Answers
By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35
How to expand and simplify algebraic expression in bracketsTo expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:
(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}
(y + 7)(y - 5) = y² - 5y + 7y - 35
by simplification, we have;
(y + 7)(y - 5) = y² + 2y - 35
Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.
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Related Questions
Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
8
x
+
14
Find the following for this parabola:
A) The value of
f
(
−
5
)
:
B) The vertex = (
,
)
C) The
y
intercept is the point (0,
)
D) Find the two values of
x
that make
f
(
x
)
=
0
. Round your answers to two decimal places. Write the values as a list, separated by commas:
x
=
Answers
Answer:
Sure, here are the answers to your questions:
**A) The value of $f(-5)$ is $-2$.**
To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:
$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$
**B) The vertex of the parabola is $(2,6)$.**
To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:
$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$
Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:
$$f(x)=-2(x+2)^2-20$$
The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.
[Image of a parabola with vertex at (-2, -20)]
**C) The $y$-intercept is the point $(0,14)$.**
The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:
$$f(0)=-2(0)^2-8(0)+14=14$$
Therefore, the $y$-intercept is the point $(0,14)$.
**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**
To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:
$$-2x^2-8x+14=0$$
We can factor the left-hand side of the equation as follows:
$$-2(x-2)(x-3)=0$$
This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:
$$x=2\text{ or }x=3$$
However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:
$$x=2.5\text{ and }x=-3.5$$
Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.
The growth of an investment is given by the formula A = 1200 × 1.3 n , where A is the amount the investment is worth and n is the number of years. Estimate how many days it would take for the investment to be valued at £3,800.
Answers
The number of days it would take for the investment to be valued at £3,800 is 4.4 days
Estimate the number of days it would takeFrom the question, we have the following parameters that can be used in our computation:
A = 1200 × 1.3^n
For the investment to be valued at £3,800, the value of A would be
A = 3800
Substitute the known values in the above equation, so, we have the following representation
1200 × 1.3^n = 3800
Divide both sides by 1200
1.3^n = 3800/1200
So, we have
n = ln(3800/1200)/ln(1.3)
Evaluate the quotient
n = 4.4
Hence, it would take 4.4 days
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List at least five combinations of nickels and dimes such that the total value of the coins is 80 cents.
Answers
Here are five combinations of nickels and dimes that add up to 80 cents:
4 dimes and 4 nickels
3 dimes and 7 nickels
2 dimes and 12 nickels
1 dime and 16 nickels
8 dimes and 4 nickels
The wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, in
miles, that the tornado travels and S is the wind speed, in miles per hour.
If the wind speed was 130 miles per hour, which equation could be used to find the distance that the tornado traveled?
Select the correct answer below:
Answers
The equation that could be used to find the distance that the tornado traveled is: log d = 0.7
How to change the subject of the equation?We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,
where:
d is the distance, in miles, that the tornado travels.
S is the wind speed, in miles per hour.
When S = 130, we have:
130 = 93 log d + 65
93 log d = 130 - 65
93 log d = 65
log d = 65/93
log d = 0.7
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Evaluate 6×[2−(4)×(–8)]
Answers
Answer:204
Step-by-step explanation:
pemdas
6x[2--32]=6×[34]=204
One month Eric rented 3 movies and 5 video games for a total of $34. The next month he rented 9 movies and 7 video games for a total of $56. Find the rental
cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
G
O
G
Answers
movies 1.75 each
games 5.75 each
Need help now please!
Answers
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ at the given quadrant is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
The value of tan θ is calculated as follows;
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Look at the picture
Answers
Answer: 84 in
Step-by-step explanation:
A = h(b)/2
h= 7
b= 24
24x7= 168
168/2= 84
84 inch !!!!!!!!!!!!!!!!
Use the trapezoid shown to new each statement below as true or false, if false rewrite the statement correctly in the space below the statement.
Answers
Note that the perimeter of the trapezoid shown is 23 units. Thus, the statement is false.
How so you arrive at that?To derive the perimeter we must know the following:
a = base = 5
b = base = 8
d = side = 4
c is the hypotenuse" = (h x base of the right triangle) = (4x3)/2 = 6
Thus, Perimeter of the trapezoid = a + b + c + d =
5 + 8 + 4 + 6
= 23 units.
Thus, the statement that the perimeter of the trapezoid shown is 22 units is false.
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Full Question>
Use the trapezoid shown to mark each statement below as true or false. if false, please rewrite the statement correctly in the space below the statement!
Q: The perimeter of the trapezoid shown is 22 units.
True false?
Solve equation by using the quadratic formula. 15 x squared + 13 x = 0
Answers
Answer:
x= -13/15
Step-by-step explanation:
x(15x +13)
x =0
15x + 13 = 0
15x = -13
x =-13/15
The Jackson Hole Aerial Tram takes passengers from an elevation of 6311 ft to an elevation of 10,450 ft up the slope of Rendezvous Mountain in Wyoming. If the tram runs on a cable measuring 12,463 ft in length, what is the angle of incline of the tram to he nearest tenth of a degree?
Answers
The angle of incline of the tram is 19.4 degree.
According to the question:
h=(10450-6311)ft
= 4139 ft
We know that, sinθ=Opposite/Hypotenuse
So, sinθ=h/12463
sinθ= 4139/12463
sinθ= 0.3321
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
θ=19.39
θ≈19.4°
Therefore, the angle of incline of the tram is 19.4 degree.
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Use the diagram of the right triangle above and round your answer to the nearest hundredth.
If Measure of angle B = 60 degreesº and a = 10 meters, find b.
a.17.32 m
b6.93 m
c.14 m
d.9.99 m
Answers
The calculated value of the side length b is 17.32 meters
Finding the side length bFrom the question, we have the following parameters that can be used in our computation:
Angle B = 60 degrees
Length a = 10 meters
The side length b is calculated as
tan(60) = b/a
So, we have
tan(60) = b/10
Make b the subject
b = 10 * tan(60)
Evaluate
b = 17.32
Hence, the side length b is 17.32 meters
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-2 square root of 2r +5=6
Answers
Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2
Evaluating the square root expressionFrom the question, we have the following expression that can be used in our computation:
-2 square root of 2r +5=6
Express properly
So, we have
-2√(2r + 5) = 6
Divide by -2
√(2r + 5) = -3
So, we have
2r + 5 = 9
Subtract 5 from both sides
2r = 4
Divide
r = 2
Hence, the solution is 2
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answers
Answer:
V = 3 × 2 × 6 = 36 cubic centimeters
can u please help me with number 3 the graph
Answers
This prompt has to do with the analysis of random outcomes. See the attached tables and graphs accordingly.
What are random outcomes?An exhaustive depiction of all possible marble combinations that may arise out of a chance experiment involving two random selections has been depicted in this table.
The table enlists five different-colored marbles available in a bag and elaborates its varying conclusions based on two distinct selections.
The columns indicate colors, whereas each result depicts two correlated choices made during an experiment's progression to illustrate randomness accurately.
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the permieter of object A is 94cm. What the value of x
Answers
The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The permieter of object A is 94cm
Assuming the object is a square
So, we have
4x = 94
Divide both sides by 4
So, we have
x = 94/4
Evaluate
x = 23.5
Hence, the value of x is 23.5cm
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perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
Answers
The length of the worktable is 82 inches and the width is 32 inches.
To find the length and width of the worktable, we can use a system of equations. Let's denote the width of the table by w.
Since the length is 18 inches more than twice the width, we can write:
Length = 2w + 18
The perimeter of the table is the sum of all its sides, which in this case is the sum of the length and the width, each multiplied by 2:
Perimeter = 2(length + width)
Perimeter = 2(2w + 18 + w)
Perimeter = 2(3w + 18)
Perimeter = 6w + 36
We know that the perimeter is 228 inches, so we can set up an equation:
6w + 36 = 228
Solving for w, we get:
w = 32
Now that we know the width, we can use the equation for the length to find:
Length = 2w + 18
Length = 2(32) + 18
Length = 82
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Select the correct answer.
What is √81y6 in simplest form?
A. 3√/9y
B. 9y^4
C.3 √9y^2
D.9y^3
Answers
Abbie needs to cover square pyramids with fabric. The dimensions of each pyramid are shown in the table. If the fabric costs $0.001 per square millimeter, what is the surface area and cost to cover each pyramid, rounded to the nearest whole cent?
PLEASE HELP !!!
Answers
The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2, 1285.8 and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10
To calculate the surface area of each pyramid, we need to use the formula
Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)
For the small pyramid, we have
Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)
Surface Area = 500 + 2 x 10 x 26.46
Surface Area = 1049.2 mm²
Cost to cover the small pyramid
Cost = Surface Area x 0.001
Cost = 1049.2 x 0.001
Cost = $1.05
For the medium pyramid, we have
Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)
Surface Area = 800 + 2 x 10 x 42.43
Surface Area = 1285.8 mm²
Cost to cover the medium pyramid
Cost = Surface Area x 0.001
Cost = 1285.8 x 0.001
Cost = $1.29
For the large pyramid, we have
Surface Area = 30 x 40 + 2 x ((30/2) x 50)
Surface Area = 1200 + 2 x 15 x 50
Surface Area = 2100 mm²
Cost to cover the large pyramid
Cost = Surface Area x 0.001
Cost = 2100 x 0.001
Cost = $2.10
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Bozo can read at a rate of 300 words every four minutes. what is his rate of reading in words per minute?
Answers
Answer:
Bozo's rate of reading in words per minute is 75 (300 words / 4 minutes = 75 words/minute).
Step-by-step explanation:
Mark Brainliest!!
Answer: 75 words per minute
Step-by-step explanation:
We will divide 300 words by 4 to find the rate of words per minute since the original rate is words per four minutes.
300 / 4 = 75 words per minute
6. Teachers' Salaries New York and Massachusetts lead the list of average teacher's
salaries. The New York average is $76,409 while teachers in Massachusetts make an
average annual salary of $73,195. Random samples of 45 teachers from each state
yielded the following.
Answers
Step-by-step explanation:
Round to the nearest whole number, then find the sum. 15.43 + 12.85 + 21.3 = ___ pls i will give 60 points!!!!!!!!!!
Answers
Answer:
15.43 + 12.85 + 21.3 = 49.58
Rounding to the nearest whole number, the sum is 50.
Step-by-step explanation:
Answer:
15.43 + 12.85 + 21.3 = 49.58
Step-by-step explanation:
Complete the sentences to compare the intervals for which each function is decreasing
Answers
The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)
Completing the sentences to compare the intervalsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
From the graph of the functions, we can see that
The function g(x) decreases all through because it is a linear function with a negative slopeThe function f(x) decreases at [0, ∝) because it a quadratic function with a maximum vertex at (0, 5)Read more about functions at
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Convert 135° from degrees to radians.
Answers
Answer: 2.35619
Step-by-step explanation: Hope this helps! :)
Rectangle ABCD is shown on the coordinate plane below. What is the perimeter of rectangle ABCD? If necessary, round your answer to the nearest tenth.
Answers
The area of the given rectangle is 34 squared units.
How to find the area of the rectangleDetermining the area of a rectangle with the coordinates
A(-5, 3), B(3, 5), C(4, 1), and D(-4, -1)can be achieved through using the distance formula to calculate the magnitude of its sides and then applying the formula for the area pf rectangle we find the area.
Length of Side AB:
= square root of [(3 - (-5))^2 + (5 - 3)^2]
= square root of 68
Length of Side BC:
= square root of [ (4-3)^2 + (1 - 5)^2]
= square root of 17
Area of this rectangle
= side AB × Side BC
= square root[68] x square root[17]
= square root of [68 times 17]
= square root of 1156
= 34 Square Units
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Katherine is going to invest in an account paying an interest rate of 5.8%
compounded monthly. How much would Katherine need to invest, to the nearest ten
dollars, for the value of the account to reach $960 in 16 years?
Answers
The amount that Katherine, who is going to invest in an account paying an interest rate of 5.8% compounded monthly, would need to invest, to the nearest ten dollars for the future value of the account for the account to reach $960 in 26 years, is $380 (present value).
What is the difference between the future value and the present value?The future value is the present value compounded at an interest rate.
The present value is the future value discounted at an interest rate.
