Jackson invested $750 into a savings bond that earned 3% interest each month. At the same time, he also began saving money in a savings account. The value of the savings account is represented by f(x) = 1,000 + 25x, where x represents the number of months since the account was opened. At the end of how many months did the value of the savings bond first begin to exceed the value of the savings account?

Answer:

x = [tex]\sqrt{10}[/tex]

Step-by-step explanation:

The 2 right triangles and the outer right triangle are similar, then ratios of corresponding sides are equal, that is

[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )

x² = 10 ( take the square root of both sides )

x = [tex]\sqrt{10}[/tex]

Answer:

√10

Step-by-step explanation:

taking the smallest triangle;

y as the hypotenuse, x as the adjacent side, 2 as the opposite side

then: y²=x²+2²

x²=y²-2²= y²-4

taking the other triangle;

z as the hypotenuse, x as the adjacent side, 5 as the opposite side

then: z²=x²+5²

x²=z²-5² = z²-25

take both equations,

x²= y²-4

x²= z²-25

y²-4= z²-25

y²= z²-25+4 = z²-21

taking the biggest triangle (whole triangle);

(5+2)= 7 as the hypotenuse, z as the adjacent side, y as the opposite side

then; 7²=z²+y²

z²+y²=7² =49

but y²= z²-21;

z²+y² =49

z²+ z²-21 =49

2z²-21=49

2z²=49+21= 70

z²= 70/2 = 35

take x²= z²-25

x²= 35-25 = 10

[tex]x = \sqrt{10} [/tex]

Answer:

I believe the answer would be the option that says: "An elephant walks with a speed of 15 steps a minute. How long was the elephant walking if she walked without stopping for 480 steps?"

Answer:

C. An elephant walks with a speed of 15 steps a minute. How long was the elephant walking if she walked without stopping for 480 steps?

Step-by-step explanation:

C yields the equation of [tex]15x=480[/tex], because 15 stands for steps/minute, 480 for steps, so [tex]x[/tex] must stand for minutes.

For your entertainment:

A gives [tex]x = 480 \cdot 15[/tex].

B gives [tex]x=32-15[/tex].

D gives [tex]x=480+15[/tex].

Answer:

58. cm^2.

Step-by-step explanation:

Area of parallelogram = 2 * area of triangle

= 2 * 29

=58.

Answer:

x=7

Step-by-step explanation:

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

5x+3−2x=24

Step 1: Simplify both sides of the equation.

5x+3−2x=24

5x+3+−2x=24

(5x+−2x)+(3)=24(Combine Like Terms)

3x+3=24

3x+3=24

Step 2: Subtract 3 from both sides.

3x+3−3=24−3

3x=21

Step 3: Divide both sides by 3.

Answer: x=7

Step-by-step explanation:

Given

5x + 3 - 2x = 24

Subtract both sides by 3

5x + 3 - 3 - 2x = 24 - 3

5x - 2x = 21

Simplify

3x = 21

Divide both sides by 3

3x / 3 = 21 / 3

x=7

Hope this helps!!

Please let me know if you have any questions

Answer:

[tex]J = 370g[/tex]

Step-by-step explanation:

Given

Represent the weight of the Jar with J and the sugar with S

Initially, we have:

[tex]J + S = 850g[/tex]

After 2/3 of sugar is removed we have:

[tex]J + S -\frac{2}{3}S= 530g[/tex]

Required

Determine the weight of the jar

[tex]J + S = 850g[/tex] --- (1)

[tex]J + S -\frac{2}{3}S= 530g[/tex] --- (2)

Simplify (2)

[tex]J + S -\frac{2S}{3}= 530g[/tex]

Take LCM

[tex]J + \frac{3S - 2S}{3}= 530g[/tex]

[tex]J + \frac{S}{3}= 530g[/tex]

Make S the subject in (1)

[tex]J + S = 850g[/tex]

[tex]S = 850g - J[/tex]

Substitute 850g - J for S in [tex]J + \frac{S}{3}= 530g[/tex]

[tex]J + \frac{850g - J}{3}= 530g[/tex]

Multiply through by 3

[tex]3 * J + 3*\frac{850g - J}{3}= 530g * 3[/tex]

[tex]3J + 850g - J= 1590g[/tex]

Collect Like Terms

[tex]3J - J= 1590g-850g[/tex]

[tex]2J= 740g[/tex]

Make J the subject

[tex]J = \frac{1}{2} * 740g[/tex]

[tex]J = 370g[/tex]

The jar weighs 370g

Answer:

370

Step-by-step explanation:

Answer:

d.

The actual price is 12.5% higher than the expected price

Step-by-step explanation:

The percent relation of the actual price and the expected price is 12.5%

The consumer price index measures the changes in price of a basket of good. It is used to measure inflation.

Price of the cast iron today = $28.35 x (166/100) = $47.06

The percent relation of the actual price and the expected price = ($52.95/$47.06) - 1 = 12.5%

To learn more about, consumer price index, please check: https://brainly.com/question/26382640

Answer:

1.366km

Step-by-step explanation:

The height of the mountain is [tex]3.34Km[/tex]

A diagram of right angle triangle PBA is attached below which describe the situation as given in the question.

Let us consider that H represent the height of mountain.

Angle of elevation at point A and C shown in the diagram.

Apply tan function in triangle CBP.

            [tex]tan(35)=\frac{H}{x} \\\\H=xtan(35)=0.7x.........(1)[/tex]

Apply tan function in triangle ABP.

           [tex]tan(30)=\frac{H}{x+1}\\ \\(x+1)tan(30)=H\\\\(x+1)=\sqrt{3}H\\ \\x=\sqrt{3}H-1........(2)[/tex]

Substituting the value of equation 2 into equation 1.

      [tex]H=0.7(\sqrt{3}H-1)\\\\H=1.21H-0.7\\\\0.21H=0.7\\\\H=0.7/0.21=3.34Km[/tex]

Hence, The height of the mountain is [tex]3.34Km[/tex]

Learn more about the right angle triangle here:

https://brainly.com/question/64787

Answer:

The x-intercept is where the graph crosses the x-axis, so in this case, the x-intercepts are (-4, 0) and (-2, 0).

The y-intercept is where the graph crosses the y-axis, so in this case, the y-intercept is (0,8).

The  line of symmetry splits the  graph in two equal halves, and it is x=-3.

Finally, because this graph opens up, the graph is positive.

Let me know if this helps!

Answer:

3/4

Step-by-step explanation:

-3/8÷(-1/2)

-3/8÷-1/2

-3/8÷2/-1

-3×2/-8

-6/-8

-(-6/8)

-(-3/4)

3/4

Answer:

3/4

Step-by-step explanation:

my teacher just told me that answer a few seconds ago

Answer:

3.14159265359

Step-by-step explanation:

Hope this helps :)

Answer:

3.14

Step-by-step explanation:

Technically, pi is a an irrational number, meaning that its decimal form neither ends or repeats. But we always shorten it to 3.14.

Answer:

3/8

Step-by-step explanation:

1/2 x 3/4 = 3/8

You multiply the top by the number beside it and do the same for the bottom.

Answer:

C) 12

Step-by-step explanation:

It is 6x2

Answer:

           6, 7, 8 are correct

Step-by-step explanation:

[tex]XV=\dfrac{RS+TU}2\\\\\\44=\dfrac{30+TU}2\\\\44\cdot2=30+TU\\\\88-30=TU\\\\TU=58[/tex]

Answer:

$1.40

Step-by-step explanation:

Answer:

The price of the book is $7.75.

Step-by-step explanation:

Let's first establish an equation.

If I buy a book costing [tex]x[/tex] dollars and a bookmark costing 1 dollars, I will have spent [tex]x + 1[/tex] dollars. So a group of 15 people doing the same will have spent [tex]15(x+1) = 15x + 15[/tex] dollars.

Analogously, the group of 3 people has spent [tex]3(x+36) = 3x + 108[/tex] dollars.

Since we know that both groups spent the same amount of money, we can set the two expressions equal to each other:

[tex]15x+15=3x+108\\12x=93\\x=7.75[/tex]

Because [tex]x[/tex] was the price of the book, which was asked for in the question, we conclude that the answer is $7.75.

Answer:

x=$75

Step-by-step explanation:

Answer:

I believe the answer would be 20.

Step-by-step explanation:

28/7 = 4

5*4 = 20

Pls mark brainliest <3

0Answer: The answer is 20

Step-by-step explanation:

Answer:

10 m

Step-by-step explanation:

We are given that the relationship between intensity of sound and distance from the source is given by

Intensity (I)=[tex]\frac{k}{d^2}[/tex]

Where I=Intensity

d=Distance of sound from the source

If distance d=1m

Intensity, I=0.1[tex]w/m^2[/tex]

We have to find how close she can to the stage if vanessa does not want the sound intensity to be more than 0.001(w)/(m^(2)).

Using the formula

[tex]0.1=\frac{k}{1}[/tex]

[tex]k=0.1[/tex]

[tex]\frac{0.1}{d^2}\leq 0.001[/tex]

[tex]\frac{0.1}{0.001d^2}\leq 1[/tex]

[tex]\frac{0.1}{0.001}\leq d^2[/tex]

[tex]100\leq d^2[/tex]

[tex]10\leq d[/tex]

[tex]d=10 m[/tex]

Hence, she can sit 10 m away from the stage.

Answer:

the answer for this problem would be 24 dollars.

Answer:10

Step-by-step explanation:

Answer:

simplified

Step-by-step explanation:

Answer: 1 -- that is, if they share no common factors other than 1

Step-by-step explanation:

Answer:

It's 7.3; 74!

Step-by-step explanation:

This was a lucky guess for me on my homework and it was correct sooooo.... I don't really have an explanation...

Definition: For vector [tex]v=<a,b>[/tex], the magnitude is defined as [tex]|v|=\sqrt{a^{2} +b^{2} }[/tex], and the direction of the vector is defined as [tex]tan^{-1}(\frac{b}{a} )[/tex].

Here, [tex]v=<2,7>[/tex].

Then, magnitude is:

[tex]|v|=\sqrt{2^{2}+7^{2} } \\|v|=\sqrt{4+49 } \\|v|=\sqrt{53} \\|v|=7.3[/tex]

The direction is:

[tex]tan^{-1}(\frac{7}{2} )=74^{o}[/tex].

So, the correct option is 7.3,74°.

For more information:

https://brainly.com/question/14942332

Answer:

125°

Step-by-step explanation:

By exterior angle theorem:

(3x - 70)° = 60° + x°

(3x - 70)° - x°= 60°

(3x - 70 - x)° = 60°

(2x - 70)° = 60°

2x - 70 = 60

2x = 60 + 70

2x = 130

x = 130/2

x = 65

(3x - 70)° = (3*65 - 70)° = (195 - 70)° = 125°

[tex] m\angle LKM = 125\degree [/tex]

Answer:

it is 10

Step-by-step explanation:

Answer:

g

Step-by-step explanation:

g

Answer:

I believe this is the answer

V=5000(1•0.085)^x

Step-by-step explanation:

sorry if its incorrect i just wanted to help

"v = 5000 * (1-0.085)x" is the formula that is used to determine the car's worth.

An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement of this decline. Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc.

Given, You bought a car for $5,000. Each year it depreciates in value by 8.5%

In this case, we have the following formula:

v = C. (1 - r)ˣ

Where C is the original value of the car, r is the depreciation rate and x is the time in years

Equation to find the value = 5000 * (1- 0.085)ˣ

Therefore, the equation that helps in calculating the value of the car is

"v  = 5000 * (1- 0.085)ˣ".

Learn more about depreciation here:

https://brainly.com/question/18276560

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