-3x + 5x +-3= 4x + 5x

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Step-by-step explanation:

Let,

Longer leg = a = x

Shorter leg = b = x - 6

Hypotenuse = c = x + 6

As the triangle is right angles, therefore, using pythagoras theorem;

[tex]a^2+b^2=c^2\\(x)^2+(x-6)^2=(x+6)^2\\x^2+(x^2-12x+36)=x^2+12x+36\\x^2+x^2-12x+36=x^2+12x+36\\ 2x^2-12x+36=x^2+12x+36[/tex]

Adding (-x² - 12x-36) on both sides

[tex]2x^2-12x+36-x^2-12x-36=x^2+12x+36-x^2-12x-36\\x^2-24x=0[/tex]

Taking x common;

[tex]x(x-24)=0\\[/tex]

Either,

x=0

or,

x-24 = 0     => x=24

As length cannot be 0 therefore,

Longer leg = x = 24 feet

Shorter leg = x-6 = 24-6 = 18 feet

Hypotenuse = x+6 = 24+6 = 30 feet.

The length of longer leg is 24 feet, shorter leg is 18 feet and hypotenuse is 30 feet.

Keywords: triangle, addition

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Store B is offering the better deal on ground beef

Step-by-step explanation:

Dean is comparing prices on ground beef

We need to know which store is offering the better deal on ground beef

To find the better deal we must to find the unit price of each store

The unit price = total price ÷ number of pounds

∵ Store A is selling 5 pounds of ground beef for $23.49

∴ The unit price of Store A = 23.49 ÷ 5 = $4.698

∴ The unit price of Store A is $4.698 per pound

∵ Store B is selling 8 pounds of ground beef for $36.96

∴ The unit price of Store B = 36.96 ÷ 8 = $4.620

∴ The unit price of Store B is $4.620 per pound

∵ $4.620 < $4.698

∴ The unit price of Store B is less than the unit price of Store B

∴ Store B is cheaper than Store A, then it is offering the better deal

Store B is offering the better deal on ground beef

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Answer:

A), B) & D).

Step-by-step explanation:

Answer:

A) y = 7.25 when x = –7

C) y = 8.5 when x = –4

D) y = 10.25 when x = 5

Answer:

"[tex]b^2-4ac=4[/tex]"

Step-by-step explanation:

By looking at the value of the discriminant in a quadratic, we can find the nature of roots.

Let the value of the discriminant be "D", so we can say:

Graphically, we can write the points in order as:

Looking at the graph, we clearly see that there is 2 cutting points in the x-axis, so there are 2 roots. This means the value of the discriminant should be greater than 0 (positive value).

Out of the 3 choices given with discriminant formula, the last one has a value that is greater than 0:

4 > 0

Hence, last answer choice is right.

The discriminant determines whether a quadratic equation has real solutions and affects the appearance of the graph.

The discriminant is calculated using the formula Δ = b² - 4ac. In order for the graph to be possible:

Therefore, for the discriminant values given:

Answer:

It's Either B Or D

Step-by-step explanation:

only because They Only number that are closer so you can reverse it is 18 or 96

Answer:

4 1/4

Step-by-step explanation:

f(x) = 2/3(6) + 1/4

f(x) = 4 + 1/4

f(x) = 4 1/4(4.25)

Answer:

The value 3 represents the vertical translation upwards of [tex]f(x)[/tex] to [tex]g(x)[/tex]

Step-by-step explanation:

The question is incomplete or missing data.

The correct question

What value represents the vertical translation from the graph of the parent function [tex]f(x) = x^2[/tex] to the graph of the function

[tex]g(x) = (x + 5)^2 + 3[/tex]?

Given functions:

Parent function

[tex]f(x) = x^2[/tex]

Translated function

[tex]g(x) = (x + 5)^2 + 3[/tex]

Translation rules

For horizontal shift

[tex]f(x)\rightarrow f(x+c)[/tex]

If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the left.

If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the right.

For vertical shift

[tex]f(x)\rightarrow f(x)+c[/tex]

If [tex]c>0[/tex] the function shifts [tex]c[/tex] units to the up.

If [tex]c<0[/tex] the function shifts [tex]c[/tex] units to the down.

From the functions given the translation rule can be given as:

[tex]f(x)\rightarrow f(x+5)+3[/tex]

[tex]g(x)=f(x+5)+3[/tex]

This shows the graph is shifted left by 5 units and upwards by 3 units.

Thus the value 3 represents the vertical translation of [tex]f(x)[/tex] to [tex]g(x)[/tex]

Answer:

The carpenter can make 9 pieces.

Step-by-step explanation:

6/(2/3)=(6/1)(3/2)=18/2=9

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

[tex](x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4[/tex]

Thus, the equation is of the form:

[tex]y = 4x + b[/tex]

We substitute one of the points and find b:

[tex](x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21[/tex]

Finally, the equation is:

[tex]y = 4x-21[/tex]

Answer:

[tex]y = 4x-21[/tex]

Np i gotchu my dude

1. represents

2. Each y value

3. to exactly

4. x value

Hope this helps my dude ^^

Answer:

The graph represents a function because each x-value corresponds to exactly one y-value.

For example, in the given graph you see that for x=2 there's only one corresponding value, which is, y=40, that's what defines a function. If you have a graph where a certain value of x has to y values, that means is not a function, because for one x-value would be more than one y-values, so that would be only a relation, not a function.

It's important to specify the right order, that is, if we say each y-value corresponds to exactly one x-value, that's not exactly de definition of a function, because it actually happens, because in a quadratic expression, 2 and -2 would be the same result 4, so one y-vale has two x-value, but it's still a function.

So, the right order is The graph represents a function because each x-value corresponds to exactly one y-value.

Answer:

The numbers increase by 3

Step-by-step explanation:

The difference between all the numbers in the sequence have a gap of 3

9 and 12 --gap of 3

12 and 15--gap of 3

18 and 21--gap of 3

21 and 24--gap of 3

Answer

y=3+ before

Step-by-step explanation:

you add 3 to every number

Step-by-step explanation:

You could add (-1.07 + 2.971) to get (1.901)

Then do (1.901 - 4.3) to get a negative number; (-2.399)

I would double check this all with a calculator

Answer:

56

Step-by-step explanation:

4 x 2 = 8

8 x 7 = 56

Answer = 56

Answer:

(6, 28) or x=6, y=28 or The numbers are 6 and 28.

Step-by-step explanation:

4x+4=y

x+y+5=39

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

4x+4=y

x+y=39-5

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

4x+4=y

x+y=34

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

x+(4x+4)=34

x+4x+4=34

5x+4=34

5x=34-4

5x=30

x=30/5=6

4(6)+4=y

24+4=y

y=28

x=6, y=28

Answer:

The 2nd term is 3y

Step-by-step explanation:

2x +       3y

__          __

1            2

term     term

Answer:

3y

Step-by-step explanation:

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Long division setup showing an incomplete calculation

We need to find this number

Lets write the steps above

∵ The dividend = 3302

∵ The divisor = 13

- 2 hundreds means 200 and 5 tens means 50

∵ The quotient = 200 + 50 + x

∵ Dividend = divisor × quotient

∴ (13 × 200) + (13 × 50) + (13 × x) = 3302

∵ 13 × 200 = 2600

- Subtract 2600 from the dividend

∴ 3302 - 2600 = 702

∵ 13 × 50 = 650

∴ 702 - 650 = 52 ⇒ 650 is the unknown value

∵ 13 × x = 13x

∵ 52 - 13x = 0

- Add 13 x to both sides

∴ 52 = 13x

- Divide both sides by 13

∴ x = 4

∴ 3302 ÷ 13 = 200 + 50 + 4

∴ 3302 ÷ 13 = 254

∴ From the steps above the missing number subtracted from

   702 is 650

The unknown value is being subtracted from 702 is 650

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Answer:

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Long division setup showing an incomplete calculation

13 is in the divisor

3302 is in the dividend

2 hundreds and 5 tens is written in the quotient

2600 is subtracted from 3302 to give 702

An unknown value represented by a box is being subtracted from 702

We need to find this number

Lets write the steps above

∵ The dividend = 3302

∵ The divisor = 13

- 2 hundreds means 200 and 5 tens means 50

∵ The quotient = 200 + 50 + x

∵ Dividend = divisor × quotient

∴ (13 × 200) + (13 × 50) + (13 × x) = 3302

∵ 13 × 200 = 2600

- Subtract 2600 from the dividend

∴ 3302 - 2600 = 702

∵ 13 × 50 = 650

∴ 702 - 650 = 52 ⇒ 650 is the unknown value

∵ 13 × x = 13x

∵ 52 - 13x = 0

- Add 13 x to both sides

∴ 52 = 13x

- Divide both sides by 13

∴ x = 4

∴ 3302 ÷ 13 = 200 + 50 + 4

∴ 3302 ÷ 13 = 254

∴ From the steps above the missing number subtracted from

  702 is 650

The unknown value is being subtracted from 702 is 650

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here we have to multiply to find the total...

30 volumes, then each individual book with 700 pages, therefore, the answer would be 21,000 pages

To calculate the total number of pages in the series, multiply the number of volumes (30) by the pages per volume (700) to get a total of 21,000 pages.

The question asks for the total number of pages in a series of books, assuming each of the 30 volumes has 700 pages. Therefore, the calculation we need to perform is: 30 volumes × 700 pages per volume.

The formula to calculate the total number of pages is:

Total Pages = Number of Volumes × Pages per Volume

By inserting the given values into the formula:

Total Pages = 30 × 700 = 21,000 pages.

Hence, the total number of pages in the series is 21,000.

Answer: 2,000,000,000

Step-by-step explanation:

Answer:

$100\%=165$100%=165​.

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

165 is what % of 4125.

Let x represent the % in decimal form

4125*x = 165

Isolate x by dividing both sides by 4125

x = 0.04

0.04 = 4%

You find this by moving the decimal two places to the right

The never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things.

Therefore, the never intersecting and the coplanar lines describe the parallel lines. The correct option is C and E.

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Answer:

Table A represents a function, but Table B does not represent a function.

Step-by-step explanation:

We have to select the correct option among the given 4 options after judging the given two tables attached to this question.

The first table shows that for each x values there is only one y value. Therefore, this is a function.

But in the second table shows that for each x value there are multiple y values since we are getting y = 1 and 2 for x = 5.

Hence, table B is not a function. it is just a relation. (Answer)

Answer:

d.

Step-by-step explanation:

Answer:

[tex]19 - \frac{6}{5}j[/tex]

written out on a computer keyboard, you would type: 19 - (6/5)j

Step-by-step explanation:

The terms that dont have a 'j' attached to them all group up and combine to this: 18 + (-5) + 6 = 18-5+6 = 13+6 = 19

The rest of the terms have a 'j', and they combine to: [tex]-\frac{2}{5}j - \frac{4}{5}j = \left(-\frac{2}{5} - \frac{4}{5}\right)j = \frac{-2-4}{5}j = -\frac{6}{5}j[/tex]

After combining both sets of like terms, we have 19 as the first result and [tex]-\frac{6}{5}j[/tex] as the second result. They are then added to get [tex]19 + \left(-\frac{6}{5}j\right) = 19 - \frac{6}{5}j[/tex]

We cant simplify any further because there are no like terms left.

Answer:

c

Step-by-step explanation:

Answer:

c = 56

Step-by-step explanation:

The two angles 'c' and '124' form a straight angle. They add to 180

c+124 = 180

c+124-124 = 180-124 ... subtract 124 from both sides

c+0 = 56

c = 56

Answer:

56 <3

Step-by-step explanation:

Answer:

Part 16) [tex]y\leq -x+2[/tex]

Part 17) [tex]y>\frac{1}{3}x-1[/tex]

Step-by-step explanation:

Part 16) we know that

The solution of the inequality is the shaded area below the solid line

The slope of the solid line is negative

The y-intercept of the solid line is the point (0,2)

The x-intercept of the solid line is the point (2,0)

The slope of the solid line is

[tex]m=(0-2)/(2-0)=-1[/tex]

The linear equation of the solid line in slope intercept form is

[tex]y=-x+2[/tex]

therefore

The inequality that represent the graph is

[tex]y\leq -x+2[/tex]

Part 17) we know that

The solution of the inequality is the shaded area above the dashed line

The slope of the dashed line is positive

The y-intercept of the dashed line is the point (0,-1)

The x-intercept of the dashed line is the point (3,0)

The slope of the dashed line is

[tex]m=(0+1)/(3-0)=\frac{1}{3}[/tex]

The linear equation of the dashed line in slope intercept form is

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

therefore

The inequality that represent the graph is

[tex]y>\frac{1}{3}x-1[/tex]

Answer:

Value of I is $4290

Step-by-step explanation:

We have been given that,

Formula for simple interest is given by

Plugging the known values

On simplifying, we get

Hence, value of I is $4290

Answer:

The number of adults who went to the zoo was 21 and the number of children was 105.

Step-by-step explanation:

The complete question is

The Jurassic Zoo charges $5 for each adult admission and $3 for each child. The total bill for the 126 people from a school trip was $420. How many adults and how many children went to the zoo?

Let

x -----> number of adults

y ----> number of children

we know that

[tex]x+y=126[/tex] ------> equation A

[tex]5x+3y=428[/tex] ----> equation B

Solve the system by graphing

The solution is the intersection point both graphs

The solution is the point (21,105)

see the attached figure

therefore

The number of adults who went to the zoo was 21 and the number of children was 105.

Question 1:

No, \(x^3 \cdot x^3 \cdot x^3\) equals \(x^9\), while \(x^3 \cdot 3 \cdot 3\) equals \(9x^3\), representing different operations and values.

Question 2:

Incomplete. The expression \(1/x^3\) can be rewritten as \(x^{-3}\) using negative exponents.

Question 3:

Incorrect. The product of \(\sqrt{x}\) and \(4\sqrt{x}\) equals \(4x\), not \(5x\). Use exponents to simplify.

Question 4:

The expression \(x^{5/6} \cdot x^{1/6}\) simplifies to \(x\). Show the steps of exponent addition.

Question 5:

Unjustified. Determine equivalent expressions by simplifying each and comparing results. Justify based on mathematical properties.

Here's a review of your work:

Question 1:

Your reasoning is incorrect. The expressions are not equivalent because they represent different operations. \( x^3 \cdot x^3 \cdot x^3 \) means \( x \) multiplied by itself 3 times, which is \( x^9 \). \( x^3 \cdot 3 \cdot 3 \) is a multiplication of constants, which equals \( 9x^3 \). So, the expressions are not equivalent because they result in different values.

Question 2:

Your answer is incomplete. It seems like you've provided a template for simplifying radicals, but you haven't actually applied it to the given expression. To simplify \( \frac{1}{x^3} \), you can rewrite it as \( x^{-3} \).

Question 3:

Your answer is incorrect. The product of \( \sqrt{x} \) and \( 4\sqrt{x} \) is not simply \( 5x \). To rewrite it in simplest rational exponent form, you should use the property of exponents which states that \( \sqrt{a} = a^{1/2} \). So, \( \sqrt{x} \) is equivalent to \( x^{1/2} \), and \( 4\sqrt{x} \) is equivalent to \( 4x^{1/2} \). Multiplying these expressions together, you get \( 4x^{1/2} \cdot x^{1/2} = 4x^{1/2 + 1/2} = 4x^1 = 4x \).

Question 4:

You haven't shown your process for simplifying \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} \). To simplify, use the property of exponents which states that when you multiply two terms with the same base, you add their exponents. So, \( x^{\frac{5}{6}} \cdot x^{\frac{1}{6}} = x^{\frac{5}{6} + \frac{1}{6}} = x^{\frac{6}{6}} = x^1 = x \).

Question 5:

You haven't justified which expressions are equivalent. To determine equivalence, you need to simplify each expression and compare them to each other.