Least common denominator: the smallest number that both denominator numbers will __ into.

Answer: 7-i√3

Step-by-step explanation:

√36+ √-75+ √1-√-108

6 + √75i + 1 - √108i

7 + 5i√3 - 6i√3

7-i√3

The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.

We know that,

Sum of all angles of triangle = 180°.

Therefore, m∠3 + 42° + 25° = 180°.

m∠3 = 180° - 67°

m∠3 = 113°

Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.

We know that,

Vertical or opposite angles have equal measures.

So, 42° and m∠2 are vertical or opposite angles.

Therefore, the value of m∠2 = 42°.

Similarly, for m∠3, We know that,

Sum of all angles of triangle = 180°.

∴ ∠1 + ∠2 + 50° = 180°.

=> ∠1 + 42° + 50° = 180°

=> m∠1 = 88°.

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Answer:

D

Step-by-step explanation:

-4x + 9 ≥ -3  Subtract 9 from both sides

-4x ≥ -12  Divide both sides by -4.  When you divide both sides by a negative number, you must flip the inequality sign.

x ≤ 3

D: 5 is not a solution.

Answer:

D) 5

Step-by-step explanation:

To solve this problem, we must first isolate the variable and simplify the inequality. Isolating the variable means having the variable on one side of an equation or inequality without any other terms?

How do you isolate a variable?

Here's an example.

x+3=18

What can we do to have x on its own side of the equation? Currently, 3 is also with it. If we subtract 3 on both sides, we are leaving the equation with the same answer.

x + 3 - 3= 18 - 3

Combine like terms.

x = 21

That's how you solve for an equation.

Next, an example with division.

3x = 21

How do we solve for x this? Well, we know that 3x = 3 times x. So, to solve for x, we remove the 3. Since its 3 times x, lets divide by 3 on both sides.

[tex]\frac{3x}{3} =\frac{21} {3}[/tex]

Simplify:

3x/3 means 3 times x divided by 3. 3/3 = 1

1x = 21/3

21/3 = 7

x = 7

Now lets get to the problem.

[tex]-4x + 9 \geq -3[/tex]

The first step is to subtract by 9 on both sides so we can work our way to isolating the variable and solving the problem.

[tex]-4x + 9 -9\geq -3 - 9[/tex]

Simplify.

[tex]-4x \geq -12[/tex][tex]-4x \geq -12[/tex]

Now heres the tricky part. To solve for an equation, we must remove -4 from x, or -4 times x. In an equality, which states that:

A [tex]\geq , \leq , > , or < B[/tex]

If you divide or multiply both sides by a negative number, which means the number is less than 0, you must flip the sign!

When you multiply/divide by a negative number or both sides in an equality:

[tex]\leq[/tex] [tex]\geq[/tex]

[tex]\geq[/tex] [tex]\leq[/tex]

> <

< >

So, we currently have:

[tex]-4x \geq -12[/tex]

Divide by -4 on both sides.

[tex]\frac{-4x}{-4} \geq \frac{-12}{-4}[/tex]

Simplify. (Use the rule which states that a negative number multiplied or divided by another negative number equates to a positive number).

[tex]x \geq 3[/tex]

Flip the sign (This is a crucial step!)

[tex]x \leq 3[/tex]

Now, [tex]x \leq 3[/tex] means any number equal to or lower than 3 satisfies the conditions of the inequality.

Is -3 lower than or equal to 3?

Yes; Lower

Is -1 lower than or equal to 3?

Yes;

Is 3 lower than or equal to 3?

Yes; Equal

Is 5 lower than or equal to 3?

No; Greater

D, 5 is your answer as it does not satisfy the inequality.

The given sequence is geometric sequence not arithmetic.

An arithmetic sequence is a sequence in which the difference between every two consecutive terms is constant

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. It is found by taking any term in the sequence and dividing it by its preceding term.

Difference between arithmetic and geometric sequence:

An arithmetic sequence has a constant difference between each consecutive pair of terms

while

A geometric sequence has a constant ratio between each pair of consecutive terms.

Here, we have a sequence 5,10,20.

So a₁ = 5, a₂ = 10, a₃ = 20

Difference = a₃- a₂ = 20 - 0 = 10

                    a₂ - a₁ = 10 - 5 = 5

Since the difference is not constant, therefore the given sequence is not arithmetic.

Now ratio a₃/a₂ = 20/10 =2 and a₂/a₁ = 10/5 =2 which is same which shows the sequence is geometric.

Therefore, the sequence is geometric sequence.

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Answer: Use your brain aka 12 and 7

Step-by-step explanation:isn't this urgent?

The size that is the better one is 30.6-ounce package costs 7.98.

The 11.5-ounce package costs 3.19. The price per package will be:

= 3.19 / 11.5

= 0.27

A 30.6-ounce package costs 7.98. The cost per package will be:

= 7.98 / 30.6

= 0.26

In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.

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Answer:

Erin would need $10 more dollars in order to buy all three books.

Step-by-step explanation:

Step one: find the cost of all books

12 +16 +11 = 39

Step two: subtract

39 -29 = 10

Step two: Get your Answer!

Erin would need $10 more dollars in order to buy all three books.

The probability that 72% or more of the women in the sample have been on a diet is, 0.1736.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

As given a sample survey interviews an SRS of 209 college women. suppose that 69% of all college women have been on a diet within the last 12 months.

p = 0.69

1 - p = 0.31

n = 209

μp = p = 0.69

σp = √(p(1-p))/n = √(0.69*0.31)/209 = 0.03199

= 1 - p(p < 0.72)

= 1 - p((p - μp) / σp < (0.72 - 0.69) / 0.03199)

= 1 - p(z < 0.94)

= 1 - 0.8264

= 0.1736

Hence, the probability is 0.1736.

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well, as I said a while back, Heron's Area formula works for any triangle, so long we have all sides, and in this case we do, since it's not a right-triangle SOH CAH TOA won't work, so let's plug the values in Heron's

[tex]\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a = 12\\ b = 8\\ c = 6\\ s=\frac{12+8+6}{2}\\ \qquad 13 \end{cases} \\\\\\ A=\sqrt{13(13-12)(13-8)(13-6)} \implies A=\sqrt{13(1)(5)(7)} \\\\\\ A=\sqrt{455}\implies {\Large \begin{array}{llll} A\approx 21.33 \end{array}}~cm^2[/tex]

Answer:

1. 30 years old

2. 7 years old

3. 5 hours

Step-by-step explanation:

We can solve all of these problems using algebraic equations.

1. In this question, we will use variable x to represent the age of Mrs. Olsen's daughter.

In 10 years, x - 20 = 2x. That means that in 10 years, Mrs. Olsen will be 40 years old. That means she is 30 right now.

2. In this question, we will use variable x to represent the age of Alyssa.

If, in 30 years, their total age is 88, their current total is 28. Tyler is 3 times as old as Alyssa, so Tyler is 21 and Alyssa is 7.

3. Ryan leaves home at 50 mph. That means, in an hour Ryan will be 50 miles away from home. At that point, Jacob leaves home at a speed of 60 mph, so the gap between them closes by 10 miles each hour. That means that Jacob will take 5 hours to catch up, counting from when he left (how far is this workplace jeez?!?!?!?).

We could also represent this with a graph.

Hour 1: R = 50, J = 0 (Jacob leaves after this hour so it doesn't count for the answer)

Hour 2: R = 100, J = 60

Hour 3: R = 150, J = 120

Hour 4: R = 200, J = 180

Hour 5: R = 250, J = 240

Hour 6: R = 300, J = 300

The Law of detachment states that if m then n and m is true then q is true.

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

The Law of detachment states that if m then n and m is true then q is true.

We have,

If two angles are complementary, then the sum of their measures is 90°.

This is in the form of,

If M then N and if M is true then N must be true.

So,

If two angles are complementary, then the two angles' sum is 90 degrees.

If the two angles are m∠E and m∠F.

m∠E + m∠F = 90

Thus,

If two angles are complementary, then the two angles' sum is 90 degrees.

This is m∠E + m∠F = 90.

Option C is the correct answer

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Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86

The new height of painting by Jacob will be 2.5 inches.

The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -

42.88/33.5 = 3.2/x

Rewriting the equation according to x

x = (3.2 × 33.5) ÷ 42.88

Performing multiplication in numerator

x = 107.2 ÷ 42.88

Performing division on Right Hand Side of the equation

x = 2.5

Thus, the new height will be 2.5 inches.

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The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

Given,

In the question:

His juggling instructor divides a box of bean bags equally among the 16 clowns in Jason's class. each clown gets 6 bean bags.

Now, According to the question:

The equation that can be used to determine the number of bean bags in the instructor's box is b = 16 x 6.

The number of bean bags in the instructor's box is 96.

What is multiplication?

Multiplication is a mathematical operation that can be used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Hence, The equation that can be used to determine the number of bean bags in the instructor's box is b = 17 x 4.

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Answer: Steph is 16 today

Step-by-step explanation:

Austin age today = x

Austin in 4 years = x+4

Steph age today = 4x (because Austin is 1/4 her age today)

Steph age in 4 years is 4x + 4

In 4 years Austin's age is 2/5 of Steph's, so:

2/5 (x+4) = 4x + 4

Now solve for x!

x+4 = (8/5)x + 8/5

12/5 = (3/5)x

Therefore Austin is 4 years old today (x=4) and...

Steph age today = 4x = 4x4 = 16

Answer: 9.

Step-by-step explanation:

These are all multiples of 9, meaning that they can all be divided by 9 into a whole number.

90/9 =10

81/9 =9

72/9 =8

63/9 =7

Answer:

9:N

Step-by-step explanation:

90-9=81

81-9=72

72-9=63

The same number (9) is used to fing the sum of the next number in the sequence therefore that is your nth term

The solutions to the expression x³ + 87 = 7x² + x are given as follows:

–3, 5 + 2i, 5 – 2i.

The equation is defined as follows:

x³ + 87 = 7x² + x.

In standard format, it is given by:

x³ - 7x² - x + 87 = 0.

It has one negative solution, hence from the options it is:

x = -3.

The verification is:

(-3)³ - 7(3)² - (-3) + 87 = 0.

Considering the linear factor (x + 3), the function can be written as follows:

x³ - 7x² - x + 87 = (x + 3)(ax² + bx + c).

As the product of a linear function and a quadratic function results in a cubic function.

Expanding the right side of the equality, we have that:

ax³ + (b + 3a)x² + (3b + c)x + 3c = x³ - 7x² - x + 87.

Hence the coefficients of the quadratic equation are given as follows:

Hence the equation is:

x² - 10x + 29 = 0.

And the solutions, using a quadratic equation calculator, are given as follows:

Which means that the third option is correct.

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Answer:

Step-by-step explanation:

this slope of a line question is such a common question.  I feel like math teachers all over don't understand how to teach this subject.  Just so you know,  I answer a question like this about 10 times a day when I am on here.  It's like one of the most common questions.  

Here is my copy and paste answer for this...

point P1 (-3,7.2)  in the form (x1,y1)

point P2(2,-2.3)  in the form (x2,y2)

slope = m

m = (y2-y1) / (x2-x1)

m = (-2.3-7.2) / (2-(-3))

notice all the minus signs and how i'm being very careful to keep close track of them.  Also, who ever has written this question is intentionally trying to trip you up by putting in all the minus signs,  there is no need for so many minus signs to teach this well.  Anyway...

m = -8.5 / 5

m = - 1.7

the problem question ends there , but there is a common place this question is supposed to take you.   to the point slope formula.  but for another question.

The slope of (-3, 7.2) and (2, -2.3) is -1.9.

Consider,

(x1, y1) = (-3, 7.2)

(x2, y2) = (2, -2.3)

slope = (y2 - y1)/(x2-x1)

slope = ((-2.3) - (7.2))/((2) - (-3))

slope = (-9.5)/(5)

slope = -1.9

Therefore, the slope of the given points (-3, 7.2) and (2, -2.3) is -1.9.

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the slope of the given point is m=9

The vector that translates P to P' is (-4 , 6)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

The points are given;

[tex]{P = (3, -2)}\\{P' = (-1, 4)}[/tex]

The translation rule is calculated as:

{(x,y) = P' - P}

So, we have:

{(x,y) =(− 1, 4) - (3, − 2)}

Combine the terms;

{(x,y) = (-1 -3 , 4 + 2)}

{(x,y) = (-4 , 6)}

Express as vectors;

(x, y) = (-4 , 6)

Hence, the vector that translates P to P' is  (-4 , 6)

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Answer:

Step-by-step explanation:

48

Answer:

51

Step-by-step explanation:

Pythagorean theorem

a^2+b^2=c^2

45^2+24^2

2025+576

2601=c^2

square root both sides

51=c

Hopes this helps please mark brainliest

Answer: $13.2

Step-by-step explanation:

You can use proportions to find the cost(x):

[tex]\frac{22}{48.40} =\frac{6}{x} \\\\22x=6*48.4\\\\22x=290.4\\\\x=13.2[/tex]

Answer: x=7°

Combine like terms and divide.

8x+5°+3x+8°=90°

(8x+3x)+(5°+8°)=90°

11x+13°=90°

-13°       -13°

11x=77°

[tex]\frac{11x}{11} =\frac{77}{11}[/tex]

x=7°

Answer:

-160 I think so

Step-by-step explanation:

(2)4-168

8-168

-160

The distance when r = 55 mi/hr and t = 3 hours is 165 miles .

In the question ,

it is given that ,

r = 55 mi/hr which means the speed is 55 mi /hr

t = 3 hours , which means time = 3 hours .

we need to find the distance when r=55 mi/hr and t =3 hours .

the formula to calculate the distance is written as

distance = Speed × time

Substituting the value of speed = 55 and time = 3 ,

we get ,

distance = 55 × 3

distance = 165 miles .

the distance is 165 miles .

Therefore , The distance when r = 55 mi/hr and t = 3 hours is 165 miles .

The given question is incomplete , the complete question is

Find the distance when r=55 mi/hr and t = 3 hours ?

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Answer:

10 - x

Step-by-step explanation:

Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:

10 - 3 - x + 3

7 - x + 3

10 - x

The Average speed is 17.4 mph.

The average speed is calculated by dividing the total distance travelled by the total amount of motion time.

The overall distance the object covers in a given amount of time is its average speed. A scalar value represents the average speed. It has no direction and is indicated by the magnitude.

Average speed = Distance travelled/ Time taken

Given:

Distance = 5 4/5 = 29/5 miles

Time= 1/3 hours

So, Average speed = Distance travelled/ Time taken

Average speed= 29/5 x 3/1

                         = 87/5

                         = 17.4 mph

Hence, the Average speed is 17.4 mph.

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Answer:

  11

Step-by-step explanation:

You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.

The ratio of interest is ...

  2B/A = 2(2115000)/(3.7×10⁵)

A calculator provides an easy answer to the value of this expression. (See attached.)

City C is about 11 times the population of City A.

__

Additional comment

If you want to work this out "by hand", you will need to find the quotient of ...

  4230000/370000 = 423/37 = 11 17/37 ≈ 11

because 17/37 < 1/2.

The converse of the conditional statement "If the streetlights are on, then the sun has gone down" is If the sun has not gone down, then the streetlights are on and is denoted as option D.

This is referred to as the type of sentence which is formed when the hypothesis and the conclusion are interchanged.

In this scenario, "If the streetlights are on, then the sun has gone down" when interchanged will be  If the sun has not gone down, then the streetlights are on which therefore makes option D the correct choice.

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Answer: y=-5/3x+4

Step-by-step explanation:

Since the line is parrallel that means that the gradient is the same

We can reorder 5x+3y=6 into 3y=-5x+6 but in order to find the gradient the number infront of y must be 1 so...

3y=-5x+6

y=-5/3x+2

Now we know that the gradient is -5/3

To find th y-intercept we just subsitute the points it passes through (3, -1) into the equation

y=-5/3x+c

-1=-5/3(3)+c

-1=-5+c

4=c