Answer:
Length of the rectangular prism = 4 meters
But other possible values = (-5meters or - 9 meters)
Step-by-step explanation:
The volume of a rectangular prism = Length × Width × Height
From the question above,
Length = x meters
Width = x - 1 meters
Height = x + 11 meters
Volume of the Rectangular prism = 180 cubic meters
Hence,
(x) × (x - 1) × (x + 11) = 180
We expand the brackets
(x)(x - 1) (x + 11) = 180
x² - x(x + 11) = 180
x² (x + 11) - x(x + 11) = 180
x³ + 11x² - x² + 11x =180
x³ +10x² - 11x = 180
x³ + 10x² - 11x -180 = 0
The above is a polynomial
We solve this polynomial to find x
x³ + 10x² - 11x -180 = 0
(x - 4)(x + 5) (x + 9) = 0
x - 4 = 0
x = 4
x + 5 = 0
x = -5
x + 9 = 0
x = -9
We are asked to find the various values for the length hence,
From the above question, we are told that
Length = x meters
Therefore, the length of this rectangular prism = 4 meters or -5 meters or -9 meters.
Answer:
(1, 4)
Step-by-step explanation:
What is the slope of the line? y+2=−2(x−3) Choose 1 answer: A. −1/2 B. 1 C. −2 D. −1
Answer:
C. -2
Step-by-step explanation:
You have to look at the factor in front of the x after normalizing the equation in to y = ax + b. In other words, find a.
y+2 = -2(x-3) =>
y = -2x + 6 - 2
y = -2x + 4
a = -2
b = 4
Answer:
C. -2
Step-by-step explanation:
y+2=−2(x−3)Bringing the equation to slope-intercept form of y = mx + b, where m is a slope:
y + 2 = - 2x + 6y = -2x + 6 -2y = -2x + 4As m = -2, the slope is -2Correct answer choice: C. -2
If you can download 6 songs for $4.68, then how much would 10 songs cost.
Answer:
$7.80
Step-by-step explanation:
Find the cost to download 1 song. Divide 6 from 4.68
4.68/6 = 0.78
Each song costs $0.78.
Find the amount 10 songs cost. Multiply 0.78 with 10:
10 x 0.78 = 7.80
$7.80 is your answer.
~
Hi
6 = 4.68
10 = X
X = 10*4.68 /6
X = 46.8/6
X = 7.8
To which subsets of numbers does 30/15 belong?
A whole, rational
B integer, rational
C whole, integer, rational
D natural, whole, integer, rational
Answer:
Step-by-step explanation:
For
The number 30 / 15 belongs to the whole, integer, and rational numbers. the correct option is C.
What is a number system?
A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
The number set from 0 to infinity are called whole numbers. The number set from negative infinity to positive infinity are called integers.
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
The given number 30 / 15 is in the form of a rational number that can also be written as 2. Then the number 30 / 15 can be the whole, integer, and rational number.
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In which of these cases can we use the Law of Sines to solve the triangle?
a. ASA
b. SSA
c. SAS
d. SSS
Answer:
ASA
SSA
Step-by-step explanation:
The law of sines states that;
a/sin A = b/sin B = c/sin C
Where a,b,c are sides of the triangle and A,B,C are sides corresponding to those angles.
Hence we can use the sine rule when;
I) two angles and one side are given
2) two sides and an angle are given
Not that sine rule applies to triangles that are not right angled triangles.
Each product is in the form ax^2+ by+c. Which of the following explains the relationship between b and c?
Answer:
c is the square of half of b
Step-by-step explanation:
A quadratic equation can be written in the following form:
[tex]ax^2+bx+c[/tex].
Based off of the information provided, we can test to see if which answer choice is correct.
OPTION A IS INCORRECT:
Although, for [tex]x^2+6x+9[/tex], c is 1.5 times b, we do not see that relationship reflected in other equations, such as [tex]x^2+10x+25[/tex] and [tex]x^2+12x+36[/tex]. There must be a different relationship.
