f p(x) = 2x2 – 4x and q(x) = x – 3, what is (p circle q) (x)
Answer:
[tex]2x^{2} - 16x + 30[/tex]
Step-by-step explanation:
Here we have to find p(q(x))
q(x) =x -3
we will plug value of q(x) in x of p(x)
p(x) =2x2-4x
p(q(x)) = 2(x-3)2-4(x-3)
= 2(x2-6x+9)-4(x-3)
=2x2-12x+18 -4x+12
[tex]2x^{2} + 16x + 30[/tex]
Factor completely 25-64x^2
Answer:
(5+8) (5-8)
Step-by-step explanation:
They are both perfect squares.
Answer:
(5+8x)(5-8x)
Step-by-step explanation:
This is a 'difference of two squares" Difference means subtraction and 25 is a perfect square and 64x^2 is a perfect square.
If you know how to factor quadratic trinomials like
ax^2 + bx + c, you can do the same thing here, using:
64x^2 +0x + 25
BUT, there's a shortcut. It is a pattern that you memorize. Since 25 is 5^2, put 5 first in the parenthesis. And since 64x^2 is 8x squared, put 8x second in the parenthesis like this:
(5 8x)
Make two of them:
(5 8x)(5 8x)
Make one a plus and one a minus.
(5 + 8x)(5 - 8x)
Done!
Well, if the directions say "factor" then you are done. If the directions say "solve" then put each piece equal to zero and solve for x.
Hope this helps!
Graph y=|3x| using as many points as needed
Answer:
Graph is below
Step-by-step explanation:
I am going to use 3 points to make this graph
(0,0)
(-1,3)
(1,3)
Answer:
(0,0), (-1,3), (1,3)
Step-by-step explanation:
The graph is below!
Hope this helps!!!!!!!!!!!!
two ships leave a harbor at
the same time. One ship travels
on a bearing S15°W at 10 miles per
hour. The other Ship travels on a
bearing N75°E at 10miles per hour.
bearing
How far apart will the ships be
after 3 hours?
Answer:
30√3 ≈ 51.96 miles
Step-by-step explanation:
The distance between the two ships can be found using the Law of Cosines, or using your knowledge of the side relationships in special triangles.
__
Each ship is traveling at 10 mph, so after 3 hours will have traveled 30 miles.
The triangle OS1S2 formed by the harbor and the two ship locations is an isosceles triangle with base angles of 30°. Each half of OS1S2 is a 30-60-90 triangle whose longer leg is √3 times half the hypotenuse. The sum of those two "longer legs" is the distance between the ships.
The distance between ships is 2×15√3 = 30√3 ≈ 51.96 miles.
_____
Additional comment
If you prefer to use the Law of Cosines, you are looking for the length of the side opposite the 120° angle in a triangle with sides of 30 miles.
c² = 30² +30² -2·30·30·cos(120°) = 30²(2-2·(-0.5)) = 3·30²
c = 30√3 . . . . . take the square root (miles)
The price of a skateboard is reduced by 25%. The original price was $120. Find the new price.
A.
$95
B.
$80
C.
$90
New price = 90 dollars
25% of 120 = 30
Price is reduced 25% from 120 so,
120 - 30 = 90
Amount of discount = 30
HElppppp pleaseee......
Answer: \sqrt[4]{xy^{2} }
Step-by-step explanation: Siplified
How many inches are in one and a half yards
Answer:
54
Step-by-step explanation:
54 inches
hope it helps...!!!
How do complementary angles relate to right angles?
Use cubic regression to find a
function that fits the following
points.
(1,-1), (2,-13), (3,-45),(-1,11)
y = [?]x3+[ ]x2+0 ]x+[ ]
The cubic regression function of the points (1,-1), (2,-13), (3,-45), (-1,11) is y = -2x³ + 2x² - 4x + 3
How to determine the function?The points are given as:
(x,y) = (1,-1), (2,-13), (3,-45), (-1,11)
A cubic regression function is represented as:
y = ax³ + bx² + cx + d
Next, we determine the cubic function using a graphing calculator.
From the graphing calculator, we have the following coefficients:
a = -2b = 2c = -4d = 3Recall that:
y = ax³ + bx² + cx + d
So, we have:
y = -2x³ + 2x² - 4x + 3
Hence, the cubic regression function of the points is y = -2x³ + 2x² - 4x + 3
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after spending 80% of her daily allowance, Ola found out she had 25k left. How much was her total allowance?
Answer:
31.25 k
Step-by-step explanation:
80 % * x = 25 k
.80 x = 25 k
x = 25 k / .80 = 31.25 k
Answer:
125k
Step-by-step explanation:
You want to know Ola's daily allowance if 25k remained after 80% was spent.
SetupThe fraction remaining was 100% -80% = 20%. If that fraction of Ola's allowance (a) is 25k, we have ...
