Answer:
[tex]2x^{2}[/tex] - 16x + 14
Step-by-step explanation:
(2x - 4)(x - 6)
= (2x + −4)(x + −6)
= (2x)(x) + (2x)(−6) + (−4)(x) + (−4)(−6)
= [tex]2x^{2}[/tex] − 12x − 4x + 24
= [tex]2x^{2}[/tex] - 16x + 14
Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B and height H. Consider these ideas or others: combine two copies of a trapezoid to make a parallelogram. Subdivide the trapezoid into two triangles one with base b and one with base a.
Answer:
Formula of Trapezoid:
A = (a + b) × h / 2
The formula can be derived in different ways. for now, we have discussed two ways:
1. By using the formula of a triangle
2. By dividing into different sections
Step-by-step explanation:
1. By using the formula of a triangle
One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.
Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.
The image is attached below.
Connect vertices P and R with a diagonal.
Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).
Its area is
S1=[tex]\frac{1}{2} *PQ*RM[/tex]
Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).
Its area is
S2=[tex]\frac{1}{2} *SR*PN[/tex]
Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.
They both are equal to the altitude of the trapezoid h.
Therefore, we can represent areas of our two triangles as
S1=[tex]\frac{1}{2}*PQ*h[/tex]
S2=[tex]\frac{1}{2}*SR*h[/tex]
Adding them together, we get the area of the whole trapezoid:
S=S1+S2=[tex]\frac{1}{2} (PQ+SR)h,[/tex]
which is usually represented in words as "half-sum of the bases times the altitude".
2. By dividing into different sections
Trapezoid PQRS is shown below, with PQ parallel to RS.
Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)
We are going to derive the area of a trapezoid by dividing it into different sections.
If we drop another line from Q, then we will have two altitudes namely PT and QU.
Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)
From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that
=> [tex]A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}[/tex]
Simplifying, we have
=>[tex]A= \frac{ah+2b_{1+C} }{2}[/tex]
Factoring we have,
=> [tex]A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}[/tex]
But, [tex]a+ b_{1} + c[/tex] is equal to [tex]b_{2}[/tex], the longer base of our trapezoid.
Hence, [tex]A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}[/tex]
We have discussed two ways by which we can derive area of a trapezoid.
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PLEASE HELP
Natalie invests $6,680 in a savings account with an interest rate of 2% compounded continuously.
How long will it take for the account balance to reach $8,838.51?
The time it will take the money to reach $8,838.51 is 14years
Compound interestThe formula for calculating compound interest is expressed as:
A = P(1+r)^t
where
P = $6,680
A = $8,838.51?
r = 2% = 0.02
Substitute and calculate the time 't"
8,838.51 = 6680(1+0.02)^t
1.3231 = 1.02^t
t = ln1.3231/ln1.02
t = 14years
Hence the time it will take the money to reach $8,838.51 is 14years
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When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.
Choose all of the following statements that are true.
a.
The domain is {4, 8, 11, 15}.
b.
An 11 gallon tank would cost $44.00 to fill completely.
c.
A 9.1 gallon fill-up would cost $35.49.
d.
A 12 gallon tank would cost $47.40 to fill completely.
Option D statement "A 12-gallon tank would cost $47.40 to fill completely" is true.
What is a domain?The whole of the independent variable's possible values makes up the domain of a function.
For the given data we need to find which of the given statements are true.
From option A:
The domain is {4, 8, 11, 15}.
The domain is all possible x values so this would be 0 to infinity as you can pay for more gallons not just to that certain set of numbers.
Therefore, option A is False.
From option B:
An 11-gallon tank would cost $44.00 to fill completely.
From the given table we can see that 11-gallon tank costs $43.45.
Therefore, option B is False.
From option C:
A 9.1-gallon fill-up would cost $35.49.
To find 9.1 gallons we need to find the cost of 1-gallon.
That is, 15.80/4 = $3.95 (Given in the table)
Now the cost of 9.1 gallon tank is $3.95 x 9.1 = $35.95 not $35.49
Therefore, option C is False.
From option D:
A 12-gallon tank would cost $47.40 to fill completely.
We found that 1 gallon is $3.95.
$3.95 x 12 = $47.40
Therefore, option D is True.
Hence, from the given statements option D is True.
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400g is what percent of 80kg?
Terry brings home $14 per hour he works. When he started this job, he had
$40 in the bank. Write and graph the equation that would represent how
much money Terry has in the bank (y) after x hours of work. Identify the x-
and the y-intercepts. Do they make sense in this context. If so, what do they
tell us about Terry's situation? Find the point (3, 82) on the graph. What does
that point represent in the context of Terry's situation?
The point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
Given that, Terry brings home $14 per hour he works. When he started this job, he had $40 in the bank.
We need to write and graph the equation that would represent how much money Terry has in the bank (y) after x hours of work.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, y=40+14x
Graph the line using the slope and y-intercept, or two points.
Slope: 14
y-intercept: (0, 40)
The coordinates to plot the graph are (0, 40), (1, 54), (2, 68) and (3, 82).
The graph for the given equation is given below.
Therefore, the point (3, 82) on the graph represents after Terry's hours his bank balance will be $82.
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There are 230 calories in a 48 gram packet of M&M's. How many calories are in a 33.6 gram bag?
Answer:
161 calories
Step-by-step explanation:
1) Divide 230 by 48
4.791666666666667
2) multiply 4.791666666666667 by 33.6
161
Done! Your answer is 161 calories in a 33.6 gram bag. Or just 161.
Hope this helps!
Consider a triangle ABC like the one below. Suppose that B=129°, a=7, and c=42. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
4-C-b-0
DOD
X
No
solution
5
?
The angles are: A =24.7° ; B = 40.6° ; C =114.7°.
What is Cosine law?
The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°
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A company makes paper labels for paint cans. As shown below, each can is in the shape of a cylinder
with a height of 7 cm and a radius of 2 cm. The paper label is wrapped around the can and covers only
the side of the can (not the top or bottom). The company uses, on average, 3612.64 cm² of paper
each minute making these labels. How many labels does the company make, on average, each
minute?
For your calculations, do not round any intermediate steps, and use the button on a calculator. Round
your answer to the nearest hundredth.
The company needs 41 labels on average, each minute.
What is the circumference of a circle?The perimeter of a circle (circumference): 2 π radius
Replacing with the values given:
C = 2 (3.14) 2 = 12.56 cm
So, the area of one label is:
Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.
Now, the number of label be n
87.92 x n = 3612.64 cm2
n = 3612.64 / 87.92
n = 41.09
Hence, The company needs 41 labels on average, each minute.
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Which of the following is the midpoint between (6, 3) and (-2, -5)
Answer:
( 2, -1)
Step-by-step explanation:
(X1 + X2)/2 , (Y1 + Y2)/2
(6-2)/2 , (3-5)/2
4/2 , -2/2
2 , -1
Answer:
(2, -1)
Step-by-step explanation:
(x1, y1)=(6, 3)
(x2, y2)=(-2, -5)
[(6+(-2))/2, (3+(-5))/2]
=(4/2, -2/2)
=(2, -1)
if p = (-1,-1) find the image of p under the following rotation. 90 degrees counterclockwise about the origin
Answer:
( 1, - 1 )
Step-by-step explanation:
HELP STAT:
Graph the function F(x)= -sec (x/4) +3 on the interval [-2pi,6pi]
Answer:
Step-by-step explanation:
evaluate question 4 only
Substitute [tex]y = \sqrt x[/tex], so that [tex]y^2 = x[/tex] and [tex]2y\,dy = dx[/tex]. Then the integral becomes
[tex]\displaystyle \int \frac{dx}{\sqrt{1 + \sqrt x}} = 2 \int \frac y{\sqrt{1+y}} \, dy[/tex]
Now substitute [tex]z=1+y[/tex], so [tex]dz=dy[/tex]. The integral transforms to
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = 2 \int \frac{z-1}{\sqrt z} \, dz = 2 \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz[/tex]
The rest is trivial. By the power rule,
[tex]\displaystyle \int \left(\sqrt z - \frac1{\sqrt z}\right) \, dz = \frac23 z^{3/2} - 2z^{1/2} + C = \frac23 \sqrt z (z - 3) + C[/tex]
Put everything back in terms of [tex]y[/tex], then [tex]x[/tex] :
[tex]\displaystyle 2 \int \frac y{\sqrt{1+y}} \, dy = \frac43 \sqrt{1+y} (y - 2) + C[/tex]
[tex]\displaystyle \int \frac{dx}{\sqrt{1+\sqrt x}} = \boxed{\frac43 \sqrt{1+\sqrt x} (\sqrt x - 2) + C}[/tex]
Scott started his bank account with $150 and is spending $7 per day on lunch. The x-axis would be labeled:
The x axis is labeled as Number of days.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
let x be the number of days and y be money.
So, the equation is
y = -7x + 150.
Hence, the x axis is labeled as Number of days.
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Help pls ???????????
The second derivative of the first function is s"(x) = = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³.
The second derivative of the second function is; k''(t) = (36t² - 6)e^(-3t²)
How to find the second derivative?1) We are given the function;
s(x) = 4/(1 + 2e^(-0.2x)
First derivative is;
ds/dx = [8e^(x/5)]/5(e^(x/5) + 2)²
Second Derivative is;
d²s/dx² = -[8e^(x/5) - 2]e^(x/5)/25(e^(x/5) + 2)³
At x = 0;
d²s/dx² = -[8e^(0/5) - 2]e^(0/5)/25(e^(0/5) + 2)³
d²s/dx² = 8/675
B) We are given the function;
k(t) = e^(-3t²)
The first derivative is;
dk/dt = -6te^(-3t²)
The second derivative is;
k''(t) = (36t² - 6)e^(-3t²)
At t = 1, we have;
k''(t) = (36(1)² - 6)e^(-3(1²))
k"(t) = 1.494
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A shop advertised a 24%-off sale. If a coat originally sold for $258, find the decrease in price and the sale price.
The decrease in price is $
The sale price is $
کے
Answer:
The decrease in price is $61.92
The sale price is $196.08
Step-by-step explanation:
24% × 258 = 61.92
258 decrease 24% =
258 × (1 - 24%) = 258 × (1 - 0.24) = 196.08
A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 3600 ft2 (including the margins).
If x denotes the left-right width (in feet) of the billboard, determine the value of x that maximizes the area of the printed region of the billboard.
An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,
The total area of the billboard, A= x·y
The total printed area of the billboard, [tex]A_p=(x-2)(y-8)[/tex]
Given in problem that the area of the billboard is 3600 ft².
x·y = 3600
y = (3600)/x
Substituting the value of y in the equation of the total printed area of the billboard,
[tex]A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}[/tex]
Now, the value of x is needed to be minimum, therefore, differentiating the given function,
[tex]\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}[/tex]
Equate the differentiated function with 0,
[tex]0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.[/tex]
Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.
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please answer me please
Step-by-step explanation:
please mark me as brainlest
A movie theater sells up to 10 tickets at a time online.what is the domain of this graph.
The domain of the function is whole numbers from 0 to 10.
How to explain the domain?Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.
As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.
Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.
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Give the “best” big-oh notation to describe the complexity of the algorithm that prints all bit strings of length n.
It is correct to state that a bit can be in one of 2 states, either 1 or 0.
What is a bit?A bit is is a single binary digit. A bit can either be "1" or "0".
What is the explanation to the above answer?We stated that It is correct to indicate that a bit can be in one of 2 states, either 1 or 0. This indicates that 2ⁿ strings must be created in total. The string must then be processed twice.
The first time, for generation andThe second for reading.Hence, Our time is now O(2ⁿ⁺¹) = O(2ⁿ)
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Circle O is shown. Line segment J E is a diameter and line segment O B is a radius. A line is drawn from point J to point B to form a chord. Tangents B D and E D intersect at point D outside of the circle.
Use the diagram to complete the statements.
The measure of angle EJB is
the measure of angle BOE.
The measure of angle BDE is
the measure of angle BOE.
The measure of angle OED is
✔ equal to
the measure of angle OBD.
The measure of angle OED is the measure of angle OBD. Then the correct option is C.
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Circle O is shown.
Line segment JE is a diameter and line segment OB is a radius.
A line is drawn from point J to point B to form a chord.
Tangents BD and ED intersect at point D outside the circle.
The radius and tangent are orthogonal to each other.
∠OED = ∠OBD = 90°
Then the correct option is C.
The complete question is given below.
Circle O is shown. Line segment J E is a diameter and line segment O B is a radius. A line is drawn from point J to point B to form a chord. Tangents B D and E D intersect at point D outside of the circle.
Use the diagram to complete the statements.
The measure of angle EJB is the measure of angle BOE.
The measure of angle BDE is the measure of angle BOE.
The measure of angle OED is the measure of angle OBD.
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Answer:
one-half, 180 minus, equal to
Step-by-step explanation:
A player shoots a basketball from a height of 6 feet. The equation, , gives the height, h, of the basketball after t seconds. Describe the height, rounded to the nearest tenth of a foot, of the basketball after 1.5 seconds, assuming no other player touches the ball.
feet above the ground
It will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).
All you need to do is to replace t in the given equation with 1.5:
[tex]h=-16(1.5)^2+25(1.5)+6[/tex]
h=-4.875
The value is negative so we can assume that after 1.5 seconds the ball will be 4.875 feet lower than it was shot from.
What is the height?
The measurement of someone or something from head to foot or from base to top.
But we also know that it was shot from a height of 6 feet,
So it will be 6 - 4.875 = 1.125 feet above the ground or 1.1 feet (rounded to the nearest tenth of a foot).
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Algebra 2 urgent I need help quickkk 20 points !!!
Answer:
(-3, -13)
(-1, -7)
(1, -1)
(3, 5)
(5, 11)
Step-by-step explanation:
Plug x into the equation y = 3x - 4 for each value of x to obtain the y value.
For example:
y = 3(3) - 4
y = 9 - 4
y = 5
When you raise (almost) anything to the power zero, you get 1.
Answer:
z^0= 1
(2v+2)^0 = 1
3^0 = 1
0^0= 0
Step-by-step explanation:
When you raise (almost) anything to the power zero, you get 1 and when you raise 0 to any number except 0 is 0
I need help with question 12
The value of the integral over limit is 20, the average is 1.73
The signed area is shown in the graph attached.
What is a Function ?A function is a mathematical statement used to find a relation between two variable.
To Evaluate the definite integral between
f(x) = 5 if 4≤x ≤9
f(x) = -1 if 9≤x≤14
[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]
The average value of the interval is
= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73
Therefore the average is 1.73.
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Select the correct answer from each drop-down menu.
Need helpp
(1st image of dropdown menu is the drop down menu on top an the second image is the second dropdown menu beneath it)
Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.
Triangle ABC and triangle RQP are similar based on side-angle-side criterion.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent.
Triangle ABC and triangle XYZ are similar based on angle-side-angle criterion.
Triangle ABC and triangle RQP are similar based on side-angle-side criterion.
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Express cos S as a fraction in simplest terms.
Answer: Read attachment.
Step-by-step explanation: Attached below is my work. Hope it helps!
Solve: 12x- +5x-4-_ = 172x+6 O x=2 0 x==5 O x=2 x=-5 no solution
The solution to the equation 12x + 5x - 4 = 172x + 6 is D. No solution.
How to calculate the equation?The information given is 12x + 5x - 4 = 172x + 6 and we are told to find the value of x.
12x + 5x - 4 = 172x + 6
Collect like terms
12x + 5x - 4 = 172x + 6
12x + 5x - 172x = 6 + 4
-155x = 10
x = 10/-155
x = -0.0645
Therefore, the correct option is no solution as the correct answer isn't given.
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3. A cylindrical tank has a radius of 15 feet and a height of 45 feet. How many cubic feet of water can the tank hold?
A. 127,170 cu. ft.
B. 31.792.5 cu. ft.
C. 675 cu. ft.
D. 15,896.25 cu. ft.
Answer: 31.792.5 cu. ft. (choice B)
=================================================
Work Shown:
[tex]V = \pi*r^2*h\\\\V \approx 3.14*15^2*45\\\\V \approx 31,792.5 \text{ cubic feet}\\\\[/tex]
The result is approximate since [tex]\pi \approx 3.14[/tex] is approximate.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
B. 31.792.5 cu. ft.Step-by-step explanation:
Given,Radius (r) = 15 feet
Height (h) = 45 feet
Volume = ?
therefore,Volume of a cylinder = π × r² × hTaking π ≈ 3.14..
V = 3.14 × 15² × 45
V = 31,792.5 cu. feet
So, the cylindrical tank can hold upto 31,792.5 cu. feet of water..
___________________________Hope it helps you!!Amy and Laura recorded the average gas mileage (MPG) of their vehicles each week for four weeks. What can be concluded about the relationships shown in the graph and table?
Amy and Laura recorded the same gas mileage each week.
Both Amy and Laura increased their gas mileage in the first two weeks.
Amy had greater gas mileage than Laura.
Laura had a constant gas mileage in the first four weeks of data.
Who runs fastest?
When do Andy and Berta cross paths?
Who is closest to the 1.5 mile mark after 6 minutes?
Both Amy and Laura increased their gas mileage in the first two weeks.
Option B is the correct answer.
The missing graph is attached with the answer.
What is a Graph ?A graph is a statistical way of showing data , it is used to show relation between the points.
A graph is useful in understanding the nature of a function.
From the data given in the question
The statements that can be concluded is , Option B
Both Amy and Laura increased their gas mileage in the first two weeks.
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A jackrabbit can run at the speed of 1.35 kilometers per minute . How fast can the jackrabbit run in miles per hour ? First fill in the two blanks on the left side of the equation using two of the ratios . Then write your answer rounded to the nearest hundredth on the right side of the equation
The speed of the rabbit in miles per hour is 50.33 mi/h.
How fast can the jackrabbit run in miles per hour?We know that the speed of the jackrabbit is:
1.35 km/min.
Now we need to use the relations:
1 hour = 60 minutes.
So, in one hour, the rabit runs 60 times the distance that it runs in one minute, then:
1.35 km/min = 60*(1.35 km/h) = 81km/h
Now we need to change kilometers for miles.
1km = 0.6214 mi
Then we can rewrite:
81km/h = 81*0.6214mi/h = 50.33 mi/h
The speed of the rabbit in miles per hour is 50.33 mi/h.
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