Consider the trinomial x2 + 10x + 16.

Which pair of numbers has a product of ac and a sum of b?

2 and 52 and 84 and 4X 4 and 6

What is the factored form of the trinomial?

(x + 2)(x + 5)(x + 2)(x + 8)(x + 4)(x + 4)X (x + 4)(x + 6)

Answer: Hello there!

We know that Jada has 12 books checked out, and Han has one third less than that.

one-third of a number is equal to the number divided by 3, in this case, we have the number 12, so a third of 12 is: 12/3 = 4

then if Han has a third less than 12, Han has 12 - 4 = 8 books checked out.

Answer:

1/3

Step-by-step explanation:

To determine the common ration, we take the second term and divide it by the first term

9/27 = 1/3

We verify this by taking the third term and diving by the second term

3/9 = 1/3

The common ratio is 1/3

Answer:

1/3

Step-by-step explanation:

Divide a term by the previous term.

For example, divide 1 by 3 to get 1/3.

Answer:

$2,000

Step-by-step explanation:

Since she has $440 dollars and adds $65 dollars a week, the equation will be 440+65(24)=X

Answer:

2000

Step-by-step explanation:

Answer:

It Is 175% Of 88.

Step-by-step explanation:

154 ÷ 88 = 1.75

To Convert A Decimal Into Percent, You Multiply By 100.

1.75 · 100% = 175%

Therefore, The Answer Is 175%.

The answer is 57.14%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here 88/154 and therefore in percentage terms it is 88/154 × 100

                                                                                                 = 57.14%

Hence, The answer is 57.14%

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Answer:

Graph A.

Step-by-step explanation:

The given graph in the question is y = (x + 2)  (x + 7)

or y = x² + 2x + 7x + 14

      = x² + 9x + 14

Now we convert this equation of parabola in vertex form

[tex]y=(\frac{x+9}{2})^{2}-\frac{81}{4}+14[/tex]

  [tex]=(x+4.5)^{2}-6.25[/tex]

This equation is in the form of y = (x-h)² + k where (h,k) is the vertex.

So in the given equation y = (x + 4.5)² - 6.25

Vertex should be (-4.5, 6.25) which lies in third quadrant.

Therefore, option A. is the graph.

The savings that Barret makes by joining the art museum instead of the science museum is $2.50 + $1.25m.

The one time fee charged by the art museum is $8.25 and the one charged by the science museum is $3.50. The saving here is:

= 10.75 - 8.25

= $2.50

The savings made per month is:

= Amount charged per month by science - Amount charged per month by art

= 3.50 - 2.25

= $1.25

In conclusion, the savings per month is $2.50 + $1.25 per month.

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Answer: $20.5

Step-by-step explanation:

Let x  denotes the amount for total bill.

We are given that ,  Sierra left $4.50 as a tip for a waiter.

This was 18% of the bill before the tip.

We can write 18% = 0.18. [To convert percent into decimal we divide it by 100.]

Then, the tip amount = 0.18 x Total bill

[tex]\Rightarrow\ 4.5=0.18x\\\\\Rightarrow\ x=\dfrac{4.5}{0.18}=25[/tex]

So, the total bill amount = $25

Hence, her total bill before the tip= Total bill amount - Tip amount

= $25- $4.50=$20.5

Thus ,her total bill before the tip= $20.5

To find Sierra's total bill before the tip, an equation can be created where the tip amount ($4.50) is 18% of the total bill. Solving the equation provides that Sierra's total bill before the tip was $25.

To solve this problem, you want to figure out the original bill amount before the tip was added. We know that the tip amount, $4.50, represents 18% of the original bill. Therefore, we can set up an equation to find the total bill before the tip was included.

The equation is as follows: 0.18x = $4.50, where 'x' stands for the total bill before the tip. By dividing both sides of the equation by 0.18, we can find 'x' which represents the initial bill.

So, x = $4.50 / 0.18 and calculating this gives us x = $25. Therefore, Sierra's total bill before the tip was $25.

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Answer:

Hope this helps, sorry for my horrible handwriting. If you have any questions feel free to ask me!

Step-by-step explanation:

Answer: [tex]x=\frac{4}{5}[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following equation given in the problem above:

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

2. Apply the Distributive property:

[tex]4x-6x+4=3x[/tex]

4. Now, you must add like terms:

[tex]4=3x-4x+6x\\4=5x[/tex]

5. Solve for [tex]x[/tex], then the result is:

[tex]x=\frac{4}{5}[/tex]

The formula of an area of a triangle:

[tex]A_{\triangle}=\dfrac{1}{2}bh[/tex]

b - base

h - height

We have b = 8in and h = 3in. Substitute:

[tex]A_{\triangle}=\dfrac{1}{2}(8)(3)=(4)(3)=12\ in^2[/tex]

The formula of an area of a rectangle:

[tex]A_{\boxed{\ }}=lw[/tex]

l - length

w - width

We have l = 8in and w = 5in. Substitute:

[tex]A_{\boxed{\ }}=(8)(5)=40\ in^2[/tex]

The area of a shaded region:

[tex]A=A_{\boxed{\ }}-A_{\triangle}\\\\A=40\ in^2-12\ in^2=28\ in^2[/tex]

Answer:

8

Step-by-step explanation:

Read a little bit at a time.

Equation

Solution

Answer:

x=8

Step-by-step explanation:

4x+30 =70-x

Add x to each side

4x+x+30 =70-x+x

4x+x +30 =70

5x +30 = 70

Subtract 30 from each side

5x +30 -30 =70-30

5x = 40

Divide each side by 5

5x/5 = 40/5

x = 8

Answer:

your answer is h=2.65 hours

A set of rules used to determine the proper order for performing operations in an expression that involves more than one operation is a(n) order of operations.

The number or amount of a group or part of something when compared to the whole is called proportion.

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression.

Something produced as a result of some input is called output.

An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.

Output of operations is the set of rules used to determine the proper order for performing operations in an expression that involves more than one operation

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Answer:

A

Step-by-step explanation:

because -4 is x and -3 is y

Answer:

A

Step-by-step explanation:

the solution to a system of equations graphically is the point of intersection of the 2 lines.

The point of intersection = (- 4, - 3) → A

Answer:

$120.

Step-by-step explanation:

We have been given that Libby sold $60 worth of vegetables at the farmer's market.

Jess sold 3/4th of what Libby sold. Let us find 3/4 of 60.

[tex]\text{Jess sold}=60\times \frac{3}{4}[/tex]

[tex]\text{Jess sold}=15\times 3[/tex]

[tex]\text{Jess sold}=45[/tex]

Therefore, Jess sold $45 worth of vegetables.

We are told that Stephanie sold 1/3rd of what Jess sold. So let us 1/3rd of 45.

[tex]\text{Stephanie sold}=45\times \frac{1}{3}[/tex]

[tex]\text{Stephanie sold}=15[/tex]

Therefore Stephanie sold $15 worth of vegetables.

Now let us add amounts of money earned by Libby, Jess and Stephanie to get the total money earned by all.

[tex]\text{The total money earned by Libby, Jess and Stephanie}=60+45+15[/tex]

[tex]\text{The total money earned by Libby, Jess and Stephanie}=120[/tex]

Therefore, they all sell $120 worth of vegetables together.

Answer:

As per the statement: Libby sold $60 worth of vegetables at the farmer's market.

⇒ Libby sold vegetables at the farmers market = $60

Jess sold 3/4th of what Libby sold.

⇒ Jess sold = [tex]\frac{3}{4} \times 60 = \$45[/tex]

Also, Stephanie sold 1/3rd of what Jess sold.

⇒ Stephanie sold = [tex]\frac{1}{3} \times 45 = \$15[/tex]

To find how much did they all sell together.

Together they all sell together = Libby sold + Jess sold + Stephanie sold

                                                    =$60 + $45+$15 = $120

Therefore, they all sell together is, $120                                                                                

Answer:

Step-by-step explanation:

First, we can transform y = cos(x) to y = 3*cos(x) by stretching the graph vertically by a factor of 3. At x = 0, the y value would now be 3 * 1 = 3 instead of 1 (the stretching would cause all new y-values to be 3 times their original values for any given x).  

Now transforming y = 3*cos(x) to y = 3*cos(10*x) will stretch the graph horizontally by a factor of 10 (for any given y value, the new x value corresponding to it is 10 times the original x value).

Finally, to transform y = 3*cos(10*x) to y = 3*cos(10(x-pi)), shift the graph to the right by pi.

Answer:

It's B or C

Step-by-step explanation:

[tex]\text{If}\ x_1,\ \text{and}\ x_2\ \text{are zeros of a polynomial function, then the function}\\\text{has equation}:\\\\f(x)=a(x-x_1)(x-x_2).\\----------------------------\\\\11.\ \text{We have the zeros}\ 3\ \text{and}\ i:\\\\f(x)=(x-3)(x-i)=(x)(x)+(x)(-i)+(-3)(x)+(-3)(-i)\\\\=x^2-xi-3x+3i=\boxed{x^2-(3+i)x+3i}\\\\12.\ \text{We have the zeros}\ -2\ \text{and}\ 2i:\\\\f(x)=(x-(-2))(x-2i)=(x+2)(x-2i)\\\\=x^2-(2i)^2=x^2-2^2i^2=x^2-4(-1)=\boxed{x^2+4}\\\\\text{used}\\\\(a-b)(a+b)=a^2-b^2\\\\i=\sqrt{-1}\to i^2=-1[/tex]

Answer:

168km

Step-by-step explanation:

132/11=12km per litre

12*14=168km

Adam can cover [tex]\boxed{{\mathbf{168 km}}}[/tex]  with [tex]14{\text{ liters}}[/tex]  of fuel.

Further explanation:

The direct relationship is the relationship between two quantities in which one quantity decreases then the other quantity also decreases and vice versa. The examples are supply function and speed distance function.

The direct relationship of the variables [tex]a{\text{ and }}b[/tex]  as

[tex]\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}[/tex]                   ......(1)

Here, [tex]{a_1},{a_2}[/tex]  are the quantities of the variable [tex]a[/tex]  and [tex]{b_1},{b_2}[/tex]  are the quantities of the variable [tex]b[/tex]  

Given:

Adam covered the distance [tex]132{\text{km}}[/tex]  by car with 11 liters of fuel.

Step by step explanation:

Step 1:

The provided data can be written in the table form as,

It can be seen that data is direct relationship.

Here, [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex]

Step 2:

Now put the values [tex]{a_1}=132,{a_2}=a,{b_1}=11{\text{ and }}{{\text{b}}_2}=14[/tex] in equation (1) to get the value of [tex]a[/tex] .

[tex]\begin{gathered}\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}\hfill\\\frac{{132}}{a}=\frac{{11}}{{14}}\hfill\\\end{gathered}[/tex]

Now calculate the further equation by the cross multiplication method.

[tex]\begin{aligned}\frac{{132}}{a}&=\frac{{11}}{{14}}\\132\times14&=11a\\1848&=11a\\a&=168\\\end{aligned}[/tex]

Thus, Adam can cover [tex]168{\text{ km}}[/tex]  distance with [tex]14{\text{ liters}}[/tex]  of fuel.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Comparing quantities

Keywords: Adam, car, fuel, distance, direct relationship, speed, positive relationship, increase, decrease, equation, cross multiplication method, variables, quantity, substitute.

Answer:

17²

Step-by-step explanation:

to find the perfect square take the square root of 289

[tex]\sqrt{289}[/tex] = 17 ⇒ 17² = 289

Answer:

17

Step-by-step explanation:

The defenition of a perfect square is "the product of a rational number multiplied by itself."

If you multiply 17 by itself you get 289, so the answer is 17.

Answer:

Distance: 435.9 ft

Step-by-step explanation:

This is a right triangle shown in the picture.

To solve for [tex]x[/tex], we can use trigonometry.

The 35° angle's opposite side is 250 ft and the hypotenuse of the triangle is [tex]x[/tex] (what we are seeking to find).

The ratio that relates opposite and hypotenuse is sine.

We know that,

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

Thus we can write:

[tex]sin(35)=\frac{250}{x}[/tex]

Cross multiplying and solving for [tex]x[/tex] gives us:

[tex]sin(35)=\frac{250}{x}\\x=\frac{250}{sin(35)}\\x=435.9[/tex]

Second answer choice is right: 435.9 ft

[tex]\left\{\begin{array}{ccc}x-4y=28\\2x+y=2&\text{multiply both sides by 4}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}x-4y=28\\8x+4y=8\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad9x=36\qquad\text{divide both sides by 9}\\.\qquad\boxed{x=4}\\\\\text{Put the value of x to the second equation:}\\\\2(4)+y=2\\8+y=2\qquad\text{subtract 8 from both sides}\\\boxed{y=-6}\\\\Answer:\ \boxed{x=4\ and\ y=-6\to(4,\ -6)}[/tex]

[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{-20v^7x^7}{4v^5x^4}+\dfrac{12v^4x^7}{4v^5x^4}=-5v^{7-5}x^{7-4}+3v^{4-5}x^{7-4}\\\\=\boxed{3v^{-1}x^3-5v^2x^3}[/tex]

Used

[tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]

Other method:

[tex]\dfrac{-20v^7x^7+12v^4x^7}{4v^5x^4}=\dfrac{4v^4x^4(-5v^3x^3+3x^3)}{4v^4x^4(v)}=\dfrac{3x^3-5v^3x^3}{v}[/tex]

[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 2 \\\\\\ \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-5=2(x-0) \\\\\\ y-5=2x\implies y=2x+5[/tex]

Answer: 2 pairs of angles

As the name "angle angle" suggests, we need 2 pairs of angles proven congruent in order to prove that two triangles are similar. Each "angle" refers to a pair of angles between the two triangles, which are corresponding angles. We could use the third pair, but it's extra unnecessary work. This theorem is often written as "AA similarity" or something along those lines.

One way to check for similar triangles is to compare the ratios of the sides. If the corresponding sides divide to the same value, then you have similar triangles. This method only works of course if you know the side lengths.

so we have s(t), namely the positional equation for the particle.

now, let's recall that the derivative of s(t) will be v(t), namely the derivative of the positional equation will be the velocity, and the derivative of the velocity will be the acceleration.

s'(t) = v(t) and s''(t) = a'(t)  <--- acceleration

so we need the 2nd derivative of s(t) firstly, and then we can check for any critical values and find its extrema.

[tex]\bf s(t)=t^4-rt^3+6t^2-20\implies \stackrel{\textit{velocity}}{s'(t)=4t^3-12t^2+12t} \\\\\\ \stackrel{\textit{acceleration}}{s''(t)=12t^2-24t+12}\implies \stackrel{\textit{derivative of acceleration}}{s'''(t)=24t-24} \\\\[-0.35em] ~\dotfill\\\\ 0=24t-24\implies 24=24t\implies \cfrac{24}{24}=t\implies 1=t[/tex]

now, if we run a first-derivative test on that acceleration derivative, namely s'''(t), let's say we test s'''(0) and that gives us a negative value, and then test s'''(2) and that gives us a positive value, so the test goes like in the picture below, clearly, 1 = t is a minumum, and is between [0, 3].

s'''(0) = -24

s'''(3) =  48

so clearly the maximum happens at the s'''(3) endpoint, when t = 3.

Answer:

x+y = 50

Step-by-step explanation:

We can find the slope of the line

m = (y2-y1)/(x2-x1)

   = (50-41)/(0-9)

   = 9/-9

   =-1

We can use the point slope form of the equation to make an equation for a line

y-y1 = m(x-x1)

y-50 = -1(x-0)

y-50 = -x

To get it in standard from, subtract y from each side

y-y-50 = -x-y

-50 = -x-y

Multiply each side by -1

50 = x+y

x+y = 50

The equation representing the relationship between the number of bus rides and the amount of bus money is  [tex]\( x + y = 50 \)[/tex]. The option (a) is correct.

The amount of bus money Shawn will have left is [tex]y[/tex].

Representing the relationship between the number of bus rides [tex]\( x \)[/tex] .

We can see that for every 9 rides, Shawn's remaining bus money decreases by $9.

This suggests that the cost of each ride is $1 (since $9 divided by 9 rides equals $1 per ride).

We know that Shawn starts with $50 and each ride costs $1.

So, after [tex]\( x \)[/tex] rides, Shawn will have spent  [tex]\( x \)[/tex] dollars.

So, the equation is :

[tex]\[ y = \text{Initial amount} - \text{Cost per ride} \times \text{Number of rides} \][/tex]

[tex]\[ y = 50 - 1 \times x \][/tex]

[tex]\[ y = 50 - x \][/tex]

This equation can be rearranged to standard form, which is [tex]\( Ax + By = C \)[/tex] , where [tex]\( A \), \( B \), and \( C[/tex]   are constants.

For our equation,[tex]\( A = -1 \), \( B = 1 \) , and \( C = 50 \)[/tex]  , so in standard form, it is :[tex]\[ -x + y = 50 \][/tex] .

We can multiply the entire equation by -1 to get :

[tex]\[ x - y = -50 \][/tex]

[tex]\[ x + y = 50 \][/tex]

This is the equation in standard form that represents the relationship between the number of bus rides, [tex]\( x \)[/tex], and the amount of bus money Shawn will have left, [tex]\( y \)[/tex].

Therefore, the correct answer is  [tex]\( x + y = 50 \)[/tex] .

The complete question is:

Shawn has a budget of $50 per month to spend on bus fare. He made a table showing the total amount of bus money he will have left after the given number of rides.

Which equation, in standard form, represents the relationship between the number of bus rides, x, and the amount of bus money Shawn will have left, y?

a) x+y = 50

b) 50x + 50y = 1

c) 50y = x

d) 50x = y

Let's go:

The centroid of a triangle is the point of intersection of its medians. The distance from de centroid to some vertex of triangle to which it belongs is equal to 2/3 of the length of its median:

BM = 18/3 = 6

I hope I helped you.

Answer:

[tex] d > -9 [/tex]

Step-by-step explanation:

[tex] -\dfrac{1}{4}(d + 1) < 2 [/tex]

First, multiply both sides by -4. You must also change the inequality sign since you are multiplying both sides by a negative number.

[tex] -4 \times \left(-\dfrac{1}{4}\right)(d + 1) > 2 \times (-4) [/tex]

[tex] d + 1 > -8 [/tex]

Subtract 1 from both sides.

[tex] d + 1 - 1 > -8 - 1 [/tex]

[tex] d > -9 [/tex]

To find the discounted price of the sweater, multiply the original price $84 by 30% to get the discount amount of $25.20. Subtract this from the original price to find that the sweater will cost $58.80 after the discount.

To calculate the cost of a sweater that is on sale for 30% off its ticketed price of $84, you will need to find 30% of $84 and then subtract that amount from the original price.

Therefore, after a 30% discount, the sweater will cost $58.80.