What expression represents the quotient?

Answer:

17.41

Step-by-step explanation:

497.50 x 0.035

Jodi's investment will earn $17.41 in interest in one year at an interest rate of 3.5%. Therefore, after one year, her investment will be worth $514.91.

To find out how much Jodi's investment is worth in one year, we can use the formula for simple interest, which is Interest = Principal x Rate x Time. In this case, the principal is $497.50, the rate is 3.5% (or 0.035 in decimal form), and the time is 1 year.

So, the interest earned in one year would be $497.50 x 0.035 x 1 = $17.41.

To find the total worth of her investment after one year, we add the interest earned to the initial principal. So, $497.50 (the principal) + $17.41 (the interest) = $514.91. Therefore, her investment is worth $514.91 after one year.

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Answer:

Last option: 63

Step-by-step explanation:

You need to observe and analize the triangle XWZ provided in the image attached.

You can observe that the lenght of the side XW of the triangle XWZ is congruent to the lenght of the side ZW. This means that the lenght of the side XW and the lenght of the side ZW are equal.

Therefore, if the measure of the angle ∠X is 63, then the measure of the angle ∠YZW is 63:

[tex]m\angle YZW=m\angle X[/tex]

[tex]m\angle YZW=63[/tex]

This matches with the last option.

Answer:

w=32

Step-by-step explanation:

w/4 = 8

4/1 * w/4 = 8*4

w=32

Answer:

Step-by-step explanation:

6/2 evaluates to 3

Multiply x and 3

Multiply x and 1

The x just gets copied along.

The answer is x

x

6/2*x evaluates to 3x

x+6/2*x evaluates to 4x

x+6/2*x+5 evaluates to 4x+5

4x + x = 5x

The answer is 5x+5

x+6/2*x+5+x evaluates to 5x+5

To divide 1 by x

The x just gets copied along in the denominator.

The answer is

5/x evaluates to  

The answer is

x+6/2*x+5+x+5/x evaluates to  

5 + 3 = 8

The answer is

B

x+6/2*x+5+x+5/x+3 evaluates to  

The final answer is

B

Answer:

(3 (pm) sqrt(7))/2

Step-by-step explanation:

First step: Identify a,b, and c

a=2

b=-6

c=1

Second step: Find b^2-4ac (this is called the discriminant-I will call this D)

(-6)^2-4(2)(1)=36-8=28

Third step: Find the square root of the discriminant aka sqrt(D)

sqrt(28)

Let's see if we can simplify sqrt(28)

Here is there a factor of 28 that is a perfect square? How about 4? Yep!

sqrt(28)=sqrt(4)sqrt(7)=2sqrt(7).

Fourth Step: What is -b? If b=-6 then -b=6.

Fifth step: What is 2a?  2(2)=4

So the formula is

x=(-b (pm) sqrt(D))/(2a)

or

x=(step4 (pm) step 3)/(step 5)

x=(6 (pm) 2sqrt(7))/4

Simplify

x=(3 (pm) sqrt(7))/2

*pm means plus or minus

*sqrt( ) means square root of the number that follows in the ( )

Answer:

Just took it!

Step-by-step explanation:

Answer:

the domain is from -5 to infinity

Step-by-step explanation:

f(x+5)+3=√x+5  +3

x+5>0

x>-5

the domain is from -5 to infinity

Answer:

A. {x | x > –5}

the greater than sign should be greater than or equal to

Answer:

The answer would be D) $180,000 in bank A, $240,000 in bank B, $240,000 in bank C.

Step-by-step explanation:

You can immediately eliminate A, B and C because the question clearly states that the limit per bank is $250,000.

Answer:

D. $180,000 in bank A, $240,000 in bank B, $240,000 in bank C

Step-by-step explanation:

She needs to deposit less than $250,000 in each bank in order to be able to have that sum of money insured, in this case she could deposit it this way:

$250,000

$250,000

$160,000

But that could be too risky and too on the verge of not being accepted, you she just takes $10,000 out of every $250,000 deposits to make them $240,00, and add it to the $160,000 deposit, so she is left with three deposits of:

$240,000

$240,000

$180,000

And with this she makes sure all of her deposits are insured by staying below the $250,000 limit.

Answer:

X=12

Step-by-step explanation:

3(80-9x)=X-96 Distribute 3 through the parenthesis

240-27x=x-96

Move the variable to the left side and change its sign

Move constant to the right side and change its sign

-27x-x+240=-96

collect the like terms

calculate the difference

-28x=-336

Divide both sides of the equation by -28

x=12

Answer:

y=2/3x+3

Step-by-step explanation:

the slope is 2 over 3 because you ride 2 up and 3 to the right to get to the next dot and the y intercept is 3 because that's where the line intercepts the y axis.

Answer: x=4y+9

Step-by-step explanation:

All of the variables, 3x, 12y, and 27 can be divided y 3, so we will simplify by dividing the whole equation by 3.

3x/3-12y/3=27/3

Which is equal to....

x-4y=9

Now you can move -4y over to the right side by changing its sign...

x=4y+9

Let the equation be 3x - 12y = 27 then, the value of x = 9 + 4y.

Given: 3x - 12y = 27

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Solve the value of x, then

Add 12y to both sides

3x - 12y + 12y = 27 + 12 y

Simplifying the above equation, we get

3x = 27 + 12y

Divide both sides by 3, then we get

[tex]$\frac{3 x}{3}=\frac{27}{3}+\frac{12 y}{3}$$[/tex]

Therefore, the value of x = 9 + 4y.

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Answer:

Step-by-step explanation:

What do we know about that prism?

It's a rectangular prism with a square base.

Height: y (from question)

base length: x (from question)

base width: x (from question, since it's a square base).

Total volume: 150 cu inches

The question lacks a relationship between x and y the "is __ times", but we can see from the answer choices that they all show a constant relationship:

y = 1.5 x  

The volume of a prism is obtained by  multiplying the lengths of its 3 dimensions: V = length * width * height.  In our case, we then have

150 = x * x *  y

then we replace y by its x-expressed equivalent:

150 = x * x * (1.5x) = 1.5x³

then we isolate x³ by dividing each side by 1.5

x³ = 100, we do the cubic root on each side

x = 4.64

So, answer is D. x = 4.6 and y = 6.9

If you you 4.64 * 4.64 * 6.96 = you get 149.8, which is very close to 150.

Answer:

the answer is 12.

Step-by-step explanation:

the explanation is in the image above

Hope this helps

Answer:

Step-by-step explanation:

We have:

two triangles with base b = 6 and height h = 1

two rectangles with length l = 4 and width w = 2

one reactangel with length l = 6 and width w = 2.

The formula of an area of a triangle:

[tex]A_T=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_T=\dfrac{(6)(1)}{2}=3[/tex]

The formula of an area of a rectangle:

[tex]A_R=lw[/tex]

Substitute:

[tex]A_{R_1}=(4)(2)=8\\\\A_{R_2}=(6)(2)=12[/tex]

The surface area of the prism:

[tex]S.A.=A_T+A_T+A_{R_1}+A_{R_1}+A_{R_2}[/tex]

[tex]S.A.=3+3+8+8+12[/tex]

[tex]\bf \log_5(3)=a\qquad \qquad \log_5(4)=b\ \\\\\\ \log_5(4)=b\implies \log_5(2^2)=b\implies 2\log_5(2)=b\implies \log_5(2)=\cfrac{b}{2} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{15}(2)\implies \stackrel{\textit{change of base rule}}{\cfrac{\log_5(2)}{\log_5(15)}}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3\cdot 5)}\implies \cfrac{~~\frac{b}{2}~~}{\log_5(3)+\log_5(5)} \\\\\\ \cfrac{~~\frac{b}{2}~~}{a+1}\implies \cfrac{b}{2}\cdot \cfrac{1}{a+1}\implies \cfrac{b}{2a+2}[/tex]

Answer:

x = 4

Step-by-step explanation:

Using the 90-60-30 theorem, the hypotenuse is equal to 2a, so a = 4 sqrt(2). The shortest leg is therefore 4 sqrt(2). Using this, to find x, plug it into the smaller triangle. The hypotenuse of the smaller triangle is therefore 4 sqrt(2). Using the 45-45-90 theorem, 4 sqrt(2) = x sqrt(2), so x = 4. This is because there are two sqrt(2)'s', so taking that out of the equation leaves x = 4.

Hope this helps!

Answer:

Step-by-step explanation:

Graph y = |x|.  This graph is v-shaped, opening up, with vertex at (0, 0).  Now translate this graph 4 units to the left and 2 units up.  The result is the graph of g(x) = |x + 4| + 2.

Next time, please share the possible answer choices.  Thanks.

The function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up

The equation of the function is given as:

[tex]g(x) = |x + 4| + 2[/tex]

The above is an absolute value function, and the equation of the parent function is:

[tex]f(x) = |x|[/tex]

This means that the function g(x) is derived from the function f(x) by translating f(x) graph 4 units to the left and 2 units up

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The histogram would change due to the different distribution of ages when all 20 students join the same event.

A histogram is a graphical representation of the distribution of numerical data. It consists of bars, where the length or height of each bar corresponds to the frequency or relative frequency of data within a specific interval or range. Histograms provide insights into data patterns and distributions.

The histogram would change when all 20 students join the same event compared to the original because the distribution of ages would be different. The original histogram would show the number of students participating in each event, while the new histogram would show the number of students in each age group. The new histogram would have different bars representing each age group, and the heights of these bars would be determined by the number of students in each age group.

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Answer:

=293.7m²

Step-by-step explanation:

Area of the shaded region = area of the circle-area of the minor segment.

The area of the minor segment is calculated as follows.

Area= Area of sector - area of the triangle bound by the radii.

=∅/360πr²-1/2r²sin∅, where r is the radius of the circle and ∅ the obtuse angle bound by the radii.

=130/360×π×11.1²-1/2×11.1²sin130

=93.43m²

Area of the whole circle =πr²

=π×11.1²

=387.08m²

Area of the shaded region

=387.08m²-93.43m²

=293.65m²

≅293.7m² to the nearest tenth.

Answer:

10 seconds.

Step-by-step explanation:

The velocity at which they are approaching each other = 59 + 41 = 1000 km per second.

Velocity = distance  / time

So time =  distance / velocity

= 1000 / 100

= 10 seconds.

10 seconds long does it take for them to collide.

Velocity exists as the measurement of the amount of distance an object covers in a given amount of time. Here's a term equation that describes the connection between distance, velocity, and time: Velocity equals distance traveled divided by the time it brings to get there.

The velocity at which they exist approaching each other = 59 + 41

= 1000 km per second.

Velocity = distance / time

So, time = distance / velocity

= 1000 / 100

= 10 seconds.

Therefore, 10 seconds long does it take for them to collide.

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Answer:

3x - 20 = 13

Step-by-step explanation:

it says difference so it cant be the last one and three times a number is 3 x so it cant be the first one leaving the middle.

please mark brainliest

Answer:

C. h(2) = 16

True statement

Step-by-step explanation:

The function has

Domain

-3 ≤ x ≤ 11

Range

1 ≤ h(x) ≤ 25

h(8) = 19

h(-2) = 2

Lets analyze each statement

A. h(13) = 18

False, x = 13 is not part of the domain

B. h(-3) = -1

False, -1 is not part of the range

C. h(2) = 16

True statement

D. h(8) = 21

False, the problem tells us that h(8) = 19

Answer:

Hi there!

Since you asked for a simplified fraction, the answer to this question is: 1/6

Step-by-step explanation:

Look at the fraction 14/84, there is a definite similar factor between 14 and 84, 2. So all you do is divide the two numbers by two to reduce the fraction into 7/42

then you divide both 7 and 42 by 7 to get 1/6

Answer:

1/6

Step-by-step explanation:

14 to 84

First lets make it a fraction

14/84

Divide the top and bottom by 14

1/6

Answer:

D

Step-by-step explanation:

We need to understand the meaning of slope. The slope means the rate of change of y with every unit change of x.

In our case, it will be rate of change of sales increase (%) with respect to unit change of discount(%).

The formula for slope is the change in y divided by change in x.

From the 2 points given, we can say that slope is:

[tex]\frac{62-32}{20-10}=\frac{30}{10}=\frac{3}{1}[/tex]

This means "as discount increases 1%, sales increase by 3%". Option D is right.

Answer:

D

Step-by-step explanation:

6 donuts. He repacked 6 donuts into each box .

Mr. Terence had 18 boxes containing 36 donuts each, that means:

Total donuts = n° boxes*n° donuts

Total donuts = 18*36 = 648

He had in total 648 donuts.

He sold 162 donuts and repacked the rest into 81 boxes. Then:

Rest donuts = Total donuts - sold donuts

Rest donuts = 648 - 162 = 486

The rest donuts are 486 donuts.

He repacked the rest into 81 boxes, then:

n° donuts (each box) = Rest donuts/n° boxes

n° donuts (each box) = 486/81 = 6

The number of donuts that he put in each box is 6 donuts.

Answer:

For the first answer (A)

The area of the base is the area of the 8 by 4 rectangle, minus the missing 2 by 2 square in the top-right.  This is 8*4-2*2=32-4=28 square centimeters.

For the second answer (B)

The volume of the prism is the base area multiplied by the height, or 28*10=280 cubic centimeters.

Answer:

Area = 28 cm² and Volume = 280 cm³

Step-by-step explanation:

A. Area of the base of the prism = Area of rectangle with dimensions 4 × 8 cm. minus area of a rectangle with dimensions 2×2 cm.

Area = 4 × 8 - 2 × 2

       = 32 - 4 = 28 cm²

B. Volume of the given prism = Volume of full prism with dimensions 10 × 4 × 8 cm. minus volume of small prism (missing) having dimensions 2×2×10 cm.

Volume = 10 × 4 × 8 - 2 × 2 × 10

             = 320 - 40

            = 280 cm³

Area = 28 cm² and Volume = 280 cm³

Answer:

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

Step-by-step explanation:

An easy way to solve this problem is divide $23.25 by 3 or $54.25 by 7. Either way, you get $7.75. This number represents the amount of money he makes for 1 hour. So with that in mind, the correct equation is:

$7.75x = y

I hope this helped! :)))

Answer: x=40

Step-by-step explanation:

The solution to log (25x) = 3 is 40. This is calculated by using log rules.

A function that has log terms is said to be a logarithmic function.

Some of the rules for solving log functions are as follows:

Given that,

log (25x) =3

Using basic form [tex]log_b(m)=n[/tex] ⇒ [tex]m=b^n[/tex]

Here base b=10, m=25x and n=3

Then,

log (25x) =3

⇒ [tex]25x = 10^3[/tex]

⇒ 25x = 1000

⇒ x = 1000/25

∴ x = 40.

Hence the solution of the given function is 40.

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Answer:

Step-by-step explanation:

If you let b = x^2 the problem becomes a whole lot easier. Note that x = √b

x^2 + x - 12

Now factor this trinomial.

(x + 4)(x - 3)

Now put b back into the equation

(√b + 4)(√b - 3)

Answer:

(2,4)

Step-by-step explanation:

The range is the y values

y = x+5

Let y=7

7 =x+5

Subtract 5

7-5 x+5-5

2=x

Let y= 9

Subtract 5

9-5 x+5-5

4=x

The domain is (2,4)