Answer:
According to the pythagorean theorem, a^2 + b^2 =c^2
c signifies the hypotenuse
a and b are the two legs
the sum of the two legs squared measures will equal the measure of the hypotenuse squared.
Step-by-step explanation:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
Answer:
JL = 32
Step-by-step explanation:
We are told in the above question that:
In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.
From the attached diagram, we can see that
JL : JK = JK: JM
Therefore,
JL/ JK = JK /JM
Where JL = Unknown
JK = 24
JM = 18
JL/ 24 = 24/18
Cross Multiply
24 × 24 = JL × 18
Divide both sides by 18
JL = (24 × 24) /18
JL = 576/18
JL = 32
Can somebody plz help me
Answer: A
Step-by-step explanation:
2x²-2x-9=0
this is a quadratic equation so we will use the quadratic formula .
Δ= b²-4*a*c
b= -2a= 2c= -9let's calculate Δ to khow how many solutions this equations have .
Δ= (-2)²-4*2*(-9)
= 76
we notice that 76>0
so this equation has two solutions : (-b-√76)/4 and (-b+√76)/4
let's calculte the values : (-b-√76)/4= [tex]\frac{-2-\sqrt{76} }{4}[/tex] (-b+√76)/4=[tex]\frac{-2+\sqrt{76} }{4}[/tex]the trick here is to notice that :
[tex]\sqrt{76}[/tex] = [tex]\sqrt{19*4}[/tex]
= [tex]\sqrt{19} *\sqrt{4}[/tex]
= 2[tex]\sqrt{19}[/tex]
Now we will simplify Δ by factoring by 2
[tex]\frac{2*(-1(+/-)\sqrt{19} }{2*2}[/tex] = [tex]\frac{-1(+/-)\sqrt{19} }{2}[/tex]so the answer is a .
Which fraction is graphed ?
Answer: B is the correct choice
Step-by-step explanation:
The values are essentially the same. You need to recognize how the symbols in the expressions match up with the symbols on the graph.
The open circle on the right end of the parabola means the function is less than (not including) 2 so <2 for that part.
The solid circle at the left of the line means f(x) includes all the values to the right are greater than or equal to 2 so ≥2 for that part.
the sum of the ages of an uncle and nephew 2 years ago was 40.In 2 years time from now the age of the uncle will be 3 times that of his nephew by then.Find their ages now
Answer:
Uncle is 34. Nephew is 10.
Step-by-step explanation:
Let u equal the age of the uncle, and n equal the age of the nephew.
First, two years ago, the sum of their ages was 40. We can represent this by subtracting 2 from each variable. Thus:
[tex](u-2)+(n-2)=40[/tex]
[tex]u+n-4=40[/tex]
[tex]u+n=44[/tex]
Next, in two years time, the uncle will be three times as old as his nephew. We can represent this by adding 2. Thus:
[tex]u+2=3(n+2)[/tex]
We now have a system of equations and can solve accordingly.
First, from the first equation, we can determine that:
[tex]u=44-n[/tex]
We can substitute this into the second equation.
[tex](44-n)+2=3(n+2)[/tex]
[tex]46-n=3n+6[/tex]
[tex]40=4n[/tex]
[tex]n=10[/tex]
Thus, the nephew's age is 10.
And the uncle's age is 44-10 or 34.
Write an equation of the line that is perpendicular to y = 1/2x +3 and passes through the point
(10,-5)
Answer:
y = -2x+15Step-by-step explanation:
[tex]y = 1/2x +3\\m =1/2\\m_1m_2 = -1\\1/2m_2 =-1\\m_2= -2\\(10 ,-5)\\x = 10\\y = -5\\y = mx+b \\-5 = -2(10) + b\\-5=-20+b\\-5+20 =b\\b = 15\\m = -2\\Substitute -given -values- into- slope -intercept-form\\y = mx+b\\y = -2x+15[/tex]
Consider event A and event B. What is the probability that event B occurs, given that event A has already occurred? A. P(B A) P(A) ∙ P(B) B. P(B A) P(A) C. P(B A) P(B) D. P(B A) P(B)
Answer:B
Step-by-step explanation:
Tim has 39 pairs of headphones and 13 music players. Tim wants to sell all the headphones and music players in identical packages what is the greatest number of packages time can make
Answer:
He will have 13 packages containing 3 pairs of headphones and 1 music player each.
Step-by-step explanation:
He has 39 pairs of headphones and 13 music players.
He wants to sell both set of items in identical packages.
To do this he has to divide them in such a way that the same number of both set of objects are in every box.
Let us find the ratio of the pairs of headphones to music players:
39 : 13 = 3 : 1
Therefore, dividing the pairs of headphones into 3 parts and the music players into 1 part, he can have identical packages.
So, he will have 13 packages containing 3 pairs of headphones and 1 music player each.
The real numbers x and y are such that x + y &= 4 x^2 + y^2 &= 22 x^4 = y^4 - 176 \sqrt{7}. Compute x - y.
PLEASE HELP ASAP
Answer:
[tex]\large \boxed{\sf \ \ \ x-y=-2\sqrt{7} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
it took me some time to understand the correct equations, I believe that you mean
[tex]x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176\sqrt{7}[/tex]
So let's play with these equations
[tex]x^4=y^4-176\sqrt{7}\\\\<=>y^4-x^4=176\sqrt{7}\\\\<=>y^4-x^4=(y^2)^2-(x^2)^2=(y^2-x^2)(y^2+x^2)=(y-x)(y+x)(x^2+y^2)\\\\=176\sqrt{7}[/tex]
So
[tex]x-y=-\dfrac{176\sqrt{7}}{(x+y)(x^2+y^2)}=-\dfrac{176\sqrt{7}}{4*22}=-2\sqrt{7}=-5.291503...[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495495 and standard deviation 118118 . You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to 118100=1.18118100=1.18 . 118100√=11.8118100=11.8 . 118100⎯⎯⎯⎯⎯⎯√=1.09118100=1.09 . 118118 .
The question is not typed properly! Complete question along with answer and step by step explanation is provided below.
Question:
Scores on the Critical Reading part of the SAT exam in a recent year were roughly Normal with mean 495 and standard deviation 118 .
You choose an SRS of 100 students and average their SAT Critical Reading scores. If you do this many times, the standard deviation of the average scores you get will be close to
a. 118
b. 118/100=1.18
c. 118/√100= 11.8
d. cannot be determined
Answer:
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Step-by-step explanation:
From the given information,
The population mean SAT critical reading score is
[tex]\mu = 495[/tex]
The population standard deviation is
[tex]\sigma = 118[/tex]
You choose an SRS of 100 students and average their SAT Critical Reading score.
[tex]n = 100[/tex]
Since the sample size is quite large then according to the central limit theorem,
The mean sample will be the same as the population mean SAT critical reading score.
[tex]\bar{x} = \mu = 495[/tex]
The standard deviation of the sample would be
[tex]s = \frac{\sigma}{\sqrt{n}} \\\\s = \frac{118}{\sqrt{100}} \\\\s = 11.8[/tex]
The correct option is (c)
Therefore, the standard deviation of the average scores you get will be close to 11.8
Module 6 What is the line of best fit? Why do we want the sum of the residuals to be as close to zero as possible?
Answer:
zero residual equals zero mean
A line of best fit is a straight line that shows the appropriate correlation among scatter plots of a given data. It is majorly used when the plotted points are not linear, it can be used to express the relationship between dependent and independent variables.
The sum of the residuals should be close to zero because it shows that the line of best fit is accurately drawn. Thus, it implies that there is a linear relationship between the two variables. Since he residual is close to zero, the graph could be said to be a linear graph.
A 20kg solution is 15% alcohol. How much water should I add to make an 8% alcohol solution?
Answer:
17.5 kg of water.
Step-by-step explanation:
The amount of alcohol in the 15% solution = 20*0.15 = 3kg.
If 3 kg is equivalent to 8% solution
then 100% is 3*100 / 8 = 37.5 kg.
So the amount of water to be added to make 8% solution = 37.5 - 20
= 17.5 kg.
The demand function of blankets at COMESA is given by the equation P=60-2Q find the units of good Q ,when P=12 and use integration to calculate the consumer surplus
Answer:
a. 24
b. 864
Step-by-step explanation:
a. The demand function is:
P = 60 - 2Q
When P = 12:
12 = 60 - 2Q
2Q = 60 - 12
2Q = 48
Q = 48/2 = 24
b. Consumer surplus is given as the integral of Demand function:
[tex]CS = \int\limits {[P(Q) - (p)(Q)] \ dQ\\[/tex]
This implies that:
[tex]CS = \int\limits {60 - 2Q} \, dQ\\\\CS = 60Q - Q^2\\\\CS = (60 * 24) - 24^2\\\\CS = 1440 - 576\\\\CS = 864[/tex]
what is the slope of these lines that contain these points (-1,10) (1,2) (3,-6) (5,-14)
Answer:
-4
Step-by-step explanation:
y = -4x + 6 is the equation and -4 is the slope
Can anybody help me solve this math problem?
Answer:
Step-by-step explanation:
It appears from our choices that this is a linear function, a line in the form
y = mx + b
We need to first find the slope. The 3 coordinates are (4, 66), (5, 77), (6, 88).
Using the slope formula twice to make sure this is in fact linear:
and between the next set of coordinates:
Since the slopes are the same, this is in fact linear. Using that slope along with 1 of the points in the point-slope formula for a line:
y - 66 = 11(x - 4) and
y - 66 = 11x - 44 and
y = 11x + 22, choice C.
y = 11x + 22
Dokota has 4/10 kg of clay. He divides the clay to make 8 equal- sized pots. How many grams of clay are in each pot?
4 1 1
--- kg x ----- = ------ kg = 0.05 kg = 50 g
10 8 20
Which of the following are roots of the polynomial function?
Check all that apply.
F(x) = x^3-6x^+7x-2
Answer:
C, D, and F
Step-by-step explanation:
The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a cubic or third-degree polynomial:
F(x) = x³ - 6x² + 7x - 2
To find the all possible roots of the cubic polynomial
By using the trial and error method:
Plug x = 1
F(1) = 1 - 6 + 7 - 2
F(1) = 8 - 8
F(1) =0
x = 1 is one of the roots of the polynomial.
We can write the cubic polynomial in the factored form:
F(x) = (x - 1)(x² -5x + 2)
We have a quadratic polynomial:
= x² -5x + 2
To find the roots of the quadratic polynomial use the quadratic formula:
a= 1, b = -5, and c =2
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]
After solving:
x = (5+√17)/2
x = (5-√17)/2
Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
Learn more about Polynomial here:
brainly.com/question/17822016
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Solve the inequality -2x < 5, illustrating your solution on a number line.
Is -6 a solution of the inequality?
Answer:
No.
Step-by-step explanation:
Let's first and try to isolate x.
-2x < 5
(Divide by -2)
x > -5/2 ( < changes to > b/c it was divided by a negative)
x > -2.5
Since x is all values greater than -2.5, -6 is not within those bounds.
Thus, -6 is not a solution to the inequality.
Hope that helps!
PLEASE PLEASE PLEASE I BEG YOUWhich graph is a function of x? On a coordinate plane, a vertical line is at x = negative 3. On a coordinate plane, a v-shaped graph opens up. On a coordinate plane, a parabola opens to the right. On a coordinate plane, one curve opens to the left and another curve opens to the right.
Answer:
On a coordinate plane, a v-shaped graph opens up.
Step-by-step explanation:
If you can draw a vertical line that intersects the graph in more than one place, the graph is NOT a function.
It appears your only function is ...
On a coordinate plane, a v-shaped graph opens up.
Answer:
On a coordinate plane, a v-shaped graph opens up.
Step-by-step explanation:
Good luck everybody and have a great day :D
NEED HELP NOW!!! Need help finding vertex form
Answer:
y = (x-.5)^2 -12.25
Step-by-step explanation:
first, find the vertex
x from (x,y) = -b/2a
ax^2-bx - c
1x^2-1x -12
-1/2(-1) = -1/-2 - 1/2
(1/2,y) then use x value to find y value
y = 1/2^2 - 1/2 - 12
y = .25 -.5 - 12 = -12.25
(.5,-12.25) input values into this formula:
y = a(x-h)^2 + k where h = x-value and k = y-value. use same a value = 1
y = (x-.5)^2 -12.25
f(x)=-3√(x-3)-1 which of the following graphs corresponds to the function above
Answer:
Step-by-step explanation:
graph attached
Answer:
graph y
Step-by-step explanation:
Glen got 48 out of 64 correct in his test. What fraction of the marks did he get wrong?
Answer:
16/64 i think
Step-by-step explanation:
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Total Marks = 64
Correct = 48
Incorrect = 64-48
=> 16
Fraction of Incorrect Answers:
=> [tex]\frac{16}{64}[/tex]
In simplest form:
=> [tex]\frac{1}{4}[/tex]
Multiply the polynomials. (2x^2 + 6x + 6)(3x – 2)
Hey there! :)
Answer:
6x³ + 14x² + 6x - 12.
Step-by-step explanation:
Given:
(2x² + 6x + 6)(3x - 2)
Multiply each term in the first polynomial by both terms in the second:
3x( 2x² + 6x + 6) - 2(2x² + 6x + 6) =
6x³ + 18x² + 18x - 4x² - 12x -12 =
Combine like-terms:
6x³ + 14x² + 6x - 12.
What is the length of line segment RS? Use the law of sines to find the answer. Round to the nearest tenth. Triangle Q R S is shown. Angle Q R S is 80 degrees. The length of Q R is 2.4 and the length of Q S is 3.1. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction 2.2 units 2.4 units 3.0 units 3.3 units
Answer: 2.4 UNITS
Step-by-step explanation:
The sine rule :
Sine A / a = Sine B / b = Sine C / c
From the diagram attached :
QR = s = 2.4 ; QS =r = 3.1 ; RS =q =?
We need to find the angle RQS
using Sine rule :
Sine R / r = Sine S / s
Sin 80° / 3.1 = sin S / 2.4
0.9848077 / 3.1 = sin S / 2.4
Sin S × 3.1 = 0.9848077 × 2.4
Sin S = 2.3635386 / 3.1
Sin S = 0.7624318
S = Sin^-1(0.7624318)
S = 49.67°
Therefore, form using ;
A + B + C = 180° ( SUM of angles in a triangle)
SQR = 180° - (QRS + QSR)
= 180° - ( 80 + 49.67)° = 50.33°
Q = 50.33°
THEREFORE,
Sine Q / q = Sin S / s
Sin 50.33° / q = Sin 49.67° / 2.4
0.7697339 / q = 0.7623295 / 2.4
0.7623295q = 0.7697339 × 2.4
q = 1.84736136 / 0.7623295
q = 2.4233108
q = Segment RS = 2.4units
Answer:
B) 2.5 is the right answer
Step-by-step explanation:
i got 100%
Liam wants to treat some friends to lunch. He has $50 and knows that lunch will cost about $8 per person, p. How many people can Liam buy lunch for?Part A- Write and solve an inequality to represent the Situation
Answer:
T ≥ 8x
50 ≥ 8x .......1
x ≤ 6
Liam can buy lunch for 6 people.
Step-by-step explanation:
Let x represent the number of people Liam can buy lunch for.
Given;
Lunch cost per person r = $8 per person
The total amount he has T = $50
The cost of buying lunch for c people is;
C = $8 × x
C = 8x
Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.
T ≥ C
Substituting C, we have;
T ≥ 8x
50 ≥ 8x ,.......1
Solving the inequalities;
8x ≤ 50
x ≤ 50/8
x ≤ 6.25
To the nearest whole number;
x ≤ 6
Liam can buy lunch for 6 people.
What is Pascal's triangle.
Answer:
Pascal's triangle is a triangular array of the binomial coefficients. It is used to find combinations.
Answer:
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.
Step-by-step explanation:
A lighthouse flashes a beam of light once every 3/5 of a minute. How many times does it flash a beam of light in half an hour?
Answer:
Total number of flash = 50 flash
Step-by-step explanation:
Given:
Time taken of a flash = 3/5 minute = 3/5 × 30 = 36 sec
Total time = 30 minute = 30 × 60= 1800 sec
Find:
Total number of flash in 30 minutes
Computation:
⇒ Total number of flash = Total time / Time taken of a flash
⇒ Total number of flash = 1800 / 36
⇒ Total number of flash = 50 flash
this is question What is the place value of the 8 in 4.328 (a)Thousands (b) Hundreds (c)Hundredths (d)Thousandths
Answer:
The answer is d
Step-by-step explanation:
The place value of the 8 is 8/1000 or 0.008 or 8 thousandths in 4.328.
What is the place value strategy?The place value of a digit is determined by the position of the digit relative to the decimal point. In a number with a decimal point, the digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractions.
here, we have,
Each place to the right of the decimal point represents a fraction that is one-tenth the size of the place to its left. For example, the hundredth place is one-tenth the size of the tenth place, the thousandth place is one-tenth the size of the hundredth place, and so on.
In the number 4.328, 8 is in the thousandth place, which is the third place to the right of the decimal point.
Thus, the place value of the 8 is 0.008, or 8 thousandths.
Learn more about the place value strategy here:
brainly.com/question/654419
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Please answer this question fast in two minutes
Answer:
A
Step-by-step explanation:
There isn’t enough info provided
Find the inequality represented by the graph
Answer:
y ≥ -2/3x +3
Step-by-step explanation:
incline is -2/3
and intercept with y-axis is 3
so the equation of the line is
y = -2/3x +3
Since the intended area in the graph I above the line, we now know enough to find the right one question:
y ≥ -2/3x +3
Answer: y>-2/3x+3 because the line is dotted its >
ANSWER ASAP PLEASE!!!!!!!!!!!! THANKS!!!!!!!!! :)
Answer: the answer is A
Step-by-step explanation: