Gloria says the two expressions;
1/3 (9x + 48) - 12x and -4(2x +4) are ecuivalent. Is she correct?
Explain how you know.

Answer:

Step-by-step explanation:

That means the chance of getting blue = 12/20

12/20 = 6/10

6/10 = 3/5

also, 3/5 = 60%, or .60

Answer:

10 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 2, 5 )

d = [tex]\sqrt{(-2-8)^2+(5-5)^2}[/tex]

   = [tex]\sqrt{(-10)^2+0^2}[/tex]

   = [tex]\sqrt{100}[/tex]

   = 10

The solution of the function [tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex] is - cos t - ¹/₄cos 2t + c.

An indefinite integral is a function that practices the antiderivative of another function.

It can be visually represented as an integral symbol, a function, and then a dx at the end.

The given function is;

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex]

Multiply by sint in the function and simplify;

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt[/tex]

Use trigonometric formulas for double angles:

[tex]\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t[/tex]

Substitute the values in the function

[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\[/tex]

And now we integrate this trigonometric form.

[tex]\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c[/tex]

Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.

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Answer: MQ=16, QL=32

Step-by-step explanation:

The centroid splits the median in a 2:1 ratio.

The measure of MQ and QL are 16 and 32 respectively.

Centroid is the point on the median which divides it in the ratio 2:1.

The ratio of lengths QL and MQ will be 2:1.

[tex]\frac{QL}{MQ}=\frac{2}{1}\\QL=2MQ[/tex]

It is known that ML is the sum of MQ and QL.

MQ+QL=ML

Substitute QL=2MQ and ML=48 into the obtained equation.

MQ+2MQ=48

3MQ=48

MQ=16

Substitute MQ=16 into QL=2MQ

QL=2(16)

=32

Thus, the lengths are MQ=16 and QL=32.

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Answer:

[tex]1.47 \times {10}^{4} [/tex]

Step-by-step explanation:

Answer:

19 sq cm

Step-by-step explanation:

2x2=4

2x3=6

1x3=3

2x3=6

6+6+4+3=19

1) Diagonals of a rectangle bisect each other, so AW=13.

2) Since diagonals of a rectangle are congruent, AC=BD. Then, since diagonals of a rectangle bisect each other, DW=13.

3) Diagonals of a rectangle are congruent, so BD=26.

4) Opposite sides of a rectangle are congruent, so AD=10.

5) Using the Pythagorean theorem, BA=24.

Answer:

1.5

Step-by-step explanation:

Step-by-step explanation:

Given quadratic equation is

px²-6qx-(9p-10q) = 0

On comparing with the standard quadratic equation ax²+bx+c = 0

a = p

b = -6q

c = -(9p-10q) = -9p+10q

Given roots of the equation = 2 Ⴛ - 3 and

2 Ⴛ - 3 and 2β – 3

We know that

Sum of the roots = -b/a

=> 2 Ⴛ - 3 + 2β – 3 = -(-6q)/p

=> 2 Ⴛ + 2β - 6 = 6q/p

=> 2 Ⴛ + 2β = (6q/p)-6

=> 2 Ⴛ + 2β = (6q-6p)/p

=> 2(Ⴛ + β) = (6q-6p)/p

=> Ⴛ + β = (6q-6p)/(2p)

=> Ⴛ + β = 2(3q-3p)/(2p)

=> Ⴛ + β = (3q-3p)/p ---------(1)

Product of the roots = c/a

=> (2 Ⴛ - 3 )( 2β – 3) = (-9p+10q)/p

=> 4Ⴛ β-6Ⴛ - 6β+9 = (-9p+10q)/p

=> 4Ⴛ β-6(Ⴛ +β)+9 = (-9p+10q)/p

=> 4Ⴛ β-6[(3q-3p)/p]+9 = (-9p+10q)/p

=> 4Ⴛ β-6[(3q-3p)/p] =[ (-9p+10q)/p]-9

=> 4Ⴛ β-6[(3q-3p)/p] = (-9p+10q-9p)/p

=> 4Ⴛ β-6[(3q-3p)/p] = (-18p+10q)/p

=> 4Ⴛ β =[(-18p+10q)/p]+6[(3q-3p)/p]

=> 4Ⴛ β =[(-18p+10q)/p]+[(18q-18p)/p]

=> 4Ⴛ β =[(-18p+10q)+18q-18p)]/p

=> 4Ⴛ β = (-36p+28q)/p

=> 4Ⴛ β = 4(-9p+7q)/p

=> Ⴛ β = 4(-9p+7q)/4p

=> Ⴛ β = (-9p+7q)/p

=> Ⴛ β = (7q-9p)/p ----------(2)

We know that

The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0

=> x²- [ (3q-3p)/p]x + [ (7q-9p)/p] = 0

=> [px²-(3q-3p)x+(7q-9p)]/p = 0

=> [px²-(3q-3p)x+(7q-9p)] = 0×p

=> px²-(3q-3p)x+(7q-9p) = 0

The required quadratic equation is

px²-(3q-3p)x+(7q-9p) = 0

Answer:

1/5

Step-by-step explanation:

0.2 is the same as 2/10. you then must reduce the fraction

Step-by-step explanation:

here is the single fraction of it

[tex] \frac{1}{5} = 0.2[/tex]

Option B is correct after applying the property of integer exponent and simplification.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have:

[tex]=\rm (x.x^{-3}.y^{\dfrac{1}{3}})^2[/tex]

[tex]=\rm (x^{-2}.y^{\dfrac{1}{3}})^2\\\\=\rm (x^{-4}.y^{\dfrac{2}{3}})\\\\=\rm \dfrac{y^{\dfrac{2}{3}}}{x^{4}}\\\\[/tex]

Thus, option B is correct after applying the property of integer exponent and simplification.

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The quadratic function that models the data given in the table is 203.8x² - 26.6x + 8.6

A quadratic function is an equation that usually has a single variable and it is raised to the power of 2.

A quadratic function has the form : ax² + bx + c = 0

Where: a, b,c are known numbers and x is unknown

Given the quadratic function: 185x²+ 1.

Given the quadratic function: 203.8x² - 26.6x + 8.6

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Answer:

It's 44 in²

Remember the diagonal formula, whereas there is p and q for the diagonals.

[tex]A = \frac{pq}{2} = \frac{11*8}{2} = 44~in.[/tex]

Answer:

Area of rhombus  = 44 square inches

Step-by-step explanation:

[tex]\sf \boxed{Area \ of \ rhombus = \dfrac{d_1*d_2}{2}}[/tex]

[tex]\sf \text{Here, $d_1$ and $d_2$ are the diagonals}[/tex]

                             [tex]\sf = \dfrac{11 *8}{2}\\\\ = 11*4\\\\ = 44 \ in^{2}[/tex]

Answer:

There are now 6.5 ounces in the new bag.

Step-by-step explanation:

To solve this question, take 30% of 5 and add it to the original amount of 5

30% = 0.30

5 * 0.30 = 1.5

5 + 1.5 = 6.5 ounces of candy.

Hope this helps!

The inverse function value in degrees will be 45°. Option C is correct.

Assuming function 'f' is a one-to-one and onto function which is a need for inverses to exist. The inverse of the considered function is. f⁻¹(x).

The given function is;

f(x)=sin⁻¹(1/2)

The given function is arranged is;

x=sin⁻¹(1/2)

The given function in terms of  sin;

sinx=1/2

Putting the values in terms of sin we get;

sinx=sin30°

x=30°

The inverse function value in degrees will be 45°.

Hence,option C is correct.

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Answer:

no 2³ = 8

Step-by-step explanation:

2³ = 2 times 2 times 2 which = 8

Answer:

D. 159

Step-by-step explanation:

Answer:

the 2 one and the last one

Step-by-step explanation:

Hey there!

5(4r + 3) - 2x

DISTRIBUTE 5 WITHIN the PARENTHESES

= 5(4r) + 5(3) - 2x

= 20r + 15 - 2x

COMBINE the LIKE TERMS (if they are any)

Seems like you don’t have any like terms so we could leave it as it is!

= 20r + 15 - 2x

= 20r - 2x + 15

Therefore, the answer should be:

20r - 2x + 15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The perimeter of the quadrilateral is the sum of the side lenths, and the perimeter is 72 units

The given parameters are:

AP = 10

EO = 12

The perimeter of the quadrilateral is calculated using:

Perimeter = 2 * (EO + 2AP) + 4

So, we have

Perimeter = 2 * (10 + 2 * 12) + 4

Evaluate

Perimeter = 72

Hence, the perimeter of the quadrilateral is 72 units

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Answer:

(D) -2

Step-by-step explanation:

Plug in r=5 and s=-7 to the equation:

-6(5)+(-7)-(5)(-7)

Now we can solve and simplify:

-30-7+35

Combine:

-2

Hey there!

-6r + s - rs

= -6(5) + (-7) - 5(-7)

= -6(5) - 7 - 5(-7)

= -30 - 7 - 5(-7)

= -30 - 7 + 5

= -37 - (-35)

= -2

Therefore, your answer is: -2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

15÷3=5

There are 5 equal groups of 3

8÷4=2

There are 4 equal groups of 2

18÷6=2

There are 3 equal groups of 3

45÷5=9

There are 9 equal groups of 5.