A man will be (x+10) years old in 8 years time.lf 2years ago he was 63years,find the value of x
Answers
The value of x is 63.
If the man was 63 years old 2 years ago, he is currently 63 + 2 = 65 years old. In 8 years, he will be (x + 10) years old. Therefore, we can write the following equation:
(x + 10) = 65 + 8
Simplifying this equation, we get:
x + 10 = 73
Subtracting 10 from both sides, we get:
x = 63
Therefore, the value of x is 63.
In summary, to find the value of x, we used the equation (x + 10) = 65 + 8, which represents the man's age in 8 years. By simplifying this equation, we found that x = 63, which is the value of the man's current age.
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Related Questions
Find the surface area of the right cylinder. Round your answer to the nearest hundredth.
Answers
Answer:
14.07 in
Step-by-step explanation:
The photo shows the formula used to get the answer.
The diagram shows the curve y = x², and the point P which is on the curve. The curve and P are translated up 3 units. Write down the new coordinates of point P.
Answers
The rule for the new coordinates of point P, after the translation up 3 units, are given as follows:
(x, x² + 3).
What are the translations?There are four translations, and they are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The function for this problem is defined as follows:
y = x².
Hence the coordinates for each point on the function are given as follows:
(x,y) = (x, x²).
Considering the translation up 3 units, the function is then defined as follows:
y = x² + 3.
Meaning that the coordinates for each point on the translated function are given as follows:
(x,y) = (x, x² + 3).
Hence you can take the coordinate of P, keep the x-coordinate constant, and add 3 to the y-coordinate.
Missing InformationThe coordinates of P are not given, hence the problem was answered in general terms.
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ayy yo who want smok wit me
Answers
Divide the following polynomial by 2x^2y14^x4y^3-6x^5y^2the ^ stands for exponentplease help!! last day to do this
Answers
In order to divide these polynomials, let's use the following property:
\(\frac{a^b}{a^c}=a^{b-c}\)So we have:
\(\begin{gathered} \frac{14x^4y^3-6x^5y^2}{2x^2y}=\frac{14x^4y^3}{2x^2y}-\frac{6x^5y^2}{2x^2y}=7x^{4-2}y^{3-1}-3x^{5-2}y^{2-1} \\ =7x^2y^2-3x^3y \end{gathered}\)HELP!
For the polynomial function f(x) = x3 - 7x2 + 10x , what is the average rate of change over the interval [2 , 4]
Answers
Answer:
The average rate of change of the given function over the interval [2, 4] is -4.
Step-by-step explanation:
To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:
\(\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}\)
Given function:
\(f(x) = x^3 - 7x^2 + 10x\)
To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).
\(\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}\)
\(\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}\)
Substitute the values into the formula for the average rate of change over the interval [2, 4]:
\(\textsf{Average rate of change} = \dfrac{f(4) - f(2)}{4 - 2} = \dfrac{-8-0}{4-2}=\dfrac{-8}{2}=-4\)
Therefore, the average rate of change of the given function over the interval [2, 4] is -4.
What are all the Factors of 7?0
Answers
The factors of 7 are 1 and 7
A factor of a number is any positive integer that can divide that number evenly without leaving a remainder.
The factors of 7 are 1 and 7, because these are the only two positive integers that evenly divide 7 without leaving a remainder.
To see why this is the case, we can list out the factors of 7 by checking which numbers divide evenly into 7.
1 × 7 = 7, so both 1 and 7 are factors of 7.
No other positive integers divide into 7 evenly, so these are the only factors of 7.
Therefore, the factors are 1 and 7
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Please help it's for trig
Answers
Answer:
-4
Step-by-step explanation:
Given the expression
h(x) = -x^2 +4x
h(-2) = (-2)^2 + 4(-2)
h(-2) = 4 + (-8)
h(-2) = 4 - 8
h(2) = -4
Hence the value of the function when x = -2 is -4
a person owns three suits, ten ties, and ten shirts. how many ways can they select a traveling wardrobe of two suits, four ties and six shirts?
Answers
There are a total of 3 x 10 x 10 = 300 possible combinations of suits, ties, and shirts that a person can select from. However, when selecting a traveling wardrobe, there are only 10 possible suit combinations, 10x10 = 100 possible tie combinations, and 10x10x10 = 1000 possible shirt combinations. This makes a total of 10 x 100 x 1000 = 100,000 possible selections of two suits, four ties and six shirts.
The sheer number of possible combinations indicates how important it is to choose wisely. The two suits should be complementary and appropriate to the occasion; the four ties can be chosen to match the suits, and the six shirts should be selected to mix and match with the ties and suits. Care should be taken to avoid repeating clothing items, and the person should also consider the climate and purpose of the trip in order to select the most suitable wardrobe.
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Find ln 5.1 to the nearest thousandth
Answers
Answer:
5.1.
Step-by-step explanation:
5.1 = 5.1000. You would then round down to find the nearest thousandth, which is 5.1.
Hope this helps!
Answer:
Step-by-step explanation:
5.1
Matteo spends a total of 38 min exercising. He walks for 6 min to warm up and then runs at a constant rate of 8 min per mile for the rest of the time. Matteo says that he ran 4.78 mi. Is he correct?
Answers
Answer:
yes, he is correct
Step-by-step explanation:
Question
Rowan reads at a constant rate of 1.5 pages per minute and has already read 20 pages. Kennedy has read 25 pages and reads at a constant rate of 3/4 pages per minute. In how much time will Rowan and Kennedy have read the same number of pages?
A 29 mins
B 30 mins
C 6 mins 40 secs
D 6 mins 23 secs
PLS ANSWERR
Answers
The amount of time till Rowan and Kennedy would have read the same number of pages is C 6 mins 40 secs.
When will they have read the same number of pages?Assume that the time they would take to read the same number of pages is x.
Rowan's reading expression is then:
= 20 + 1.5x
Kennedy is:
= 25 + 3/4x
Equate them:
20 + 1.5x = 25 + 3/4x
1.5x - 3/4 = 25 - 20
0.75x = 5
x = 5/0.75
x = 6.67 minutes
= 6 minutes 40 secs
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Write about the difference between monomials,
binomials, and trinomials
Answers
Answer:
The relationship between these terms may be sums or difference. You call an expression with a single term a monomial, an expression with two terms is a binomial, and an expression with three terms is a trinomial. An expression with more than three terms is named simply by its number of terms. Plz give brainiest
Step-by-step explanation:
I need help please———————————————————
Answers
Answer:
x = 9
Step-by-step explanation:
first step, multiply both sides by 6. This is going to get rid of that fraction-looking situation on the left.
3x+9 / 6 = x - 3
6• 3x+9 /6 = 6(x-3)
On the left the 6s cancel (cancel is not a technical math term, but 6/6 is 1, so you are left with only the 3x+9)
3x + 9 = 6(x - 3)
Next, use distributive property on the right side.
3x + 9 = 6x - 18
Subtract 3x from both sides.
9 = 3x - 18
Add 18 to both sides.
27 = 3x
Divide both sides by 3.
27/3 = x
9 = x
x = 9
Jorge’s family has visited 38 of the 50 states in America. What fraction of the states
have they visited?
Answers
To find the fraction of the states that Jorge's family has visited, we can use the formula:
visited states / total states
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
So, Jorge's family has visited 19/25 of the states in America.
Jorge's family has visited 19/25 of the states in America.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
In this case, Jorge's family has visited 38 states out of a total of 50 states, so the fraction of states they have visited is:
38 / 50
You can simplify this fraction by dividing both the numerator and denominator by the greatest common divisor of 38 and 50 which is 2, so the fraction is
19/25
19 out of the 25 American states have been visited by the Jorge family.
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What is the y-intercept in this equation: y=5x + 21
Answers
Answer:
21
Step-by-step explanation:
y=mx+b
b is your y-intercept
Answer:
y = 21
Step-by-step explanation:
The y-intercept when in slope intercept form is the constant (the term with no x).
Express the division expression as a fraction. 4 ÷ 3
Answers
Answer:
4/5 or 1 1/3
Step-by-step explanation:
4 over 5, or 1 and then 1 over 3
Tengo la mitad de un recipiente de 3/4 Litro de agua, si el agua se vierte en un vaso de medio litro. ¿Qué parte del recipiente se llena?
Answers
Aproximadamente el 100% del recipiente se llena, ya que el agua ocupa toda la capacidad del vaso.
Llenado de un recipiente: Determinando la parte ocupada por el aguaSi tienes la mitad de un recipiente de 3/4 de litro de agua, eso significa que tienes 3/8 de litro de agua.
Si viertes esa cantidad en un vaso de medio litro (que es igual a 1/2 litro), entonces el vaso se llenará por completo, ya que 3/8 de litro es más pequeño que 1/2 litro.
En términos de partes del recipiente, se puede decir que aproximadamente el 66.67% del recipiente se llena.
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(a)A line through (2,1) meets the curve x²-2x-y=3at A (-2,5)and at B. Find the coordinates of B
(b) A(3,1) lies on the curve (x-1)(y+1)=4. A line through A perpendicular to x+2y=7 meets the curve again at B. Find the coordinates of B.
Answers
The slope of the line passing through these two points is:
m = (y2 - y1) / (x2 - x1) = (1 - 5) / (2 - (-2)) = -4/4 = -1
Using the point-slope form of the equation of a line, the equation of the line passing through A and (2,1) is:
y - 5 = -1(x + 2)
y - 5 = -x - 2
y = -x + 3
To find the coordinates of point B, we need to solve the system of equations formed by the equation of the line and the equation of the curve:
x² - 2x - y = 3
y = -x + 3
Substituting the second equation into the first, we get:
x² - 2x - (-x + 3) = 3
x² - x - 6 = 0
Solving for x using the quadratic formula, we get:
x = (1 ± √(1 + 24)) / 2 = 3 or -2
When x = 3, y = -x + 3 = 0, which means that point B is (3,0).
When x = -2, y = -x + 3 = 5, which means that point B is (-2,5).
Therefore, the coordinates of point B are (3,0) and (-2,5).
(b) We know that point A (3,1) lies on the curve (x-1)(y+1)=4.
Substituting x=3 and y=1 into this equation, we get:
(3-1)(1+1) = 4
4 = 4
Therefore, point A satisfies the equation of the curve.
We need to find the equation of the line passing through point A that is perpendicular to the line x+2y=7.
The slope of the line x+2y=7 is:
m = -1/2
The slope of a line perpendicular to this line is the negative reciprocal, which is:
m' = 2
Using the point-slope form of the equation of a line, the equation of the line passing through A(3,1) with slope 2 is:
y - 1 = 2(x - 3)
y - 1 = 2x - 6
y = 2x - 5
To find the coordinates of point B, we need to solve the system of equations formed by the equation of the line and the equation of the curve:
(x-1)(y+1) = 4
y = 2x - 5
Substituting the second equation into the first, we get:
(x-1)(2x-4) = 4
2x³ - 6x² + 4x - 5 = 0
We can use numerical methods to solve this cubic equation to get the value of x, and then substitute it back into the equation y = 2x - 5 to get the value of y. One possible solution is:
x ≈ 2.632
y ≈ -0.736
Therefore, the coordinates of point B are approximately (2.632, -0.736).
Please help me I on 1-15 it’s past due ty!!❤️
Answers
Answer:
Problem 1 all you need to do is move the decimal place over four times as it says in your text book. Start out by making the decimal point visible by doing this 58,927. right there then move it over four times like this 5,892.7 one 589.27 two 58.927 three 5.8927 four. When they say move it over four places that's what it means. Now you should be able to do the rest on your own. GOOD LUCK!!!
I need help solving this, it’s from my trigonometry prep bookIt asks to answer (a) and (b)Please put these ^ separately so I know which is which
Answers
ANSWER
\(\begin{gathered} (a)\sum ^4_{k\mathop{=}0}\begin{bmatrix}{} & 4 \\ {} & {k}\end{bmatrix}(3x^5)^{4-k}(-\frac{1}{9}y^3)^k \\ (b)81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12} \end{gathered}\)EXPLANATION
We want to expand the given expression using binomial expansion:
\((3x^5-\frac{1}{9}y^3)^4\)(a) In summation notation, binomial expansion is written as:
\((a+b)^n=\sum ^n_{k\mathop=0}\begin{bmatrix}{} & n \\ {} & {k}\end{bmatrix}a^{n-k}b^k\)where:
\(\begin{gathered} a=3x^5 \\ b=-\frac{1}{9}y^3 \\ n=4 \end{gathered}\)Therefore, the summation notation for the expansion is:
\((3x^5-\frac{1}{9}y^3)^4=\sum ^4_{k\mathop{=}0}\begin{bmatrix}{} & 4 \\ {} & {k}\end{bmatrix}(3x^5)^{4-k}(-\frac{1}{9}y^3)^k\)(b) Now, we want to expand the expression. To do this, find each term taking k to go from 0 to 4, find the sum of the terms, and simplify.
That is:
\(\begin{gathered} k=0\colon \\ ^{}\begin{bmatrix}{4} & {} \\ {0} & {}\end{bmatrix}(3x^5)^{4-0}(-\frac{y^3}{9})^0 \\ \frac{4!}{(4-0)!0!}(3x^5)^4 \\ \Rightarrow81x^{20} \end{gathered}\)\(\begin{gathered} k=1\colon \\ \begin{bmatrix}{4} & {} \\ {1} & {}\end{bmatrix}(3x^5)^{4-1}(\frac{-y^3}{9})^1_{} \\ \frac{4!}{(4-1)!1!}(3x^5)^3(\frac{-y^3}{9}) \\ \Rightarrow-12x^{15}y^3 \end{gathered}\)\(\begin{gathered} k=2\colon \\ \begin{bmatrix}{4} & {} \\ {2} & {}\end{bmatrix}(3x^5)^{4-2}(-\frac{y^3}{9})^2 \\ \frac{4!}{(4-2)!2!}(3x^5)^2(-\frac{y^3}{9})^2 \\ \Rightarrow\frac{2}{3}x^{10}y^6 \end{gathered}\)\(\begin{gathered} k=3\colon \\ \begin{bmatrix}{4} & {} \\ {3} & {}\end{bmatrix}(3x^5)^{4-3}(-\frac{y^3}{9})^3 \\ \frac{4!}{(4-3)!3!}(3x^5)(-\frac{y^3}{9})^3 \\ \Rightarrow-\frac{4}{243}x^5y^9 \end{gathered}\)\(\begin{gathered} k=4\colon \\ \begin{bmatrix}{4} & {} \\ {4} & {}\end{bmatrix}(3x^5)^{4-4}(-\frac{y^3}{9})^4 \\ \frac{4!}{(4-4)!4!}(-\frac{y^3}{9})^4^{} \\ \frac{1}{6561}y^{12} \end{gathered}\)Therefore, in simplified form, the expanded expression is:
\((3x^5-\frac{y^3}{9})^4=81x^{20}-12x^{15}y^3+\frac{2}{3}x^{10}y^6-\frac{4}{243}x^5y^9+\frac{1}{6561}y^{12}\)Katie's swim team is having an end-of-season pizza party. When the party started, there was 50 slices of pizza. Now there are 20 slices left. Which of the following shows how much of the pizza has been eaten? Select THREE that apply(show how and why you got those answers)
Answers
Answer:
30alice of pizza they eat
What transformation to the linear parent function, f(x) = x, gives the function
g(x) = x - 9?
O A. Shift 9 units right.
O B. Shift 9 units left.
O C. Shift 9 units up.
D. Vertically stretch by a factor of 9.
Answers
Answer:
D. Horizontal stretch by a factor of 3.
Step-by-step explanation:
I hope this helps! :D
Answer:
Shift 9 units right
Step-by-step explanation:
please i need ASAPPPPP ILL GIVE BRAINLIEST!!!!
Hans baked 51 cookles. His family ate m of them. Using m, write an expression for the number of cookles that remained. + ローロ ロメロ
Answers
Answer:
\(51-m=n\)
Step-by-step explanation:
M - Number of cookies his family ate
N - The remaining number of cookies left
Question Progress
Homework Progress
6/18 Marks
Work out the equation of the line which has a gradient of ½ and
passes through the point (4, -2).
Optional working
Answer
Answers
the equation of the line that has a gradient of 1/2 will be y = 1/2x -4.
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given that a line passes through the point (4, -2) and has a slope of 1/2.
Since the slope-intercept form of the line is:
y = mx +c
where,
m = slope
and c is constant
in our case, slope = 1/2
so, the equation of a line
y = 1/2x + c
Since the line passes through the point (4, -2) this point will satisfy the equation
-2 = 4*1/2 +c
-2 = 2 +c
c = -4
Thus,
the equation of the line that has a gradient of 1/2 will be y = 1/2x -4.
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X y
-1 4
0 7
1 10
2 13
What is the slope?
Answers
Answer:
slope = 3
Step-by-step explanation:
calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (2, 13) ← 2 ordered pairs from the table
m = \(\frac{13-4}{2-(-1)}\) = \(\frac{9}{2+1}\) = \(\frac{9}{3}\) = 3
My question is on the pic Find the equation of the line
Answers
ANSWER
D. y = -5x + 3
EXPLANATION
The equation of a line in slope-intercept form is,
\(y=mx+b\)Where m is the slope and b is the y-intercept.
In this graph, we can see that the y-intercept - which is the value of y where the line intersects the y-axis, is 3,
To find the slope, we will use the second point shown in the graph above. The formula to find the slope of a line passing through points (x₁, y₁) and (x₂, y₂) is,
\(m=\frac{y_1-y_2}{x_1-x_2}\)Using the points (0, 3) and (1, -2),
\(m=\frac{3-(-2)}{0-1}=\frac{3+2}{-1}=-5\)Hence, the equation of the line is y = -5x + 3.
solve the system by graphing y=-x+10 y=x+8
Answers
Answer:
Step-by-step explanation:
I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...
Find the length of side a .
how do I find the length of side a?
Answers
Step-by-step explanation:
might be correct
according to Pythagoras
Answer:
A. 12
Step-by-step explanation:
AP3X
(ANSWER #17!)
PLEASE HELP!
Answers
The linear function y = -x + 2 is graphed at the end of the function.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have that:
The y-intercept is of 2, hence b = 2.The x-intercept of 2 means that when y = 0, x = 2.The limits mean that the function is decaying, that is, the slope is negative.Then:
y = mx + 2.
When y = 0, x = 2, hence:
0 = 2m + 2
2m = -2
m = -1.
Then the function is:
y = -x + 2.
The function is graphed at the end of the answer.
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I need help!!
Solve the equation. Give the exact solution and an approximate solution to three decimal places.
5^(7x) = 60
Answers
Answer:
0.363
Step-by-step explanation:
5^7x=60
x= ln(60)/7ln(5)
x= 0.363