Leo deposited $2494.05 in an account that earned 2.5% interest compounded weekly for 13 years. After 13 years, how much had Leo earned in interest?

Answer:

[tex]B=12x[/tex]

Step-by-step explanation:

Given: [tex]cos^2(6x)-sin^2(6x)=cos(B)[/tex]

Let's simplify the left part of the equation:

[tex]cos(12x)=cos(B)[/tex]

Solve for B:

[tex]B=12x[/tex]

Final answer:

To find the value of B for the given equation, we employ the cosine double angle identity, which leads us to determine that B equals 12x or 12x ± 2kπ, considering the periodic nature of the cosine function.

Explanation:

The question asks us to find the value of B given that cos2(6x) - sin2(6x) = cos(B). This expression can be rewritten using a trigonometric identity, the cosine difference identity, which states that cos(A) - cos(B) = -2sin((A+B)/2)sin((A-B)/2). However, in our case, we use the cosine double angle identity, which states that cos(2θ) = cos2(θ) - sin2(θ). Applying this identity to the given expression gives us cos(12x) = cos(B). Therefore, B = 12x or B = 12x ± 2kπ, where k is an integer, because the cosine function is periodic with a period of 2π.

Answer:

(-1, 1), (-2, 2), and (-1, 3)

Step-by-step explanation:

The formula for rotation of a point (x,y) by an angle θ about the origin is  

x' = xcosθ  -  ysinθ

y' = ycosθ + xsinθ

If θ = 90°, sinθ = 1 and cosθ = 0, and the formula becomes

x' = -y

y' =  x

P: (1, 1)   ⟶ (-1,  1)

Q:(2, 2) ⟶ (-2, 2)

R: (3, 1) ⟶  (-1,  3)  

The vertices of P'Q'R' are (-1, 1), (-2, 2), and (-1, 3).

The Figure below shows the triangle before and after the rotation.

The unknown measure of the angle x is (c) 98 degrees

From the question, we have the following parameters that can be used in our computation:

The lines (see attachment)

By definition, the sum of angles on a line is 180

using the above as a guide, we have the following:

x + 82 = 180

So, we have

x = 180 - 82

Evaluate

x = 98

Hence, the solution is (c) 98 degrees

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Answer:

1. add up all of the arcs.

2x+3x+4x-8+x-12

2. all of the arcs equal 360

2x+3x+4x-8+x-12=360

3. Find x

10x-20=360, x=38

4. angle LTE is equal to half of the sum of the intercepted arcs.

.5(arc LE +GF)

5. plug in LE +GF with x

.5(76+144)

LTE=110

Applying the angles of intersecting chords theorem, m∠LTE = 110°.

When two chords intersect inside a circle, according to the angles of intersecting chords theorem, the vertical angle formed equals the half the sum of the measures of the intercepted arcs.

Given the following:

A full circle = 360°

Therefore we would have:

2x + 3x + 4x - 8 + x - 12 = 360

Add like terms

10x - 20 = 360

10x = 360 + 20

10x = 380

x = 38

Based on the angles of intersecting chords theorem, we have:

m∠LTE = 1/2(EL + GF)

Substitute

m∠LTE = 1/2(2x + 4x - 8)

m∠LTE = 1/2(6x - 8)

Plug in the value of x

m∠LTE = 1/2(6(38) - 8)

m∠LTE = 1/2(220)

m∠LTE = 110°

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Answer:

Let the no. Of students from Indiana be x

Let the no. Of students from the rest of the country and abroad be y

x = 3y (Given) (i)

x + y = 884 (Given) (ii)

Subtract equation (ii) from 1

x -3y = 0

-(x+y = 884)

-4y = -884

Therefore y = 221

Therefore no. Of students from the rest of the country and abroad is 221

Substituting the value of y in (i)

x = 3 x 221

Therefore x = 663

Therefore no. Of students from Indiana is 663

Hope this helps!

Answer:

A and C

Step-by-step explanation:

The area formulas for the shapes area as follows:

Knowing this, you can see that rhombus and trapezoids have different formulas then other quadrilaterals. This means A and C can be considered false.

Answer: 215 seconds

Step-by-step explanation:

This is a ratio problem so you can set up the ratio like this:

120 words : 100 second.

If you divide both sides of the ratio by 120 you get:

1 word: 0.8333 seconds

Multiply both sides of the ratio by 258 and you get:

258 words: 215 seconds.

Therefore typing 258 will take them 215 seconds.

This will take 215  seconds  to type 258 words.

This problem is solved by the concept of unitary method.

Given that  Typist types 120 words in 100 seconds

so in one second he types 120/100 words = 1.2 Words per second

let us suppose he types  258 words in 'x' seconds  

so in one second he types 258/x words

258/x = 1.2  

x = 258/1.2  

x = 215 seconds  

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Answer: Radius = 1,250

Step-by-step explanation: The circumference of a circle equals the 2 x radius x π.

The formula to solve the radius is 2r x 3.14 = 7,850

Divide both sides by 3.14 = 2r = 2,500

Divide both sides by 2 = r = 1,250.

The radius = 1,250

Answer: 1,250 units

Step-by-step explanation:

Answer:

[tex]\sqrt[3]{a^{2}+b^{2}}=(a^{2}+b^{2})^{\frac{1}{3}}[/tex]

Step-by-step explanation:

∵∛x = (x)^1/3

∴ [tex]\sqrt[3]{a^{2}+b^{2}}=(a^{2}+b^{2})^{\frac{1}{3}}[/tex]

So you can replace the radicals by fractional exponents

Answer:

The required expression is: [tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex].

Step-by-step explanation:

Consider the provided expression.

[tex]\sqrt[3]{a^2+b^2}[/tex]

Now use the property: [tex]\sqrt[n]{x+y}=(x+y)^{\frac{1}{n}}[/tex]

By using the above property the provided expression can be written as:

[tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex]

Therefore, the required expression is: [tex]\sqrt[3]{a^2+b^2}=(a^2+b^2)^{\frac{1}{3}[/tex].

Answer: 6 x 7 = 42

Step-by-step explanation: I believe this is because there are 6 different ways from the school to the park and seven routes from the park to his grandmother's house. To find the total you multiply 6 and 7.

Answer:

x² + 50x + 600

Step-by-step explanation:

The length changes from 20 yards to 20 + x. The width changes from 30 to 30+x.

The area will be A = l*w = (20+x)(30+x).

Use the distributive property to find the polynomial simplified.

A = (20+x)(30+x) = 600 + 30x + 20x + x² = 600 + 50x + x²

Write the polynomial in descending order by writing the exponents first.

x² + 50x + 600

The polynomial representing the area of the new parking lot would be 600 + 50x + x^2 square yards, where x is the amount by which both the length and width are increased.

The area of the initial parking lot can be computed using the formula for the area of a rectangle, which is length times width. In this case, the area would be 20 yards times 30 yards, or 600 square yards.

If we let x be the amount by which both the length and the width are increased, the new length becomes 30 + x yards, and the new width becomes 20 + x yards.

Therefore, the polynomial representing the area of the new parking lot would be (30+x)(20+x), which equals 600 + 50x + x^2 square yards.

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If the crayons are replaced after they are drawn, the probability of drawing any particular color is 1/7.Also the result of each draw is independent of any previous result. Therefore the solution to the first part of the question is found from:P(violet\ then\ orange)=\frac{1}{7}\times\frac{1}{7}=\frac{1}{49}

If the crayons are not replaced after they are drawn, the probability of drawing violet on the first pick is 1/7. Then there are only six crayons left, so the probability of drawing orange is 1/6. The solution to the second part of the question is found from:

P(violet\ then\ orange)=\frac{1}{7}\times\frac{1}{6}=\frac{1}{42}

Does this help

Answer:

Step-by-step explanation:

We have two squares S × S and four rectangles S × L.

S = 5 ft and L = 10 ft.

The area of a square:

[tex]A_s=(5)(5)=25\ ft^2[/tex]

The area of a rectangle:

[tex]A_r=(5)(10)=50\ ft^2[/tex]

The Surface Area:

[tex]S.A.=2A_s+4A_r[/tex]

Substitute:

[tex]S.A.=2(25)+4(50)=50+200=250\ ft^2[/tex]

Answer:

Some of the possible factorizations of the monomial given are:

[tex](16x^5)(3x^5)[/tex]

[tex](48x)(x^9)\\\\(4x^5)(12x^5)\\\\(16x^2)(3x^8)\\\\(2x^2)(4x^7)(6x)[/tex]

Step-by-step explanation:

 To factorize the monomia you need to express it as a product of two or more monomials.  Therefore, you must apply the proccedure shown below:

- Descompose into prime numbers:

[tex]48x^{10}=2*2*2*2*3*x*x*x*x*x*x*x*x*x*x[/tex]

- Then, keeping on mind that, according to the Product of powers property, when you have two powers with equal base you must add the exponents, you can make several factorizations.  Below are shown some of the possible factorizations of the monomial given:

[tex](2^4x^5)(3x^5)[/tex]

[tex](48x)(x^9)\\\\(4x^5)(12x^5)\\\\(16x^2)(3x^8)\\\\(2x^2)(4x^7)(6x)[/tex]

Answer with step-by-step explanation:

We are given the following monomial and we are to factorize it:

[tex] 4 8 x ^ { 10 } [/tex]

We have a number of options that we can opt for in order to factorize the given monomial:

[tex] ( 16 x ^ 2 ) ( 3 x ^ 8 ) [/tex]

or

[tex] ( 12 x ^ 5 ) ( 4 x ^ 5 ) [/tex]

or

[tex] ( 24 x ^ 3 ) ( 2 x ^ 7 ) [/tex]

So basically it depends how do you want to break the coefficient and the exponent in order to get a product of [tex] 4 8 x ^ { 10 } [/tex].

Step-by-step explanation:

Put y's on the one side and divided by what they have in the front so it would be

y=2x-4

and

y=x+2  

and they y intercept for first one is -4

and slope is 2 which it goes up twice and goes right once because its positive

second one, y intercept is 2

and slope is 1 goes one up and one right because it is positive

Answer:

See the attached image

Step-by-step explanation:

You must graph the system of equations. To do so, find the intersection points of each line with the axes.

2x-y=4   intersection with the x axis. -----y=0

2x = 4

x = 2.

2x-y=4   intersection with the y axis. -----x=0

-y = 4

y = -4.

Now we have

3y-3x=6     intersection with the x axis. -----y=0

-3x = 6

x = -2

3y-3x=6     intersection with the y axis. -----x=0

3y = 6

y = 2.

Now you can graph both lines. The solution the system will be the intersection of both lines

Step-by-step explanation:

Set up a proportion.

x/10=110/100

x=11

Set up a proportion.

3.5/50=y/100

y=7

Answer:

(3,1)

Step-by-step explanation:

Calculate the rise-over-run ratio to find the slope between the points.

r/r between 0,5 and 2,2 was -3/2

r/r between 2,2 and 4,-1 was -3/2

r/r between 0,5 and 4,-1 was -6/4 = -3/2

r/r between 0,5 and 3,1 was -4/3

r/r between 2,2 and 3,1 was -1/1

as you can see the r/r for the points involving 3,1 was inconsistent with the rest, therefore it is not part of the linear system.

The point that the graph does not pass through is (3 ,1)

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.  

An equation in which the slope is constant is called a linear equation.

Slope of the graph between points (0, 5), (2, 2) =   [tex]\frac{2-5}{2-0} = -\frac{3}{2}[/tex]

Slope of the graph between points (2, 2) , (4, -1) = [tex]\frac{-1-2}{4-2} = - \frac{3}{2}[/tex]

Slope of the graph between points (0, 5), (4, -1) =  [tex]\frac{-1-5}{4-0} = -\frac{-6}{4} = - \frac{3}{2}[/tex]

Slope of the graph between points (3, 1) , (0, 5) = [tex]\frac{5-1}{0-3} = - \frac{4}{3}[/tex]

Slope of the graph between points  (3, 1) ,  (2, 2) = - 1

Slope of the graph between points  (3, 1) , (4, -1) = -2

So, we can say the graph is not passing through the point (3 , 1).

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Answer:

49x^2 - 9 = 0As there is no x term, we can pretty much guess we have a situation where we factlrise by something known aa difference of two squares, so to factorise it:49 = 7^29 = 3^2x^2 = (x)^2so...(7x - 3)(7x + 3) = 07x - 3 = 0 7x + 3 = 0x = 3/7 x = -3/7

Step-by-step explanation:

49x² = 9

Divide both sides by 49:

x² = 9/49

Take the square root of both sides:

x = +/- √9/49

Simplify:

x = -3/7 and 3/7

Answer:

-9.5

Step-by-step explanation:

To solve for z, use inverse operations by multiplying both sides by 2.

-4.75 = z/2

-9.5 = z

To solve the equation -4.75 = z/2, multiply both sides by 2 to isolate z, which gives you the solution z = -9.5.

To solve for z in the equation -4.75 = z/2, you need to isolate z on one side of the equation. This can be achieved by multiplying both sides of the equation by 2 (the reciprocal of 1/2, which is the current coefficient of z) to cancel out the division.

Here's the calculation step by step:

Therefore, the solution to the equation is z = -9.5.

