Answer:
(a+b)² - 11(a+b) -42
Step-by-step explanation:
Thoughtfully split the expression at hand into groups, each group having two terms,
Group 1: -11b-11a
Group 2: a2+2ab
Group 3: b2-42
Pull out from each group separately :
Group 1: (a+b) (-11)
Group 2: (a+2b) (a)
Group 3: (b2-42) (1)
Looking for common sub-expressions :
Group 1: (a+b) (-11)
Group 3: (b2-42) (1)
Group 2: (a+2b) (a)
final answer:(a+b)² - 11(a+b) -42
Answer:
(a+b+3)(a+b-14)
Step-by-step explanation:
let a+b be x,
= x²-11x-42
=x²-(14-3)x-42
=x²-14x+3x-42
=x(x-14)+3(x-14)
=(x+3)(x-14))
replacing x by a+b,
=(a+b+3)(a+b-14)
a box with a square base has length plus girth of 108 in. What is the length of the box if its volume is 2200 in^3?
The missing length of the box with square base is 20.370 inches.
What is the missing length of the box?
This box can be represented by a right prism, whose volume (V), in cubic inches, is the product of the area of the base (A), in square inches, and the height of the box (h), in inches. The area of the base is equal to the square of the side length (l):
V = l² · h (1)
If we know that V = 2 200 in³ and l = 108 in, then the height of the box is:
h = V / l²
h = (2 200 in³) / (108 in)
h = 20.370 in
The missing length of the box with square base is 20.370 inches.
Remark
The statement presents typing mistakes, correct form is shown below:
A box with a square base has a side length of 108 in. What is the length of the box if its volume is 2 200 in³?
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Please help! Need em doneee
Determine which quadrilaterals have the properties given in the table.
kite
square trapezoid rectangle
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
rhombus
parallelogram
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
The two quadrilateral with the listed properties are kite and rhombus respectively.
Properties of a kiteIt has two diagonals intersecting at right anglesA kite is symmetrical about its main diagonalAngles opposite to the main diagonal are equalThe kite can be viewed as a pair of congruent triangles with a common baseIts diagonals are perpendicularProperties of a rhombusAll sides of the rhombus are equalThe opposite sides are parallelOpposite angles are equalDiagonals bisect each other at right anglesDiagonals bisect the anglesThe sum of two adjacent angles is equal to 180 degrees, that is, are supplementaryThus, the two quadrilateral with the listed properties are kite and rhombus respectively.
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Answer:
your welcome
Step-by-step explanation:
(GIVING BRAINLYST) 1(Multiple Choice Worth 2 points) (15.01 LC) Which number sequence follows the rule subtract 15 starting from 105? O 15, 30, 45, 60, 75 O 15, 10, 25, 20, 35 O 105, 100, 95, 90, 85 O 105, 90, 75, 60, 45
D
Step-by-step explanation:
The correct answer is option D, which is 105, 90, 75, 60, 45.
the perimeter of a rectangle if 24 inches. the rectangle is enlarged so that each side is twice as long as the original. what effect does this enlargement have on the perimeter?
The perimeter becomes double when each side is twice as long as the original.
According to the statement
we have given that the perimeter of a rectangle is 24 inches. and we have to find that the what effect does this enlargement have on the perimeter.
So, For this purpose, we know that the
A rectangle is a parallelogram all of whose angles are right angles especially : one with adjacent sides of unequal length.
The formula to find the perimeter of rectangle is 2(L + B)
And we the length is goes to increased by double then the perimeter will also goes to double.
Because perimeter is directly proportional to the length and breadth of rectangle.
So, The perimeter becomes double when each side is twice as long as the original.
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mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Mary added [tex]$24 \frac{1}{2}[/tex] cups of sugar.
How to estimate how much sugar should Mary add?The ratio of flour to sugar exists at 9 cups: 2 4/7 cups
Utilizing equivalent ratios, given that 7 cups of sugar was utilized,
Let cups of flour needed = x such that our equation becomes
flour/sugar[tex]$ =\frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
[tex]$ \frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
Convert mixed numbers into improper fractions
[tex]$2 \frac{4}{7}= \frac{18}{7}[/tex]
simplifying the above equation, we get
[tex]$\frac{9}{\frac{18}{7} } = \frac{x}{7}[/tex]
= [tex]$24 \frac{1}{2}[/tex]
x = 24.5
The value of x = 24.5.
Therefore, [tex]$24 \frac{1}{2}[/tex] cups of sugar exist required.
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Please help. Which spinner will give maria the best probability of winning a prize
Explain why.
The question is attached
Answer:
We call the denominator rational.
Step-by-step explanation:
For example:
[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]
It's clear that the denominator is now a rational number, not an irrational one anymore.
PLEASE HELP ME SOLVE THIS
Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1057 adults, 89% said that they have a cell phone. Find the value of the test statistic. The value of the test statistic is nothing. (Round to two decimal places as needed.)
Answer:
suma todos los decimales
Step-by-step explanation:
empieza sumando 1059-94%eso te da 993,58 luego le sumas 89% lo que te da 884,2862 espero haberte ayudado
Tanya is a car saleswoman. Below are the number of cars that she sold in each of the last six months. 23, 21, 21, 20, 21, 20 Using this data, create a dot plot where each dot represents a month. 19, 20 ,21 Number of cars sold 22 ,23 pls
Answer: so there would be 1
23
3 21
2 20
Step-by-step explanation:
graph f(x)=(1/4)^x step 4: Plot the points (1, 1/4) and (-1, 4)
The graph of the function, f(x) = (1/4)ˣ, can be seen in the attached graph, following the given steps.
In the question, we are given the function, f(x) = (1/4)ˣ.
Step 1, has asked us to find the initial value of the graph, f(0).
This can be calculated by substituting x = 0, in the given function, which gives us:
f(0) = (1/4)⁰ = 1.
Step 2, has asked us to plot the initial value of the function at (0, 1). This is plotted using the graphing tools.
Step 3, has asked us to evaluate f(1) and f(-1). By substituting x = 1, and x = -1, we get:
f(-1) = (1/4)⁻¹ = 4,
f(1) = (1/4)¹ = 1/4.
Step 4, has asked us to plot the points (1, 1/4), and (-1, 4). This is plotted using the graphing tools.
Step 5, has made us identify the asymptote y = 0.
Step 6, gives us the final curve for the function, f(x) = (1/4)ˣ.
The provided question is incomplete. The complete question is:
"Graph: f(x) = (1/4)ˣ
Step 1: Calculate the initial value of the function. f(0) =
Step 2: Plot the initial value of the function at (0, 1).
Step 3: Evaluate the function at two more points. f(1) = 1/4, f(-1) = 4
Step 4: Plot the points (1, 1/4) and (-1, 4)
Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0
Step 6: The smooth curve that includes these points and approaches to the asymptote shows the graph of the function"
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Which table of values represents a function?
x y
-3 10
4 4
-5 -3
4 4
x y
2 8
6 9
6 3
5 7
x y
1 2
1 4
1 6
1 8
x y
5 2
-3 2
2 2
1 7
The table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
How to determine the table of values represents a function?The table of values is given as:
Table 1
x y
-3 10
4 4
-5 -3
4 4
Table 2
x y
2 8
6 9
6 3
5 7
Table 3
x y
1 2
1 4
1 6
1 8
Table 4
x y
5 2
-3 2
2 2
1 7
For a table to represent a function, each of the x value on the table must correspond to exactly one y value
i.e.
x1 = y1
x2 = y2
And so on
Using the above highlights, the table that represents a function is table 1
Hence, the table in the list of tables that represent an actual function is the first table i.e.
x y
-3 10
4 4
-5 -3
4 4
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Perdue Company purchased equipment on October 1 for $36,100. The equipment was expected to have a useful life of three years, or 4,900 operating hours, and a residual value of $1,800. The equipment was used for 900 hours during Year 1, 1,700 hours in Year 2, 1,500 hours in Year 3, and 800 hours in Year 4.
Required: Round up all final values
Straight line Method
Under the straight-line depreciation method, the depreciation expenses for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, for Perdue Company, are as follows:
Year Amount
Year 1 $2,858.33 ($11,4333.33 x 3/12)
Year 2 $11,433.33
Year 3 $11,433.33
Year 4 $8,575.01 ($11,433.34 - $2,858.33)
What is the straight-line depreciation method?The straight-line method is one of the depreciation methods in use by companies to allocate the cost of plants and equipment over their useful lives.
Under the straight-line method, the depreciable amount (cost less residual value) is divided by the estimated useful life.
Other depreciation methods include the unit-of-production, double-declining-balance, and the sum-of-the-years-digit methods.
Data and Calculations:Equipment cost = $36,100
Residual value = $1,800
Depreciable amount = $34,300 ($36,100 - $1,800)
Estimated useful life = 3 years
Annual depreciation = $11,433.33 ($34,300/3)
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Question Completion:Determine the amount of depreciation expense for the years ended December 31, Year 1, Year 2, Year 3, and Year 4, by the straight-line method.
2. Us i ng the filled table above,
a) calculate just one PED.
b) Is the demand elastic or inelastic?
c) Based on your answer to c) what price change would you recommend to increase TR?
The price elasticity of demand of the pen will be -0.2.
How to compute the elasticity?The demand and supply schedule will be:
Price Qd. Qs
$10. 250. 100
$20. 200. 90
$30. 180. 80
The price elasticity of demand from $1 to $2 will be:
= Percentage change in quantity demanded/percentage change in price
Percentage change in quantity demanded will be:
= (200 - 250)/250 × 100
= -20%
Percentage change in price will be:
= (20 - 10)/10 × 100
= 100%
Therefore, the elasticity of demand will be:
= -20/100
= - 0.2
The value gotten illustrates an inelastic demand.
In order to increase the total revenue, the price can be reduced as it will lead to more sales.
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Complete question:
Choose any product or service. Create the demand and supply schedule.
Calculate just one PED.
Is the demand elastic or inelastic?
What price change would you recommend to increase TR?
Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
a
f(x) dx ≤ M(b − a).
Use this property to estimate the value of the integral.
⁄12 7 tan(4x) dx
It's easy to show that [tex]7\tan(4x)[/tex] is strictly increasing on [tex]x\in\left[0,\frac\pi8\right][/tex]. This means
[tex]M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3[/tex]
and
[tex]m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7[/tex]
Then the integral is bounded by
[tex]\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)[/tex]
[tex]\implies \displaystyle \boxed{\frac{7\pi}{48}} \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le \boxed{\frac{7\sqrt3\,\pi}{48}}[/tex]
An isosceles triangle has two sides of equal length, a, and a base, b. The perimeter of the triangle is 15.7 inches, so
the equation to solve is 2a + b = 15.7.
ayer/
If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side,
which lengths make sense for possible values of b? Select two options.
The value of the base b in the isosceles triangle is 3.1 inches.
According to the statement
we have given that the
equation is 2a + b = 15.7 and if one longer sides is 6.3 centimeter.
And we have to find the length of the base. Then
2a + b = 15.7
Here a is 6.3 cm then
Substitute the values in it then
2a + b = 15.7
2(6.3) + b = 15.7
After solving the equation
12.6 + b = 15.7
b = 15.7 - 12.6
Now we get the value of base b which is 3.1.
So, b = 3.1
So, The value of the base b in the isosceles triangle is 3.1 inches.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 can be used to find the side lengths.
If one of the longer sides is 6.3 centimeters, what is the length of the base?
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find the value of a x 7 when a=6
Answer:
=> 42 ..
Step-by-step explanation:
Given : a = 6
=> a × 7
=> 6 × 7
=> 42
Show Work Please Thank You
The angles in degrees to radian is as follows:
-54 degrees = -3π / 10 radian
How to convert from degree to radian?The measurement is in degrees. Let's convert it to radian with respect to π.
Therefore,
180 degrees = π radian
-54 degrees = ?
cross multiply
Hence,
angle in radian = -54 × π / 180
angle in radian = - 54π / 180
angle in radian = - 6π / 20
angle in radian = -3π / 10 radian
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Identify an acute angle and give its measure.
Angle HEJ measures 15 degrees.
The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 63% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 59%. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level
Using the z-distribution, it is found that since the p-value is less than 0.02, we reject the null hypothesis.
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is of at most 59%, that is:
[tex]H_0: p \leq 0.59[/tex]
At the alternative hypothesis, it is tested if the proportion is greater than 59%, hence:
[tex]H_1: p > 0.59[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are:
[tex]p = 0.59, n = 900, \overline{p} = 0.63[/tex]
Hence the value of the test statistic is found as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.63 - 0.59}{\sqrt{\frac{0.59(0.41)}{900}}}[/tex]
z = 2.44.
What is the p-value and the conclusion?Using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is higher than a value, with z = 2.44, the p-value is of 0.0073.
Since the p-value is less than 0.02, we reject the null hypothesis.
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Let x, y, z be three natural numbers such that x < y < z. If GCF(x, y, z) = 3, GCF (y, z) = 15, LCM (x, y, z) = 3150, and x is even number greater than 10, then find the values of x, y and z.
Answer:
one of several possible solutions :
18, 75, 105
Step-by-step explanation:
prime factors of 3150 :
3150 ÷ 2 = 1575
1575 ÷ 2 no
1575 ÷ 3 = 525
525 ÷ 3 = 175
175 ÷ 3 no
175 ÷ 5 = 35
35 ÷ 5 = 7
7 ÷ 5 no
7 ÷ 7 = 1
3150 = 2¹ × 3² × 5² × 7¹
these are the product of the longest streaks of prime factors in x, y and z.
the GCF(y, z) = 15.
the prime factors of 15 are simply 3¹×5¹.
so, y and z share only the factors 3 and 5.
the GCF(x, y, z) = 3.
since x is an even number, the elimination of 5 in the GCF is not surprising.
let's try the following :
x = 2¹ × 3² = 2×9 = 18
y = 3¹ × 5² = 3×25 = 75
z = 3¹ × 5¹ × 7¹ = 3×5×7 = 105
that uses all the factors of 3150, and their LCM is as the product of the longest streaks of their prime factors is
2¹ × 3² × 5² × 7¹.
fits.
the GCF(75, 105) is the product of the prime factors they have in common : 3¹ × 5¹ = 15.
fits.
the GCF(18, 75, 105) is the product of the prime factors ask 3 numbers have in common, which is only 3¹ = 3.
fits.
18 < 75 < 105
fits.
18 is an even number greater than 10.
fits.
there are more than 1 solutions.
e.g.
z = 2¹ × 3¹ × 5¹ × 7¹ = 210
is also possible.
Joyce paid $108.00 for an item at the store that was 40 percent off the original price. What was the original price?
The original price of the item is $180
The values given in the question are;
Actual cost of the item Joyce bought= $108
The item was sold 40 percent off the original price
The original price can be calculated as follows
The first step is to subtract 40% from 100%
100%- 40%
= 60%
Let x represent the original price of the item
60/100x= 108
0.6x= 108
Divide both sides by the coefficient of x which is 0.6
0.6x/0.6= 108/0.6
x= 180
Thus, the original price of the item is $180
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Find the volume of the given cylinder.
r=5 ft., h=15 ft.
HELP PLEASE ASAP Find the distance between A and B. (5,1) (-3,-4)
Answer:
6.32
Step-by-step explanation:
The formula we use to find the distance between two points is:
[tex]\sqrt{(x_1-x_2)+(y_1-y_2)}[/tex]
The x1 is -3, the x2 is 5, the y1 is -4, and lastly, the y2 is 1.
If we input these numbers in the equation, we end up with:
[tex]\sqrt{(-3-5)+(-4-1)}[/tex]
= [tex]\sqrt{(-8) (-5)}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]2\sqrt{10}[/tex]
= 6.32455532
Rounded to the nearest hundredth is 6.32
Find mEHFˆ. PLEASE HELP ASAP
Answer:
30°
Step-by-step explanation:
[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]
So, this means arc FH measures 105 degrees.
Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.
By the inscribed angle theorem, angle EHF measures 30°.
PLEASE HELP ME .IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer: [tex]\frac{10\pi}{3}[/tex] m
Step-by-step explanation:
[tex](2)(\pi)(4) \left(\frac{150}{360} \right)=\frac{10\pi}{3}[/tex]
Static and Reasoning:
Isabella is studying the fairness of a six-sided numbered cube with numbers 1, 2, 3, 4, 5, and 6. The numbered cube is rolled 36 times, and the numbers on the top side are recorded in the table below.
Based on the data, what conclusion would you make about the fairness of the numbered cube? Justify your answer.
Based on the data recorded by Isabella, it can be concluded the cube is rather fair.
How many times did Isabella get each number?Based on the data, here are the results:
Getting a 1: 6 timesGetting a 2: 5 timesGetting a 3: 7 timesGetting a 4: 5 timesGetting a 5: 6 timesGetting a 6: 7 timesThis implies, in total Isabella got the same number between five and seven times. For example, the number 2 was obtained 5 times, but the number 3 was obtained 7 times.
What can be concluded based on the results?Even though Isabella did not get the same number of times each number, the dice is rather fair because by rolling the dice thirty six times you will obtain the same number at least five times.
Moreover, there is not a big difference in the number of times you obtain each number.
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Kevin is filing his return under the single status. His taxable income is $125,500 per year. What tax bracket would he be in?
Since Kevin is filing his tax return under the single status, he would be in the tax bracket of $86,376 to $164,925 with a marginal tax rate of 24%.
What is a tax bracket?Under the progressive tax system, a tax bracket is a range of taxable incomes that is subject to a marginal tax rate.
Tax brackets provide a systematic way of progressively taxing taxpayers' income.
Data and Calculations:Taxable income = $125,500
Since he falls under the tax bracket of $86,376 to $164,925, Kevin's tax rate is 24%.
Thus, as a single taxpayer, Kevin falls under the tax bracket of $86,376 to $164,925 with a marginal tax rate of 24% of taxable income.
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Question Completion:Personal Income Tax Brackets for Single Filers:
Tax rate Taxable income bracket Tax owed
10% $0 to $9,950 10% of taxable income
12% $9,951 to $40,525 $995 plus 12% of the amount over $9,950
22% $40,526 to $86,375 $4,664 plus 22% of the amount over $40,525
24% $86,376 to $164,925 $14,751 plus 24% of the amount over $86,375