Answer:
The answer is 3( x - 2)(x + 6)Step-by-step explanation:
3x² - 12x - 36
To factorize the expression first factor 3 out of the expression
That's
3( x² - 4x - 12)
Factorize the terms in the bracket
To do so write - 4x as a difference
That's
3( x² + 6x - 2x - 12)
Factor out x from the expression
3[ x( x + 6) - 2 ( x + 6) ]
Next factor x + 2 out
We have the final answer as
3( x - 2)(x + 6)Hope this helps you
If g (x) is the inverse of f (x) and f (x) = 4 x + 12, what is g (x)
g (x) = 12 x + 4
g (x) = one-fourth x minus 12
g (x) = x minus 3
g (x) = one-fourth x minus
Answer:
[tex]g(x) = \frac{1}{4} x - 3[/tex]Step-by-step explanation:
Since g(x) is the inverse of f (x) to find g(x) must first find f-¹(x)
To find f-¹(x) equate f(x) to y
That's
f(x) = y
y = 4x + 12
Next interchange the terms x becomes y and y becomes x
That's
x = 4y + 12
Next make y the subject
4y = x - 12
Divide both sides by 4
[tex]y = \frac{1}{4} x - 3[/tex]Therefore
[tex]g(x) = \frac{1}{4} x - 3[/tex]Hope this helps you
The Varners live on a corner lot. Often, children cut across their lot to save walking distance. The children’s path is represented by a dashed line. Approximate the walking distance that is saved by cutting across their property instead of walking around the lot. Hypotenuse: 32 ft , Short leg: x , Long leg: x+6
Answer:
[tex]x= \sqrt{503}-3[/tex]
Step-by-step explanation:
Hypotenuse = 32 feet
Short leg = x
Long leg = x+6
We will use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]32^2=x^2+(x+6)^2[/tex]
[tex]1024=x^2+x^2+36+12x[/tex]
[tex]2x^2+12x-988=0[/tex]
[tex]x=-3-\sqrt{503}, \sqrt{503}-3[/tex]
Since the distance cannot be negative
So,[tex]x= \sqrt{503}-3[/tex]
Help and show work please.
Any rectangle is also a parallelogram (but not the other way around). So AB is parallel to CD. The angles BAC and ACD are alternate interior angles that are congruent due to the parallel sides mentioned.
(angle BAC) = (angle ACD)
3x+4 = x+28
3x-x = 28-4
2x = 24
x = 24/2
x = 12
So,
angle BAC = 3x+4 = 3*12+4 = 40 degrees
and
angle CAD = 90 - (angle BAC) = 90 - 40 = 50 degrees
With any rectangle, the four interior angles are always 90 degrees. So that's why angles BAC and CAD add to 90.
Iy
What is the domain of the function f(x) = 3|x + 4[ + 1?
ca
4+
3
-2-
1+
O all real numbers
O all real numbers less than or equal to -4
O all real numbers greater than or equal to 1
O all real numbers greater than or equal to -4
-7-5-5
3-2-11
5.6
X
2.
2Y
16
Answer:
all real numbers
Step-by-step explanation:
The function f(x) = 3|x +4| +1 is defined for all values of x. Its domain is all real numbers.
solve the following inequality for v. 4v-8≤5v+5
[tex]\text{Solve for v:}\\\\4v-8\leq5v+5\\\\\text{Subtract 5v from both sides}\\\\-v-8\leq5\\\\\text{Add 8 to both sides}\\\\-v\leq13\\\\\text{Divide both sides by -1, while also flipping the inequality}\\\\\boxed{v\geq-13}[/tex]
Answer:
v>=-13
Step-by-step explanation:
4v-8<=5v+5
4v-5v-8<=5
-v-8<=5
-v<=5+8
-v<=13
v<=-13
v>=-13
A store pays $10 for each shirt it buys. The store sells each shirt for 60%
more. What is the price of a shirt at the store?
Answer:
16$ per shirt
Step-by-step explanation:
60% of 10 is 6
10 + 6 = 16
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answer:
A. 0
Step-by-step explanation:
In order for there to be a 1 in 3 chance, there would have to be an equal number of the three chalices. Since four is the smallest number, the other two must have four left as well. That means Donavan drank 1 spoiled milk and 2 flat sodas. Therefore, he drank 0 purified water.
Among Patients who did not relapse which statement was most effective and what’s its conditional relative frequency
Answer:
For those who achieve a year of sobriety, less than half will relapse. If you can make it to 5 years of sobriety, your chance of relapse is less than 15 percent.
So A
Answer:
2
Step-by-step explanation:
The coefficient of 6x is
1
6
Х
Answer:
6
Step-by-step explanation:
If a number and a variable were together in a term, the number would the the coefficient. The coefficient would multiply the variable.
In '6x', the number '6' is the coefficient. '6' would be multiplying 'x'.
The correct answer should be 6.
Help, please show work
Answer:
132
Step-by-step explanation:
If US bisects the angle then
BUS = SUL
2x+10 = 3x-18
Subtract 2x from each side
2x+10 -2x = 3x-18-2x
10 = x-18
Add 18 to each side
10+18 =x
28 =x
We want to find BUL
BUL = BUS + SUL
2x+10 + 3x-18
5x-8
5*28 -8
140-8
132
Answer:
m<BUL=132
Step-by-step explanation:
Since US bisects <BUL, we know that <BUS ≅ <SUL
This is based on the angle bisector definition.
Hence, we can set up an equation to solve for x.
<BUS≅<SUL
2x+10=3x-18
Subtract 10 from both sides
2x+10-10=3x-18-10
2x=3x-28
Subtract 3x from both sides
2x-3x=3x-3x-28
-x=-28
Divide both sides by -1
x=28
m<BUL is the sum of m<BUS and m<SUL
m<BUL=m<BUS+m<SUL
m<BUS=2x+10
m<SUL=3x-18
Plug it in
m<BUL=2x+10+3x-18
Combine like terms
m<BUL=5x-8
Plug in 28 for x
m<BUL=5(28)-8
m<BUL=140-8
m<BUL=132
Kitty buys hot chocolate sachets. There are 14 hot chocolate sachets in a small box. A small box costs £3.49. Kitty uses 3 hot chocolate sachets each day. Work out the how much Kitty spends on hot chocolate sachets in a four-week period.
Answer:
24.43
Step-by-step explanation:
first find the price of One sachets
next Find the no. of sachets consumed for four weeks..
and at last the product of the price of one sachet and no. of sachets consumed will give the answer...
Mathematical operation are above...
please help real quick
Answer:
B. 945 m^3
Step-by-step explanation:
We just need to find the volume of the big box and the small box and find the difference.
To find the volume of a box, we multiply length, width, and height
Big box:
15.3x7x10=1071
1071
Small box:
4.2x3x10=126
126
1071-126=945
945 m^3
Answer:
b
Step-by-step explanation:
What is the area of triangle PQR to the nearest tenth of a square meter? Drawing is not to scale. A. 24.1 m2 B. 34.4 m2 C. 48.2 m2 D. 68.8 m2
Answer:
b
Step-by-step explanation:
The area of triangle PQR which is an SAS triangle, to the nearest tenth, is: A. 24.1 m²
What is the Area of an SAS Triangle?The area of an SAS triangle = ½ × bc × sin(A).
Given the following:
PQ (b) = 14 mRQ (c) = 6 mAngle Q (A) = 35°Area of triangle PQR = ½ × (14)(6) × sin(35)
Area of triangle PQR = 24.1 m²
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This table shows values that represent a quadratic function.
What is the average rate of change for this quadratic function for the interval
from x= 1 to x= 3?
Answer:
D. -4
Step-by-step explanation:
Using the general formula, [tex] m = \frac{f(b) - f(a)}{b - a} [/tex] , average rate of change for the quadratic function from x = 1 to x = 3, can be calculated as shown below:
Where,
[tex] a = 1, f(1) = -2 [/tex]
[tex] b = 3, f(3) = -10 [/tex]
Plug in the above values in the average rate of change formula:
[tex] m = \frac{-10 - (-2)}{3 - 1} [/tex]
[tex] m = \frac{-10 + 2}{2} [/tex]
[tex] m = \frac{-8}{2} [/tex]
[tex] m = -4 [/tex]
Average rate of change is D. -4
A. ASA
B. CPCTC
C. AAS
D. SAS
Answer:
It is ASA congruence rule as the 2 angles and the included side of the triangle are equal
Choose the function whose graph is given by
C)
Because if you choose some points for example x = 0 and x = 3.14 (≈ pi)
you will see that there's only one match.
Answer:
Option C. y = cos x -2
Step-by-step explanation:
Please find the perimeter!
Answer:
1. half circle: C = (2πr) / 2
a. C = (2π4) / 2 ≈ 12.566
2. triangle:
a. find slant / hypotenuse.
i. 4² + 10² = c²
ii. 16 + 100 = c²
iii. c² = 116
iv. c ≈ 10.770
b. add both slants to find triangular area
i. 10.77 + 10.77 ≈ 21.54
3. add:
a. 12.566 + 21.54 ≈ 34.106 cm
hope this helps :)
The product (5+ i) (5 – i) is a real number, 26. What are the factors (5 + i) and (5 – i) called? (1 point)
o complex numbers
O imaginary units
complex conjugates
O imaginary numbers
please help :( suck at math all the way
Answer:
complex conjugates
Step-by-step explanation:
The factors (5 + i) and (5 – i) are called complex conjugates.
Answer:
complex conjugates
Step-by-step explanation:
Numbers of the form a+ bi and a - bi are complex conjugates.
Their product is real.
Two birds start from the same nest and head off in opposite directions. The speed of the first bird is 15mph more than the speed of the second.After 6 hours the two birds are 402 miles apart. Find the speed of each bird?
Answer:
41 mph26 mphStep-by-step explanation:
The rate at which distance is increasing between the birds is ...
r = d/t = (402 mi)/(6 h) = 67 mi/h
This is the sum of the speeds of the two birds, so is 15 mph more than double the speed of the slower bird. That bird's speed is then ...
(67 -15)/2 = 26 . . . miles per hour
The faster bird is 15 mph faster so is 26+15 = 41 mph.
The slower bird's speed is 26 mph; the faster bird's speed is 41 mph.
What is the median of the data represented in the box plot shown in the image? A. 15 B. 25 C. 35 D. 45 Show all work!
Answer:
35
Step-by-step explanation:
The median is the middle number in the data
The middle is the line in the middle of the box
Median is 35
In a box plot, the median can be found by looking the middle dot in the rectangle.
As we can we, the middle dot represents 35 and the median.
Best of Luck!
Directions: Calculate the percent increase or decrease between the starting and ending
quantities below. Round your answer to one decimal place.
1. Start: 3
End: 10
2. Start: 9
End: 20
3. Start: 100
End: 85
4. Start: 45
End: 20
5. Start: 30
End: 60
I'll do the first two to get you started
===============================================
Problem 1
A = 3 = starting value
B = 10 = ending value
C = percent change
C = [ (B - A)/A ] * 100%
C = [ (10-3)/3 ] * 100%
C = (7/3) * 100%
C = 2.3333333 * 100%
C = 233.33333%
C = 233.3%
The positive C value means we have a percent increase. If C was negative, then we'd have a percent decrease.
Answer: 233.3% increase===============================================
Problem 2
A = 9 = start value
B = 20 = end value
C = percent change
C = [ (B - A)/A ] * 100%
C = [ (20-9)/9 ] * 100%
C = (11/9)*100%
C = 1.2222222222*100%
C = 122.22222222%
C = 122.2%
Answer: 122.2% increaseHELP QUICK!
A parabola, (y + 2)2 = 8(x - 3), is changed to (y + 10)2 = 8(x - 3). How will this affect the graph of the parabola?
A)
The vertex will shift up.
B)
The vertex will shift down.
C)
The vertex will shift to the left.
D)
The vertex will shift to the right.
Answer:
B) The vertex will shift down.
Step-by-step explanation:
In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.
The original parabola's vertex was (3, -2).
In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).
So, the parabola's vertex shifted down 8 units from -2 to -10.
Translate the following into an algebraic expression: The number that is 40% more than five more than a number a.
Answer:
1.4a > 5+a
Step-by-step explanation:
If the number is increased by 40% of that number, then it multiplies by 1.4. So, the left side of the equation is 1.4a.
On the right side of the equation, if the number is increased by 5, then the equation is a + 5.
Since the left side of the equation is more than the right side of the equation, we add a greater than sign. So the expression is 1.4a > 5+a
Find the value of x.
Answer:
I think it is 32 hopes its right
Sheila cuts 60 foot wire cable in equal stripes of [tex]\frac{4}{5}[/tex] of a feet each. how many strips does she make?
a) 48 b) 51 c)60 d) 70 e) 75
Answer:
e) 75
Step-by-step explanation:
Given the following :
Total length of cable = 60 foot
Length of each stripe = (4/5) of a feet
Number of stripes = ( total cable length / length of each stripe)
Number of stripes = ( 60 / (4/5))
Number of stripes = 60 ÷ 4/5
Number of stripes = (60 * (5/4)
= (60 * 5) / 4
= 300 / 4
= 75
Number of stripes made = 75
Two birds start from the same nest and head off in opposite directions. The speed of the first bird is 15mph more than the speed of the second.After 6 hours the two birds are 402 miles apart. Find the speed of each bird?
Answer: Speed of first bird =41 mph
Speed of second bird = 26 mph
Step-by-step explanation:
Let x be the speed of the second bird, then the speed of first bird will be x+15.
After 6 hours ,
Distance covered by first bird= (x+15)(6) [Distance = speed × time]
= 6x+90
Distance covered by second bird= (x)(6) = 6x
After 6 hours the two birds are 402 miles apart.
[tex]\Rightarrow\ 6x+90+6x=402\\\\\Rightarrrow\ 12x=402-90\\\\\Rightarrow\ 12x=312\\\\\Rightarrow\ x=\dfrac{312}{12}\\\\\Rightarrow\ x=\dfrac{312}{12}=26[/tex]
Speed of second bird = 26 mph, Speed of first bird = 26+15 = 41 mph.
The hanger image below represents a balanced equation. Find the value of r that makes the equation true.
Step-by-step explanation:
R is 4 times so the equation will be
32 = 4r
32/4 = r
8 = r
find a^4 + b^4 + c^4
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------------
Question: "Prove that a^{4} + b^{4} + c^{4} > abc(a + b + c) , where a, b, c are different positive real numbers."
------------------------------------------------------------------------------------------------------------
From the AM and GM inequality, we have:
a^4 + b^4 ≥ 2a^2b^2
b^4 + c^4 ≥ 2b^2c^2
c^4 + a^4 ≥ 2a^2c^2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From adding the inequalities we have above and dividing by 2, we have:
a^4 + b^4 + c^4 ≥ a^2b^2 + b^2c^2 + c^2a^2......1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now we need to repeat the process of a^2b^2, b^2c^2, and c^2a^2 to get:
a^2b^2 + b^2c^2 ≥ 2b^2ac
b^2c^2 + c^2a^2 ≥ 2c^2ab
c^2a^2 + a^2b^2 ≥ 2a^2bc
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now, we add from what we have above and divide by 2 to get:
a^2b^2 + b^2c^2 + c^2a^2 ≥ (b^2ac + c^2ab + a^2bc) or abc(b + c + a).....2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So, from (1) and (2) it follows:
a^4 + b^4 + c^4 ≥ abc( a + b + c)
Answer:
0.5
Step-by-step explanation:
a+b+c=0—(1)
a2+b2+c2=1—(2)
We know that:
(a+b+c)2=a2+b2+c2+2ab+2bc+2ca—(3)
Substituting (1) and (2) in (3) , 0=1+2(ab+bc+ca)
=>ab+bc+ca=−0.5—(4)
Squaring: (ab+bc+ca)2=0.25
=>a2b2+b2c2+c2a2+2ab2c+2bc2a+2a2bc=0.25
=>a2b2+b2c2+c2a2+2abc(a+b+c)=0.25
Since a+b+c=0 ,
a2b2+b2c2+c2a2=0.25—(4)
squaring (2) :
(a2+b2+c2)2=12
=>a4+b4+c4+2a2b2+2b2c2+2c2a2=1
=>a4+b4+c4+2(a2b2+b2c2+c2a2)=1—(5)
Substituting (4) in (5),
a4+b4+c4+2(0.25)=1
=>a4+b4+c4=0.5
Hope this helps :D
A ladder is leaning against a wall. The ladder is 5 metres long. The top of the ladder is 3 metres above the ground. The top of the ladder is sliding down at 8 metres/second. At what rate is the bottom of the ladder moving away from the wall?
Answer:
it is moved away in .625 seconds
Step-by-step explanation:
i did 5 divided by 8 though this question is weriod
Assuming the ladder is leaning against the wall and there are no spaces in between (that doesn't make sense sorry), it is still at a rate of 8 meters per second because it is standing straight up. It is moving at the same rate, since it is the same ladder.
Find the equation of a line that is perpendicular to line g that contains (P, Q).
coordinate plane with line g that passes through the points negative (3, 6) and (0, 5)
3x − y = 3P − Q
3x + y = Q − 3P
x − y = P − Q
x + y = Q − P
Answer:
x-y is parallel, im confused on what your asking for and what you mean by "negative"
Step-by-step explanation:
The equation of a line that is perpendicular to line g that contains (P, Q). is 3x − y = 3P − Q
What is Equation of line?The general form of the equation of a line with a slope m and passing through the point (x1, y1) is given as: y - y1 = m ( x- x1)
Further, this equation can be solved and simplified into the standard form of the equation of a line.
Given:
Line g passes through (3,6) and (0,5).
Slope of lone= y2 - y1/ (x2 - x1)
Perpendicular lines have opposite, reciprocal slopes, so negative change in x over change in y.
slope of line= -(-3 - 0)/(6 - 5)
= - -(-3)/1 =
slope of line = 3
Now, Two lines are perpendicular if they have the same slope.
Line parallel to line g has a slope of 1. Since it passes through (P, Q),
y - y1 = m ( x- x1)
y- Q =3 ( x- P)
y- Q = 3x- 3P
3x − y = 3P − Q
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