-3√7r³-6√7r²
How do I solve this step by step?

120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

Let we have to mix existing mixture in x,y respectively in amount to make the new mix of 70% purity.

Given that the first type is 65% pure.

So the pure juice = 65x/100

Given the second type is 100% pure.

So amount of pure juice in it = 100y/100

So the amount of pure juice in new mix = 65x/100+100y/100 = (65x+100y)/100

So the total amount of new mix = x+y

According to question,

((65x+100y)/100)/(x+y) = 70/100

(13x+20y)/(20x+20y) = 7/10

(13x+20y)/(2x+2y) = 7

13x+20y = 14x+14y

14x-13x = 20y-14y

x = 6y

x:y = 6:1

So we have to mix the existing mixture in 6:1 ratio.

So to make 140 pints of new mix need,

first mix = 140*(6/(6+1)) = 140* (6/7) = 120

second mix = 140*(1/(6+1)) = 140*(1/7) = 20

Hence 120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

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[tex]\sqrt[3]{-8x^{24}y^{36}} = \sqrt[3]{-8}\cdot \sqrt[3]{x^{24}}\cdot \sqrt[3]{y^{36}}[/tex]

[tex]\sqrt[3]{8}=-2[/tex]   because [tex](-2)(-2)(-2)= -8[/tex]

[tex]\sqrt[3]{x^{24}}=x^8[/tex]   because [tex](x^8)(x^8)(x^8)=x^{24}[/tex]

[tex]\sqrt[3]{y^{36}}=y^{12}[/tex]   because [tex](y^{12})(y^{12})(y^{12})=y^{36}[/tex]

Therefore [tex]\sqrt[3]{-8x^{24}y^{36}} = -2x^8y^{12}[/tex]

Answer:

[tex]-2x^8y^{12}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[3]{-8x^{24}y^{36}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]

[tex]\implies \sqrt[3]{-8}\sqrt[3]{x^{24}}\sqrt[3]{y^{36}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \left(-8\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]

Rewrite 8 as 2³:

[tex]\implies \left(-2^3\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies -2^{\frac{3}{3}}x^{\frac{24}{3}}y^{\frac{36}{3}}[/tex]

Simplify:

[tex]\implies -2x^8y^{12}[/tex]

The annual premium of Susie's insurance company apply as a result of accident is $255 for an year. This is because the monthly insurance payment has been increased by $21.25.

What is Health insurance?

Health insurance or the medical insurance is an insurance which covers the whole or a part of the risk of a person which is incurring the medical expenses. Depending upon the health insurance plan, the risk is shared among many individuals.

Main body:

The increase in monthly insurance payment = $21.25

So, the annual increase in the premium amount paid by Susie will be:

Monthly increase in insurance payment × 12

(As there are 12 months in an year)

Annual increase in premium amount = $21.25 × 12

Annual increase in premium amount = $255

Therefore, the annual increase in the amount of premium paid by Susie for health insurance is $225.

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Answer:

1.786

Step-by-step explanation:

Answer: A change from 20 to 22 represents a positive change (increase) of 10% Use the formula found below on this webpage to find the percent change by replacing the given values: Percent change = New - Old|Old| × 100% Percent change = 22 - 20 |20| × 100% = 2 20 × 100 = 10% (increase)

Answer: 10%

How: you know that 10 percent of 20 is 2 because you divide it by 10. by this you'll know that you are adding an extra 10 percent onto 20 to make it 22.

Answer:

True, True, False, True

Step-by-step explanation:

For line 2:

[tex]0 + 5(2) = 10[/tex]

[tex]0 + 10 = 10[/tex]

True

-2x - 2y = 4-------> -x - y = 2

x + 5y = 10-----> x + 5y = 10

--------------

4y = 12

y = 3, x = -5

(-5, 3) is a solution to the system----True

(4, 10) is a solution to the system----False

For Line 1:

[tex] - 2( - 10) - 2(8) = 4[/tex]

[tex]20 - 16 = 4[/tex]

True

The given triangles DEF and LNM are similar "by the SSS similarity postulate"

As given in the question, for LNM:

∠N=90°, LN(base)=5 and MN(prependicular)=3

and for DEF:

∠E=90°, DE(base)=10 and MN(prependicular)=6

Two triangles are similar when all their corresponding angles are congruent.

So far we have ∠N≅∠E=90°

Now, for the remaining angles, we first compare ∠L and ∠D.

From Pythagoras' theorem, we get:

For triangle LNM

[tex]LM^{2}=MN^{2}+LN^{2}\\LM=\sqrt{3^{2}+5^{2}}\\LM=\sqrt{34}[/tex]

For triangle DEF

[tex]DF^{2}=EF^{2}+DE^{2}\\DF=\sqrt{6^{2}+10^{2}}\\DF=\sqrt{136}\\DF=2\sqrt{34}[/tex]

Now we have all sides for both triangles and we compare the ratio of corresponding sides;

Side 1: LN:DE = 5:10 = 1:2

Side 2: MN:FE = 3:6 = 1:2

Side 3: LM:DF = [tex]\sqrt{34}[/tex]:[tex]2\sqrt{34}[/tex] = 1:2

As all three ratios are the same, by SSS similarity postulate, we can deduce that triangles LNM and DEF are similar.

This problem can also be solved with the other two (SAS & AA) similarity postulates.

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Answer: Option (C) : Yes, by the SSS Similarity Postulate

Step-by-step explanation:

The end behavior of the function is as x → -∞, f(x) → -∞ and s x → +∞, f(x) → +∞.

The nature of the value when the function parameter gets closer to +∞ and - ∞ is the end behavior of a function. The term with the highest degree determines how a polynomial function will behave in the end.

Look at the polynomial function's leading term to identify its final behavior. The leading term will dominate the graph because it has the highest power and will therefore grow much more quickly than the other terms as x gets very large or very small.

The given function is f(x) = 7x⁷ + 12x⁵ - 6x³ + 2x - 18

Graph the function. From the graph, the end behavior of the function is given as

As x → -∞, f(x) → -∞

As x → +∞, f(x) → +∞

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Answer:

Step-by-step explanation:

Only set (B) represents the side lengths of a right triangle.

In right triangle,

[tex](Hypotenuse)^{2} = (Perpendicular)^{2}+(Base)^{2}[/tex]

(A) [tex]8^{2} = 16[/tex]

     [tex]12^{2} = 144[/tex]

     [tex]15^{2} = 225[/tex]

    225 ≠ 144 + 16

(B) [tex]10^{2} = 100[/tex]

     [tex]24^{2} = 576[/tex]

     [tex]26^{2} = 676[/tex]

    676 = 576 + 100

(C) [tex]12^{2} = 144[/tex]

     [tex]20^{2} = 400[/tex]

     [tex]25^{2} = 625[/tex]

    625 ≠ 400 + 144

(D) [tex]15^{2} = 225[/tex]

     [tex]18^{2} = 324[/tex]

     [tex]20^{2} = 400[/tex]

    400 ≠ 324 + 225

Only (B) satisfies the condition.

Correct question,

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

(A) 8, 12, 15  (B) 10, 24, 26  (C) 12, 20, 25  (D) 15, 18, 20.

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Based on the given parameters, the amount owed is $10865

The given parameters about the compound interest are

Principal Amount, P = $5300

Interest Rate, R = 8%

Time, t = 6 years

To calculate the amount owed, we make use of the following formula

A = P + CI

Where

Compound interest, CI = P(1 + R)^t - P

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

In this question, the formula is given as

A = P(1 + r/n)^nt

Where

n = 12, i.e compounded monthly

Substitute the known values in the above equation

A = 5300 * (1 + 8%/12)^(6*12)

Express 8% as decimal

A = 5300 * (1 + 0.08/12)^(6*12)

Evaluate the sum

A = 5300 * (1.01)^(6*12)

Evaluate the exponent

A = 5300 * 2.05

Evaluate the product

A = 10865

Hence, the value of the amount after 6 years is $10865

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The probability of selecting a woman among students is 27/59.

According to the question,

We have the following information:

A class consists of 27 women and 32 men. And a student is randomly selected.

Now, we know that the following formula is used to find probability:

Probability of an event = Number of women in class/total number of students in the class

(More to know: probability of an event can be equal to 1 or less than 1.)

Total number of students in the class = 27+32

Total number of students = 59

Probability of selecting a woman = 27/59

Hence, the probability of selecting a woman among students is 27/59.

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Answer:

emily and her friend each paid $4 for the parking fee.

Step-by-step explanation:

The parking fee is 48% increase in the cost of a ticket.

Answer:

48%

Step-by-step explanation:

Answer:

1,750m

Step-by-step explanation:

3x9x10x5 = 1,750

Answer:

x = 45 Yes

Step-by-step explanation:

x+3x+2x+90= 360°

6x= 270

x=45

A= 2x = 90°

so yes both A and B makes 90° so they should be parallel

(a) k(x) = x-1, m(x) = x+ 2 , n(x) = x - 3  all  shown into the graph .

(b) The degree of the function fn(x) is 3.

(c) The zeros of the function fn(x) is x = 1 , x = -2 and x = 3.

(d)  The intervals over which the value of function f(x) is negative (0,6).

What is function explain?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range.

Given that;

k(x) = x - 1

m(x) = x + 2

n(x) = x - 3

[tex]f(x) = k(x)\times m(x)\times n(x)[/tex]

[tex]f(x) = (x-1)\times (x+2)\times (x-3)[/tex]

[tex]f(x) = (x^2+x-2)(x-3)[/tex]

[tex]f(x) = x^3 +x^2-2x-3x^3-3x+6[/tex]

[tex]f(x) = x^3-2x^2-5x+6[/tex]

a) k(x) = x-1,

   m(x) = x+ 2

    n(x) = x - 3

all  shown into the graph .

b)[tex]f(x) = (x-1)\times (x+2)\times (x+3)[/tex]

   [tex]f(x) = x^3-2x^2-5x+6[/tex]

∴degree of function is 3.

degree of function/polynomial is the highest power/degree of the polynomial's monomials.

c) for finding zeros put F(x) = 0 and solve for x

  [tex]f(x) = (x-1)\times (x+2)\times (x-3)\\f(0) = (0-1)\times (0+2)\times (0-3)\\[/tex]

x = 1 , x = -2 and x = 3 are the zeros of f(x).

d) for y-intercept put x = 0

f(0) = (0-1)(0+2)(0-3)

f(0)=6

y-intercept is (0,6).

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The linear function graphed is defined as follows:

y = -1/3x + 11/3.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph and from the options, the function crosses the y-axis at y = 11/3, hence the intercept is given as follows:

b = 11/3.

When x increases by 5, from 0 to 5, the function decays from 11/3 to 2, hence the slope is obtained as follows:

m = (2 - 11/3)/5 = (6/3 - 11/3) x 1/5 = -5/3 x 1/5 = -1/3.

Hence the equation is:

y = -1/3x + 11/3.

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Answer:

Step-by-step explanation:

as

The proportion statement is 2/3. The missing angles are CK = 12, GN = 15 and GT = 9

Given that: Polygon ROCK ~  Polygon GNAT.

The symbol ~ means the polygons are similar to each other. That means the ratios of all their corresponding sides are the same. Thus:

CO/AN = 4/6 = 2/3 (This is the proportion statement)

We can also say CK/AT= 2/3 because the ratios of all their corresponding sides are the same

With this, we can determine  the missing sides:

CK/AT= 2/3     where AT = 18

CK/18= 2/3

CK = (18×2)/3 = 12

OR/GN = 2/3    where OR = 10

10/GN = 2/3

2GN = 10×3

2GN = 30

GN = 30/2 = 15

KR/GT = 2/3   where KR = 6

6/GT = 2/3

2GT = 6×3

2GT = 18

GT = 18/2 = 9

Therefore, the proportion statement is 2/3, and the missing angles are CK = 12, GN = 15 and GT = 9

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Using the given model, we can complete the expression

                       12 + 16 = 4 × (4 + 3).

What are the area of a rectangle and a square?

The area of a rectangle having length "l" and breadth "b" is

                 Area of a Rectangle = l × b.

The area of a square with side "a",

                 Area of a square = side².

Let the given expression be 12 + 16 =  x × (y + x)

For the given figure the area of the square which is displayed in pink portion can be expressed as

                   Area = y²

                      16 = y²

Taking square root on both sides, we get

                      y = 4.

Now for the red part, we get the length of the rectangle i.e., y = 4.

                   Area of a rectangle = length * breadth

                                            12 = 4 * x

                                             x = 3.

Hence, the expression would look like

                        12 + 16 = 4 × (4 + 3)

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Answer:

simplify the equation

5x+3x

4+2

8x+6

The answer will be 8x+6

The required measure of m∠BVC is 90 degrees in the given figure.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

A parallelogram is a square and a rhombus is a square.

We have been given a figure which shows a rhombus as a parallelogram

The adjacent sides of a parallelogram must be equal, and the angles formed by the four sides must be 90 degrees for a rhombus to be a square.

According to the given figure,

This represents m∠BVC = 90°

Therefore, the required measure of m∠BVC is 90 degrees.

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The perpendicular height of the parallelogram is 13 cm.

A right triangle is a triangle that has an angle that measures 90 degrees. The three sides of a right -angled triangle are known as the length, base and the hypotenuse.

Area of a right-angled triangle = 1/2 x base x height

Area of a right-angled triangle = 1/2 x 13 x 6 = 39 cm²

A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

Area of the parallelogram = 4 x 39 = 156 cm²

Height = area / base

156 cm² / 12 = 13 cm

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1) The probability that the sum of the spots on the up-faces is 7 : 1/6

2)the probability that the sum of the spots on the up-faces is 11 : 1/18

3) the probability that the sum of the spots on the up-faces is 7 or 11: 2/9

For the experiment of rolling two Casino dice,

Let event A: the sum of the spots on the up-faces is 7

We have 1+6, 2+5, 3+4, 4+3, 5+2, 6+1

There are 6 ways for this to happen. so,

P(A) = 6/36

P(A) = 1/6

event B: the sum of the spots on the up-faces is 11

We have 5 + 6, 6 + 5

There are 2 ways for this to happen, therefore,

P(B) = 2/36

P(B) = 1/18

We need to find the probability that the sum of the spots on the up-faces is 7 or 11

P(A or B) = P(A) + P(B)

               = 6/36 + 2/36

               = 8/36

               = 2/9

Therefore, the probability that the sum of the spots on the up-faces is 7 : 1/6

the probability that the sum of the spots on the up-faces is 11 : 1/18

the probability that the sum of the spots on the up-faces is 7 or 11: 2/9

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(A) stamped envelope will cost 5+s pence

6 stamped envelopes will cost 6(5+s) pence

n stamped envelopes will cost n(5+s) pence

(B) expanded form of the ii part is 30+6s pence

and expanded form of the iii part is 5n+ns pence

As an envelope cost 5 pence and stamp cost s pence

(I) to get an stamped envelope we need to buy an envelope and the we have to get a stamp so the collective sum will be the cost that is

5+s pence

(II)to get 6 stamped envelope we need to buy 6 envelopes and the we have to get 6 stamps so the collective sum will be the cost that is

6(5+s) pence

(III))to get n stamped envelope we need to buy n envelopes and the we have to get n stamps so the collective sum will be the cost that is

n(5+s) pence

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Answer:

x=14

y=2

Step-by-step explanation:

a: to do this we isolate x

x-2=6y

 +2.  +2

x=6y+2

b now substitute it into an equation

6y+2-2y=10

4y+2=10

    -2. -2

4y=8

/4. /4

y=2

now fill in y to find x

x-2(2)=10

x-4=10

 +4. +4

x=14

Hopes this helps please mark brainliest

The two column method can be used to prove that BD is congruent to CE BD ≅ CE as follows;

Statement [tex]{}[/tex]                                            Reasons

1. ΔABC is an isosceles triangle [tex]{}[/tex]       1. Given

2. AB and AC are legs of ΔABC [tex]{}[/tex]       2. Given

3. BD ⊥ DC   [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]         3. Given

CE ⊥ BE

4. ∠BDC = 90° and ∠CEB = 90° [tex]{}[/tex]      4. Definition of perpendicular lines

5. ∠BDC = ∠CEB  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       5. Substitution property

6. ∠BDC ≅ ∠CEB  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]      6. Definition of congruency

7. ∠ABC ≅ ∠ACB [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]  7. Base angles of an isosceles triangle

8. [tex]\overline{BC}[/tex] ≅ [tex]\overline{BC}[/tex]  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       8. Reflexive property of congruency

9. ΔBCE ≅ ΔCBD  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]      9. SAA congruency postulate

10. BD ≅CE [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]  10. CPCTC

Two figures are congruent if they have the same size and shape.

The properties, postulates, and theorem used in the prove that BD ≅ CE are as follows;

Perpendicular lines;

Perpendicular lines are lines that form 90° angles where they intersect.

Substitution property

The substitution property of equality states that if one quantity a = b, then b can be substituted for a in equations and expression, such that the value of the expressions and equations remain the same.

Definition of congruency

Congruent figures are figures that have the same shape and size

Base angles of an isosceles triangles

The base angles of an isosceles triangle are congruent

Reflexive property

The reflexive property of congruency states that a figure is congruent to itself

SAA congruency postulate

The Side-Angle-Angle, SAA congruency postulate states that if two angles and  the non included side of one triangle are congruent to two angles and the non included side of the other triangle, then the two triangles are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent, CPCTC states that the corresponding parts of congruent triangles are also congruent.

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The probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Given information:

A company is considering purchasing materials:

The probability of purchasing mineral rights

Form the first mountain P1 = 0.55

From the second mountain P2 = 0.4

As the decision is made independently

So, P(P2∩ notP1) = 0.55 * 0.6

P(P2∩ notP1) = 0.33

Similarly, the value of

P(P2∩ notP1) =0.4 * 0.45

P(P2∩ notP1) = 0.15

Hence ,

P = 0.33 + 0.18

P = 0.51

Hence , the probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

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Answer:

Step-by-step explanation: Machine A makes 144 parts in 6 hours. Machine B makes 468 parts in 9 hours. If we divide 144 from 6 we will get 24 parts per hour. 468 divided by 9 would be 52. Now 52 times 12 is 624. 24 times 12 is 288 So if we subtracted 624-288=336.

So Machine B Makes 336 more parts after 12 hours. Hoped this helped!