14. Which of the following is true about given APQR given in Figure 7.82 to the right? a. p²+q²=² b. q²+r²=p² c. (p+q)²=r² d. p²+r²=q² Q P R T 9 Figure 7.82 P
Answers
a. p²+q²=r²
According to the Pythagorean theorem :
p²+q²=r² ,because this is a right triangle and r is the length of the hypotenuse.
Related Questions
i could use some help with this question pleaseeeee, i'll give brainliest and an explanation for future reference would be appreciated^^
if L,M are the two roots of the equation : 8x² - 40x + 11 = 0 , then L+M = ...........
a) 40
b) -40
c) 5
d) -5
Answers
Answer:
c) 5
Step-by-step explanation:
we know that,
alpha + beta = -b/a
here, we are given that alpha is L and beta is M (roots of the quadratic equation)
therefore,
L+M = -b/a
L+M = -(-40)/8
L+M = 40/8
L+M = 5
HOPE IT HELPS!!
PLEASE MARK BRAINLIEST... ♡
Answer:
L + M are 5.122 and -0.122 so I am assuming the answer you want is 5 or c.
Step-by-step explanation:
SOME OF THIS I NEEDED TO RESEARCH BECAUSE I FEEL LIKE THIS IS OUT OF MY DEPTH BUT I GUESS HERE YOU GO
STEP
1
:
Equation at the end of step 1
(23x2 - 40x) - 5 = 0
STEP
2
:
Trying to factor by splitting the middle term
2.1 Factoring 8x2-40x-5
The first term is, 8x2 its coefficient is 8 .
The middle term is, -40x its coefficient is -40 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 8 • -5 = -40
Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -40 .
-40 + 1 = -39
-20 + 2 = -18
-10 + 4 = -6
-8 + 5 = -3
-5 + 8 = 3
-4 + 10 = 6
-2 + 20 = 18
-1 + 40 = 39
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
2
:
8x2 - 40x - 5 = 0
STEP
3
:
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = 8x2-40x-5
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 8 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C ,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 2.5000
Plugging into the parabola formula 2.5000 for x we can calculate the y -coordinate :
y = 8.0 * 2.50 * 2.50 - 40.0 * 2.50 - 5.0
or y = -55.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = 8x2-40x-5
Axis of Symmetry (dashed) {x}={ 2.50}
Vertex at {x,y} = { 2.50,-55.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-0.12, 0.00}
Root 2 at {x,y} = { 5.12, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving 8x2-40x-5 = 0 by Completing The Square .
Divide both sides of the equation by 8 to have 1 as the coefficient of the first term :
x2-5x-(5/8) = 0
Add 5/8 to both side of the equation :
x2-5x = 5/8
Now the clever bit: Take the coefficient of x , which is 5 , divide by two, giving 5/2 , and finally square it giving 25/4
Add 25/4 to both sides of the equation :
On the right hand side we have :
5/8 + 25/4 The common denominator of the two fractions is 8 Adding (5/8)+(50/8) gives 55/8
So adding to both sides we finally get :
x2-5x+(25/4) = 55/8
Adding 25/4 has completed the left hand side into a perfect square :
x2-5x+(25/4) =
(x-(5/2)) • (x-(5/2)) =
(x-(5/2))2
Things which are equal to the same thing are also equal to one another. Since
x2-5x+(25/4) = 55/8 and
x2-5x+(25/4) = (x-(5/2))2
then, according to the law of transitivity,
(x-(5/2))2 = 55/8
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-(5/2))2 is
(x-(5/2))2/2 =
(x-(5/2))1 =
x-(5/2)
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-(5/2) = √ 55/8
Add 5/2 to both sides to obtain:
x = 5/2 + √ 55/8
Since a square root has two values, one positive and the other negative
x2 - 5x - (5/8) = 0
has two solutions:
x = 5/2 + √ 55/8
or
x = 5/2 - √ 55/8
Note that √ 55/8 can be written as
√ 55 / √ 8
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving 8x2-40x-5 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 8
B = -40
C = -5
Accordingly, B2 - 4AC =
1600 - (-160) =
1760
Applying the quadratic formula :
40 ± √ 1760
x = ——————
16
Can √ 1760 be simplified ?
Yes! The prime factorization of 1760 is
2•2•2•2•2•5•11
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 1760 = √ 2•2•2•2•2•5•11 =2•2•√ 110 =
± 4 • √ 110
√ 110 , rounded to 4 decimal digits, is 10.4881
So now we are looking at:
x = ( 40 ± 4 • 10.488 ) / 16
Two real solutions:
x =(40+√1760)/16=5/2+1/4√ 110 = 5.122
or:
x =(40-√1760)/16=5/2-1/4√ 110 = -0.122
Consider the quadratic function shown in the table below. x y 0 0 1 3 2 12 3 27 Which exponential function grows at a faster rate than the quadratic function for 0< x < 3?
Answers
So values are
(0,0)(1,3)(2,12)(3,27)The rule is
3/1=312/2=627/3=9Explicit formula
x(3x) where x is set of integersEquation here is
y=3x²Answer:
[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.
Step-by-step explanation:
Given table:
[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]
First Differences in y-values:
[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]
Second Differences in y-values:
[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]
As the second differences are the same, the function is quadratic.
The coefficient of [tex]x^2[/tex] is always half of the second difference.
Therefore, the quadratic function is:
[tex]f(x)=3x^2[/tex]
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]
An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3 is [tex]f(x)=4^x[/tex]
[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]
As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.
1. 6 tractors take 7 days to collect the harvest. How long does it take 12 tractors to do the same work? ANSWER MUST BE IN 1 DECIMAL PLACE.
2. 3 kitchen assistants can prepare 10kg of vegetables in 45 minutes. How long would it take 20 assistants to prepare the same amount? ANSWER MUST BE IN 1 DECIMAL PLACE.
MARKING FIRST ANSWER AS BRAINLIEST.
Answers
Answer:
1.
3.5 days
2.
6.75 minutes, 6 minutes 45 seconds, 6.8 minutes to 1 dp
Step-by-step explanation:
1.
With double the amount of tractors it will take half the time.
7 divided by 2 is 3.5
2.
This is an example of inverse proportion. The job that has to be done to to prepare the vegetables, That stays the same.
However, the more people there are to do the work, the quicker it will get done.
There is a constant to be found:
x multiplied by y equals k
3 x 45 = 135
For 20 people:
20 x y = 135
135 divided by 20 is:
6.75, or 6.8
The numbers in this sequence increase by 12 each time
24
36
48
60
The sequence is continued with the same rule.
Which number in the sequence will be closest to 100?
Answers
A town with a population of 5,000 people grows 3% per year. How long will it take for the population to reach 8,000?
Answers
answer is: Notice that if the population doubles every 12 years, it quadruples (4 times) in 24, multiplies by 8 in 36, and multiplies by 16 in 48 years.
I want help solving Id also like to know how you got the answer for future reference. ♥️
Answers
Answer:
5 seconds and 488 ft
Step-by-step explanation:
(a)
given a quadratic in standard form
y = ax² + bx + c ( a ≠ 0 ), then
the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
y = - 16x² + 160x + 88 ← is in standard form
with a = - 16 and b = 160 then
[tex]x_{vertex}[/tex] = - [tex]\frac{160}{-32}[/tex] = 5
the maximum height is at the vertex, the turning point on the graph
then it takes 5 second to reach its maximum height
(b)
to find the maximum height substitute x = 5 into the equation
y = - 16(5)² + 160(5) + 88
= - 16(25) + 800 + 88
= - 400 + 888
= 488
maximum height is 488 ft
median and the data 11 , 17 , 7 , 4 , 15 , 9
Answers
Answer:
10.
Step-by-step explanation:
median means the "middle" number in a set of numbers.
(I always the meaning of median by remembering "middle" because they rhyme).
NOTE: to find the median of a set of numbers you have to arrange that set of numbers in either ascending order (smallest to biggest value) or descending order (biggest to smallest value) .
sooo....
we were given :
11, 17, 7, 4, 15, 19
let's arrange in ascending order
4, 7, 11, 15, 17 , 19
now you can cancel them out ( cancel left number, right number)
i mean....
cancel out 4, cancel out 19
cancel out 7, cancel out 17
and we are left with 2 numbers which are11 and 15.
NOTE; (when you have two numbers or values remaining instead of one number, add those two numbers and divide by 2).
soooo...
11 + 15 = 20
20/2 = 10
median of the set of numbers is equal to 10.
Hope this helps.
Good luck ✅.
An insurance firm wants to estimate the percentage of senior citizens in a small town with approximately 2,534 residents. it asks a group of 85 randomly selected people in the town about their age.
select the statement that is true.
a. the sample is 2,534 people. the population is 85 people.
b. the sample is 85 people. the population is 2,449 people.
c. the sample is 85 people. the population is 2,534 people.
d. none of the answer choices are true.
Answers
Using sampling concepts, it is found that the correct statement is given by:
c. the sample is 85 people. the population is 2,534 people.
What is sampling?It is a common statistics practice, when we want to study something from a population, we find a sample of this population, which is a group containing elements of a population. A sample has to be representative of the population, that is, it has to involve all segments of the population.
In this problem, a group of 85 people, which is the sample, is taken from the entire population of 2,534 people, hence option c is correct.
More can be learned about sampling concepts at https://brainly.com/question/25122507
#SPJ1
Help me please I beg
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
calculate the gradient (slope) m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = O (0, 0 ) and (x₂, y₂ ) = A (- 5, 2 )
[tex]m_{OA}[/tex] = [tex]\frac{2-0}{-5-0}[/tex] = [tex]\frac{2}{-5}[/tex] = - [tex]\frac{2}{5}[/tex]
(b)
the angle between a tangent and a radius at the point of contact is 90°
given a line with slope m then the gradient of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{5} }[/tex] = [tex]\frac{5}{2}[/tex]
(c)
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{5}{2}[/tex] , then
y = [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
to find c substitute A (- 5, 2 ) into the partial equation
2 = - [tex]\frac{25}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{25}{2}[/tex] = [tex]\frac{29}{2}[/tex]
y = [tex]\frac{5}{2}[/tex] x + [tex]\frac{29}{2}[/tex] ← equation of tangent
1. Amelia's annual salary increases by the same quantity every year. In her 1st
year at her job, she earned $24,000.In her 2nd year, she earned $36,000. In
her 3rd year, she earned $48,000. How much will she earn in her 20th year?
Then sketch a graph that represents the above information.
SALARY
Solution:
Answers
Answer:
Amelias salary increase by $12,000 every year so 12*20 = $240,000 salary in 20th year.
How many different possible outcomes are there when jillana spins the spinner below and then flips the coin? a spinner with 6 equal sections labeled 1 through 6. a penny. 2 6 8 12
Answers
Answer:
12
Step-by-step explanation:
6 X 2
the 6 sides of the spinner and the two faces of the coin
Answer: 36
Step-by-step explanation:
I just took the test on Edge :)
can anyone help with this? i dont know it
Answers
It is a right angle and right angles add up to 90 degrees.
63+27=90
Last week a pizza restaurant sold 36 cheese pizzas, 64 pepperoni pizzas, and 20 veggie pizzas. based on this data, which number is closest to the probability that
the next customer will buy a cheese pizza?
a) 0.84
b) 0.64
c 0.36
d 0.30
Answers
36+ 64 + 20 = 120
For cheese: 36/120 = 0.3
Which of these scenarios illustrate independent events?
Answer:
A. Only ll
B. only ll
C. Both l and ll
D. Neither l nor ll
Answers
Answer:
The answer would be C, Both I and II.
Step-by-step explanation:
You can find an attached file which shows the scenarios incase your confused.
After the translation, where is A located?
Answers
Answer:
(-3, 13)
Step-by-step explanation:
The transformation that moves a point 4 left and 8 up is ...
(x, y) ⇒ (x -4, y +8)
The transformation that reflects a point across the y-axis is ...
(x, y) ⇒ (-x, y)
Applied after the translation, the transformation of ∆ABC becomes ...
(x, y) ⇒ (-(x -4), y +8) = (4 -x, y +8)
Then point A gets moved to ...
A(7, 5) ⇒ A'(4 -7, 5 +8) = (-3, 13)
What is the answer of 11 6/9 - 4 4/9
Answers
Answer:
[tex]7 \frac{2}{9} [/tex]
Step-by-step explanation:
here is your answer
Calculation steps:
[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
[tex] = (14 - 4) + ( \frac{6}{9} - \frac{4}{9} )[/tex]
[tex] = 7 + \frac{6 - 4}{9} [/tex]
[tex] = 7 + \frac{2}{9} [/tex]
[tex]7 \frac{2}{9} [/tex]
[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
solution:[tex]11 \frac{6}{9} - 4 \frac{4}{9} [/tex]
[tex] = \frac{35}{3} - \frac{40}{9} [/tex]
[tex] = \frac{(35 \times 9) - (40 \times 30)}{3 \times 9} [/tex]
[tex] = \frac{315 - 120}{27} [/tex]
[tex] = \frac{195}{27} [/tex]
[tex] = 7 \frac{2}{9} [/tex]
Please help, thanks!!
A cylinder has a height of 4 inches and a
base with a surface area of 113 square
inches. What is its volume?
Answers
Answer:
The volume is 452 square inches.
Step-by-step explanation:
Volume=area of base*height
just plug in the values
A store is giving out cards labelled 1 through 10 when customers enter the store. If the card is an even number, you get a 10% discount on your purchase that day. If the card is an odd number greater than 6, you get a 40% discount. Otherwise, you get a 20% discount. The table shows the results of 400 customers. What is the relative frequency for each discount? Use pencil and paper. If the manager of the store wants to approximately half of the customers to receive the 20% discount, does this seem like an appropriate method? Explain.
Answers
Answer:
Relative frequency for each discount :
10% - 0.4925, 20% - 0.3325, 40% - 0.175
Since only 33.25% of customers got 20% discount, it is not an appropriate method.
Step-by-step explanation:
relative frequency = number of frequency/total number of frequency
you can find out relative frequency for each number and add them up to get relative frequencies of discounts.
4+4(5+2²)
Using order of operations
Answers
Hey there!
Do PEMDAS to solve.
PEMDAS simply means.
• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtract
Some people use this method to make PEMDAS easier to understand
• Please
• Excuse
• My
• Dear
• Aunt
• Sally
4 + 4(5 + 2^2)
= 4 + 4(5 + 2 * 2)
= 4 + 4(5 + 4)
= 4 + 4(9)
= 4 + 36
= 40
Therefore, the answer should be: 40
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
11
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
Answers
Answer:
28 cmStep-by-step explanation:
The area of a square is 49 cm2. What is the perimeter, in cm, of the square?
first we use the inverse formula to find the side (√49 = 7), then multiply the side by 4 (7 x 4 = 28)
or you can use an expression
4 * √49 = 28
What is the answer F, G, H or J
Answers
Answer:
G its G
Step-by-step explanation:
Quickly Help will make you brainliest These figures are congruent. What series of transformations moves
quadrilateral ABCD onto quadrilateral A'B'C'D'?
y
-8 4
8
B
A
-8
Note: Rotations are clockwise. Reflections are over the x- or y-axis.
G
8
4
+
D
B
A
4
C
D'
X
Answers
The series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is C. reflection, translation.
What is transformation?It should be noted that transformation simply means the movement of object in a coordinate plane.
The common type of transformation in mathematics include translation, rotation, reflection, and dilation.
Here, the series of transformations that moves quadrilateral ABCD onto quadrilateral A'B'C'D' is reflection, and translation. Reflection is flipping the pre image and producing the mirror image while translation is movement of the pre image
Learn more about transformation on:
brainly.com/question/9028159
#SPJ1
Answer:
A
Step-by-step explanation:
SURFACE AREA QUESTION: the cargo area of the moving truck will be completely filled by 45 identical cube-shaped boxes. What will be the Surface area of one layer of boxes on the floor of the truck bed. (the truck has a height of 6 ft, a length of 6ft, and a width of 10ft.)
Answers
I believe it is 312, hope this helps, sorry if it doesn't!:)
What is the equation of the line shown in the graph?
Answers
Answer:
y = -x – 2
Step-by-step explanation:
Slope is ΔY/ΔX = -1
plug this into the equation:
1=-(-3) +b
= -2=b
so we get; y = -x – 2
Answer: y = -x - 2
Step-by-step explanation:
I will be writing this equation in slope-intercept form.
First, we will find our m value, also known as the slope.
[tex]\displaystyle \frac{\text{change in y}}{\text{change in x}} =\frac{1--4}{-3-2} =\frac{5}{-5}=-1[/tex]
Now, we will find our b value, or the y-intercept.
-> The line intercepts the y-axis at (0, -2), so our y-intercept is -2.
Lastly, we will write our equation.
y = mx + b
y = -x - 2
Read more about writing slope-intercept equations here:
https://brainly.com/question/15143525
I need the answer soon please help. 20 points
Divide. −3 6/8 Enter your answer as a mixed number, in simplified form, in the box.
Answers
Answer:
The solution is in the image
zolas mother spends 39 minutes braiding zolas hair she finishes at 7:52 what time did she start braiding zolas hair
Answers
11 x_
= 121 what is the missing number?
Answers
Answer:
11
Step-by-step explanation:
11x=121
11x/11 = 121/11
x = 11
So, 11*11 = 121
x/13 - 1 = 5x/2 + 1/2
please answer the question pls pls pls pls
Answers
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
the given expression can be solved as follows ~
[tex] \frac{x}{13} - 1 = \frac{5x}{2} + \frac{1}{2} \\ [/tex]
taking LCM both the sides ,
[tex] \frac{x - 13}{13} = \frac{5x + 1}{2} \\ [/tex]
on cross multiplying ,
[tex](x - 13)2 = (5x + 1)13 \\ \\ \implies \: 2x - 26 = 65x + 13[/tex]
let's now gather the like terms at either sides of the equation ~
[tex]65x - 2x = - 26 - 13 \\ \\ \implies \: 63x = - 39 \\ \\ \implies \: x = \frac{\cancel{ - 39}}{\cancel{63}} [/tex]
on simplifying the equation ,
[tex] \implies \frac{-13}{21}\\[/tex]
hope helpful ~
Which property is illustrated by the statement 4+(9+12)=(4+9)+12
Answers
Answer:
Associative Property of Addition
Step-by-step explanation:
Associative Property of Addition:
For any real numbers a, b, and c, (a + b) + c = a + (b + c).
Answer:
Commutative Property of Addition
Step-by-step explanation:
Simplify 3(2x+6)+4x-1
Answers
Answer: 10+17
Step-by-step explanation:
Distribute:
3(2+6)+4−1
6+18+4−1
Subtract the numbers:
6+18+4−1
6+17+4
Combine like terms:
6+17+4
10+17
solution:
10+17