Answer:
[tex]\boxed{\sf \ \ 25 \ \ }[/tex]
Step-by-step explanation:
Hello,
we can see that
[tex]x^2-10x = x^2-2*5x[/tex]
is the beginning of
[tex]x^2-2*5x+5^2=(x-5)^2[/tex]
so we must add 5*5=25 to both sides of the equation to make the left side a perfect square trinomial
hope this helps
Answer:
25.
Step-by-step explanation:
To find the value that will make the left side a perfect-square trinomial, you need to find (b/2)^2. In this case, b = -10.
(-10 / 2)^2
= (-5)^2
= (-5) * (-5)
= 25
Once you add 25 to both sides, the left side becomes x^2 - 10x + 25, which is equal to (x - 5)^2.
Hope this helps!
Describe how to simplify the expression
3^-6
3^-4
Answer:
For 3^-6 = 1/3^6 = 726 and for 3^-4 = 1/3^4 = 81
Step-by-step explanation:
ARE THE NUMBERS SEPARATED OR THEY ARE TO BE JOIN TOGETHER,IF THERE ARE SEPARATED THE SOLUTION IS GOING TO BE...
3^-6
using law of indices x^-a = 1/x^a
So 3^-6 = 1/3^6
Now find the power of 3^6
which is the same as 3×3×3×3×3×3 = 729
therefore 1/3^6 = 729
For 3^-4
using the above method
3^-4 is same as 1/3^4
which is equal to
finding the nominator
3×3×3×3 = 81
so the answer is 81
Brainliest for whoever gets this correct! What is the sum of the rational expressions below?
Answer:
second option
Step-by-step explanation:
x / x - 1 + 3x / x + 2
= x(x + 2) / (x - 1)(x + 2) + 3x(x - 1) / (x - 1)(x + 2)
= (x² + 2x) / (x² + x - 2) + (3x² - 3x) / (x² + x - 2)
= (4x² - x) / (x² + x - 2)
Lisa is 34 years old. Two years ago, she was twice as old as her brother. How old is her brother now?
Answer:
18
Step-by-step explanation:
Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.
Solve for x: 125^(3x+7)=25^(5x−11)
Answer:
x = 43
Step-by-step explanation:
125^(3x+7)=25^(5x−11)
Rewriting the bases as powers of 5
125 = 5^3 and 25 = 5^2
5^3 ^ (3x+7) = 5^2^(5x-11)
We know a^b^c = a^ (b*c)
5^(3 * (3x+7)) = 5^(2*(5x-11))
Distribute
5^(9x+21) = 5^(10x-22)
The bases are the same so the exponents are the same
9x+21 = 10x-22
Subtract 9x from each side
9x+21 -9x = 10x-9x-22
21 = x-22
Add 22 to each side
21+22 = x-22+22
43 = x
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
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A study compared surgery and splinting for subjects suffering from carpal tunnel syndrome. It was found that among 73 patients treated with surgery,
there was a 92% success rate. Among 83 patients treated with splints, there was a 72% success rate. Calculations using those results showed that if
there really is no difference in success rates between surgery and splints, then there is about 1 chance in 1000 of getting success rates like the ones
obtained in this study. Which statement cannot be said?
The better treatment for carpal tunnel syndrome is surgery.
The result has practical significance.
The recommended treatment for carpal tunnel syndrome is splinting.
The result has statistical significance.
Answer:
the answer is c
Step-by-step explanation:
because if the surgery has a 92% success rate and the splints have a 72% success rate then surgery would be recommended because it has a higher success rate
Part A: Factor 3x2c2 + 5xc2 − 2c2. Show your work. (4 points) Part B: Factor x2 + 6x + 9. Show your work. (3 points) Part C: Factor x2 − 9. Show your work. (3 points) (10 points)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A) 3x²c² + 5xc² - 2c²
Factor c² from all terms in the expression.
c²(3x² + 5x - 2)
Factor 3x² + 5x - 2
c²(3x-1)(x+2)
B) x² + 6x + 9
x² + 3x + 3x + 9
Factor common terms.
x(x+3)+3(x+3)
Take x+3 common.
