Answer:
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Step-by-step explanation:
Given expression is [tex]2x^4-32[/tex]
To find the completed factor for the given expression:
[tex]2x^4-32[/tex]:
Taking the common number "2" outside to the above expression we get
[tex]2x^4-32=2(x^4-16)[/tex]
Now rewritting the above expression as below
[tex]=2(x^4-2^4)[/tex] (since 16 can be written as the number 2 to the power of 4)
[tex]=2((x^2)^2-(2^2)^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x^2[/tex] and [tex]b=2^2[/tex]
Therefore it becomes
[tex]=2(x^2+2^2)(x^2-2^2)[/tex]
[tex]=2(x^2+4)(x^2-2^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x[/tex] and [tex]b=2[/tex]
Therefore it becomes
[tex]=2(x^2+4)(x+2)(x-2)[/tex]
[tex]=2(x+2)(x-2)(x^2+4)[/tex]
Therefore [tex]=2(x+2)(x-2)(x^2+4)[/tex]
[tex]2x^4-32=2(x-2)(x+2)(x^2+4)[/tex]
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Answer:
b
Step-by-step explanation:
An engineering student answered 81 questons correctly ona 90 question test. What percent of the question did she answer correctly? questions correctly on a 90 question test. What percent of the questions she answered correctly?
Answer:
correct answer = 90%
Step-by-step explanation:
Let x be the percent of the question did she answer correctly.
Given:
An engineering student answered 81 questions correctly on a 90 question test.
Find the percent of the question did she answer correctly.
Solution:
Percentage formula is given below
% answer [tex]=\frac{correct\ answer}{total\ questions}\times 100[/tex]
% answer [tex]=\frac{81}{90}\times 100[/tex]
% answer [tex]=\frac{81\times 100}{90}[/tex]
% answer [tex]=\frac{81\times 10}{9}[/tex]
% answer [tex]=9\times 10[/tex]
% answer [tex]=90[/tex]
correct answer = 90%
Therefore, she answered 90% correctly.
Answer:
90%
Step-by-step explanation:
The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function () = −0.0018 + 212. In terms of altitude and temperature, which statement describes the meaning of the slope?
A. The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.
B. The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.
C. The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.
D. The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.
The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet " ⇒ D
Step-by-step explanation:
The boiling point of water (measured in degrees), at altitude (measured in feet), is modeled by the function T(a) = −0.0018 a + 212, where
a is the altitude measured in feetT(a) is the boiling point of water in degreeThe form of the linear function is f(x) = mx + b, where m is slope (the rate of change), and b is the y-intercept (the value of f(x) at x = 0)
By comparing between the form of the function and the given function
∴ m = -0.0018 ⇒ degrees per foot
∵ The sign of the slope is negative
∵ The slope = Δf(x)/Δx
- That means T(a) is decreasing function
∴ The boiling point is decreases when the altitude increasing
∵ -0.0018 = [tex]-\frac{18}{10,000}[/tex] degrees per feet
∴ The boiling point decreases by 18 degrees as the altitude
increases by 10,000 feet or the boiling point decreases by 1.8
degrees as the altitude increases by 1,000 feet
The statement which describes the meaning of the slope is " The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet "
Learn more:
You can learn more about the linear function in brainly.com/question/9801816
#LearnwithBrainly
The meaning of slope is best described by the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet. The option (D) is correct.
To understand the meaning of the slope in the given function[tex]\( T(a) = -0.0018a + 212 \)[/tex], where [tex]\( T \)[/tex] represents the boiling point of water in degrees and [tex]\( a \)[/tex] represents the altitude in feet, we need to analyze the slope of the function.
The slope of the function is given by the coefficient of [tex]\( a \)[/tex], which is [tex]\( -0.0018 \)[/tex]. This slope tells us how the boiling point of water changes with altitude. To interpret the slope in terms of degrees per foot:
A slope of [tex]\( -0.0018 \)[/tex] means that for every 1 foot increase in altitude, the boiling point decreases by 0.0018 degrees.
