[tex](4 {x}^{2} + 9x - 7) - ( - 7 {x}^{2} + 5x - 1) \\ = (11 {x}^{2} + 4x - 6)[/tex]
Answer:
11x^2+4x-6
Step-by-step explanation:
[tex]4x^2+9x-7+7x^2-5x+1\\\\simplify: 11x^2+4x-6[/tex]
A small bank vault is being designed in the shape of a rectangular prism. The vault’s sides and top should all be 3 feet thick. The outer length of the vault should be twice the outer width. The outer height should be the same as the outer width. What should the outer dimensions of the vault be if is to have 972 cubic feet of space?
(^ incase the words got cut off in the pic)
This represents the exterior length, width and height in that order.
============================================================
Work Shown:
The steps you have written so far are 100% correct.
From there, you multiply the interior width, length and height to get the interior volume 972. Solve for x
So,
(length)*(width)*(height) = volume
(2x-6)(x-6)(x-3) = 972
(2x-6)(x^2-9x+18) = 972
2x(x^2-9x+18)-6(x^2-9x+18) = 972
2x^3-18x^2+36x-6x^2+54x-108 = 972
2x^3-24x^2+90x-108 = 972
2x^3-24x^2+90x-108-972 = 0
2x^3-24x^2+90x-1080 = 0
2(x^3-12x^2+45x-540) = 0
x^3-12x^2+45x-540 = 0
From here, we can use the factor by grouping method
x^3-12x^2+45x-540 = 0
(x^3-12x^2)+(45x-540) = 0
x^2(x-12)+45(x-12) = 0
(x^2+45)(x-12) = 0
Setting each factor equal to 0 leads to....
x^2+45 = 0 doesn't have any real valued solutions for x, since sqrt(-45) is a complex number. We'll ignore this case and move on.x-12 = 0 solves to x = 12So x = 12 is the only solution here.
If x = 12, then we have these exterior dimensions:
length = 2x = 2*12 = 24 ftwidth = x = 12 ftheight = x = 12 ftThe outer dimensions are 24 ft by 12 ft by 12 ft
From that, the inner dimensions would be:
L = 24-6 = 18 ft
W = 12-6 = 6 ft
H = 12-3 = 9 ft.
Then note how L*W*H = 18*6*9 = 972 ft^3 to help confirm the answer.
Please help I don’t understand! Giving brainliest
Answer:
b
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
A is 27
B is 1/3
D is also 1/3
hope this helps!
a batch of granola uses 2 cups of honey to make 24 servings. how much honey is needed to make 42 servings
Answer:
hi hlo wat is ur help tell me quick
Everyone learns differently. Some people like to use models and tools to help them learn math concepts. Many people like to use a combination of these strategies. What tools and strategies do you use to help yourself learn new ideas in math?
Answer:
Kindly check explanation
Step-by-step explanation:
Learning could be explained as a process of acquiring knowledge about a certain subject, trade or other aspects of life. In terms of learning about certain school subjects, a student needs to discover him or herself in other to make acquiring knowledge easy and less tedious for him or her. Now, there are designated tools more than evwr which could aid learning. A very important recommendation which could aid acquiring matematicka knowledge is the use of models to gain an insight to the fundamentals of a mathematical problem and thus seeing how it works. After this one can then break down the mathematical procedure embedded or used it aid the model manually in other to grasp the full concept of the principle.
i will mark brainliest to the first 2 people who answer
Answer:
B
-15 < 99 and | -9 | < | 15 |
Step-by-step explanation:
Those lines " | " refer to absolute value, meaning it is the distance from 0. You can easily get this just by cutting off a negative sign.
So we do know -9 is greater than -15 obviously, and the absolute value of -9 is 9, because -9 is 9 units from 0.
-15 is 15 units away, so when using absolute value, -15 is greater than -9.
Btw, you can only give one brainliest, you don't get the option to give two on brainly.
Just saying.
Idc if I get it honestly.
. A pitcher’s mound on a women’s softball field is 43 feet from home plate and the distance between the bases is 60 feet. How far is the pitcher’s mound from first base?
Answer:
42.43 ft
Step-by-step explanation:
Please find attached an image of the softball pitch
h² = p² + f² -2x p×f×cos45
h² = 43² + 60² - 2x (43)(60) x 0.7071
h² = 1849 + 3600 - 3648.636
h² = 1800.364
h = √1800.364
h = 42.43 feet
A machine can pack 80 cans in 5 minutes. Choose all of the values that show the ratio of cans to minutes.
Answer:
16 cans per minute
Step-by-step explanation:
Its simple 80 divided by 5 is 16 so ever minute 16 cans are packed.
The ratio of the cans to minutes is 80 : 5 or 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.
What is the ratio?It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign: between the numbers.
A machine can pack 80 cans in 5 minutes.
let's denote the number of cans with X and
Time with T
So we have to find the value of X : T
X = 80 and
T = 5 minutes
X : T = 80 : 5 or
X : T = 16 : 1 (divide by 5 on both sides)
It means the machine can pack 16 cans per minute.
Thus, the ratio of the cans to minutes is 16 : 1, and the machine can pack 16 cans per minute if a machine can pack 80 cans in 5 minutes.
Learn more about the ratio here:
brainly.com/question/13419413
Pls, help with this math question
Step-by-step explanation:
OCB=CBO(base angle of isosceles triangle are equal)
now,
OCB+CBO+BOC=180°(sum of angles of triangles)
BOC=180-62
BOC=118°
again,
x=BOC/2{inscribed angle is half of central angle standing on Same base}
x=118/2
x=59°
stay safe healthy and happy...The circular rug is placed on a square floor. The rug touches all four walls. How much of the floor space is not covered by the rug? Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
To solve this, we first need the area of the square, then subtract from it the area of the circle. Since our instructions tell us to round to the nearest hundredth, we will use 3.1415 for pi. First the square:
A = s * s so
A = 15 * 15 and
A = 225; next the circle:
A = 3.1415 * 7.5*7.5 (the area of a circle is pi times the radius squared. The radius is half of the diameter which is 15, so r = 7.5) so
A = 176.709
Subtracting the area of the circle from the area of the square:
225 - 176.709 = 48.29 ft squared.
Help! Need this done quickly! picture is upside down so please flip your screen! sorry!
Answer:
x=6
Step-by-step explanation:
Hi there!
1) Determine the perimeter of the square
We're given that the perimeters of the square and the rectangle are equal. Therefore, after finding the perimeter of the square, we will also know the perimeter of the rectangle.
Find the side length of the square using the area formula:
[tex]A=l^2[/tex] where l is the side length
Plug in the given area 121 in.²
[tex]121=l^2[/tex]
Take the square root of both sides
[tex]\sqrt{121} = \sqrt{l^2} \\11=l[/tex]
Therefore, the side length of the square is 11 inches. Plug this into the perimeter formula:
[tex]P=4l[/tex] where l is the side length
[tex]P=4(11)\\P=44[/tex]
Therefore, the perimeter of the square is 44 inches. The perimeter of the rectangle is also 44 inches.
2) Determine the value of x
Use the formula for the perimeter of a rectangle:
[tex]P=2(l+w)[/tex] where l is the length and w is the width
Plug in 3x and x-2 as the length and width
[tex]P=2(3x+(x-2))\\P=2(3x+x-2)\\P=2(4x-2)[/tex]
Plug in the perimeter 44 in.
[tex]44=2(4x-2)[/tex]
Expand the parentheses
[tex]44=8x-4[/tex]
Add 4 to both sides to isolate 8x
[tex]44+4=8x-4+4\\48=8x[/tex]
Divide both sides by 8 to isolate x
[tex]\frac{48}{8}=\frac{8x}{8} \\6=x[/tex]
Therefore, the value of x is 6.
I hope this helps!
(x ^ 3 + 3x ^ 2 - 4x + 5)/(x ^ 2 - 2)
Answer:
4x(3x^2 + 1)(x – 5) glad to help!!!!
what value of x will solve the equation 3/4x + 10 = 4
Answer:
-8
Step-by-step explanation:
Answer:
x = -8
Step-by-step explanation:
[tex]\frac{3}{4}x+10=4[/tex]
[tex]\frac{3}{4} x-10[/tex] [tex]-10[/tex] Subtract 10 from both sides
[tex]\frac{3}{4}x=[/tex] [tex]-6[/tex]
[tex]\frac{3}{4}(-8)[/tex] [tex]=-6[/tex] Substitute x for [tex](-8)[/tex] then Multiply [tex](-8)[/tex] by [tex]\frac{3}{4}[/tex]
[tex]-\frac{24}{4}[/tex] [tex]=-6[/tex] Simplify [tex]-\frac{24}{4}[/tex]
[tex]-6=-6[/tex]
Please help I am really confused with this
The answer should be A. 4 Meters
Expand the logarithm. Assume all expressions exist and are well-defined.
Write your answer as a sum or difference of common logarithms or multiples of common
logarithms. The inside of each logarithm must be a distinct constant or variable.
log 3y
Answer:
Step-by-step explanation:
log 3y = log(y)^3 (exponent)
or
= log(y)*log(y)*log(y) (multiples)
The logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).
What is logarithm? What is a mathematical function, equation and expression?logarithmic : It is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -[tex]$\log_{b}({b^x})=x[/tex] {where [b] is logarithmic base}
function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the following logarithmic expression as -
y = log(3y)
We have the following logarithmic expression -
y = log(3y)
Using the identity of logarithm -
log(AB) = log(A) + log(B)
log(3y) = log(3) + log(y)
Therefore, the logarithmic expression y = log(3y) can be written as sum or difference of common logarithms as log(3y) = log(3) + log(y).
To solve more questions on functions, expressions and polynomials, visit the link below -
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What is the measure of angle 2 in degrees?
Answer:
The measure of angle 2 is... 60 degrees.
Angle 1 - 93 degrees
Angle 2 - 60 degrees
Angle 3 - 27 degrees
Pls help me a quick financial maths problem
Answer:
$74 492.30
Step-by-step explanation:
P= 50 000
r= 8/100 = 0.08
n= 12
t= 5
P(1 + r/n) ^ (nt)
[tex] = 50000(1 + { \frac{0.08}{12} )}^{(12 \times 5)} [/tex]
=74492.285
please help meeee!!!
Answer:
90
Step-by-step explanation:
because 9x10 is 90 hope this helps
Of the 585 people that live in Benton, 187 live within two miles of the post office. Use mental math to find how many people live farther than two miles from the post office.
It clearly states to use mental math not brainly, sorry bro can't do anything for you
A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7 feet more than the distance of the base of the ladder from the building. At what height does the ladder hit the building
Answer:
Step-by-step explanation:
The length of the ladder is the length of the hypotenuse of the right triangle formed. Since the height up the building is based on the distance the ladder is from the base of the building, and that distance is x, then the height up the building is x + 7. So what we have is a right triangle with one leg measuring x, the other leg measuring x + 7, and the hypotenuse measuring 13. Set up using Pythagorean's Theorem:
[tex]13^2=(x+7)^2+x^2[/tex] and do some simplifying. The left side is easy since 13-squared is 169; the right side not so much. We first have to expand that set of parenthesis by multiplying x + 7 by itself twice to get a second degree polynomial:
[tex](x+7)(x+7)=x^2+14x+49[/tex] and now we have:
[tex]169=x^2+14x+49+x^2[/tex] which simplifies down a bit to
[tex]169=2x^2+14x+49[/tex]
The only way to solve this for x, the height up the side of the building, is to factor. In order to do that, everything has to be on one side of the equals sign, setting the whole messy thing equal to 0:
[tex]2x^2+14x+49-169=0[/tex] and
[tex]2x^2+14x-120=0[/tex]. Begin by factoring out a 2:
[tex]2(x^2+7x-60)=0[/tex] and then factor the remaining quadratic using whatever method you are currently using in class to solve for x. Doing this will give that
x = -12 and 5. Since a side length will never be negative, we determine that x = 5 which is the distance between the bases of the buildings, and the height up the building where the ladder hits it is 12.
Yes invests $1500 that compounds interest monthly with a 4.5% rate. How much money will he have after the 12 years?
Answer:
FV= $2,571.41
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Interest rate (i)= 0.045/12= 0.00375
Number of periods (n)= 12*12= 144 months
To calculate the future value, we need to use the following formula:
FV= PV*(1 + i)^n
FV= 1,500*(1.00375^144)
FV= $2,571.41
Someone pls help me!!!!
Answer:
J) 2r⁴s⁴
Step-by-step explanation:
if you know the area and the base, you can divide them to find the height
16r⁸s⁶ ÷ 8r⁴s² = 2r⁴s⁴
PLSSSS HELPP MEEEEE BRAINLIEST REWARDD
Answer:
40.) the third one
42.)the last one
Step-by-step explanation:
A study was conducted by a certain firm to determine who curses at their computer. The results indicated that 30% of people age 18-34 years have cursed at their computer. What are the odds against a randomly selected 18- to 34-year old having cursed at his or her computer. LOADING... Click the icon to view an explanation of odds. The odds, in the most simplified form, are nothing to nothing against a randomly selected 18- to 34-year old having cursed at his or her computer. (Type whole numbers.)
Answer:
The odds, in the most simplified form, are 7 to 3 against a randomly selected 18- to 34-year-old having cursed at his or her computer.
Step-by-step explanation:
Given
[tex]p = 30\%[/tex] ---- proportion that cursed their computer
Required
Odds against the selected
Using the complement formula, the proportion that the selected has not cursed at their computer is:
[tex]p' = 1 - p[/tex]
[tex]p' = 1 - 30\%[/tex]
[tex]p' = 70\%[/tex]
So, the odds against the selected is:
[tex]Odds = p' : p[/tex]
[tex]Odds = 70\% : 30\%[/tex]
Divide by 10%
[tex]Odds = 7: 3[/tex]
what is the solution 6x-4 =2(3x-2)
Answer:
x= 0
Step-by-step explanation:
6x-4=2(3x-2)
or,6x-4=6x-4
or,x=o
There are infinite solution of the expression.
We have to given that,
An expression to solve,
6x - 4 = 2 (3x - 2)
Now, We can simplify as,
6x - 4 = 2 (3x - 2)
Apply distributive property,
6x - 4 = 6x - 4
Combine like terms,
6x - 6x = 4 - 4
0 = 0
Hence, There are infinite solution of the expression.
Learn more about the mathematical expression visit:
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how many solutions does 3 (y-2) = 3y - 6 have
Answer:
Infinitely many solutions
Step-by-step explanation:
Simplify this
3 (y-2) = 3y-6
3 (y) + 3 ( -2) = 3y-6
3y-6=3y-6
Because these two equations are equal to each other, it is infinitely many solutions.
If this helps please mark as brainliest
Select the graph of Y = sec X Please help!!!!
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Select the correct answer.
What is the solution of 3x + y = 9 and 3x - 5y = 15?
OA.
= y = -1
OB.
r = g.y = 1
O c.
x = -1,4 = 12
OD. I = ly =
Reset
Next
Answer:
c
Step-by-step explanation:
i calculated and x was -1 and y was 10/3
As a contestant on a televised game show, Kiara gets to spin the big prize wheel, which has a radius of 2 meters. What is the prize wheel's area
Answer:
12.57
Step-by-step explanation:
We need to find of area of a circle and the formula for that is pie * radius ^2.
Pie * 2 squared = 12.57 rounded to the nearest hundredth
hii! i’ll give brainliest pls help
Answer:
b is correct
Step-by-step explanation:
how much would you need to pay?
Answer:
a
Step-by-step explanation: