Answer:
Damien is 74 years old now
Step-by-step explanation:
Define the variables:
Let d = age of DamienLet k = age of KeyannaGiven information:
The sum of the ages of Damien and Keyanna is 100 years. 10 years ago, Damien's age was 4 times Keyanna's age.From the given information, create 2 equations:
Equation 1: d + k = 100
Equation 2: d - 10 = 4(k - 10)
Rewrite Equation 1 to make k the subject:
⇒ k = 100 - d
Substitute this into Equation 2 and solve for d:
⇒ d - 10 = 4(100 - d - 10)
⇒ d - 10 = 400 - 4d - 40
⇒ d - 10 = 360 - 4d
⇒ d - 10 + 10 = 360 - 4d + 10
⇒ d = 370 - 4d
⇒ d + 4d = 370 - 4d + 4d
⇒ 5d = 370
⇒ 5d ÷ 5 = 370 ÷ 5
⇒ d = 74
Therefore, Damien is 74 years old now.
Please help! Will give the brainliest :)
Answer:
First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.
Angle CBA and DBE are vertical angles, meaning they are congruent.
so set the equation as:
(2x+21)=(5x)
21=5x-2x
21=3x
x=7
It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees
So to find angle measure of ABE:
We know that ABE and DBE form linear pair, so
180-35=145 degrees
145 degrees is the answer.
Hope it helps!
Answer:
∠ABE = 145°
Step-by-step explanation:
because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees
and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees
we can set this up as a system of equations (I will be writing ABE as "y")
2x + 21 + y = 180
5x + y = 180
We can combine this to beL
2x + 21 + y = 5x + y
- 2x -2x
21 + y = 3x + y
- y - y
21 = 3x
x = 7
If we plug this back into our original equations (which is set to 180 degrees), we can find y
2(7) + 21 + y = 180
14 + 21 + y = 180
35 + y = 180
- 35 - 35
y = 145
(remember, "y" is angle ABE)
we can check this value (ABE = 145) by substituting our second equation
5(x) + ABE = 180
35 + 145 = 180
180 = 180
(TRUE)
so, the measure of ∠ ABE is 145°
hope this helps!!
Need help with this geometry question
Answer: 59
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle intercepted by it.
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next
The coordinates of point C that forms the triangle is; (2, -1)
How to partition a line segment?We are told that point D divides line segment AB in the ratio of 5:3.
The line segment division formula is;
(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)
For this question;
x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3
Thus, (x, y) gives us;
(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)
D(x, y) = (7, -1)
Now, we need to find the coordinates of C
We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line
And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).
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A boat travels upstream for 42 miles in 3 hours and returns in 2 hours traveling downstream in a river. What is the rate of the boat in still water and the rate of the current?
The rate of the boat in still water is : miles per hour
The rate of the current is: miles per hour:
Answer:
17.5 mph
Step-by-step explanation:
Let the speed of the boat in still water be B mph
Let the rate of the current be R mph
When going upstream the effective speed is B-R mph. In terms of values given effective upstream speed = 42/3 = 14 mph
So,
B-R = 14 ... (1)
Similarly downstream speed is B + R (faster downstream)
B + R = 42/2 = 21 .... (2)
(1) + (2) ==> 2B = 35
B = 35/2 = 17.5 mph
How many square decimeters are in 687.1 cm²?
Answer:
6.871 decimeters
Step-by-step explanation:
687.1 square centimeters = 6.871 square decimeters
1 dm² = 100 cm²
Answer:
6.871
Step-by-step explanation:
calculator
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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Bob has decided to make his move to his new house easier, so he is going to rent a truck to get it all moved in one trip. He is looking at two truck rental companies. U-Haul rents a 32 ft truck for $19.95 plus 49 cents per mile driven. The formula to calculate the cost with U-Haul is C = 19.95 + 0.49x, where x represents the number of miles driven. Penske rents a truck for 69 cents per mile but has no extra fees. The formula to calculate costs for Penske is C = 0.69x, where x represents miles driven. How many miles indicate that the cost of renting a truck from U-Haul is equal to the cost of renting a truck from Penske?
What are m and b in the linear equation y=2x+8
Answer:
m=2 and b=8
Step-by-step explanation:
this is a linear equation, which takes on the formula of y=mx+b
therefore in the equation y=2x+8, 2 is the m, and 8 is the b
Find the inverse of the function.
y=x+8
Answer:
y^-1= x +8
Step-by-step explanation:
this may be helpful for you
Given that G=ab find the percentage increase in G when both a and b
increase by 10%
The percentage change in G is 21 %
What is Percentage change ?Percentage change is defined as the increase or decrease in the value as compared to the original value multiplied by 100.
It is given that
G = ab
when a is increased by 10% the new a will be = 1.1 a
When b is increased by 10% the new b will be 1.1 b
So,
G' = 1.1a *1.1 b
G' = 1.21 ab
G' = 1.21
(G' - G)*100/G = (1.21-1)*100/1
The percentage change is 21 %
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A quadratic function and an exponential function are graphed below. How do the decay rates of the functions compare over the interval
The exponential function decays at one-half the rate of the quadratic function.
The exponential function decays at the same rate as the quadratic function.
The exponential function decays at two-thirds the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The exponential function decays at three-fourths the rate of the quadratic function.
The given inequality is -2≤x≤0.
We need to determine how do the decay rates of the functions compare over the interval.
What is the quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
We calculate the average slope of each graph in the indicated interval, the slope can be calculated as [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].
Now, for the exponential function:
[tex]m_{c} =\frac{4-1}{-2-0} =\frac{3}{-2}[/tex]
For the quadratic function:
[tex]m_{q} =\frac{4-0}{-2-0} =\frac{4}{-2}=-2[/tex]
Now, the ratio of both average slopes is[tex]\frac{m_{c} }{m_{q}} =\frac{\frac{3}{-2} }{-2} =\frac{3}{4}[/tex].
Therefore, the exponential function decays at three-fourths the rate of the quadratic function.
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D − 37 = 40
D =
Check your solution.
− 37 = 40
1) Which relation is a function?
es
A) x = y² - 3
B) x = y - 4x²
C) y² = 4x - 6
D) x² = y²-10
Answer:
B
Step-by-step explanation:
x = y-4x^2 can be rearranged to get y = 4x^2 + x, which is a function
MAT 171
1. The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-4
Find a possible formula for P(x)
2. The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=-4. It goes through the point (5, 36).
Find a formula for P(x).
3. The polynomial of degree 3. P(x), has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=-2. The y-intercept is y=-1.8.
Find a formula for P(x).
Using the Factor Theorem, the polynomials are given as follows:
1. [tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
2. [tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
3. P(x) = -0.1(x³ - 4x² - 3x + 18)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Item a:
The parameters are:
[tex]a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4[/tex]
Hence the equation is:
P(x) = (x - 1)²x²(x + 4)
P(x) = (x² - 2x + 1)(x + 4)x²
P(x) = (x³ + 2x² - 7x + 1)x²
[tex]P(x) = x^5 + 2x^4 - 7x^3 + x^2[/tex]
Item b:
The roots are:
[tex]x_1 = x_2 = 4, x_3 = 0, x_4 = -4[/tex]
Hence:
P(x) = a(x - 4)²x(x + 4)
P(x) = a(x² - 16)x(x - 4)
P(x) = a(x³ - 16x)(x - 4)
[tex]P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
It passes through the point x = 5, P(x) = 36, hence:
45a = 36.
a = 4/5
a = 0.8
Hence:
[tex]P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)[/tex]
Item 3:
The roots are:
[tex]x_1 = x_2 = 3, x_3 = -2[/tex]
Hence:
P(x) = a(x - 3)²(x + 2)
P(x) = a(x² - 6x + 9)(x + 2)
P(x) = a(x³ - 4x² - 3x + 18)
For the y-intercept, x = 0, y = -1.8, hence:
18a = -1.8 -> a = -0.1
Thus the function is:
P(x) = -0.1(x³ - 4x² - 3x + 18)
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If : f(x)=x^2, g(x)=x-1. Find (f×g)(x).
Answer:
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Step by step explanation:
Given that,
[tex]f(x) = {x}^{2} [/tex]
[tex]g(x) = x - 1[/tex]
Solution:
Solving for (f•g)(x):
[tex] = f(x) \cdot g(x)[/tex]
Now substitute the given values.
[tex] = x {}^{2} \cdot(x - 1)[/tex]
[tex] = x {}^{2} (x - 1)[/tex]
Apply distributive property:
[tex] = (x ^{2} \cdot x) - x {}^{2} \cdot 1[/tex]
[tex] \boxed{ f\cdot{g}(x) = x {}^{3} - x {}^{2}}[/tex]Hence,f•g(x) will be [tex] x {}^{3} - x {}^{2}[/tex].
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms which ones should he check
Step-by-step explanation:
please attach a picture for us to see the choices
Giving the brainliest to those who answer!
Rewrite the following expression
X 9/7
Answer:
X1 2/7
Step-by-step explanation:
Step-by-step explanation:
We can write it in radical form, and the denominator of the exponent became the power of the radical. That is
And
We can also write it as
And that's the simplified form of the given exponential form .
Solve the following systems using the elimination method. -3x+4y=-8 and 3x+ y=-17
Answer:
(-4, -5)
Step-by-step explanation:
-3x + 4y = -8
+
3x + y = -17
= 5y = -25 = y = -5
-3x + 4(-5) = -8
-3x - 20 = -8
-3x = 12
x = -4
If k(x) = 5x-6, which expression is equivalent to (k+ k)(4)?
Example:
[tex](f+g)(x)=f(x)+g(x)[/tex]
To add this, we can substitute in the functions and combine like terms.
Solving the QuestionWe're given:
[tex]k(x)=5x-6[/tex][tex](k+k)(4)=?[/tex]Add k to k:
[tex](k+k)(x) = k(x)+k(x)\\(k+k)(x) = 5x-6+5x-6\\(k+k)(x) = 10x-12[/tex]
Input x as 4:
[tex](k+k)(4) = 10x-12\\(k+k)(4) = 10(4)-12\\(k+k)(4) = 40-12\\(k+k)(4) = 28[/tex]
Answer[tex](k+k)(4)=28[/tex]
(k+k)(4) is equivalent to 28.
What is function ?If we have two non-empty sets X & Y, then each element of X is relative to at least one element of Y. This relation between elements of two sets is called function.
Addition of two functions : If f(x) & g(x) be two functions, then
(f+g)(x) = f(x)+g(x)
What is the required result ?Given, k(x) = 5x-6
Now, Adding function k with k we get,
(k+k)(x) = k(x)+k(x)
= (5x-6)+(5x-6)
= 5x-6+5x-6
= 10x-12
We have to find, (k+k)(4)
∴ (k+k)(4) = (10×4)-12
= 40-12
= 28
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Which of the following values are in the domain of the function graphed
below? Check all that apply.
Answer:
A. -2B. -1D. 0E. 4Step-by-step explanation:
The domain includes all x values, and here, it is [-2, 4].
Two trains going in opposite directions leave at the same time. Train B travels 5 mph faster than train A. In 3 hours the trains are 315 miles apart. Find the speed of each train
Answer:
Step-by-step explanation:
Can y’all help me with ! I need correct anwsers ! Please
Answer:
-0.875
Step-by-step explanation:
So you have the points -4.25 and 2.50. To find the midpoint you simply add the two and then divide by 2. This results in (-4.25 + 2.50) / 2 = -0.875
I need help pronto!!
Answer:
There were 42 fewer students who chose Football than Hockey.
Step-by-step explanation:
Fraction of students who chose Hockey
= 1 - [tex]\frac{1}{6}[/tex] - [tex]\frac{1}{3}[/tex]
= [tex]\frac{1}{2}[/tex]
[tex]\frac{1}{2}[/tex] units = 21
1 unit = 42
No. of students who chose Football
= 2 units ([tex]\frac{2}{6}[/tex])
= 84 students
No. of students who chose Hockey
= 3 units ([tex]\frac{3}{6}[/tex])
= 126 students
Difference between no. of students who chose Football and Hockey
= 126 - 84
= 42 students
∴There were 42 fewer students who chose Football than Hockey.
The adjusted trial balance columns of the worksheet for Whispering Winds Company are as follows.
Answer:
Question?
Step-by-step explanation:
10 problems for 50 points
Answer:
1. F
2. F
3. T
4. F
5. F
6. T
7. T
8. F
9. F
10. T
Step-by-step explanation:
1. For the rays to be opposite, they need to have the same starting point and go in different directions. Rays AP and BP use Point A and Point B, respectively, for their starting points.
2. They do not lie on the same line.
3. Points A, B, C, D all lie in the same plane therefore making them coplanar.
4. Points X, Y do not lie in the same plane as A, B.
5. Point X does not lie in the same plane as C, D, B
6. A, P, B are all points on the same line therefore any two of them could be used to represent the same line.
7. PX and PY start at the same point and go in the opposite directions, defining them as opposite rays.
8. Plane AXY cannot be defined as point X and Y are not in a plane.
9. Lines AB and CD cannot both be in a different plane.
10. Both rays sum up to equal Line XY.
RQ=5x+1 and QT =3x+15. Find QT.
The length QT is 36 units
How to determine the length QT?The attached image represents the missing information in the question
From the image, we have:
RQ =QT
Substitute known values
5x + 1 = 3x + 15
Evaluate the like terms
2x = 14
Divide by 2
x = 7
Substitute x = 7 in QT = 3x + 15
QT = 3 * 7 + 15
Evaluate
QT = 36
Hence, the length QT is 36 units
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What is the simplified form of StartRoot 144 x Superscript 36 Baseline EndRoot?
12x6
12x18
72x6
72x18
The simplified form of the provided expression is 12x¹⁸ option second is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have an expression:
[tex]\rm = \sqrt{144x^{36}}[/tex]
[tex]\rm = \sqrt{(12^2)(x^{36})}[/tex]
[tex]\rm = \sqrt{(12^2)}\sqrt{(x^{36})}[/tex]
12x¹⁸
Thus, the simplified form of the provided expression is 12x¹⁸ option second is correct.
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Answer:
12x18
Step-by-step explanation:
Edge 2023
Which statement about –2h2 – 15h – 7 is true?
One of the factors is (h + 2).
One of the factors is (3h – 2).
One of the factors is (2h + 1).
One of the factors is (h – 7).
Answer:One of the factors of the given expression is (2h + 1).
Step-by-step explanation:
ed
Answer:
C on edge 23
Step-by-step explanation:
because i said so
GUYS HELP NOW PLS WHAT IS THE PROBABILITY NOTATION FOR THE PROBABILITY OF CHOOSING A GREEN MARBLE HELPPPP PLS
The probability notation for the probability of choosing a green marble is P(G)
What is probability?This is simply defined as the extent to which something is likely to occur.
The probability that an event will occur is given as the ratio of the number of favorable outcomes to the total number of outcomes.
How to determine the probability notationProbability notation is a symbol used in indicating the probability of an occurring event. Since our focus is on the probability of obtaining a green marble, then the probability notation will be P(G). This is illustrated below:
Event of green marble = nGTotal event = nTProbability of green marble = P(G)P(G) = nG / nT
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