Answer:
Step-by-step explanation:
You could have a good credit score and good credit history.
At a store sales tax is charged at a rate of 2% on the cost price of an item . the sales tax on a dress which cost $180 is
Answer:
$3.60
Step-by-step explanation:
100% = 180
1% = 180/100 = $1.80
2% = 1%×2 = 1.8×2 = $3.60
4. Cindy purchased a pair of boots which had a sticker price of $85. Cindy paid $5.95 in sales tax. What was the tax rate on Cindy's purchase?
Simplify this math problem show Your work
9514 1404 393
Answer:
(p -9q)/(4p² +12pq)
Step-by-step explanation:
The least common denominator will be the product of the denominators.
[tex]\dfrac{-3}{4p}+\dfrac{1}{p+3q}=\dfrac{-3(p+3q)+1(4p)}{(4p)(p+3q)}=\boxed{\dfrac{p-9q}{4p^2+12pq}}[/tex]
I WILL GIVE BRAINLIEST FAST
Answer:
is opposite line BC. Answer is letter E.
Which problem has a greater (bigger) answer? Solve both, choose the one that has the bigger answer and explain (1-2 sentences) how you found your
answer.
1) (2 + 3) (5 + 5)
2)2 + 3 x 5 + 5 =
Find dy/dx of the function y = √x sec*-1 (√x)
Hi there!
[tex]\large\boxed{\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}}[/tex]
[tex]y = \sqrt{x} * sec^{-1}(-\sqrt{x}})[/tex]
Use the chain rule and multiplication rules to solve:
g(x) * f(x) = f'(x)g(x) + g'(x)f(x)
g(f(x)) = g'(f(x)) * 'f(x))
Thus:
f(x) = √x
g(x) = sec⁻¹ (√x)
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{\sqrt{x}\sqrt{\sqrt{x}^{2} - 1}} * \frac{1}{2\sqrt{x}}[/tex]
Simplify:
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \sqrt{x} * \frac{1}{2|x|\sqrt{{x} - 1}}[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2\sqrt{x}}sec^{-1}(\sqrt{x}) + \frac{1}{2|\sqrt{x}|\sqrt{{x} - 1}}[/tex]
Answer:
[tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]
General Formulas and Concepts:
Algebra I
Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Exponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Calculus
Derivatives
Derivative Notation
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Arctrig Derivative: [tex]\displaystyle \frac{d}{dx}[arcsec(u)] = \frac{u'}{|u|\sqrt{u^2 - 1}}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{x}sec^{-1}(\sqrt{x})[/tex]
Step 2: Differentiate
Rewrite: [tex]\displaystyle y = \sqrt{x}arcsec(\sqrt{x})[/tex]Product Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})][/tex]Chain Rule: [tex]\displaystyle y' = \frac{d}{dx}[\sqrt{x}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[\sqrt{x}] \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{d}{dx}[x^\bigg{\frac{1}{2}}]arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{d}{dx}[x^\bigg{\frac{1}{2}}] \bigg][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{1}{2} - 1}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{1}{2} - 1} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{1}{2}x^\bigg{\frac{-1}{2}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2}x^\bigg{\frac{-1}{2}} \bigg][/tex]Rewrite [Exponential Rule - Rewrite]: [tex]\displaystyle y' = \frac{1}{2x^\bigg{\frac{1}{2}}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2x^\bigg{\frac{1}{2}}} \bigg][/tex]Rewrite [Exponential Rule - Root Rewrite]: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{d}{dx}[arcsec(\sqrt{x})] \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Arctrig Derivative: [tex]\displaystyle y' = \frac{1}{2\sqrt{x}}arcsec(\sqrt{x}) + \bigg[ \sqrt{x}\frac{1}{|\sqrt{x}|\sqrt{(\sqrt{x})^2 - 1}} \cdot \frac{1}{2\sqrt{x}} \bigg][/tex]Simplify: [tex]\displaystyle y' = \frac{arcsec(\sqrt{x})}{2\sqrt{x}} + \frac{1}{2|\sqrt{x}|\sqrt{x - 1}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
A line that passes through the origin also passes through the point (6,2). What is the slope of the line?
please answer with an explanation
9514 1404 393
Answer:
1/3
Step-by-step explanation:
The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\qquad\text{where $(x_1,y_1)$ and $(x_2,y_2)$ are points on the line}[/tex]
In this problem, you are told the line passes through the origin, which is point (x, y) = (0, 0), and through point (6, 2). Using these coordinates in the slope formula gives ...
[tex]m=\dfrac{2-0}{6-0}=\dfrac{2}{6}=\boxed{\dfrac{1}{3}}[/tex]
__
You may notice that when the line passes through the origin, the slope is simply the ratio y/x of any point on the line. Here, that ratio is 2/6 = 1/3.
_____
Additional comment
A line through the origin is the graph of a proportional relationship. That is, y is proportional to x. The slope of the line is the constant of proportionality. The equation of the line is ...
y = kx . . . . . . where k is the constant of proportionality.
The line in this problem statement will have the equation ...
y = (1/3)x
Re-write this subtraction as an ADDITION of signed numbers. 7- (-5) =
Now actually compute 7 - (-5) =
Answer: 12
Step-by-step explanation: Whenever you have a minus a negative in a problem, you can change it to plus a positive.
So we can think of 7 - (-5) as 7 + (+5).
Whenever we have two negatives in a row, we can think of those
negatives as being multiplied together and a negative times a negative
will always result in a positive.
So just add 7 + 5 to get 12.
A box has length 4 feet, width 5 feet, and height 8 inches. Find the volume of the box in cubic feet and in cubic inches.
Answer:
13.4 cubic feet and 23040 inches
Step-by-step explanation:
Answer:
In cubic feet = 13.3 ft^3 ...........or 13.33ft^3
In cubic inches = 23040in^3
Step-by-step explanation:
In cubic feet it becomes
4(5) = 20 feet ^2 ................but we need volume in feet
so 8 inches = .............2/3 of a foot = 0.666667
Answer therefore is (4) x (5) x (0.666667) = 13.32ft^3
In cubic inches it becomes
4 x 12 = 48 inches
5 x 12 = 60 inches
and 8 inches
48 x 60 x 8 = 23040 in^3
We check by squaring the divider
23040/12^3 = 13.333
We only square and square again to find a cube but to square once we do this with area too.
Area 1. = 4 x 5 = 20 feet^2
Area 2. = 48 x 60 = 2880 in ^2 / 12^2 = 20
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
Answer:
a) 0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
b) 0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
c) 0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
d) None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100.
This means that [tex]\mu = 273, \sigma = 100[/tex]
A) What is the probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 30, s = \frac{100}{\sqrt{30}}[/tex]
The probability is the p-value of Z when X = 273 + 16 = 289 subtracted by the p-value of Z when X = 273 - 16 = 257. So
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = 0.88[/tex]
[tex]Z = 0.88[/tex] has a p-value of 0.8106
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{30}}}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.8106 - 0.1894 = 0.6212
0.6212 = 62.12% probability that the mean price for a sample of 30 federal income tax returns is within $16 of the population mean.
B) What is the probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 50, s = \frac{100}{\sqrt{50}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = 1.13[/tex]
[tex]Z = 1.13[/tex] has a p-value of 0.8708
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{50}}}[/tex]
[tex]Z = -1.13[/tex]
[tex]Z = -1.13[/tex] has a p-value of 0.1292
0.8708 - 0.1292 = 0.7416
0.7416 = 74.16% probability that the mean price for a sample of 50 federal income tax returns is within $16 of the population mean.
C) What is the probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean?