To find out how much the boiling point changes over an increase of 1,000 feet in altitude, we multiply the slope by 1,000:
[tex]\( \text{Change in boiling point} = \text{slope} \times \text{change in altitude} \)[/tex]
[tex]\( \text{Change in boiling point} = -0.0018 \times 1000 \)[/tex]
[tex]\( \text{Change in boiling point} = -1.8 \)[/tex]
Therefore, the correct interpretation of the slope is that the boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet, which corresponds to option D.
The complete question is:
The boiling point of water, T (measured in degrees), at altitude a (measured in feet) is modeled by the function T(a)=-0.0018a+212. In terms of altitude and temperature, which statement describes the meaning of the slope?
A. The boiling point increases by 18 degrees as the altitude increases by 1,000 feet.
B. The boiling point increases by 1.8 degrees as the altitude increases by 1,000 feet.
C. The boiling point decreases by 18 degrees as the altitude increases by 1,000 feet.
D. The boiling point decreases by 1.8 degrees as the altitude increases by 1,000 feet.
two consecutive even integers have a sum of 254. write the equation that will solve for the two integers.
Answer: 126 and 128
Step-by-step explanation: In this problem have two consecutive even integers whose sum is 254.
Consecutive even integers can be represented as followed.
X ⇒ first even integer
X + 2 ⇒ second even integer
Since the sum of these is 254, our equation reads X + X + 2 = 254.
We can simplify on the left side of the equation to get 2x + 2 = 254.
Now, we subtract 2 from both sides of the equation to get 2x = 252.
Lastly, we will divide both sides of the equation by 2 in order to isolate x. On the left side, the 2's cancel out and on the right, 252 divided by 2 is 126.
If our first integer is 126, our next consecutive even integer will be 126 + 128 which simplifies to 254.
Therefore, our two consecutive even integers are 126 and 128.
Ben's family went on a car trip. They
stopped for gas 4 times. Each time
they stopped they spent an average
of 15 minutes at the gas station. On their
trip, about how much time did Ben's
family spend stopping for gas?
A 45 minutes
B 60 minutes
C 75 minutes
Answer:
B. 60 Minutes
Step-by-step explanation:
URGENT!! I need help on this and my last question
The Value of t from given convex polygon is 41.
Step-by-step explanation:
Let us consider,
a=61°.
b=2t.
c=3t.
d=42°.
e=52°.
The sum of exterior angles of convex polygon is always 360°.
a+b+c+d+e=360°.
The exterior angles of any convex polygon is same as if any angle drawn inside a circle.
Steps to reform the angles:
Step 1: Draw the ∠a as given in the original diagram.
Step 2: The ∠b is adjacent to ∠a 's end and draw a parallel line of ∠b in the ∠a. The angle measure will also be same.
Step 3: Continue the same for next angles ∠c,∠d and ∠e.
(refer the image dotted lines are the parallel lines.)
⇒ 61°+42°+52°+2t+3t=360°.
155°+5t=360°.
5t=205°.
t=41°.
Also,
∠b=82°.
∠c=123°.
Check,
61°+82°+123°+42°+52°=360°.
If sin theta +cos theta=root2cos theta then the value of tan theta is
Answer:
√2 - 1
Step-by-step explanation:
Please see attached picture for full solution.
easy + brainliest
2x(^3) + 10x(^2) − 4x(^2)y − 20xy
factor this pls, (show all work)
Answer:
Answer:
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((2•(x3))+(10•(x2)))-(22x2•y))-20xy
Step 2 :
Equation at the end of step 2 :
(((2 • (x3)) + (2•5x2)) - 22x2y) - 20xy
Step 3 :
Equation at the end of step 3 :
((2x3 + (2•5x2)) - 22x2y) - 20xy
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
2x3 - 4x2y + 10x2 - 20xy =
2x • (x2 - 2xy + 5x - 10y)
Final result :
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Answer:
2x • (x2 - 2xy + 5x - 10y)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((2•(x3))+(10•(x2)))-(22x2•y))-20xy
Step 2 :
Equation at the end of step 2 :
(((2 • (x3)) + (2•5x2)) - 22x2y) - 20xy
Step 3 :
Equation at the end of step 3 :
((2x3 + (2•5x2)) - 22x2y) - 20xy
Step 4 :
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
2x3 - 4x2y + 10x2 - 20xy =
2x • (x2 - 2xy + 5x - 10y)
Final result :
2x • (x2 - 2xy + 5x - 10y)
[tex] 5 - 14 = [/tex]
Answer:
The answer is -11.
Step-by-step explanation:
5-14 =
Now, to solve :
[tex]5-14=-11.[/tex]
As, we see in the question that 11 is subtracted from 5 and when any number is subtracted from its higher number the results are in negative.
Therefore, the answer is -11.
After collecting eggs from his chickens, Dale puts the eggs into cartons to sell. Dale fills 15 cartons and has
7 eggs left over. Each carton holds 12 eggs.
How many eggs did Dale collect?
What’s this answer y=10 4x-5y=3
Answer:
x = 13.25 or 13 1/4
Step-by-step explanation:
4x - 50 = 3
4x = 53
x = 13.25 or 13 1/4
Answer:
53 / 4
13 whole number, 1/4
Step-by-step explanation:
At a local food store a child stole $500 from the shopkeeper's cash register to purchase goods in the store. The items the child purchased total $350 which he paid using the money he stole and received change of $150. How much money in total did the shopkeeper lose
Answer:
The shopkeeper lost $500
What is the quote that of 2^4/2^-4
Answer:
[tex]2^8[/tex]
Step-by-step explanation:
To find the quotient of:
[tex]\frac{2^4}{2^{-4}}[/tex]
Solution:
We will apply quotient rule of exponents to find the quotient of the given expression.
By Quotient rule: [tex]\frac{a^x}{a^y}=a^{(x-y)}[/tex]
Thus the quotient for the expression can be given as:
[tex]\frac{2^4}{2^{-4}}[/tex]
⇒ [tex]2^{(4-(-4))}[/tex]
⇒ [tex]2^{(4+4)}[/tex]
⇒ [tex]2^8[/tex] (Answer)
The expression [tex]\frac{2^4}{2^-4}[/tex] can be simplified to 256.
To solve the expression [tex]\frac{2^4}{2^-4}[/tex], we can use the properties of exponents :
Recall that when you divide powers with the same base, you subtract the exponents: [tex]\frac{2^a}{2^b}[/tex] [tex]=[/tex] [tex]2^(a-b)[/tex].So, for our expression : [tex]\frac{2^4}{2^-4}[/tex] = [tex]2^(4-(_4))[/tex] = [tex]2^(4+4)[/tex] = [tex]2^8[/tex].Next, calculate [tex]2^8[/tex] : [tex]2^8[/tex] = 256.Therefore, the value of the expression [tex]\frac{2^4}{2^-4}[/tex] is 256.
helpppppppppppppp.....
Answer:
B
Step-by-step explanation:
If we understand 2 properties of isosceles trapezoids, then we can solve for x and y easily.
First, the two sides, "2x-13" and "x-3" are equal, as shown also by red line.
So, we equate them and find x first. Shown below:
[tex]2x-13=x-3\\2x-x=-3+13\\x=10[/tex]
Now, another property is:
Any lower base angle is supplementary to any upper base angle. That means the angle y is supplementary to "3y-4". Supplementary means that if we add up the two angles, it will be 180 degrees. So:
[tex]y+3y-4=180\\4y=180+4\\4y=184\\y=46[/tex]
From the answer choices, answer choice B is right
f(x)=2x+3 and g(x)=x^2-8, find (f+g)(x)
Answer:
[tex](f+g)(x)=x^2+2x-5[/tex]
Step-by-step explanation:
Given:
The functions given are:
[tex]f(x)=2x+3\\g(x)=x^2-8[/tex]
To find: [tex](f+g)(x)[/tex]
[tex](f+g)(x)[/tex] is equal to the addition of both the functions. So, we need to add the values of both the functions and then simplify to arrive the final answer.
Therefore, [tex](f+g)(x)[/tex] is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]
Plug in the values of [tex]f(x)\ and\ g(x)[/tex] and simplify. This gives,
[tex](f+g)(x)=2x+3+x^2-8[/tex]
Combining like terms using commutative property of addition, we get
[tex](f+g)(x)=x^2+2x+3-8\\(f+g)(x)=x^2+2x-5[/tex]
Therefore, the addition of the two functions is simplified to:
[tex](f+g)(x)=x^2+2x-5[/tex]
what is 14.79 as a rounded number
Answer:
15
Step-by-step explanation:
Answer:
15 or 14.8, depending on whether it is a ehole number on on decimal place
Step-by-step explanation:
1
2
3
4
5
6
7
8
9
10
You have a spinner, shown below. You wish to test its fairness, so you conduct several trials in which you repeatedly spin the spinner and record how many times you come up with a result of violet. Your results are shown in the table next to the spinner.

Trial
1
2
3
4
Times Spun
85
156
34
127
Times Violet
10
18
2
14
Calculate the experimental probability of your spinner showing a result of violet, written as a percentage to two decimal places.
a.
10.05%
b.
10.95%
c.
11.02%
d.
11.11%
Answer:
B
Step-by-step explanation:
85+156+34+127=402
10+18+2+14=44
44/402=10.95%
Answer is B. 10.95%
Rhonda deposits $5,600 in a savings account that pays 1.5% interest, compounded semi-annually.
Round to the nearest cent.
Answer:
Part a) [tex]\$42[/tex]
Part b) [tex]\$5,642[/tex]
Part c) [tex]\$42.32[/tex]
Part d) [tex]\$5,684.32[/tex]
Part e) [tex]\$84.32[/tex]
Step-by-step explanation:
The complete question is
Rhonda deposits $5,600 in a savings account that pays 1.5% interest, compounded semi-annually. Round to the nearest cent.
a. How much interest does the account earn in the first 6 months?
b. What is the ending balance after 6 months?
c. How much interest does the account earn in the second 6 months?
d. What is the balance after 1 year?
e. How much interest does the account earn the first year?
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part a) How much interest does the account earn in the first 6 months?
in this part we have
[tex]t=6/12=0.5\ years\\ P=\$5,600\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]
substitute in the formula above
[tex]A=5,600(1+\frac{0.015}{2})^{2*0.5}[/tex]
[tex]A=5,600(1.0075)^{1}[/tex]
[tex]A=\$5,642[/tex]
Find out the interest
[tex]I=A-P[/tex]
[tex]I=\$5,642-\$5,600=\$42[/tex]
Part b) What is the ending balance after 6 months?
we know that
The ending balance after 6 months is the same that the final investment value of A after 6 months
so
[tex]A=\$5,642[/tex] ----> see part a)
Part c) How much interest does the account earn in the second 6 months?
in this part we have
[tex]t=6/12=0.5\ years\\ P=\$5,642\\ r=1.5\%=1.5/100=0.015\\n=2[/tex]
substitute in the formula above
[tex]A=5,642(1+\frac{0.015}{2})^{2*0.5}[/tex]
[tex]A=5,642(1.0075)^{1}[/tex]
[tex]A=\$5,684.32[/tex]
Find out the interest
[tex]I=A-P[/tex]
[tex]I=\$5,684.32-\$5,642=\$42.32[/tex]
Part d) What is the balance after 1 year?
we know that
The balance after 1 year is equal to the initial deposit of $5,600 plus the interest earned in the first 6 months plus the interest earned in the second 6 months
so
[tex]\$5,600+\$42+\$42.32=\$5,684.32[/tex]
Part e) How much interest does the account earn the first year?