Answer:   [tex]\bold{\dfrac{3}{2}}[/tex]

Step-by-step explanation:

[tex]\dfrac{12z^2}{2y^2}\\\\\\y = -2\quad z=-1\\\dfrac{12(-1)^2}{2(-2)^2}=\dfrac{12(1)}{2(4)}=\dfrac{12}{8}\\\\\\\dfrac{12}{8}\div \dfrac{4}{4}=\boxed{\dfrac{3}{2}}[/tex]

Answer:

A

Step-by-step explanation:

The inverse of a statement is the negation of both the hypothesis and conclusion. This means that both parts of the statement gets a not.

If the perimeter of a square is NOT 20cm, then its area is NOT 25cm2.

Answer:

Step-by-step explanation:

We have the rectangle and the right triangle.

The formula of an area of a rectangle:

A = lw

l - length

w - width

We have l = 10 in and w = 5 in. Substitute:

A = (10)(5) = 50 in²

The formula of an area of a triangle:

A = 1/2 bh

b - base

h - height

We have b = 5 in and h = 5 in + 5 in = 10 in. Substitute:

A = 1/2(5)(10)=1/2(50)=25 in²

The area of figure:

ANSWER

d. 6

EXPLANATION

The given functions are

[tex]f(x) = - 2x + 8[/tex]

and

[tex]g(x) = 3x[/tex]

We find

[tex](g \circ f)(x) = g(f(x))[/tex]

[tex](g \circ f)(x) = g( - 2x + 8)[/tex]

[tex](g \circ f)(x) = 3( - 2x + 8)[/tex]

[tex](g \circ f)(x) = - 6x + 24[/tex]

We now substitute x=3

[tex](g \circ f)(3) = - 6(3) + 24[/tex]

This gives us

[tex](g \circ f)(x) = - 18 + 24[/tex]

[tex](g \circ f)(3) = 6[/tex]

The correct choice is D.

Answer:

Step-by-step explanation:

6

See the image attached for solution

Answer:

D

Step-by-step explanation:

1 cup = 8 fluid ounces.

1.25 cups = 8 fluid ounces + 1/4 of 8.

1/4 of 8 = 2

8 + 2 = 10.

10 fluid ounces should be used.

Answer:

d

Step-by-step explanation:

i had the question

The scale factor of triangle ABC to triangle DEF is 1/6.

Compare corresponding side lengths:

I observed that a side length of triangle ABC (2 units) is 6 times smaller than the corresponding side length of triangle DEF (12 units).

This initial comparison hinted at a scale factor of 1/6.

Checked other side lengths:

To confirm, I verified that the other side lengths also have a ratio of 1/6.

AB = 2 units, DE = 12 units (2/12 = 1/6)

AC = 4 units, DF = 24 units (4/24 = 1/6)

BC = 2 units, EF = 12 units (2/12 = 1/6)

Since all corresponding side lengths have a ratio of 1/6, this confirms that triangle ABC is a scaled-down version of triangle DEF with a scale factor of 1/6.

Complete question:

Answer:

the sum of the angles in a quadrilateral is 360 degrees

Step-by-step explanation:

360 - (60 + 150 + 70) = 360 - 280 = 80 degrees

The answer is A, there are 3 books to every 1 non fiction book.

Answer:

I think it's  B  but I'm not sure hope this helped. <3

Step-by-step explanation:

First, you need to find out the are of the whole rectangle, which as you probably know, you just need to multiply base by height.

Then, you need to substract the are of the two little squares, which luckily are both the same size. To find out the are of a square you multiply a side twice.

Therefore,

Whole rectangle area:

(32+8) * (8+8) = 40 * 16 = 640 sq. ft.

Two small squares:

2 * (8 * 8) = 2 * 64 = 128 sq. ft.

We substract:

640 - 128 = 512 sq. ft.

Answer:

512

Step-by-step explanation:

i fond the area of the whole big rectangle , so to do this i did 32+8 because i needed to find length. then i found the width, which was 8+8, 16. to find area , i need to multiply with times height so i did 40 x 16. this gets me to 640, but now i need to take out the two smaller cubes since i included them when i found the are of the rectangle. since the sides of both squares are 8 by 8, we can do 8 x 8 x 2 to find the area of both of them. now we taake 128(the product of 8 x 8 x 2) and subtract it from the big rectangle with the area of 640. 640-128 is 512.

Answer:

The new amount is $86.10

Step-by-step explanation:

First we find the increase

82*5%

82 *.05

4.1

Next we add the increase to the original amount

82+4.1

86.10

The new amount is $86.10

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ First, you need to find what 5% of 82 is.

82*5%=4.1

Now, you need to add 4.1 to 82:

82+4.1=    $86.10 is the new amount.

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ TROLLER (don't worry, I didn't troll you)