The Pythagorean Theorem says that in a right triangle, a2 + b2 = c2 , where a and b are the lengths of the legs, and c is the length of the hypotenuse. If b = 2, what is the length of side a in terms of c? Remember, “in terms of c” means that the variable c will appear in your answer.

Answer:

Solutions: (2,10), (4,5)

Not solutions: (1,12), (6,10), (12,8), (18,6)

Step-by-step explanation:

Let x be the number of packages of pasta and y be the number of jars of pasta sauce. If pasta costs $1 for a 1-pound package, then x packages of pasta cost $x and weigh x pounds. If pasta sauce costs $3 for a 1.5 pound jar, then y jars cost $3y and weigh 1.5y pounds.

1. Tyler has $36, then

[tex]x+3y\le 36.[/tex]

2. Tyler can carry up to 20 pounds of food in his backpack, then

[tex]x+1.5y\le 20.[/tex]

You get the following system of inequalities:

[tex]\left\{\begin{array}{l}x+3y\le 36\\ x+1.5y\le 20\end{array}\right.[/tex]

Now substitute the coordinates of each point:

(1,12):

[tex]\left\{\begin{array}{l}1+3\cdot 12=37> 36\\ 1+1.5\cdot 12=19\le 20\end{array}\right.[/tex]

False, because first inequality doesn't hold.

(2,10):

[tex]\left\{\begin{array}{l}2+3\cdot 10=32\le 36\\ 2+1.5\cdot 10=17\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(4,5):

[tex]\left\{\begin{array}{l}4+3\cdot 5=19\le 36\\ 4+1.5\cdot 5=11.5\le 20\end{array}\right.[/tex]

True, both inequalities hold.

(6,10):

[tex]\left\{\begin{array}{l}6+3\cdot 10=36\le 36\\ 6+1.5\cdot 10=21> 20\end{array}\right.[/tex]

False, because secondt inequality doesn't hold.

(12,8):

[tex]\left\{\begin{array}{l}12+3\cdot 8=36\le 36\\ 12+1.5\cdot 8=24> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

(18,6):

[tex]\left\{\begin{array}{l}18+3\cdot 6=36\le 36\\ 18+1.5\cdot 6=27> 20\end{array}\right.[/tex]

False, because second inequality doesn't hold.

Answer:

y = 3x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 3) and (x₂, y₂ ) = (1, 0) ← 2 points on the line

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

The line crosses the y- axis at (0, - 3) ⇒ c = - 3

y = 3x - 3 ← equation of line

The equation of line l will be;

⇒ y = 3x - 3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (1, 0) and (0, -3).

Now,

Since, The equation of line passes through the points (1, 0) and (0, -3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 3 - 0) / (0 - 1)

m = - 3 / - 1

m = 3

Thus, The equation of line with slope 3 is,

⇒ y - 0 = 3 (x - 1)

⇒ y  = 3x - 3

Therefore, The equation of line passes through the points (1, 0) and

(0, -3)  will be;

⇒ y = 3x - 3

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Answer:

About 57.5 inches

Step-by-step explanation:

From the points which relates height and age a linear model was made. This allow us to estimate joanna’s height in those years the points are missing. For example, when she was 11 years old, her height was about 57.5 inches.

Answer:

57.5

Step-by-step explanation:

Answer:

3x+24 more widgets

Step-by-step explanation:

A company owns two manufacturing plants:

To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,

[tex](8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24[/tex]

Answer:

3x + 24

Step-by-step explanation:

The question simply requires us to find the difference between the daily production levels of the two plants;

The first plant produces 8x + 17

The second plant produces 5x - 7

The difference between these two expressions will be our required solution;

(8x + 17) - ( 5x - 7) = 8x + 17 - 5x + 7

= 8x - 5x +17 + 7 = 3x + 24

Answer:

1.27, -6.27 to the nearest hundredth,

or if you require it in exact form,

-2.5 + √14.25,   -2.5 - √14.25.

