Answers
Answer:
[tex]\boxed{u = 13.7}[/tex]
Step-by-step explanation:
Using cosine rule
[tex]c^2 = a^2+b^2-2ab\ CosC[/tex]
Here c = u, a = 9 , b = 21 and C = 28
[tex]u^2 = 9^2+21^2-2(9)(21)\ Cos 28\\u^2 = 81+441-(378)(0.88)\\u^2 = 522 - 333.75\\u^2 = 188.24[/tex]
Taking sqrt on both sides
u = 13.7
Answer:
u ≈ 13.7
Step-by-step explanation:
Using the Cosine rule in Δ STU, that is
u² = s² + t² - 2stcosU
Here s = 21, t = 9 and U = 28°, thus
u² = 21² + 9² - (2 × 21 × 9 × cos28°)
= 441 + 81 - 378 cos28°
= 522 - 378 cos28° ( take the square root of both sides )
u = [tex]\sqrt{522-378cos28}[/tex]
≈ 13.7 ( to the nearest tenth )
Related Questions
2/3 divided by 5?If she walks 2/3 by another 5.
Answers
Answer:
The answer is 0.133
Step-by-step explanation:
All you have to do is take 2/3 as if it was a whole number and divide it by 5, or if you are able to use a calculator, you can just but it in as 2 divided by 3 and then divide 5 by whatever answer you get.
Answer:
Hello! 2/3 divided by 5 in fraction will be 2/15
Step-by-step explanation:
Since we have a 5 we need to change that into a fraction
5 would turn into 1/5
Now you have to multiply both of the fractions to get your answer.
2/3 x 1/5
= 2/15
(So 2/15 will be your answer.)
Hope this helps! :)
i neeeed help quickkkk
Answers
Answer:
20 hours
Step-by-step explanation:
If your computer can download a movie in 5 hours, then it downloads [tex]\frac{1}{5}[/tex] of a movie in 1 hour.
The extra processor in 1 hour, reduces the time down to 5 hours, so it downloads [tex]\frac{1}{4}[/tex] of the movie in 1 hour.
The time that the extra processor will spend to download a whole movie added to [tex]\frac{1}{5}[/tex] will equal [tex]\frac{1}{4}[/tex] .
So our equation is [tex]\frac{1}{5} + \frac{1}{x} = \frac{1}{4}[/tex].
To simplify this, lets multiply all sides by 20x.
[tex](\frac{1}{5}+\frac{1}{x} \cdot 20x) = \frac{1}{4}\cdot20x\\ 4x + 20 = 5x[/tex]
Now we can simplify this equation.
[tex]20 = 5x-4x\\\\20 = x\\x = 20[/tex]
So the extra processor alone would take 20 hours to download the movie.
Hope this helped!
f(x)=x^2-3x-2 is shifted 4 units right. The result is g(x). What is g(x)?
Answers
Answer:
[tex]\boxed{\mathrm{C.}\:\: g(x)=(x-4)^2-3(x-4)-2}[/tex]
Step-by-step explanation:
The function is shifted 4 units right.
The value of x in the function is subtracted from 4, because this is a horizontal translation.
[tex]f(x)=x^2-3x-2[/tex]
[tex]g(x)=(x-4)^2-3(x-4)-2[/tex]
Answer:
c
Step-by-step explanation:
if you shift to the right funnily enough, you have to "compensate" for that by SUBTRACTING the number of units.
EXTRA
To check, use a simple function f(x)= x²
The top of this parabola is at (0,0).
We want to check if g(x) = (x-4)² is the right function....
Now if f(x) is shifted 4 units right than all variables with x in them, need to be compensated for. The question is do you need to add or subtract...
We know that the result is g(x), and we know that the top of g(x) would end up at (4,0).
For that to happen you need to compensate with g(x) = (x-4)²
Now check if (4,0) is on g(x) by substituting x=4. if the result turns out to be 0, then you know it is ok...
Substituting x=4 indeed results to
4-4 = 0, so (4,0) is on g(x).
Conclusion, by checking this one special value, you now know you have found the correct compensation factor!
Where L is the length, in feet, of the pendulum, and π is approximately 22 7 . How long must the pendulum be if one complete cycle takes 8 seconds?
Answers
Answer:
Length L = 51.88 feet
Step-by-step explanation:
From the given information,
The length of the pendulum can be determined by using the Formula for the period T which is the time of one full oscillation of a simple pendulum.
[tex]T = 2 \pi \sqrt {\dfrac{L}{g}}[/tex]
where;
T = period of the time of one full oscillation = 8 seconds
L = length in feet
g = acceleration due to gravity in feet = 32 ft/s²
π = 22/7
[tex]8 = 2 \times \dfrac{22}{7} \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]8 = 6.2857 \times \sqrt {\dfrac{L}{32}}[/tex]
[tex]\dfrac{8}{6.2857} =\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273=\sqrt {\dfrac{L}{32}}[/tex]
[tex]1.273= {\dfrac{\sqrt L}{ \sqrt {32}}}[/tex]
[tex]1.273 \times { \sqrt {32}}}= {\sqrt L}[/tex]
[tex]7.2012= {\sqrt L}[/tex]
L = 7.2012²
L = 51.88 feet
Find the equation of the line.
Answers
Answer:
y = (-1/3)x + 5
Step-by-step explanation:
The format of the equation of line required is in slope-intercept form:
y = mx + c
m is the slope, and c is the y-intercept.
First, lets find the slope.
Randomly find 2 points on the line. Label them as (x1, y1) and (x2, y2)
Let's say I pick the points (0,5) and (9, 2).
slope m = (y2 - y1) / (x2 - x1)
slope = (2-5 ) / (9-0)
= -3 / 9
= -1/3
the y-intercept is the point where the line cuts through the y-axis, which is 5 in this case.
Therefore, the equation of the line will be:
y = (-1/3)x + 5
Write as an algebraic expression and simplify if possible: *150% of 50% of z whoever answers the fastest gets brainliest
Answers
Answer:
3z/4
Step-by-step explanation:
Here, we start by calculating the 50% of z
mathematically, that would be 50/100 * z = 50z/100 = z/2
Now we want to calculate the 150% of this.
That would be 150/100 * z/2 = 150z/200 = 3z/4
I need a. Correct answer I’ll mark brainliest
Answers
Answer:
7^11 / 4^11
Step-by-step explanation:
( 7/4) ^ 11
We know that ( a/b) ^c = a^c / b^c
7^11 / 4^11
Answer: B. [tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]
Step-by-step explanation:
There is exponent rule that states [tex](\frac{a}{b})^{x} = \frac{a^x}{b^x}[/tex]
So we can apply this rule to this problem.
[tex](\frac{7}{4})^{11} = \frac{7^{11}}{4^{11}}[/tex]
3. Callum rolled a single six sided die 12 times and it landed on a six, three of the times. The probability that it will land on a six on the 13th roll is?
Answers
Answer:
1/6
Step-by-step explanation:
Each roll is independent. So the probability of rolling a six is 1/6, regardless of the previous rolls.
Graph the line that represents this equation 3x - 4y = 8
Answers
The graph of the given linear equation can be seen at the end.
How to graph the line?
Here we have the linear equation:
3x - 4y = 8
Isolating, y, we can rewrite:
-3x + 4y = -8
4y = -8 + 3x
y = (-8 + 3x)/4
y = (3/4)*x - 2
Now, we can evaluate the line in two values of x, so we can get two points on the line.
Evaluating in x = 0 and x = 4 we get:
if x = 0
y = (3/4)*0 - 2 = -2
So we have the point (0, -2)
If x = 4 we get:
y = (3/4)*4 - 2 = 1
Then we have the point (4, 1).
Now we can graph these two points and connect them with a line, that is the graph of the linear equation.
The graph can be seen below.
If you want to learn more about linear equations:
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The length of a garden is 2 feet more than its height. Write an equation for the area of the rectangles in terms of height, h. Area = ? sq. ft.
Answers
Answer:
h^2+2h
Step-by-step explanation:
Let h be the heigth of this garden
The length of this garden is 2 feet more than the heigth.
So the length can be expressed as h+2
The area of this triangle is the product of the heigth and the length.
A = h*(h+2)
A= h^2 +2h
the area of a square ground is 42025 metre square.Find the perimeter of the field.
Answers
Answer:
[tex] \boxed{820 \: m}[/tex]Step-by-step explanation:
Given,
Area of square ground = 42025
Now, let's find the length of square ground
Area of square = [tex] = {l}^{2} [/tex]
plug the values
[tex]42025 = {l}^{2} [/tex]
Swipe the sides of the equation
[tex] {l}^{2} = 42025[/tex]
Squaring on both sides
[tex] \sqrt{ {l}^{2} } = \sqrt{42025} [/tex]
Calculate
[tex]l = 205[/tex] meters
The length of square ground = 205 meters
Now,Let's find the perimeter of square
Perimeter of square [tex] = 4l[/tex]
plug the value of length
[tex] = 4 \times 205[/tex]
Multiply the numbers
[tex] = 820[/tex] meters
Hope I helped.
Best regards!!
5x+4y=25 - (5x+2y=3)
Answers
Answer:
T1he values for x and y of the equations is y = 11, and x = -19/5.
Step-by-step explanation:
To solve this question, we need to rearrange the expression:
5x+4y=25 - (5x+2y=3)
Look, if we subtract one equation to the other, then:
5x+4y=25 [1]
-(5x+2y=3) [2]
Which is the same as:
5x+4y=25
-5x-2y=-3
Subtract them:
5x+4y=25
-5x-2y=-3
---------------
2y =22
y = 22/2 = 11
Then, y = 11.
To find x, we can substitute y in either equation [1] or [2].
Let us use [1]
5x+4y=25
5x+4(11)=25
5x+44=25
5x=25-44
5x=-19
x = -19/5
Then, the values for x and y of the equations is y = 11, and x = -19/5.
PLEASE HELP If f(x) = 2x-1 + 3 and g(x) = 5x - 9, what is (f-g) (x)
Answers
Answer:
2^(x-1) -5x +12
Step-by-step explanation:
f(x) = 2^(x-1) + 3
g(x) = 5x - 9
(f-g) (x) = 2^(x-1) + 3 - ( 5x-9)
Distribute the minus sign
2^(x-1) + 3 - 5x+9
Combine like terms
2^(x-1) -5x +12
Can anyone answer this?
Answers
Answer:
Because the triangle is isosceles, the base angles are congruent. Since the sum of angles in a triangle is 180° we can write:
24 + x + x = 180
24 + 2x = 180
2x = 156
x = 78°
Answer:
[tex]\boxed{x=78}[/tex]
Step-by-step explanation:
The triangle is an isosceles triangle.
The two base angles are equal.
Angles in a triangle add up to 180 degrees.
x + x + 24 = 180
Combine like terms.
2x + 24 = 180
Subtract 24 on both sides.
2x = 156
Divide both sides by 2.
x = 78
As mountain climbers know, the higher you go, the cooler the temperature gets. At noon on July 4th last summer, the temperature at the top of Mt. Washington — elevation 6288 feet — was 56◦F. The temperature at base camp in Pinkham Notch — elevation 2041 feet — was 87◦F. It was a clear, still day. At that moment, a group of hikers reached Tuckerman Junction — elevation 5376 feet. To the nearest degree, calculate the temperature the hikers were experiencing at that time and place. When you decided how to model this situation, what assumptions did you make?
Answers
Answer:
a. 63 °F
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
Step-by-step explanation:
a. To model this situation, we assume the temperature varies inversely as elevation decreases since at elevation 6288 ft the temperature is 56 °F and at elevation 2041 ft, the temperature is 87 °F
So, we model this as a straight line.
Let m be the gradient of the line.
Let the (6288 ft, 56 F) represent a point on the line and (2041 ft, 87 °F) represent another point on the line.
So m = (6288 ft - 2041 ft)/(56 °F - 87 °F) = 4247 ft/-31 °F = -137 ft/°F
At elevation 5376 ft, let the temperature be T and (5376 ft, T) represent another point on the line.
Since it is a straight line, any of the other two points matched with this point should also give our gradient. Since in the gradient, we took the point (6288 ft, 56 °F) first, we will also take it first in this instant.
So m = -137 ft/ °F = (6288 ft - 5376 ft)/(56 °F - T)
-137 ft/°F = 912 ft/(56 °F - T)
(56 °F - T)/912 ft = -1/(137 ft/ °F)
56 °F - T = -912 ft/(137 ft/°F)
56 °F - T = 6.66 °F
T = 56 °F + 6.66 °F
T = 62.66 °F
T ≅ 62.7 °F
T ≅ 63 °F to the nearest degree
b. When i decided to model the situation, I assumed that the temperature varied inversely as the elevation and that the change in elevation or temperature was linear.
Please help.. tysm if you do
Answers
Answer:
the answer is option A one graph
and I think or am sure it is correct ans.
simultaneous equations 5x+y=28 x+y=2
Answers
Answer:
[tex]( \frac{13}{2} \:, - \frac{9}{2} )[/tex]Step-by-step explanation:
[tex]5x + y = 28[/tex]
[tex]x + y = 8[/tex]
Solve the equation for y by moving 'x' to R.H.S and changing its sign
[tex]5x + y = 28[/tex]
[tex]y = 2 - x[/tex]
Substitute the given value of y into the equation 5x + y = 28
[tex]5x + 2 - x = 28[/tex]
Solve the equation for x
Collect like terms
[tex]4x + 2 = 28[/tex]
Move constant to R.H.S and change its sign
[tex]4x = 28 - 2[/tex]
Subtract the numbers
[tex]4x = 26[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{26}{4} [/tex]
Calculate
[tex]x = \frac{26}{4} [/tex]
Reduce the numbers with 2
[tex]x = \frac{13}{2} [/tex]
Now, substitute the given value of x into the equation y = 2 - x
[tex]y = 2 - \frac{13}{2} [/tex]
Solve the equation for y
[tex]y = - \frac{9}{2} [/tex]
The possible solution of the system is the ordered pair ( x , y )
[tex](x \: y) = ( \frac{13}{2} , \: - \frac{9}{2} )[/tex]-------------------------------------------------------------
Let's check if the given ordered pair is the solution of the system of equation:
plug the value of x and y in both equation
[tex]5 \times \frac{13}{2} - \frac{9}{2} = 28[/tex]
[tex] \frac{13}{2} - \frac{9}{2} = 2[/tex]
Simplify the equalities
[tex]28 = 28[/tex]
[tex]2 = 2[/tex]
Since , all of the equalities are true, the ordered pair is the solution of the system.
[tex](x \:, y \: ) = ( \frac{13}{2} \: , - \frac{9}{2}) [/tex]
Hope this helps....
Best regards!!
Answer:
[tex]\boxed{x=6.5} \\ \boxed{y=-4.5}[/tex]
Step-by-step explanation:
5x + y = 28
x + y = 2
Subtract both equations. (eliminating y variable)
4x + 0 = 26
4x = 26
Divide both sides by 4.
x = [tex]\frac{26}{4}[/tex]
x = 6.5
Plug x as 6.5 in the second equation and solve for y.
6.5 + y = 2
Subtract 6.5 on both sides.
6.5 - 6.5 + y = 2 - 6.5
y = -4.5
At the souvenir shop. Theo buys k key chains and p photo frames
where each chain and frame costs $2.49. He also buys a T-shirt for
$5.99. What is the total cost of Theo's purchases in terms of k and p?
Answers
Answer:
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
Step-by-step explanation:
Cost of k key chain=$2.49
Cost of p photo frames=$2.49
Cost of a T-shirt=$5.99
Total cost of all items=cost of k key chain + cost of p photo frame + cost of The shirt
=2.49k + 2.49p + 5.99
Factorise
2.49 is common to both k and p
=2.49(k + p) + 5.99
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
the question is in the attachment...
Answers
Answer:
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
Step-by-step explanation:
Let the sum total of parts of garden be x
If it is divided into 10 equal parts then
one part will be equal to x/10
Given carrots are planted on 5/10 of the garden
parts on which garden is planted = 5/10 * total part of garden = 5x/10
Given peas are planted on 1/10 of the garden
parts on which peas are is planted = 1/10 * total part of garden = x/10
On rest of the part corn is planted.
Rest of the part will be = total parts of garden - part on which carrots are planted - part on which carrots are planted
Rest of the part will be = x - 5x/10- x/10 = (10x-5x-x)/10 = 4x/10
Model will be
Rest of the part will be = x - 5x/10- x/10
solution will be 4x/10 i.e 4/10 part of the garden
So the polynomial 24r squared represents the surface are of a cube a : determine the polynomial that represents the area of one face of the cube b: use this answer to determine a polynomial that represents the length of an edge of the cube c: what is the length of an edge of the cube when r = 3 cm
Answers
Answer:
a. 4r² b. 2r c. 6 cm
Step-by-step explanation:
The surface area A of the cube is A = 24r². We know that the surface area, A of a cube also equals A = 6L² where L is the length of its side.
Now, equating both expressions, 6L² = 24r²
dividing both sides by 6, we have
6L²/6 = 24r²/6
L² = 4r². Since the area of one face is L², the polynomial that determines the area of one face is A' = 4r².
b. Since L² = 4r² the rea of one face of the cube, taking square roots of both sides, we have
√L² = √4r²
L = 2r
So, the polynomial that represents the length of an edge of the cube is L = 2r
c. The length of an edge of the cube is L = 2r. When r = 3 cm.
L = 2r = 2 × 3 cm = 6 cm
So, the length of an edge of the cube is 6 cm.
Which choice is equivalent to the expression below?
V-64
Answers
Explanation:
By definition, i = sqrt(-1)
Which means,
sqrt(-64) = sqrt(-1*64)
sqrt(-64) = sqrt(-1)*sqrt(64)
sqrt(-64) = i*sqrt(8^2)
sqrt(-64) = i*8
sqrt(-64) = 8i
On the second line, I used the rule sqrt(x*y) = sqrt(x)*sqrt(y). The fourth line used the rule sqrt(x^2) = x when x is nonnegative.
Answer:
Click 8i for Correct Answer
Step-by-step explanation:
What is the value of 13 squared?
Answers
Answer: 169
Step-by-step explanation:
13 squared = 13*13
Simply plug this into a calculator to get 169
Hope it helps <3
Answer:
169
Step-by-step explanation:
the answer is 169 because u will square the 13
Find the volume of the prism.
لا
A. 120 cm3
B. 630 cm2
C. 120 units2
D. 120 units 3
Answers
First, let's find the area of the triangle:
[tex]A=\dfrac{1}{2}bh=\dfrac{1}{2}\times3\times4=6[/tex]
Now, we multiply this area by the length of the prism, which is 20
[tex]20\times6=120[/tex]
All 3 answers have 120. However, since we're calculating volume, it will be represented by [tex]\text{units}^3[/tex]. Since no specific unit (such as cm or in) is specified, it will be left at that.
Thus, the answer is answer choice D.
Let me know if you need any clarifications, thanks!
The volume of prism is 120 unit³.
The correct option is D.
What is Volume?Volume is a three-dimensional measurement that's used to gauge a solid shape's capacity. It implies that the volume of a closed form determines how much space it can occupy in three dimensions.
First, Area of Triangle
= 1/2 x b x h
= 1/2 x 3 x 4
= 3 x 2
= 6
So, the volume of prism is
= 6 x 20
= 120 unit³
Thus, the volume of prism is 120 unit³.
Learn more about Volume here:
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Which list of ordered pairs represents solutions to x+y=2?
(-4, 6), (0, 2), (4, 2)
(-4, 6), (0, 2), (4, -2)
04-4, -6), (0, 2), (4, 2)
Answers
Answer:
(-4, 6), (0, 2), (4, -2)
Step-by-step explanation:
You just need to guess and check.
(-4,6) → -4 + 6 = 2 ✔
(0,2) → 0+2 = 2 ✔
(4,2) → 4 + 2 = 6
(4, -2) → 4 - 2 = 2 ✔
(-4,-6) → -4 - 6 = -10
The correct answer is the second list (-4, 6), (0, 2), (4, -2)
help me pls with this complete a and B I will give you brainliest if answer is correct:-)
Answers
Answer:
a) Multiplied by 1.04
b)160(1.06)=169.6
Step-by-step explanation:
Its increasing so (1+4%) will be what it multiplied to.
Hope it helps u
160(1+6%)=169.6
HELP ASAP MONEY & WAGES
Answers
Answer: Annual Gross Income = $55,489.20
Annual Net Income = $46,439.72
Step-by-step explanation:
Total hours worked per week = 3(10) + 5 + 11 = 46
Regular hours worked = 3(8) + 5 + 8 = 37
Overtime hours worked = 3(2) + 0 + 3 = 9
Weekly Tips at 20% of $60 for 46 hours:
0.2(60)(46) = $552.00
Annual tips = $552.00 x 52 weeks = $28,704.00
Weekly Regular pay at $10.20 per hour for 37 hours:
10.20(37) = $377.40
Annual regular pay = $377.40 x 52 weeks = $19,624.80
Weekly Overtime pay at time and a half for 9 hours:
10.20(1.5)(9) = $137.70
Annual overtime = $137.70 x 52 weeks = $7,160.40
Total Annual Gross Income = Tips + Regular Pay + Overtime
$28,704.00 + $19,624.80 + $7,160.40 = $55,489.20
****************************************************************************************
Deductions (per question 5):
a) Pension at 5% = $55,489.20(0.05) = $2,774.46
b) Employee Insurance at 2.4% = $55,489.20(0.024) = $1,331.74
c) Income Tax at 0% for $0-$11,000 = $11,000(0) = 0
Income Tax at 8% for $11,000-$25,000 = $14,000(0.08) = $1,120.00
Income Tax at 12% for $25,000-$50,000 = $25,000(0.12) = $3,000.00
Income Tax at 15% for $50,000-$100,000 = $5,489.2(0.15) =$823.38
Total Income Tax = $4,943.28
Annual Net Income = Gross - Pension - Employee Insurance - Income Tax:
$55,489.20 - $2,774.46 - $1,331.74 - $4,943.28 = $46,439.72
SOMEONE PLS HELP ASAP!!!
The exponential function h, represented in the table, can be written as h(x)=a⋅b^x.
x h(x)
0 10
1 4
Complete the equation for h(x) h(x)=?
Answers
Answer: [tex]h(x)=10(0.4)^x[/tex]
Step-by-step explanation:
The exponential function h, represented in the table, can be written as [tex]h(x)=ab^x[/tex]
From table, at x=0, h(x) =10
Put theses values in equation,, we get
[tex]10=a.b^0\\\\\Rightarrow\ 10= a (1)\\\\\Rightarrow\ a= 10[/tex]
Also, for x= 1 , h(x) = 4, so put these values and a=10 in the equation , we get
[tex]4=10b^1\\\\\Rightarrow\ b=\dfrac{4}{10}\\\\\Rightarrow\ b= 0.4[/tex]
Put value of a and b in the equation ,
[tex]h(x)=10(0.4)^x[/tex] → Required equation.
130 students choose to attend one of three after school activities: football, tennis or running. There are 58 boys. 49 students choose football, of which 27 are girls. 27 students choose tennis. 24 girls choose running. A student is selected at random. What is the probability this student chose running? Give your answer in its simplest form.
Answers
Answer: [tex]\dfrac{27}{65}[/tex]
Step-by-step explanation:
There are 130 students.
There are 58 boys --> 72 girls
A) 49 chose football: 27 are girls --> 22 are boys
B) 72 girls: 24 chose running, 27 chose football --> 21 girls chose tennis
C) 27 students chose tennis: 21 are girls --> 6 are boys.
D) 58 boys: 22 chose football, 6 chose tennis --> 30 boys chose running.
[tex]\large\boxed{\begin{array}{l|cc||c}&\underline{Boys}&\underline{Girls}&\underline{Total}\\Football&22&27&49\\Tennis&6&21&27\\\underline{Running}&\underline{\quad 30\quad}&\underline{\quad 24\quad}&\underline{\quad 54\quad}\\Total&58&72&130\end{array}}[/tex]
Total running = 30 boys + 24 girls = 54
Total students = 130
[tex]\dfrac{\text{Total running}}{\text{Total students}}=\dfrac{54}{130}\quad \rightarrow \large\boxed{\dfrac{27}{65}}[/tex]
Paul is a year older than his wife and they have two children who are also one year apart. Paul notices that on his birthday in 2011, the product of his age and his wife's age plus the sum of his children's ages is 2011. What would have been the result if he had done this calculation thirteen years before?
Answers
Answer:
997
Step-by-step explanation:
Well let's find the square root of 2011 because Paul and his wife are about the same age.
[tex]\sqrt{2011}[/tex]
= 44.8
Paul is 45 and his wife is 44.
44 + 45 = 1980.
2011 - 1980
= 31
So the children are 15 and 16.
45 + 44 + 15 + 16
= 997
Paul and wife - 45 and 44
Children - 15 and 16
Thus,
13 years ago they would be 997.
Hope this helps :)
The coordinates of A, B, and C in the diagram are A (p, 4), B (6, 1 ), and C (9, q). Which equation correctly relates p and q? ↔ ↔ ↔ ↔ Hint: Since AB is perpendicular to BC, the slope of AB × the slope o BC = -1. A. -q − p = 7 B. q − p = 7 C. p − q = 7 D. p + q = 7
Answers
Answer:
D. p + q = 7
Step-by-step explanation:
The slope of AB is ...
mAB = (y2 -y1)/(x2 -x1) = (1 -4)/(6 -p) = -3/(6 -p)
The slope of BC is ...
mBC = (q -1)/(9 -6) = (q -1)/3
We want the product of these slopes to be -1:
mAB·mBC = -1 = (-3/(6 -p))·((q -1)/3)
-(q-1)/(6 -p) = -1 . . . . cancel factors of 3
q -1 = 6 -p . . . . . multiply by -(6 -p)
q + p = 7 . . . . . matches choice D
Answer:
C p+q=7
Step-by-step explanation:
I did it on plato and it was right