Answer:
In 8th grade math, it's essential to know the following words: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages. Understanding geometric principles such as area, perimeter, and volume is also vital. Mastery of these terms and concepts will help your nephew excel in 8th grade math.
Answer: variable, coefficient, expression, equation, absolute value, function, slope, y-intercept, x-intercept, exponent, rational number, irrational number, proportion, ratio, and statistic. It's also crucial to have a solid understanding of basic arithmetic operations, including addition, subtraction, multiplication, and division, as well as properties of fractions, decimals, and percentages
Im Proud of you Bryson :)
Write the expression in complete factored form.
3b(p+2) - 7(p + 2) =
Enter the correct answer.
Answer:
(p + 2)(3b - 7)
Step-by-step explanation:
3b(p + 2) - 7(p + 2) ← factor out common factor (p + 2) from each term
= (p + 2)(3b - 7)
Interferes that are closest to the number in the middle 69 squared
The numbers closest to the middle of the squares of consecutive integers around 69² are 4624 and 4761, which are at the squares of 68 and 69, respectively.
To find the number closest to the middle of the squares of consecutive integers around 69², we can use the fact that the squares of consecutive integers increase by an odd number. Specifically, the difference between the squares of consecutive integers n and n+1 is
(n+1)² - n² = 2n + 1
Therefore, the squares of consecutive integers around 69² are
67² = 4489
68² = 4624
69² = 4761
70² = 4900
71² = 5041
The middle of these squares is between 69² and 70², which is
(69² + 70²)/2 = 9674.5
So, we want to find the squares of the integers closest to 9674.5. Since 69 is closer to 9674.5 than 70, the two squares that are closest are
68² = 4624
69² = 4761
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--The given question is incomplete, the complete question is given
" What Interferes are closest to the number in the middle of 69²? "--
A foot all coach needs to choose 11 players to start on offense. There are 6 freshmen 6sophmores,8 juiniors, and 7 seniors. How many ways can the starting 11 be chosen if the coach wants all seniors to play
The number of ways to choose the starting 11 players with all seniors playing is 4845.
We have,
Since the coach wants all seniors to play, we must choose the remaining
(11 - 7 = 4) players from the remaining (6 + 6 + 8 = 20) players who are not seniors.
The number of ways to choose 4 players from 20 players is given by the combination formula:
[tex]^{20}C_4[/tex]
= 20! / (4! * 16!)
= 4845
Therefore,
The number of ways to choose the starting 11 players with all seniors playing is 4845.
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PLSSS HELPPPP
Each pair of polygons is similar. Find the value of x.
Answer:
6
Step-by-step explanation:
y2=144 +81 = 225
225 sqaure root =. 15
so the triangle lenghts are 9 12 15
the other ones lenghts are x 8 10
to find how they changed you could use cross multiplication.
so you will get 12 x = 72 and simply it to get x = 6
14. Evaluate the indefinite integral.
The indefinite integral of ∫ (4x⁴ - 5)⁵ . 32x³ dx is (4x⁴ - 5)⁶/3 + C.
What is the indefinite integral?The solution of the indefinite integral is calculated by using substitution method.
Let u = 4x⁴ - 5
du/dx = 16x³
dx = du/(16x³)
Substituting into the integral;
∫ (4x⁴ - 5)⁵ . 32x³ dx = ∫ u⁵ . 32x³ du/(16x³)
∫ u⁵ . 32x³ du/(16x³) = ∫ 2u⁵ du
∫ 2u⁵ du = 2∫u⁵ du
2∫u⁵ du = 2 (u⁶/6 + C)
2 (u⁶/6 + C) = u⁶/3 + C
Substituting back for u;
∫ (4x⁴ - 5)⁵ . 32x³ dx = (4x⁴ - 5)⁶/3 + C
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An investment of R1 500 000, made two years ago, has increased in value to R1 700 000, and has delivered R40 000 worth of dividends over the two years. What is the return on the investment? 1.6% 2.16% 3.28% 4.33%
Two years ago, an investment of R1 500000 has increased to R1 700000 and has delivered R40 000 worth of dividends over the two years. Then the return on investment would be 16%.
We can use the following formula to calculate ROI:
ROI = (gain from investment - cost of investment) / cost of investment
where, gain from investment is the total value of the investment (including dividends), and cost of investment is the initial investment.
Using the values given in the question, we can calculate the ROI as:
ROI = ((R1,700,000 + R40,000) - R1,500,000) / R1,500,000 = R240,000 / R1,500,000
ROI = 0.16 or 16%
Therefore, the return on the investment is 16%.
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To plan for retirement, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 26 years.
Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formalas.
The total value of the annuity in 26 years is 179163.85 dollars.
Given that, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Here, 26 years = 26×4
= 104
Now, A=97(1+7.5/100)¹⁰⁴
A=97(1+0.075)¹⁰⁴
A=97(1.075)¹⁰⁴
A=97×1847.05
A=$179163.85
Therefore, the total value of the annuity in 26 years is 179163.85 dollars.
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The area of a rectangle is 40 square feet. What
could be the perimeter of the rectangle? Circle
the letter for all that apply.
A 82 ft
B
C
44 ft
40 ft
D 28 ft
E 26 ft
The possible perimeter for the rectangle would be 28(Letter D)
Evaluate the function below it’s a given output value of 6
f(x)=72/2x-2
Abe purchased a candle at the candle store. The candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour. Write a function to determine the length of the candle, y, after burning for x number of hours.
After burning for x hours, the candle's length, y, is calculated using the formula: y = 9 - (1/2)x.
Let y represent the length of the candle that is still burning after burning for x hours.
Since the candle burns at a rate of 1/2 inch per hour, we can use the following equation to explain the connection between the candle's length and the number of hours burned:
y = 9 - (1/2)x
Here, 9 represents the original length of the candle, and (1/2)x represents the length of the candle burned after x hours.
By subtracting the length burned from the original length, we obtain the length remaining after x hours.
Therefore, the function that determines the length of the candle, y, after burning for x number of hours is:
y = 9 - (1/2)x
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Are these right? And if not can someone help me with this pleeease, this is geometry btw
The measure of arc CFE is 246⁰.
The measure of arc FED is 190⁰.
The value of the angle CFE is 57⁰.
The value of the angle DEF is 85⁰.
What are the values of the angles?The value of the angles is calculated by applying intersecting chord theorem.
This theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.
angle CFE = 180 - 123 (opposite angles of a cyclic quadrilateral)
angle CFE = 57
arc CDF = 2 x 57
arc CDF = 114
arc CFE = 360 - 114 = 246⁰
angle DEF = 180 - 95
angle DEF = 85
arc DCF = 2 x 85 = 170
arc FED = 360 - 170 = 190
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Which of the following is the graph of f(x) = 5 cos (2x)? Select one: a. graph with points 0, 5 and pi over 4, 0 and pi over 2, negative 5 and 3 pi over 4, 0 and pi, 5 b. graph with points at 0, 0 and pi over 4, negative 3 and pi over 2, 0 and 3 pi over 4, 3 and pi, 0 c. graph with points 0, negative 5 and pi over 4, 0 and pi over 2, 5 and 3 pi over 4, 0 and pi, negative 5 d. graph with points at 0, 5 and pi over 4, 2 and pi over 2, negative 1 and 3 pi over 4, 2 and pi, 5
The required graph has been attached below that represents the function f(x) = 5 cos (2x).
The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.
Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.
The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).
Thus, the graph has been attached below that represents the given function.
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Convert the polar equation r
4 = 2 sin θ cos θ into an equation in Cartesian (rectangular) coordinates.
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos²θ sinθ
y = 4 sin²θ cosθ
We have,
We can use the following conversions from polar to Cartesian coordinates:
x = r cosθ
y = r sinθ
To convert the polar equation r = 4 sin(θ)cos(θ) into Cartesian coordinates, we substitute r with its equivalent value 4 sin(θ)cos(θ) and use the above conversions:
x = (4 sinθ cosθ) cosθ
y = (4 sinθ cosθ) sinθ
Simplifying these expressions, we get:
x = 4 cos^2θ sinθ
y = 4 sin^2θ cosθ
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos^2θ sinθ
y = 4 sin^2θ cosθ
or, in standard form:
x = 4xy
This is the Cartesian equation in terms of x and y, obtained by replacing sinθ and cosθ with x and y, respectively.
Thus,
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos²θ sinθ
y = 4 sin²θ cosθ
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CONSTRUIRE UN TRIANGLE EQUILATERAL ABC DE 3 cm.
The construction of an equilateral triangle is shown in the solution.
Steps -
When the length of three sides of the triangle is given, then follow the below steps to construct the required triangle.
Draw a line segment AB, of length equal to the longest side of the triangle.Now using a compass and ruler take the measure of the second side and draw an arc.Again, take the measure of the third side and cut the previous arc at a point C.Now join the endpoints of the line segment to point C and get the required triangle ABC.Learn more about equilateral triangle click;
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write an equation for the line of best fit below
Answer:
[tex]m = \frac{29 - 20}{33 - 8} = \frac{9}{27} = \frac{1}{3} [/tex]
[tex]20 = \frac{1}{3} (8) + b[/tex]
[tex] \frac{60}{3} = \frac{8}{3} + b[/tex]
[tex]b = \frac{52}{3} [/tex]
[tex]y = \frac{1}{3} x + \frac{52}{3} [/tex]
[tex]3y = x + 52[/tex]
[tex] - x + 3y = 52[/tex]
[tex]x - 3y = - 52[/tex]
Determine the type of tax described in each sentence. payroll tax property tax corporate tax sales tax excise tax gift tax Sharon's employer deducts taxes from her salary to pay the federal government directly. arrowRight Nelson's company pays taxes based on a percentage of profits for the year. arrowRight Priscilla pays more than the value listed on the price tag of a summer dress. arrowRight Lincoln pays taxes directly to the government for the land he owns. arrowRight
Sharon's employer deducts taxes from her salary to pay the federal government directly, which is a type of payroll tax. Nelson's company pays taxes based on a percentage of profits for the year, which is a type of corporate tax.
Priscilla pays more than the value listed on the price tag of a summer dress, which is a type of sales tax. Lincoln pays taxes directly to the government for the land he owns, which is a type of property tax.
Payroll taxes are levied on the earnings of employees and are used to fund social security, Medicare, and other federal and state programs. Corporate taxes are taxes on the profits earned by businesses.
Sales taxes are levied on the price of goods or services sold to consumers. Property taxes are levied on real estate owned by individuals or businesses based on the assessed value of the property.
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The graph of part of an exponential function is given below. Write the domain and range as Inequalities.
The domain and range of the exponential function for the given graph is equal to Domain = [ -1 , 3 ) and range = [ -36 , -1/36 ).
For the plotted graph of exponential function f(x),
Plotted graph represents the endpoints.
In the fourth quadrant ( -1 , -36 ) represents the closed interval.
In the first quadrant ( 3 , -1/36 ) represents the open interval.
Domain of the function is represented by all input values.
Here x-values represents the domain.
Domain of the exponential function = [ -1 , 3)
Or -1 ≤ x < 3
Range of the function is all output values.
Here y-values represents the range.
Range of the exponential function = [ -36 , -1/36 ).
Therefore, the domain and range of the exponential function of the graph is equal to [ -1 , 3 ) and [ -36 , -1/36 ).
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At a circus, 135 clowns are getting into cars. Blue cars hold 20 clowns and red cars only hold 15. There are a total of 8 cars. How many of each are there?
The number of blue cars and the number of red cars are 3 and 5 respectively
How to find how many of each car are there?Let b and r represent the number of blue cars and the number of red cars respectively.
There are a total of 8 cars, we have:
b + r = 8
There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:
20b + 15r = 135.
Thus, we have a system of equations with two variables:
b + r = 8 ---- (1)
20b + 15r = 135 ---- (2)
We can use elimination to solve for b and r.
Let's use elimination. Multiplying the first equation by 20 and second equation by 1:
20 * (b + r = 8) = 20b + 20r = 160 (subtract)
1 * (20b + 15r = 135) = 20b + 15r = 135
...............................................
5r = 25
...............................................
r = 25/5
r = 5
Using (1):
b + r = 8
b + 5 = 8
b = 8 - 5
b = 3
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The drawer contains 18 spoons and 12 forks. you randomly choose two utensils. What is the probability that both utensils are spoons?
Answer:8.52%
Step-by-step explanation:
There are 14 utensils in the drawer, and then there will be one less in the bowl after each successive utensil is removed. There are then 3 possibilities for the same kind being removed on all pulls:
P(3 spoons) = (6/14)*(5/13)*(4/12)
P(3 forks) = (5/14)*(4/13)*(3/12)
P(3 knives) = (3/14)*(2/13)*(1/12)
Add all of these outcomes together and you'd get about 8.52%
Simplify the following expression 12a3b6c5/3a2b4c5
4ab² is the simplified value of the given expression.
To simplify the expression, we can divide the coefficients and variables separately:
[tex]12a^3b^6c^5 / 3a^2b^4c^5\\\\= (12/3) * (a^3/a^2) * (b^6/b^4) * (c^5/c^5)\\\\= 4 * a^{3-2}* b^{6-4} * c^{5-5}\\\\= 4a * b^2 * 1\\\\= 4ab^2\\[/tex]
Therefore, the simplified expression is 4ab².
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7.
The lateral area of the triangular prism is [A. 288 B. 336 C. 960]
square inches, and the surface area is [A. 288 B. 336 C. 960] square inches.
8 in.
10 in.
12 in.
The lateral area of the triangular prism is 288 square inches and the surface area is 336 square inches
How to find the lateral area and surface area of a triangular prism?The lateral area of a right triangular prism is given by:
LA = perimeter of base triangle * height
LA = (a + b + c) * h (check attached image for labeling)
where a, b and c are the bases of the rectangular faces and h is the total height of the prism.
a = 10 in, c = 8 in and h = 12 in
b = √(10² - 8²) (Pythagoras)
b = 6 in
LA = (10 + 6 + 8) * 12
LA = 288 square inches
The surface area of a right triangular prism is sum of the areas of the faces that make the prism.
The surface area of a right triangular prism is given by:
SA = (a + b + c)h + bc
SA = [(10 + 6 + 8)*12] + [6 * 8]
SA = 288 + 48
SA = 338 square inches
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Complete Question
Check image
The radius of the earth is about 3960 miles.
The length of a 1°
arc on the equator to the nearest tenth of a mile is ____ miles.
The length of arc on equator is 69.08 miles.
We have
Radius of Earth = 3960 miles
Angle = 1 degree
So, the length of arc on equator is
= θ/360 x 2πr
= 1/360 x 2 (3.14) (3960)
= 69.08 miles
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Bear Mountain Ski Resort is building a new ski lift. They want to add weather-resistant paint to the cylindrical poles that will support the ski lift.
Each pole is 22 feet tall and have a diameter of 1.6 feet. There are 11 poles in all. How much paint will they need to paint all the surfaces of the 11 poles? Use 3.14 for m, and round your final answer to the nearest whole number.
The amount of paint needed to paint all the surfaces of the 11 poles is; 1260 ft².
What is the quantity of paint required for all the surfaces of the 11 poles?It follows from the task content that the amount of paint required to paint all the surfaces of the 11 poles is required to be determined.
First, since the surface area of a cylindrical pole is; A = 2πr (r + h).
where height,h = 22 and radius, r = diameter / 2 = 1.6 / 2 = 0.8 feet.
Therefore, A = 2 × 3.14 × 0.8 (22 + 0.8)
A = 114.5472 ft²
Therefore, for all 11 poles; the total area is; 11 × 114.5472 = 1260 ft² to the nearest whole number.
Ultimately, the quantity of paint needed is such that it is sufficient for an area of; 1260 ft².
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I am truely not sure how to do
Answer:
[tex]x=4.865[/tex]
Step-by-step explanation:
We know the area of a rectangle to be [tex]base*height[/tex]. In this instance, [tex]base=(2x+10)in[/tex], [tex]height=(3x) in[/tex], and [tex]area=288in^2[/tex]
The next step is to plug these known values into the [tex]area=base*height[/tex] equation. It'll look like this:
[tex]288=(2x+10)*(3x)=6x^2+30x[/tex]
This simplifies to:
[tex]48=x^2+5x[/tex]
Next, we want to rewrite the equation so we can apply the quadratic formula to it. We are going to do this by subtracting 48 from each side. The new equation looks like this:
[tex]x^2+5x-48=0[/tex]
Next, we plug this into the quadratic formula:
[tex]x=\frac{-(5)+\sqrt{5^2-4(1)(-48)} }{2(1)}=4.865[/tex]
[tex]x=\frac{-(5)-\sqrt{5^2-4(1)(-48)} }{2(1)}=-9.865[/tex]
The second value of x is negative, and since a side length cannot be negative this leaves us with just the first answer of [tex]x=4.865[/tex].
Answer:
[tex]\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
Step-by-step explanation:
The area of a rectangle is equal to the base × height:
[tex]\large \textsf{$\rm A $ $= (2x+10)\times(3x)$}\\ \\\large \textsf{$\rm \phantom{A}=$ $6x^2+30x$, and since A = 288,}\\ \\\large \textsf{$\therefore 288 = 6x^2+30x$}[/tex]
Rearranging this equation, we get:
[tex]\large \textsf{$6x^2+30x-288=0$}\\\\\large \textsf{$6(x^2+5x-48)=0$}\\\\\large \textsf{$\therefore x^2+5x-48=0$}[/tex]
Here we are left with a quadratic equation, which we can solve using the quadratic formula:
[tex]\Large \boxed{\textsf{$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$}} \textsf{ where $ax+bx+c=0$}[/tex]
Plugging values into the formula, we get:
[tex]\Large \textsf{$x = \frac{-(5)\pm \sqrt{(5)^2-4(1)(-48)}}{2(1)}$} \\\\\Large \textsf{$x=4.87, -9.87$,} \large \textsf{ but length cannot be negative.}\\\\\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
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solve the set of algebraic equationsc11 c12 c13 0 h1 1-5c14c21 c22 c23 0 h2 -5c24c31 c32 c33 0 h3 -5c340 0 0 1 h4 5
The solution to the set of equations are:
x = 17/7
y = 20/7
We have,
The two equations are:
x + y = 7 ______(1)
x² - y² = 15 _______(2)
We can use the method of substitution.
From the first equation.
y = 7 - x
We can substitute this expression for y into the second equation.
x² - (7 - x)² = 15
Expanding the square in the second term gives:
x² - (49 - 14x + x²) = 15
Simplifying this equation.
-14x + 34 = 0
Solving for x gives:
x = 17/7
Substituting this value of x into the first equation.
y = 7 - x = 20/7
Therefore,
The solution to the set of equations are:
x = 17/7
y = 20/7
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The complete question:
Solve the set of algebraic equations.
x + y = 7
x² - y² = 15
help !)There are 30 students in her class.
⅕ paid for the trip with a check.
½ paid for the trip with cash.
30% have paid half of their money.
The rest have not paid anything for the trip yet.
How many students have not paid for the trip?
The number of students have not paid for the trip is 0.
Given that, there are 30 students in her class.
⅕ paid for the trip with a check.
That is, 1/5 ×30=6 students
½ paid for the trip with cash.
Now, 1/2 ×30 =15 students
30% have paid half of their money.
Here, 30% of 30
30/100 ×30
= 900/100
= 9 students
Total students = 6+15+9
= 30
So, rest of students = 30-30=0
Therefore, the number of students have not paid for the trip is 0.
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A=(sin x.secx)² - (tan x.cosec.x)² B=2-2 cos² x + cos⁴ x - sin⁴ x için 2A+3B toplamını ayrıntılı bir şekilde bulunuz
Öncelikle verilen A ve B ifadelerinin değerlerini hesaplayalım:
A = (sin x . sec x)² - (tan x . cosec x)²
A = (sin x / cos x)² - (sin x / cos x)²
A = sin² x / cos² x - sin² x / cos² x
A = 0
B = 2 - 2cos² x + cos⁴ x - sin⁴ x
B = 2 - 2cos² x + (cos² x)² - (sin² x)²
B = (cos² x)² - 2cos² x + 2
Şimdi 2A + 3B'yi hesaplayalım:
2A + 3B = 2(0) + 3[(cos² x)² - 2cos² x + 2]
2A + 3B = 3cos⁴ x - 6cos² x + 6
Bu şekilde 2A + 3B ifadesinin ayrıntılı hesaplanması tamamlanmış oldu.
help please pcture !!really fast please!!!!
Answer:
13 years
Step-by-step explanation:
Someone pls help me with this.
The value of angle k is 129⁰.
The value of angle b is 64.5⁰.
What is the value of angle b and angle k?The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.
k + 113 + 118 = 360 (sum of angles in a circle)
k + 231 = 360
k = 360 - 231
k = 129⁰
The value of angle b is calculated by applying the principle of intersecting chord theorem.
b = ¹/₂ arc k
b = ¹/₂ x 129
b = 64.5⁰
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Which of the following statements is TRUE?
The volume of a_________
A. prism is thrice the volume of a pyramid.
B. pyramid is thrice the volume of a prism.
C. cylinder is twice the volume of a cone.
D. cone is twice the volume of a cylinder.
The volume of C.a .cylinder is twice the volume of a cone.
How is the volume of cylinder related to the volume of cone?The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.
The cylinder's volume can be expressed as π r² h, along with the surface area which can be expressed as 2π r h + 2π r² and this can be used to get the values.
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