Find the least common denominator for these fractions. Enter your answer in
the space provided.

Pedro has $13.65 in his wallet left.

Pedro had $14.90 in his wallet.

He spent $1.25 on a drink.

How much does he have left: 14+90 - 1.25 = 13.65

Pedro has $13.65 in his wallet left.

The difference is $1.95.

Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.

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Given that

Sin θ = a/b

LHS = Sec θ + Tan θ

⇛(1/Cos θ) + (Sin θ/ Cos θ)

⇛(1+Sin θ)/Cos θ

We know that

Sin² A + Cos² A = 1

⇛Cos² A = 1-Sin² A

⇛Cos A =√(1-Sin² A)

LHS = (1+Sin θ)/√(1- Sin² θ)

⇛ LHS = {1+(a/b)}/√{1-(a/b)²}

= {(b+a)/b}/√(1-(a²/b²))

= {(b+a)/b}/√{(b²-a²)/b²}

= {(b+a)/b}/√{(b²-a²)/b}

= (b+a)/√(b²-a²)

= √{(b+a)(b+a)/(b²-a²)}

⇛ LHS = √{(b+a)(b+a)/(b+a)(b-a)}

Now, (x+y)(x-y) = x²-y²

Where ,

On cancelling (b+a) then

⇛LHS = √{(b+a)/(b-a)}

⇛RHS

⇛ LHS = RHS

Sec θ + Tan θ = √{(b+a)/(b-a)}

Hence, Proved.

Answer: If Sinθ=a/b then Secθ+Tanθ=√{(b+a)/(b-a)}.

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Answer:

4 tenths or 4/10

Step-by-step explanation:

Answer:

Part A - he will need 2 cups of sugar  

Part B - 12 : 6 : 3

Step-by-step explanation:

Part A :

8 divided by 4 is 2

Part B :

Multiply all the numbers by 3

Hope this helped! :)

Answer:

your grade will be an 76

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

2x + 1 + 3 = 0

2x + 4 = 0

x = -2

Answer:

2:3:7

Step-by-step explanation:

a/b = 2/3

That gives us a clue that a=2 and b=3

But to make sure it states b/c = 3/7

So A:B:C is

2:3:7

Hope this helps!

Answer:

The original price of the sweatshirt was $127.50

Step-by-step explanation:

$40.80 / .32(32%) = $127.50

[tex]\dfrac 13 \times \dfrac 15 = \dfrac 1{15}[/tex]

The product of the two fraction numbers whose result is 1/15 will be 1/3 and 1/5.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The result of the product of the two fraction numbers is given below.

1/15

The factor of the number 15 is given as,

15 = 3 x 5

Then the expression is written as,

1/15 = 1/ (3 x 5)

1/15 = (1/3) x (1/5)

The multiplication of the two rational numbers whose result is 1/15 will be 1/3 and 1/5.

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Answer:

They are congruent by SAS

Step-by-step explanation:

MQ=PN

The angles with markings also go together

The line right in the middle is the second side because of the reflexive property

Answer:

Please select all of the things below that were the main issues the Anti Federalists

had with the US Constitution.

Select 3 correct answer(s)

A-They felt that the states did nothing to protect peoples' rights

B-They felt that the state had too much power

C-Many people felt that the representatives of the convention in Philadelphia had

overstepped its authority and that the articles should have been amended

D-They were concerned in giving the national government more power

E-They felt that the Constitution did nothing to protect the peoples' rights

Please hurry I’m soo stressed!!!!!!!

Step-by-step explanation:

1 Which of these objects are made from magnetic materials?

a copper pipe

b plastic paper clip

c steel nail

d glass bottle

e iron bar

g nickel coins

frubber tyre

Answer:

It'd be a rational number

Step-by-step explanation:

Real numbers are a set of numbers containing all of the rational numbers and all of the irrational numbers.

Types of numbers in the rational number "section" are decimals, whole, mixed, and fraction numbers whether they are negative or positive they are rational numbers.

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. So they would be square root, pi and more.

Answer:

mario lost the race and luigi won

Step-by-step explanation:

Answer:

a = -2

Step-by-step explanation:

3(a + 1.5) = -1.5

3a + 4.5 (-4.5) = -1.5 (-4.5)

3a = -6

a = -2

If the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833

The given exponential equation is:

[tex]y=ab^x[/tex]

The function passes through the points (3, 25) and (8, 10)

Substitute x = 3 and y = 25 into the function [tex]y=ab^x[/tex]

[tex]25=ab^3[/tex]............................(1)

Substitute x = 8 and y = 10 into the function [tex]y=ab^x[/tex]

[tex]10=ab^8[/tex].............................(2)

Divide equation (2) by equation (1)

[tex]\frac{10}{25}=\frac{ab^8}{ab^3} \\\\0.4=b^5\\\\b=0.4^\frac{1}{5} \\\\b=0.4^{0.2}\\\\b=0.833[/tex]

Therefore, if the exponential function [tex]y=ab^x[/tex] passes through the points (3,25) and (8,10), the value of b is 0.833

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Answer:

ANSWER: Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents.

Step-by-step explanation:

convert all % to decimals

0.06 x 21 = $1.26 tax

0.15 x 21 = $3.15 tip

1.26 + 3.15 = $4.41 added payment

4.41 + 21 = = $25.41 total bill

(yes i am aware i did the method differently since i learned it another way but the answer should till be correct.)

Answer:

Yes. They have enough to pay their bill: 21 dollars times 1.06 = 22 dollars and 26 cents and 22 dollars and 26 cents times 1.15 = 25 dollars and 60 cents. Otherwise B.

Considering the definition of equation, for a value of n of 10 the cost and revenue are equal.

A first degree equation is a mathematical equality with one or more unknowns.

Solving an equation consists of finding the value that the unknown must take so that equality is fulfilled.

The steps to solve an equation are as follows:

The cost C in dollars of producing a certain item is represented by the equation C = [tex]\frac{n}{2}[/tex]+ 20, where n represents the number of items produced.

The revenue R, in dollars, from selling n items is represented by the equation R=2n+ 5.

The cost and revenue are equal. Then:

[tex]\frac{n}{2}[/tex]+ 20= 2n+ 5

Solving:

When a term passes to the other side of equality, its sign changes (if it is positive it becomes negative and vice versa):

20 -5= 2n - [tex]\frac{n}{2}[/tex]

15= [tex]\frac{3}{2}n[/tex]

The X is cleared. Since the term in front of it is multiplying, it goes to the other side of the equation by dividing.

15 ÷[tex]\frac{3}{2}[/tex]= n

10= n

Finally, for a value of n of 10 the cost and revenue are equal.

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Answer:

-1

Step-by-step explanation:

Using the exponential function, it is found that:

The exponential function is:

[tex]y(x) = 30078(1.003)^x[/tex]

Hence, considering today as an starting point, the function is:

[tex]y(x) = 30078(1.003)^{x + 260}[/tex]

One week from now, we have y(1), hence:

[tex]y(1) = 30078(1.003)^{1 + 260} = 65734.37[/tex]

One week from today, the stock is predicted to close at $65,734.37.

One month from now, we have y(4), hence:

[tex]y(4) = 30078(1.003)^{4 + 260} = 66327.75[/tex]

One month from today, the stock is predicted to close at $66,327.75.

One year from now, we have y(52), hence:

[tex]y(52) = 30078(1.003)^{52 + 260} = 76584.35[/tex]

One year from today, the stock is predicted to close at $76,584.35.

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Answer:

One week from today, the stock is predicted to close at $65,734.37.

One month from today, the stock is predicted to close at $66,327.75.

One year from today, the stock is predicted to close at $76,584.35.

Step-by-step explanation:

Answer:

If there was another dog whose weight was greater than or less than 12.

Step-by-step explanation:

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 4

When we add 4 to the data set we have:

184 ÷ 16 = 11.5

This changed the median.

12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 28

When we add 28 to the data set we have:

208 ÷ 16 = 13

This also changed the median.

By adding dog of  weight other than 12 pounds could change the median.

What is median?

The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.

If we add the dog whose weight is more than 12 pounds, median will increase .

If we add the dog whose weight is less than 12 pounds, then median will decrease.

Hence, adding  dog of  weight other than 12 pounds could change the median.

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[tex]\large\huge\green{\sf{Answer:-}}[/tex]

<AEC =X°

<EAB = 116°

the by (consecutive)

180 = <EAB + <1

<1 = (180 - 116 )

<1=. 64°

<ECD = 124°

then ,180 = <ECD + <2

<2= (180 - 124)

<2= 56°

= Now add <1 + <2

= (64+ 56)°

➡x° = 120°

Answer:

Solution given:

Construction:

EF parallel to AB and CD is drawn.

let suppose <AEF=a

and

<CEF=b

now

<EAB+<EAB=180°[being co interior angle]

116°+a=180°

a=180°-116°=64°

again

<DCE +<CEF=[being co interior angle]

124°+b=180°

b=180°-124°

b=56°

Now

we know

x=a+b=64°+56°=120°

Value of x is 120°

Th e correct equation will be y = 5x

Ratios is a way dividing two integers. For instance, the ratio of a to b is written as a:b.

Given the ratios expressed as x:y = 1:5

Since ratio means division hence;

x:y = 1:5

x/y = 1/5

Cross multiply

1 * y = 5 * x

y = 5x

Hence the correct equation will be y = 5x

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Answer:

{x,y,z} = {-22/13,29/13,6/13} 

Write the system as the following augmented matrix:

[tex]\left[ \begin{array}{ccc|c} 3 & -2 & 5 & -7 \\ 1 & -1 & 3 & -5 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Swap rows 1 and 2 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 3 & -2 & 5 & -7 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Eliminate the x coefficient from the last two rows by add -3 (row 1) to row 2, and -4 (row 1) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 0 & 1 & -4 & 8 \\ 0 & 5 & -11 & 26 \end{array} \right][/tex]

Eliminate the y coefficient from the first and last rows by adding row 2 to row 1, and -5 (row 2) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 1 & -4 & 8 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the second row by adding 4 (row 3) to 9 (row 2) :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the first row by adding row 3 to 9 (row 1) :

[tex]\left[ \begin{array}{ccc|c} 9 & 0 & 0 & 13 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Then the solution to the system is (x, y, z) such that

9x = 13 and 9y = 16 and 9z = -14

or

x = 13/9 and y = 16/9 and z = -14/9

Answer:

5/9

Step-by-step explanation:

Answer:

Click the picture and u will see the answer.

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The summation of the given function from 1 to 4 is 10.5x³.

The given parameters:

[tex]\Sigma \ x^3 \times \Delta x, \ \ \ \Delta x = 2 + \frac{i}{4} \\\\[/tex]

The summation of the given function from i = 1, to i = 4, is calculated as follows;

[tex]\Sigma \ x^3 \times \Delta x = x ^3 (2 + \frac{1}{4} ) + x ^3 (2 + \frac{2}{4} ) + x ^3 (2 + \frac{3}{4} ) + x ^3 (2 + \frac{4}{4} )\\\\= x^3(10\frac{1}{2} )\\\\=\frac{21}{2} x^3\\\\= 10.5x^3[/tex]

Thus, the summation of the given function from 1 to 4 is 10.5x³.

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Answer:

5.164×10^-5

Step-by-step explanation:

[tex]5.164 \times {10}^{ - 5} [/tex]

Answer:

9, 12

Step-by-step explanation:

the rule is +3 for each step in the sequence

Answer:

Education and health services

Step-by-step explanation:

It has had the most increase over the years, so it will most likely keep increasing and let you get more wages and job opportunities.

Answers:

=========================================================

Explanation:

For equation A, I'll transform the right hand side into a similar form as the left side. Throughout the steps below, the left hand side stays the same.

[tex]\sqrt{448x^c} = 8x^3\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{(8x^3)^2}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{3*2}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}}\sqrt{7x}\\\\\sqrt{448x^c} = \sqrt{64x^{6}*7x}\\\\\sqrt{448x^c} = \sqrt{64*7x^{6+1}}\\\\\sqrt{448x^c} = \sqrt{448x^{7}}\\\\[/tex]

Therefore, c = 7

Notice that 7/2 = 3 remainder 1. The quotient 3 is the exponent for the term outside the root for [tex]8x^3\sqrt{7x}[/tex] while the remainder 1 is the exponent for the x term inside the root.

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

We do the same idea for equation B.

[tex]\sqrt[3]{576x^{d}} = 4x\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{(4x)^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3}\sqrt[3]{9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64x^3*9x^{2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{64*9x^{3+2}}\\\\\sqrt[3]{576x^{d}} = \sqrt[3]{576x^{5}}\\\\[/tex]

This must mean d = 5

Note: 5/3 = 1 remainder 2, which means [tex]\sqrt[3]{x^5} = x^1\sqrt[3]{x^2} = x\sqrt[3]{x^2}[/tex]