The future value and the present value can be computed using an online finance calculator.
N (# of periods) = 192 months (16 years x 12)
I/Y (Interest per year) = 5.8%
PMT (Periodic Payment) = $0
FV (Future Value) = $960
Results:
Present Value (PV) = $380.38
Total Interest = $579.62
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The vertices of a quadrilateral are listed below.
Answers
The strongest classification of the quadrilateral with the given vertices is rhombus.
The vertices of the quadrilateral is given as,
E(5, 4), F(9, 2), G(5, 0) and H(1, 2).
Find the adjacent sides EF and FG whether they are equal.
Using the distance formula,
EF = √(9 - 5)² + (2 - 4)² = √(16 + 4) = √20
FG = √(5 - 9)² + (0 - 2)² = √(16 + 4) = √20
Adjacent sides are equal.
So they are either square or rhombus.
Find the lengths of the diagonals whether they are equal.
EG = √(5 - 5)² + (0 - 4)² = √(0 + 16) = 4
FH = √(1 - 9)² + (2 - 2)² = √(64 + 0) = 8
Diagonals are not equal.
So it is a rhombus.
Hence the quadrilateral is a rhombus.
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
Using the table, we can see that the loan increases by a factor of 1.058 after 1 year and by a factor of 1.058/1.045 = 1.0124 after 2 years. Thus, we have:
1.058 = (1 + r/n)^(n*1)
1.0124 = (1 + r/n)^(n*2)
Dividing the second equation by the first, we get:
1.0124/1.058 = (1 + r/n)^(n*1)
Taking the nth root of both sides, we get:
(1 + r/n) = (1.0124/1.058)^(1/n)
Solving for r, we get:
r = n * [(1.0124/1.058)^(1/n) - 1]
We don't know the value of n, but we can make an educated guess that it's either 1 or 2, since the loan is increasing by roughly 5.8% per year. If we try n = 1, we get:
r = 1 * [(1.0124/1.058)^(1/1) - 1] = -0.0427
This is clearly not the correct answer, since the interest rate cannot be negative. If we try n = 2, we get:
r = 2 * [(1.0124/1.058)^(1/2) - 1] = 0.0574
This is a reasonable answer, since it's close to the observed increase in the loan value of 5.8% per year. Therefore, the rate of interest per annum is 5.7% to 1 d.p.
(b) Using the formula for compound interest, we can find the value of the loan 10 years after it starts:
A = P * (1 + r/n)^(n*t) = 2500 * (1 + 0.0574/1)^(1*10) = £4,745.60 (to the nearest 1p
Answer:
25000
Step-by-step explanation:
How many solutions does this equation have 10+ 6k6k
Answers
Answer:
10 + 36k²
Step-by-step explanation:
considering that it is not an equation but an algebraic expression we solve it like this
10 + 6k6k =
10 + 36k²
Mitra drives her car 469.8 miles and uses 14.5 gallons of gasoline. Adira drives her car 355 miles and uses 12.5 gallons of gasoline. What is the difference between the gas mileage for Mitra's car (in miles per gallon) and the gas mileage for Adira's car (in miles per gallon)?
A) 2 miles per gallon
B) 4 miles per gallon
C) 8 miles per gallon
D) 9 miles per gallon
Answers
Answer:
4 miles per gallon. Answer choice B is correct.
Step-by-step explanation:
To find the gas mileage for each car, we need to divide the distance traveled by the amount of gasoline used.
For Mitra's car, the gas mileage is:
gas mileage = distance traveled / amount of gasoline used
gas mileage = 469.8 / 14.5
gas mileage = 32.4 miles per gallon
For Adira's car, the gas mileage is:
gas mileage = distance traveled / amount of gasoline used
gas mileage = 355 / 12.5
gas mileage = 28.4 miles per gallon
To find the difference in gas mileage, we can subtract the gas mileage for Adira's car from the gas mileage for Mitra's car:
difference = gas mileage for Mitra's car - gas mileage for Adira's car
difference = 32.4 - 28.4
difference = 4 miles per gallon
Therefore, the difference in gas mileage between the two cars is 4 miles per gallon. Answer choice B is correct.