Please help me
Use (x − 4)^2 − 28 = 8 for the following:
a. Explain why (x − 4)^2 − 28 = 8 has two solutions. (5 pts)
b. Solve the equation to find the solutions. Show your work. (5 pts)
Answer:
a) Because both sides are perfect squares b) (x-4)² – 28 = 8
(x–4)² = 36
Square root both sides
√(x–4)² = √36
x–4 = 6
x= 10
Step-by-step explanation:
(x–4)(x–4) = 36
x² – 8x+ 16 = 36
x² – 8x – 20 = 0
(x² + 2x)( –10x – 20) = 0
x(x+2) – 10(x+2) = 0
(x+2)(x–10) = 0
x = 10 or –2
x = 10
a. If the power of x is 2 then the value of x will be 2.
b. The values of the x are 6 and -2.
What is simplification?Simplification is to make something easier to do or understand and to make something less complicated.
Given
The equation is [tex]\rm (x- 4)^2 - 28 = 8[/tex].
a. If the power of x is 2 then the value of x will be 2. And in the equation the power of x is 2 then the solution for the x will be two.
b. The equation is [tex]\rm (x- 4)^2 - 28 = 8[/tex].
On simplifying
Add 28 both the sides, we have
[tex]\rm (x- 4)^2 = 36[/tex]
Taking square root both the sides, then we have
[tex]\rm x- 4 = \pm 6[/tex]
Add 4 both the sides,
[tex]\rm x = \pm 6+ 4\\\\x = 6 + 4, - 6 + 4\\\\x = 10 , -2[/tex]
Thus, the values of x are 6 and -2.
More about the simplification link is given below.
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Delta makes 12-volt car batteries. These batteries are known to be normally
distributed with a mean of 45 months and a standard deviation of 8 months.
What percent of Delta car batteries last between three and four years?
Answer:
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = 0.5188
The percentage of that Delta car batteries last between three and four years
P(3≤X≤4) = 52%
Step-by-step explanation:
Step(i):-
Given that the sample size n =12 -volt car batteries
Let 'X' be a Random variable in a normal distribution
Given that mean of the normal distribution = 45 months
Given that the Standard deviation of the normal distribution = 8months
Step(ii):-
Let X₁ = 3 years = 12 × 3 = 36 months
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{36-45}{8} = -1.125[/tex]
Let X₂ = 4 years = 12 × 4 = 48 months
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{48-45}{8} = 0.375[/tex]
Step(iii):-
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = P(-1.125≤Z≤0.375)
= P(Z≤0.375) - P(Z≤-1.125)
= 0.5 +A(0.375) - (0.5-A(1.125)
= 0.5 + 0.1480 - (0.5 -0.3708)
= 0.1480 + 0.3708
= 0.5188
Final answer:-
The probability that Delta car batteries last between three and four years
P(36≤X≤48) = 0.5188
The percentage of that Delta car batteries last between three and four years
P(3≤X≤4) = 52%
CAN SOMEONE LLEASE HELP ME IM SO LOST!!
Answer: 1324 in^2
Step-by-step explanation:
A cylinder has a volume 8m cube and a height of 2m.find the base radius of the cylinder.
Answer:
1.12838m or 1.13m
Step-by-step explanation:
hope this helps
What is the distance between (2,8) and (8, 16)?
Answer:
For any two points there is exactly one line segment connecting them. The distance between two points is the length of the line segment connecting them. Note that the distance between two points is always positive. Segments that have equal length are called congruent segments.
(6, 8)
Step-by-step explanation:
please mark this answer as brainliest
Answer:
10
Step-by-step explanation:
please help no links please.
Answer:
I think it's A, if you just subtract 25 from each top # you should get the right one
edit; yah it's A
Answer:
B is the correct answer
Step-by-step explanation:
Look at the graph. For every day, there should be 25 less containers of peanuts than popcorns. Let X represent popcorns. Everyday, X - 25 should be your amount of peanut containers.
Only A and B works, so now just add the total amount of containers for both peanuts and popcorns.
225 + 200 + 150 + 300 + 200 + 175 + 125 + 275 = 1650
Only B matches the description of 1650 total containers. So, B is your answer.
Pls help me!
Which represents a measure of volume?
5cm3
5 square cm
5 cm
5 cm2
can someone plz help no links plz
Brandon needs to order some new supplies for the restaurant where he works. The restaurant needs at least 549 spoons. There are currently 273 spoons. If each set on sale contains 10 spoons, write and solve an inequality which can be used to determine ss, the number of sets of spoons Brandon could buy for the restaurant to have enough spoons.
Answer:
28 sets
Step-by-step explanation:
Because 10x3=30+73=103 then 103+200=303 keep that in mind then you
^
3 sets
Do 549-303=246=25 sets then 25 sets+3sets=28 sets
Answer:
Inequality: 10s + 273 ≥ 549
Answer: s ≥ 27.6
Step-by-step explanation:
Have a good day :)
Write the equation that results from transmitting the absolute value equation down 4. Y=|x|
Answer:
y = |x| - 4
Step-by-step explanation:
this translates the function y down by 4 as is required
Can someone please help me?
Answer:
D
Step-by-step explanation:
This is a pythagoream thereom question, the area of a square can be found by multiplying the sides. All the sides of a sqaure are the same so we are basically sqauring the side lengths. That is where the [tex]BE^{2}[/tex] and [tex]BH^{2}[/tex] come from. The problem tells us that the area of the two small squares are equal to the one bigger square. And the area of the bigger sqaure can be found by squaring that side EH. So [tex]BE^{2}[/tex]+[tex]BH^{2} =EH^{2}[/tex].
John is moving from Portland to Sacramento, which is 600 miles away. He is traveling at an average speed of 55 miles per hour. Jon stops for gas after a couple of hours and wonders how much further he needs to go. If y represents distance from Sacramento and x represents time, which linear equation would indicate the amount of miles Jon still has to travel to Sacramento?
Answer:
Y=-55x + 600
Step-by-step explanation:
Compare the costs of bike trips from the two companies
shown. For both, the cost is a linear function of the
number of days.
Which statement is true?
Backcountry Tours
Scenic Pathways
Number of Days
on Trip (d)
Cost of trip (5)
1
45
charges $25 to sign up
and $35 per day
2
90
3
135
4
180
5
225
Scenic Pathways has no sign-up fee
and a greater cost per day.
Backcountry Tours has a lower
sign-up fee and a greater cost per
day.
Scenic Pathways has a higher
sign-up fee and a greater cost per
day.
Backcountry Tours has a higher
sign-up fee and a greater cost per
day.
Answer:
Step-by-step explanation:
The answers is Scenic pathway has no sign up fee and a greater cost per day
A consumer agency is interested in examining whether there is a difference in two common sealant products used to waterproof residential backyard decks. With cooperation of several builders in the area, they randomly assign 38 newly constructed decks to be treated with Very Clear deck sealant and another 37 newly constructed decks to be treated with Sure Seal deck sealant. After one year of being exposed to similar weather conditions, the decks are rated on a scale of 1 to 100. The mean rating for the decks treated with Very Clear is 89.2 with a standard deviation of 3.1. The mean rating for the decks treated with Sure Seal is 92.4 with a standard deviation of 3.8.
Required:
What represents the 90 percent confidence interval to estimate the difference (Very Clear minus Sure Seal) in mean ratings for the two deck sealants?
Answer:
(89.2 - 92.4) ± 1.666*√(3.1²/38 + 3.8²/37)
Step-by-step explanation:
Very clear deck :
n1 = 38
x1 = 89.2
s1 = 3.1
Sure seal
n2 = 37
x2 = 92.4
s2 = 3.8
Confidence interval for difference in sample means :
(X1 - X2) ± margin of error
(X1 - X2) ± Tcritical * sqrt(s1²/n1 + s2²/n2))
Using the degree of freedom calculator ; df = 70
Margin of Error : Tcritical * sqrt(s1²/n1 + s2²/n2))
Tcritical at 90% confidence interval, df = 70 = 1.688
Margin of Error = 1.666 * sqrt(3.1²/38 + 3.8²/37)
Confidence interval :
(89.2 - 92.4) ± 1.666*√(3.1²/38 + 3.8²/37)
Find the lateral area of the prism.
4cm
3cm
6cm
5cm
Lateral Area = [?]cm2
Answer:
The lateral surface area of a prism is the sum of the surface areas of the sides of the prism.
Since the bases of the prism are triangles, there are three sides. The area of each lateral is the product of a side of the triangle times the height of the prism.
We can express this as Lateral Surface Area LSA = (s1xh) + (s2xh) + (s3+h), where "s1, s2, s3" are the lengths of the sides of the triangle and "h" is the height of the prism.
We can factor out "h" to get LSA = hx(s1+s2+s3) where the factor "s1+s2+s3" is the perimeter of the triangle.
Solving for "h", we get h = LSA / (s1+s2+s3)
For your specific problem, h = 300 / (4 + 5 + 6) = 300 / 15 = 20
The table shows the number of raisins found in 17 half-ounce boxes. Which line plot (dot plot) correctly displays the
data?
Answer: I think C.
Step-by-step explanation:
Could you please answer? I'm on a big test
Answer:
it is option C
Step-by-step explanation:
download to help your work
1/ a cube and b to the power 4
which of the following is equal to the rational expression?
Answer:
d
Step-by-step explanation:
please mark as brainliest if correct
thank you
have a great day/night
:)
Write the ratio as a fraction in the simplest form:
36 months to 3 years
Answer:
1
Step-by-step explanation:
36 months is equal to 3 years.
There are 12 months in a year.
36/12=3
3/3=1
HELP MEEEE !!!
Plsssss
someone help me answer this
Answer:
a = 65 yd is the answer.
Step-by-step explanation:
a = ?
b = 72 yd
c = 97 yd
According to the Pythagoras theorem,
a² + b² = c²
a² + 72² = 97²
a² + 5184 = 9409
a² = 9409 - 5184
a² = 4225
a = 65 yd
∴ a = 65 yd is the length of the missing leg.
please help solve x and z find the number for x and find what degrees is z
Answer:
x = 19
z = 102°
Step-by-step explanation:
✔️5x - 17 = 78 (vertical angles area congruent)
5x - 17 + 17 = 78 + 17
5x = 95
5x/5 = 95/5
x = 19
✔️78 + z = 180° (angles on a straight line).
78 + z - 78 = 180 - 78
z = 102°
PLEASE HELP ITS DUE TODAY FOR A GRADE!!!!
Answer:
11
Step-by-step explanation:
Find the length of the hypotenuse of the right triangle with sides 9 and 6
[tex]a^{2} +b^{2} =c^{2} \\9^{2} +6^{2} =c^{2} \\81+31=c^{2} \\\sqrt{117} =c[/tex]
Use c and the height 2 to find the hypotenuse of the triangle with the dotted line
[tex]\sqrt{117} ^{2} +2^{2} =c^{2} \\117+4=c^{2} \\221=c^{2} \\11=c[/tex]
the dotted line is 11
A random sample of 40 students from each grade level was surveyed regarding their preference for a class trip. If there are 220
members of the 7th grade class, then how many students can be expected to prefer the zoo?
zoo
MUSEUM
18
SPORTS COMPLEX
10
7TH GRADE
12
8TH GRADE
14
19
7
39
48
120
66
Answer:
66 students prefer the zoo
Step-by-step explanation:
I got it correct :)
Please help me FAST (no links!)
Answer:
A.
Step-by-step explanation:
42/48=7/8
40/48=5/6
(お役に立てれば！)
Madison was given a large box of 48 chocolates for her birthday. If she eats exactly 5
chocolates each day, how many chocolates would Madison have remaining 5 days
after her birthday?
Answer:
The answer is 23 chocolates
Step-by-step explanation:
You do 5 times 5 for her eating 5 chocolates a day for 5 days to get 25 and then you take 48 and subtract it by 25 and you get 23
Solve for X. Assume that segments that appear to be tangent are tangent Round to the nearest tenth as necessary.
9514 1404 393
Answer:
11.1
Step-by-step explanation:
The tangent makes a right angle with the diameter at the point of tangency. So, the triangle is a right triangle, and the Pythagorean theorem can be used to find the length of x. The radius is shown as 7.1, so the diameter will be 14.2.
x^2 + 14.2^2 = 18^2
x^2 = 122.36
x = √122.36 ≈ 11.1
The length of the tangent is about 11.1 units.
Find the interest earned on $5,750 deposited into a savings account for 3 1/2 years at an annual interest rate of 4.5%
The required interest earned on $5,750 deposited into savings account for 3 1/2 years at an annual interest rate of 4.5% is $905.63.
Principal amount (p) = $ 5750, Rate = 4.5%
Tenure or time = 3 1/2 = 3.5 years. Interest earned to be determined.
Interest is the outlay you pay to borrow money. Interest is often deliberated as an annual percentage of a loan amount.
Here,
[tex]Interest = principle*rate*time[/tex]
Interest = 5750 * 4.5%*3.5
interest = 5750*0.045*3.5
= 2587.75*3.5
= 905.63
Intrest earned = $905.63 against $5,750 deposited into savings account for 3 1/2 years.
Thus, the required interest earned on $5,750 deposited into savings account for 3 1/2 years at an annual interest rate of 4.5% is $905.63.
Learn more about interest here:
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Leo buys a new car for $17,600. The simple interest rate is 8.4% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?
Round your answer to the nearest dollar and do not round until the final answer.
Answer:
$24,992
Step-by-step explanation:
The equation for simple interest is I = PRT where I is the interest earned, P is the principal deposited/borrowed, R is the rate as a decimal, and T is time in years.
I = (17,600)(0.084)(5)
I = 7,392
The total amount that must be repaid is the interest + the principal:
7,392 + 17,600 = 24,992
Please let me know if you have questions
Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the development of a recreational
park on the west side of town. A community action group interested in preserving the environment claims that 45% of the town's
residents favor the development of a recreational park.
To determine whether the sample supports the
population proportion, a simulation of 100 trials is run, each with a
sample of 200, using the point estimate of the population. The minimum sample proportion from the simulation is 0.46 and the
maximum sample proportion is 0.76.
What is the point estimate of the population?
The margin of error of the population proportion is found using an estimate of the standard deviation. What is the
interval estimate of the true population proportion?
The margin of error of the population proportion is found using the half the range.
What is the interval estimate of the true population proportion?
Is the community action group's claim likely based on either interval estimate of the true population proportion?
Explain.
The probability computed shows that the point estimate of the population is 6.2%.
How to calculate the probability?Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes.
a. The point estimate of the population will be calculated thus:
= 62% = 62/100 = 0.62
b. The margin of error of the population will be:
= z value × [✓0.62 × ✓0.38 / ✓200]
= 1.96 × (0.78 × 0.61 / 14.14)
= 0.0672
Therefore, the interval estimate is 6.72%.
c. The margin of error of the population proportion is found using half the range will be:
= [0.76 - 0.46] /2
= 0.30/2
= 0.15
d. The community action group’s claim is likely based on either interval estimate of the true population proportion since the confidence interval value is greater than 0.45.
Find out more information about probability here:
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