p+q = 12
Squaring both the sides
(p+q)^2 = 12^2
p2 + q2 + 2pq = 144
p2 + q2 + 2x 22 = 144
p2 + q2 = 144 - 44
p2 + q2 = 100
Answer:
q2=
Step-by-step explanation:
The formula for p^2+q^2p
2
+q
2
is
p^2+q^2 = (p+q)^2 -2pqp
2
+q
2
=(p+q)
2
−2pq
Write the equation of the line in fully simplified slope-intercept form.
12
11
10
-12-11-10-9-8
1 2 3
5 6
8 9 10 11 12
-3
-4
-9
-10
Answer:
y=1/2x+6
Step-by-step explanation:
Is the relationship between the variables in the table a direct or inverse variation or neither? If it is direct or inverse, write a function to model it.
x 4 8 16 32
y 32 16 8 4
Step-by-step explanation:
this is inverse variation
the function is
xy = 128
=> y = 128/x
Which best describes the product of these two radicals?
√2-√7
The product is rational because both V2 and V7 are rational numbers,
The product is irrational because both 2 and 7 are irrational numbers.
The product is rational because at least one factor is rational,
The product is irrational because one of the factors is an odd number.
Answer:
second option: product is irrational because both are irrational
Step-by-step explanation:
The second option which is the product is irrational because both are irrational numbers.
What is irrational number?
These are those numbers which are impossible to be written in the form of p/q.
How to determine the product?
We have been the given the following numbers.
[tex]\sqrt{2 } and \sqrt{7}[/tex] and we have been asked to find the description of the product of both. We know that these are irrational numbers because it cannot be written in the form of p/q. When we multiply this we can get root 14 which is also a irrational number.
Learn more about irrational numbers at https://brainly.com/question/124495
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Find the length of the missing side
Answer:
25 in and 9 cm
Step-by-step explanation:
Using Pythagoras' identity
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let x be the missing side
A
x² = 7² + 24² = 49 + 576 = 625 ( take square root of both sides )
x = [tex]\sqrt{625}[/tex] = 25
B
x² + 12² = 15²
x² + 144 = 225 ( subtract 144 from both sides )
x² = 81 ( take square root of both sides )
x = [tex]\sqrt{81}[/tex] = 9
Answer:
A) [tex]\sqrt{7^{2} +24^{2} }[/tex] = 25
B) [tex]15^{2} -12^{2} = B^{2}[/tex]
[tex]B^{2} =81\\[/tex]
B = 9
Step-by-step explanation:
A 68-year old retiree has a pension savings of $51,000, a 401k of $58,000, and an IRA account of $68,000. Before 2008, he had 2% more cash in the pension, 12% more in the IRA, and −1% in the 401k. He wants to take out 2% from each account before he turns 72, which will cost him a penalty of an extra 1% from the pension, 2% from the 401k, and 6% from the IRA. What is the relevant information for the amount that the retiree will have in his pension if he doesn't take money out now?
A: The retiree had 2% more cash in the pension in 2008
B: The retiree has a pension savings of $51,000
C: The retiree has a 401k of $58,000
D: The retiree has an IRA account of $68,000
Answer:
B: The retiree has a pension savings of $51,000
Step-by-step explanation:
How many kilograms equals 984.2 grams?
solve for " x "
[tex]x = 42 - 9[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {x\:=\:33}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]x = 42 - 9[/tex]
➼[tex]\:x = 33[/tex]
Therefore, the value of [tex]x[/tex] is 33.
[tex]\sf\pink{Thank\:you. \:ヅ}[/tex]
Answer:
x =33
Step-by-step explanation:
x = 42-9
We are solving for x, which is already isolated
42-9 = 33
x = 33
Check 33+9 = 42
What is the surface area of LMNOPQRS? If necessary, round your answer to the nearest tenth.
Answer:
5
Step-by-step explanation:
Solve for x
-6/5x-4=-46
Answer:
x = 35
Step-by-step explanation:
-6/5x-4=-46
Add 4 to each side
-6/5x-4+4=-46+4
-6/5x=-42
Multiply each side by -5/6 to isolate x
-5/6 * -6/5x=-42 * -5/6
x = 35
Answer:
x = 35
Step-by-step explanation:
-6 / 5x - 4 = - 46
Add 4 to each side
- 6 / 5 x - 4 + 4 = - 46 + 4
- 6 / 5 x = - 42
To find x, multiply 42 by 5 and then divide by 6.
x = 42 × 5 / 6
x = 7 × 5
x = 35
Solve for x.
3x + 7
2x + 3)
Answer: x = 34
Step-by-step explanation:
2x+3+3x+7=180
5x+10=180
5x=170
x = 34
A group of people were asked if they had run a red light in the last year where 140 responded "yes," and 208 responded "no." If a person is randomly chosen, find the probability that he/she has run a red light in the last year. Give your answer as a fraction or decimal.
Answer:
35/87
Step-by-step explanation:
To find the probability, we must find (total number of favorable outcomes)/ (total number of outcomes). We thus need to find the total number of outcomes. As people have only answered "yes" or "no", the total number of outcomes is 208+140 = 348.
The total number of favorable outcomes, or what we're looking for, is 140 (140 people responded that they had run a red light). Thus, our fraction is 140/348, or 35/87
The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4 → 10x − 5y = −20 3x + 5y = 59 → 3x + 5y = 59 13x = 39 Which equation can replace 3x + 5y = 59 in the original system and still produce the same solution?
Answer:
[tex]13x=39[/tex]
Step-by-step explanation:
Given
[tex]2x - y = -4 \to 10x - 5y =-20[/tex]
[tex]3x +5y =59 \to 3x +5y = 59[/tex]
Required
What can replace [tex]3x +5y = 59[/tex] ?
We have:
[tex]10x - 5y =-20[/tex]
and
[tex]3x +5y = 59[/tex]
Add up both equations:
[tex]10x +3x-5y+5y=-20+59[/tex]
[tex]10x +3x=39[/tex]
[tex]13x=39[/tex]
Since [tex]13x=39[/tex] is a result of [tex]10x - 5y =-20[/tex] and [tex]3x +5y = 59[/tex],
[tex]13x=39[/tex] can replace [tex]10x +3x=39[/tex]
0lease help I would really appreciate
Step-by-step explanation:
a)50°
b)75°
c)125°
d)d=40°
Answer:
Step-by-step explanation:
A)180-(60+70)=50
C)180-30=150 150/2=75
B)180-(35+20)=125
D)2d+d+60=180
3d+60=180
3d=120 ; d=40 ; 2d=40×2=80
The two lines graphed below are not parallel. How many solutions are there to
the system of equations?
5
5
A. Infinitely many
B. One
C. Two
D. Zero
Answer:B
Step-by-step explanation:
simple, there is one point of intersection or where the lines meet
Answer:
B: One solution
Step-by-step explanation:
The graphs show that the two lines intersect at one point. This point represents the ONE solution of this system of equations.
If the lines did not intersect, the system would have no solution.
If the lines coincide, the system would have infinitely many solutions.
Write an equation for the data shown in each table.
Answer:
1) f(x) = 500·(1.1)ˣ
2) f(x) = 500·(0.9)ˣ
Step-by-step explanation:
1) The given values in the table are;
x; 0, 1, 2, 3
f(x); 500, 550, 605, 665.5
By observation, we have that each two subsequent term of f(x) have a common ratio, given as follows;
550/500 = 11/10 = 1.1 = 605/550 = 665.5/605
From which we have;
The values of f(x) are in a geometric progression
The nth of a geometric progression = a·rⁿ
The common ratio, r = 1.1
The first term, a = 500
The number of terms, n = x
Therefore, xth term, f(x) = a×(r)ˣ
Substituting the values gives;
The equation for the data shown in the table is f(x) = 500·(1.1)ˣ
2) The given table of values is presented as follows;
x; 0, 1, 2, 3
f(x); 500, 450, 405, 364.5
The common ratio, f(xₙ)/f(xₙ₋₁) = 450/500 = 9/10 = 0.9 = 405/450 = 364.5/405
The terms of f(x) are in a geometric progression
The first term. a = 500
The common ratio, r = 9/10 = 0.9
The nth term of a geometric progression, G.P. = a·rⁿ
By plugging in the values of 'a', 'r', and 'n', the value of the xth term, f(x), therefore;
The equation for the data shown in the table is f(x) = 500·(0.9)ˣ.
(b) Find the coordinate of the foot of the perpendicular from (4,-2) to line 2x-3y-4=0
Answer:
{3,-1}Step-by-step explanation:
[tex]carry\: on \: learning[/tex]
One day in the playground,the ratio of the number of boy to the number of girl is 3:5 later 6girls come, 9boy leave, the ratio of the number of girl become 1:4. Find the difference between the number of boy and girl originally
Answer:
The number of boys are 18 and the number of girls are 30.
Step-by-step explanation:
The ratio of number of girls to the boys = 3 : 5
Let the number of girls is g and boys is b initially.
b : g = 3 : 5
5 b = 3 g ..... (1)
Now, girls are 6 + g and boys are b - 9
So, the ratio is
(b - 9) : (6 + g) = 1 : 4
4 b - 36 = 6 + g
4 b - g = 42 .... (2)
From ( 1 ) and ( 2 )
[tex]4 b - \frac {5 b}{3}= 42\\\\\frac{7 b }{3} = 42\\\\b = 18[/tex]
And , g = 5 x 18/3 = 30
So, the number of boys are 18 and the number of girls are 30.
Can someone pleaseee help me been stuck on this problem?
Answer:
-10
-7
-4
-1
2
Step-by-step explanation:
Substitute in the x value
Remember a negative minus a negative is a negative.
Answer:
(-2,-10),(-1,-7),(0,-4),(1,-1),(2,2)
Step-by-step explanation:
f(x)=3x-4
f(x)=y
y=3x-4 ; x(-2)
y=3(-2)-4
y= -6-4
y= -10
y=3x-4
y = -1(3)-4
y= -7
y= 3x-4
y = 3(0) -4
y= -4
y= 3x-4
y = 3(1)-4
y= -1
y=3x-4
y=3(2)-4
y= 6-4
y =2
translate the sentence into an inequality
the sum of 2 and y is greater than 16
Answer:
2 + y > 16
Step-by-step explanation:
the sum of 2 and y is greater than 16
2 + y > 16
2 + y > 16
What is the amount of material required to creat a Toblerone box? The triangular base is equilateral.
Answer:
21 x 3.1 / 2 = 32.55
Step-by-step explanation:
78.4 divided by 0.56
If f(x)=2x2+3x−6, determine the value of f(2)
Answer: 4
2x2+3(2)−6
lets make sure we do OOO (order of operations correctly)
2x2+3(2)−6
4+3(2)−6
4+6−6
10−6
4
Step-by-step explanation:
someone please help, I need it, show all work.
Sadia works at a theatre selling popcorn. Large boxes of popcorn sell
for $5.00 and small boxes of popcorn sell for $3.00. During her shift
last night, she sold 60 boxes of popcorn. Her receipts totalled $260,
not including taxes. Determine the number of large and small
popcorn boxes she sold last night.
Answer:
its 55 not 60
Step-by-step explanation:
just divide 260 by 5 and 3
The required number of large and small popcorn boxes sold are 40 and 20 respectively.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the number of the large box be x and the small box is y.
According to the question,
5x + 3y = 260 - - - - - - -(1)
x + y = 60
x = 60 - y - - - - - - - - (2)
Put the value of equation, (2) in equation 1
5 (60 - y) + 3y = 260
300 - 5y + 3y = 260
2y = 40
y = 20
Now,
x = 60 - 20
x = 40
Thus, the required number of large and small popcorn boxes sold are 40 and 20 respectively.
Learn more about arithmetic here:
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The tile along the edge of a triangular community pool needs to be replaced. A right triangles, where the hypotenuse is labeled 8 x squared, the height is labeled 4 x squared + 15, and the base is labeled 8 x + 10. Which expression represents the total perimeter of the pool edge? 12x2 + 15 20x2 + 25 12x2 + 8x + 25 24x2 + 16x + 50
Answer:
C. 12x² + 8x + 25
Step-by-step explanation:
A. 12x² + 15
B. 20x² + 25
C. 12x² + 8x + 25
D. 24x² + 16x + 50
Hypotenuse = 8x²
Height = 4x² + 15
Base = 8x + 10
Perimeter of the triangle = hypotenuse + height + base
= 8x² + (4x² + 15) + (8x + 10)
= 8x² + 4x² + 15 + 8x + 10
Perimeter of the triangle = 12x² + 8x + 25
C. 12x² + 8x + 25
Answer:The answer is C
What is the value of x?
Answer:
98deg
Step-by-step explanation:
Angles in a triangular add to 180.
180-(53+45) is the top angle.
Angles on a line add a up to 180
180 - triangles top angle = x
Need help please anwer all its one page question i put in two bc it didnt fit
Answer:
sorry only doing the ones i know how to do
b) for the histogram, just write all the numbers on the table on the bottom, theres 13 lines but 2 repeats so it should be even. on the side write a range of minutes
c) mean = 7.8 ; standard deviation = 3.13
d)
min = 2
max = 13
range = 11
q1 = 5.5
q3 = 10.75
iqr = 5.25
median = 8
what does iqr represent? it represents the middle 50% of all the values
e) write the numbers from the table without repeats and mark them how many times theyre written
what should I do if I accidentally break my pet rock that has googly eyes on him? i need to fix Rocky Ronny McRonkster
Answer:
Try to glue it back together
Step-by-step explanation:
I heard gorilla glue works, but be careful and don't get the glue on your body. If that happens it can cause irritation and call posion control immediately.
3/2 Find three rational numbers between and 5/2 ?
Answer:
Step-by-step explanation:
[tex]\frac{3*4}{2*4}=\frac{12}{8}\\\\\frac{5*4}{2*4}=\frac{20}{8}[/tex]
Three rational numbers:
[tex]\frac{13}{8};\frac{14}{8};\frac{15}{8}[/tex]
¿Cuánto mide el lado de un terreno cuadrado, si su área 144 m2?
Answer:
72
Step-by-step explanation:
all you had to do was divide by 2
Someone please help me It’s getting late and it’s due tomorrow
Explain why the equation
1- x= 5(x - 4) - 6x has no solution.
Answer:
After the distribution of the 5 and the addition of x to both sides, the x variable is cancelled out leaving 1 = - 20.
This statement is false. Hence, no solution
Step-by-step explanation:
1 - x = 5(x - 4) - 6x (Distribute 5)
1 - x = 5x - 20 - 6x (Combine like terms)
1 - x = -x - 20 add x to both sides
1 = - 20 False