Step-by-step explanation:

x^2 = -5x + 8

x^2 + 5x  = 8

Competing the square:

(x + 2.5)^2 - 6.25 = 8

(x + 2.5) = 14.25

x + 2.5 = +/-√14.25

x = -2.5 + √14.25,   -2.5 - √14.25

x = -2.5 + 3.77,  -2.5 - 3.77

= 1.27, -6.27.

Answer:

linear:  slope =10,y-intercept=25

Step-by-step explanation:

Yes, a linear equation can be used to model the situation because for any two given pints, there is a constant value of 10 for change in (p) over change in (n).

The slope is given by:

[tex]m=\frac{Change\:in\:p}{Change\:in\:n}[/tex]

Using (1,35) and (5,75) from the table, we have:

[tex]m=\frac{75-35}{5-1}[/tex]

[tex]m=\frac{40}{4}=10[/tex]

Therefore the slope is 10.

Using the formula

[tex]y=mx+b[/tex], and the point (1,35) we have:

[tex]35=10(1)+b[/tex]

[tex]\implies 35-10=b[/tex]

[tex]\implies 25=b[/tex]

Therefore the y-intercept is 25.

Pythagorean Theorem

[tex]7^2 + 24^2 = x^2[/tex]

[tex]49 + 576 = x^2[/tex]

[tex]x^2=625[/tex]

[tex]x = 25[/tex]

Circumference

1. Since the diameter is 25 the formula to find the circumference is [tex]c = d\pi[/tex]

2. Plug in 25 into the formula

3. [tex]c = 25\pi[/tex]

Answer

[tex]25\pi[/tex]

The circumference of the circle is approximately 78.54 cm.

To find the circumference of the circle, we first need to find the length of the hypotenuse (which is also the diameter of the circle) using the Pythagorean theorem. Then, we can use the formula for the circumference of a circle, which is C = π * d, where C is the circumference and d is the diameter.

Let's calculate it step by step:

Step 1: Find the length of the hypotenuse using the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the chords (24 cm and 7 cm, respectively), and c is the length of the hypotenuse (diameter).

[tex]24^2 + 7^2 = c^2\\\\576 + 49 = c^2\\\\625 = c^2[/tex]

c = √625

c = 25 cm

Step 2: Calculate the circumference using the formula C = π * d:

C = π * 25 cm

C ≈ 78.54 cm

The circumference of the circle is approximately 78.54 cm.

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Convert the decimal number to a fraction by placing the decimal number over a power of ten. So convert the mixed number which is 2 1 /4 into an improper fraction first by multiplying the denominator which is (4)(4) by the whole number part which is (2)(2) and add the numerator (1)(1) to get the new numerator.

Place the new numerator (9)(9) over the old denominator (4)(4).94

Answer:

(3a-1)(3a+1)

Step-by-step explanation:

This is the difference of two squares so we can factorise using the rules

x^2-y^2 = (x-y)(x+y)

In this case x = 3a and y = 1 since (3a)^2 = 9a^2 and 1^2 = 1

Answer :

1. -3x + 6 = -9

-3x = -9 - 6

-3x = -15

x = -15 / -3

x = 5

2. 5m + 4m = 72

9m = 72

m = 72 / 9

m = 8

3. 6d - 10d = 40

-4d = 40

d = 40 / -4

d = -10

4. 2(x + 4) = 30

2x + 8 = 30

2x = 30 - 8

2x = 22

x = 22 / 2

x = 11

5. 78 = -2(m + 3) + m

78 = -2m - 6 + m

78 = -m - 6

78 + 6 = -m

84 = -m

m = -84

Answer:

First option: [tex]y=(x + 8)(x + 3)[/tex]

Step-by-step explanation:

Given the quadratic equation [tex]y = x^2 + 11x + 24[/tex], you need to factor it.

To do this, you need to find two number that when you add them you get 11 and when you multply them you get 24. These numbers are: 8 and 3.

Therefore, knowing this, you can factor the quadratic equation:

[tex]y = x^2 + 11x + 24\\\\y=(x + 8)(x + 3)[/tex]

Then, [tex]y = x^2 + 11x + 24[/tex] is equivalent to the graph of the equation [tex]y=(x + 8)(x + 3)[/tex], which matches with the first option.

For this case we must solve each of the equations proposed:

A) [tex]m ^ 2 + 9 = 58[/tex]

Subtracting 9 from both sides of the equation we have:

[tex]m ^ 2 = 49[/tex]

Applying root to both sides of the equation:

[tex]m = \sqrt {49}\\m = \pm7[/tex]

B) [tex]7e ^ 2 = 28[/tex]

We divide between 7 on both sides of the equation:

[tex]e ^ 2 = \frac {28} {7}\\e ^ 2 = 4[/tex]

We apply root to both sides of the equation:

[tex]e = \pm \sqrt {4}\\e = \pm2[/tex]

C) [tex]d ^ 2 + 6 = 70[/tex]

Subtracting 6 on both sides of the equation:

[tex]d ^ 2 = 64[/tex]

We apply root to both sides of the equation:

[tex]d =\pm \sqrt {64}\\d = \pm8[/tex]

D) [tex]\frac {1} {2} n ^ 2-10 = 62[/tex]

We add 10 to both sides of the equation:

[tex]\frac {1} {2} n ^ 2 = 72[/tex]

We multiply by 2 both sides of the equation:

[tex]n ^ 2 = 144[/tex]

We apply root to both sides of the equation:

[tex]n = \pm \sqrt {144}\\n =\pm12[/tex]

Answer:

[tex]m = \pm7\\e = \pm2\\d = \pm8\\n = \pm12[/tex]

Answer:

[tex]x = 20[/tex] or [tex]x = -5[/tex]

Step-by-step explanation:

To solve the quadratic equation we must factor the expression

Look for 2 numbers that when you multiply them, obtain the result -100 and when you add them, obtain the result -15.

You can verify that these numbers are -20 and 5

[tex]-20 +5 = -15\\\\-20 * 5 = -100[/tex]

Then the polynomial factors are

[tex](x-20) (x + 5) = 0[/tex]

 The zero product property says that if two terms [tex]a * b = 0[/tex] then

[tex]a = 0[/tex] or [tex]b = 0[/tex]

So

[tex](x-20) = 0[/tex] or [tex](x + 5) = 0[/tex]

[tex]x = 20[/tex] or [tex]x = -5[/tex]

Answer:

x = -5 or x = 20

Step-by-step explanation:

There fore the answer is C

Answer: First Option

Step-by-step explanation:

The formula to calculate the volume of a cylinder is:

[tex]V = \pi(\frac{d}{2})^2*h[/tex]

Where d is the diameter of the cylinder and h is the height.

Notice that the term d is squared. This means that to increase the volume of a cylinder it is more efficient to increase its diameter as well. Therefore, look for the cylinder with the largest diameter among the options.

The first cylinder is 90 ft in diameter and 40 ft in height and its volume is

[tex]V = \pi(\frac{90}{2})^2*40[/tex]

[tex]V=254469\ ft^3[/tex]

You can verify that it is the tank that has the highest volume

[tex]\bf y=\cfrac{2}{3}x\stackrel{\stackrel{b}{\downarrow }}{-3}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf 6x-7y=21\implies -7y=-6x+21\implies y=\cfrac{-6x+21}{-7}\implies y=\cfrac{6x-21}{7} \\\\\\ \stackrel{\textit{distributing the denominator}}{y=\cfrac{6x}{7}-\cfrac{21}{7}}\implies y=\cfrac{6}{7}x\stackrel{\stackrel{b}{\downarrow }}{-3}[/tex]

y=mx+b

b=y intercept

get into this form with no coefficient to y

Original: yint: -3

1)x+4y=12

4y=-x+12

y=-.25+3

b=3

2)2/3x+3y=-3

3y=2/3x-3

y={doesn't matter}x-1

b=-1

3)-2/3x+3y=6

3y=-2/3x+6

y={doesn't matter} +2

b=2

4) 6x-7y=21

-7y=-6x+21

y=6/7-3

b=-3

4 is the answer

Rel. Max:

-1 , x=0

Rel. Min:

-6 ,x=5

Increasing in the interval(s)

(-infinty ,0) U (5, infinity)

[ i doubt the above answer]

Decreasing in the interval(s)

(0,5)

Domain

it could be R

Range

R

Step-by-step explanation:

Look at the picture.

The function has a realtive maximum of -1 at x = 0.

The function has a realtive minimum of -6 at x = 5.

The function is increasing on the intervals: (-∞, 0> and <5, ∞).

The function is decreasing on the interval: <0, 5>.

The domain of the function is: (-∞, ∞) = R

The range of the function is: (-∞, ∞) = R

ANSWER

"If x=7, then x - 2 = 5"

EXPLANATION

Let

[tex]p \to \: q[/tex]

be a propositional statement.

The converse of this statement is

[tex]q \to \: p[/tex]

In other words, the converse of the statement,

"If p then q" is "If q, then p"

The given given conditional statement is

"If x - 2 = 5, then x = 7"

Therefore the converse is

"If x=7, then x - 2 = 5"

Answer:

$16.50/hr

Step-by-step explanation:

Current pay is 1.00($15/hr).

Current pay plus a 10% raise is 1.10($15/hr) = $16.50/hr

After receiving a 10% raise on a $15 per hour wage, you would be earning $16.50 per hour.

If you are currently making $15 per hour and you receive a 10% raise, you can calculate your new hourly wage by first determining the amount of the raise and then adding it to your current wage. To find the raise amount, you multiply your current wage by the raise percentage expressed as a decimal. In this case:

Amount of raise = Current hourly wage  imes Raise percentage

Amount of raise = $15 per hour  imes 0.10 (since 10% = 0.10)

Amount of raise = $1.50 per hour

Now, you add this raise to your current hourly wage to find your new hourly wage:

New hourly wage = Current hourly wage + Amount of raise

New hourly wage = $15 per hour + $1.50 per hour

New hourly wage = $16.50 per hour

To give an example for comparison, if your job pays $10 per hour and your boss gives you a $2 per hour raise, that is a 20% increase because the percentage change is calculated as $2/$10 = 0.20 or 20%. In your case, the 10% raise increases your wage by $1.50, making it $16.50 per hour after the raise.

Answer:

Step-by-step explanation:

[tex]x^2+5x+6=0\\\\x^2+2x+3x+6=0\\\\x(x+2)+3(x+2)=0\\\\(x+2)(x+3)=0\iff x+2=0\ \vee\ x+3=0\\\\x+2=0\qquad\text{subtract 2 from both sides}\\x=-2\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3[/tex]

Answer: 1.25

Step-by-step explanation:

Because...

All you have to do is divide the length value by 3

and your answer will be 1.25.

* Hopefully this helps:) Mark me the brainliest:)!!!

Answer:

1.25yd

Step-by-step explanation:

couted through table

Check the picture below.

so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5.  So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.

[tex]\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96[/tex]

For this case we have that by definition, the surface area of a regular pyramid, is given by:

[tex]SA = \frac {1} {2} p * l + B[/tex]

Where:

p: Represents the perimeter of the base

l: The inclination height

B: The area of the base

Now, since the base is square we have:

[tex]B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm[/tex]

Then, replacing the values:

[tex]SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2[/tex]

ANswer

[tex]96 \ cm ^ 2[/tex]

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

A triangle is a three-sided polygon that consists of three edges and three vertices.

If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a quadrilateral, specifically a parallelogram.

The two identical triangles, when combined in this way, will have their bases aligned and their vertices opposite each other, forming two pairs of parallel sides.

A parallelogram, which is a quadrilateral with opposite sides that are parallel and congruent.

Hence, If you make an identical copy of a triangle, rotate the copy 180 degrees and combine the two triangles, you will form a parallelogram.

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well, let's grab a couple of points off the line hmmmm let's see, the lines runs through (0, 4) and also (3,5), so let's use those to get its slope and thus its function.

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) ~\hfill slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{5-4}{3-0}\implies \cfrac{1}{3}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{1}{3}(x-0)\implies y-4=\cfrac{1}{3}x \\\\\\ y=\cfrac{1}{3}x+4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

Step-by-step explanation:

Eliminate the last two possible answers immediately, because their constants are negative.  A perfect square trinomial MUST have a positive constant.

If we factor the first answer choice, we get (3x - 2)(3x - 2) = 9x^2 - 12x + 4.  This is a perfect square trinomial.

Looking at the second answer choice:  (4x - 3)(4x - 3)  = 36b² - 24x + 9.  This is also a perfect square trinomial.

Please note:  Please use " ^ " to indicate exponentiation:

9x^2 is correct; 9x2 is incorrect.                                            

Answer:

its C 16x2 + 24x + 9

Step-by-step explanation:

for z the fraction value is 1/26 and for other letters then Z is 25/26

The answer is:

The total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

To calculate the surface area of a square pyramid, we need to use the following formula:

[tex]TotalSurfaceArea=\frac{1}{2}pl+BaseArea[/tex]

Where,

p, is the perimeter of the base.

l, is the slant of the pyramid.

Base area, is the area of the square base.

Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.

So, calculating, we have:

[tex]BaseArea=BaseLength^{2}=(6ft)^{2} =36ft^{2}[/tex]

[tex]Perimeter=4*side=4*6feet=24feet[/tex]

The total surface area will be:

[tex]TotalSurfaceArea=\frac{1}{2}l+BaseArea[/tex]

[tex]TotalSurfaceArea=\frac{1}{2}*24ft*13ft+36ft^{2}[/tex]

[tex]TotalSurfaceArea=156ft^{2}+36ft^{2}=192ft^{2}[/tex]

Hence, we have the total surface area of the pyramid is:

[tex]TotalSurfaceArea=192ft^{2}[/tex]

Have a nice day!

Answer: 15/4

Step-by-step explanation:

1. 12/1 - 33/4

2.  48/4 -33/4

3. 15/4

Answer: (x - 3) (2x-1)

Answer:

(x+3)(2x+1)

Step-by-step explanation:

I got it right on khan academy.

Given:

f(x)=4x-3

f(x) +g(x) =9x +4

To find:g(x)

Solution:

f(x) + g(x) =9x +4

Replacing f(x) with its value.

4x -3 +g(x) = 9x +4

=> g(x) = 9x+ 4 -(4x-3)

=> g(x) = 9x+4 -4x +3

=> g(x) = 5x +7

Hence;

Option A g(x)=5x+7 is the answer.

Hope it helps...

Regards;

Leukonov/Olegion.

Answer:

(a) What is the probability that you roll a 6?

1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

1

(c) What is the probability that you don't roll a 6?

5/6

Step-by-step explanation:

(a) What is the probability that you roll a 6?

In a 6- sided cube, a 6 occurs only once. That is only one face is labelled 6. Therefore, the probability that you roll a 6 is;

(number of faces labelled 6)/(totals number of sides) = 1/6

(b) What is the probability that you either roll a 6 or do not roll a 6?

The probability of rolling a 6 was found to be, 1/6.

On the other hand, the probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

Therefore, the probability that you either roll a 6 or do not roll a 6 is;

1/6 + 5/6 = 1

These two events are mutually exclusive and exhaustive.

(c) What is the probability that you don't roll a 6?

The probability of not rolling a 6 is;

(number of faces not labelled 6)/(totals number of sides) = 5/6

We have 5 faces not labelled 6 out of 6 possible faces or outcomes