Solve the quadratic equation x2 − 4x = 21 by factoring.
Answer:
[tex]x=7, x=-3[/tex]
Step-by-step explanation:
Bring the 21 on the LHS:
[tex]x^2-4x-21=0[/tex]
At this point we need to find two numbers whose product is -21, and whose sum is -4.
From the product we can tell that one has to be positive, and one is negative.
From the sum, we can tell that the greater of the two is negative.
At this point we look at the factors of 21: 1,3,7,21.
In particular, 3 and -7 added togheter do -4, which is what we need. At this point we can factor the trinomial as
[tex](x-7)(x+3)=0[/tex]
Considering that a product is zero if any of the factors is zero, it's:[tex]x-7=0 \rightarrow x=7\\x+3=0 \rightarrow x=-3[/tex]
how many soultions does 6-3x=4-x-3-2x
Answer:
No solution
Step-by-step explanation:
Im not 100% sure this is right, I looked it up????
Step-by-step explanation:
I don't really understand your question as in how many solutions.
Well if its to combine like terms the solution is below.
6-3x = 4-x-3-2x
combining like terms.
Note: Any sign to be taken across the sign (=) changes. e.g From + to - ...
6-4+3= 3x-x-2x
5 = 0
The Question is incorrect.how can you justify inequalities in one triangle
Answer:
The greater angle and greater side theorem states that within a triangle, longer sides lie opposite larger angles, and the triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.Dennis drove for 12 minutes and went 8 1/2 miles in a time. At this rate, how many miles can he drive in one hour
161,743 vinyl records were sold in 1967.
Answer:
yes thats right 161,743 vinyl records were sold in 1967.
Aaron is having his birthday party at King's Castle Laser Tag. He is making crowns for his guests to wear. He opens a bag of 100 stick-on gems. His sister asks for some, so he gives her 12 gems. He evenly divides the remaining gems among the 8 crowns.
Answer: 11 gems
Step-by-step explanation:
After Aaron gives 12 gems to his sister, he is left with 100-12 gems = 88 gems.
If he divides the gems evenly among the crowns, each one will have 88/8 gems = 11 gems.
Factor completely 16x8 − 1. (4x4 − 1)(4x4 1) (2x2 − 1)(2x2 1)(4x4 1) (2x2 − 1)(2x2 1)(2x2 1)(2x2 1) (2x2 − 1)(2x2 1)(4x4 − 1).
The factors of the expression specified is given by: Option B: [tex](2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
What are some basic properties of exponentiation?If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c[/tex]
What is the product result of (a+b)(a-b) ?Suppose two numbers are there as 'a' and 'b'.
Then, we get:
[tex](a+b)(a-b) = a(a-b) + b(a-b) = a^2 -ab + ab - b^2 = a^2 - b^2\\(a+b)(a-b) = a^2 - b^2[/tex]
For the considered case, factoring the considered expression [tex]16x^8 - 1[/tex] by rewriting it as:
[tex]16x^8 - 1 = (4 \times 4 \times x^4 \times x^4) - 1^2 = (4x^4)^2 -1^2\\\\\\[/tex]
Now, since we've got [tex](a+b)(a-b) = a^2 - b^2[/tex], therefore,
[tex]16x^8 - 1 = (4x^4)^2 -1^2\\16x^8 - 1 = (4x^4 +1 )(4x^4 - 1)[/tex]
The second term can also be factored using same property, as shown below:
[tex]16x^8 - 1 = (4x^4 +1 )(4x^4 - 1) = (4x^4 + 1)((2x^2)^2 - 1^2) \\16x^8 - 1 = (4x^4 + 1)(2x^2 + 1)(2x^2 - 1)\\\\\text{Rearranging the terms, we get}\\16x^8 - 1 = (2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
Therefore, the factors of the expression specified is given by: Option B: [tex](2x^2 - 1)(2x^2 + 1)(4x^4 + 1)[/tex]
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Answer:
Option B
Step-by-step explanation:
I took the test.
a function has factors of (x-2) and (x + 3) which graph could represent the function
Answer:
the fourth choice.
Step-by-step explanation:
it has to be a parabola that crosses the x axis at positive 2 and negative 3
Alex wants to pay off his credit card balance before he gets married. He decides to take the $2,300 out of his savings and apply it to his credit card debt of $5,390. The credit card has an APR of 16. 5%. What will Alex's minimum monthly credit card payment be in order to pay off his debt in 14 months? a. $109. 40 b. $190. 83 c. $244. 15 d. $572. 32.
Answer:
$244.51
Step-by-step explanation:
Credit card payment =$5390
After paying $2300 from savings account,
Remaining payment left = 5390-2300 = $3090
APR = 16.5% or 0.165
Time (t) = 14 months = 14/12 years
Using credit card payment calculator,
Monthly payment = $244.15
Hence, minimum monthly payment to be made to pay off the whole debt in 14 months = $244.15
Please help!!! I’ll mark you brainliest if you answer!!!
Answer:
The cordinate is (7,6)
Step-by-step explanation:
First you count how many squares (units) until you are directly under P. Then you cound how many squares up it is till you get to P.
Have an amazing day!
Please rate!
Answer:
7,6
Step-by-step explanation:
cuz yes
lien walked 7/8 mile in 1/4 hour. what was her speed in miles per hour
Answer:
3.5 miles per hour of speed
Step-by-step explanation:
Given:
Distance Lien walked = 7/8 of a mile = 0.875 milesTime of walking = 1/4 of an hour = 15 minutesTo find:
Let's use the Direct Rule of Three Distance in miles 2. Time in minutes0.875 15
x 60
-----------------------------------------------------------------------------15x = 0.875 * 6015x = 52.5x = 52.5/15x = 3.5-----------------------------------------------------------------------------Answer: 3.5Answer: Lien walked 3.5 miles per hour of speed.
Step-by-step explanation:
Distance Lien walked = 7/8 of a mile = 0.875 miles
Time of walking = 1/4 of an hour = 15 minutes
Distance in miles Time in minutes
0.875 15
x 60
Calculations:
15x = 0.875 * 60
15x = 52.5
x = 52.5/15
x = 3.5
Hope this wasn't too confusing and it helps you out!
what is the output on this graph when the input is 2?
How to find input and output from the co-ordinates on the graph?
If a pair be (x,y) then x is the input and y is the outputHere the co-ordinate having x=2 is
(2,0)So the output is 0
Every pair have ( x , y ) which means x is input and y is output .
Here , input is 2 (x)
then , let output be y ( indicate with 0 )
So , the co- ordinates are ( x , y ) = ( 2 , 0 ) .
Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 22 and 15
Answer: 7<x<37
Step-by-step explanation:
HELPPP FOR BRIANLEST???!
Answer:
3/17
Step-by-step explanation:
multicolored and 1 passenger (3) over total (17)
3/17 doesn't simplify
Hello! How to do question 5 (iii)?
Answer:
using your brain you have to find it on your own
PLEASE HELP DUE SOON! THANK YOU ( Will give brainliest!!!)
Consider that a barn loft is shaped like a rectangular pyramid, as ahsown. Calculate the volume of the loft.
A)2,750 ft3
B)4,375 ft^3
C)6,425 ft^3
D)13,125 ft^3
Answer:
B
Step-by-step explanation:
answer is B, 4,375 ft^3
[tex]V= \frac{lwh}{3}=\frac{25 x 35 x 15}{3} = 4 ,375ft^3[/tex]
(x = multiplication symbol)
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
These two triangular prisms are similar. Figure 2 is similar to figure 1 by a scale factor of 4.
If the perimeter of [tex]ABC[/tex] is 21 cm, the perimeter of [tex]PQR[/tex] is cm.
The perimeter of the face PQR is 84 cm.
What is perimeter?The perimeter of an object is the sum of the lengths of the sides of the object.
Given that, there are two similar triangular prisms. Figure 2 is similar to figure 1 by a scale factor of 4.
We know that, the ratio of the perimeters of similar objects is equal to their scale factor.
Therefore,
P(ABC) / P(PQR) = 1/4
21 / P(PQR) = 1/4
P(PQR) = 84
Hence, the perimeter of the face PQR is 84 cm.
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Find the measure of b.
Answer:
I'm not so sure but it's 90°
Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,596 was collected on the sale of 1,216 tickets. How many of each type of ticket were sold?
Step-by-step explanation:
Suppose adult tickets are x ticket
Student tickets are 1216 - x ticket
x(5) + (1216 - x)(1) = 2596
5x + 1216 - x = 2596
4x = 2596 - 1216
4x = 1380
x = 345
Adult tickets have 345 tickets
and student tickets have 1216 - 345 = 871 tickets.
In a right triangle, sin (x+4)^\circ(x+4)
∘
= cos (3x+2)^\circ(3x+2)
∘
. Find the larger of the triangle’s two acute angles
The larger of the triangle’s two acute angles is 65 degrees
Angles in a triangleGiven the expression
sin(x+4) = cos(3x + 2)
Since sin theta = cos(90 - theta), hence;
cos(90 - (x+4)) = cos(3x +2)
cos(86 - x) = cos (3x+2)
Cancel out the cosine functions to have:
86 - x = 3x + 2
-4x = -84
x = 21
Substitute x = 21 into the expression
sin(x+4) = Sin25 =
Hence the larger of the triangle’s two acute angles is 65 degrees
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The measure of an angle is 11.3°. What is the measure of its supplementary angle?
Answer:
168.7
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Choose the student who modeled the relationship correctly in a table.
Beatriz makes $7.80 per hour.
Zohar's work. A 2-column table with 3 rows. Column 1 is labeled Dollars (x) with entries 7.80, 15.60, 23.40. Column 2 is labeled hours (y) with entries 1, 2, 3.
Felipe's work. A 2-column table with 3 rows. Column 1 is labeled hours (x) with entries 1, 2, 3. Column 2 is labeled dollars (y) with entries 7.80, 15.60, 23.40.
Leonie's work. A 2-column table with 3 rows. Column 1 is labeled 1 (x) with entries 2, 3, 4. Column 2 is labeled 7.80 (y) with entries 1, 2, 3.
Answer:
The second choice
Step-by-step explanation:
Answer: Felipe's work!
Step-by-step explanation:
A cylinder and its dimensions are shown in the diagram. Which measurement is closest to the lateral surface area of the cylinder in square inches? 1,597.9 in2 677.3 in2 555.7 in2 1111.4 in2
Answer:
555.7 in²
Step-by-step explanation:
Lateral surface area of a cylinder is the "side" surface area only. Lateral SA does not include the surface area of the 2 circular ends.
[tex]\textsf{lateral SA}=2\pi rh[/tex]
(where r is the radius and h is the height)
Given:
diameter = 8.8 in ⇒ radius = 4.4 inheight = 20.1 inSubstituting these values into the formula:
[tex]\implies \textsf{lateral SA}=2\pi \cdot 4.4 \cdot 20.1[/tex]
[tex]\implies \textsf{lateral SA}=555.7 \textsf{ in}^2 \textsf{ (nearest tenth)}[/tex]
If Joshua borrows $300 from his older sister to buy a bike and he promises to pay the total amount plus 5% simple interest in one year how do I describe how to find the total amount to pay on a loan when paying simple interest
Answer:
you multiply 300 by 5 % and that gives you 15
Step-by-step explanation:
Blake is signing a lease for a studio apartment that rents for $425/month. How much will Blake pay to move in if he must pay the first and last months’ rent and a security deposit equal to 50% of his monthly rent? $637. 50 $850. 00 $1062. 50 $1275. 0.
Answer:
(c) $1062.50
Step-by-step explanation:
The total of the rental and security deposits amounts to two and a half months' rent:
2.5 × $425 = 1062.50
It will cost Blake $1062.50 to move in.
Find the equation of the line that passes through the point (8, - 3) and is perpendicular to the line y = 1/2x - 2.
Answer: y+3=0.5(x-8)
Step-by-step explanation:
PLEASE HELP
Which formula represents a linear function?
A
area of a circle: A = tr^2
B
volume of a sphere: V = 4/3tr^3
С
area of a square: A = s^3
D
circumference of a circle: C = 2tr
t = pi
Answer:
Option D
Step-by-step explanation:
Standard equation of a linear function
Ax+By+C=0Means the degree is 1
Let's observe
Degree 2(tr^2)Degree 3(r^3)Degree 3(s^3)degree 1Option D is correct
Write expression without absolute value |120+x| if x<-120
The expression without absolute value |120+x| if x<-120 is -120 - x
How to write an absolute value of an expressionGiven the absolute value expression |120 + x|
If x < -120, the resulting expression will be;
|120 + x| = -(120 + x)
|120 + x| = -120 - x
Hence the expression without absolute value |120+x| if x<-120 is -120 - x
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Jill has an old bike. her parents gave her 40$ to repair it new tires is 21$ she also wants to buy a bell 5$ and a basket 13$ how much will she have left
Answer:
1$
Step-by-step explanation:
Her total amount is 40$
She then buys the tires(tires = 21$) so she bought that subtract 21$ from 40$ 40$ - 21$=19$
She next wanted to buy a bell so she did the bell was 5$ so subtract 5$ from 19$ 19$-5$=14$ left
So remember she has 14$ left and she is buying a basket which is 13$ so her buying the basket is remaining her with 1$ because basket is 13$ and she has 14$ so what is 14$-13$ it is 1$ and there's your answer.
1$
__________
Hope this helps have a awesome afternoon:)
Steve started an after-school homework club. The club starts with 6 members and 3 more students join each
week. Define variables and write an equation to model the number of students in the club.
Answer:
y: students in the clubx: weeks after it was formedmodel: y = 3x +6Step-by-step explanation:
We are told to model the number of students in the club. That is the dependent variable, so we will assign 'y' to that quantity. The number of students in the club is a function of the number of weeks since it was formed, so we can assign 'x' to that independent variable.
The initial value of y is 6, and it increases by 3x (that is, 3 students each week). The model of the number of homework club students can be ...
y = 3x +6