A rectangle measures 10 feet by 6 feet. The length and width are each increased by 50%. What is the area of the new rectangle? Work shown with it please

[tex]~~~~~~ \textit{Compound Interest Earned Amount \underline{in 15 years}} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$400\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yeary, thus once} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases}[/tex]

[tex]A=400\left(1+\frac{0.03}{1}\right)^{1\cdot 15}\implies A=400(1.03)^{15}\implies A\approx 623.19 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=400(1.03)^x~\hfill[/tex]

Sin theta, cosine theta and tangent theta are the angle of trigonometry.

What are the angle in trigonometry?

There are total six angles in the trigonometry which are sin theta, cosine theta,  tangent theta, cotangent theta, secant theta, co secant theta.

Given information-

The value of the cosine theta given in the problem is 0.3090.

It can be written as,

[tex]\cos\theta=0.3090[/tex]

To find the value of theta, took the cosine function to other side of the equation.

This will make the cosine angle as arc cosine. Thus,

[tex]\theta=\cos^{-1}(0.3090)[/tex]

Solve it further as,

[tex]\theta=72^o[/tex]

Hence the value of the angle is 72 degrees.

Use this value to fine the angle of sin theta and tangent theta.

            [tex]\sin72^o=0.9511[/tex]

        Hence, the value of sine theta is 0.9511.

          [tex]\tan72^o=3.078[/tex]

        Hence, the value of tangent theta is 3.078.

Hence,

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Answer:

B)   x = 8[tex]\sqrt{3}[/tex] ;  y = 4[tex]\sqrt{3}[/tex]

Step-by-step explanation:

in a 30-60-90° triangle the sides, respectively, are in the ratio of

1 : [tex]\sqrt{3}[/tex] : 2

we can find 'x' by creating this proportion:

12/[tex]\sqrt{3}[/tex] = x/2

cross-multiply to get:

[tex]\sqrt{3}[/tex]x = 24

x = 24/[tex]\sqrt{3}[/tex]

we can simplify this by 'rationalizing the denominator' which is to

multiply numerator and denominator by [tex]\sqrt{3}[/tex] to get:

(24[tex]\sqrt{3}[/tex])÷3, which is 8[tex]\sqrt{3}[/tex]

we know that side 'y' is half that of side 'x'

therefore y = 4[tex]\sqrt{3}[/tex]

Answer: You just get 66 and 30 and add it together so 96 and the you minus 96 from 180 which equals 84 so the missing degree is 84!

Step-by-step explanation:

[tex]y = a(b)^x \\\\\\ \textit{we know that} \begin{cases} x=0\\ y=9 \end{cases}\implies 9=a(b)^0 \implies 9=a(1)\implies 9=a \\\\\\ \underline{y=9(b)^x}\qquad \qquad \stackrel{\textit{and with a multiplier of 0.6}}{\underline{y = 9(0.6)^x}}[/tex]

Answer:

A. about 800 points

Step-by-step explanation:

how is this possible

[tex]\qquad\huge\underline{\boxed{\sf Answer}}[/tex]

[tex]\sf\longmapsto 5( - x) + 3 = 23[/tex]

[tex]\sf\longmapsto - 5 + 3 = 23[/tex]

[tex]\sf\longmapsto - 5x + 3 = 23 - 3[/tex]

[tex]\sf\longmapsto - 5x = 20[/tex]

[tex]\sf\longmapsto x = \frac{20}{5} [/tex]

[tex]\sf\longmapsto x = - 4[/tex]

Hope it helps ~

Step-by-step explanation:

Given that:

5(9 - x) + 3 = 23

Multiply the number outside of the bracket with numbers in the bracket on LHS.

⇛45 - 5x + 3 = 23

Shift constants from LHS to RHS, changing it's sign.

⇛-5x = 23 - 45 - 3

⇛-5x = 23 - 42

⇛-5x = -19

Shift the number 5 from LHS to RHS.

⇛x = -19/-5

Therefore, x = 19/5

Please let me know if you have any other questions.

Answer:

1/4 of the work

Step-by-step explanation:

A quarter (1/4) of the work is done in 2 days. Let's break it down:

Work can be finished in 8 days total so with 2 days it is only partially completed. If we set it up as 2/8 we can simplify to get 1/4. Therefore, we know only a quarter of the work is done so far.

Answer:

2(8a + 8)

Step-by-step explanation:

The easiest way to do this is to substitute a for a number. For example, let's just make things easy and make a = 1.

So, if a = 1, the expression 16a + 8 would be 16(1) + 8 = 24.

Let's find all the expressions that would also equal 24 if a = 24.

Plug in 1 for a in each of the equations. You will find that 2(8a + 8) will not equal 24 if a equals 1.

2(8a + 8)

2(8(1) + 8

2(8 + 8)

2(16)

32

Answer:

42.27

Step-by-step explanation:

6.5 + 5.3 + 5.3 + 7.1 + 9.7 + 1.0 + 8.0 =  42.27

Answer:

1

Step-by-step explanation:

Use the Negative Power Rule:

x^-a=1/x^a

3*1/3

Cancel 3

=1

Answer:

1.

Step-by-step explanation:

Use the Order of Operations method to solve. (P.E.M.D.A.S.)

Simplify the exponent:

[tex]3(3^{-1} )[/tex]

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

Multiply 3 and 1/3:

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

Answer:

x = -5; y = 7

Step-by-step explanation:

We can use elimination to solve for x.

3x + 2y = -1

-1 (4x + 2y) = -1 (-6)

3x + 2y = -1

-4x -2y = 6

The 2y's cancel out and solving for x gives us x = -5.

Plugging -5 into any one of the equations gives us y = 7

[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]

so

[tex] \sqrt{ {x}^{18} } = {( {x}^{18}) }^{ \frac{1}{2} } = {x}^{9} [/tex]

[tex]0.1 \sqrt{ {a}^{6} } = 0.1 \times {a}^{3} [/tex]

Answer:

Factors for 18: 1, 2, 3, 6, 9, and 18. Factors for 49: 1, 7, and 49.

Step-by-step explanation:

Answer:

Step-by-step explanation:

First things first put them under a square root sign

Second think about what squared can go into that number

Third if there’s a number that can go into it and there’s leftover numbers like if your square rooting 18 you’ll take the number put them under the square root and take whatever can be squared like the 9 and turn it into is squared counter part the three so it’ll look like (is shown in the picture equation below).

And that’s kind of how you do it but if this doesn’t help I’ve used this video before and it might it’s called Finding Factors - Video Lesson for Kids (4.OA.4).

(I know it’s a kid video but it’s simple and works well fair warning it’s a little long).

Answer:

120

Step-by-step explanation:

the angle.of all of these is 180 and 35+25+X=180..

60+X=180...... X=120

The measure of angle D is equivalent to 120 degrees.

A triangle is a two - dimensional figure with three sides and three angles.

The sum of the angles of the triangle is equal to 180 degrees.

∠A + ∠B + ∠C = 180°

Given is that the measure of angle B is 25° and the measure of angle C is 35°.

For the triangle, we can write the measure of angle D as -

∠B + ∠C + ∠D = 180°

25° + 35° + ∠D = 180°

∠D = 180° - 60°

∠D = 120°

Therefore, the measure of angle D is equivalent to 120 degrees.

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Answer:

14

Step-by-step explanation:

To evaluate 2 + 3x for x = 4, substitute x = 4 into the expression.

x=4⇒2+3×4=2+12=14

Answer:

not congruent

Step-by-step explanation:

angles are not equal

Answer:

-1

Step-by-step explanation:

Formula: [tex]y=mx+b[/tex]

Using two points:

Since we are given the [tex]y[/tex] and [tex]x[/tex] value, what is left is the [tex]m[/tex] and [tex]b[/tex] in the formula, which represent slope and the y-intercept.

Slope

[tex]m[/tex] is slope

Formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Plug points:  [tex]\frac{3-(-2)}{4-9}[/tex]

Solve:            [tex]\frac{5}{-5}[/tex]

Simplify:       [tex]\bold{m=-1}[/tex]

Therefore, the slope is -1

Learn more:

y-intercept

[tex]b[/tex] is the y-intercept

Plug one of the points and the slope into the formula, solve for b: (4, 3)

[tex]3=-1(4)+b[/tex]

[tex]3=-4+b[/tex]

[tex]3+4=-4+b+4[/tex]

[tex]\bold{b=7}[/tex]

The sequence of the areas of the squares is a geometric progression,

and the sum to infinity can be determined by using a formula.

Correct responses:

a. 1,  0.5·√2,  0.5,  0.25·√2

b. 1, 0.5, 0.25, 0.125

c. The sum of the areas of the infinite squares is 2

Given;

Length of the side of the square = 1 cm.

The inscribed square is drawn by connecting the midpoints.

Pythagoras's theorem is; Hypotenuse² = Perpendicular² + Base²

Leg length of the second (inscribed) square = 1 ÷ 2 = 0.5

Side length of the second square = √(0.5² + 0.5²) = 0.5·√2

Leg length of the third square = 0.5·√2 ÷ 2 = 0.25·√2

Side length of the third square = √((0.25·√2)² + (0.25·√2)²) = 0.5

Leg length of the fourth square = 0.5 ÷ 2 = 0.25

Side length of the fourth square = √(0.25² + 0.25²) = 0.25·√2

The sequence of the sides of the first 4 terms is therefore;

(b) The sequence for the areas for the first 4 terms are;

1², (0.5·√2)², 0.5², (0.25·√2)², which gives;

c. The given sequence of the areas is a geometric progression, G.P.

Where;

The first term, a = 1

The common ratio, r = 0.5

The sum of a G.P to infinity is given as follows;

[tex]\displaystyle \sum \limits^{\infty}_{k = 0} a \cdot r^ k= \mathbf{ \dfrac{a}{1 - r}}[/tex]

Which gives;

[tex]\displaystyle \sum \limits^{\infty}_{k = 0} 1 \times \frac{1}{2} ^ {k}= \dfrac{1}{1 - 0.5}= 2[/tex]

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The unit cost of the fencing and the cost of a bag of mulch together with

the area and perimeter of the garden give a cost sum of $36.5.

Response:

Cost of the barrier per feet (unit cost) = $0.75

Area covered by one bag of mulch = 7 square feet

Cost of one bag of mulch (unit cost) = $5

From the given diagram, we have;

Area of the garden = 8 ft. × 2 ft. + 0.5 × 8 ft. × 3 ft. = 28 ft.²

[tex]Number \ of \ bags \ of \ mulch \ required = \dfrac{28 \, ft.^2}{7 \, ft.^2/ bag} = \mathbf{ 4 \, bags}[/tex]

Length of fencing = 2 ft. + 8 ft. + 2 ft. + 5 ft. 5 ft. = 22 ft.

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Answer:

8x²+8x-2

Step-by-step explanation:

P = 2l + 2w

P = 2(4x²-x+2) + 2(5x-3)

P = 8x²-2x+4 + 10x-6

combine like terms:

P = 8x²+8x-2

Answer: 106

Step-by-step explanation: you have a total of 180 degrees in there, so you only gotta find the unknown value of the other side so you do 180 - 64 which is 116. then you see that in order to get 116 you gotta add it times ten which you are gonna subtract by 10 which is 106, and 106 will be your answer.

The found value of x is 106°

We know that the measures of the sum of an inner triangle are equal to 180. So, to solve this question, we will just: add the like terms with equality equal to 180.

Finally, let's calculate as a first degree equation, just: isolating x and dividing both sides.

Therefore, the answer will be x = 106°

Answer:

Substitution

Step-by-step explanation:

No, both temperatures are positive numbers and not the same distance from 0, so they cannot be opposites. Both numbers have to be the same distance from zero, but one has to be above zero and the other has to be below zero in order to be opposites.

The conclusion made by Sarah is correct.

We have Sarah notices that her room's temperature is 4°F above the recommended temperature, and the downstairs bedroom's temperature is 4°F below the recommended temperature. She graphs 72 and 64 on a vertical number line and determines they are opposites.

Yes she is correct. The recommended temperature is 68. She marked -

(68 + 4) = 72 and (68 - 4) = 64 on the scale. So, she is correct.

Therefore, the conclusion made by Sarah is correct.

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Answer:

Answer:I think the answer is 60.