Answers
Answer:
p = 5 ; q = -11
Step-by-step explanation:
Simplify the radicals:[tex]\sf (a - b)^2 = a^2 + b^2 - 2ab\\\\(\sqrt{5}-3)^2 = (\sqrt{5})^2+3^2-2*\sqrt{5}*3[/tex]
[tex]\sf = 5 + 9 -6\sqrt{5}\\\\= 14 - 6\sqrt{5}[/tex]
[tex]\sf \dfrac{(\sqrt{5}-3)^2}{\sqrt{5}+1}=\dfrac{14-6\sqrt{5}}{\sqrt{5}+1}[/tex]
Multiply the denominator and the numerator by (√5 - 1).
[tex]\sf= \dfrac{(14-6\sqrt{5})(\sqrt{5}-1)}{(\sqrt{5}+1)(\sqrt{5}-1)}\\\\\\= \dfrac{14*\sqrt{5}-14*1-6\sqrt{5}*\sqrt{5}+6\sqrt{5}*1}{(\sqrt{5})^2-1^2}\\\\\\=\dfrac{14\sqrt{5}-14-6*5+6\sqrt{5}}{5-1}\\\\\\=\dfrac{14\sqrt{5}+6\sqrt{5}-14-30}{4}[/tex]
[tex]\sf = \dfrac{(14+6)\sqrt{5}-44}{4}\\\\\\= \dfrac{20\sqrt{5}-44}{4}\\\\=\dfrac{20\sqrt{5}}{4}-\dfrac{44}{4}\\\\\\=5\sqrt{5}-11[/tex]
p = 5
q = -11
Related Questions
Use the given information to write an equation to represent the linear relationship in point-slope form.
A polar bear gained 0.4 kilogram each week after it was born. After 3 weeks, it weighed 1.7 kilograms.
Answers
The polar bear has a birth weight of 0.5 kilogram.
The linear equation is y = x + 0.4t
Given,
The weight gained by polar bear each week after it was born = 0.4 kg
The weight of polar bear after 3 weeks = 1.7 kilo grams
We have to write an linear equation to represent this ;
Here,
y be the weight of polar bear
x be the initial weight
t be the number of week.
So,
the equation be like;
y = x + 0.4t
Then,
1.7 = x + 0.4 x 3
x = 1.7 - 1.2 = 0.5
The polar bear has a birth weight of 0.5 kilogram.
The linear equation is y = x + 0.4t
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Find the slope of the line that passes through the given points. Write the slope in simplest form
(2.-2).(-7. - 5)
Slope:
Answers
3/9
1/3
then answer is 1/3
There are 32 students in Ms. Bryant's class. 1/4 of those students use social media. How many students are allowed to use social media?
Answers
The most appropriate choice for fraction will be given by -
8 children are allowed to use social media.
What is fraction?
Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
Here,
Total number of children in class of Ms Bryant = 32
Fraction of students who use social media = [tex]\frac{1}{4}[/tex]
Number of children who use social media = [tex]\frac{1}{4} \times 32[/tex]
= 8
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Please help if you can
Answers
Answer: w < 24
Step-by-step explanation:
You first take the - 3 on the left side and transfer over to the other side adding 3 more to the 3
Then you want to get rid of 1/4 by multiplying both sides by 4 multiplying 6 x 4 giving...
w < 24
At its farthest point, the moon is
252,088 miles away from Earth.
Jillene said the moon is about
250,000 miles away from Earth.
To what place did Jillene round
the distance?
Answers
The moon is 252,088 miles from Earth at its farthest point. The Jilene travel distance rounding the corner is 250000 miles.
Given that,
The moon is 252,088 miles from Earth at its farthest point.
According to Jillene, the moon is located roughly 250,000 miles from Earth.
We have to find where did Jillene travel distance rounding the corner.
From the given,
We have distance as 252088 miles.
We can say the approximation of the given miles.
Which we can approximately write as
250000 miles
Therefore, the Jilene travel distance rounding the corner is 250000 miles.
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Find the interest rate needed for the sinking fund to reach the required amount. Assume that the compounding period is the same as the payment period.
$60000 to be accumulated in 11 years; annual payments of 4173$.
The interest rate needed is approximately ___%
Answers
The interest rate is approximately 5.23%.
Interest is the amount paid over and above the principal amount to a lender or depositor by a borrower or financial institution at a predetermined rate in the domains of finance and economics (the amount borrowed).
It differs from any fees the borrower may be required to pay to the lender or another party. It also contrasts from dividends, which are paid out to shareholders (owners) by a company from its profit or stockpile, but not at a predefined rate but rather on a pro rata basis as a portion of the reward received by risk-taking businesspeople when the revenue obtained exceeds the overall expenses.We know that the amount from an loan is calculated by the formula
[tex]A=P[\frac{(1+i)^n-1}{i}][/tex]
Now we will substitute that values to calculate the value of i.
putting the values we get that the value of i is 0.05229...
Therefore the rate of interest is approximately 5.23%.
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PLS HELP!!!
Marcus was offered a position which pays a salary of $250 every week and a 25-cent commission for each ice cream cone he sells. Marcus sells an average of 128 ice cream cones each week. How much will Marcus make in the new position? Compare this to how much he made for a week at his current job. Should he take the new position? Why or why not? (5 points)
Answers
Answer:
His salary will be $282
Step-by-step explanation:
There is not written the salary of his current job, so i can't answer all questions.
anywwy for the first one you just have to do:
[tex]250 + 128 \times 0.25[/tex]
and the results is $282
The water level of a lake rose by 1 1/4 in. during a 1 1/2-week-long wet spell. Simplify the complex fraction below to find the average rate at which the water level changed every week.
Answers
The average rate at which the water level changed every week is 5/6 inches.
What is a fraction?It should be noted that a fraction is represented as a/b. In this case, a implies the numerator and b is the denominator.
In this case, the water level of a lake rose by 1 1/4 in. during a 1 1/2-week-long wet spell
The average rate at which the water level changed will be:
= The fraction at which it rose / Number of weeks
= 1 1/4 ÷ 1 1/2
= 5/4 ÷ 3/2
= 5/4 × 2/3
= 10/12
= 5/6
It rose at 5/6 inches every week.
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A tulip is 2 inches tall after 1 week, 5 inches after 2 weeks, and 8 inches after 3 weeks. Which functions shown below can be used to determine the height, f(n), of the tulip in n weeks. 1. f(n) = 3n-1 2. f(n) = 3+2(n-1) 3. f(n) = f(n-1) + 3 where f(1) = 2
Answers
The answer is option(1) i.e, f(n) = 3n-1, This question is of Arithmetic Sequence
What is Arithmetic Sequence?
Arithmetic Sequence the difference between one term and the next is a constant. Formula is,
aₙ = a + (n-1)d
aₙ = the nᵗʰ term in the sequence
a = the first term in the sequence
d = the common difference between terms
According to question the sequence is,
2 inches, 5 inches, 8 inches .....
where, a = 2
d = 5 - 2 = 3
Now, put these value in formula i.e, aₙ = a + (n-1)d
aₙ = 2 + (n - 1) * 3
= 2 + 3n - 3
= 3n - 1
Therefore, the answer is option(1) i.e, f(n) = 3n-1.
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5y+6x=40
3y-8x=-46
x=
y=
Answers
Answer: (x,y) = (175/29, 22/29)
Step-by-step explanation:
solve the equation
y = 8 - 6/5x
3y - 8x = -46
substitute the value of y
3(8 - 6/5x) - 8x = -46
solve the equation
x = 175 / 29
substitute the value of x
y = 8 - 6/5(175/29)
solve the equation
y = 22/29
answer: (x,y) = (175/29, 22/29)
In the figure above, what is the value of x?
Answers
x=y because they are opposite corners at the top
Got an rented a truck for one day. There was a base fee of $20.95, and there was an additional charge of 76 cents for each mile driven. Goes. Had to pay $216.27 when he returned the truck. For how many miles did he drive the truck?
Answers
Solution
[tex]\begin{gathered} 20.96+0.76m=216.27 \\ \\ \Rightarrow0.76m=216.27-20.96 \\ \\ \Rightarrow m=\frac{195.31}{0.76}=257\text{ miles} \end{gathered}[/tex]The weight of 6 eggs is 258 grams. Identify the constant of proportionality of total weight to number of eggs.
45
39
41
43
Answers
Answer: 45
Step-by-step explanation:
Ta'Niyah and Aaron are racing around a track. Ta'Niyah started the race with a 50 feet head start. Ta'Niyah runs at a pace of 48 feet per second. Aaron runs at a
pace of 32 feet per second. Write an inequality to represent when Ta'Niyah's distance is greater than Aaron.
Answers
Answer:
123
Step-by-step explanation:
did it in my head
Isaac factored 8x^2-20x-12 to (8 x+4)(x-3) and claims this is the correct answer because his factored solution simplifies back to the original quadratic expression. is Issac's statement correct? please explain.
Answers
If we multiply the second expression by using the distributive property and it matches the first expression, then Isaac is correct.
The distributive property is:
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]Let's use this property to multiply out the 2nd expression:
[tex]\begin{gathered} (8x+4)(x-3) \\ =\mleft(8x\mright)\mleft(x\mright)-\mleft(8x\mright)\mleft(3\mright)+\mleft(4\mright)\mleft(x\mright)-\mleft(4\mright)\mleft(3\mright) \\ =8x^2-24x+4x-12 \\ =8x^2-20x-12 \end{gathered}[/tex]This expression is exactly the same as the original expression. Thus, Isaac is correct.
Answer:
Isaac's statement is correct
If MJ is 25 ft. long and M'J' is 5 feet long, what was the scale factor, k?
Answers
The scale factor, if MJ is 25 ft. long and M'J' is 5 feet long is 1/5
If MJ is considered as the original figure, it is 25 ft. long.
The image of MJ, M'J' is 5 feet long
Scale factor is generally understood as the number of times the dimensions of the image is enlarged or diminished
Scale factor = Dimension of the new image ÷ Dimension of the original shape
Scale factor = M'J' length/ MJ length
k = 5/25
k = 1/5
The value of scale factor = 1/5, which means the new image is diminished.
Therefore the scale factor, if MJ is 25 ft. long and M'J' is 5 feet long is 1/5.
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the edges of a cube are expanding at a rate of 5 centimeters per second. how fast is the surface area increasing
Answers
The surface area is increasing at the rate of (60 x + 150) cm² per second.
Let the side of the cube be x cm.
s = x cm
Surface area of the cube will be:
S = 6 x² cm²
Now, we are given that, the side of the cube is expanding 5 cm per second.
So, the side of the cube after 1 second will be:
s' = x + 5 cm
Surface area will be:
S' = 6 (x + 5)² cm²
S' = (6x² + 150 + 60 x) cm²
Change in the surface area is:
ΔS = (6x² + 150 + 60 x) cm² - 6 x² cm²
ΔS = (60 x + 150) cm²
Therefore, the surface area is increasing at the rate of (60 x + 150) cm² per second.
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The graph shows g(x), which is a translation of f(x)=x^2. Write the function for g(x)
Answers
The function after the transformation of f(x) is g(x) = (x - 2)^2
How to determine the transformation of the graph?The equation of the graph is given as
f(x) = x^2
The above equation a parent equation of a quadratic equation
Using the graph as a guide, we can see that
The function f(x) is translated to the right by 2 units to get g(x)
This means that
g(x) = f(x - 2)
So, we have
g(x) = (x - 2)^2
Hence, the equation of g(x) is g(x) = (x - 2)^2
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b) suppose that pearson’s test of goodness of fit will be used to evaluate the claim that half of restaurants go out of business every three years, with a significance level of 0.01.(approximately) what will the chance of a type i error for this test be?
Answers
The Pearson's test of goodness fit can be used to check the significance of 0.01 but there would not be any type 1 error.
A statistical test that measures how well sample data matches a distribution from a population with a normal distribution is referred to as goodness-of-fit. Simply put, it hypothesizes if a sample is skewed or represents the data found in the actual population.
The goodness-of-fit test determines the difference between the actual and predicted values of the model in the case of a normal distribution. The chi-square is one of the approaches for determining goodness-of-fit.
Goodness-of-fit testing is a statistical technique used to draw inferences about observed values.
For example, check to see if a sampling group truly represents the entire population. That is, they establish the relationship between measured and predicted values in a model. When used in a decision-making process, goodness-of-fit tests allow you to foresee future trends and patterns.
Hence we can conclude that there would not be any error to the problem with a significance of 0.01 .
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Least to greatest PLEASE HELP ASAP!!!
Answers
Answer: d a c b
Step-by-step explanation:
A sloppy joe restaurant gave 9 napkins for every 8 items ordered. If someone bought 16 items. How many napkins would they get
Answers
18 because 9x2=18
Hope this helped
Answer:
ur answer is 18
9 napkins every 8 items
8x2=16 then since u have 16 and u get 9 napkins every 8 items u get 18 bc
9×2=18
Someone please help????
Answers
Answer:
11.68 m^2
Step-by-step explanation:
area of triangle = 1/2(b)(h)
b = 7.3, h = 3.2
1/2(7.3)(3.2) = 11.68
Answer:
11.68m
firstly remember area of triangle is half multiplied by base multiplied by height
The graph of y=f(x) is shown on the grid. The graph G is a translation of the graph y=f(x)
Answers
The translated function is:
G(x) = f(x) - 1
b) The maximum of y = 2*f(x) is the point (0, 8).
How to write the equation of the translated function?
We know that G(x) is a translation of f(x), and the graph of G(x) is the pink one.
We can see that it is 1 unit below f(x), then we have a translation of one unit downwards, so we can write:
G(x) = f(x) - 1
This is the rule for G(x).
b) If the maximum of f(x) is (0, 4), then:
f(0) = 4
The maximum of 2*f(x) is also at x = 0, we will get:
2*f(0) = 2*4 = 8
So the maximum here is (0, 8).
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Can somebody help with number 10
Answers
Check the picture below.
Which of the following shows the power of a Quotient Property?
Answers
The power of a quotient states that if you power a quotient, the result is equal as if you had powered the numerator and denominator by the same index separatelly before makinf the division
[tex](\frac{a}{b})^2=\frac{a^2}{b^2}[/tex]Find the slope of the line containing the pair of points.
(8,-2) and (1,7)
Answers
Answer:
-9/7
Step-by-step explanation:
∆ y = 7-(-2) = 9
∆ x = 1-8 = -7
m = ∆y/∆x = -9/7
a machine produces 6 pairs of jeans in one hour work out how many hours it would take to make 39 pairs
Answers
4) Which one of these pictures is not like the others? Use ratios to explain your reasoning. (From Unit 2, Lesson 1) co ΝΗ e M
Answers
We are shown three pictures and asked to identify which one of them is not like others.
Let us find the ratio of width and length of each inscribed cricle.
Picture L:
Width = 3 units
Length = 4 units
Ratio = 3/4 = 0.75
Picture M:
Width = 4 units
Length = 8 units
Ratio = 4/8 = 0.50
Picture N:
Width = 9 units
Length = 12 units
Ratio = 9/12 = 0.75
As you can see, picture L and N has the same ratio of width and length that is 0.75 but the picture M has a different ratio of width and length that is 0.50
Therefore, we can conclude that picture M is not like others.
Kalani had a lot of science homework last week. She started off with 3/4 hour on Monday. Every day after that, she had 1/4 hour more than the day before.
1- How many hours of science homework did Kalani have on Thursday?
2-How many hours of science homework did she have for the whole school week?
Answers
1. The number of hours of science homework that Kalani have on Thursday is 1 1/2 hours.
2. The hours of science homework that she have for the whole school week is 4 1/2 hours.
How to calculate the value?From the information, Kalani started off with 3/4 hour on Monday and every day after that, she had 1/4 hour more than the day before.
1. This will be illustrated as:
Monday = 3/4 hour
Tuesday = 3/4 + 1/4 = 1 hour
Wednesday = 1 hour + 1/4 hour = 1 1/4 hour
Thursday = 1 1/4 + 1/4 = 1 1/2 hours.
2 The total hours will be the addition of all the values for the days of the week.
= 3/4 + 1 + 1 1/4 + 1 1/2
= 4 1/2 hours.
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at the beginning of the day the stock market goes up 30 1/2 points .at the end of the day the stock market goes down 120 1/4 points what is the total chnage in the stock market from the day beginning of the day to the end of the day. PLSSS HURRY ITS INPORTANT PLSSSSSSSSSSSSSSSSSSSSSSSS HURRY
Answers
The total chnage in the stock market from the day beginning of the day to the end of the day is -89 3/4 points.
How to calculate the value?A stock market simply means the market where shares and stocks are sold.
In the information illustrated, at beginning of the day the stock market goes up 30 1/2 points and at the end of the day the stock market goes down 120 1/4 points.
The change will be the the operation of the numbers through the use of addition when it goes up and subtraction when it comes down. This will be:
= 30 1/2 - 120 1/4
= -89 3/4
The change is -89 3/4 points.
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