0.20a = 25k
SolutionDividing by 0.20, the value of 'a' is shown to be ...
a = 25k/0.20 = 125k
Ola's total daily allowance was 125k.
Quadrilateral CDEF is similar to quadrilateral GHIJ. Find the measure of side
GH. Round your answer to the nearest tenth if necessary.
5
E
23.3
H
C
7
Answer: 32.6
Step-by-step explanation:
Solve the system using elimination.
Answer:
3x +2y = 11 .... 1
x +5y = 8....2
x + 5y = 8
multiply by -3 on both sides
-3x - 15y = -24
-3x - 15y = - 24
3x +2y = 11
-13y = -13
y = 1
substitute the value of y in 1 or 2
3x +2y = 11
3x = 11 - 2y
3x = 11 - 2(1)
3x = 9
x = 3
(x;y) ( 3 ; 1)
eq(2)×3
3x+15y=24-(3)eq(1)-eq(3)
-13y=-13y=-13/-13y=1Putting in eq(2)
x+5=8x=8-5x=3Pair
(3,1)
Triangle E has a perimeter of 125 inches. Two of
its side lengths are 26 inches and 55 inches.
What is its missing side length?
Answer:
44 inches
Step-by-step explanation:
perimeter of triangle = length of side 1 + length of side 2 + length of side 3
length of side 1 = 26
length of side 2 = 55
125 = 26 + 55 + length of side 3 = 81 + length of side 3
subtract 81 from both sides to get the length of side 3
length of side 3 = 44 inches
HELP NEED ANSWER VERY SOON Which of the following box plots has the HIGHEST overall speed The box plots compare the speeds of cars traveling on a highway
Answer
North of the box plot speed over 72 is the answer because it is a very high speed of the chart and it shows that the its going over the average speed
Place the following temperatures in order from coldest to hottest: -8°C, 10°C, -5°F, 40°F
a.
-5°F, -8°C, 40°F, 10°C
b.
-5°F, -8°C, 10°C, 40°F
c.
-8°C, -5°F, 10°C, 40°F
d.
-8°C, -5°F, 40°F, 10°C
Answer: A
Step-by-step explanation: I hate when theres problems like this, considering theres celcius and fahrenheit but the correct answer is A
What is the probability that he will hit fewer than 8 of the bottles?
Using the binomial distribution, it is found that the probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, we have that:
The probability of a bottle being hit is of p = 0.95.There are n = 10 bottles.The probability that he hits fewer than 8 of the bottles is given by:
[tex]P(X < 8) = 1 - P(X \geq 8)[/tex]
In which:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)[/tex]
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{10,8}.(0.95)^{8}.(0.05)^{2} = 0.0746[/tex]
[tex]P(X = 9) = C_{10,9}.(0.95)^{9}.(0.05)^{1} = 0.3151[/tex]
[tex]P(X = 10) = C_{10,10}.(0.95)^{10}.(0.05)^{0} = 0.5987[/tex]
Hence:
[tex]P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.0746 + 0.3151 + 0.5987 = 0.988[/tex]
[tex]P(X < 8) = 1 - P(X \geq 8) = 0.012[/tex]
The probability that he will hit fewer than 8 of the bottles is of 0.012, given by option A.
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what is the slope of a line that is perpendicular to the line shown? A-1/3 B-1 C-2/3 D-3/2
Answer:
-1
Step-by-step explanation:
perpendicular = always has a slope of neg 1
Answer:
-1
Step-by-step explanation:
It is -1. I can't explain, I just did it in my head, so sorry!
Solve for x
4(x + 6) = 3x – 7
Answer:
-31 = x
Step-by-step explanation:
Step 1 4x + 24 = 3x - 7
Step 2 x + 24 = -7
Step 3 x = -31
Hope this help!!!
Which term describes BCD
Check the picture below.
A rectangle has a perimeter of 36 feet and a base of 14 feet. What is the height?
Answer:
The answer is 4.
Step-by-step explanation:
If this shape has a perimeter of 36, and the base has a length of 14, you subtract 36 - 28 because there are two sides that have a length of 14. You get 8 by subtracting 36 - 28, and divide the answer by 2.
Pls help me and show work! Thank you <3
Answer: 18
Step-by-step explanation:
By the consecutive interior angles theorem, [tex]5x+7x+24=180 \longrightarrow x=13[/tex].
So, this means that using the corresponding angles theorem, [tex]7x+24=6y+7[/tex], and since [tex]x=13[/tex], this means that [tex]7x+24=115[/tex].
So, [tex]6y+7=115 \longrightarrow \boxed{y=18}[/tex]
Find the area of the pyramid net
Step 1
Find the area of the Square in the middle
Formula for finding square:
[tex]A = L*W[/tex]
Let's apply the formula and find our answer:
[tex]A = 2*2\\=4[/tex]
The area of the square is 4 units
Step 2
Find the area of all 4 triangles around the square
As you know, the formula for finding 1 triangle is as follows:
[tex]A = \frac{1}{2} *B*H[/tex]
But, to find the area of 2 triangles, we can use this formula:
[tex]A=B*H[/tex]
And to find 4 of them (with same dimensions;as required here), we can use this one:
[tex]A=2*B*H[/tex]
Let's apply the formula then! What are we waiting for!!!!
[tex]A=2*2*2\\=2*4\\=8[/tex]
The area of ALL of the triangles around the square is 8 units
Step 3
Add all areas to find FINAL ANSWER!
Easy!
4+8=12
The area of the Pyramid Net is 12 unitsAnswer:
12 is the answer because 2 x 2 = 4 but since it is a triangular face we half it and end up with 2, 2 x 4 is 8, the square it 2 x 2 = 4 so we add 4 and 8 which equals 12
Can someone help with this I don't understand
Answer:
1. B 15
2. C Hexagon
Step-by-step explanation:
1.Euler's formula tells you the relation between numbers of faces, vertices, and edges of a polyhedron is ...
F +V = E +2
Solving for the number of faces, we have ...
F = E +2 -V
For the given numbers, the missing number is ...
F = 26 +2 -13 = 15
Faces: 15
__
2.The cross section (shaded figure) is described by the number of edges it has. You can count them. There are three pairs of parallel edges, for a total of 6 edges. That makes the figure a hexagon.
What is the missing fifth term in the
pattern below?
1,8, 27, 64, ___
Answer:
the pattern is going in the form of 1³ , 2³ , 3³ , 4³
therefore next term should be 5³ which is equal to 125. So the missing term is 125
I hope you got that.
By : Modern Einstein
Question 10
If y varies inversely as x and y = -6 when x = 4, find the value of y when x = 5.
use the graph of the parabola to fi in the table
Answer:
line of symmetry: x = -3
intercepts...
x - intercept: (-4, 0) and (-2, 0)
y - intercept: (0, 8)
vertex: (-3, -1)
Step-by-step explanation:
The image isn't that clear but what I can get is what listed
line of symmetry is the line straight down the middle as if the graph is reflected to the other side
intercepts...
x - intercept is when y = 0, note there is 2 of these a negative and positive root
y - intercept is when x = 0
vertex is the turning point
for an upward curve its a min
for a downward curve it a max
I attached an example of each on of these
The angle XYZ has and angle y which is twice the size of x. If the third angle is 20 degree what is the value of x and y
The value of angle x and y in the triangle XYZ are 53.33 degrees and 106.66 degrees, respectively.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
The angle XYZ has an angle y which is twice the size of x. Thus,
2x=y
The third angle is 20 degree, which is Z. Thus,
z=20
By the triangle angle sum theorem,
x+y+x=180
x+2x+20=180
3x=180-20
x=160/3
x=53.33
The measure of angle y is,
y=2×53.33
y=106.66
Thus, the value of angle x and y in the triangle XYZ are 53.33 degrees and 106.66 degrees, respectively.
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F(x)=2x-5 if x is 0
Please help hurry
Answer: -5
Step-by-step explanation:
2(0)-5
0-5 = -5
HELP ME PLEASE!!!!!!!!!!!!!!!!
Answer:
40
Step-by-step explanation:
you multiply them all together
Lydia received her salary on Friday. She spent one-half of her salary on rent and then spent $168 on her electric and water bill. Next she spent one-half of what was left on her phone bill. After spending $57.00 on gas for her car, Lydia had $92.00 left. How much did Lydia spend on rent?
A. $298
B. $466
C. $764
D. $932
Answer:
B) $466Step-by-step explanation:
Let the amount of rent is R
Calculate the value of R in reverse order of spending
R = (92 + 57)*2 + 168 = 466Correct choice is B
Answer:
B. $466
Step-by-step explanation:
[tex]\textsf{let}\: x= \textsf{Lydia's salary}[/tex]
[tex]\implies \textsf{rent}=\dfrac{1}{2}x[/tex]
Modelling the given information to find the total salary:
[tex]\implies \left(x-\dfrac{1}{2}x-168\right)-\dfrac{x-\frac{1}{2}x-168}{2}-57=92[/tex]
[tex]\implies \dfrac{1}{2}x-168-\dfrac{\frac{1}{2}x-168}{2}-57=92[/tex]
[tex]\implies \dfrac{1}{2}x-\dfrac{\frac{1}{2}x-168}{2}=317[/tex]
[tex]\implies x-(\frac{1}{2}x-168)=634[/tex]
[tex]\implies x-\frac{1}{2}x+168=634[/tex]
[tex]\implies \dfrac{1}{2}x=466[/tex]
[tex]\implies x=932[/tex]
Therefore, Lydia's total salary was $932
[tex]\implies \textsf{rent}=\dfrac{1}{2}(932)=\$466[/tex]
