Answer:
(2x - 3) cm
Step-by-step explanation:
Area of window = height × length
Given:
Area = (4x² + 2x - 12) cm²Height = (2x + 4) cmTo find the length of the window, factor the expression for Area.
Factor [tex]4x^2+2x-12[/tex]:
Find 2 two numbers that multiply to the product of the leading coefficient and the constant (4 × -12 = -48) and sum to the coefficient of the middle term (2): -6 and 8
Rewrite the middle term as the sum of these 2 numbers:
[tex]\implies 4x^2-6x+8x-12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(2x-3)+4(2x-3)[/tex]
Factor out the common term (2x - 3):
[tex]\implies (2x+4)(2x-3)[/tex]
Therefore, the length of the window is (2x - 3) cm
(2x-3)cm
Answer:
Solution given:
height =2x+4
length=?
Area of window =(4x²+2x-12)cm²
we have
length*height =Area
length*(2x+4)=4x²+2x-12......(1)
Firstly let factorize 4x²+2x-12
taking common 2(2x²+x-6)
doing middle term factorization 2(2x²+4x-3x-6)
=2(2x(x+2)-3(x+2))
=2(x+2)(2x-3)
substituting it in equation 1
length*(2x+4)=2(x+2)(2x-3)
length*2(x+2)=2(x+2)(2x-3)
length =2x-3 cm
The length of window is (2x-3)cm
this box can be packed with 48 unit cubes. The edge length of each unit cube is 1 meter. What is the volume of the box?
Answer:
48 m^3
Step-by-step explanation:
along the length = 8 cubes = 8 m
breadth = 3 cubes = 3 m
height = 2 cubes = 2 m
volume = 48 m^3
Of all rectangles with a perimeter of 12 which one has the maximum area
The rectangle maximum area will be A=9 square units with the length=3 and the width=3.
What is area of rectangle?Area is defined as the space occupied by a plane or rectangle having length and width in two dimensional plane.
It is given that the perimeter of rectangle is P=12
So from the formula of perimeter of rectangle
2(L+W)=12
L+W=6
L=6-W
Now the area of rectangle will be
A=LxW
A=(6-W)W
Now for maximum area we will find the derivative and equate to zero.
[tex]A=(6W-W^2})[/tex]
[tex]A'=6-2W=0[/tex]
[tex]W=3[/tex]
[tex]L=6-W=6-3=3[/tex]
So the area will be
[tex]A=3\times 3=9 \ square \ units[/tex]
Hence the rectangle maximum area will be A=9 square units with the length=3 and the width=3.
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Tina will use the number cube, the spinner, and the coin shown below in a game. The number cube has faces numbered 1 through 6. Tina will roll the cube, spin the spinner, and flip the coin one time each to form an outcome. How many unique outcomes where the number on the cube is greater than 4 are possible?
Answer:
2
Step-by-step explanation:
We dont know how many spinner slots there are so I assume 8.
to get greater than 4 you need the cube which has 6 sides. Only 5 and 6 are > 4. So 2.
Sorry if this is incorrect...
9.1% of 80 is closest to which number?
The given function 9.1% of 80 is the closest to the number which is approximate 7.
How to find how much percent 'a' is of 'b'?Suppose a number is 'a'
Suppose another number is 'b'
We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
[tex]\dfrac{a}{b} \times 100[/tex]
(in percentage)
We have to find that 9.1% of 80 is the closest to which number.
[tex]\dfrac{9.1}{100} \times 80\\\\= 0.91 \times 8\\\\\= 7.28[/tex]
Hence, The given function 9.1% of 80 is the closest to the number which is approximate 7.
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Help:
[tex]1.\ &x^4-61x^2+900=0 \\ 2. \ & x^4-25x^2+144=0[/tex]
[tex]\bf{1) \ x^4-61x^2+900=0 }[/tex]
Applying the factorization method, for example:
[tex]\bf{ 0=(x^2)^2-61(x^2)+900=(x^2-36)(x^2-25)}[/tex]
[tex]\bf{\\ &=(x+6)(x-6)(x+5)(x-5); }[/tex]
[tex]\bf{ x_1=6 \quad x_2=-6 \quad \ \ \ x_3=5 \quad x_4=5 }[/tex]
[tex]\bf{2) \ x^4-25x^2+144=0 }[/tex]
Applying the factorization method:
[tex]\bf{0&=(x^2)^2-25(x^2)+144=(x^2-16)(x^2-9) }[/tex]
[tex]\bf{ =(x-4)(x+4)(x-3)(x+3); }[/tex]
[tex]\bf{ x_1=4 \quad x_2=-4 \quad x_3=3 \quad x_4=-3 }[/tex]
The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:
graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 8, 0. The vertex is at 4, 270
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?
Answer:
A. x-intercepts: prices at with profit is zero
maximum: price at which profit is a maximum
increasing: (-∞, 3); decreasing: (3, ∞) — profit increases with increasing pen price below $3, decreases with increasing pen price above $3
B. -26 2/3; loss of profit for each dollar increase in pen price
Step-by-step explanation:
Part A:
The definition of the function tells you what points on the graph represent. The x-intercept at x=0 tells you the company's profit will be zero when the price of pens sold by the company is zero.
The x-intercept at x=6 tells you the company's profit will be zero when the price of pens sold is $6.
The maximum value of 120 at x=3 tells you the company's profit will be $120 when the price of pens sold is $3.
The graph goes "uphill" for x < 3, so the function is increasing for x < 3. The function goes "downhill", so is decreasing, for x > 3. This tells you profit increases with pen price when the price is below $3, and decreases with pen price above $3.
__
Part B:
The equation of the function describing the graph is ...
f(x) = -120/9x(x -6)
so, at x=5, the value is ...
f(5) = -120/9(5)(-1) = 600/9 = 66 2/3
Then the average rate of change from x=3 to x=5 is ...
m = (f(5) -f(3))/(5 -3) = (66 2/3 -120)/2 = (-53 1/3)/2 = -26 2/3
This represents the average change in profit for each dollar increase in the price at which pens are sold.
Simplify the expression
Answer:
sin²x
Step-by-step explanation:
[tex]\frac{\tan \left(x\right)}{\tan \left(x\right)+\cot \left(x\right)}[/tex]
[tex]=\frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)+\sin ^2\left(x\right)}[/tex]
Rewrite using trigonometric identities
[tex]=\sin ^2\left(x\right)[/tex]
What are the zeros oh g(x)=x(x+1)(x-2)^2
[tex]~~~~~x(x+1)(x-2)^2 =0\\\\\implies x = 0~~ \text{or}~~ x +1 = 0~~ \text{or}~~ (x-2)^2 = 0\\\\\implies x = 0, ~ x = -1 , ~x=2\\\\\text{Hence the roots are}~0,-1 ,~2[/tex]
What is the range of the graphed function?
{x |-2 < x < 2}
{y |-2 < y < 2}
{x | x is a real number}
{y | y is a real number}
Answer:
{y| y is a real number}
Step-by-step explanation:
The range is all the y's that an equation can produce or all the y's on a graph of the function.
This graph has every and any real y (because it keeps going forever, even off the screen or paper) It's a little hard to see, bc we just see it going left and right mostly, but it is also slightly going up (to the left) and down (to the right)
Which of the following is the best definition of radiation?
Answer:
Radiation is the emission and propagation of energy in the form of waves, rays or particles
Step-by-step explanation:
The formula below is used to convert a temperature in degrees Celsius, C to a temperature in degrees Fahrenheit, F
F = 1.8C + 32
The high temperature in a mountain city was 15 C. What was the high temperature in degrees Fahrenheit?
Jaclyn bought some decorative letters for a scrapbook project. If she selected a permutation of the letters shown, what is the probability that they would form the word “photography”?
Answer:
1 over 4,989,600 That's the answer yw btw
A clearance rack has items for 75% off. Harriet uses the expression p−0.75p to find the new price of an item that originally cost p dollars. Use the drop-down menus to complete each sentence.
The expression p - 0.75p can be simplified to p.
A: -1.75
B: 1.75
C: 0.25
This means Harriet can find the new price of an item by finding A: -175 % of the original price B: 175
C: 25
If the discount is 75% so the new price of the product will be 0.25P.
What is discount?Discount is the reduced amount on the MRP of any product. So we will give the less amount then the MRP of the product.
Here the discount on P is given as 75% so the price of the product now becomes P-0.75P;
The expression will be calculated as:
P-0.75P=0.25P
Hence If the discount is 75% so the new price of the product will be 0.25P.
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math question on photo please
[tex]2ay + 3az = 2dx + 3dy[/tex]
[tex]2ay - 3dy = 2dx - 3az[/tex]
[tex]y(2a - 3d) = 2dx - 3az[/tex]
[tex]y = \frac{2dx - 3az}{2a - 3d} \\ [/tex]
Solve the trigonometric equation for all values 0 < x ≤ 2.
sec 4x – 1=0
Answer:
x=1/4
Step-by-step explanation:
4x - 1 = 0 /+1
4x = 1 /:4
x= 1/4
What is the measure of ∠B?
Answer:
∠B=19°
Step-by-step explanation:
At the endpoints of a diameter, angle c meets the circle. It intercepts a 180-degree arc.We know that the measure of C is 90 degrees because the measure of an inscribed angle is half the measure of its intercepted arc. Angles of triangle of ABC must add up to 180.
m∠A+m∠B+m∠C= 180°
71°+m∠B+90°=180°
m∠B+161°=180°
m∠B=19°
what is 56.78 to one significant figure
Answer:
60.
Step-by-step explanation:
The second digit is 6, so we round up the first digit and add training zero. There is no need to add the '00' after the decimal point.
help asap check picture
The remainder of the given expression will be 66.
What is division?Division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic.
The given polynomlal x⁴+3x³-6x²-12x-8 will be divided by x-3 so we need to find the remainder:-
x-3) x⁴+3x³-6x²-12x-8 ( x³-6x²+12x+24
x²-3x³
_______________
6x³-6x²-12x-8
6x³-18x²
________________________
12x²-12x-8
-12x²-36x
_____________________
24x-8
24x-72
_______________________
66
Hence the remainder of the given expression will be 66.
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Three times x decreased by four is 17.
What is x?
(06.01)What type of association does the graph show between x and y?
(A) Linear positive association
(B) Nonlinear positive association
(C) Linear negative association
(D) Nonlinear negative association
Answer:
(A) Linear positive association
Step-by-step explanation:
Hope it helps you in your learning process.
PLEASE HELP FAST
X=
Y=
Find value of missing variable
Step-by-step explanation:
hope u understand......
HELP ME WITH THIS QUES
Answer:
3 [tex](\frac{5}{6}) ^{4}[/tex]
Step-by-step explanation:
each post is [tex]\frac{5}{6}[/tex] the height of the previous post
there are 4 poles between the tallest 3 ft and the smallest
this involves multiply the heights of previous poles by [tex]\frac{5}{6}[/tex] , 4 times
shortest pole = 3 × [tex](\frac{5}{6}) ^{4}[/tex]
Consider the following binomial experiment: a company owns 6 copiers. the probability that on a given day any one copier will break down is 0.63. what is the probability that at least 4 copiers will break down on a given day
Answer:
0.6063
Step-by-step explanation:
Just substitute in the binomial probability formula from 4 successes until 6 successes.
what’s the area and the perimeter and of the triangle?
Answer:
Perimeter: 26.43 m
Area: 27.99 sq m
Step-by-step explanation:
To find the perimeter we just add all the sides, 11.1+9.33+6 = 26.43
To find the area of a triangle, we use the formula we do (bh)/2
9.33 * 6 = 55.98
55.98 / 2 = 27.99
Hope this helped you! I would appreciate a Brainliest if this helped you a lot! Thank you, and have a good day!
Answer:
We first need to determine the perimeter of the triangle which is done by adding up all of the sides. When combining [tex]11.1\ m[/tex], [tex]9.33\ m[/tex], and [tex]6\ m[/tex] we get a final answer of [tex]26.43\ m[/tex] as the perimeter of the triangle.
The second part that we need to determine is the area of the triangle which is done by using [tex]A=\frac{1}{2}*b*h[/tex]. In this example our base is [tex]6\ m[/tex] and our height is [tex]9.33\ m[/tex]. So when inputting those values into our area equation, we get [tex]A=27.99\ m^2[/tex]
Hope this helps! Let me know if you have any questions
please asap i dont need explaination correct answer gets brainliest
Answer:
it is 65 byeeeeeeeeeeeeeeeeee
Answer:
well total surface area of this prism is sum of area all sides of prism.
therefore 170 + 170 + 160 + 120 + 120 = 740m²
Therefore total surface area is 740m² i didn't give explanation since you said you don't need it.
By : Modern Einstein
An angle measures 130.8° more than the measure of its supplementary angle. What is the measure of each angle
Answer:
The angles are 24.6° and 155.4°
Step-by-step explanation:
Supplementary angles:Supplementary angles add up to 180°
Let the measure of the supplementary angle = x
So, the angle is 130.8 more than 'x'
The angle = x + 130.8
The angles are supplementary.
x + (x + 130.8) = 180
x + x + 130.8 = 180
2x + 130.8 = 180
2x = 180 - 130.8
2x = 49.2
x = 49.2/2
x = 24.6
x + 130.8 = 24.6 + 130.8
= 155.4
The angles are 24.6° and 155.4°
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[tex]\blue{\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
An angle measures 130.8º more than its supplementary angle. What is the measure of each angle?
[tex]\blue{\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Supplementary angles add up to 180º.
In order to find the unknown angles, we should first let the angle be x.
Set up an equation:-
(remember, there are 2 angles, x and x+130.8):-
x+x+130.8=180
Add the x's:-
2x+130.8=180
Subtract 130.8 from both sides:-
2x=49.2
Divide by 2 on both sides:-
x=24.6º
To find the other angle, add 130.8º:-
24.6+130.8=155.4º
Second angle=155.4º
Now, we need to make sure our solution is correct.
We can easily check it by adding both angles together and seeing whether or not we end up with 180:-
155.4+24.6=180
180=180
Since the left-hand side equals the right-hand side, our solution is indeed correct.
The angles are 24.6º and 155.4º
Good luck.
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Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of xx that support your conclusion.
x-5= -5+x
Since the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.
What is a linear equation?The equation which have a degree of one will be called as the linear equation the graph of the equation will be always a straight line.
Here we have the equation:
x-5=-5+x
or
x-5=x-5
Here we can see that the ratios are same:
[tex]\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}\\\\\\\\\dfrac{1}{-5}=\dfrac{1}{-5}[/tex]
So the equations will be coincident to each other or line one will coincide with line 2. Hence the two equations are of line and coincident to each other so the equations will have an infinite number of solutions.
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ANdy has some sweets. He gives on quator of them sweets to Dan. Dan eats five sweets and has one left. How many sweets did Andy start with
Answer: 24
Step-by-step explanation:
¼ of Andy's sweets = 5 + 1 with Dan
¼ of Andy's sweet is 6
Andy has 6×4 sweet
Use the drop-down menus to complete the statements.
is the illegal capture or killing of wild animals.
results in the complete loss of an organism’s home.
can use up important resources that other organisms need.
is the release of harmful substances into the environment.
Answer:
Step-by-step explanation:
Keep going I believe in you!
Suppose Josh Borrows $2000 at an interest rate of 3% compounded each year. Assume that no payments are made on the loan.
Do not do any rounding.
(A) Find the amount owed at the end of year 1.
(B) Find the amount owed at the end of 2 years.
Answer:
a)2975
b)3450
Step-by-step explanation:
