Answer:
x = - 7, x = 1
Step-by-step explanation:
Given
x² + 6x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(3)x + 9 = 7 + 9
(x + 3)² = 16 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( subtract 3 from both sides )
x = - 3 ± 4
x = - 3 - 4 = - 7
x = - 3 + 4 = 1
Solution set = { - 7, 1 }
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#1. An orange contains about 80 milligrams of vitamin C. This is 10 times the amount of vitamin C that an apple contains.
If x represents the amount of vitamin C in an apple, which equation can be used to find x?
Question 1 options:
80x=10
10x=80
10+x=80
80+x=10
#2. Select all the situations that can be represented by the equation 12(x+40)=60.
Question 2 options:
40 more than 50% of a number is 60.
60 is half the sum of a number and 40.
A test is worth 100 points. Each question, x, is worth 12a point.
A store has a sale in which all items are 50% off. At the store, Tony spends a total of $60 for a jacket that costs x dollars and a pair of pants that costs $40.
#3. A basket contains some apples and oranges. The number of apples is 4 more than 2 times the number of oranges. The total number of pieces of fruit in the basket is 22.
Which equation finds the number of oranges in the basket, x?
Question 3 options:
2x−4=22
2x+4=22
3x−4=22
3x+4=22
#4. The equation 2y+53=165 represents the situation "Joel spends $165 on a pair of jeans and two shirts that were the same price."
What does y represent?
Question 4 options:
Price of one pair of jeans
Number of shirts Joel bought
Price of one shirt
Amount Joel spent on the shirts
#5. Jamar and Henry sell insurance policies. Henry sells 20 policies less than Jamar does. One half of the total policies they both sell is 89.
Does Jamar sell 99 policies? Why or why not?
Question 5 options:
Yes, because if Jamar sells x number of policies then the equation representing the scenario is12(2x−20)=89.
No, because if Jamar sells x number of policies then the equation representing the scenario is12(2x+20)=89
Yes, because if Jamar sells x number of policies then the equation representing the scenario is 2(2x+20)=89.
No, because if Jamar sells x number of policies then the equation representing the scenario is 2(2x−20)=89 .
#1: 10x=80
#2: A test is worth 100 points. Each question, x, is worth 12a point.
#3: 2x+4=22
#4: Price of one shirt
#5: Yes, because if Jamar sells x number of policies then the equation representing the scenario is12(2x−20)=89.
Answer:
hope this helps
Step-by-step explanation:
#1: 10x=80
#2: A test is worth 100 points. Each question, x, is worth 12a point.
#3: 2x+4=22
#4: Price of one shirt
#5: Yes, because if Jamar sells x number of policies then the equation representing the scenario is12(2x−20)=89.
The sum of a number and three times the number is 92 . Find the number
Step-by-step explanation:
Let the number be x
x + 3x = 92
4x = 92
x = 92/4
x = 23
Order the values from least to greatest.
30. 8,|3|, -5,1 -2], -2
32. – 12,1-26], -15,|-12, 10|
Answer:
30. -5,-2,|-2|,|3|,8
32. -12,|10|, |-12|,|-15|,|-26|
Step-by-step explanation:
Answer:
[tex]-12, -2,|-2|, |3|, |-5|, 8, |10|, |-12|, |-15|, |-26|[/tex]
Step-by-step explanation:
We can start with -12
Because this is in the negatives
Along with -2
so:
-12, -2
We then put |-2| because when the |x| are around a number, it makes the number in the bars always positive. Therefore:
-12, -2, |-2|
The same goes for |3|:
-12, -2, |-2|, |3|
Same for |-5|:
-12, -2, |-2|, |3|, |-5|
8 will go next:
-12, -2, |-2|, |3|, |-5|, 8
|10| is positive, and next:
-12, -2, |-2|, |3|, |-5|, 8, |10|
Same for |-12|:
-12, -2, |-2|, |3|, |-5|, 8, |10|, |-12|
Same for |-15|:
-12, -2, |-2|, |3|, |-5|, 8, |10|, |-12|, |-15|
Same for |-26|:
-12, -2, |-2|, |3|, |-5|, 8, |10|, |-12|, |-15|, |-26|
A hungry elf ate 20 of your muffins. That was 5/8 of all of them! With how many did you start?
Answer:
answer and explanation is in the image :)
Step-by-step explanation:
Triangle FGH is reflected across a vertical line to produce ABC. Which statement is true
a. The perimeter of triangle FGH is equal to the perimeter of triangle ABC.
b. The length of side BC is equal to the length of side FG
c. The length of side AB is equal to the length of side FH.
d. The length of side AC is equal to the length of side FG.
Answer:
answer is a
Step-by-step explanation:
answer would be a because a reflection does not change the size or shape of any figure
A reflection of a shape maintains its size and shape, changing only its position and orientation. Thus, the perimeters and corresponding side lengths of reflected triangles FGH and ABC are equal.
Explanation:When a shape is reflected across a line, its shape and size remain the same, although its orientation and position may change. Therefore, a reflection is a type of transformation called an isometry, also known as a congruence transformation. In the case of triangle FGH being reflected to form triangle ABC:
The perimeter of triangle FGH is equal to the perimeter of triangle ABC. This is because the lengths of the sides remain the same under a reflection.The length of side BC is equal to the length of side GH, assuming that BC corresponds to GH in the reflection.The length of side AB is equal to the length of side FG, assuming that AB corresponds to FG in the reflection.The length of side AC is equal to the length of side FH, assuming that AC corresponds to FH in the reflection.Learn more about Reflection of Triangles here:https://brainly.com/question/28097210
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Which of the following are solutions to the question below? Check all that apply.
6x^2-2x+36=5x^2+10x
A. -4
B. -3
C. 4
D. 6
E. -6
F. 18
Answer:
D
Step-by-step explanation:
Given
6x² - 2x + 36 = 5x² + 10x ( subtract 5x² + 10x from both sides )
x² - 12x + 36 = 0 ← in standard form
(x - 6)² = 0 ← in factored form, thus
x - 6 = 0 ⇒ x = 6 → D
There are 7 students at the Math Club picnic. If 2 students are drinking punch and 5 are drinking lemonade, what fraction are drinking punch?
Answer:
2/7
Step-by-step explanation:
2 are drinking punch
5 are drinking lemonade
------------------------------------
7 in total
Liam bought a comic book and had $5 left. If he had a total of $8 walking into the store, how much did he spend on the comic book?
Liam used the equation 5x=8 to model the problem. He said that x represents the amount of money he spent. Liam said that the solution, x=1.6, means that he spent $1.60. Is he correct? Why or why not? If he is incorrect find the correct answer showing your work.
Pls Help Me
Answer:
Liam is incorrect
He spent $3 on the comic book
Step-by-step explanation:
Let
x -----> represents the amount of money he spent
we know that
The amount of money he spent plus the money he had left must be equal to the money he had when he walked into the store.
so
The linear equation that represent this problem is
x+5=8
solve for x
subtract 5 both sides
x=8-5=$3
therefore
Liam is incorrect
He spent $3 on the comic book
Can someone explain how to do this please ASP thank you
Answer:
2) 10
4) 7
6) 7
Step-by-step explanation:
what equals 10? 10
what is subtracted from 3 equals 4? 7
what is multiplied by 7 and equals 49? 7
Have a nice day!!!!!!!!!! :-)
KA
how do i rearrange f-ex=g-hx to get x?
Answer:
x = [tex]\frac{g-f}{h-e}[/tex]
Step-by-step explanation:
Given
f - ex = g - hx
Collect the terms in x on the left side by adding hx to both sides
hx - ex + f = g ( subtract f from both sides )
hx - ex = g - f ← factor out x on the left side
x(h - e) = g - f ← divide both sides by (h - e)
x = [tex]\frac{g-f}{h-e}[/tex]
please help will give brainiest to whoever answers correctly!!!!
Answer:
○ B
Step-by-step explanation:
It is exactly similar to A:
One unit north over one unit west
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What is the relationship between 7 and -7
Answer:
14
Have a nice day!!!!!!!! :-)
KA
Answer:
there 14 away from each other
Step-by-step explanation:
If f(n) = n2 - 2n, which of the following options are correct? Select all that apply. f(2) = 0 f(1) = 3 f(-4) = 24 f(5) = 35 f(-2) = 0
Answer:
f(2)=0
f(-4)=24
Step-by-step explanation:
We are given
f(n)=n^2-2n
We are asked which of the following are true?
f(2)=0
f(1)=3
f(-4)=24
f(5)=35
f(-2)=0
Let's start with f(2)=0.
f(2)=2^2-2(2)
f(2)=4-4
f(2)=0
So f(2)=0 is true.
Moving on to f(1)=3.
f(1)=1^2-2(1)
f(1)=1-2
f(1)=-1
So f(1)=3 is false.
Now for f(-4)=24.
f(-4)=(-4)^2-2(-4)
f(-4)=16+8
f(-4)=24
So f(-4)=24 is true.
f(5)=35?
f(5)=5^2-2(5)
f(5)=25-10
f(5)=15
So f(5)=35 is false.
Finally f(-2)=0.
f(-2)=(-2)^2-2(-2)
f(-2)=4+4
f(-2)=8
So f(-2)=0 is false.
Answer:
The correct option are,
f(2) = 0, and f(-4) = 24
Step-by-step explanation:
Given function,
[tex]f(n) = n^2 - 2n[/tex]
By substituting n = 2,
[tex]f(2) = 2^2 - 2(2) = 4 - 4 = 0[/tex]
By substituting n = 1,
[tex]f(1) = 1^2 - 2(1) = 1 - 2 = -1[/tex]
By substituting n = -4,
[tex]f(-4) = (-4)^2 - 2(-4) = 16 + 8 = 24[/tex]
By substituting n = 5,
[tex]f(5) = (5)^2 - 2(5) = 25 - 10 = 15[/tex]
By substituting n = -2,
[tex]f(-2) = (-2)^2 - 2(-2) = 4 + 4= 8[/tex]
A. Sydney invests $100 every month into an account that pays 5% APR
compounded monthly. How much money will Sydney have in the
account after 10 years? Round your answer to the nearest dollar.
Step-by-step explanation:
compound interest --> initial sum × increase^years
the increase is 1 + (percentage increase / 100)
initial sum = 100
increase= 1.05
years= 10
100 × 1.05^10 = 162.8894627...
so Sydney will have 164 dollars (to the nearest dollar)
the sum of 12 and a number x is equal to 15
Answer:
The answer would be 3.
Step-by-step explanation:
This can be found by subtracting 12 from both sides and then the x will be alone on one side and be set equal to 3 on the other side.
Willis can jump rope at a rate of 8 jumps every 10 seconds. find the unit rate
Answer:
0.8 jumps per second
0.8 jumps/second
what is the sum of the complex numbers below? 4−7i and −3+5i
a −i
b 1+2i
c 3
d 1−2i
Answer:
d 1–2i
Step-by-step explanation:
(4–7i)+(–3+5i)=1–2i
The sum of the complex numbers 4−7i and −3+5i is obtained by adding the real parts and the imaginary parts separately. This gives a result of 1 - 2i.
Explanation:To find the sum of two complex numbers, you simply add the real parts together and the imaginary parts together separately.
So, you add the real parts (4 and -3), which equals 1, and the imaginary parts (-7i and 5i), which equals -2i.
Thus, the sum of the complex numbers 4−7i and −3+5i is 1 - 2i.
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point O lies in the interior of angle MNP. if the measure of MNO is x^2 + 10x, the measure of ONP is x^2 - 2x , and the measure of MNP is 3x^2 + 12, find the value of x. then find the measure of ONP
Answer:
x = 6; ∠ONP = 24°
Step-by-step explanation:
1. Find the value of x
[tex]\begin{array}{rcl}\angle MNP & = & \angle MNO + \angle ONP\\3x^{2} + 12 & = & x^{2} + 10x + x^{2} - 2x\\3x^{2} + 12 & = & 2x^{2} + 8x\\x^{2} + 12 & = & 8x\\x^{2} -8x + 12 & = & 0\\(x - 2)(x - 6) & = & 0\\\end{array}[/tex]
[tex]x = 2 \text{ or }x = 6[/tex]
2. Find the measures of the angles
(a) x = 2
∠ ONP = x² - 2x = 2² - 2(2) = 4 - 4 = 0
This answer does not make sense because O lies in the interior of ∠MNP.
We disregard x = 2.
(b) x = 6
∠ ONP = x² - 2x = 6² - 2(6) = 36 - 12 = 24
The product of six and three less than the number
The product of six and three less than the number is 6(x - 3) where x is the variable.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
Write the mathematical expression, and use x as a variable.
The product of six and three less than the number
x is the variable;
Three less than a number = x - 3
The product of 6 and (x - 3)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 6(x - 3)
Thus, the product of six and three less than the number is 6(x - 3) where x is the variable.
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In Troy's toy bin there are 14 red blocks. There are 6 more yellow blocks than red blocks. There are 2 more blue blocks than red blocks. How many blocks are there in all?
The total number of blocks in Troy's toy bin is 50, which is the sum of 14 red blocks, 20 yellow blocks, and 16 blue blocks.
Explanation:To solve the problem regarding Troy's toy bin, we need to use basic arithmetic to calculate the total number of blocks of each color and then add them together to find the total number of blocks in the bin.
Troy has 14 red blocks, so let's represent the number of red blocks as R = 14. It's mentioned that there are 6 more yellow blocks than red blocks, which means the number of yellow blocks Y = R + 6 = 14 + 6 = 20.
The problem states that there are 2 more blue blocks than red blocks, so the number of blue blocks B = R + 2 = 14 + 2 = 16.
Now, to find the total number of blocks in the bin, we simply add the numbers of red, yellow, and blue blocks:
Total blocks = R + Y + B = 14 + 20 + 16 = 50.
Therefore, there are 50 blocks in Troy's toy bin in all.
Calvin had 30 minutes in time-out. For the first 23 1/3 minutes, Calvin counted spots on the ceiling. For the rest of the time, he made faces at his stuffed tiger. How long did Calvin spend making faces at his tiger?
Answer: 6 2/3 minutes
Step-by-step explanation:
30-23 1/3=6 2/3
Answer: [tex]\frac{20}{3}\ minutes[/tex] or [tex]6 \frac{2}{3}\ minutes[/tex]
Step-by-step explanation:
For this exercise you can convert the mixed number to an improper fraction:
1. Multiply the whole number part by the denominator of the fraction.
2. Add the product obtained and the numerator of the fraction (This will be the new numerator).
3. The denominator does not change.
Then:
[tex]23\frac{1}{3}= \frac{(23*3)+1}{3}= \frac{70}{3}\ minutes[/tex]
You know that he had 30 minutes in time-out, he counted spots on the ceiling for [tex]\frac{70}{3}[/tex] minutes and the rest of the time he made faces at his stuffed tiger.
Then, in order to calculate the time Calvin spent making faces at his stuffed tiger, you need to subract 30 minutes and [tex]\frac{70}{3}[/tex] minutes:
[tex]30\ min-\frac{70}{3}=(\frac{3(30)-70}{3})=\frac{20}{3}\ minutes[/tex] or [tex]6 \frac{2}{3}\ minutes[/tex]
HELP PLS! THANK YOU!
1) In the morning, the temperature was -4.6 F. By the afternoon, the temperature was -9.4 F. What was the change in temperature
2) Ron made withdrawals of $46.79 and $18.93 from his checking account. He also deposited $30. If his balance before these transactions was $71.24, what is his balance now?
EXPLANATION PLS!
Answer:
#1 is 4.8 F and #2 is $35.52
Step-by-step explanation:
#1 Basic subtraction
9.4-4.6=4.8
#2
71.24-46.79-18.93+30
Break it out 71.24-46.79=24.45
Then 24.45 - 18.93= 5.52
Lastly 5.52+30=35.52
If x^4-3x+5 is divided by 2x-1,then what is the remainder
Answer:
[tex] \frac{3 \frac{9}{16}}{2x - 1} [/tex]
Step-by-step explanation:
Use Polynomial Long Division to get this:
[tex] \frac{x^{3}}{2} + \frac{ {x}^{2} }{4} + \frac{x}{8} - 1 \frac{7}{16} + \frac{3 \frac{9}{16}}{2x - 1} [/tex]
The remainder is the quantity being set over the divisor, which is 2x - 1.
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Please help me with this Algebra 2 question！
The upper boundary on x is 5. Divide this over each endpoint of the y inequality
5/0.25 = 20
5/4 = 1.25
we see that the first result 20 is largest
This means that the upper bound of x/y is 20.
Therefore b = 20.
----------------------------
The lower boundary on x is -4. Divide this over each endpoint of the y inequality
-4/0.25 = -16
-4/4 = -1
The result -16 is further to the left compared to -1, so therefore it is smaller.
The lower bound of x/y is -16.
This means a = -16.
----------------------------
We found that a = -16 and b = 20. Therefore, a+b = -16+20 = 4
The final answer is 4what is the answer to a-5<1
Answer:
a < 6
Step-by-step explanation:
Given
a - 5 < 1 ( isolate a by adding 5 to both sides )
a < 6
What is 5x23x2 using any property
Answer:
230
Step-by-step explanation:
First, you multiply 5 x 23. You'll get 115 as your answer. Multiply 115 x 2, and you'll get 230 as your answer.
Answer:
Step-by-step explanation:
230
Bev scored 540 points . This was 158 points more then Ike scored . How many points did Ike score
For this case we have to:
x: Variable that represents the points scored by Bev
y: Variable that represents the points scored by Ike
According to the data we have:
[tex]x = 540\\x = y + 158[/tex]
We substitute the first equation in the second one:
[tex]540 = y + 158[/tex]
We clear the variable "y":
[tex]y = 540-158\\y = 382[/tex]
So, Ike scored 382 points.
Answer:
Ike scored 382 points.
kimberly is driving 1323 miles from wichita to charleston. She drives 443 miles the first day and 409 the second day. Round each distance to the nearest ten and estimate how many miles kimberly has left to drive.
Answer:
1323 rounds to 1320
443 rounds to 440
409 rounds to 410
1320 - (440 + 410) =
1320 - 850 =
470 <=== malcolm has about 470 miles left to go
Step-by-step explanation:
Answer:
Step-by-step explanation:1323 rounds to 1320
443 rounds to 440
409 rounds to 410
1320 - (440 + 410) =
1320 - 850 =
470 <=== kimberly has about 470 miles left to go
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To make orange paint, Roger next 5/8 cup of red paint to his cup of yellow paint. He really likes of the resulting color and wants to make a large batch of the orange paint. How much yellow paint is needed to mix with one cup of red paint?
Answer:
It is needed [tex]\frac{8}{5}[/tex] cups of yellow paint to mix with one cup
of red paint
Step-by-step explanation:
* Lets explain how to solve the problem
- To make the orange pint, Roger mixed 5/8 cup of red paint to one
cup of yellow paint
∴ The ratio of red paint to yellow paint is 5/8 : 1
- Lets simplify it by multiplying the two terms of the ratio by 8
∵ [tex]\frac{5}{8}(8):1(8)[/tex]
∴ The ratio of red paint : yellow paint = 5 : 8
∴ For every 5 cups of red paint we need 8 cups of yellow paint to
make the orange paint
- We need to know how many yellow paint is needed to mix with
one cup of red paint
∵ red paint : yellow paint
5 : 8
1 : ?
- By using cross multiplication we can find the number of yellow cups
∴ The number of the yellow cups = [tex]\frac{1*8}{5}=\frac{8}{5}[/tex]
∴ It is needed [tex]\frac{8}{5}[/tex] cups of yellow paint to mix with one
cup of red paint
A rectangle has a length of 8.3cm and a perimeter of 22.4cm
Answer:
width = 2.9 cm
Step-by-step explanation:
Since there are two sides that equal to length on a rectangle, you double the length. Then, you subtract that number to find (width * 2). Then you divide that by 2 to get your answer (2.9 cm).