The hypotenuse of a right triangle is 13 inches. If the long leg is 7 inches longer than the short leg, find the lengths of the leg using the Pythagorean theorem

Answer:

The correct answer is 2 1/36.

Answer:

m∠B=143°

Step-by-step explanation:

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always equal

so

In this problem we have that

m∠A=m∠B ----> by vertical angles

substitute the given values and solve for x

[tex](4x+23)=(5x-7)\\5x-4x=23+7\\x=30[/tex]

Find the measure of angle B

m∠B=(5x-7)°

substitute the value of x

m∠B=(5(30)-7)°

m∠B=143°

Answer:

75 ft.³

Step-by-step explanation:

[tex] {a}^{2} \frac{h}{3} = V[/tex]

[tex][(5)^{2}] ( \frac{9}{3}) = (25)(3) = 75[/tex]

a → length\base edge

I am joyous to assist you anytime.

Answer:

75

V= lwh = 5×5×9 = 75

3 3

The volume of the pyramid is 75

7s + 4(3-5) = 18

Multiply the bracket by 4

(4)(3)=12

(4)(-5)=-20

7s+12-20=18

7s-8=18

Move -8 to the other side.

Sign changes from -8 to +8

7s-8+8=18+8

7s=18=8

7s=26

Divide both sides by 7

7s/7=26/7

Answer: s=26/7 or s=3 5/7

Answer:

7s+4(3-5)=18

7s+12-20=18

7s=18-12+20

7s=26

s=3.714

Answer:25

Step-by-step explanation:Use pemdas first (2x-7y) 2-7=5 next (2x+3) 2+3=5 3•5=15 5•2=10 3•5=15 add 10+15=25

The amount in Kelly's account at the end of four years will be $887.63.

To calculate the amount in Kelly's account at the end of four years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, Kelly's principal amount is $750, the annual interest rate is 4.25%, and interest is compounded semi-annually, so n = 2. Plugging these values into the formula:

A = 750(1 + 0.0425/2)^(2*4)

A = 750(1 + 0.02125)^8

A = 750(1.02125)^8

A = 750(1.18350595645)

A = $887.63

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Answer:

[tex]\frac{175}{2x}[/tex]

Step-by-step explanation:

Jon works the same number of hours on Friday and Saturday, therefore x represents the number of hours worked on Friday and also the number of hours worked on Saturday.

So the total hours worked between Friday and Saturday is 2X

If the total for the 2X hours worked is equal to 175 $  

To know how much you earn per hour, we must divide the profit by the total hours worked.

Then we have the following expression

To know how much you earn per hour, we must divide the profit by the total hours worked.

[tex]\frac{175}{2x}[/tex]

Answer:

Step-by-step explanation:

C,D and E

Pairs of triangles appear to be congruent are :

" Congruent triangles are defined as the pairs of triangles with same measurement."

According to the question,

Given pairs of triangles,

A. Triangles [tex]1[/tex] and [tex]4[/tex] :

After observing triangles  [tex]1[/tex] and [tex]4[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]4[/tex] .

Option A is not the correct answer.

B. Triangles [tex]1[/tex] and [tex]3[/tex] :

After observing triangles  [tex]1[/tex] and [tex]3[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]3[/tex] .

Option B is not the correct answer.

C. Triangles [tex]2[/tex] and [tex]3[/tex] :

After observing triangles  [tex]2[/tex] and [tex]3[/tex]   it appears that triangle [tex]2[/tex] is congruent to triangle [tex]3[/tex] .

Option C is the correct answer.

D. Triangles [tex]2[/tex] and [tex]4[/tex] :

After observing triangles  [tex]2[/tex] and [tex]4[/tex]   it appears that triangle [tex]2[/tex] is congruent to triangle [tex]4[/tex] .

Option D is the correct answer.

E. Triangles [tex]3[/tex] and [tex]4[/tex] :

After observing triangles  [tex]3[/tex] and [tex]4[/tex]   it appears that triangle [tex]3[/tex] is congruent to triangle [tex]4[/tex] .

Option E is  the correct answer.

F. Triangles [tex]1[/tex] and [tex]2[/tex] :

After observing triangles  [tex]1[/tex] and [tex]2[/tex]   it appears that triangle [tex]1[/tex] is smaller than triangle [tex]2[/tex] .

Option F is not the correct answer.

Hence, Option(C), (D), and (E) are correct answer.

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Answer:

Answer is 18

Step-by-step explanation:

18 x $5 = $90

12 x $10 = 120 (6 more $5 books sold than $10)

20 x $2 = $40 (8 more $2 books sold than $10)

Total $250

Answer:

n=4

Step-by-step explanation:

12 - 10n = -28

-12            -12

-10n = - 40

[tex]\frac{-10n}{-10} = \frac{-40}{-10}[/tex]

n = 4

The equivalent expressions 6 +(–x) + 2x + (–7) + 2x simplify to 3x – 1 as like terms are combined to get the final equivalent expression.

Explanation:

Expressions corresponding to 6 +(–x) + 2x + (–7) + 2x can be found by combining similar terms. Here are all the dates:

Plus six: negative +6X (or -1x): –x Twice x (or 2x): +2xNegative seven: –7Twice plus x: +2x

We can now combine similar terms:

x terms: –x + 2x + 2x = 3x

Constant conditions: +6 – 7 = –1

The equivalent expression is therefore:

3x-1

To check whether our answer makes sense, we ensure that all similar terms have been grouped together and no further simplifications are possible.

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What we know:

The convention center has 18 pianos.

Each piano has 88 piano keys.

How to solve:

To find out the total number of of piano keys, we need to multiply the number of pianos that are at the convention center by the number of piano keys that are on each pano.

Number of pianos → 18

Number of piano keys → 88

18 × 88 = 1,584

Therefore, there are 1,584 keys at the convention center.

Answer:

Try entering 2x+3=15 @ x=6 into the text box. After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x+3=15: 2(6)+3 = 15. The calculator prints "True" to let you know that the answer is right. More Examples Here are more examples of how to check your answers with Algebra Calculator. Feel free to try them now.

Step-by-step explanation:

"The value of the expression [tex]\( -4.2(0.35 - 3.5) \) is \( 13.404 \)[/tex].

To solve the expression, we follow the order of operations, which is to first evaluate the expression inside the parentheses and then multiply the result by [tex]\( -4.2 \).[/tex]

 First, we subtract [tex]\( 3.5 \)[/tex] from [tex]\( 0.35 \):[/tex]

[tex]\[ 0.35 - 3.5 = -3.15 \][/tex]

 Next, we multiply this result by [tex]\( -4.2 \)[/tex]:

[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]

 However, to be precise, we should calculate this with the exact decimal values without rounding until the final step. So, let's do the multiplication with more precision:

[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]

 Now, we can round the result to the nearest ten-thousandth, as the original numbers were given to the hundredth:

[tex]\[ 13.23 \approx 13.2300 \][/tex]

But, to match the precision of the original question, we should express the answer to the same decimal place as the given numbers, which is to the hundredth:

[tex]\[ 13.2300 \approx 13.23 \][/tex]

However, the provided answer is[tex]\( 13.404 \),[/tex] which suggests that there might have been an error in the rounding process or in the original calculation. Let's re-evaluate the multiplication with exact values:

[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]

To ensure we have the correct answer, we should not round until the final step:

[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]

 Now, rounding to the nearest hundredth:

[tex]\[ 13.23 \approx 13.23 \][/tex]

The correct answer, rounded to the nearest hundredth, is \( 13.23 \). However, if the original question or the provided answer requires more decimal places, we should calculate accordingly. Assuming the original values are exact, the precise answer calculated with more decimal places is:

[tex]\[ -4.2 \times -3.15 = 13.23 \][/tex]

 If we were to use a calculator or perform the multiplication with more precision, we would find:

[tex]\[ -4.2 \times -3.15 = 13.22999999999998 \][/tex]

 Rounding this to the nearest ten-thousandth, we get:

[tex]\[ 13.22999999999998 \approx 13.2300 \][/tex]

 And if we round to the nearest hundredth, we still get:

[tex]\[ 13.2300 \approx 13.23 \][/tex]

The correct final answer, rounded to the same precision as the given numbers in the question, is [tex]\[ \boxed{13.23} \][/tex]

Hey!

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

[tex]\boxed{ \bf 0.03~dollars~difference~per~ounce}[/tex]

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

Solution:

Brand A ~ 2.31 / 11 = $0.21 per ounce.

Brand B ~ 2.70 / 15 = $0.18 per ounce.

Difference ~ 0.21 - 0.18 = $0.03 per ounce.

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

Hope This Helped! Good Luck!

Answer:

$0.03

Step-by-step explanation:

Answer:

- 5

Step-by-step explanation:

Note that - (- 12) = + 12

Thus

- 17 - (- 12) = - 17 + 12 = - 5

It looks like Tom subtracted 12 from - 17, that is - 17 - 12 = - 29

Answer:-17-(-12)=-5

Step-by-step explanation:when there’s a negative number in parenthesis and there’s a minus outside the parenthesis that majestic the number inside the parenthesis a positive

Answer:

7.24/7= 1.03

1.0 is the nearest

The provided statement is an example of deductive reasoning, where a specific conclusion is drawn from general observations. On the other hand, inductive reasoning forms broad generalizations from specific instances and is heavily used in scientific studies.

The question relates to the concept of inductive and deductive reasoning in logic and proofs. The given statement “All flying birds and insects have wings. Birds and insects flap their wings as they move through the air. Therefore, wings enable flight.” is an example of deductive reasoning.

Deductive reasoning follows a logical progression from general observations to a specific conclusion, assuming the initial general statement is true. If all flying birds and insects have wings and these creatures flap their wings for flight (general observations), it logically concludes that wings enable flight (specific conclusion).

In contrast, inductive reasoning involves creating broad generalizations from specific instances. Even though conclusions from inductive reasoning may not always be accurate, they contribute significantly to the progression of scientific knowledge. Scientists often use both inductive and deductive reasoning in their scientific methods for formulating hypotheses and theories.

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Answer:

Horizontally to the left.

Step-by-step explanation:

Adding The pi/2 moves the graph pi/2 units to the left.

The graph of y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in Horizontally to the left direction.

Suppose the considered function whose graph is to be made is  f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values   f(x) are plotted on the vertical axis.

We are given that the function y=cos (x+ pi/2) is the graph of the y = cos(x) shifted in unknown direction.

Therefore, we can conclude that by Adding the pi/2 moves the graph pi/2 units to the left.

Hence, it got shifted in the Horizontally to the left.

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Answer:

f(-1)=

[tex] \frac{ - 2}{3} [/tex]

f(2)=

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

let f(x)=f(-1)

but f(x) =3x+1

substituting it into the equation

3x+1=-1

3x=-1-1

3x=-2

dividing through by 3

[tex] \frac{3x}{3} = \frac{ - 2}{3} [/tex]

[tex]x = \frac{ - 2}{3} [/tex]

f(-1) =

[tex] \frac{ - 2}{3} [/tex]

f(2)

let f( x )=f(2)

then

3x+1=2

3x=2-1

3x=1

dividing through by 3

[tex] \frac{3x}{3} = \frac{1}{3} [/tex]

[tex] x = \frac{1}{3} [/tex]

f(2)=

[tex] \frac{1}{3} [/tex]

To find ƒ(2), substitute x = 2 into the Function ƒ(x) = 3x + 1. The answer is 7.

To find ƒ(2), we need to substitute x = 2 into the function ƒ(x) = 3x + 1.

Given: ƒ(x) = 3x + 1

Step 1: Substitute x = 2 into the function:

ƒ(2) = 3(2) + 1

Step 2: Perform the calculations:

ƒ(2) = 6 + 1

Step 3: Simplify the expression:

ƒ(2) = 7

Therefore, ƒ(2) = 7.

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Answer:

See below.

Step-by-step explanation:

If the number is even you divide by 2 , if  it is odd you try by the next prime number 3, the 5 and so on, so:

5. 36:-

36/ 2 = 18

18/2 = 9

9 / 3 = 3

We finish on the prime number 3.

So the prime factors are ( the numbers in bold ) = 2*2*3*3.

I'll do the next 3 for you, so you'll be able to do the rest on your own:

6. 180

180/ 2 = 90, 90 / 2 = 45, 45 /3 = 15, 15/3 = 5.

So 180 = 2*2*3*3*5.

7. 525

525/ 3 = 175, 175 / 5 = 35,  35 / 5 = 7.

So 525 = 3*5*5*7.

8. 165

165 / 3 = 55,  55/5 = 11.

So 165 = 3*5*11.

Answer:

168

Step-by-step explanation:

u can eperate the 14 to 10 and 4 then multiple each to 12 then add the two answer so it would be 10×12 and 4×12 then add them so (10×12=120)+(4×12=48)

Answer:

$8.8

Step-by-step explanation:

Let the original price of shares be [tex]x[/tex]

Profit earned = $1.320

percentage profit = 15%

∴ [tex]\frac{15x}{100} = 1.320\\15x = 132.0\\x = \frac{132}{15} \\x = 8.8[/tex]

Original price of shares were = $8.8

Answer:

Second statement 2x2 + 8x – 24 = 0 Is true for the given conditions. When x = -6 2x2 + 8x – 24 = 0 Becomes 2(-6)2 + 8(-6) – 24 = 0 2(36) - 48 - 24 = 0 72 - 48 - 24 = 0 0 = 0 Which is true. When x = 2 2x2 + 8x – 24 = 0 Becomes 2(2)2 + 8(2) – 24 = 0 2(4) + 16 - 24 = 0 8 + 16 - 24 = 0 0 = 0 Which is true. So 2x2 + 8x – 24 = 0 will be answer.

The characteristics of the solutions of the polynomials are listed below:

Let be a second order polynomial of the form [tex]a\cdot x^{2}+b\cdot x + c = 0[/tex], there are no real roots if and only if [tex]b^{2}-4\cdot a \cdot c < 0[/tex]. Now we proceed to determine the nature of the roots of each polynomial:

1) [tex]x^{2} = 49[/tex]

This expression is equivalent to the polynomial [tex]x^{2}-49 = 0[/tex], then the discriminant is:

[tex]d = 0^{2}-4\cdot (1)\cdot (-49)[/tex]

[tex]d = 196[/tex]

The polynomial has two distinct real roots.

2) [tex]2\cdot x^{2} = -128[/tex]

This expression is equivalent to the polynomial [tex]2\cdot x^{2} +128 = 0[/tex], then the discriminant is:

[tex]d = 0^{2} - 4\cdot (2)\cdot (128)[/tex]

[tex]d = -1024[/tex]

The polynomial has two conjugated complex roots.

3) [tex]3\cdot x^{2}-16 = 32[/tex]

This expression is equivalent to the polynomial [tex]3\cdot x^{2}-48 = 0[/tex], then the discriminant is:

[tex]d = 0^{2}-4\cdot (3) \cdot (-48)[/tex]

[tex]d = 576[/tex]

The polynomial has two distinct real roots.

4) [tex]x^{2}+x+1 = 0[/tex]

The discriminant of this expression is:

[tex]d = 1^{2}-4\cdot (1)\cdot (1)[/tex]

[tex]d = -3[/tex]

The polynomial has two conjugated complex roots.

Nota - The original statement reports typing mistakes. Corrected form is presented below:

Select all the equations that do not have a real solution:

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Answer:

x = 8

Step-by-step explanation:

Since P is at the midpoint of HR, then

HP = PR ← substitute values

7x + 2 = 58 ( subtract 2 from both sides )

7x = 56 ( divide both sides by 7 )

x = 8

Answer:

Amount of Arabica coffee mixing =   1.016 pounds

Step-by-step explanation:

Cost of Arabica coffee = 28$ per pound

Cost of Robusta coffee = 8.75$ per pound

Amount of Robusta coffee mixing = 5 pounds

Cost for 5 pounds of Robusta coffee = 5 x 8.75 = 43.75 $

Let m be the Amount of Arabica coffee mixing, we have price of mix = 12$ per pound

That is

               43.75 + m x 28 = ( m + 5 ) x 12

               43.75 + 16 m = 60  

                           16 m = 16.25

                               m = 1.016 pounds

    Amount of Arabica coffee mixing =   1.016 pounds

The solution involves the use of weighted averages to determine the amount of Arabica coffee needed. Solving the equation ((28*x) + (8.75*5)) / (x + 5) = 12 for x results in approximately 2.4 pounds of Arabica coffee.

In this problem, we have two types of coffee: Arabica costing $28 per pound and Robusta costing $8.75 per pound. We are asked to find the amount of Arabica coffee to mix with 5 pounds of Robusta to create a blend that costs $12 per pound.

This can be solved using weighted averages. We'll denote the amount of Arabica coffee as 'x' pounds. We multiply the price of each coffee by its amount, add those values, and then divide by the total weight to get the average cost. This can be represented as ((28*x) + (8.75*5)) / (x + 5) = 12.

Solving this equation for 'x' will give the required amount of Arabica coffee needed. Applying the arithmetic operation gives 28x + 43.75 = 12x + 60. Which simplifies to x = 2.38 pounds. So approximately 2.4 pounds of Arabica coffee is needed.

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Margaret can invite up to 102 guests and still stay within her budget for the wedding reception. This constraint is illustrated on a number line with a break at 103.

To find out how many guests Margaret can invite to the reception and stay under her budget of $5,323, given that she's already spent $2,748 and the meal price per guest is $25, let's determine the inequality and solve for x.

Formulate the Inequality

Margaret's remaining budget after her initial spending is:

[tex]\[ 5,323 - 2,748 = 2,575.[/tex]

If she wants to stay within this budget, and the meal price per guest is $25, the total cost for (x ) guests is:

[tex]\[ 25 \times x. \][/tex]

Margaret wants to spend less than her remaining budget, so the inequality is:

[tex]\[ 25 \times x < 2,575. \][/tex]

Solve for x :

To find x, divide by 25:

[tex]\[ x < \frac{2,575}{25}, \][/tex]

x < 103.

Since x must be a whole number (you can't invite a fraction of a guest), Margaret can invite a maximum of 102 guests to stay under budget.

Graph on a Number Line

On a number line, draw an open circle at 103, indicating that 103 is not included in the set of possible guest counts.

Extend the line leftwards to 0 (as you cannot have a negative number of guests).

|------|------|------|------|------|

0      25     50     75     100    125

The asterisk represents the open circle, indicating that the maximum number of guests is strictly less than 103.

Margaret can invite 103 guests to the reception and stay under budget. Number line A includes the largest number of guests.

In order to write a linear inequality to describe this situation, we would assign a variable to the number of guests can Margaret invite while staying within her budget, and then translate the word problem into algebraic equation as follows:

Let the variable x represent the number of guests.

Since Margaret wants to spend less than her budget of $5,323, and she has already spent $2,748, and the meal price per guest is $25, a linear inequality that models this situation is given by;

2748 + 25x < 5323

25x < 5323 - 2748

25x < 2575

x < 2575/25

x < 103

In this context, we can logically deduce that the largest number of guests Margaret can invite without exceeding her budget is correctly represented by number line A, with a hollow dot located at 104.

Complete Question;

Margaret is planning a wedding reception. She wants to spend less than her budget of $5,323, and Margaret has already spent $2,748. The meal price per guest is $25. How many guests, x, can Margaret invite to the reception and stay under budget?

Select the number line that includes the largest number of guests Margaret can invite without exceeding her budget.

Answer:

2x-3 = -11

Step-by-step explanation:

|2x-3| = 11

by definition of absolute numbers,

2x-3 = 11 (given)

or

2x-3 = -11 (answer)

Answer:

A. Translation 5 units up and 4 units to the right

Step-by-step explanation:

A translation is a point-by-point movement by a prescribed number of units up/down and/or left/right.

Point A is moved from (-3,-1) up 5 and right 4 units to A prime at (1,4)

Point B is moved from (-4,-3) up 5 and right 4 units to B prime at (0,2)

Point C is moved from (-2,-3) up 5 and right 4 units to C prime at (2,2)

Answer:

A. Translation 5 units up and 4 units to the right

Step-by-step explanation:

→ Point C moves up to [-2, 2]

Transition up: → Point B moves up to [-4, 2]

→ Point A moves up to [-3, 4]

→ Point C moves to C'[2, 2]

To the right: → Point B moves up to B'[0, 2]

→ Point A moves up to A'[1, 4]

This is a genuine statement!

I am joyous to assist you anytime.

Answer:

B

Step-by-step explanation:

Answer:

25200

Step-by-step explanation:

The nature of the graph from point A to B : The graph increases, then decreases.

Given,

Graph is x -y coordinates.

Now,

Graph is concave downwards.

Coordinates of point A : (0,0)

Coordinates of point B : (6,0)

So,

The graph firstly increases from x = 0 to x = 3.

Then,

The graph decreases from x = 3 to x = 6 .

Therefore the graph increases and then decreases.

Thus option D is correct.

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