Mathematics High School

Which of the binomials below is a factor of this trinomial?

x2 - 3x - 10

A. x + 2
B. x - 2
C. x - 1
D. x + 1

Answers

Answer 1
x² - 3x - 10 =
x² + 2x - 5x - 10 =
x(x+2) - 5(x+2) = 
(x+2)(x-5)

A. x + 2
Answer 2

The binomials below are a factor of this trinomial that will be x + 2. Option A  is correct.

What is a polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

It is given that, the expression is, x² - 3x - 10

Binomials in algebra are two-term expressions joined by a plus or minus sign, such as ax+b. While the second term might or might not, the first term always contains a variable.

A binomial can be solved or simplified for further work by factoring, which is the process of looking for simpler terms that, when multiplied together, produce the original binomial expression.

Thus, the binomials below are a factor of this trinomial that will be x + 2. Option A  is correct.

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Related Questions

The sum of two complementary angles is 90°. For one pair of complementary angles, the measure of the first angle is 15 less than twice the measure of the second angle. Write a system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b.
•a+b=90
a-2b=15
•a+b=90
2b-15=a
•a+b=90
2b+15=a
•a+b=90
2a-15=b

Answers

Let
a---------------> first angle
b---------------> second angle
we know that
a+b=90
and
the measure of the first angle is 15 less than twice the measure of the second angle
a=(2b)-15

A system of equations that can be used to determine the measure of the first angle, a, and the measure of the second angle, b is
a+b=90
a=(2b)-15


Which number completes the square? x2 + 18x + _____?

Answers

81 because (a + b)^2 = a^2 + 2ab + b^2
Thus x^2 + 2(9)(x) + (9)^2 = x^2 + 18x + 81

The length of a rectangular garden is 8 feet longer than the width. The garden is surrounded by a 4-foot sidewalk. The sidewalk has an area of 320 square feet. Find the dimensions of the garden.

Answers

Final answer:

The width of the garden is 12 feet and the length of the garden is 20 feet.

Explanation:

Let's denote the width of the garden as 'w'. The length will then be 'w + 8'. Measurements are in feet. The garden is surrounded by a 4-foot sidewalk. Therefore, the total length of the garden including the sidewalk is 'w + 8 + 4 + 4 = w + 16', and the total width is 'w + 4 + 4 = w + 8'.

The area of the sidewalk surrounding the garden is the area of the large rectangle minus the area of the garden. So, we set up the following equation:
(w + 16)(w + 8) - (w)(w + 8) = 320.

After simplifying, we can get a quadratic equation: w² + 8w - 320 = 0 and then solve this equation, which gives us w = 12 or w = -28. We ignore the negative solution as the width cannot be negative. So, the dimensions of the garden are:
Width: 12 feet
Length: 20 feet.

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99 POINT QUESTION!!!!!
The prime factorization of a number is 2^3*3^2*5. Which is a true statement about the factors of the number?

Answers

2^3 = 8 and 3^2 = 9

 so the number = 8 * 9 * 5 = 360

 15 is a factor of 360, so the answer would be the first one: Fifteen is a factor of the number because both 3 and 5 are prime factors
2³ = 8
3² = 9

8 x 9 x 5 = 360
 15 is a factor of 360, so the answer would be 1. Fifteen is a factor of the number because both 3 and 5 are prime factors

Ryanne is 14. her brother's age is three more than half her age. how old is her brother?

Answers

Ryanne = 14 
half her age : 14 ÷ 2 = 7
three more  : 7 + 3 = 10
Her brother is 10 years old.

Answer:

10 years old

Step-by-step explanation:

I will use the letter r to denote Ryanne's age:

r = 14

And  according to the problem, her brother's age is THREE MORE THAN HALF HER AGE

so, we start by finding  how much is half of Ryanne's age:

r/2 = 14/2 = 7

and next, we find that three more than half her age is:

7 + 3 = 10

Her brother is 10 years old

The square of the sum of two consecutive natural numbers is greater than the sum of the squares of these two numbers by 112. find the two numbers.

