how many seconds are in 2 1/2

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:

11

Step-by-step explanation:

5.5 x 4= 22 divided by 2= 11

Final answer:

To compare the area of two squares, calculate each area by squaring the length of a side, then form a ratio. A square with a side length twice that of another has four times the area.

Explanation:

Calculating the Area of a Square and Comparing to Another Square

To calculate the area of a square, you need to multiply the length of one side by itself since all sides of a square are equal in length. If we have a square with a side length of 4 inches, its area would be 4 inches × 4 inches = 16 square inches. Now, if we take another square with dimensions that are twice the first square, its side length would be 8 inches.

The area of this larger square is 8 inches × 8 inches = 64 square inches. When we compare the area of the larger square to the smaller one, we create a ratio. The ratio of their areas is 64 to 16, or simplified, 4 to 1. This means the larger square has an area that is four times as big as the area of the smaller square.

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

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:

-5 and 1

Step-by-step explanation:

Ask yourself these questions:

Where does the graph cross the X axis?  Or,

At what x's is y=0?

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

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: 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:

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

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:

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:

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

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:

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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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

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

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:

P = 95%

Step-by-step explanation:

The average is:

[tex]\mu = 3\ minutes[/tex]

The standard deviation is:

[tex]\sigma = 0.25\ minutes[/tex].

We want the probability that the red light lasts between 2.5 minutes and 3.5 minutes

This is:

[tex]P(2.5 <X <3.5)[/tex]

Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.

[tex]P(2.5-3 <X- \mu<3.5-3)\\\\P(\frac{2.5-3}{0.25} <\frac{X- \mu}{\sigma}<\frac{3.5-3}{0.25})\\\\P(-2<Z<2)[/tex]

This is:

[tex]P(-2 <Z <2) = P(Z <2) - P(Z <-2)[/tex] ---------- (By the symmetry of the standard normal distribution)

When you search for the normal standard table, you get the following value:

[tex]P(Z <2) = 0.9772\\\\P(Z <-2) = 0.0228\\\\P(-2 <Z <2) = 0.9772 - 0.0228\\\\P(-2 <Z <2) = 0.9544[/tex]

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:

Step-by-step explanation:

60 mph hope that helps

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:

See the image attached for solution

Answer:

the sum of the angles in a quadrilateral is 360 degrees

Step-by-step explanation:

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

Answer:   25x⁴ - 49

Step-by-step explanation:

  (5x² - 7)(5x² + 7)

= 5x²(5x² + 7)  - 7(5x² + 7)

= 25x⁴ + 35x² - 35x² - 49

= 25x⁴ + (       0      )  - 49

= 25x⁴ - 49

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.

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:

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: