one third the difference of two number is 12. if the larger number is 9, what is the sum of the two numbers

Step-by-step explanation:

Change the mixed fraction into improper fraction:

2 1/4 = 2 (1/4)(25/25) = 2 25/100 = 2.25

Divide 4 with 2.25

2.25/4 = 0.5625

0.5625 or a little over 1/2 cup of raisins are in each serving.

~

Answer:

D. <JEK = <CFL

Step-by-step explanation:

If angle JEK is complementary to angle DFH,

then <JEK = <CFL

Answer is D.

Answer:

angle JEK is congruent or equal to angle CFL

Step-by-step explanation:

ANSWER

[tex]\frac{5 - x}{x + 2}[/tex]

EXPLANATION

We want to simplify the rational expression:

[tex]( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 9x - 20}{x + 2} )[/tex]

We split the middle term to obtain:

[tex]( \frac{1}{x - 4)} )( \frac{ - {x}^{2} + 5x + 4x- 20}{x + 2} )[/tex]

We now factor to obtain;

[tex]( \frac{1}{x - 4)} )( \frac{-x(x - 5) + 4(x - 5)}{x + 2} )[/tex]

[tex]( \frac{1}{x - 4)} )( \frac{(x - 5)(4 - x)}{x + 2} )[/tex]

Or

[tex]( \frac{1}{x - 4)} ) ( \frac{ - (x - 5)(x - 4)}{x + 2} )[/tex]

We cancel the common factors to get;

[tex]\frac{ - (x - 5)}{x + 2}[/tex]

[tex] = \frac{5 - x}{x + 2}[/tex]

the answer would be 860 ft²

Answer:

920 ft^2

Step-by-step explanation:

What is the surface area of the triangular prism shown?

its 8 inches, because 2 inches is to short, and a yard is too long for the width of a book

Answer:

8 inches

Step-by-step explanation:

2 feet is too long, 1 yard is way too long, and 2 inches is too short

First of all, we can find the angle B by using the fact that the interior angles of a triangle sum up to 180:

[tex]32.5+26.8+B=180 \iff B = 180-32.5-26.8=120.7

[/tex]

Now use the law of sines, which states that the ratio between a side and the sine of its opposite angle is constant. In particular, we have

[tex]\dfrac{\overwrite{BC}}{\sin(A)}=\dfrac{b}{\sin(B)}[/tex]

Plug in the known values and solve for b:

[tex]\dfrac{25}{\sin(32.5)}=\dfrac{b}{\sin(120.7)}\iff b=\dfrac{25\sin(120.7)}{\sin(32.5)}=40.01[/tex]

Answer:

2nd graph (in the attached pics)

Step-by-step explanation:

Graphically, the x-intercepts of the graph of a quadratic function are its zeroes.

There can be

Looking at the figures, the 2nd graph has no real zeroes, because the graph doesn't cut the x-axis at all!

So, the answer is the second graph.

The graph that represents a quadratic function that has no real zeros is the second graph

For a graph to be a quadratic function, and not have real zeros, then the following must be true

From the list of given options, the second graph does not touch the x-axis

Hence, the graph that represents a quadratic function that has no real zeros is the second graph

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Answer:

26 cuts

Step-by-step explanation:

1. convert 42 feet into inches by multiplying by 12 (12 inches=1 foot)

    42*12 = 504 inches

2. divide the total number of inches (504) by 20 (where Chad cuts)

    504/20 = 25.2

Since Chad cannot make a partial cut (.2) round up to the next whole number - 26

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = - 6 and (a, b) = (- 9, - 3), thus

y - (- 3) = - 6(x - (- 9)), that is

y + 3 = - 6(x + 9)

Answer:

Option D. [tex]x=82\°[/tex]

Step-by-step explanation:

Remember that

In a inscribed quadrilateral opposite angles are supplementary

so

In this problem

[tex]m<C+m<A=180\°[/tex]

we have

[tex]m<C=x\°[/tex]

[tex]m<A=98\°[/tex]

substitute the values and solve for x

[tex]x\°+98\°=180\°[/tex]

[tex]x=180\°-98\°=82\°[/tex]

Answer:

82

Step-by-step explanation:

a pex

Answer:

1/(5^6)

Step-by-step explanation:

Which expression is equivalent to (3^2)^-2

Answer:

C

Step-by-step explanation:

Since the figures are similar then the ratio of corresponding sides are equal, that is

[tex]\frac{3}{15}[/tex] = [tex]\frac{1}{x}[/tex] ( cross- multiply )

3x = 15 ( divide both sides by 3 )

x = 5 → C

Note that result of this division is 4, as 28 divided by 7 equals 4.

The phrase "28 divided by 7" can be written as an expression using the division symbol (/) or the fraction bar (÷).

Using the division symbol  -

28 / 7

Using the fraction bar  -

28 ÷ 7

Both expressions represent the division operation where the number 28 is divided by the number 7.

The result of this division is 4, as 28 divided by 7 equals 4.

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Final answer:

The phrase '28 divided by 7' is written as the expression 28/7, which simplifies to the value 4.

Explanation:

The phrase '28 divided by 7' can be written as an arithmetic expression using the division symbol. The expression is 28 ÷ 7 or using the slash notation, it is 28/7.This is the most concise and universally understood way to express the division in mathematical terms.

When you perform this division, the result is 4, since 28 is evenly divisible by 7. When using a calculator to evaluate similar expressions, such as 337/217, you would get a decimal result.

However, for the phrase provided, no calculator is needed because the division is straightforward.

Answer:

D

Step-by-step explanation:

given the 2 equations

x + 2y = 27 → (1)

2x + 3y = 46 → (2)

Rearrange (1) expressing x in terms of y by subtracting 2y from both sides

x = 27 - 2y ← substitute into (2)

2(27 - 2y) + 3y = 46

54 - 4y + 3y = 46

54 - y = 46 ( subtract 54 from both sides )

- y = - 8 ( multiply both sides by - 1 )

y = 8 → D

Answer:

Step-by-step explanation:

There are two Pythagorean Triples containing 8:

6^2+8^2=10^2

8^2+15^2=17^2

chad has 280 baseballs because if miguel has 125 MORE than chad then you have to subtract 125 from 405 to get chads baseball cards

To find out how many baseball cards Chad has, subtract 125 from Miguel's total of 405 baseball cards.

To find out how many baseball cards Chad has, we can use the information given in the question. It is stated that Miguel has 125 more baseball cards than Chad and Miguel has a total of 405 baseball cards. So, to find out how many cards Chad has, we subtract 125 from Miguel's total:

Chad's total = Miguel's total - 125

Chad's total = 405 - 125 = 280 baseball cards

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This trigonometric function can be written as:

[tex]tan (3 cos^{-1} (\frac{3}{4}))[/tex]   (1)

Firstly, we have to solve the inner parenthesis:

[tex]cos^{-1} (\frac{3}{4})= 41.409[/tex]   (2)

Substituting (2) in (1):

[tex]tan (3(41.409))=tan(124.228)[/tex]   (4)

Finally we obtain the value:

[tex]tan(124.228)=-1.469[/tex]  

Answer:

[tex]tan(3 \times arc \ cos(\frac{3}{4} ))=\frac{\sqrt{7} }{3}[/tex]

Step-by-step explanation:

The given expression is

[tex]tan(3 \times arc \ cos(\frac{3}{4} ))[/tex]

Where

[tex]cos^{-1}(\frac{3}{4} )=x\\[/tex], which means that, [tex]cosx=\frac{3}{4}[/tex]

If we analyse this trigonometric reason in a right triangle, we would find the hypothenuses is 4 and the adjacent leg is 3. Then, using pythagorean theorem, we find the other leg

[tex]y^{2}=4^{2} -3^{2}\\ y=\sqrt{16-9}=\sqrt{7}[/tex]

Which means the opposite leg of our right triangle is the square root of seven.

Finally, using such right triangle, we find the tangent reason, which is the quotient between the opposite leg and the adjacent leg

[tex]tan(radian \ value)=\frac{\sqrt{7} }{3}[/tex]

Therefore, the answer is [tex]\frac{\sqrt{7} }{3}[/tex]

Answer:

The quotient of r and 9

Answer:

Step-by-step explanation:

The quotient of r divided by nine. The quotient is unspecified: you only know that there is one.

Answer:

right angle triangle.

Step-by-step explanation:

I take it that these are angles and not sides.

x + x + 2x = 180                All triangles have 180 degrees. Combine the left.

4x = 180                            Divide by 4

4x/4 = 180/4                     Do the division

x = 45

Therefore the angles are

x = 45

x = 45

2x = 90

The triangle is a right triangle because it has 1 angle that is 90 degrees.

Answer:

We are working with 2 vertical angles which are ALWAYS equal.

Therefore, 2 + 3x = 62

3x = 60

Therefore, x = 20

Step-by-step explanation:

Answer:

option b

137.1 cm²

Step-by-step explanation:

The given figure consist of two shapes

1) half circle

2) rectangle

Formula to use to calculate the area of this figure

half circle + rectangle

where r = radius = diameter/2 = 8/2 = 4 cm

          h = height = 14 cm

          b = base = 8 cm

plug in values in the formula

1/2(3.14)(4)² + (8)(14)

25. 133 + 112

137.13 cm²

Answer:

We have 17 inches = (37/100) · x;

x = 17 ÷ (37/100);

x = 17 · (100/37);

x = 1700 / 37;

x ≈ 46;

Step-by-step explanation:

Final answer:

To find out how much rain a city usually gets, divide the rain it received last year (17 inches) by the percentage of normal rainfall it represented (37%). The city normally receives about 45.95 inches of rain annually.

Explanation:

The student is asking how to calculate the usual annual rainfall for a city if the city received 17 inches of rain last year which was only 37% of their normal rainfall. To find the answer, we want to determine what 100% of their normal rainfall would be. We can use the formula:

Normal Rainfall = (Last Year's Rainfall / Percentage of Normal Rainfall) x 100

Substituting the given values into our formula, we get:

Normal Rainfall = (17 inches / 37%) x 100

Normal Rainfall = (17 / 0.37) inches

Normal Rainfall = 45.95 inches

Therefore, the city usually receives about 45.95 inches of rain annually.

Answer:

C.

Step-by-step explanation:

The first two questions couldn't be correct. C. Is the only logical answer.

Final answer:

The ordered pair (10, -52) is not a solution to the equation y = -5x - 4 because when x is substituted with 10, the equation yields -54, not -52.

Explanation:

To determine which ordered pair is not a solution of the equation y = -5x - 4, you need to plug the x-value from each ordered pair into the equation and see if the y-value matches the result.

The ordered pair that is not a solution is thus (10, -52).

50 quarts is greater than 12 gallons.

Given that, 12 gallons and 50 quarts.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, 1 quarts = 0.25 gallons

Here, 50 quarts = 50×0.25

= 12.5 gallons

So, 12.5 gallons > 12 gallons

Therefore, 50 quarts is greater than 12 gallons.

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Answer:

3,384 miles

Step-by-step explanation:

If can cover 94 miles in 1/6 of an hour.  (1/6 hour)*6 = 1 hour, so multiply 94 by 6 to see how far the plane will travel in 1 hour.  

94(6) = 564 miles in one hour

Multiply that by 6 to see how far the plane travels in 6 hours

564(6) = 3,384  miles

The airplane can cover 3,384 miles in 6 hours.

The formula for finding the distance covered is:

Distance = speed*time

It is given that it can cover 94 miles in 1/6 hours.

This should be converted to per hour.

For this, multiply the distance by 6.

94 miles * 6 = 564 miles

The speed of the plane is 564 miles per hour.

The distance that the plane covers in 6 hours = 564 miles per hour * 6 hours

= 3,384 miles.

Therefore, we have found that the plane can cover 3,384 miles in 6 hours.

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Answer:

Step-by-step explanation:

[tex]\dfrac{x}{2}-7=15\qquad\text{add 7 to both sides}\\\\\dfrac{x}{2}-7+7=15+7\\\\\dfrac{x}{2}=22\qquad\text{multiply both sides by 2}\\\\x=44[/tex]

Answer:

A. 7 more than 2 times m

Step-by-step explanation:

If there's a variable (letter) right next to a coefficient (the number) like in this problem, that means that 2 is being multiplied by m.

Since there's a +7 in the problem, that means thats its being added to or "more than."

Multiplication is "times"

7 is not being multiplied by two or m, it's being added.

So, 2m + 7.

Hope this helps!!!

Answer: OPTION D

Step-by-step explanation:

You can apply the SUBSTITUTION method:

- Solve for x from the second equation and substitute it into the first equation.

- Solve for y:

[tex]x-8y=-57\\x=-57+8y[/tex]

[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\19y=133\\y=7[/tex]

- Substitute y=7 into any of the original equations ans solve for x. Then:

[tex]x-8(7)=-57\\x-56=-57\\x=-57+56\\x=-1[/tex]

The answer is:

D.

[tex]x=-1\\y=7[/tex]

Substitution method for solving system of equations consists in isolate one variable in terms of the other variable.

So, isolating x in terms of y from the second equation, we have:

[tex]x-8y=-57\\x=-57+8y[/tex]

Then, substituting x into the first equation, we have:

[tex]2(-57+8y)+3y=19\\-114+16y+3y=19\\20y=19+114\\19y=133\\y=\frac{133}{19}=7[/tex]

Now, substituting y into the second equation we have:

[tex]x-8(7)=-57\\x-56=-57\\x=-57+56=-1[/tex]

Have a nice day!