I will mark brainliest for the first person to answer my question

[tex] \sqrt{75} + \sqrt{108} = a \sqrt{b} [/tex]

[tex] \sqrt{75} = \sqrt{3 \times 5 {}^{2} } = 5 \sqrt{3} [/tex]

[tex] \sqrt{108} = \sqrt{2 {}^{2} + 3 {}^{3} } = 2 \times 3 \sqrt{3} = 6 \sqrt{3} [/tex]

[tex] \sqrt{75} + \sqrt{108} = 5\sqrt{3} + 6 \sqrt{3} = 11 \sqrt{3} [/tex]

[tex]a = 11[/tex]

[tex]b = 3[/tex]

The balance in his account at the end of 4 years will be $289.67.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Principal amount (P) = $250

Rate (r) = 3.75%

Time (t) = 4 years

Now,

Since, We know that;

⇒ [tex]A = P (1 + \frac{r}{100} )^t[/tex]

Where, A is the future amount.

P is the principal amount.

t is the time.

r is the rate.

Thus, By substitute all the values, we get;

⇒ [tex]A = P (1 + \frac{r}{100} )^t[/tex]

⇒ A = 250 (1 + 3.75/100)⁴

⇒ A = 250 (103.75/100)⁴

⇒ A = $289.67

Thus, The balance in his account at the end of 4 years will be $289.67.

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Answer:

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Answer:

[tex](3;-2)[/tex]

Step-by-step explanation:

Let's add together the two equations

[tex]I + II : x-8y +9x +8y = 19+11 \rightarrow 10x=30 \rightarrow x =3[/tex]

At this point I would recommend simply using the value of x in the firs equation to find y. [tex]3-8y=19 \rightarrow -8y=16 \rightarrow y=-2[/tex]

Or just multiply the first by 9 and subtract the second.

[tex]9\times I-II: 9x-72y-9x-8y=171-11 \rightarrow -80y=160 y=-2[/tex]

Answer:

5 and 3 pints

Step-by-step explanation:

there are 4 pints in 1 cup.

23 pints is equal to 46 cups using the conversion factor 2 cups = 1 pint.

As, 2 cups = 1 pint.

Using the conversion factor 2 cups = 1 pint, convert 23 pints to cups.

So, to convert pints to cups, multiply the number of pints by 2 as

= 23 pints x 2 cups/pint

= 46 cups

Therefore, 23 pints is equal to 46 cups.

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Answer:

Plug in those values for the x in the equations.

Step-by-step explanation:

f(x) = x^2 + x

   (x = -1) :: f(-1) = (-1)^2 + (-1)

                 f(-1) = -1 + -1

                 f(-1) = -2

   (x = 2) :: f(2) = (2)^2 + (2)

                 f(2) = 4 + 2

                 f(2) = 6

f(x) = x^2 - x

   (x = -1) :: f(-1) = (-1)^2 - (-1)

                 f(-1) = 1 - (-1)

                 f(-1) = 2

   (x = 2) :: f(2) = (2)^2 - (2)

                f(2) = 4 - 2

                f(2) = 2

f(x) = -x^2 - x

   (x = -1) :: f(-1) = -(-1)^2 - (-1)

                 f(-1) = -1 + 1

                 f(-1) = 0

   (x = 2) :: f(2) = -(2)^2 - (2)

                 f(2) = -4 - 2

                 f(2) = -6

Step-by-step explanation:

5x+6x=70-4

11x=66

x=66/11

x=6

Answer:

[tex]3\sqrt{6}[/tex]

Step-by-step explanation:

[tex](\sqrt{3} )^{3} \sqrt{2}[/tex]

[tex](\sqrt{3} )^{3}=\sqrt{3} \sqrt{3} \sqrt{3} =3\sqrt{3}[/tex]

[tex]3\sqrt{3} \sqrt{2} =3\sqrt{6}[/tex]

The length of the arc subtending a central angle of 9π/5 radians is 152.12m.

The radius of the given circle r = 26.9m

The measure of the central angle α = [tex]\frac{9\pi }{5}[/tex] radians

The arc of a circle is defined as the part or segment of the circumference of a circle. Its length is the product of the central angle(in radian) and radius of the circle.

So, the length of the arc subtending a central angle of 9π/5 radians

l = rα

l = 26.9 * 9π/5

l = 152.12m

Therefore, the length of the arc subtending a central angle of 9π/5 radians is 152.12m.

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Answer: 15%

Step-by-step explanation:  

I hope this helps,

have an wonderful Day!

The tax rate Tasha will pay on her investment income is 15%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25

We are given that;

Ordinary taxable income= $90,000

Capital gains= $12,000

Now,

The tax rate Tasha will pay on her investment income depends on her ordinary taxable income and the tax brackets for qualified dividends and long-term capital gains. Since Tasha’s ordinary taxable income is $90,000, she falls in the 15% tax bracket for her investment income.

Therefore, by the percentage the answer will be 15%.

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Answer:

the correct answer is choice 2

Step-by-step explanation:

reason being that both bc and ac would both be vertical lines so they have the same slope of undefined

Answer:

3.) A reflection across the y-axis

Hope this helps!

Answer:

Greatest common factor (GCF) of 60 and 64 is 4.

Step-by-step explanation:

The HCF of two numbers 60 and 64 is 4.

LCM is the least common multiple is the smallest number that is divisible by two or more than two given numbers.

We know that the greatest common factor of two or more than two numbers is the largest number that divides the given numbers completely.

Given we have to find HCF of 60 and 64.

2 can divide both the numbers but 4 also divides the numbers and n such no. more than 4 divide them completely and simultaneously.

∴ HCF of 60 and 64 is 4.

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4,7

Step-by-step explanation:

17x+6=19x-2(being vertically opposite)

6+2=19x-17x

8=2x

x=8/2

x=4

10x-5=9+8x(being corresponding angle)

10x-8x=9+5

2x=14

x=14/2

x=7

Answer: Axis of Symmetry at x=1

Step-by-step explanation:

Internet Definition: The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

So pretty much you see the "hill shape" on the graph... the highest part of the hill is the axis of symmetry so the axis of symmetry is at x=1  

Hope this helps! :)

Answer: 8.4 cm

Step-by-step explanation:

Lets shift

[tex]\\ \rm\Rrightarrow f(x)=x^2[/tex]

[tex]\\ \rm\Rrightarrow g(x)=(x+2)^2[/tex]

[tex]\\ \rm\Rrightarrow g(x)=x^2+2x+4[/tex]

Answer:

g(x) = (x + 2)²

Step-by-step explanation:

In function notation, if we want to shift a function to the left, we add the number we are asked to move to the left inside the function's argument:

⇒ To shift f(x) b units to left → f(x + b)

Similarly, if we want to shift a function to the right, we subtract the number we are asked to move to the right inside the function's argument:

⇒ To shift f(x) b units to right → f(x - b)

Given function f(x) = x²

Shift 2 units to the left:  f(x + 2) = (x + 2)²

Therefore, g(x) = (x + 2)²

Answer:

Please post the full question/picture ^-^

Step-by-step explanation:

I believe some part of the question is missing.

Answer: sorry kid

that too easy

Step-by-step explanation:

Answer:

[tex]\frac{14}{15}[/tex]

Step-by-step explanation:

We require to create 2 equations with the repeating 3 after the decimal point.

let x = 0.93333333333 ( multiply both sides by 10 and 100 )

10x = 9.3333333333 → (1)

100x = 93.333333333 → (2)

Subtract (1) from (2) , eliminating the repeating decimal

90x = 84 ( divide both sides by 90 )

x = [tex]\frac{84}{90}[/tex] = [tex]\frac{14}{15}[/tex]

Thus

0.933333333333 = [tex]\frac{14}{15}[/tex]

The inequality which are true when the number line for √0.9 is plotted are equal to the option A and C.

[tex]0 < \sqrt{0.9}[/tex]

[tex]\sqrt{0.9} < \sqrt{1}[/tex]

The number line is the way of representation of number and digits in a arranged form to understand the data batter.

Plot startroot 0.9 endroot on the number line. The number line for the √0.9 is plotted and attached in the below image.

The value of √0.9 is greater than the zero as shown. Hence the correct inequality is,

[tex]0 < \sqrt{0.9}[/tex]

On the number line, the √0.9 is less than the number √1. Thus,

[tex]\sqrt{0.9} < \sqrt{1}[/tex]

Hence, the inequality which are true when the number line for √0.9 is plotted are,

[tex]0 < \sqrt{0.9}[/tex]

[tex]\sqrt{0.9} < \sqrt{1}[/tex]

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Answer: A and C :)

Step-by-step explanation: Got it right on edge! Love y'all and good luck!

Using the area of a rectangle, it is found that her patio should have a width of 12 feet and a length of 27 feet.

The area of a rectangle of length l and width w is given by:

A = lw.

In this problem:

Thus:

324 = w(15 + w)

w^2 + 15w - 324 = 0

w = -27 or w = 12.

We take the positive value, hence l = 15 + w = 15 + 12 = 27 feet.

The dimensions should be a width of 12 feet and a length of 27 feet.

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Answer:

-3y^8-3y^2

Step-by-step explanation:

Answer:

2: Rate of change is the comparision between the x and y values. 3: For one pound of fish, it costs $15

Step-by-step explanation:

2: For example, if you have 4y and 1x, the rate of change is 4 because rise/run, 4/1= 4

3: The cost would be y while pounds of fish would be x. so $15/1 pound = 15

Hope this helps

Answer:

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. ... Subtract one and multiply the resulting number by 100 to give it a percentage representation.

Step-by-step explanation:

2. Say you have like 5y and 1x, the rate of change is 5 because rise/run, 5/1= 5

Answer:

-35

Step-by-step explanation:

Using the rules of BIMDAS, division goes before addition, hence -20/2 which gives you -10

Put that in the equation and it would be:

-10 + (-15)

A negative and a positive make a negative hence, you could simply write it as:

-10 - 15

Which equals -35

Answer:

420 × 2 = 820 feet total

100 yards = 300 feet

125 yards = 375 feet

300 + 375 = 675

820 - 675 = 145 feet

they have 145 feet left

Answer:

The correct option is A....

Step-by-step explanation:

We have a table of x,y pairs. To compute the slope we can use any two pairs, say the first two, and plug them into our formula:

m = y2-y1 / x2-x1

m = 5-13/ 0-(-2)

m = -8/0+2

m = -8/2

m = -4

We can check this answer by using a different pair: Take the last two pairs.

m = -27-(-15)/ 8-5

m = -27+15/3

m = -12/3

m = -4

Thus the slope is -4

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

now, we only need to calculate :

9 × 16 / 2 = 9 × 8 = 72 m²

Answer: 72

Hope this helps!