Choose the number sentence that applies the commutative property to the example.
3 × 4 = 12
6 + 6 = 12
12 × 1 = 12
6 × 2 = 12
4 × 3 = 12
The number sentence that applies the commutative property to the example is 4 × 3 = 12
Commutative propertyCommutative property can be additive or multiplicative. It is a way of changing the position of a function or value in an expression without affecting the result
Examples are
A +B = B +A
AB = BA
Although the value were interchanged, the result were not affected. Hence the number sentence that applies the commutative property to the example is 4 × 3 = 12 since changing 3 and 4 does not affect the result
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Find the surface area of the figure. See picture to solve.
The surface area of trapezoidal prism is: D. 385.6 yd².
What is the Surface Area of a Trapezoidal Prism?Surface area = (b1 + b2)h + PH.
The parameters are:
b1 = 10 yd
b2 = 6 yd
h = 4.6 yd
Perimeter of base (P) = 6 + 10 + 5 + 5 = 26 yd
H = 12 yd
Plug in the values
Surface area = (10 + 6)4.6 + (26)(12)
Surface area = 385.6 yd²
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An 8-cylinder Crown Victoria gives 18 miles per gallon in city driving and 21 miles per gallon in highway driving. A 300-mile trip required 15.5 gallons of gasoline. How many whole miles were driven in the city?
Answer:
Step-by-step explanation:
let he drives at 21 m/hr=x gallons
gas used at 18 m/hr=15.5-x
21x+18(15.5-x)=300
divide by 3
7x+6(15.5-x)=100
7x+93-6x=100
x=100-93=7 gallons
gas used in city=15.5-7=8.5 gallons
distance travelled in city=18×8.5=153 miles
On a coordinate plane, parallelogram A B C D is shown. Point A is at (negative 3, negative 1), point B is at (7, 9), point C is at (8, negative 1), and point D is at (negative 2, negative 11). Create a rectangle around the parallelogram. The dimensions of this rectangle are ✔ 11 by 20 . Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is square units. Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is square units.
The coordinates plane is illustrated below.
How to illustrate the information?A coordinate plane simply means the graphing system for points and lines.
Based on the information given, the area of teb triangle will be:
= 1/2 × b × h
= 1/2 × 11 × 20
= 110
Other information are attached.
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In a graphing program, graph the following 4 functions in the same coordinate plane.
y=1x
y=5x
y=14x
y=-2x
How does a change the exponential graph? (Hint – see choices from k section)
a. When a is large (graph b):
b. When a is small (graph c):
c. When a is negative (graph d):
See below for the changes when the exponential function is transformed
How to determine the effect of aThe exponential functions are given as:
[tex]y = \sqrt x[/tex]
[tex]y = 5\sqrt x[/tex]
[tex]y = 14\sqrt{x[/tex]
[tex]y = -2\sqrt{x[/tex]
An exponential function of the above form is represented as:
[tex]y = a\sqrt{x[/tex]
See attachment for the graph of the four functions.
When a is large
This is represented by [tex]y = 14\sqrt{x[/tex]
In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves closer to the y-axis
When a is small
This is represented by [tex]y = 5\sqrt x[/tex]
In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and it moves away from the x-axis
When a is negative
This is represented by [tex]y = -2\sqrt{x[/tex]
In this case, the curve of the base form [tex]y = \sqrt x[/tex] is vertically stretched and is reflected across the y-axis.
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Compute the probability of drawing two spades from a deck of cards
In a playing card there are 52 cards. (i) '2' of spades: Number of favourable outcomes i.e. '2' of spades is 1 out of 52 cards.
Which is the following descibes a median of a triangle
According to the internet it states, The median of a triangle is a line segment joining the vertex of the triangle to the mid-point of its opposite side.
It bisects the opposite side, dividing it into two equal parts.
The median of a triangle further divides the triangle into two triangles having the same area
If 24 women can dig a field in 14 days, how long will 16 women take to dig the same field?
The Campbell Company is considering adding a robotic paint sprayer to its production line. The sprayer's base price is $1,020,000, and it would cost another $22,000 to install it. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $599,000. The MACRS rates for the first three years are 0.3333, 0.4445, and 0.1481. The machine would require an increase in net working capital (inventory) of $19,500. The sprayer would not change revenues, but it is expected to save the firm $386,000 per year in before-tax operating costs, mainly labor. Campbell's marginal tax rate is 25%. (Ignore the half-year convention for the straight-line method.) Cash outflows, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest dollar. What is the Year-0 net cash flow? $ What are the net operating cash flows in Years 1, 2, and 3? Year 1: $ Year 2: $ Year 3: $ What is the additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital)? $ If the project's cost of capital is 11%, what is the NPV of the project? $ Should the machine be purchased? -Select-
1. The Year-0 net cash flow is -$1,061,500.
2. The net operating cash flows in Years 1, 2, and 3 are as follows:
Year 1: $288,750 ($386,000 x 1 - 0.25)
Year 2: $288,750 ($386,000 x 1 - 0.25)
Year 3: $288,750 ($386,000 x 1 - 0.25)
3. The additional Year-3 cash flow (i.e, the after-tax salvage and the return of working capital) is $468,750 {($599,000 x 1 - 0.25) + $19,500}.
4. The NPV of the project is ($13,139).
5. The machine should not be purchased because it does not yield a positive NPV.
What is the net present value?The net present value (NPV) shows the difference between the present value of cash inflows and the present value of cash outflows over a period of time.
It is determined by calculating the present values of cash flows using their present value factors as below:
Data and Calculations:Initial cash outlay = $1,061,500 ($1,020,000 + $22,000 + $19,500)
Salvage value = $599,000
Increase in net working capital = $19,500
Annual savings before tax = $386,000
Tax rate = 25%
Annuial savings after tax = $288,750 ($386,000 x 1 - 0.25)
Determination of Net Present Value (NPV):Year Cashflows PV Factor Present Value
0 -$1,061,500 1 -$1,061,500
1 $288,750 0.901 $260,164
2 $288,750 0.812 $234,465
3 $288,750 0.731 $211,076
3 $468,750 0.731 $342,656
Net present value -$13,139
Thus, the project should not be undertaken by The Campbell Company due to the negative NPV that it yields.
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How many integers n satisfy both of the inequalities 4n + 3 < 25 and -7n + 5 < 24?
Answer:
1) All real numbers n such that [tex]n < 5.5[/tex]
2) All real numbers n such that [tex]n > -\frac{19}{7}[/tex]
Step-by-step explanation: How did I come up with such answers? Let me show you!
For the first problem, we just solve the inequality easily.
Subtracting 3 from both sides, we get:
4n < 22
Dividing by 4 from both sides, we get:
n < 5.5
Thus, all real numbers n that is less than 5.5 when plugged in for x will be less than 25.
For the next problem, it will be slightly trickier.
Subtracting 5 from both sides, we get:
-7n < 19
Dividing -7 from both sides, we get:
n > -19/7
Did you catch that? We just flipped the inequality sign and turned it from less than to a greater than. Whenever we divide by a negative number, the signs always change.
Thus, for all real numbers n greater than -19/7, when plugging in for x, you will get less than 24.
Hope this helped!
What is the value of k in the product of powers below?
10^3 x 10 x 10^k = 10^-3= 1/10^-3
-3
-1
0
1
Answer:
it's-3
Step-by-step explanation:
please mark me as brainlist
Darryl just received his credit scores from the three major credit bureaus. his experian score is 719, his equifax score is 741, and his transunion score is 780. what is his mean credit score? (round to the nearest whole point, if applicable.) a. 719 b. 741 c. 760 d. 747 please select the best answer from the choices provided a b c
The correct answer is D
Introduction to mean:The mean is also called average. The arithmetic mean is found by adding the numbers in the list and dividing the sum by the number of numbers in the list.
Mean = (Sum of all the observations/Total number of observations)
Given:Darryl's credit scores are Experian score is 719, Equifax's score is 741, and Transunion's score is 780.
To find the mean we have to add the given values i.e., the sum of Experian score, Equifax's score, and Transunion's score.
719+741+780
there are a total of 3 scores so we have to divide them by 3.
[tex]\frac{719+741+780}{3}[/tex]
≅[tex]746.67[/tex]
The nearest whole point is 747.
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Whats the correct answer answer asap for brainlist
Answer:
Russia is so vast that it has eleven time zones.
Explanation:
"Russia has 11 time zones across its vast territory - and its leaders believe that's just too many hours in the day." - NBC News
What combination of transformations is shown below?
2
3
reflection, then translation
translation, then reflection
reflection, then rotation
translation, then rotation
1
the sequence is:
Translation, then reflection.
The correct option is the second one.
What combination of transformations is shown?
We start with figure 1.
In the image, we can see that the image is shifted 4 units up and 4 units left to make figure 2.
Then you can see that the image is reflected across a horizontal line to make figure 3, you can see that because now the "L" is facing upwards.
Then the sequence is:
Translation, then reflection.
The correct option is the second one.
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A triangle has points dallas, destination 1, and destination 2. the distance from dallas to destination 1 is 720 miles, and the distance from destination 1 to destination 2 is 290 miles. the angle formed between dallas, destination 1, and destination 2 is 125 degrees. a pilot flies 720 miles from dallas, texas, to his first destination. after dropping off his cargo, he flies southeast 290 miles to his second destination. if the angle formed by his trip is 125°, what is the distance he will fly from the second destination back to dallas? 490 miles 918 miles 1,010 miles 842,026 miles
The distance from the second destination back to Dallas is 918 miles
GivenA triangle has points Dallas, destination 1, and destination 2.
The distance from Dallas to destination 1 is 720 miles
The distance from destination 1 and destination 2 is 290 miles
the angle formed between Dallas, destination 1, and destination 2 is 125 degrees.
He moves from destination 1 to Dallas then destination 2
We could use cosine law to find the distance
What is cosine law?The Law of cosines or cosine law means the relation between the length of sides of a triangle with respect to the cosine of its angle. It is also called the cosine rule
[tex]b^{2}=a^2+c^2-2ac*cosB[/tex]
=[tex]290^2+720^2-2*720*290*cos125[/tex]
=84100+518400-417600 cos 125
=602500-417600*(-0.5735)
=602500+239493.6
=841993.6
b=917.6 miles
≅918 miles
The distance is 918 miles he will fly from the second destination back to Dallas
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Answer:
918 miles
Step-by-step explanation:
got it right on edge
I need help please to get my HS diploma...did not graduate :(
Which of the following equations has roots x=−2, x=3 (multiplicity 2), and x=1, and passes through the point (0,-18)?
f(x) = x^4 - 5x^3 + x^2 + 21x - 18
=======================================================
Explanation:
The root x = -2 means x+2 is a factor. This is because we add 2 to both sides of x = -2 to get x+2 = 0.
Similarly, x = 3 leads to x-3 being another factor. It's a double root so we really have two copies of (x-3)
The last root is x = 1 which gives the factor x-1.
The four factors are: (x+2)(x-3)(x-3)(x-1)
Let's use the FOIL rule to expand out the first two factors
(x+2)(x-3) = x^2-3x+2x-6 = x^2-x-6
Do the same for the last two factors
(x-3)(x-1) = x^2-1x-3x+3 = x^2-4x+3
--------------------
So far we have:
(x+2)(x-3) = x^2-x-6
(x-3)(x-1) = x^2-4x+3
which leads to
(x+2)(x-3)(x-3)(x-1) = (x^2-x-6)(x^2-4x+3)
From here I'll use the box method to multiply these trinomials. Check out the diagram below. Each inner cell is the result of multiplying the headers. Example: x^2 times x^2 = x^4 in the upper left corner.
I've color-coded the inner cells to show the like terms. Add up those like terms:
-4x^3 + (-x^3) = -5x^33x^2 + (4x^2) + (-6x^2) = x^2-3x + 24x = 21xTherefore we end up with
(x^2-x-6)(x^2-4x+3) = x^4 - 5x^3 + x^2 + 21x - 18 which is choice B
--------------------
To verify this answer, plug in x = 0 and you should get y = -18 to show that we have the correct y intercept. If we tried this with choice A, then we'd get y = 18 which helps eliminate choice A.
Furthermore, plug in x = -2 into choice B and you should get y = 0 as an output. The same applies to x = 3 and x = 1. This confirms that they are roots or x intercepts of the polynomial.
Another way to verify the answer is to use something like WolframAlpha to type in (x+2)(x-3)(x-3)(x-1). Under the "expanded form" subsection, it says x^4 - 5x^3 + x^2 + 21x - 18
Brainlyest to first correct. Report to incorrect
Add.
(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)
Express the answer in standard form.
Enter your answer in the box.
Answer:
6x^5-5x^4+6x^3-x^2+12x-31
Step-by-step explanation:
(−5x^4+6x^3−43)+(6x^5−x^2+12x+12)
To add, combine like terms
6x^5-5x^4+6x^3-x^2+12x-43+12
6x^5-5x^4+6x^3-x^2+12x-31
Standard form means from the highest power of x to the lowest power of x
Help me!! Please anwser fast.
Answer:
only the first one
Step-by-step explanation:
all the others sign to at least one x value 2 different y values. and that violates the definition of a function.
In the equation above k is a constant if y = 2 when x= 5 what is the value of x when y= 5
The value f x when y= 5 is 2
VariationsLet the given equation be y = k/x
where k is the constant
if y = 2 when x= 5, then;
k = xy
k= 2(5)
k = 10
In order to determine the value of x when y = 5
x = k/y
x = 10/5
x = 2
Hence the value f x when y= 5 is 2
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simplify the expression
Answer:
-4sin(2x)
Step-by-step explanation:
Angle sum identities can be used to simplify this expression.
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)sin(a+b) = sin(a)cos(b) +sin(b)cos(a)sin(2x) = 2sin(x)cos(x)NumeratorThe cosine function is even, so cos(-x) = cos(x). The cosine of the sum is ...
cos(90°+x) = cos(90°)cos(x) -sin(90°)sin(x) = -sin(x)
Then the numerator simplifies to ...
4cos(-x)cos(90°+x) = -4cos(x)sin(x) = -2sin(2x)
DenominatorMatching the denominator expression to the sine of a sum relation, we see
sin(30° -x)cos(x) +sin(x)cos(30° -x) = sin((30°-x) +x) = sin(30°) = 1/2
Simplified ExpressionThe simplified expression is the ratio of the simplified numerator to the simplified denominator:
= -sin(2x)/(1/2)
= -4sin(2x)
Which function has a vertex at the origin?
Help
Answer:
Option D
Step-by-step explanation:
y=-x²This function has vertex at origin
Let's verify
Put (0,0)
0=-(0)²0=-00=0Hence verified
Answer:
[tex]f(x)=-x^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]y=a(x-h)^2+k[/tex]
where:
(h, k) is the vertexa is some constantIf the vertex is at the origin:
h = 0k = 0Substituting the vertex into the equation:
[tex]\implies y=a(x-0)^2+0[/tex]
[tex]\implies y= ax^2[/tex]
Comparing with the available answer options:
[tex]f(x)=-x^2[/tex] has its vertex at the origin.
Additional Information:
[tex]\textsf{The vertex of }\:f(x)=(x+4)^2 \: \textsf{ is }\:(-4,0)[/tex]
[tex]\textsf{The vertex of }\:f(x)=x(x-4) \: \textsf{ is }\:(2,-4)[/tex]
[tex]\textsf{The vertex of }\:f(x)=(x-4)(x+4) \: \textsf{ is }\:(0,-16)[/tex]
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Which of the following are reasons used in the proof that the angle-bisector
construction can be used to bisect any angle?
Check all that apply.
0 A. All of the radii of a circle
are congruent.
. B. SSS triangle congruence postulate
. C. Any line segment can be extended
indefinitely.
. D. CPCTC
The angle-bisector construction can be used to bisect any angle and this is proven by:
A. All of the radii of a circle are congruent.B. SSS triangle congruence postulate. D. CPCTC.What is the proof that the angle-bisector construction can bisect any angle?The angle-bisector construction means that a line is made that can divide an angle into two congruent angles.
This is shown by the fact that all the radii of a circle are congruent and that the corresponding parts of congruent triangles are also congruent (CPCTC) when an angle bisector is made on a circle or triangle respectively.
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1. For the month of July, calculate the following:
a. Budgeted sales
b. Budgeted merchandise purchases
c. Budgeted cost of goods sold
d. Budgeted net operating income
2. Prepare a budgeted balance sheet as of July 31.
Answer:
you can use the spreadsheet
c = √a² + b². This is the formula for the length of the hypotenuse c of a right triangle. Solve this formula for a.
Answer:
a = sqrt(c^2 - b^2)
see image.
Step-by-step explanation:
If you square both sides of the equation, you get the Pythagorean Theorem back again.
c = sqrt(a^2 + b^2)
c^2 = a^2 + b^2
Solve for a means to get a all by itself on one side of the equation. Subtract b^2 and then take the square root. See image.
A curve goes from 8 to 20 on the x-axis.
What would the height need to be for this curve to be a density curve?
StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 12 EndFraction
StartFraction 1 Over 20 EndFraction
1
Picture posted below…
Answer: 1/12
Step-by-step explanation:
The total area of the rectangle needs to be 1.
Since 20-8=12, the height needs to be 1/12.
NO LINKS!!! Part 1:
What is the Transformation of f(x)= x^3:
THIS IS NOT MULTIPLE CHOICE!!!!
1. f(x)= 1/5x^3
2. f(x)= (x-5)^3
3. f(x)= x^3 + 5
Answer:
1. Vertical shrink by a factor of ¹/₅
2. Right 5
3. Up 5
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 1
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\dfrac{1}{5}x^3[/tex]
Comparing the parent function with the given function, we can see that the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=\dfrac{1}{5}\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:\dfrac{1}{5}[/tex]
As 0 < a < 1, the transformation visually is a compression in the y-direction, so we can also say: Vertical shrink by a factor of ¹/₅
Question 2
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x-5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been subtracted from the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x-5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units right}[/tex]
Question 3
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=x^3+5[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the parent function.
Therefore, the transformation is:
[tex]f(x)+5 \implies f(x) \: \textsf{translated}\:5\:\textsf{units up}[/tex]
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Answer:
1) Vertical shrink by a factor of 1/5
2) Right 5
3) Up 5
Explanation:
Given main function: f(x) = x³
1.) f(x) = 1/5 (x³)
Comparing with a(f(x)) which gives vertical stretch or compression.
Here the function f(x) has been shrinked vertically by a factor of 1/5
2.) f(x) = (x - 5)³
Comparing with f(x - c) which gives horizontal translation c units right.
Here the function f(x) has been shifted 5 units to the right.
3.) f(x)= x³ + 5
Comparing it with f(x) + d which gives vertical translation d units up.
Here the function f(x) has been moved 5 units up.
When finding the area of a rectangular prism, do you prefer to find the area of the base first and then multiply it by the height or to multiply all three dimensions at once?
Answer: I prefer to find the area of the base first and then multiply by the height
one of the two of A two digit is three times the other digit. if you interchange the digits of this two digit number and add the resulting number to the original number you get 88.what is the original number. give solution
ASAP PLEASE
Given that, one digit of a two digit number is three times the other digit.
Let assume that digit at ones place be x.
digit at ones place be x.So, digit at tens place be 3x.
digit at ones place be x.So, digit at tens place be 3x.So, two digit original number = 10 × 3x + 1 × x = 30x + x = 31x
Now, number formed on interchanging its digits, i.e.
Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x
According to statement, if we interchange the digits of this two digit number and add the resulting number to the original number, we get 88.
[tex]\begin{gathered}\sf \: 31x + 13x = 88 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: 44x = 88 \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf \: x = \dfrac{88}{44} \\ \\ \end{gathered}[/tex]
[tex]\begin{gathered}\sf\implies \: x = 2 \\ \\ \end{gathered}[/tex]
So, two digit number is 31 × 2 = 62
Hence,
[tex]\begin{gathered}\sf\implies \: \boxed{ \bf{ \:Original \: number \: = \: 62 \: \: }} \\ \\ \end{gathered}[/tex]
[tex]\rule{190pt}{2pt}[/tex]
Answer:
26 or 62
Step-by-step explanation:
If one of the two digits of a two-digit number is three times the other digit, then the options for the two-digit number are:
13 or 3126 or 6239 or 93If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.
From inspection of the listed pairs of numbers, the only pair that sums to 88 is 26 and 62:
⇒ 26 + 62 = 88
Therefore, the original number is either 26 or 62.
Here is a list of numbers:
7.3, 1, 3.6, 3.6, 1.6, 7.8,
5.4, 6.4, 6.1, 3.3
State the median.
Give your answer as a decimal.
ABC Check
←
↑
Ix
X
Answer:
4.5
Hope it helps
Find the maximum and minimum values of the function g(θ) 5θ-9sin(θ) on the interval [0, π] Minimum value =
Maximum value =
Answer:
max=50
min=41
Step-by-step explanation:
graph