Sample of 30 means that [tex]n = 100, s = \frac{100}{\sqrt{100}}[/tex]
X = 289
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{289 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a p-value of 0.9452
X = 257
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{257 - 273}{\frac{100}{\sqrt{100}}}[/tex]
[tex]Z = -1.6[/tex]
[tex]Z = -1.6[/tex] has a p-value of 0.0648
0.9452 - 0.0648 =
0.8804 = 88.04% probability that the mean price for a sample of 100 federal income tax returns is within $16 of the population mean.
D) Which, if any of the sample sizes in part (a), (b), and (c) would you recommend to ensure at least a .95 probability that the same mean is withing $16 of the population mean?
None of them ensure, that one which comes closer is a sample size of 100 in option c), to guarantee, we need to keep increasing the sample size.
C is actually 0.8904
for anybody else stuck on this wondering why cengage is telling you c is wrong
AB is a diameter of Circle O. Find the measure of BCA
Answer:
∠ BCA = 90°
Step-by-step explanation:
∠ BCA is an angle in the semicircle and equals 90°
If a business borrows $12,600 and repays $23,940 in 5 years, what is the simple interest rate?
Answer:
18%
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 12600
A = 23940
t = 5
Step 2: Solve for r
Substitute in variables [Simple Interest Rate Formula]: 23940 = 12600(1 + 5r)[Division Property of Equality] Divide 12600 on both sides: 19/10 = 1 + 5r[Subtraction Property of Equality] Subtract 1 on both sides: 9/10 = 5r[Division Property of Equality] Divide 5 on both sides: 9/50 = rRewrite: r = 9/50Evaluate: r = 0.18Convert: r = 18%I’m struggling with this question someone help ASAP plz
Answer:
The correct answer is:
30 = 10 + 3(h - 2)30 = 10 + 3h - 6
26 = 3h
h = 8.67
Step-by-step explanation:
We're gonna calculate by our part the hours a new costumer can rent a bike and pay a total of $30, using the original function:
f (h) = 10 + 3(h - 2)Where:
f (h) = Total cost. h = the number of hours.We know The total money spent must be $30, by this reason, the function change to:
30 = 10 + 3(h - 2)Now, we must clear the h variable, by this reason, we multiply 3 by h and 2:
30 = 10 + 3*h - 3*2 30 = 10 + 3h - 6We pass the 10 and the -6 to the left side of the equality:
30 - 10 + 6 = 3h (Remember to change the signs when you do this step) 26 = 3hFinally, we pass the 3 to the left side of the equality:
26 / 3 = h (the 3 pass to divide because is multiplying the x)
8.666666666667 = hIf we just use two decimals, the number of hours is:
h = 8.67How the third option is the one that shows this calculation and result, that is the correct answer.
Which ordered pairs are in the solution set of the system of linear inequalities?
y > Negative one-thirdx + 2
y < 2x + 3
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (6, 0. Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (negative 3, negative 3) and (0, 3). Everything above the line is shaded.
Options:
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Given
[tex]y > -\frac{1}{3}x + 2[/tex]
[tex]y < 2x + 3[/tex]
Required
Solve for x and y
To solve this, we make use of graphical method (see attachment for graph)
All points that lie on the shaded region are true for the inequality
Next, we plot each of the given options on the graph
A. (2, 2), (3, 1), (4, 2)
All 3 points lie on the shaded region.
Hence, (a) is true
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Two groups were moving from one campsite to another. The first group traveled the distance in 5 hours. The second group finished in 7 hours. Find the distance between the campsites if the first group was going 4mph faster than the second group.
Answer:
The distance between the campsites was 70 miles.
Step-by-step explanation:
Since two groups were moving from one campsite to another, and the first group traveled the distance in 5 hours while the second group finished in 7 hours, to find the distance between the campsites if the first group was going 4mph faster than the second group, the following calculation must be performed:
X + 4 = 5
X = 7
4 x 7 = 28
(4 + 4) x 5 = 40
10 x 7 = 70
(10 + 4) x 5 = 70
Therefore, the distance between the campsites was 70 miles.
help me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me me
Volume of the 3d composite figure is,
(7×6×5)+(7×6×5)/3
= 210+70
= 280 cm³
Relationship between the two volumes,
Volume of the rectangular prism is 3 times the volume of the pyramid.
Answered by GAUTHMATH
Answer:
I was gonna anwer it but somone already did.
Step-by-step explanation:
Mrs Lee used 6 Meters of material to make 3 dresses. She used 4 ties as much material for a curtain as for a dress. How much material did she use for the curtain? (Dress)
Answer:
for each dress she used 6/3 of material
=2
then for a curtain =2x4=8 materials
At the end of the day, a local bakery sold 83 cakes and had to throw out 7 cakes due to baking errors. Each cake cost the bakery $6.25 to make. The bakery, in turn, sold each cake for $12.75. What was the total profit earned by the bakery today?
Answer:
The total profit earned by the bakery today was of $495.75.
Step-by-step explanation:
Spending:
83 + 7 = 90 cakes made, each costing 6.25. So
[tex]S = 90*6.25 = 562.5[/tex]
Earnings:
83 cakes sold by $12.75, so:
[tex]E = 83*12.75 = 1058.25[/tex]
Profit:
Earnings subtracted by spending, so:
[tex]P = E - S = 1058.25 - 562.5 = 495.75[/tex]
The total profit earned by the bakery today was of $495.75.
If you multiply 0.47 × 3.2, then what is the answer?
Answer:
1.504
Step-by-step explanation:
0.47×100 = 47
3.2×100 = 320
47×320 = 15040
15040÷10000 = 1.504
I need help on this please answer all three of them median range and mode
Answer:
1. median :- 82. mean :- 403. mode. :- 7Step-by-step explanation:
❣️(◍Jess bregoli◍)❣️#keep learning!!HELPPPPPPP PLEASEEEEEEE
Answer:
150 dollars. if I am wrong correct me
Answer:
C and D
Step-by-step explanation:
15 to 30 galons at $9.95 to $21.00
the minimum amount can be found by calculating the minimum amount sold at a minimum price 15*9.95 = $149.25
the maximum amount can be found by calculating the maximum amount sold at a maximum price 30*21 = $630
there are 2 choices that are between 149.25 and 630, C, and D
4. How many square feet of carpet are
needed?
The floor plan below shows the Green family's
basement
28 ft.
12 ft.
121
6 ft.
5 ft.
5 ft.
11 ft.
11 ft.
Answer:
Step-by-step explanation:
It is a 28×12 rectangle, minus a 5×6 cutout.
area of 28×12 rectangle = 336 ft²
area of 5×6 cutout = 30 ft²
area of carpet = 336-30 = 330 ft²
What is the value of the expression [-7] + [-4]
Answer:
11
Step-by-step explanation:
I'm assuming that [.] fldenote absolute value even tho the absolute value function is represented by (|.|)
value of [-7] will be positive that us 7.
= 7 + 4
= 11
Method of Least Squares, Evaluation of Cost Equation Lassiter Company used the method of least squares to develop a cost equation to predict the cost of moving materials. There were 80 data points for the regression, and the following computer output was generated:
Intercept $17,350
Slope 12.00
Coefficient of correlation 0.92
Standard error $220
The activity driver used was the number of moves.
Required:
1. What is the cost formula?
2. Using the cost formula, predictthe costofmovingmaterialsif340movesaremade.Nowpreparea95 percent con?dence interval forth is prediction.(Round to the nearest dollar.)
3. What percentage of the variability in moving cost is explained by the number of moves? Do you think the equation will predict well? Why or why not?
Solution :
1). The cost of the formula is given as :
$ 19,350 + $12 x
2). 95% [tex]\text{confidence interval}[/tex] for the prediction is :
[tex]$21430 - 1.96 \times 220 < \text{Yf} < 21430+1.96 \times 220$[/tex]
[tex]$20998.8 < \text{Yf} < 21861.2$[/tex]
[tex]$20999 < \text{Yf} < 21861$[/tex] (rounding off)
3). r = 0.92
Therefore, [tex]$r^2 = 0.8464$[/tex]
That is 84.64 % of the variability in the moving cost is best explained by the number of moves.
What is the surface area of the rectangular prism pictured below?
3 meters
9 meters
4 meters
Answer:
108 meters with the formula lxhxw
The coordinator of the vertices of the triangle are (-8,8),(-8,-4), and
Answer with Step-by-step explanation:
Complete question:
The coordinates of the vertices of the triangle are (-8,8),(-8,-4), and. Consider QR the base of the triangle. The measure of the base is b = 18 units, and the measure of the height is h = units. The area of triangle PQR is square units.
Let
P=(-8,8)
Q=(-8,-4)
QR=b=18 units
Height of triangle, h=Length of PQ
Distance formula
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using the formula
Height of triangle, h=[tex]\sqrt{(-8+8)^2+(-4-8)^2}=12units[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times base\times height[/tex]
Area of triangle PQR=[tex]\frac{1}{2}\times 18\times 12[/tex]
Area of triangle PQR=108 square units
Length of QR=18units
Let the coordinates of R(x,y)
[tex]\sqrt{(x+8)^2+(y+4)^2}=18[/tex]
[tex](x+8)^2+(y+4)^2=324[/tex]
[tex]x^2+64+16x+y^2+8y+16=324[/tex]
[tex]x^2+y^2+16x+8y=324-64-16[/tex]
[tex]x^2+y^2+16x+8y=244[/tex] ......(1)
Using Pythagoras theorem
[tex]H=\sqrt{P^2+B^2}[/tex]
[tex]H=\sqrt{(18)^2+(12)^2}[/tex]
[tex]H=6\sqrt{13}[/tex]units
[tex](6\sqrt{13})^2=(x+8)^2+(y-8)^2[/tex]
[tex]x^2+64+16x+y^2+64-16y=468[/tex]
[tex]x^2+y^2+16x-16y=468-64-64=340[/tex]
[tex]x^2+y^2+16x-16y=340[/tex] .....(2)
Subtract equation (2) from (1) we get
[tex]24y=-96[/tex]
[tex]y=-96/24=-4[/tex]
Using the value of y in equation (1)
[tex]x^2+16x+16-32=244[/tex]
[tex]x^2+16x=244-16+32[/tex]
[tex]x^2+16x=260[/tex]
[tex]x^2+16x-260=0[/tex]
[tex]x^2+26x-10x-260=0[/tex]
[tex]x(x+26)-10(x+26)=0[/tex]
[tex](x+26)(x-10)=0[/tex]
[tex]x=-26, x=10[/tex]
Hence, the coordinate of R (10,-4) or (-26,-4).
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
Find the volume of the figure.
8 cm
4 cm
10 cm
14 cm
Answer: 440 cm^3
Step-by-step explanati
For its grand opening, a store gives every 12th customer a calendar and every 20th customer a mug. Which guest is the first to receive both a calendar and a mug?
Answer: yes
Step-by-step explanation:
2√m^2 if m is greater than or equal to 0
Answer:
[tex] \displaystyle \boxed{|2m| }[/tex]
Step-by-step explanation:
we are given that
[tex] \displaystyle 2 \sqrt{ {m}^{2} } [/tex]
since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus
[tex] \displaystyle \boxed{2 |m|}[/tex]
remember that,|a|•|x|=|ax| hence,
[tex] \displaystyle \boxed{ |2m|}[/tex]
and we're done!
Answer:
2m
Step-by-step explanation:
Given :-
2√m² , m is greater than or equal to 0 .By question,
→ 2√m²
→ 2 * m
→ 2m