The total interest the first year is equal to the interest earned in the first 6 months plus the interest earned in the second 6 months
so
[tex]\$42+\$42.32=\$84.32[/tex]
For the function f(x)=8(x−3)+13, find the value of f(5) please help
Answer:
29
Step-by-step explanation:
f(x)=8(x−3)+13
f(5)= 8(5-3)+13
f(5) = 8(2) +13
f(5) = 16 +13
f(5)= 29
Hope this helps!
Please mark brainliest if you think I helped! Would really appreciate!
Answer:
Your correct answer is 29! Here is the step by step explanation!
Step-by-step explanation:
f(x)=8(x−3)+13
f(5)= 8(5-3)+13
f(5) = 8(2) +13
f(5) = 16 +13, wich means when you do this,
f(5)= 29
you get your answer of 29! Please mark brainliest! Hope it helped! Have a nice day!
The Read and Feed restaurant wants to know how satisfied their customers are with their service. They printed an internet link to a survey on every receipt, and 150150150 of their customers chose to answer the survey. The data showed that 60\%60%60, percent of the customers were satisfied with their service.
Based on this data, which of the following conclusions are valid?
Answer: The answer is A my bro trust me *Fist Bump*
Answer:
A
Step-by-step explanation:
I did it and got it right.
Hope this helps:)
Sam and Odel have been selling frozen pizzas for a class fundraiser. Sam has sold half as many pizzas as Odel. Together they have sold a total of 126 pizzas. How many pizzas did Sam sell
Answer:
63 pizzas
Step-by-step explanation:
In the problem it states that Sam sold half as many pizzas as Odel and sold 126 together in total. If you divide 126 pizzas by 2 or 1/2, you should get 63 pizzas for both people. Hope this helps.
The total number of frozen pizzas which Sam sell for a class fundraiser is 42 which is half as many pizzas sell by Odel.
What is system of equation?A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Sam and Odel have been selling frozen pizzas for a class fundraiser. Let the Sam has sold x number of pizzas and Odel is sold y number of pizzas.
Now it is given in the problem that, Sam has sold half as many pizzas as Odel. Thus,
[tex]x=\dfrac{y}{2}\\y=2x[/tex] ......1
Together Sam and Odel have sold a total of 126 pizzas. Thus,
[tex]x+y=126\\[/tex]
Put the value of y from the equaiton 1 in the above equation,
[tex]x+2x=126\\3x=126\\x=\dfrac{126}{3}\\x=42[/tex]
Hence, the total number of frozen pizzas which Sam sell for a class fundraiser is 42 which is half as many pizzas sell by Odel.
Learn more about the system of equations here;
https://brainly.com/question/13729904
Model and partial quotient solve:
783/4
Answer:
195.75
Step-by-step explanation:
The temperature at sunrise was -2 degrees Fahrenheit. The temperature at sunset was 18 degrees warmer than it was at sunrise. What was the temperature at sunset?
a) -20 degrees Fahrenheit
b) -16 degrees Fahrenheit
c) 20 degrees Fahrenheit
d) 16 degrees Fahrenheit
Answer:
d) 16 degrees Fahrenheit
Step-by-step explanation:
What do we know? Initial temperature: -2. Then the temperature rose by 18 degrees. We can express this mathematically:
[tex]-2+18[/tex]
If you are not particularly comfortable with negatives, you can rewrite this expression as such:
[tex]18-2[/tex]
[tex]16[/tex]
Thus the temperature at sunset was 16 degrees Fahrenheit.
Answer:
16 degrees
-2 + 18 is 16
Step-by-step explanation:
If this is wrong EXPLAIN HOW ITS WRONG
Tara paid $3.52 for 4 boxes of macaroni and cheese. Jarrett paid $5.40 for 6 boxes of macaroni and cheese. Which of
the following statements is true?
Tara paid more per box
Jarrett paid more per box.
Tara and Jarrett paid the same per box
Answer: Tara paid more per box
Step-by-step explanation:
And Another Question 35 points
Answer:
50
Step-by-step explanation:
The x-axis represents the number of broken light bulbs, as labelled on the histogram. The highest range is 41 to 50, therefore the greatest possible number of broken light bulbs is 50.
Answer:
50
Step-by-step explanation:
The last bar on the number of broken light bulbs (x) axis covers the range 41-50. Thus, 50 is the maximum number of broken light bulbs that can be and is represented in this histogram.
Given the equation square root of quantity 2x minus 1 end quantity equals 7, solve for x and identify if it is an extraneous solution.
one half; solution is extraneous
one half; solution is not extraneous
25; solution is extraneous
25; solution is not extraneous
Answer:
x=25 solution is not extraneous
Step-by-step explanation:
given, [tex]\sqrt{2x-1}[/tex]=7
squaring both side we get,
2x-1=7^2
2x-1=49
2x=50
x=25 solution is not extraneous answer
Select the correct answer. If f(x)=x/1+x , what is the value of f(x+h)?
Answer:
Step-by-step explanation:
Solve the equations:
Answer:X=5/3
Step-by-step explanation:
(2∧(3*x-4))2=(-2)²
2∧2*(3*x-4)=2²
-------------------------
2*(3*x-4)=2
3*x-4=1
3*x=5
x=5/3
please help me ill appreciate it
Answer:
D
Step-by-step explanation:
Two figures are similar.
It means that the corresponding sides are proportional.
TM corresponds to SC
MV corresponds to CI
Lets write the ratios and equate:
[tex]\frac{3}{2}=\frac{MV}{6}[/tex]
Now, we can cross multiply and use algebra to solve for MV. Process shown below:
[tex]\frac{3}{2}=\frac{MV}{6}\\2MV=3*6\\2MV=18\\MV=\frac{18}{2}\\MV=9[/tex]
Correct answer is D
A bird at the top of a tree looks down on a field mouse at an angle of depression of 65°. If the field mouse is 30 meters from
the base of the tree, find the vertical distance from the ground to the bird's eyes. Round the answer to the nearest tenth
a 14 m
b. 28.6 m
C. 58.3 m
d. 64.3 m
Answer:
14m
Step-by-step explanation:
Answer:
d. 64.3 m
Step-by-step explanation:
caprice adds equations a and b to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?
Answer:
Its the Adding a quantity one or the bottom right
Adding equations is a legitimate method in solving systems because it utilizes the elimination process to simplify the system. It also respects the fundamental properties of equations and provides a precise analytical technique for finding solutions, which can be more accurate than graphical methods.
Explanation:Adding equations, known as the method of elimination, is a valid method for solving a system of equations. This approach works because it leverages the property that if two equations both equal the same variable, they can be added together to eliminate one of the unknowns, simplifying the system. For instance, suppose we have equation a: x + 2y = 6, and equation b: 3x - y = 4. Adding them gets 4x + y = 10, which is a new equation that can help solve for one of the variables more directly. This takes advantage of the fact that equations describe relationships between variables that hold true under various mathematical operations, including addition.
Another key aspect is the understanding that solutions to equations are often not unique when they include an unknown squared, leading to two potential solutions. However, contextual knowledge can determine which solution is reasonable, such as in physics problems where time or velocity must make sense in the real world.
Moreover, while analytical methods of solving systems are precise, solving equations graphically can offer a visual understanding but may lack accuracy due to potential scaling and drawing inaccuracies. Therefore, analytical techniques, like adding equations, are generally more accurate but can be complemented with graphical methods for a better conceptual grasp.