(x+3)(x+3)
C) x² - 9
x² -3²
Apply formula : a² - b² = (a+b)(a-b)
(x+3)(x-3)
Answer:
A) [tex]c^2(3x-1)(x+2)[/tex]
B) [tex](x+3)(x+3)[/tex]
C) [tex](x+3)(x-3)[/tex]
Step-by-step explanation:
Part A:
[tex]3x^2c^2+5xc^2-2c^2[/tex]
Taking [tex]c^2[/tex] common
[tex]c^2(3x^2+5x-2)[/tex]
Using mid term break formula
[tex]c^2 (3x^2+6x-x-2)[/tex]
[tex]c^2[3x(x+2)-1(x+2)][/tex]
[tex]c^2(3x-1)(x+2)[/tex]
Part B:
[tex]x^2 + 6x + 9.[/tex]
[tex](x)^2+2(x)(3)+(3)^2[/tex]
[tex](x+3)^2[/tex]
[tex](x+3)(x+3)[/tex]
Part C:
[tex]x^2-9[/tex]
[tex](x)^2-(3)^2[/tex]
[tex](x+3)(x-3)[/tex]
[PLEASE HELPP] write an equation that represents the area Bruce covered (y) in terms of the number of tiles he used, x?
Answer:
y=(x/6)
Step-by-step explanation
divide every input by 6 to get the output
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fill
volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987
Answer:
0.8413
Step-by-step explanation:
Find the z score.
z = (x − μ) / σ
z = (992 − 999) / 7
z = -1
Use a chart or calculator to find the probability.
P(Z > -1)
= 1 − P(Z < -1)
= 1 − 0.1587
= 0.8413
The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct
Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined
Probability can be defined as the ratio of favorable outcomes to the total number of events.
We use Z-statistic to find out the probability,
z = (x − μ) / σ
x = raw score = 992 mL
μ = population mean = 999 mL
σ = standard deviation
z = [992 − 999]/7
z = -1
P-value from Z-Table:
P(x<992) = 0.15866
P(x>992) = 1 - P(x<992) = 0.84134
Thus, the required probability that a bottle has a volume greater than 992 mL is 0.84134
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Determine all numbers at which are function Continuous..
f(x)={
x^2 + 5x - 36/
x^2 + 8x - 9
if x≠-9
if x= -9}
a.
continuous at every real number except x = 1 and x = -9
b. continuous at every real number except x = -9
c.continuous at every real number except x = 1
d. continuous at every real number except x = -9 and x = 4
Answer:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Step-by-step explanation:
For this case we have this function:
[tex] f(x) =\frac{x^2 +5x-36}{x^2 +8x-9}, x=9[/tex]
We can factor the denominator and we got:
[tex] f(x) =\frac{x^2 +5x-36}{(x+9)(x-1)}, x=9[/tex]
And since we can't divide by 0 then the value of x can't be 1 or -9 so then the best answer for this case would be:
Continuous at every real number except x=1 and x=-9
Answer:
A or continuous at every real number except x=1 and x=-9
Step-by-step explanation:
Just took the test :)
Assuming that ten (10) candidates are presented in a random order, what is the probability that hire exactly one candidate
Answer:
The probability that only one candidate is hired is 0.10.
Step-by-step explanation:
The probability of event E occurring is the ration of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
It is provided that N = 10 candidates are presented in a random order.
Compute the probability that only one candidate is hired as follows:
[tex]P(\text{Only 1 Hire})=\frac{1}{10}=0.10[/tex]
Thus, the probability that only one candidate is hired is 0.10.
-15≤-3c plz helpppppppppp
Answer:
5 ≥ c
Step-by-step explanation:
-15≤-3c
Divide each side by -3, remembering to flip the inequality
-15/-3 ≤ -3c/-3
5 ≥ c
Answer:
c ≤ 5
Step-by-step explanation:
Since you have to divide both sides of the equation by a negative number, you have to flip the equality sign.
-15 ≤ -3c
(-15)/(-3) ≤ (-3c)/-3
5 ≥ c
c ≤ 5
what are the coordinates of the vertex of the function f(x) = x2 -12x +5?
Answer:
[tex]\huge\boxed{(6;\ -31)}[/tex]
Step-by-step explanation:
METHOD 1:Let: [tex]f(x)=ax^2+bx+c[/tex].
The coordinates of the vertex:
[tex](h;\ k)\to h=\dfrac{-b}{2a};\ k=f(h)=\dfrac{-(b^2-4ac)}{4a}[/tex]
We have
[tex]f(x)=x^2-12x+5\to a=1;\ b=-12;\ c=5[/tex]
Substitute:
[tex]h=\dfrac{-(-12)}{2(1)}=\dfrac{12}{2}=6\\\\k=f(6)=6^2-12(6)+5=36-72+5=-31[/tex]
METHOD 2:The vertex form of an equation of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
We have:
[tex]f(x)=x^2-12x+5\to a=1[/tex]
Complete to the square [tex](a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]x^2-12x+5=x^2-\underbrace{2(x)(6)}_{12x}+5=\underbrace{x^2-2(x)(6)+6^2}_{a^2-2ab+b^2}-6^2+5\\\\=\underbrace{(x-6)^2}_{(a-b)^2}-36+5=(x-6)^2-31\\\\h=6;\ k=-31\to(6;\ -31)[/tex]
Find the measure of y. Polygon Angle-Sum theorems
Answer:
z = 70°
y = 103°
Step-by-step explanation:
From the picture attached,
110° + z° = 180° [Supplementary angles]
z = 180 - 110
z = 70°
Since sum of interior angles of a polygon = (n - 2)×180°
where n = number of sides of the polygon
For a quadrilateral (n = 4),
Sum of interior angles = (4 - 2) × 180°
= 360°
z° + y° + 100° + 87° = 360°
70° + y° + 187° = 360°
y = 103°
Therefore, measure of the angles x = 70° and y = 103°.
The amount of carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27% of its carbon-14. How old are the paintings?
Answer:
The painting is [tex]t = 10911.1 \ years \ old[/tex]
Step-by-step explanation:
From the question we are told that
The amount of carbon present after t year is
[tex]y(t) = y_o * e ^{-0.00012t}[/tex] {Note ; This is the function }
Here [tex]y(t)[/tex] is the amount of carbon-14 after time t
[tex]y_o[/tex] the original amount of carbon-14
Now given that the paint as at now contain 27% of the original carbon-14
Then it mean that
[tex]y(t) = 0.27 y_o[/tex]
So the equation is represented as
[tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]
=> [tex]0.27 = * e ^{-0.00012t}[/tex]
=> [tex]ln(0.27) = -0.00012t[/tex]
=> [tex]- 1.30933 = -0.00012t[/tex]
=> [tex]t = \frac{-1.30933}{-0.00012}[/tex]
=> [tex]t = 10911.1 \ years[/tex]
Assume that y varies directly with
x, then solve.
If y=2when x=, find y when x=1
y =
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
120
Step-by-step explanation:
Answer: 120
Hope that helped!(:
Simplify the following algebraic expression.
square root of 392x^7
Answer:
[tex] \sqrt{392 {x}^{7} } [/tex]
Simplify
that's
[tex] \sqrt{392} \times \sqrt{ {x}^{7} } \\ \\ = \sqrt{196 \times 2} \: \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2} \times \sqrt{ {x}^{7} } \\ \\ = 14 \sqrt{2x ^{7} } [/tex]
Hope this helps you
Find the value of y........
Answer:
hope this is right y=74
Step-by-step explanation:
have not done this since two years ago so...
but anyway 148-180 = 32
32 is that angle
if this were a right triangle my answer would be different but 148/2 still completes this triangle and somewhat makes sense.
The correct answer is 90.
Subtract the rational expressions: (x/x+2)-(2/x)
Use the cubic model y = 6x3 - 5x2 + 4x – 3 to estimate the value of y when x = 2.
a 25
(b 33
c 48
d 79
Done
Try Again
-
Answer:
The answer is B.
Step-by-step explanation:
You have to substitute x = 2, into the equation of y :
[tex]y = 6 {x}^{3} - 5 {x}^{2} + 4x - 3[/tex]
[tex]let \: x = 2[/tex]
[tex]y = 6 {( 2)}^{3} - 5 {(2)}^{2} + 4(2) - 3[/tex]
[tex]y = 48 - 20 + 8 - 3[/tex]
[tex]y = 33[/tex]
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
All sides of the building shown above meet at right angles. If three of the sides measure 2 meters, 7 meters, and 11 meters as shown, then what is the perimeter of the building in meters?
Answer:
69 meters
Step-by-step explanation:
Answer:
Please privately chat to us why you chose to cheat during online class, otherwise we will contact your parents and kick you out of our program for the reason stated.
Step-by-step explanation:
Please contact your Quantitive Reasoning teacher at her email, as stated in Google Classroom.
Consider the density curve plotted below:
Find PX < 6.4):
Find P(X> 4.8):
Answer:
[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]
[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]
Step-by-step explanation:
Part a
We want to find:
[tex] P(X<6.4)[/tex]
And we just need to find the area below the curve until x=6.4, since we have a triangle we can do this:
[tex] P(X<6.4)= \frac{6.4*0.2}{2}= 0.64[/tex]
Part b
For this case we want to find this probability:
[tex] P(X>4.8)[/tex]
And we can use the complement rule and we got:
[tex] P(X>4.8) =1-P(X<4.8)= 1- \frac{4.8*0.15}{2}= 1-0.36= 0.64[/tex]
Pleased help with this
Answer:
A
Step-by-step explanation:
Which set of ordered pairs represents a function? {(0,1), (1,3), (1,5) (2,8)}, {(0,0), (1,2), (2,6), (2,8)}, {(0,0), (0,2), (2,0), (2,4)}, {(0,2), (1,4), (2,6), (3,6)}
Answer:
The last set.
Step-by-step explanation:
The first 3 sets contain 'one-to-many' relations , for example (1, 3) and (1, 5) in set 1 and (0, 0) and (0, 2) in set 3 , so they are not functions.
The last set does not have any of these and is a function.
HELP- find the volume of the prism
Answer:
The answer is
1728″Step-by-step explanation:
From the above question the prism in the picture is a cube since all it's sides are equal
So the formula for finding the volume of a cube is
V = l³
where l is the length of one side
From the question l = 12″
Volume of the prism = 12³
= 1728″
Hope this helps you
What is the missing segment?
Answer:
78.
Step-by-step explanation:
12 / (48-12) = 26 / x
12/36 = 26/x
1/3 = 26/x
x = 26*3 = 78.
Find three consecutive odd integers so that the sum of twice the first, the second
and three times the third is 152.
Answer: 23, 25, 27
Step-by-step explanation:
Let the 3 consecutive odd numbers be x, x+2 and x+4.
So
2x+(x+2)+3(x+4)=152
2x + x + 2 + 3x + 12 = 152
6x+14=152
6x = 152 - 14
x=138/6
x=23
So, the numbers are 23, 25 and 27.
among a group of students 50 played cricket 50 played hockey and 40 played volleyball. 15 played both cricket and hockey 20 played both hockey and volleyball 15 played cricket and volley ball and 10 played all three. if every student played at least 1 game find the no of students and how many students played only cricket, only hockey and only volley ball
Answer:
Cricket only= 30
Volleyball only = 15
Hockey only = 25
Explanation:
Number of students that play cricket= n(C)
Number of students that play hockey= n(H)
Number of students that play volleyball = n(V)
From the question, we have that;
n(C) = 50, n(H) = 50, n(V) = 40
Number of students that play cricket and hockey= n(C∩H)
Number of students that play hockey and volleyball= n(H∩V)
Number of students that play cricket and volleyball = n(C∩V)
Number of students that play all three games= n(C∩H∩V)
From the question; we have,
n(C∩H) = 15
n(H∩V) = 20
n(C∩V) = 15
n(C∩H∩V) = 10
Therefore, number of students that play at least one game
n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)
= 50 + 50 + 40 – 15 – 20 – 15 + 10
Thus, total number of students n(U)= 100.
Note;n(U)= the universal set
Let a = number of people who played cricket and volleyball only.
Let b = number of people who played cricket and hockey only.
Let c = number of people who played hockey and volleyball only.
Let d = number of people who played all three games.
This implies that,
d = n (CnHnV) = 10
n(CnV) = a + d = 15
n(CnH) = b + d = 15
n(HnV) = c + d = 20
Hence,
a = 15 – 10 = 5
b = 15 – 10 = 5
c = 20 – 10 = 10
Therefore;
For number of students that play cricket only;
n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30
For number of students that play hockey only
n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25
For number of students that play volleyball only
n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15
Answer:
Cricket only= 30
Volleyball only = 15
Hockey only = 25
Explanation of the answer:
Number of students that play cricket= n(C)
Number of students that play hockey= n(H)
Number of students that play volleyball = n(V)
From the question, we have that;
n(C) = 50, n(H) = 50, n(V) = 40
Number of students that play cricket and hockey= n(C∩H)
Number of students that play hockey and volleyball= n(H∩V)
Number of students that play cricket and volleyball = n(C∩V)
Number of students that play all three games= n(C∩H∩V)
From the question; we have,
n(C∩H) = 15
n(H∩V) = 20
n(C∩V) = 15
n(C∩H∩V) = 10
Therefore, number of students that play at least one game
n(CᴜHᴜV) = n(C) + n(H) + n(V) – n(C∩H) – n(H∩V) – n(C∩V) + n(C∩H∩V)
= 50 + 50 + 40 – 15 – 20 – 15 + 10
Thus, total number of students n(U)= 100.
Note;n(U)= the universal set
Let a = number of people who played cricket and volleyball only.
Let b = number of people who played cricket and hockey only.
Let c = number of people who played hockey and volleyball only.
Let d = number of people who played all three games.
This implies that,
d = n (CnHnV) = 10
n(CnV) = a + d = 15
n(CnH) = b + d = 15
n(HnV) = c + d = 20
Hence,
a = 15 – 10 = 5
b = 15 – 10 = 5
c = 20 – 10 = 10
Therefore;
For number of students that play cricket only;
n(C) – [a + b + d] = 50 – (5 + 5 + 10) = 30
For number of students that play hockey only
n(H) – [b + c + d] = 50 – ( 5 + 10 + 10) = 25
For number of students that play volleyball only
n(V) – [a + c + d] = 40 – (10 + 5 + 10) = 15
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