X2 - 13x + 40 = 0
Hey, I got this on my math homework and I need help with figuring out how to solve it
Answer:
x=8 x=5
Step-by-step explanation:
X^2 - 13x + 40 = 0
What two numbers multiply to 40 and add to -13
-8*-5 = 20
-8-5 = -13
( x-8) (x-5) =0
Using the zero product property
x-8=0 x-5 =0
x=8 x=5
To solve this polynomial equation, we will first factor the left side.
On the left, we have a special type of trinomial
that can be factored as the product of two binomials.
X² breaks down as x · x and we are looking for
the factors of 40 that add to the middle term, -13.
Since the middle term is negative, we use negative factors of 40.
The factors that work are -8 and -5.
So we have (x - 8)(x - 5) = 0.
If (x - 8)(x - 5) = 0, that means that either x - 8 = 0 or x - 5 = 0.
Solving for x in each equation, we have x = 8 or x = 5.
We can write this as the set of numbers {8, 5}.
1. Multiply the following polynomials to write an equivalent expression.
Part A: -7x2y2 (8x2y – 5xy + 11xy2 – 31)
Part B: (t3 – 5t) E+2 – 3t)
Part C: (4x2 – 7x + 5)(2x - 5)
Part D: (3m2 - 5m + 2)2
Answer/Step-by-step explanation:
A. [tex] -7x^2y^2(8x^2y - 5xy + 11xy^2 - 31) [/tex]
[tex] -7x^2y^2(8x^2y) - (-7x^2y^2)(5xy) + (-7x^2y^2)(11xy^2) - (-7x^2y^2)(31) [/tex] (distributive property)
[tex] -56x^4y^3 + 35x^3y^3 - 77x^3y^4 + 217x^2y^2 [/tex] (note: - × - = + and - × + = -)
B. [tex] (\frac{4}{5}t^3 - 5t)(\frac{1}{4}t^2 - 3t) [/tex]
[tex] (\frac{4}{5}t^3)(\frac{1}{4}t^2 - 3t) - 5t(\frac{1}{4}t^2 - 3t) [/tex] (distributive property)
[tex] \frac{4*1}{5*4}t^3*t^2 - \frac{4*3}{5}t^3*t - \frac{5*1}{4}t*t^2 + 15t^2 [/tex]
[tex] \frac{1}{5}t^5 - \frac{12}{5}t^3 - \frac{5}{4}t^3 + 15t^2 [/tex]
Combine like terms
[tex] \frac{1}{5}t^5 - \frac{73}{20}t^3 + 15t^2 [/tex] (note: -12/5 - 5/4 = -73/20)
C. (4x² - 7x + 5)(2x - 5)
4x²(2x - 5) - 7x(2x - 5) + 5(2x - 5) (distributive property)
8x³ - 20x² - 14x² + 35x + 10x - 25
Combine like terms
8x³ - 34x² + 45x - 25
D. (3m² - 5m + 2)²
= (3m² - 5m + 2)(3m² - 5m + 2)
= 3m²(3m² - 5m + 2) - 5m(3m² - 5m + 2) + 2(3m² - 5m + 2) (distributive property)
= 9m⁴ - 15m³ + 6m² - 15m³ + 25m² - 10m + 6m² - 10m + 4
Combine like terms
= 9m⁴ - 15m³ - 15m³ + 6m² + 25m² + 6m² - 10m - 10m + 4
= 9m⁴ - 30m³ + 37m² - 20m + 4
Can someone please help me on this one!
Answer:
The answer is (1,-1)
Step-by-step explanation:
The best approach for this problem is to plug in the coordinates into the given inequality.
[tex]7x-3y\geq 10\\[/tex]
(3,4) ------> [tex]7(3)-3(4)=9[/tex]
9 is less than 10 so, we can rule this one out.
(1,0) -------> [tex]7(1)-3(0)=7[/tex]
7 is less than 10 so, we can rule this one out.
(1,2) -------> [tex]7(1)-3(2)=1[/tex]
1 is less than 10 so, we can rule this one out.
(1,-1) -------> [tex]7(1)-3(-1)=10[/tex]
10 is equal to 10, so this is the answer.
Hope this helps!
As mentioned by Mark there are an unlimited number of pairs that satisfy your equation. So let us see how you can characterize these solutions
if 7x - 3y > 10 then
7x > 10 +3y
Now we can substitute any value for y and get the appropriate value for x. For example I can choose y to be 6
then by substitution
7 must be > 10+ 3*6
or 7x must be > 28
or x must be > 4
So all pairs such that x is > 4 and y = 6 are solutions.
I can create an infinite number of pairs choosing any number for y. Likewise I could have chosen x and solved the problem for y. In the above example I chose 6 for y to make the division easy. I could have chosen any number(real or integer) for y and solved the equation for x to derive appropriate pairs
Someone help me on this.
Answer:
[tex]-57-39i[/tex]
Step-by-step explanation:
So we have the expression:
[tex](7+2i)(-9-3i)[/tex]
FOIL:
[tex]=7(-9)+7(-3i)+2i(-9)+2i(-3i)[/tex]
Simplify:
[tex]=-63-21i-18i-6i^2[/tex]
Recall that i² is just -1. Thus:
[tex]=-63-21i-18i-6(-1)[/tex]
Simplify:
[tex]=-63-21i-18i+6[/tex]
Combine like terms:
[tex]=(-63+6)+(-21i-18i)[/tex]
Add:
[tex]=-57-39i[/tex]
And we're done!
3. Round 9995.2 to the nearest ten. Explain in your
own words the reasoning behind why we round
the number the way we do. Use a number line to
support your explanation
Answer:
10000
Step-by-step explanation:
First, highlight parts of the question. Since it says round to the nearest ten, draw a number line to start. Start by drawing a number line from 9990 to 10000. Whenever a number has the digit from 5 till any number less than 10, you round up. If the number you are trying to round to any digit is less than 5, then you can round down. Since the part of the number that is important for the question is 5.2, we round above. You get 10000 from this.
G(n) = n^2 +4n find g(2)
Answer:
12
Step-by-step explanation:
G(2)= 2^2 +4(2)
Solve via order of operations
G(2)=4 +8
G(2)=12
Solve 16x + 9 = 9y – 2x for y.
y =
Simplify: 5m (5m* +5m -4)
A 10m +10m² + m
B 10m + 10m + m
25m + 25m-20m
D 25m + 25m-20m
Angles, angles everywhere! Big ones, little ones, right
ones too! But this angle is something new. It has two
rays that meet at a vertex, and it measures 180
degrees. How complex! What angle am I? Draw me.
Answer:
Straight angle
<----------------------------->
You can determine if an angle is a straight angle only if it is 180 degrees. You can also draw it by drawing a straight line and drawing an arrow facing outward at each end.
Evaluate f (x) = 2x – 13 for f (x) = 9, x =
Answer:
11
Step-by-step explanation:
f(x) = 2x - 13
9 = 2x - 13 Add 13 to both sides
9 + 13 = 2x Add the left
22 = 2x Divide by 2
22/2 = x
x = 11
Find the value of x.
X=8
X=10
X=16
X=20
Answer:
D. 20Step-by-step explanation:
Find the required diagram to the question in the attachment.
From the diagram it can be seen that the distance of the lines projecting from the centre of the circle to the line segment is equal i,e they are both 8. This means that the length of both chords given will be equal. For the known chord length, it can be seen that the line perpendicular to the chord cuts them at the centre. and since both sides of the chord are parallel, the other sides too will be 10 making the total length to be 10+10 = 20.
Since the length of the known chord is equal to the length of the unknown chord x, hence, the value of x will also be 20
Answer:
D. x=20
Step-by-step explanation:
correct on EDGE2021
Solve for x 9x - 1 = -11
Answer:
x=[tex]-\frac{10}{9}[/tex]
Step-by-step explanation:
We start by moving the constant to the right. In this case -1 (it becomes positive 1).
9x=-11 +1
9x= - 10
divide 9 by both sides.
x=- [tex]\frac{10}{9}[/tex]
What two numbers should be placed in the blanks below so that the difference between the
consecutive numbers is the same?
13,_,_,34
Answer:
20,27
Step-by-step explanation:
let 13,a,b,34 be consecutive numbers.
a=13
l=34
n=4
l=a+(n-1)d
34=13+(4-1)d
34-13=3d
21=3d
d=21/3=7
a=13+7=20
b=20+7=27
Answer:
20, 27
Step-by-step explanation:
The difference 34-13 = 21 must be divided into three equal parts. Each is 21/3 = 7.
The numbers are 13+7 = 20, 20+7 = 27. As a check, 27 +7 = 34
The missing numbers are 20 and 27.
A 6- foot roll of waxed paper costs $3.60. What is the price per inch?
Answer:
0.3
Step-by-step explanation:
1 foot = 12 inches so 3.60/12=0.3
Answer as a fraction (please help)
Jamal owes $424.04 on his credit card. He returns two items, one for $49.95 and the other for $50.42.
Then he makes purchases of $39.19 and $37.41. What is the new balance on the card?
Answer:
$400.27
Step-by-step explanation:
owes $424.04
returns an item for $49.95
-424.04 + 49.95 = -374.09
he now owes $374.09
returns an item for $50.42
-374.09 + 50.42 = -323.67
he now owes $323.67
makes a purchase of $39.19
-323.67 - 39.19 = -362.86
he now owes $362.86
makes a purchase of $37.41
-362.86 - 37.41 = -400.27
he now owes $400.27
Solve the equation for y
the answer is C). y= 1/4x + 2
How much string would you need to go around the bottom of a hat shaped like a cone if the radius is 4 inches? (Use 3.14 for π)
Answer:
25.12 inches
Step-by-step explanation:
To find the circumference or the perimeter of a circle it is the diameter times pi. (pi = 3.14) Or you can do radius times 2 times pi.
Answer is 4 times 2 times 3.14 which is 25.12
A rectangle or prism has dimensions of 2 cm x 2 cm x 3 cm what is the surface area
Answer:
32 cm²
Step-by-step explanation:
SA = 2(lw + lh + hw)
= 2(2x2 + 2x3 + 3x2)
= 2(4 + 6 + 6)
= 2(16)
= 32 cm²
A coin flipped 10 times and the results is recorded. What is the probability of getting exactly 5 tails?
Answer:
50%
Ste50p-by-step explan%ation:
Complete the table
30x – 6y = -6x2
Answer:
-0.5
Step-by-step explanation:
30x - 6x = -6(2)
24x -12
24 24
x = -.5
if x and 3x are linear pair then find the value of x.
Answer:
x = 45°
Step-by-step explanation:
x + 3x = 180°
--> 4x = 180°
--> x = 180 / 4 = 45°
Step-by-step explanation:
x+3x=180 (sum of linear pair=180)
or, 4x =180
or, x = 180/4
therefore x =45
Solve for x.
16 = -2x - 1
x = -8
x = -7
x = 7
x = 8
Step-by-step explanation:
16=-2x-1
17=-2x
x=-17/2
x=-8.5
(this one isn't in the correct order but it's one of the answers ¯\_(ツ)_/¯
16 = -2x - 1
-8=x-1
-7=x
x=-7
If 4 times a number is 156, then 1/3 of the number is
Answer:
[tex]\huge\boxed{\sf \frac{x}{3} = 12}[/tex]
Step-by-step explanation:
Let the number be x
4x = 156
Dividing both sides by 4
x = 36
Dividing both sides by 3
[tex]\frac{x}{3}= \frac{36}{3}[/tex]
[tex]\frac{x}{3} = 12[/tex]
is is 6 2/7 rational or irrational
is -19 rational or irrational
is -√100 rational or irrational
Step-by-step explanation:
6 2/7is rational
-19is rational but next I dont know
For income tax purposes, a man uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. A man assumes that he can use the machine for years. The following graph shows the value of the machine over the years. What loss in value occurred during the first year?
Answer: $500
Step-by-step explanation:
The vertical axis of the graph represents the value of the copy machine and the horizontal axis represents the years.
Using the line, one can see that in the first year, the value of the machine went from $7,000 to $6,500.
The loss in value is therefore;
= 7,000 - 6,500
= $500
The needed graph is attached.
What is the average density of a laptop?
Which question relates to setting a long-term financial goal?
Choose the correct answer below.
A.
When would I like to buy a new car?
B.
How much does it cost to buy a movie ticket and snacks at the theater?
C.
On which day of the month is my credit card bill sent out?
D.
What is the late payment fee on my car loan?
Which step is incorrect when solving the equation 2(x+9)=4(x+7)+2?
Choose the first step that made an error.
1. 2(x+9)=4(x+7)+2
2. 2x+18=4X+28+2
3. 2x+18=4x+26
4. -8=2x
5. -4=x
(i think it's step 3)
Answer:
3. 2x+18=4x+26
Step-by-step explanation:
2(x+9)=4(x+7)+2
2x+18=4x+28+2
2x+18=4x+30
The step that made an error in solving this linear equation is step 3.
Hope this helps ;) ❤❤❤
Express each rational number in decimal form.
[tex] \frac{3}{4} [/tex]
Answer:
.75
Step-by-step explanation:
there is only 1 number
0.75
The decimal forms of rational numbers either end or repeat a pattern. To convert fractions to decimals you just divide the top by the bottom — divide the numerator by the denominator — and if the division doesn't come out evenly, you can stop after a certain number of decimal places and round off.