Tomas is at least 7 years older than Larry. If Tomas is 16 years old, how old is Larry

Answer: (-12,-6)

Step-by-step explanation:

If we already have two points of the line, we can find its slope ([tex]m[/tex]), its intersection with the y-axis ([tex]b[/tex]), hence its equation:

Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

Point 2: [tex](x_{2},y_{2})=(-2,-2)[/tex]

Slope equation:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m=\frac{-2-0}{-2-3}[/tex]

[tex]m=\frac{2}{5}[/tex] This is the slope of the line

Now, the equation of the line is:

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

We already know the slope, now we have to find [tex]b[/tex] with any of the given points. Let's choose Point 1: [tex](x_{1},y_{1})=(3,0)[/tex]

[tex]0=\frac{2}{5}(3)+b[/tex]

Isolating [tex]b[/tex]:

[tex]b=-\frac{6}{5}[/tex]

Then, the equation of the line is:

[tex]y=\frac{2}{5} x-\frac{6}{5}[/tex]

With this equation we can find which point is a solution. Let's begin with the first point (-12,-6):

[tex]-6=\frac{2}{5} (-12)-\frac{6}{5}[/tex]

[tex]-6=-\frac{24}{5} -\frac{6}{5}[/tex]

[tex]-6=-6[/tex] Since both sides of the equation are equal, (-12,-6) is the point that fulfills the solution of the equation.

Answer:

Step-by-step explanation:

P(x)=  x³ - x² - 18

Q(x) = P(2x-1)

       = (2x-1)³ - (2x-1)² -18

       = (2x)³ - 3*(2x)² * 1 + 3*2x* 1² - 1³ - [ (2x)² - 2*2x*1 + 1 ] - 18

=8x³ - 12x² + 6x - 1 - [4x² - 4x +1 ] - 18

= 8x³ - 12x² + 6x - 1 - 4x² + 4x - 1  - 18

= 8x³ - 16x² + 10x - 20

Hint : (a-b)³ = a³-3a²b+3ab²-b³

(a-b)² = a² -2ab + b²

Answer:

(- 2, - 7 )

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ), thus

P(- 2, 7 ) → P'(- 2, - 7 )

3 + 8x = 19 is the equation for given sentence three more than eight times a number is equal to 19

Solution:

Given sentence is:

Three more than eight times a number is equal to 19.

We have to translate the sentence into an equation

Let us first break the sentence and find out the equation

Let "x" be the required number

Given that, Three more than eight times a number is equal to 19.

Here "more than" represents addition

"times" represents multiplication

eight times a number = [tex]8 \times x[/tex]

So the required equation is:

Three more than eight times a number is equal to 19

[tex]3 + 8 \times x = 19\\\\3 + 8x = 19[/tex]

Thus the required equation for given sentence is found

Answer:

  y = 3(x -4)^3 -3

Step-by-step explanation:

As you know, the transformations are

  g(x) = (vertical stretch factor) · f(x - (right shift)) +(vertical shift)

For the given transformations, the equation becomes ...

  y = 3(x -4)^3 -3

The equation of y=x^3 with the given transformations is y = 3(x - 4)^3 - 3.

The equation of y = x^3 after the given transformations is y = 3(x - 4)^3 - 3.

The vertical stretch by a factor of 3 means that all y-values will be multiplied by 3, so the equation becomes y = 3x^3.

The horizontal shift 4 units to the right means that x-values will be replaced by (x - 4), so the equation becomes y = 3(x - 4)^3.

The vertical shift 3 units down means that all y-values will be decreased by 3, so the equation becomes y = 3(x - 4)^3 - 3.

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Answer:

Step-by-step explanation:

[tex]x+5+2x=x+15\qquad\text{combine like terms}\\\\(x+2x)+5=x+15\\\\3x+5=x+15\qquad\text{subtract 5 from both sides}\\\\3x+5-5=x+15-5\\\\3x=x+10\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x-x=x-x+10\\\\2x=10\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{10}{2}\\\\x=5[/tex]

I'm not sure, but I know that it is longer than 5

Answer:

5.5-6ish sorry its hard to tell

Happy Holidays!

Answer:

i think 10.30 according to my calculation

Answer:

10.30

Step-by-step explanation:

Answer:

4725

Step-by-step explanation:

25-10=15

15^2=225

10*45*10=4500

225+4500=4725

Answer:

Step-by-step explanation:

No, unless the function decides to follow a different pattern. See more explanation below.

Step-by-step explanation:

He is wrong, the table doesn't tell us what happens at x=6.

It does tell us the following:

1) When x=-4, f(x)=6.

2) When x=-2, f(x)=3.

3) When x=0, f(x)=-1.

4) When x=2, f(x)=-4.

So maybe he got it the x and f(x) value switched in his brain.

Because according to 1) x=-4 when f(x)=6.

If the points keep having x increase while y decreases, then every x>2 will have a y less than -4 correspond to it.

Rob's determination that the function X = 6 when f(x) = -4 appears to be correct based on the provided data.

An equation is a mathematical statement that shows that two expressions are equal.

It typically includes variables, constants, and mathematical operations and is used to solve for unknown values.

Rob seems to be correct. If you look at the table of values:

x | f(x)

-4 | 6

-2 | 3

0 | -1

2 | -4

When x = 6,

we find that the function f(x) = -4 (as indicated in the last row of the table).

So, Rob's determination that X = 6 when f(x) = -4 appears to be correct based on the provided data.

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Answer:

She gets a raise of 91 cents per hour. So that means each hour, she makes $13.91

Kelli's raise per hour is $13.91.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Kelli makes $13 an hour working at the bakery,

and her boss gave her a 7% raise.

That means,

Kelli's raise per hour = 13 + 13 x 7/100

= $13.91

Therefore, $13.91 raise per hour.

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Answer:

s=2

Step-by-step explanation:

-5s-(-6s)+8=3+7

-5s+6s+8=10

s+8=10

s=10-8

s=2

The word problem would be translated as s + 8 = 10.

The solution is: s = 2

First, let's translate the statement given to form an algebraic equation, then solve for the unknown variable.

Therefore, the equation would be:

s + 8 = 10

s + 8 - 8 = 10 - 8

s = 2

Therefore, the word problem would be translated as s + 8 = 10.

The solution is: s = 2

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Answer:

Step-by-step explanation:

5y + 6y + 7y = 18y......any numbers that add(or subtract) to equal 18, stick them before the y....

or it could be : 10y + 10y - 2y = 18y or 5y + 10y + 3y or 30y - 20y + 8y....I could go on forever...lol

Answer:

2.75 or 2 3/4

Step-by-step explanation:

Divide the total cost by the price of each ribbon.

$1.54 ÷ $0.56/yard = 2.75 yards

If the answer needs to be in mixed fractional form, convert 0.75 to a fraction.

3/4 = 0.75

The fraction form of 2.75 is 2 3/4.

Therefore Olivia bought 2 3/4 yards of ribbon.

Answer:

Domain: (-∞,∞)

Range: {3}

Step-by-step explanation:

The domain is the x-values of the function, and the range is the y value of the function.

F(x)=3 is really just a fancy way of saying y=3. The range is 3.

Since the function makes a horizontal line, the domain is ∞.

Answer:

16. B

17. B

Step-by-step explanation:

16. The intercept form of the parabola is

[tex]y=a(x-x_1)(x-x_2),[/tex]

where [tex]x_1, x_2[/tex] are two x-intercepts.

In your case,

[tex]x_1=2\\ \\x_2=-8[/tex]

so

[tex]y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)[/tex]

To find a, substitute coordinates of the point (-6,-4) parabola is passing through

[tex]-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}[/tex]

and

[tex]y=\dfrac{1}{4}(x-2)(x+8)[/tex]

17. The vertex form of the parabola equation is

[tex]-2p(y-k)=(x-h)^2,[/tex]

where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.

In your case, vertex is (2,3), so

[tex]-2p(y-3)=(x-2)^2[/tex]

The vertex is 3 units from the focus, then

[tex]\dfrac{p}{2}=3\\ \\p=6[/tex]

The equation of the parabola is

[tex]-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3[/tex]

Answer:

No idea what the other person who answered was trying to say since it has to be 1 answer but i think its multiplication because to get 1/5 to be 1 so x you multiply by 5 and it matches because to get 6 to be 30 you multiply by 5 and to get 5 to be 25 you multiply by 5

ANSWER A

Step-by-step explanation:

The farmer's hog pen, with length of 12 meters and a width of 11 meters, is 32 square meters larger than the goat pen which has a length and width of 10 meters.

First, let's establish the dimensions of both pens. For the goat pen, given that the farmer used 20 meters of fencing and one side was provided by the barn, the fence was distributed between two sides. If we assume these two sides to be equal (maximizing the area), each side would be 10 meters long.

On the other hand, the hog pen had 24 meters of fence distributed between two sides, with the length being 2 meters more than the goat pen and the width being 1 meter more than the goat pen. So, the length of the hog pen is 12 meters and width is 11 meters.

To find the difference in areas, we subtract the area of the goat pen from the hog pen. The area of a rectangle is calculated by multiplying the length by the width. For the goat pen, the area is 10m * 10m = 100m² and for the hog pen, the area is 12m * 11m = 132m². Thus, the area of the hog pen is 32m² larger than the goat pen.

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Answer:

2700 degrees.

Step-by-step explanation:

The external angles add up to 360 degrees

So 1 external angle in a regular 17-gon = 360/17

= 21.176 degrees

The internal angle = 180 - 21.176

= 158.824 degrees

Sum of internal angles = 158.824 * 17

= 2700 degrees.

Answer:

Step-by-step explanation:

Every closed curve called a polygon can be separated into a specific number of triangles.  Then, because the sum of the interior angles of a triangle is 180, you take the number of triangles and multiply by 180 to get the sum of the interior angles of the n-gon.  To find the number of triangles that exist within an n-gon, subtract 2 from the number of sides.  If our figure is a 17-sided polygon, then the number of triangles within it is 17 - 2 = 15.  15 triangles, each with a sum of 180 for its angles.  15 * 180 = 2700.

Each central angle is 360 divided by 17 to get 21°10'35"

Each interior angle is 2700 divided by 17 to get 158°49'24"

Answer:

[tex]\large \boxed{\text{101 pieces}}[/tex]

Step-by-step explanation:

1. Calculate the area of the floor

The formula for the area of a trapezoid is  

A = ½(a + b)h,

where a and b are the lengths of the parallel sides and h is the distance between them.

However, we are not given the value of h, so we must use Brahmagupta's formula.

If the four sides are a, b, c, and d, the area A is

[tex]A = \sqrt{(s - a) (s - b) (s - c) (s - d)}[/tex]

where s is the semiperimeter

[tex]s = \frac{1}{2}(a + b + c + d)[/tex]

Data:

a = 13 ft

b = 16 ft

c = 13 ft

d = 26 ft  

(a) Calculate the semiperimeter

[tex]\begin{array}{rcl}s & = & \sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\ & = & \frac{1}{2}(13 + 16 + 13 + 26)\\\\ & = & \frac{1}{2}(68)\\\\ & = & 34\\\end{array}[/tex]

(b) Calculate the area

[tex]\begin{array}{rcl}A & = &\sqrt{(s - a) (s - b) (s - c) (s - d)}\\\\& = &\sqrt{(34 - 13) (34 - 16) (34 - 13) (34 - 26)}\\\\& = &\sqrt{21 \times 18 \times 21 \times 8}\\\\& = & \sqrt{63504}\\\\ & = & \mathbf{252}\\\end{array}[/tex]

The area of David's floor is 252 ft².

2. Calculate the number of pieces of material

[tex]\text{No. of pieces} = \text{252 ft}^{2} \times \dfrac{\text{1 piece}}{\text{2.5 ft}^{2}} = \textbf{100.8 pieces}\\\\\text{David can't buy a fraction of a piece, so he must buy $\large \boxed{\textbf{101 pieces}}$}[/tex]

Answer:

50.4

Step-by-step explanation:

First, add the values. You will get 756. The you divide the sum by the number of data values, which is 15. You will end up with 50.4

Answer: 50.4

Step-by-step explanation: The mean of a data set is equal to the sum of the set of numbers divided by how many number are in the set.

So to find the mean of the data set shown here, let's begin by adding the numbers.

12 + 16 + 22+ 23 + 34 + 44 + 46 + 47 + 48 + 64 + 67 + 73 + 83 + 88 + 89 = 756

756 will be divided by how many numbers are in the set which is 15 which gives us 50.4.

50.4 is already rounded to the nearest tenth.

Answer:

6 complex numbers

There are 6 solutions to the polynomial over the complex number system.

The given equation is 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

The Fundamental Theorem of Algebra states that every polynomial of degree one or greater has at least one root in the complex number system. A further theorem, in some cases referred to as the Linear Factorization Theorem, states that a polynomial of degree n has exactly n linear factors, and each can be written in the form (x - c), where c is a root. These n complex roots are counted with multiplicity.

In polynomials, the number of roots or highest power is equal to the degree of the polynomial.

Here, 3[tex]x^{6}[/tex]-x³-4x²+5x+52=0.

We can see that the polynomial is a sixth-degree polynomial.

Therefore, there are 6 solutions to the polynomial over the complex number system.

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Answer: 1st 3rd and 5th trust me

A) 4.17 is equivalent to 4.17 x 100

C) The product has a positive exponent.

E) The E in the product is the indicator that the solution is in scientific notation.

Given that,

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Answer:

Step-by-step explanation:

-2(x+3)=-10

Open the bracket

-2x - 6 = -10

Collecting like terms

-2x = -10 + 6

-2x = -4

Dividing through by -2

x = -4/-2

x = 2

Answer:

$ 9.99  almost  $ 10 she would save every week.

Step-by-step explanation:

Weekly Salary = $ 628

Tax deduction= $149.8

Superannuation Fund = 4.5 % of $ 628= $28.26

Mortgage = 8 % of 628= $ 50.24

Income after deductions = $ 628- $ 149.8 - $ 28.26- $ 50.24=  $ 399.7

10 % of $ 399.7 = $ 39.97 almost $ 40

In one week  she would save $39.97/4= $ 9.99 = $ 10

Answer:

11m

Step-by-step explanation:

2(5m)+m=10m+m=11m

Answer:

AAS I just answered this question and I got it right.

Final answer:

Given W=N, S=T, and WA=NO, no congruence theorems (SSS, SAS, ASA, AAS) demonstrate that triangles WAS and NOT are congruent, so the triangles are not congruent.

Explanation:

The student is asking which postulate or theorem supports the conclusion that triangle WAS is not congruent to triangle NOT. Given that W = N, S = T, and WA = NO, we can determine that the two triangles are not congruent. The four options provided are abbreviations for congruence theorems in geometry: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS).

However, none of these congruence theorems apply here because those would be used to prove congruence, not the lack thereof. In this case, if we look at the information given, we see that we have two pairs of sides and one pair of angles that are congruent. But the postulated congruent angles, A in triangle WAS and O in triangle NOT, are not included between the sides of the triangles that are known to be congruent. Therefore, none of the listed congruence postulates or theorems (SSS, SAS, ASA, AAS) can be used to conclude that the triangles are congruent. As a result, it can be concluded that the triangles are not congruent without needing to invoke a specific congruence theorem.

A customer will pay $225.5 for one rug.

Step-by-step explanation:

Given,

Purchase price of rug = $82.00

Mark up = 150%

Amount of mark up = 150% of purchase price

Amount of mark up = [tex]\frac{150}{100}*82[/tex]

Amount of mark up = 1.5*82 = $123

Price of rug after mark up = Purchase price + Mark up

Price of rug after mark up = 82+123 = $205

Sales tax = 10%

Amount of sales tax = 10% of price after markup

Amount of sales tax = [tex]\frac{10}{100}*205=\$20.5[/tex]

Selling price = Price after markup + Amount of sales tax

Selling price = 205+20.5 = $225.5

A customer will pay $225.5 for one rug.

Keywords: percentage, markup

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