What are the first four terms of 3n²

Answer:

The length side of the original square banner was 9 ft

Step-by-step explanation:

Let

x-----> the length side of the original square banner

we know that

The new area of the banner is equal to

[tex]91=(x+4)(x-2)[/tex]

Solve for x

[tex]91=(x+4)(x-2)\\ \\91=x^{2}-2x+4x-8\\ \\x^{2}+2x-99=0[/tex]

Solve the quadratic equation by graphing

The solution is x=9 ft

see the attached figure

To determine the length of the original square banner, we can set up an equation using the given information and solve for the side length.

To solve this problem, let's first represent the length of the original square banner as x. According to the question, 4 feet is added to the width, so the width becomes x + 4. Also, 2 feet is subtracted from the height, so the height becomes x - 2. The area of a square is calculated by multiplying the side lengths, so we have (x + 4)(x - 2) = 91.

Expanding the equation, we get x² + 2x - 8 = 91. Rearranging the equation, we have x² + 2x - 99 = 0. This is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula.

By factoring, we find (x + 11)(x - 9) = 0. So, x = -11 or x = 9. Since we cannot have a negative length for a banner side, we discard x = -11. Therefore, the length of the side of the original square banner is 9 feet.

https://brainly.com/question/14510781

#SPJ3

k(3)=13(3)-2

k(3)= 39-2

Answer is k(3)= 37

ANSWER

[tex]k(3) = 37[/tex]

EXPLANATION

The given expression is

[tex]k(t) = 13t - 2[/tex]

We want to find k(3).

We substitute t=3 into the expression to get:

[tex]k(3) = 13(3) - 2[/tex]

We multiply out to get,

[tex]k(3) = 39- 2[/tex]

Simplify to get,

[tex]k(3) = 37[/tex]

Answer:

1/4

Step-by-step explanation:

because if you use the process of breaking down the numbers they will end up going down to simplest form.

Answer:

3/12 = 1/4

Step-by-step explanation:

If we know 12 is equal to a fraction with the denominator of 4, we can divide 12 by 4 and get 3. This means we must also divide the numerator by 3 to get 3/3 = 1. Another way to solve this is to cross multiply. If 3/12 = _/4, we multiply the numerator of the first fraction by the denominator of the second fraction. Then, we get 12. Divide the 12 by the denominator of the first fraction to get 12/12. This will give you an answer of 1 as well.

y=0 because no matter what x value you have, y will always be 0

Y=0 because the y-axis of the line is 0

Answer:

45-40

Step-by-step explanation:

The first interval is 15-19.

The width of this interval is: 19-15=4

The second interval is 30-34.

The width of this interval is: 34-30=4

The third interval is 40-45.

The width of this interval is: 45-40=5

The fourth interval is 45-49.

The width of this interval is: 49-45=4

Answer: 29,500.

Step-by-step explanation: percentagecalculator.com

Answer: $8.35

Step-by-step explanation:

Given: The amount as gross pay= $576.00

The rate of Medicare tax =1.45%  = 0.0145

Now, to calculate the medicare tax we need to multiply the rate of Medicare tax with the gross pay , we get

[tex]\text{Medicare tax=0.0145*Gross Pay}\\\\\Rightarrow\ \text{Medicare tax}=0.0145\times576.00\\\\\Rightarrow\ \text{Medicare tax}=\$8.352\approx\$8.35[/tex]

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=x,\ leg=15.6cm:2=7.8cm,\ hypotenuse=8.8cm[/tex]

Substitute:

[tex]x^2+7.8^2=8.8^2[/tex]

[tex]x^2+60.84=77.44[/tex]          subtract 60.84 from both sides

[tex]x^2=16.6\to x=\sqrt{16.6}\\\\x\approx4.1\ cm[/tex]

Answer:

yes

Step-by-step explanation:

The formula to finding the hypotenuse of a right triangle is a^2+b^2=c^2. So since the longest side is the hypotenuse, the 82 in. is the hypotenuse. 18^2+80^2= 6724, then we square root it, square root of 6725 is 82.

Answer:

This is a right triangle

Step-by-step explanation:

We can check this using the Pythagorean theorem

a^2 +b^2 = c^2

where a and b are the legs and c is the hypotenuse

18^2  + 80^2 = 82^2

324+6400=6724

6724 = 6724

True, so this is a right triangle

Answer:

30°

Step-by-step explanation:

Segment MP is the diameter of the circle, hence angle MOP has the measure of 180°.

Angles MON and NOP are supplementary angles (add up to 180°). Thus,

m∠MON+m∠NOP=180°

m∠MON=180°-m∠NOP

m∠MON=180°-150°=30°.

Angle MON is the central angle subtended on the arc MN. Thus, the measure of the arc MN is 30°.

Answer:

Step-by-step explanation:

It's important to know that the whole arc of a circle is 360°.

So, if MP is a diameter, that means it divides the circle in two equal parts of 180° each.

Now, one half of this arc is formed by MN and 150°, so we can formulate the expression

[tex]MN+150\° = 180\° \\MN= 30\°[/tex]

Therefore, the arc MN is 30°.

[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{5}{6} \\\\\\ \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{5}{6}[x-(-3)]\implies y-4=\cfrac{5}{6}(x+3) \\\\\\ y-4=\cfrac{5}{6}x+\cfrac{5}{2}\implies y=\cfrac{5}{6}x+\cfrac{5}{2}+4\implies y=\cfrac{5}{6}x+\stackrel{\textit{LCD of 2}}{\cfrac{(1)5+(2)4}{2}}[/tex]

[tex]\bf y=\cfrac{5}{6}x+\cfrac{13}{2}\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:The solution is x > 3

Answer:

10

Step-by-step explanation:

Answer:

Slope = 0

Step-by-step explanation:

(y2 - y1) ÷ (x2 - x1) = (-3 - [-3]) ÷ (1 - [-9]) = 0 ÷ 10 = 0

Answer:

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

Step-by-step explanation:

[tex]\begin{array}{rcll}4 - 2(6x - 5) & = & -4 &\\- 2(6x - 5) & = & -8 &\text{Subtracted 4 from each side}\\6x - 5 & = & 4 &\text{Divided each side by -2}\\6x & = & 9 &\text{Added 5 to each side}\\x & = &\mathbf{\frac{3}{2}} &\text{Divided each side by 6}\end{array}[/tex]

Check:

[tex]\begin{array}{rlc}4 - 2(6\times\frac{3}{2} - 5)& = &-4\\4 - 2(9 - 5) & = & -4\\4 - 2\times4 & = & -4\\4 - 8 & = & -4\\-4 & = & -4\\\end{array}[/tex]

Answer:

[tex]\large\boxed{x=\dfrac{3}{2}}[/tex]

Step-by-step explanation:

[tex]4-2(6x-5)=-4\qquad\text{subtract 4 from both sides}\\\\-2(6x-5)=-8\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(-2)(6x)+(-2)(-5)=-8\\\\-12x+10=-8\qquad\text{subtract 10 from both sides}\\\\-12x=-18\qquad\text{divide both sides by (-12)}\\\\x=\dfrac{-18\!\!\!\!\!\diagup^3}{-12\!\!\!\!\!\diagup_2}\\\\x=\dfrac{3}{2}[/tex]

Answer:

A.

Rotational symmetry is when things look the same rotated.

Answer:

A

Step-by-step explanation:

It has buttons which are on the top but not on the other faces

Answer: 9

Step-by-step explanation:

M=3 and the equation is 3m so your going to multiply. So the equation would be 3*3 and 3*3=9 so that's your answer

Answer:scott

Step-by-step explanation:

I’m pretty sure Scott. Hope this helps!!!

Answer:

[tex]\large\boxed{\bold{No\ solution}}[/tex]

Step-by-step explanation:

[tex]C:\ y=6x+9\\\\D:\ y=6x+2\\\\\left\{\begin{array}{ccc}y=6x+9&(1)\\y=6x+2&(2)\end{array}\right\\\\\text{substitute (1) to (2):}\\\\6x+9=6x+2\qquad\text{subtract 6x from both sides}\\\\9=2\qquad\bold{FALSE}\\\\\text{Therefore the answer is:}\ \bold{no\ solution}[/tex]

Answer:

The desired equation is y = -2x - 4

Step-by-step explanation:

The general slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Starting from that, substitute the given values for m, x and y and calculate b:

6 = -2(-5) + b.  Then 6 = 10 + b, and b = -4.

The desired equation is y = -2x - 4.

Answer:

90

Step-by-step explanation:

BP PERPENDICULAR 2 PC SO

BC=90

Answer: 90

Step-by-step explanation:

Given: A circle with center P and B and C are two points on circle such that

BP is perpendicular to PC, it gives [tex]\angle{BPC}=90^{\circ}[/tex]

We know that in a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

Therefore, the measure of  [tex]\overarc{BC}[/tex]= Central angle made by  [tex]\overarc{BC}[/tex].

⇒ the measure of  [tex]\overarc{BC}=90^{\circ}[/tex]

Answer:

the average rate of change is -1/6 per unit increase in x

Step-by-step explanation:

Looking at the table, we see that for each unit change in x, y decreases by 1/6.  Thus, the average rate of change is -1/6 per unit increase in x.

Answer with explanation:

Average rate of Change

             [tex]=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}\\\\=\frac{\frac{25}{3}-\frac{17}{2}}{4-3}\\\\=\frac{50-51}{6*1}\\\\=\frac{-1}{6}[/tex]

You can find average rate of change by taking any two distinct points on the curve.

Option B      

Answer:

The second answer is correct.

Step-by-step explanation:

To build a school;

20 workers -> 18 days.

So 1 worker -> 18/20 days.

So; 12 workers -> (12×18)/20 days.

-> (12×9)/10 days

->10.8 days.

so 10.8 days is your answer.

Hope it helps...

Regards;

Leukonov/Olegion

If 20 workers can build a school in 18 days, how many days will it take 12 workers to build the same school?

In this question we are provided that 20 workers can build a school in 18 days. We are asked to calculate how many days will 12 workers will take to do the same work.

We can solve this question using two methods :

[tex] \small\bf{ Unitary \: Method}[/tex]

20 workers can build a school in 18 days

1 worker can build a school in 20 × 18 days

12 workers can build a school in [tex]\dfrac{20 × 18 }{12}[/tex] = 30 days.

[tex] {{\rule{40mm}{4pt}}}[/tex]

[tex] \small\bf{ Method \: of \: proportion }[/tex]

Let us assume that 12 workers can finish the work in x days.

[tex]\begin{array}{c|c} \bf{Number \: of \: workers }& \bf{Number \: of \: days}\\ 20 & 18 \\ 12 & x\end{array}[/tex]

Ratio of workers = Inverse ratio of days

[tex] \small\sf{ 20 : 12 :: x : 18}[/tex]

Product of mean = Product of extreme

[tex] \small\rm{ 12 \times x = 20 \times 18}[/tex]

[tex] \small \rm{ \dfrac{20 \times 18}{12} = 30 \: days}[/tex]

[tex] \rule{72mm}{5pt}[/tex]

Distributive property means that you must multiply the number directly outside the parentheses to all the numbers inside the parentheses

Look at the image below for the work!

Hope this helped!

Using the Distributive Property to expand and evaluate an expression.

Given expression: (5 + 1)3

Step 1: Apply the Distributive Property to expand the expression:  (5 + 1)3 = 5 x 3 + 1 x 3

Step 2: Evaluate the expression: (5 + 1)3 = 15 + 3 = 18

Answer:

  Graph C; (2, 1)

Step-by-step explanation:

When equations are in standard form, finding the x- and y-intercepts is relatively easy. For ...

  ax +by = c

Using this idea on the first equation, we find its x-intercept to be -2. There is only one graph showing that has a line going through the point (-2, 0). That is Graph C. Checking the remaining intercepts for the two equations confirms that Graph C is the graph of this system of equations.

The two lines intersect at point (2, 1), so that is the solution to the system.

The correct graph is: Graph C

and the solution for this system is: (2,1)

The first equation is given by:

         [tex]x-4y=-2-------(1)[/tex]

and the second equation is given by:

   [tex]-2x-y=-5----------(2)[/tex]

from (1) we have:

[tex]x=-2+4y-------------(3)[/tex]

We put the value of x in equation (2) to get:

[tex]-2(-2+4y)-y=-5\\\\i.e.\\\\-2\times (-2)-2\times 4y-y=-5\\\\i.e.\\\\4-8y-y=-5\\\\i.e.\\\\4-9y=-5\\\\i.e.\\\\-9y=-5-4\\\\i.e.\\\\-9y=-9\\\\i.e.\\\\y=1[/tex]

Now on putting this value of y back to equation (3) we get:

[tex]x=-2+4\times 1\\\\x=-2+4\\\\x=2[/tex]

Hence, the solution to this system of equality is: (2,1)

Finding rectangle surface areas(RSA) are: 2(14×7)+2(14×5)=336

R.S.A+side surface areas: 336+2(7×5)=406

Ans:406

To find the surface area of a prism using a net, you simply calculate the area of each individual shape in the net and then add those areas together. The sum of these areas is the prism's surface area.

To find the surface area of the prism using a net, you need to first understand what a net of a prism is. A net of a prism is essentially a 'flat' version of the shape. It's what you would get if you cut along the edges of the prism and flattened it out.

For a rectangular prism, for instance, the net would consist of 2 rectangles (the bases) and 3 or 4 rectangles (the sides), depending on whether the prism is a right prism or an oblique prism.

To find the surface area, calculate the area of each individual shape in the net and then add all those areas together. The sum of these areas is the surface area of the prism.

As an example, suppose we have a rectangular prism with length 4 cm, width 3 cm, and height 2 cm. The areas of the two bases are each 4*3=12 square cm. The areas of the four sides are two of 4*2=8 square cm and two of 3*2=6 square cm. So the total surface area is 2*12+2*8+2*6=48 square cm.

https://brainly.com/question/35439753

#SPJ2

The answer is:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

To find the correct option (or options) , we need to remember the following:

- When a function intercepts the y-axis, it means that the "x" coordinate will be equal to 0.

- When a function intercepts the x-axis, it means that the "y" coordinate will be equal to 0.

Now, to find the correct option, we also need to compare the graphed function (f(x))  to the given table (g(x)).

So, discarding each of the given options to find the correct option, we have:

- First option, f(x) and g(x)  intersect at exactly two points: True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), it means that the functions intersect at exactly two points.

Hence,  we have that f(x) and g(x)  intersect at exactly two points.

- Second option, the x-intercepts of f(x) are common to g(x): True.

From the graph we can see that f(x) intercepts the x-axis at two points (-1,0) and (1,0), also, from the table we can see that g(x) intercepts the x-axis at the same two points (-1,0) and (1,0), so, both functions intercepts the x-axis at common points.

Hence,we have that the x-intercepts of f(x) are common to g(x)

- Third option, he minimum value of f(x) is less than the minimum value of g(x): False.

From the graph, we can see that the minimum value of f(x) is located at the point (0,-1), also, from the given table for g(x) we can see that there are values below the point (2,-3), meaning that the minimum value of f(x) is NOT less than the minimum value of g(x).

Hence, we have that the minimum value of f(x) is NOT less than the minimum value of g(x).

- Fourth option, f(x) and g(x) have the same y-intercept: False.

We can see that for the function f(x) the y-intercept is located at (0,-1) while from the given table, we can see the y-intercept for the function g(x) is located at (0,1)

Hence,  we have that f(x) and g(x) have differents y-intercepts.

Therefore, the correct answers are:

The first and second options:

f(x) and g(x) intersect at exactly two points.

The x-intercepts of f(x) are common to g(x)

Have a nice day!

Note: I have attached an image for better understanding.

The graph of f(x) overlaps with the graph of g(x). Then the correct option is A.

A statement, principle, or policy that creates the link between two variables is known as a function.

The table of values represents the function g(x) and the graph shows the function f(x).

The graph of f(x) overlaps with the graph of g(x).

Then the correct option is A.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ5

Answer:

1 5/6

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

You have a right triangle, so you can use the Pythagorean Theorem.

a^2 + b^2 = c^2

x^2 + 12^2 = 13^2

x^2 + 144 = 169

x^2 = 25

x = 5

Answer: x = 5

Answer:

just do 13 time 12

Step-by-step explanation: