A(14)=240(1+0.09)^14-1
A(14)=240(1.09)^13
A(14)=240(3.065)
A(14)=735.79
Make sure the calculations m
Factorize: 9(2a – b)^2 – 4(2a – b)
Answer:
(2 a - b) (18 a - 9 b - 4)
Step-by-step explanation:
Factor the following:
9 (2 a - b)^2 - 4 (2 a - b)
Factor 2 a - b out of 9 (2 a - b)^2 - 4 (2 a - b):
(2 a - b) (9 (2 a - b) - 4)
9 (2 a - b) = 18 a - 9 b:
Answer: (2 a - b) (18 a - 9 b - 4)
What is the sum of the fractions? Use the number line and equivalent fractions to help find the answer. Negative 1 and one-fourth + one-half A number line going from negative 3 to 0 in increments of one-fourth. Negative 1 and three-fourths Negative 1 and one-half Negative three-fourths Negative one-half
Answer:
C. Negative three-fourths
Step-by-step explanation:
Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:
-1 1/4 + 1/2
Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:
-5/4 + 1/2
Taking the LCM of the expression
= (-5+2)/4
= -3/4
Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths
Answer:
-3/4
Step-by-step explanation:
-1 1/4 +1/2
-5/4 + 2/4
-3/4
State whether the data described below are discrete or continuous, and explain why The durations of movies in minutes A Choose the correct answer below OA. The data are continuous because the data can take on any value in an interval. St O B. The data are continuous because the data can only take on specific values OC. The data are discrete because the data can take on any value in an interval. O D. The data are discrete because the data can only take on specific values. G D
Answer:
D. The data are discrete because the data can only take on specific values.
Step-by-step explanation:
Continuous variables are variables that can take on any value in an interval. Examples of continuous variables are length, time, etc.
Discrete variables on the other hand are variables that can only take on specific values.
The durations of movies in minutes can only take on integer values from 0 to 60. Therefore, it is a discrete data.
The correct option is D.
Write the slope-intercept form (y=mx + b) of the blue line. Explain or show your work. Write a one sentence summary comparing the blue line to the black line. Hint: Find the y-intercept. Then count up and over (y/x) to the next point on the line to determine the slope.
Answer:
y=1/2x+2(2 is the y-intercept)
The blue line and black line have the same y-intercept, but the black line has a slope 1/6 greater than the blue line.
Hope it helps <3
Answer:
[tex]\boxed{y=\frac{1}{2} x+2}[/tex]
Step-by-step explanation:
Let's take any of the coordinates of blue line to find the slope
The coordinates are (4,4) and (0,2)
Slope = [tex]\frac{y2-y1}{x2-x1}[/tex]
Slope = [tex]\frac{2-4}{0-4}[/tex]
Slope = [tex]\frac{-2}{-4}[/tex]
Slope = m = 1/2
Y-intercept = b = 2 (Because here x= 0)
So, the slope intercept equation becomes:
=> [tex]y = mx+b[/tex]
=> [tex]y = \frac{1}{2} x+2[/tex]
If the diagonal path is 750 feet long and the width of the park is 450 feet, what is the length, in the feet, of the park?
Answer:
The length is 600 ft
Step-by-step explanation:
We can use the Pythagorean theorem since we know the diagonal which is the hypotenuse and the width
a^2 + b^2 = c^2
450 ^2 + b^2 = 750^2
b^2 = 750^2 - 450^2
b^2 =562500-202500
b^2 =360000
Taking the square root of each side
sqrt(b^2) = sqrt(360000)
b =600
The diagram shows three angles at point. Work out the value of x
Answer:
x = 69°Step-by-step explanation:
[tex]168 + 123 + x = 360 \\2 91 + x = 360 \\ x = 360 - 291 \\ x = 69 \: \: degrees[/tex]
Helppp!!!! please!!!
Answer:
I. (x - 6)² + (y + 7)² = 121
Step-by-step explanation:
Given a circle with coordinates of the center as (6, -7), and with a diameter of 22, equation of the circle is given below using the standard equation formula of a circle:
Formula => (x - a)² + (y - b)² = r²
Where,
a = 6
b = -7
r = radius of circle = ½ of diameter = ½ of 22 = 11
Thus, plug in the above values into the standard equation formula:
(x - 6)² + (y - (-7))² = 11²
(x - 6)² + (y + 7)² = 121
Our answer, which is the equation of the circle is I. (x - 6)² + (y + 7)² = 121
What is the slope of the function, represented by the table of values below?
Answer:
b.) -4
Step-by-step explanation:
rise/run so its 8/2
The slope of a function will be -4. Then the correct option is B.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall, and the difference between the abscissa is called run.
Slope = (y₂ - y₁) / (x₂ - x₁)
Take two point from table.
(-2, 13) and (3, -7)
(x₁, y₁) = (-2, 13)
(x₂, y₂) = (3, -7)
Then the slope of a function will be
Slope = (–7 – 13) / (3 + 2)
Slope = –20 / 5
Slope = –4
Then the correct option is B.
More about the slope link is given below.
https://brainly.com/question/3605446
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Find the number of terms in this polynomial 7b^7
Answer:
1
Step-by-step explanation:
The number of terms in the polynomial;
7b^7
The number of terms in this polynomial is simply 1
Since the two are together, they are treated as a single term in the polynomial.
Take for example a quadratic polynomial;
3x^2 + 2x + 1
This is a polynomial with 3 terms.
All multiplications are treated as a single unit.
This is the case in terms of what we have too
One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?
Answer:
29
Step-by-step explanation:
Let the smaller integer be x.
The other integer is 1 greater than 3 times x, or 3x + 1.
The product is 154.
x(3x + 1) = 154
3x^2 + x - 154 = 0
157 = 2 * 7 * 11
14 * 11 = 154
22 * 7 = 154
(3x + 22)(x - 7) = 0
3x + 22 = 0 or x - 7 = 0
3x = -22 or x = 7
x = -22/3 or x = 7
-22/3 is not a positive integer, so we discard that solution.
The smaller integer is 7.
3x + 1 = 3(7) + 1 = 22
The greater integer is 22.
The sum of the integers is 7 + 22 = 29
Answer: 29
Step-by-step explanation:
what is the rule of the rectangle tell me plz
Answer:
The formula for perimeter is 2l+2w, where l is the length and w is the width.
The formula for area is lw, where l is the length and w is the width.
Smplify the radical expression. How many different ways can you write your answer?
Answer:
[tex]2xy\sqrt[3]{2x^2z}[/tex] and [tex]2xy(2x^2z)^{\frac{1}{3}}[/tex].
Step-by-step explanation:
The given radical expression is
[tex]\sqrt[3]{16x^5y^3z}[/tex]
We have to simplify the above expression.
The above expression can be written as
[tex]\sqrt[3]{(2\times 8)(x^{3+2})y^3z}[/tex]
[tex]\sqrt[3]{(2\times 2^3)(x^3\times x^2)y^3z}[/tex] [tex][\because a^{m+n}=a^ma^n][/tex]
[tex]\sqrt[3]{(2^3x^3y^3)(2x^2z)}[/tex]
[tex]\sqrt[3]{(2xy)^3}\sqrt[3]{2x^2z}[/tex] [tex][\because (ab)^m=a^mb^m][/tex]
[tex]2xy\sqrt[3]{2x^2z}[/tex] [tex][\because \sqrt[n]{x^n}=x][/tex]
It can be written as exponent form.
[tex]2xy(2x^2z)^{\frac{1}{3}}[/tex] [tex][\because \sqrt[n]{a}=a^{\frac{1}{n}}][/tex]
Therefore, the required expressions are [tex]2xy\sqrt[3]{2x^2z}[/tex] and [tex]2xy(2x^2z)^{\frac{1}{3}}[/tex].
Find the equation of the line passing
through the points (3, 3) and (4, 5).
y = [? ]x + [
Hey everyone, can you please help me with this question? THANKS!
Answer:
6 granite, 3 marble, 14 sandstone, 1 slate
ratio of sandstone to marble
how many sandstone does she have .....14
how many marble does she have......3
so the ratio would be 14:3
Answer:
C. 14:3
Step-by-step explanation:
Dana has 14 pieces of sandstone.
Dana has 3 pieces of marble.
The ratio of pieces of sandstone to pieces of marble is 14:3.
The ratio cannot be simplified further.
Simplify the following expresion. Classify the resulting polynomial 4x(x+1)-(3x-8)(x+4) A) quadratic monomial B) quadratic trinomial C) quadratic binomial D) linear binomial
Answer:
Quadratic binomial
Step-by-step explanation:
4x(x+1) - (3x-8)(x+4)
Open parenthesis
(4x^2+4x) - (3x^2+12x-8x-32)
(4x^2+4x - 3x^2-12x+8x+32)
Collect like terms
4x^2-3x^2+4x+8x-12x+32
=x^2+32
Quadratic binomial
Answer:
B. Quadratic trinomial
Step-by-step explanation:got it right on Pluto hope it helps
What is the Greatest common divisor of 378 and 420?
Answer:
42
Step-by-step explanation:
When calculating the greatest common divisor, you must look for the smallest divisors that can divide the no. s given simultaneously.
So in this case the smallest divisor will be 2.
378 =189. 420 =210
2. 2
The next divisor that 189 and 210 can both be divided with is 3
189 =63. 210 =70
3. 3
The third smallest divisor that can 63 and 70 can be divided with is 7
63 =9. 70 =10
7. 7
9 and 10 have no common divisors that can divide them fully without leaving a remainder
So to get the greatest common divisor, multiply all the divisors you have used
In this case we've used 2,3,7
2x3x7= 42
What is the next term of the arithmetic sequence?
