The value of the equation is A = x² ( 4 + x )
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 equation be represented as A
Now , the value of A is
A = 4x squared + x cubed
Substituting the values in the equation , we get
A = 4x² + x³ be equation (1)
On simplifying the equation , we get
Taking the common factor as x² in the equation , we get
A = x² ( 4 + x )
Therefore , the value of A is x² ( 4 + x )
Hence , the factorized equation is x² ( 4 + x )
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I need help with the working
Answer:
288 cm^3.
Step-by-step explanation:
The volume of each small square = 2*2*2 = 8 cm^3
Each rectangular length of end 2*2 is made up of 12/2 = 6 squares.
There are 6 of these rectangular lengths.
So the volume = 6 * 6 * 8 cm^3
288 cm^3.
A bag contains 9 tiles, each with a different number from 1 to 9. You choose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. In how many different ways can you choose three tiles
Using the combination formula, it is found that there are 84 ways to choose the three tiles.
The order in which the tiles are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, three tiles are chosen from a set of nine, hence:
[tex]C_{9,3} = \frac{9!}{3!6!} = 84[/tex]
There are 84 ways to choose the three tiles.
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The equation 4x – 45 = y is used to find your profit, y, in dollars from buying $45 of supplies and washing cars for $4 each. What does the x stand for?
The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is _____ × 10–8
The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The sample-set S consists of all combinations of 6 distinct elements of the set of 50 elements, and;
[tex]\rm |S| =C(50, 6)=\dfrac{50!}{44!6!}[/tex]
The winning event E ⊆ S is just one winning combination, so that
|E| = 1.
Therefore, the probability of winning a lottery is;
[tex]\rm P(E)=\dfrac{|E|}{|S|}\\\\ P(E)=\dfrac{1}{\dfrac{50!}{44!6!}}\\\\\\ P(E)=\dfrac{44!6!}{50!}\\\\ P(E)= 6 \times 10 {-8}[/tex]
Hence, The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
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The scores at a golf course recorded last year followed a normal distribution with mean 78 and
standard deviation 11. you choose an srs of 15 scores and calculate xbar = mean score. which of
the following are the mean and standard deviation of the sampling distribution of x bar?
Using the Central Limit Theorem, it is found that the mean of the sampling distribution is of 78 and the standard deviation is of 2.84.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, for the population, we have that [tex]\mu = 78, \sigma = 11[/tex].
Then, considering samples of n = 15, we have that the standard deviation is given by:
[tex]s = \frac{11}{\sqrt{15}} = 2.84[/tex].
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please help me ( if you get it right i will rate you 5/5)
Answer:
D.
Step-by-step explanation:
Okay, so 8:15 to 12:00 is 225 minutes, or 3.75 hours
12:45 to 17:30 is 285 minutes, or 4.75 hours
3.75 + 4.75 = 8.5 hours (total)
She earns 14.50 dollars per hour
8.5 * 14.5 = 123.25 dollars
D.
Answer:
The answers is D: 8.5 hours x $14.50 = $123.25
Step-by-step explanation:
This employee worked a total of 8.5 hours on Monday (3.75 hours in the morning and 4.75 hours in the afternoon).
Then, you have to multiply the total amount of hours worked by the number of dollars paid per hour.
8.5 hours x $14.50 = $123.25
Help what's the correct question
A construction crew has just built a new road. They built the road at a rate of 3 kilometers per week. They built 18.75 kilometers of road. How many weeks did
it take them?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 and divide it by 3, since the crew is finishing 3 km per week. You get 6.25, so it took the crew 6.25 weeks to finish the road.
Hopefully this helps- let me know if you have any questions!
A rectangular prism has a base area of 23 cm² and a height of 6 centimeters. What is the volume of the prism?
Answer:
volume = 138 cm³
Step-by-step explanation:
Equation
volume of a prism = base area × height
Given:
base area = 23 cm²height = 6 cmSubstituting given values into the equation:
⇒ volume = 23 × 6
= 138 cm³
Don recently received his first credit card, a MasterCard with a credit line of $500. In the first month he had it, he ran up charges of $425. How much of that must he pay if he wants to charge a discount airline ticket, which costs $200, on his card without going over his credit limit
The amount Don must pay on his card without going over the credit limit is $125.
How much must Don pay?
Don's credit limit is $500. If Don does not want to go over the limit, he must not exceed the $500 limit. In order to determine the amount he should pay, add the sum of the charges and subtract it from the credit limit.
Amount to be paid = (425 + 200) - 500 = $125
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Determine the scale factor for each reduction.
a) Quadrilateral B is a reduction of quadrilateral A.
b) Quadrilateral C is a reduction of quadrilateral A.
c) Quadrilateral B is a reduction of quadrilateral C.
Answer:
c
Step-by-step explanation:
A box of tissues is shaped like a rectangular prism and has a volume of 288 cubic inches. The box has a height of 4 inches and a length of 12 inches.
What is the width of the tissue box?
Answer:
6 in
Step-by-step explanation:
4×12×w=288
48×w=288
/48. /48
w=6
PLS HELP ILL GIVE EXTRA POINTS NEED ASAP
Answer:
5
Step-by-step explanation:
Median from 24 to 28
24 + 28 / 252 / 226Median from 28 to 34
28 + 34 / 262 /231Interquartile range
M2 - M131 - 265The speed of the jet Alyssa flew on from Boston to London was 480 mph. on her return flight, the speed of the jet was 600mph with a tail wind. What was Alyssa's average speed on the round trip?
Based on the speed Alyssa used to get to London and the speed back to Boston, the average speed was 540 mph.
What is the average speed?The average speed that Alyssa was going can be found by the formula:
= (Initial speed + Final speed) / 2
Solving gives:
= (480 + 600) / 2
= 1,080 / 2
= 540 mph
In conclusion, Alyssa's average speed was 540 mph.
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PYTHAG THEOREM!
Aubrey is building a slide for her kids. If the ladder is 6 feet tall and she wants the bottom of the slide to be 5 feet from the ladder, how long does the slide need to be? If necessary, round to the nearest tenth.
Answer:
sqrt(11)
Step-by-step explanation:
a^2+b^2 = c^2
a = 5
c = 6
b = ?
25 - b^2 = 36
36 - 25 = b^2
b = sqrt(11)
The ladder should be 7.81 feet long.
What is Pythagoras theorem?Pythagoras theorem tell us the relation between the sides of a right-angled triangle, it states, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.
Given that, Aubrey is building a slide for her kids. If the ladder is 6 feet tall, and she wants the bottom of the slide to be 5 feet from the ladder,
This slide is in the form of a right triangle, therefore applying the Pythagoras theorem, we have,
a²+b² = c² (refer to the figure attached)
5²+6² = c²
c² = 25+36
c² = 61
c = √61
c ≈ 7.81
Hence, the length of the slide should be 7.81 feet.
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b= c= Please help I need to do this asap
Consider the first 4 transactions in this check register. For what check number did a mistake occur in calculating the balance when the check amount qas debited from the register
A check register is also known as a cash disbursements journal, is a document that holds the record of all of the check and cash transactions that one's business has for an accounting period.
What kind of transactions are recorded in a Check Register?The kind of transactions that are recorded in a Check Register or a Cash Disbursement Journal are:
Do note that the register referenced in the questions is unavailable hence the general answer.
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What is the area of rectangle PQRS?
The area of a rectangle is l*w. We have the length as 4.5 in and we can find the width by doing 3+2+4.5 = 9.5 in.
Then, we multiply them. 4.5*9.5 = 42.75 inches²
What shapes have only one pair of parallel sides?
Answer:
A TRAPEZOID!!
Step-by-step explanation:
Answer:
Trapezoids have only one pair of parallel sides
15 POINTS
Identify the center and radius of a circle with equation (x-4)^2 + (Y+2)^2 =9
A.) Center at (4,2); radius: 9
B.) Center at (-4,2); radius: 9
C.) Center at (4,-2); radius: 3
D.) Center at (-4, 2); radius: 3
The basic formula for a circle is (x - h)^2 + (y - k)^2 = r^2, where the center is (h, k) and the radius is found by taking the square root.
h = 4
k = -2
Center: (4, -2)
square root of 9 = 3
Radius: 3
Correct Answer: C
Hope this helps!
Due to an economic downturn, a company had to decrease its staff from 364 employees to 91 employees. What was the percentage decrease in staff?
Answer:
25%
Step-by-step explanation:
First, divide 91 by 364
91/364 = 0.25
Multiply this answer by 100
0.25 × 100 = 25%
This gives you what percent of 364 that 91 is
So it is a 25% decrease
The small cylinder can fill the big cylinder to a height of 5cm. Work out the radius if the big cylinder
How do you find perimeter?
Finding perimeter is simple. All you do is add up all of the side lengths, and bada bing bada boom, you got the perimeter.
Which number is written in scientific notation? 4. 5 times 10 Superscript negative 3 14. 5 times 10 Superscript 2 0. 78 times 10 Superscript negative 6 5. 7 times 4 Superscript 8.
The number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.
Given numbers are:
1)[tex]4.5*10^{-3}[/tex]
2)[tex]14.5*10^{2}[/tex]
3)[tex]0.78*10^{-6}[/tex]
4)[tex]5.7*4^8[/tex]
What is the scientific notation of numbers?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
In the first number [tex]1 < 4.5 < 10[/tex] multiplied by [tex]10^{-3}[/tex]
As per the definition [tex]4.5*10^{-3}[/tex] is written in scientific notation.
The Rest of the numbers do not follow the definition of scientific notation so they are not in scientific notation.
Hence, the number [tex]4.5*10^{-3}[/tex] is written in scientific notation whereas the rest of the numbers are not written in scientific notation.
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let a and b be the roots of the equation x^2 - 3x - 1 = 0. Find a^3 + b^3
hint: a^3 + b^3 = (a+b)(a^2-ab+b^2)
URGENT PLEASE
Answer:
Correct option is A)
Given,a,b are distance roots of x
3
+3x
2
−1=0
⇒a
3
+3a
2
−1=0 and b
3
+3b
2
−1=0
let the third root be c
then c
3
+3c
2
−1=0
product of roots =
a
−d
=
1
−(−1)
=1
⇒
abc=1
c=
ab
1
but c is root of x
3
+3x
2
−1=0
⇒c
3
+3x
2
−1=0
⇒
(ab)
3
1
+
(ab)
2
3
−1=0
⇒
1+3ab−(ab)
3
=0
.....(1)
in equation (1)
(ab)
3
−3(ab)−1=0
⇒ab is root of
x
3
−3x−1=0
∴(ab) is root of
x
3
−3x−1=0
23.-28. In a manner similar to Example 1, (a) identify input and
output consistent with the general proportional model; (b) write
an equation for the model; (c) determine a numerical value for the
constant k; and (d) solve the problem.
23. The maximum distance that you can see from the top of a tall
building is (directly) proportional to the square root of the
height of the building. You can see approximately 41 mi from
the Canadian National Tower lookout level, which is 1,135 ft
tall. How far can you see from the top of the Sears Tower in
Chicago (now the Willis Tower), which is 1,454 ft tall?
23. How far can you see from the top of the sears tower in Chicago, which is 1,454 ft tall?
The distance I can see from the top of the sears tower in Chicago is 46.41 mi.
How far can you see the from the top of the Sears Tower?The equation for direct proportionality = y = b√x
where:
y = dependent variable = distance you can seeb = constantx = independent variable = square root of the height of the building.b = y /√x
41 / √1135
b = 1.217
y = 1.217√1454
y = 46.41 mi
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Impaired brain function as a result of drug use involves all of the following except: a. increased confusion b. errors in judgment c. memory loss d. increased concentration
Increased concentration is the answer as drug impairs our ability to control ourselves.
Hope it helps!
Impaired brain function as a result of drug use doesn't involve: Option D: Increased concentration.
What is impaired brain function?A significant deterioration in one or more domains of conscious mental activity, such as language, learning, and memory, that interferes with everyday function and independence are some of the traits of impairment of brain.
Thus, as we see, first three options are showing acts of impaired brain but the fourth option contradicts, as impairment from drug use isn't going to increase concentration and if it somehow does, then it isn't impairment.
Thus, impaired brain function as a result of drug use doesn't involve: Option D: Increased concentration.
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Is -4,6 a solution to y=-9
Answer:
No, (-4, 6) is not a solution to y = -9.
Step-by-step explanation:
y= -9 has a horizontal line graph. Every point on this line has -9 as its y-coordinate. (-4, 6) does not lie on that line and is therefore not a solution to y = -9.
please answer it quickly
Hey there!
This is the formula:
V=πr²h
V=π(7)²5
V=49π5
V=245π
V≈769.7 ft³(cubic feet)
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg were
used in a procedure. Write an equation that can be used to determine how much of
the isotope is left after x number of half-lives.
How much would be left after 70 days?
After x half-lifes, the amount of the isotope is:
A(x*T) = 90mg*e{-x*ln(2)}
And after 70 days, there are 5.628 mg
What is the half-life?
We define the half-life as the time such that the inital amount of a given substance reduces to half of it.
If the half-life is T, the amount of the substance can be written as:
A(t) = a*e^{-λ*t}
Where λ = ln(2)/T.
and a is the initial amount.
In this case, T = 17.5 days, then:
λ = ln(2)/17.5 days = 0.0396 / day
And we also have a = 90mg
Then the exponential equation is:
A(t) = 90mg*e^{-t*0.0396 / day}
After x half-lifes, the amount of the isotope left is:
A(x*T) = 90mg*e^{-x*T*ln(2)/T} = 90mg*e^{-x*ln(2)}
And after 70 days the amount is:
A(70 days) = 90mg*e^{-70 days*0.0396 / day} = 5.628 mg
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Answer:
Y=90mg(0.5)^5
1.86 after 70 days
Step-by-step explanation: