cost 88 dollars.

They are 30% less than that.

This basically means that the shoes will cost 70 percent of their orginal price.

We can basically find the new cost by multiplying the 88 dollars by the 70 percent.

Or, multiplying 88 by 0.7, which is the decimal form of 70%.

88*0.7=61.6

How did I get this?

Multiply 80 by 0.7:

7*8=56

We have 0.7 so it = 5.6

However, it's tens place is 80, not 8, so it will be = 56

It is the same thing in the ones place, however it is 8 not 80, so it will be 0.7*8

= 5.6

56+5.6=61.6

So 61.6 is our answer.

Hope this helps!

Answer:

$61.60

Step-by-step explanation:

the other answer is correct.

just to add some explanation about the % considerations.

we know $88 is 100%

in order to get any other % value, we need to divide the original value by 100 (that gives us 1%), and then multiply with the number of % we want to have - in our example 70, as the discount is 30% (so the remaining part is 70% of the original price).

so, in order to get 70% we actually have to do the above things and divide by 100 and multiply by 70.

70% = (100% / 100) × 70 = 100% × 70 / 100

70 / 100 = 0.7 (that is how answer 1 actually got that multiplication factor)

70% = 100% × 0.7

70% = $88 × 0.7 = $61.60

The measure of angle OCD from the given figure is 58°.

Given that, the points A, B, C and D lie on a circle Centre O.

A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.

Here, OC and OB are radius of a circle, then BOC is isosceles triangle

Now, ∠BOC+∠OBC+∠OCB=180°

50°+∠OBC+∠OBC=180°

⇒ 2∠OBC=130°

⇒ ∠OBC=65°

Here, ∠OCD=∠BCD-65°

⇒ x=123-65=58°

Hence, the measure of angle OCD from the given figure is 58°.

To learn more about the circle visit:

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Answer:

C. Add 9.6, then divide by 3.2.

Step-by-step explanation:

[tex]3.2x−9.6=38.4[/tex]

[tex]3.2x=38.4+9.6[/tex]

[tex]3.2x=48[/tex]

[tex]x = 15[/tex]

Answer:

3ab

Step-by-step explanation:

because it is answer

Answer:

-1625

Step-by-step explanation:

→ (-125) × 5 + (-125) × 8

Taking (-125) as in common,

→ (-125) × (8 + 5)

→ (-125) × 13

→ -1625

Answer:

116 cm²

Step-by-step explanation:

a = side length of A

b = side length of B

b = a + 4

b² = a² + 70

(a+4)² = a² + 70

a² + 8a + 16 = a² + 70

8a + 16 = 70

8a = 54

a = 54/8 = 27/4 = 6.75

b² = a² + 70 = 6.75² + 70 = 45.5625 + 70 =

= 115.5625 ≈ 116 cm²

our does your teacher mean 3 significant figures after the decimal point ? then it would be

115.563 cm²

Answer:

227 * 7^2

Put into calculator

Step-by-step explanation:

Area of a circle is pi * r^2 (pi times radius squared)

Just put the numbers in

227 * 7^2

Put into calculator and there you go

Answer:

Option (2)

Step-by-step explanation:

ΔDEF is a dilation image of ΔABC.

Rule for the dilation,

Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the original triangle}}[/tex]

                    = [tex]\frac{DE}{AB}[/tex]

                    = [tex]\frac{4}{8}[/tex]

                    = [tex]\frac{1}{2}[/tex]

Therefore, scale factor by which ΔABC is dilated is [tex]\frac{1}{2}[/tex].

Option (2) will be the correct option.

Answer:

641654654

Step-by-step explanation:

Answer:

1) r=9 v=972

2) r=6 v=288

3) r=12 v=2,304

Step-by-step explanation:

Sample Answer on edmentum

Answer:

The slope of this line is 3/4.

Step-by-step explanation:

Solving this equation 3x–4y–12=0 for y puts the equation into the form

                                            y = mx + b, where m is the slope of the line.

One way of solving for 4y here is to add 4y to both sides, obtaining:

                                           3x - 12 = 4y

Dividing all three terms by 4 yields

                                              y = (3/4)x - 3

The slope of this line is 3/4.

Answer:

A. y=-6

Step-by-step explanation:

Using the answer, it would make a horizontal line which would be perpendicular to the y axis.

Answer:

Step-by-step explanation:

total cost of the meal = $120

tip = 20%

tip amount = ?

total cost of the meal with tip = ?

tip amount = tip% 0f total cost of the meal

=20/100 * $120

=$2400/100

=$24

total cost of the meal with tip = total cost of the meal without tip + tip amount

=$120 + $24

=$144

Answer:

Hey there!

The given equation helps us understand the relationship between Amber's tips earned and the money she earned through her hourly wage. This information will add up to equal a grand total of $69.20.

We know that Amber earns $15.50 in tips during her 6 hour shift. Therefore, this is not considered part of her wage. This would be one of the constants of our equation.

We also know that Amber earns a fixed hourly wage, but we don't know what this wage is. We need to find w.

[tex]6w+15.5=\$69.20[/tex]

Subtract 15.5 from both sides of the equation (and get rid of the currency symbol).

[tex]6w=69.20-15.5\\6w=53.7[/tex]

Divide both sides of the equation by 6.

[tex]\displaystyle \frac{6w}{6}=\frac{53.7}{6}\\\\w=8.95[/tex]

Therefore, Amber's hourly wage is $8.95.

Answer:

its 8

Step-by-step explanation:

4 times 2 is 8 and you cant get 6 or 12

Answer:

A

Step-by-step explanation:

Area of base = length x width = 4 * 2 = 8 square units

Answer:

3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic

(ii). Sequence [tex]W_{n}[/tex] is in Geometric

3b. 2520 Sum of First 20 Arithmetic Sequence

3c. 98292 Sum of First 13 Geometric Sequence

Step-by-step explanation:

According to the Question,

3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....

it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12

(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....

A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2

3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]

(Where, a=first term of sequence , n= number of term & d=common difference)

[tex]S_{n}[/tex]=10[2×12 + 19×12]

[tex]S_{n}[/tex] =10×252  ⇔  2520

3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]

(Where, a=first term of sequence , n= number of term & r= common ratio)

[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1

[tex]S_{n}[/tex]=12×8191  ⇔  98292

Answer: 0.13 cents per minute.

Step-by-step explanation:

7.80 divided by 60(min per hour.)= .13 cents.

Answer:

∠RST = ∠SRU because they are alternate angles.

Step-by-step explanation:

Hope it helps .

Answer:

4.9 x 10^5

Step-by-step explanation:

the answer is 4.9 x 10^5

Answer:

$1674

$16926

Step-by-step explanation:

A used automobile dealership recently reduced the price of a used compact car by 9%. If the price of the car before the discount was $18,600, find the discount and the new price?

Discount = percentage discount x original price

0.09 x  $18,600 = $1674

New price = original price - discount

$18,600 - $1674 = $16926

Answer:

6^2 + 6^2 = 72 sqrt(72) =     8.49

Step-by-step explanation:

use pythagorean therom a^2 + b^2 = c^2

where c is the hyp.

Answer: 6 sqrt 2

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

you know that (a+b+c)/d is the same as a/d + b/d + c/d.

and (a×b)/(c×d) is the same as (a/c)×(b/d).

and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.

14a⁸y³ / 7a⁴y

14/7 = 2

a⁸/a⁴ = a⁴

y³/y = y²

=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.

but let's practice and look at the second part :

-7a⁴y⁵ / 7a⁴y

-7/7 = -1

a⁴/a⁴ = 1

y⁵/y = y⁴

=> -y⁴ is the second part. B is still confirmed.

the third part :

28a¹²y² / 7a⁴y

28/7 = 4

a¹²/a⁴ = a⁸

y²/y = y

=> + 4a⁸y is the third part. B confirmed.

Given:

In parallelogram PQRS, [tex]m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ[/tex].

To find:

The value of x.

Solution:

In a parallelogram, the consecutive interior angles are supplementary angles.

In parallelogram PQRS,

[tex]m\angle Q+m\angle R=180^\circ[/tex]            (Supplementary angles)

[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]

[tex](20+8x)^\circ=180^\circ[/tex]

[tex]20+8x=180[/tex]

Subtracting 20 from both sides, we get

[tex]8x=180-20[/tex]

[tex]8x=160[/tex]

Divide both sides by 8.

[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]

[tex]x=20[/tex]

Therefore, the correct option is C.

Answer:

c

Step-by-step explanation:

Answer:

The answer (D)

x=log2(50/3)

Thus, [tex]x=10log_{2}\frac{50}{3}[/tex] so option (B) is the correct answer.

"A logarithm tells what exponent (or power) is needed to make a certain number, so logarithms are the inverse (opposite) of exponentiation. Just as an exponential function has three parts, a logarithm has three parts as well: a base, an argument, and an answer (also called power)".

For the given situation,

The equation is

[tex]-6(2)^{0.1x} = -100[/tex]

The equation can be expressed in logarithm as

[tex]a^{x}=b\\[/tex]

⇒ [tex]x=log_{a}b[/tex]

So, [tex]-6(2)^{0.1x} = -100[/tex]

⇒ [tex]2^{0.1x}=\frac{-100}{-6} \\[/tex]

⇒ [tex]0.1x=log_{2}\frac{50}{3}[/tex]

⇒[tex]\frac{1}{10}x=log_{2} \frac{50}{3}[/tex]

⇒[tex]x=10log_{2}\frac{50}{3}[/tex]

Hence we can conclude that [tex]x=10log_{2}\frac{50}{3}[/tex]  option (B) is the correct answer.

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Answer:

83.5units

Step-by-step explanation:

Find the diagram attached

Since both triangles are similar, then;

AB/DB = BC/EF

11/54 = 17/EF

Cross multiply

11EF = 17 * 54

11EF = 918

EF = 918/11

EF = 83.5

Hence the length of EF to the nearest tenth is 83.5units