Answer:
[tex]x=7 + \sqrt{3}[/tex]
[tex]x=7 - \sqrt{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]5x^2-70x=-230[/tex]
Divide both sides by 5:
[tex]x^2-14x=-46[/tex]
Square half of the coefficient of [tex]x[/tex]: [tex](-14 \div 2)^2=49[/tex]
and add this to both sides:
[tex]x^2-14x+49=-46+49[/tex]
Factor the left side and simplify the right side:
[tex](x-7)^2=3[/tex]
Square root both sides:
[tex]x-7=\pm\sqrt{3}[/tex]
Add 7 to both sides:
[tex]x=7 \pm \sqrt{3}[/tex]
[tex]\sf x=\pm \sqrt{3}+7[/tex]
solving step wise:
[tex]\sf 5x^2-70x=-230[/tex]
divide the following by 5
[tex]\sf x^2-14x=-46[/tex]
completing square
[tex]\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2 =-46[/tex]
should look like this
[tex]\sf (x-7)^2-49=-46[/tex]
simplify by changing sides
[tex]\sf x-7=\pm \sqrt{3}[/tex]
final answer:
[tex]\sf x=\pm \sqrt{3}+7[/tex]
Nine wolves, eight female and one male, are to be released into the wild three at a time. if the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed? 28 ways 36 ways 56 ways 84 ways
The number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
What is the rule of product in combinatorics?If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in [tex]p \times q[/tex] ways.
Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.
Thus, doing A then B is considered same as doing B then A
For the considered case, we have:
There are 3 wolves to be included in first group.There are 8 female wolves, and 1 male wolf.1 male wolf is sure to be in the first group.So 2 spaces are remaining and are to be filled by 2 of 8 wolves.
Assuming that all 8 of them are distinguishable, choosing 2 of them is done in [tex]^8C_2 = 28[/tex] ways.
The first process of choosing male wolf for first place is done in 1 way only.
And the second process of choosing 2 female wolves can be done in 28 ways(ordering doesn't matter),
and since first and second process have no necessary order, using product rule, we get;
Number of ways of forming first group of wolves = [tex]1 \times 28 = 28[/tex] ways.
Thus, the number of ways the first group of three wolves (necessary to include the male wolf) is given by: Option A: 28
Learn more about product rule here:
https://brainly.com/question/2763785
Answer:
The above answer is correct! The right answer is option A. 28 :)
Hope this helped! Brainliest would be greatly appreciated :D
Step-by-step explanation:
Answer choices
A) eleven twenty sevenths
B) eighteen twenty sevenths
C) eleven thirds
D) eighteen thirds
Answer:
The answer is D) eighteen thirds.
Step-by-step explanation:
9/1 times 2/3
equals 18/3
18/3 is "eighteen thirds"
Can someone please answer the attachment
Step-by-step explanation:
linear pair
linear pair
alternate angles.
alternate angles
cointerior angles
I will hope that you like my answer
Hei has $1,400 in a retirement account earning 4% interest compounded annually. Each year after the first, she makes additional deposits of $1,400. After 5 years, what was her account balance if she did not make any withdrawals? Round each year's interest to the nearest cent if necessary. HELP ASAP
Answer:
$7886.16
Step-by-step explanation:
If the balance increases by 4%, it will be 104% of the original amount. 104% as a decimal is 1.04. Therefore, to calculate the balance with annual compound interest applied, multiply the balance of the account by 1.04 each year.
As Hei makes additional deposits of $1,400 for each year after the 1st year, add $1,400 to the account balance from year 2 onwards before adding the interest.
Let A = account balance
After 1 year
A = 1400 × 1.04 = $1456
After 2 years
A = (1456 + 1400) × 1.04 = $2970.24
After 3 years
A = (2970.24 + 1400) × 1.04 = $4545.05
After 4 years
A = (4545.05 + 1400) × 1.04 = $6182.85
After 5 years
A = (6182.85 + 1400) × 1.04 = $7886.16
Therefore, after 5 years her account balance will be $7886.16
My Math Problem.
Please Answer This one
Step-by-step explanation:
class 6 to 8 students come here I will give you notes class is started come here fast I am waiting come with your name and class i am also girl come please please please please please please
Answer:
148°or 4x
Step-by-step explanation:
For a four sided Polygon (quatrilateral) the measure of four angles=360
Therefore,
2x+3x+4x +(x -10)=360
9x+x-10=360
10x-10=360
10x=360+10
10x=370
x=37
Therefore all angles are
74, 111, 148, 27
Therefore, largest angle = 148°
MARK ME AS BRAINLISTA plumber charges $25 to come to a home, and $15 per hour for a repair. Which equation gives the total cost, y, for a repair that lasts x hours?
Answer:
15x + 25 = y
Step-by-step explanation:
$25 is a fixed cost and will have to be paid if the plumber comes and $15 times the number of hours it takes to do the repair is the variable cost. 'x' in this case is the number of hours. So the equation will be 15x + 25 = y
What is the solution to this system of equations?
4x+y=6
x-2y=6
A (-2)
B (1,2)
C (1/2, 4)
D (-2,2)
Will give brainliest, thanks, and 5 stars! LOTS OF POINTS! 50 POINTS!
I need help with these questions! Please help me. The choices are all true/false.
Please help me!!!!!!
Please provide in depth explanation too!!
Answer in order:
False
True
False
False
False
False
False
True
True
Step-by-step explanation:
All of the solutions to the equation[tex]3x^2 - 12 = 0[/tex]are x = 12 and x = -12
Solve:
Common factor - [tex]3(x^2-4)=0[/tex]
Divide both sides
[tex]x^2-4=0[/tex]
Use the quadratic formula
[tex]x=\sqrt{4,x}=\sqrt{-4[/tex]
x = 2, x = -2
Thus, This is false..
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There are two unique solutions to the equations (x-3)^2 = 16
one variable in matrix = one possible value.
Therefore, x = 7, x = -1
Hence this is True
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The solutions for the equation 2(x-3)^2-18 = 0 are x = 6 and x = 0
[tex]2x^3-18x^2+54x-72=0[/tex]
[tex]x=5.080084[/tex]
Hence this is false
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The solutions for the equation 2(x-5)^2-8=0 are x = 7 and x = -7
Add both sides by 8
2(x-5)^2-8+8=0+8
2(x-5)^2=8
(x-5)^2=4
x = 7, x = 3
Hence, this is false
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The solutions for the equation (x + 3)^2-25 = -8 are x = 2 and x = -8
[tex](x+3)^2=17[/tex]
[tex]x=\sqrt{17-3,}=-\sqrt{17}-3[/tex]
Hence this is false.
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The solutions for the equation 2(2x-1)^2=18 are x = 5 and x = -4
[tex](2x-1)^2=9[/tex]
x=2, x = -1
Hence this is false.
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The only solution for equation (2x-1)^2-49=0 is x = 4
[tex](2x-1)^2=49[/tex]
x = 4, x = -3
Hence, this is false
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The solutions for the equation 3(x+2)^2 - 3 = 0 are x = -3 and x = -1
[tex]3(x+2)^2=3[/tex]
[tex](x+2)^2=1[/tex]
x = -1, x = -3
Hence, this is true
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The solutions for the equation 5x^2 - 180 = 0 are x = 6 and x = -6
Add 180 to both sides
[tex]5x^2-180+180=0+180[/tex]
[tex]5x^2 = 180[/tex]
[tex]x^2 = 36[/tex]
[tex]x=\sqrt{36},x=-\sqrt{36}[/tex]
x = 6, x = -6
Hence, this is true.
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[RevyBreeze]
Cameron will spend $285.00 for a car repair. He has $277.00 in the account linked to his debit card. The bank charges a $7 penalty fee per day for using his debit card to make a purchase if he does not have enough funds in his account. What will he pay altogether if he chooses to use his debit card and does not put any more money in his account for 6 days?
Using proportions, considering the daily penalty fee paid, it is found that he will pay $50 altogether.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, since he will spend $285.00, having $277.00, he will be $8.00 in debt.
He will pay a penalty fee of $7.00 per day for 6 days, along with the $8.00, hence the total payment in dollars will be given by:
P = 6 x $7.00 + $8.00 = $50.00.
More can be learned about proportions at https://brainly.com/question/24372153
Kyle goes to the movies with his friends. Each person buys a ticket and two equally priced snacks at the snack bar. Let ticket price be represented by t and the price of the snacks be represented by s. Kyle says the total cost can be represented by the expression 5(t + 2s). Which explanation represents Kyle’s thinking about how to find the total price?
A.
Add the price for each item bought by each person.
B .
Add the total cost of the tickets with the total cost of the snacks for all the people that went to the movie.
C .
Multiply the ticket total by the snack total.
D .
Multiply the total spent on tickets plus snacks by the number of people who went to the movie.
Answer:
The correct answer is actually D
Step-by-step explanation:
i am 100% correct because i just answered this
See
one ticket means it's only 1t or tTwo equally packed snacks means
2×s2sSo if no of friends be 5
Then total is 5(t+2s)Option D
Two soup cans p and q are right circular cylinders. each can has the same height, 5 inches, but the radius of can p is 2 inches, and the radius of can q is 4 inches. how many times larger is the volume of can q than the volume of can p?
Answer: B. 4
Sorry for the really late answer
Step-by-step explanation:
If the radius of a right circular cylinder is multiplied by k, and its height does not change, then the volume of the cylinder is multiplied by k². The radius of can Q is twice as great as the radius of can p. Therefor, the volume of can Q is 2², or 4 times larger than the volume of can p.
Kimberly has 2 1/3 bottles of milk in her refrigerator.
She used 3/4 bottle in the morning and 1 1/8 bottle in the afternoon.
How many bottles of milk does Kimberly have left over?
Answer:
1 3/20
Step-by-step explanation:
what is 0.63 divided by 0.21 (can you please show work)
[tex]\dfrac{0.63}{0.21}=\dfrac{0.63 \times 100}{0.21 \times 100}=\dfrac{63}{21}=\dfrac{21 \times 3}{21}=3[/tex]
Answer: in the file
Step-by-step explanation: in the file
which of these numbers is a solution of the inequality 3x>18?
Answer:
x>6
Step-by-step explanation:
3x>18
x>6
Any number over 6 can satisfy this inequality.
If x=3, calculate the value of:
X squared + 2x
[tex]x^2+2x\\\\\text{If x = 3,}\\\\3^2 + 2(3) = 9 + 6 = 15[/tex]
Find the values of x and y. State which theorem(s) you used.
Answer:
3x+45=180
3x=180-45
x=135/3
x=45
(y-4)=45
y=45+4
y=49
Answer:
x=45° and y=49° (180°in a straight line, co-interior angles add up to 180°)
Step-by-step explanation:
There are 180° in a straight line so 180°-45=135, 135=3x
135 divided by 3= 45, so x=45°, then because co-interior angles always add up to 180°, 45+ the missing angle=180, 180-45=135, so the angle next to angle (y-4) is 135°.
Then, solving the equation u have 135+(y-4)=180 because there are 180° in a straight line.
The equation ends up as y=49°
In 20 years Lillian will be three years older than twice her current age. Set up an equation that
can be used to solve for x, Lillian's current age.
Answer:
ok so x is her currect age y is her age in 20 years
2x+6=y
x+20=y
that means that both sides are equal
2x+6=x+20
-6
2x=x+14
-x
x=14
so her currect age is 14 and lets plug in
14+20=34
her currect age is 14 and her age in 20 years is 34
Hope This Helps!!!
Please help me with this
Answer:
should be 42
Step-by-step explanation:
5. The points used to model a parabola are (-3,0), (6,0) and (4,-5). Write an equation for this parabola.
Which form is most helpful and why?
Complete the sentence.
13. The slopes of perpendicular lines are?
Answer:
negative reciprocals of each other
Step-by-step explanation:
internet
kassim has amoney box containing 100 mixed sh 5 and sh 10 coins with a totalvalue of sh 600. How many of each type of coin does the box contain
Answer:
sh 5 coins=80
sh 10 coins=20
How long does it take for a 15 by 15 ft pond to evaporate
Answer:
Evaporation is when liquid turns into a gas or vapor.
This process happens to almost any body of water under the right conditions, including swimming pools.
This means, as a pool owner, you lose a measurable amount of pool water every day through evaporation. Several thousands of gallons of water per year for an average residential pool, in fact.
Step-by-step explanation:
Maya started to run on a treadmill after setting its timer for 57 minutes. The display says that she has finished 27% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
15.4 minutes :)
Step-by-step explanation:
We need to turn the percentage into a decimal first :)
27/100 = 0.27
Now we multiply it by 57 to see how much time has gone by!! :)
0.27 x 57 = 15.39
Now to finish, we round!
9> 5
So 3 becomes 4
She has been on the treadmill for 15.4 minutes!
Now you know how to solve this type of problem!!
Have an amazing day!!
Please rate and mark brainliest!!
Evaluate the function (f-g)(x) for x=6
Answer: I think its 8
Step-by-step explanation:
In what areas is leslie's overspending
hurting her budget?
select all that apply.
ignore my check marks those weren’t right pleas help
Answer:
is there a picture to answer?
Step-by-step explanation:
3 is 9 greater than an unknown number
find unknown number
-6
Step-by-step explanation:
First we see 3 is greater than the subject so 3<x 3-9 = -6
Which of these is the algebraic expression for the verbal expression "ten times the difference of a number and twelve?" can someone tell me the answer plus i cann't even log in
Answer:
10(x - 12)
Step-by-step explanation:
10(x - 12)
10x - 120 Distributive Property
What is the measure of angle x?
Enter your answer in the box.
x = ?°
Answer:
x = 43°
Step-by-step explanation:
The three angles to the right of the diagonal line add up to give the angle measure of the line:
x +90° +47° = 180°
x = 43° . . . . . . . . . . . . . subtract 137° from both sides
What is the measure of angle ADC in circle F?
Answer:
90°
Step-by-step explanation:
Triangle ACD has one vertex on the circle, and the other two at the opposite ends of a diameter. It is then a right triangle.
One way of thinking of it is the fact that angle AFC measures 180°, and all angles that have end points on the same arc (in our case, the part of arc AC on the bottom right part of the circle)and vertexes on the circle measure half of it, or 90°
Answer:
90
Step-by-step explanation:
since AC is a diameter and hypothenus of ADC
so triangle ADC is a right triangle
so angle ADC = 90°
An eight-sided dice is rolled twice. The numbers are 1 through 8. What
is the probability that it will land on the number 7 twice in a row?
Answer:
1/64
Step-by-step explanation:
The probability of both dice being a 1 is 1/8 * 1/8 = 1/64