OPTION B IS INCORRECT:
Although c is double b for x^2+8x+16, this rule is not applicable for the rest of the equations. C is double b for the is 1.5 times that of b for x^2+6x+9, and for and for x^2+10x+25, c is 2.5 times b, and for x^2+12x+36, c is 3 times of b.
OPTION C IS CORRECT:
We can test this relationship based off of the information given.
for x^2+6x+9, c equals (6/2)^2 which is 9
for x^2+8x+16, c equals (8/2)^2 which is 16
for x^2+10x+25 c equals (10/2)^2 which is 25
and finally, for x^2+12x+36 c equals (12/2)^2 which is 36.
OPTION D IS INCORRECT:
C is not the square of B.
for x^2+6x+9, b^2 which is 36 (c here is 9)
for x^2+8x+16, b^2 is 64 (c here is 16)
for x^2+10x+25 b^2 is 100 (c here is 25)
and finally, for x^2+12x+36 b^2 is 144 (c here is 36).
What is the prime factorization of 75?
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
Answer:
V = 150π units^3
Step-by-step explanation:
The volume of this cylinder is V = πr²h = π(5 units)^2·(6 units), or
V = 150π units^3
The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.
What is the volume of a solid?The volume of a solid is the total space it contains in the three-dimensional space.
What is the volume of a cylinder?The volume of a cylinder can be given by the formula,
V = πr²h cube units,
where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
How to solve the given question?In the question, we are asked to find the volume of the cylinder shown in the figure.
The cylinder has a base radius (r) of 5 units, and height (h) of 6 units.
So, we can find its volume using the formula,
V = πr²h cube units,
where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
∴ The volume of the cylinder = π(5²)6 cube units
or, the volume of the cylinder = π*25*6 cube units
or, the volume of the cylinder = 150π cube units
or, the volume of the cylinder = 150*3.14 cube units = 471 cube units.
∴ The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.
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1/2(6+18)-2²
Help me my good ppl it asks to evaluate
Answer:
8
Step-by-step explanation:
1/2(6+18)-2^2
=1/2(24)-4
=12-4
=8
Kimberly's grade in Algebra is comprised of tests (40%), quizzes (40%), and a final project (20%). Her scores for each of the categories are 82 on tests, 100 on quizzes, and a 84 on her final project. Compute her weighted average for the class. (to the nearest tenth of a percent) A) 86.4% B) 88.6% C) 89.1% D) 89.6%
Answer:
D) 89.6 %
Average or mean of the given data = 89.6 %
Step-by-step explanation:
Step(i):-
Given data
X : 82 100 84
P(X=x) : 0.40 0.40 0.20
Step(ii)
Let 'X' be the discrete distribution
Mean of the discrete distribution = ∑ x P( x=x)
= 82 ×0.40 +100 ×0.40 +84 ×0.20
= 89.6
Final answer:-
Average of the given data = 89.6 %
The ratio of men to women working for a company is 4 to 3. If there are 203 employees total, how many women work for the company?
Answer:
87 women
Step-by-step explanation:
4x+3x=203
7x=203
x=29
29*3=87 :D
Consider the sequence {an} = {nrn}. Decide whether {an} converges for each value of r.
(a) r = 1/5
(b) r = 1
(c) r = 1/6
For what values of r does the sequence {nr^n} converges?
Answer:
a). converges
b). diverges
c). converges
Step-by-step explanation:
{ [tex]$ a_n $[/tex] } = { [tex]$ nr^n $[/tex] }
Using radio test,
L = [tex]$ \lim_{n \rightarrow \infty} |\frac{a_n + 1}{a_n}| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |\frac{(n+1)r^{n+1}}{nr^n}| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |(1+\frac{1}{n})^r| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |r| $[/tex]
= |r|
Therefore, [tex]$a_n$[/tex] converges in |r| < 1
a). r = 1/5
[tex]$\{ a_n \}= \{\frac{1}{5}, n \}$[/tex]
This sequence is monotonically decreasing and bounded.
0 < [tex]$ a_n $[/tex] < 1
Hence, { [tex]$ a_n $[/tex] } converges.
b). r = 1
{ [tex]$ a_n $[/tex] } = { n }
This sequence is monotonically increasing sequence which is not bounded.
Hence, { [tex]$ a_n $[/tex] } diverges.
c). r = 1/6
[tex]$\{ a_n \}= \{\frac{1}{6}, n \}$[/tex]
This sequence is monotonically decreasing and bounded.
0 < [tex]$ a_n $[/tex] < 1
Hence, { [tex]$ a_n $[/tex] } converges.
For |r| < 1, the [tex]$a_n$[/tex] converges.
Describe the translation. y=(x−6)2+7 → y=(x−1)2+3
The translation of the given graph has done in two steps.
1. Horizontal shift of 5 units to the left
2. Vertical shift of 4 units in the downwards direction.
What is the translation of a graph?"The translation of a graph is its rigid movement, vertically or horizontally."
The given translation of graph is:
[tex]y = (x - 6)^{2} + 7[/tex] to [tex]y = (x - 1)^{2} + 3[/tex]
Here, two types of translation has done to the first graph.
1. First of all, there is a horizontal shift of 5 units to the left has done.
[tex]y = (x - 6)^{2}[/tex] ⇒ [tex]y = [(x - 1) - 5)]^{2}[/tex]
2.After that, there is a vertical shift of 4 units in the downwards direction.
[tex]y = (x - 6)^{2} + 7[/tex] ⇒ [tex]y = (x - 1)^{2} + 3[/tex]
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Jeff and Cameron are arguing about which one of them is faster. Jeff says I can run 7 kilometers per hour!"
and Cameron says "I can run 100 meters per minute!!
Which one is faster?
Answer:
So Jeff is faster with 7 km per hour
Step-by-step explanation:
Jeff says I can run 7 kilometers per hour!
Cameron says "I can run 100 meters per minute!!
To actually know which one of them is the fastest we will convert their speed to be in the same unit
Let's convert meters per minute to kilometers per hour
100 meters per minute= 100 M/m
100 meters per minute= 100 *60/1000
100 meters per minute= 6000/1000
100 meters per minute= 6 km /h
100 meters per minute= 6 kilometers per hour
So Jeff is faster with 7 km per hour
Answer:
Jeff is faster than Cameron. Khan Academy
Step-by-step explanation:
using the number 5,647,210.392 the digit 2 is in the... place and the... place
Answer:
the 2 is in the hundreds and hundredths place
Need help will mark brainliest
Step-by-step explanation:
Range = highest value - lowest value
=25 – 12
= 13
First Quartile = 15
Third Quartile = 22
Interquartile = 7
Answer:
a) 7
b) 15
c) 13
d) 22
PLEASE HELP!
Use the values x = -0.5,0,1 to prove your solution to the equation 5 + x - 12 = 2x - 7 . In your final answer, include all of your calculations.
Answer:
0
Step-by-step explanation:
Hello!
To solve this we put in the values given to us for x and go till we get one this is true.
The values given for x are -0.5, 0, and 1
1
5 + 1 - 12 = 2(1) - 7
Combine like terms
-6 = -5
Since -6 does equal -5 the answer is not 1
0
5 + 0 - 12 = 2(0) - 7
Combine like terms
-7 = -7
Since -7 equals -7 the answer is 0
Hope this Helps!
6. What is the slope of the line given by the equation y = 4x +12?
Answer:
4
Step-by-step explanation:
y = 4x + 12
In y = mx+b
The coefficient of x (m) is the slope.
So the slope is 4
Answer:
The slope is 4
Step-by-step explanation:
y = 4x +12
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 4 and the y intercept is 12
The following dot plot shows the number of weekly challenge questions each of the 30 members the Math Bowl team answered correctly last season. Each dot represents a different member. Which of the following is a typical number of challenge questions one member answered correctly?
Answer:
10
Step-by-step explanation:
The most number of questions answered correctly are 10 and 11.
The typical number of questions a student answered correctly can be represented by the middle most value that is common to the data set.
If the data set is distributed evenly, the median, or the middle most value will fall on the 15th and 16th dots, which represents 10 correct correct challenge questions answered.
The typical number is 10.
Answer:
[tex]10[/tex]
Point r is on line segment qs. Given qr =2 and rs = 10, determine he length qs.
Answer:
[tex]\huge \boxed{\mathrm{12}}[/tex]
Step-by-step explanation:
R is a point on the line segment QS.
QR = 2
RS = 10
QS = 2 + 10
QS = 12
The length of the line segment QS is 12 units.
Given that, point R is on the line segment QS. Given QR =2 and RS = 10.
We need to determine the length of QS.
What is the line segment?A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.
Here, since R is in between QS, QS=QR+RS
=2+10=12 units
Therefore, the length of the line segment QS is 12 units.
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Jean saw a basic computer for $695.00 and a printer for $95.00. In order to buy the computer, Jean would work each week for four months. He earned $157.00 in May, $210.00 in June, $377.00 in July and $145.00 in August. Has Jean earned enough money to buy the computer and printer? If so, how much will he have left over after the purchase?
Answer:
YES
Step-by-step explanation:
$157+$210+$377+$145=$889
$695+$95=$790
Leftover
$889-$790 =$99
he would have $99 leftover
The amount left over with Jean is given by the equation A = $ 99
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount left over be represented as A
Now , the equation will be
The cost of basic computer is = $ 695.00
The cost of printer is = $ 95.00
The amount saved in month of May = $ 157.00
The amount saved in month of June = $ 210.00
The amount saved in month of July = $ 377.00
The amount saved in month of August = $ 145.00
The total amount saved = $ 157.00 + $ 210.00 + $ 377.00 + $ 145.00
The total amount saved = $ 889
The total cost of computer and printer = $ 695 + $ 95
The total cost of computer and printer = $ 790
The amount of money left over with Jean A = total amount saved - total cost of computer and printer
Substituting the values in the equation , we get
The amount of money left over with Jean A = $ 889 - $ 790
The amount of money left over with Jean A = $ 99
Therefore , the value of A is $ 99
Hence , the amount left over is $ 99
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change these percentage to decimals. 1. 40%. 2. 35%. I want to know how to solve it.
Answer:
1. 40 % is 40 / 100
by cancelling it the output is 2 /5
2. 35% is 35 / 100
7 / 20 is your answer
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Simplify 16x^2 9y^2/(4x-3y)^2
Hey There!!
STEP 1:
1
Simplify ——————————
(4x + 3y)2
Equation at the end of step
(4x-3y) 1
——————————————————————————— ÷ ————————
(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2
STEP 2:
Equation at the end of step
2
:
(4x-3y) 1
——————————————————————— ÷ ————————
(((16•(x2))+24xy)+32y2) (4x+3y)2
STEP 3:
Equation at the end of step
(4x - 3y) 1
—————————————————————— ÷ ——————————
((24x2 + 24xy) + 32y2) (4x + 3y)2
STEP 4:
4x - 3y
Simplify —————————————————
16x2 + 24xy + 9y2
Trying to factor a multi variable polynomial :
4.1 Factoring 16x2 + 24xy + 9y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (4x + 3y)•(4x + 3y)
Detecting a perfect square :
4.2 16x2 +24xy +9y2 is a perfect square
It factors into (4x+3y)•(4x+3y)
which is another way of writing (4x+3y)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Equation at the end of step
4:
(4x - 3y) 1
—————————— ÷ ——————————
(4x + 3y)2 (4x + 3y)2
STEP 5:
4x-3y 1
Divide ———————— by ————————
(4x+3y)2 (4x+3y)2
5.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
4x - 3y 1 4x - 3y (4x + 3y)2
—————————— ÷ —————————— = —————————— • ——————————
(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1
Canceling Out :
5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.
Final result :
4x - 3y
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Which function does this graph represent ?
Answer: B
Step-by-step explanation:
a is negtive bcs grph opens down. h value is -1 and k is +2
If a is an integer and n is a positive integer, we define a mod n to be the remainder when a is divided by n. The integer n is called the __________
Answer:
Divisor
Step-by-step explanation:
Given
[tex]a\ mod\ n[/tex]
Required
What does n represents
In arithmetic, the number that divides another is referred to as divisor;
Take for instance;
[tex]5\ mod\ 3 = 2[/tex]
This implies that when 5 is divided by 3, the remainder is 2
The bold text (divided by 3) means that 3 is the divisor of 5;
When compared to [tex]a\ mod\ n[/tex]
We have that
n = 3
Reason being that, n and 3 are in the same position base on order of appearance;
Hence, n represents the divisor
Solve for x. x−53 = 4
Answer:
x = 57
Step-by-step explanation:
x−53 = 4
Add 53 to each side
x-53+53 = 4+53
x = 57
Answer:
x = 57
Step-by-step explanation:
x−53 = 4
x (- 53 + 53) = 4 + 53
x = 57
There are only HB and F type pencils in the store. The ratio of the number of HB to F is 7 : 3. If there are 15F type pencils, how many pencils are there altogether?
Answer:
50
Step-by-step explanation:
Ratio is
7 : 3Total number is
7x + 3x = 10xSince F type pencils number is known:
3x = 15 x = 15/3x = 5Then total number is:
10x = 10 *5 = 50In the following regression (n = 91), which coefficients differ from zero in a two-tailed test at α = .05? Confidence Interval Variables Coefficients 95% lower 95% upper Intercept 9.8080 − 23.9968 43.6129 NumCyl − 1.6804 − 2.8260 − 0.5349 HPMax − 0.0369 − 0.0648 − 0.0090 ManTran 0.2868 − 2.2604 2.8341 Length 0.1109 − 0.0087 0.2305 Wheelbase − 0.0701 − 0.4111 0.2709 Width 0.4079 − 0.1735 0.9893 RearStRm − 0.0085 − 0.4100 0.3931 Weight − 0.0025 − 0.0064 0.0014 Domestic − 1.2291 − 3.4955 1.0374
Complete Question
The complete question is shown on uploaded image
Answer:
The correct option is B
Step-by-step explanation:
The reason the correct answers is [tex]NumCyl \ and\ HPMax[/tex] is because from the table we see that the 95% confidence interval for [tex]NumCyl \ and\ HPMax[/tex] does not contain zero
Which means the [tex]NumCyl \ and\ HPMax[/tex] differ form zero in a two-tailed test
pt 3 6/7 Pleasee helpp
Answer:
7p + 4
Step-by-step explanation:
7p - (-5) + (-1)
7p + 5 -1
7p + 4
How many people averaged 4,000 or more steps each day? (25 POINTS FOR BRAINLIEST) How many people averaged 4,000 or more steps each day? A): 10 B): 12 C): 19 D): 22
Answer:
D.)22
Step-by-step explanation:
D. 22 people has an average of 4000 or more than 4000 steps each day.
How to find an average ?To find an average sum up the weights of each individuals and divide by no. of individuals.
From the given diagram
2 people has an average of 0 to 1999 steps.
5 people has an average of 2000 to 3999 steps.
12 people has an average of 4000 to 5999 steps.
7 people has an average of 6000 to 7999 steps.
3 people has an average of 8000 to 9999 steps.
We have been asked how many people has an average of 4000 or more steps.
∴ ( 12 + 7 + 3) people has 4000 or more average steps each day.
= 22 people.
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HELP PLEASE!! I DONT UNDERSTAND!!!!!!!!!! THANKS SO MUCH
Hello, please consider the following.
We will multiply the numerator and denominator by
[tex]4+\sqrt{6x}[/tex]
to get rid of the root in the denominator.
First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.
[tex]4-\sqrt{6x} =0<=>\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}[/tex]
We need to take any x real number different from 8/3 then and simplify the expression.
Let's do it!
[tex]\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}[/tex]
Thank you