6,2, -2, -6,
Answer:
-10
Step-by-step explanation:
-4 between each number
Find the gradient of the line y - x = 2
Q.3
Answer:
The gradient is 1
Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the gradient
c is the y intercept
first write the equation in the formula above
That's
y = x + 2
the coefficient of x is 1
so the gradient is 1
Hope this helps you
7.959 to one decimal place .
Answer:
8.0
Step-by-step explanation:
Since we are trying to find the nearest tenth decimal place, we look at the hundredths place to figure it out. Since it is ≥5, we round up.
Answer:
The answer would be 8
Step-by-step explanation:
If you have a decimal and you need to round, if it is four and below, you would have just leave the number as it is if it is five and above, you round up.
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
D.
Step-by-step explanation:
As long as the function's largest power is two, it is a quadratic function.
a. (3x - 2)(4x + 7)
= 12x^2 - 8x + 21x - 14
The largest power is 2. This is a quadratic function.
b. 7x^2 + 8x
The largest power is 2. Quadratic function.
c. (2x - 1)^2
= 4x^2 - 4x + 1
Largest power is 2. Quadratic function.
d. 8x^4- 3x^3 + 5x^2
Largest power is 4. Non-quadratic function.
Hope this helps!
2/3a= -15 - a Please Explain
Hi there! :)
Answer:
a = -9
Step-by-step explanation:
Starting with:
2/3a = -15 - a
Solve for 'a' by isolating the variable:
2/3a = -15 - a
On the right-hand side of the equal sign, make 'a' have a common denominator of 3 to make the simplifying easier:
2/3a = -15 - 3/3a
Add 3a/3 to both sides:
5/3a = -15
Divide both sides by 5/3, or multiply by its reciprocal (3/5)
5/3a(3/5) = -15(3/5)
a = -9
Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.
Answer:
The cup holds 26.2 in3 more ice cream than the cone.
Step-by-step explanation:
1. Let's find the volume of ice cream that the cone holds, this way:
Volume = π * r² * h/3
Replacing with the real values, we have:
Volume = 3.14 * 2.5² * 5/3
Volume =32.7 inches³
2. Let's find the volume of ice cream that the cup holds, this way:
Volume = π * r² * h
Diameter = 5 inches ⇒ Radius = 2.5 inches
Replacing with the real values, we have:
Volume = 3.14 * 2.5² * 3
Volume =58.9 inches³
3. Let's find the difference, this way:
Volume of the cup - volume of the cone = 58.9 - 32.7 = 26.2 inches³
The cup holds 26.2 in³ more ice cream than the cone.
Joe takes out a 30-year fixed rate amortized loan for 220,000, and makes equal size payments at the end of each month. The rate is quoted as being an annual nominal interest rate of 5.25% compounded monthly and Joe also has to pay closing fees equal to 5% of the value of the loan. Based on this information, find the actual interest rate realized by Joe (i.E. Taking into account the loan given to Joe and the 5% that he pays for the closing fees). Give the value as an annual nominal rate compounded monthly, and round your percent answer to two decimal places.
Answer:
Annual Interest Rate, r = 5.69%
Step-by-step explanation:
Amount of loan taken = 220,000
Closing fee is 5% of the loan value
Closing fee = 5% of 222,000 = 0.05 * 220000 = 11000
Therefore, Principal, P = Loan amount + closing fee
P = 220000 + 11000
P = 231, 000
Annual rate, r= 5.25% = 0.0525
Monthly rate, i = 0.0525/12 = 0.004375
Time, n = 30 years = 30*12 = 360 months
The monthly payment will be calculated by:
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\PMT = \frac{231000 * 0.004375}{1 - (1 + 0.004375)^{-360}} \\\\PMT = 1275.59[/tex]
Assuming payments are made based on 220,000, let us calculate the monthly interest rate.
[tex]PMT = \frac{P*i}{1 - (1 + i)^{-n}} \\\\1275.59 = \frac{220000 * i}{1 - (1 + i)^{-360}} \\\\i = 0.00474229[/tex]
Annual rate, r = 12 * 0.0047429
r = 0.0569 = 5.69%
root( x-1 ) = 2 - root (x+3)
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]\sqrt{x-1} =2-\sqrt{x+3}[/tex]
Square both sides.
[tex]\left(\sqrt{x-1}\right)^2=\left(2-\sqrt{x+3}\right)^2[/tex]
[tex]x-1=x+7-4\sqrt{x+3}[/tex]
Subtract x on both sides.
[tex]x-1-x=x+7-4\sqrt{x+3}-x[/tex]
[tex]-1=-4\sqrt{x+3}+7[/tex]
Subtract 7 on both sides.
[tex]-1-7=-4\sqrt{x+3}+7-7[/tex]
[tex]-8=-4\sqrt{x+3}[/tex]
Square both sides.
[tex]\left(-8\right)^2=\left(-4\sqrt{x+3}\right)^2[/tex]
[tex]64=16x+48[/tex]
Subtract 48 on both sides.
[tex]64-48=16x+48-48[/tex]
[tex]16=16x[/tex]
Divide both sides by 16.
[tex]\frac{16}{16} =\frac{16x}{16}[/tex]
[tex]1=x[/tex]
Switch sides.
[tex]x=1[/tex]
Calculate the equation of the line through the points (1, 1), (4,3), (10, 7) and (40, 27).
Answer:
y = 2/3x + 1/3
Answer:
y = 2/3x + 1/3
Step-by-step explanation:
Write "3 divided by n to the fifth" as an expression.
A. 3/n^5
B. (5/n)3
C. 5/n^3
D. (3/n)5
Answer:
The answer is option A.
[tex] \frac{3}{ {n}^{5} } [/tex]
Hope this helps you
The expression for " 3 divided by n to the fifth" is given by
[tex]\frac{3}{n^{5} }[/tex].
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
According to the given question.
We have a statement
" 3 divided by n to the fifth"
Since, n to the fifth can be written as [tex]n^{5}[/tex].
Therefore,
the expression for " 3 divided by n to the fifth" is given by
[tex]\frac{3}{n^{5} }[/tex].
Thus, option A is the correct.
Find out more information about expression here:
https://brainly.com/question/14083225
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in the given figure angle 1 is equal to angle 2 then the measurements of angle 3 and angle 4 are
Answer:
(3) = 119
(4) = 119
Step-by-step explanation:
Given isosceles triangle with vertex angle 58.
Need exterior angles of base angles 1 & 2.
Solution:
Vertex angle = 58.
Base angle = x
Sum of triangles = 180 =>
x + x + 58 = 180
Solve for x
x = (180-58)/2 = 122/2 = 61
Exterior angles are supplementary to interior (base) angles, so
(3) = 180-(1) = 180 - 61 = 119
(4) = 180-(2) = 180 - 61 = 119
* note: supplementary means sum of two angles = 180.
The measurements of angle 3 and angle 4 are 119degrees and 119degrees respectively.
The sum of the interior angle of the triangle is 180degrees.
According to the diagram shown:
m<1 + m<2 + 58 = 180
Since <1 = <2, hencce:
m<1 + m<1 + 58 = 180
2m<1 = 180 - 58
2m<1 = 122
m<1 = 122/2
m<1 = 61 degrees
Since <1 = <2, thereofore m<3 = m<4
Get the measure of m<3
m<1 + m<3 = 180 (supplementary angles)
61 + m<3 = 180
m<3 = 180 - 61
m<3 = 119 degrees
Recall that m<3 = m<4, hence m<4 = 119degrees
The measurements of angle 3 and angle 4 are 119degrees and 119degrees respectively.
Learn more here: https://brainly.com/question/21680544
Which graph represents the scenario? PLEASE HELP VERY EASY
Answer:
The answer is option B.
The second graph.
Hope this helps you
What conclusion can you make from the information below?
Three people (Jack, Karen, and Louis) drive three different types of cars
(Ford, Chevrolet, Honda).
• Jack does not drive a Chevrolet.
• Karen does not drive a Chevrolet,
A. Louis drives a Chevrolet
B. Jack drives a Honda
C. Karen does not drive a Ford.
D. Louis does not drive a Chedly let.
M
Answer:
A.louis drive a chevolet
Step-by-step explanation:
from the question three different people drive different cars . since two out of the three people has been excluded from driving a particular car i.e the third person is the one driving Chevrolet
plz help its urgent i will rate brainliest Your actual height: ___154.cm__________ Your height in the picture: 10cm The height of the object in the picture: 13cm Your guess of the actual height of the object: 170cm Show your calculations to determine the actual height of the object. The actual height of the object:
Answer:
The actual height of the object is 200.2 cm
Step-by-step explanation:
The parameters given are;
The actual height = 154 cm.
The height in the picture = 10 cm.
The height of the object = 13 cm
The scale of the picture is 154 is to 10 or 154:10 which is equivalent to 77:5
Therefore the scale of the actual object height to the image height = 77:5
Where the image of the object = 13 cm
Let the height of the actual object = X, then we then have;
[tex]\dfrac{77}{5} = \dfrac{X}{13}[/tex]
[tex]X = 13 \times \dfrac{77}{5} = \dfrac{1001}{5} = 200\frac{1}{5} \ cm = 200.2 \ cm[/tex]
The actual height of the object = 200.2 cm.