Answers

We solve the equation, ( a + a + 1 )^2 = 112 + a^2 + ( a + 1 )^2;
Then, ( 2a + 1 )^2 = 112 + a^2 + a^2 + 2a +1;
4a^2 + 4a + 1 = 113 + 2a^2 + 2a;
Finally, 2a^2 + 2a - 112 = 0;
a^2 + a - 56 = 0; 
We use Quadratic Formula for this Quadratic Equation;
The solutions are a1 = 7 and a2 = -8;
But a is a natural number; so, a = 7;
The natural consecutive numbers are 7 and 8.

The two consecutive numbers are 7 and 8.

Consecutive numbers are numbers that follow each other. For example, 1,2,3,4 are consecutive numbers.

Let:

x = first number

(x + 1) = second number

From the question, this expression can be derived:

[(x) + (x + 1)] ²

This can be simplified to (2x +1)²

The second expression is : x² + (x +1)²

(2x +1)² -  [x² + (x +1)²] = 112

expanding the bracket gives:

(4x²  + 4x + 1) - [x² + (x² + 2x +1) = 112

4x²  + 4x + 1 - 2x² - 2x - 1 = 112

Add like terms

2x² + 2x = 112

Divide both sides by 2

x² + x = 56

x² + x - 56 = 0

Factorise the equation

The factors of -56x² that add up to x are : 8x and -7x

(x² - 7x) (8x - 56)  = 0

x(x - 7) 8(x -7) = 0

x = 7

or

x = -8

Since x cannot be a negative number, x is 7 and (x + 1) = 8

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3/4 of what number is 8?

Answers

I got 10.6666 but I am not sure if it’s right ( ◠‿◠ )

Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.

Answers

so, we know the center is at -1, -3, hmmm what's the radius anyway?

well, the radius will be the distance from the center to any point on the circle, it just so happen that we know -7, -5 is on it, thus

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -1 &,& -3~) % (c,d) &&(~ -7 &,& -5~) \end{array} \\\\\\ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{[-7-(-1)]^2+[-5-(-3)]^2}\implies r=\sqrt{(-7+1)^2+(-5+3)^2} \\\\\\ r=\sqrt{36+4}\implies r=\sqrt{40}\\\\ -------------------------------[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\sqrt{40}}{ r} \\\\\\\ [x-(-1)]^2+[y-(-3)]^2=(\sqrt{40})^2\implies (x+1)^2+(y+3)^2=40[/tex]

Twenty-seven minus of a number (x) is not more than 36. What is the number? x > 42 x ≥ -6 x < 3 x ≤ -6

Answers

27 - 1.5x ≤ 36
54 - 3x ≤ 72
-3x ≤ 72 - 54
-3x ≤ 18
x ≥ 18/(-3)
x ≥ -6
..........................................................

Find an angle between 0° and 360° that is coterminal with 538°.

Answers

To find a positive and a negative angle coterminal with a given angle, you can add and subtract if the angle is measured in degrees or if the angle is measured in radians

table Mary used Delicious (d) and Golden Delicious (g) apples to make homemade applesauce. Delicious apples are $0.75 each and Golden Delicious apples are $1.25 each. Mary spent $21.00 on 22 apples. How many Golden Delicious apples did Mary buy?

Answers

1. To solve this problem, you must make a System of equations.

 2. The equations are:


 d+g=22 (i) 
 0.75d+1.25g=21 (ii)

 3. If you clear "d" from the equation (i), you have:

 d+g=22
 d=22-g

 4. Now, you must substitute d=22-g into the equation (ii):

 0.75d+1.25g=21
 0.75(22-g)+1.25g=21

 5. When you clear "g", you obtain its value:

 16.5-0.75+1.25g=21
 16.5+0.5g=21
 0.5g=21-16.5
 g=4.5/0.5
 g=9 Golden Delicious apples

 6. If you also want to know the value of "d", you can substitute g=9 into the equation (i) and clear "d":

 d+g=22
 d+9=22
 d=22-9
 d=13 Delicious apples

 How many Golden Delicious apples did Mary buy?

 The answer is: Mary bought 9 Golden Delicious apples.

Tldr: The answer is 9

Pablo folds a straw into a triangle with side lengths of 4x -2 inches and 4x -1 inched . The perimeter of the triangle is 12x -6 inched . If x =1.5 what was the length of the straw before it was folded ?

Answers

If x = 1.5, than the length of the straw before it is folded is 21 inches. You can find this in the following steps :

12(1.5)^2 -6 = length

12(2.25) -6 = 

27 -6 =

21 

Your answer is: 21 inches 

Have an amazing day mate!

Shoutout to: @Apologiabiology 

Answer:

21

Step-by-step explanation:

express the perimeter of the rectangle as a polynomial. help please.

Answers

7y-9+7y-9+10y+2+10y+2=34y-14

How many odd integers from 1000 through 9999 have distinct digits?

Answers

we know that
step 1
the number of elements in a list from n to m is (m-n)+1
therefore
from 1000 to 9999 there are
(9999-1000)+1 = 9000 elements
step 2
Since even and odd numbers alternate, half of our list is composed of odd numbers. Therefore, there are 4500 of them
step 3
To construct a 4 digit odd number, we have 5 choices for the last digit.
(1-3-5-7-9)
then
we have
8 choices for the first (not 0 or same as last digit),
8 choices for the second
7 choices for the third.
there are (8)(8)(7)(5) = 2240 

the answer is 2240 odd numbers with distinct digits in the list

The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. in what year of operation does mr cash’s business show the maximum profit?

Answers

Answer: 3rd year of operation

Explanation:

Note that p(t) is a quadratic function and so its graph is a parabola. Since the coefficient of t² in p(t) is negative, the maximum point in p(t) exist at its vertex. Moreover, the maximum value of p(t) is the y-coordinate of its vertex.

Note that p(t) can be expressed as:

[tex]p(t) = a(t-h)^2 + k [/tex]   (1)

Where (h, k) are the coordinates of the vertex of p(t).

To manipulate p(t) in the form expressed in equation (1), we factor out the coefficient of t² in p(t) so that

[tex]p(t) = -3t^2+18t-4 \\ \boxed{p(t) = -3 \left( t^2 - 6t + \frac{4}{3} \right)}[/tex]

Then, we let

[tex]q(t) = t^2 - 6t + \frac{4}{3}[/tex]

So that 

[tex]p(t) = -3q(t)[/tex]    (2)

We need q(t) to be expressed as the sum of a perfect square trinomial and a constant. To form the perfect square trinomial in q(t), we can find a constant k such that [tex]t^2 - 6t + k [/tex] is a perfect square.

To find the value of k, we divide the coefficient of t by 2 and get the square of the result. Since the coefficient of t in q(t) is -6, 

 [tex]k = \left( \frac{-6}{2} \right)^2 = 9[/tex]

To avoid changing the value of q(t), if we add the constant k = 9, we need to subtract it by the same number. Since k = 9,

[tex]q(t) = t^2 - 6t + \frac{4}{3} + k - k \\ = t^2 - 6t + \frac{4}{3} + 9 - 9 \\ = (t^2 - 6t + 9) + \frac{4}{3} - 9 \\ \boxed{q(t) = (t - 3)^2 - \frac{23}{3}} [/tex]

From equation (2),

[tex]p(t) = -3q(t) \\ p(t) = -3\left( (t - 3)^2 - \frac{23}{3} \right) \\ \boxed{p(t) = -3 (t - 3)^2 + 23}[/tex]

Hence the vertex of p(t) is (3, 23) and maximum value is attained at t = 3. Therefore, the Mr. Cash's business has maximum profit at the 3rd year of operation. 

help me please asap!!!!!!!

Answers

The incenter tells you two things
1. It is where the bisectors meet. This fact creates the next statement.
2. It is the same distance from the incenter to the sides of triangle. Three lines each drawn from the incenter perpendicularly to the sides will create 3 equal lines. These lines will each be equal. Put another way AI = BI = CI which are radii for the incircle.

Any two of AI, BI, and CI and make them equal to each other.

3x + 7 = 5x - 11 Now you can just use algebra to solve. Add 11 to both sides
3x + 7 + 11 = 5x
3x + 18 = 5x. Now subtract 3x from both sides.
18 = 5x - 3x
18 = 2x
x = 9

You should really check this. Do this by equating CI to either AI or BI. I leave it to you to figure out which one I choose.

Check
=====
This will be short so you can fill in the steps for yourself.
3x + 7 = 52 - 2x
 5x = 45
x = 45/5
x = 9 

A pair of shoes that normally costs $75 is on sale for $55. What is the percent decrease in the price, to the nearest whole percent?

Answers

So you subtract 75-55=20 then you divide 20/75 and you get the answer of .26 then you make the decimal into a percent making it 26%
I think it would be 15%

At how many points does the graph of the function below intersect the x-axis?

y = 25x2 - 10x + 1

A. 0
B. 1
C. 2

Answers

Answer:

It is one.

Step-by-step explanation:

If you didn't get 1 re read the problem

What is the first error he made in computing the standard deviation?



A.Yuri failed to find the difference between each data point and the mean.

B.Yuri divided by n instead of n -1.

C.Yuri did not subtract 9 - 14 correctly.

D.Yuri failed to square -2 correctly.

Answers

b.yuri divided by n instead of n-1

Answer:

Step-by-step explanation:

Given is a sample with 4 items as

12,9,14,21

Mean = average of 4 = 14

s is the square root of sample variance

Sample variance is the sum of squares divided by n-1

But Yuri divided by 4 = n instead of 3 = n-1

That is the only mistake he did and all other steps are right.

WILL GIVE BRAINLIEST




WILL GIVE BRAINLIEST AND 50 points


out of a port departed a steam boat with a speed of 36.8km/h. In 1.75 hours out of the same port and going the Sam direction departed a speed boat. In 1.8 hours after the the department of the speed boat, the distance between the speed boat and the steam boat was 86.9km. What was the speed boats speed in km/h?

Answers

To solve this, you need to use the equation that gives the relationship between time(t), speed(s), and distance(d):

s=d/t
d=st

For the steam boat, the velocity was 36.8, and the time was 1.75 hours before the speedboat left plus the 1.8 hours after the speedboat left. Substitute this information into the equation to find the distance it travels:

d=36.8*(1.75+1.8)
d=130.64 km

According to the question, we know that the distance the speedboat travels is 86.9 km behind the steam boat. So d for the speedboat is 130.64-86.9, or
43.74 km. It is also given that the speedboat travels for 1.8 hours, so t=1.8. Substitute this information into the equation to find the speed.

s=43.74/1.8
s=24.3 km/h

So the speed of the boat is 24.3 km/h

Hi there!


My name is Chris and I'll be helping you today!


So your question states that a boat departed the port at 36.8 km/h.

After 1.75 hours, a second boat emerges from the port.

After 1.8 hours, the second boat is 86.9 km away from the first boat.

Also, remember that speed equals distance over time.


Therefore, your answer will be: The speed boat's speed in km/h was 24.3 km/h. Forgive me if I am incorrect.


Enjoy your day!


Find the slope and the y-intercept of the equation y − 3(x − 1) = 0.



slope = -3 and y-intercept = -3



slope = 3 and y-intercept = 3



slope = -3 and y-intercept = 3



slope = 3 and y-intercept = -3

Answers

The slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)

To determine the slope and y-intercept of the equation, we will rewrite the equation in the form of the slope-intercept form of the equation of a straight line.

The slope-intercept form equation of a straight line is

y = mx + c

Where m is the gradient

and c is the y-intercept

From the question, the given equation is  y − 3(x − 1) = 0

This can be rewritten in form of the equation of a straight line as

y -3x +3 = 0

Then,

y = 3x - 3

Now, compare this to y = mx + c  (the slope-intercept form of the equation of a straight line)

Then,

m = 3 and c = -3

That is,

slope = 3 and y-intercept = -3

Hence, the slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)

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A cube has a length of 9.3 cm. what is the surface area of the cube?

Answers

Answer: 518.94 square centimeters

Explanation:

The surface area of the cube is given by

           Surface Area = 6*(edge)²

Since the edge of the cube in this problem is its length, the egde is 9.3 cm. Hence, the surface area of the cube is calculated as

           Surface Area = 6*(edge)²
                                 = 6*(9.3 cm)²
           Surface Area = 518.94 square centimeters

Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm

Answers

check the picture below.

This one helps too.

Ur welcome.

Factor and find all the zeros of 2x^3+3x^2-8x+3 if -3 is a zero

Answers

Using synthetic division, you can find the quadratic factor to be
.. 2x^2 -3x +1
That, in turn, factors as
.. (2x -1)(x -1)
So the complete factorization is
.. (2x -1)(x -1)(x +3)

and the zeros are confirmed by a graphing calculator to be
.. x = 1/2, 1, -3

Nadia needs half of a dollar for bus fare. Which amount is equivalent to her bus fare?

Answers

50 cents is half of a dollar
50 cents is equivalent to half of a dollar. It could also be 50% of a dollar, or 1/2 of a dollar, although those are probably not the answers you are looking for. The answer is 50 cents.

is -4 real, complex, pure​ imaginary, or nonreal complex.​ (More than one of these descriptions may​ apply.)

Answers

-4 is real and partially complex, since it does not exist in all situations involving numbers, but is still a widely used number that can be real when calculating.

Hope this helps!

which or the following will happen if you miss a monthly credit card payment?

A)You will be charged a late fee.
B)You loose reward points
C)Your APR will increase the next month
D)Both A & B

Answers

The answer is A you will be charged a late fee

Is the system of equations is consistent, consistent and coincident, or inconsistent?

y=−12x+3y=4x+2



Select the correct answer from the drop-down menu.

Drop-down Menu: consistent, consistent and coincident, or inconsistent

Answers

A system that is consistent has at least 1 solution. (That's what you have). It is also called a consistent dependent relationship when there is one solution. A consistent system can have many solutions or an infinite number. 

You can eliminate an inconsistent system. That would happen when the lines are parallel.
It is consitent
! Hope this helps!

Kim solved the equation below by graphing a system of equations. log2(3x-1)= log4(x+8) What is the approximate solution to the equation?

Answers

The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel

The steps used to find the solution of the logarithm equation can be presented as follows;

The logarithm equation is;  [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]

Converting the logarithm to the same base, we get;

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]

[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]

2 × log₂(3·x - 1) = log₂(x + 8)

log₂(3·x - 1)² = log₂(x + 8)

(3·x - 1)² = (x + 8)

(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0

Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575

Plugging in the value of x = 1.353, we get;

log₂(3 × 1.353 - 1) ≈ 1.613

log₄(1.353 + 8) ≈ 1.613

The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353

Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353

Final answer:

To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.

Explanation:

To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.

Anybody know the answer to this?

Answers

If the radius of the circle is 1, its area is π*1^2 = π units^2.
If the radius of the circle is 1, the side length of the square is √2 and its area is (√2)^2 = 2.

The ratio of square area to circle area is 2/π ≈ 63.7%.
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