Answer:
Man's present age: 32 years
Older son's present age: 8 years
Younger sons present age: 4 years
Step-by-step explanation:
Let their present ages be represented by:
Man = a
Older boy = b
Younger boy = c
A man has two sons, one twice as old as the other:
b = 2 × c
b = 2c......... Equation 1
The man is four times as old as the older boy:
a = 4 × b
a = 4b.......Equation 2
In three years he will be five times as old as the younger boy:
a + 3 = 5 (c + 3)
a + 3 = 5c + 15........Equation 3
Since b = 2c and a = 4b
Subtitute 2c for b in Equation 2
a = 4b
a = 4 × 2c
a = 8c
Subtitute 8c for a in Equation 3
a + 3 = 5c........Equation 3
8c + 3 = 5c + 15
Collect like terms
8c - 5c = 15 - 3
3c = 12
c = 4
Therefore since c, represents the present age of the younger son, the younger son is 4 years old
b = 2c
b = 2 × 4
b = 8
Since b is the present age of the older son, the older son is 8 years old
a = 4b
b = 8
a = 4 × 8
a = 32
Since a is the present age of the man, the man is 32 years old
Therefore,
Man's present age: 32 years
Older son's present age: 8 years
Younger sons present age: 4 years
evaluate x³ for x=2.
Answer:
8
Step-by-step explanation:
If we have anything to the third power, we are multiplying the number by itself 3 times.
If x = 2, then the expression is [tex]2^3[/tex].
[tex]2\cdot2\cdot2=8[/tex]
Hope this helped!
Answer:
8
Step-by-step explanation:
Exponents is repeated multiplication, so what we are doing in this problem is that we are multiplying 2 by itself 3 times.
2 * 2 = 4
4 * 2 = 8
Find the value of p.
Answer:
[tex]\huge\boxed{p = 3}[/tex]
Step-by-step explanation:
7p + 7 = 37 - 3p (They both are equal)
7p + 3p = 37-7
10p = 30
Dividing both sides by 10
p = 3
Answer:
p=3
Step-by-step explanation:
7p+7=37-3p
7p[+3p]+7=37-3p[+3p]
10p+7=37
10p+7[-7]=37[-7]
10p=30
10p/10=30/10
p=3
I hope this helps!
Find the missing the side of the triangle. A. 0 yd B. 30−−√ yd C. 25–√ yd D. 17−−√ yd
Answer:
Step-by-step explanation:
This a right triangle so we will use the Pythagorian theorem. x is the hypotenus.
■■■■■ Pythagorian theorem ■■■■■
● x^2 = √10^2 + √10^2
● x^2 = 10 + 10
● x^2 = 20
● x = √20 yd
A 4-pack of greeting cards costs $7.40. What is the unit price?pls answer fast
Answer:
The unit price of the problem is that one pack of greeting cards costs $1.85
Step-by-step explanation:
In order to find the unit rate, you have to divide the price by the quantity of the product. So, we will divide 7.40 by 4 so we can see the price of one pack.
7.40 ÷ 4 = 1.85
So, one pack of greeting cards costs $1.85 which is also our unit price.
Answer:
1.85
Step-by-step explanation:
First, divided the money ( $7.40 ) by the whole number ( 4 )
Then, you will receive your answer
what is the value of -19- (-18)?
Answer:
-1 is the answer
Step-by-step explanation:
I can't do the explanation of this question
Answer:
-1
Step-by-step explanation:-19 + 18 is basically how it is they end up canceling each other out except for the -1 which is the answer.
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1 . 108 kilometers. About how
many more kilometers is the distance of Venus from the Sun than the distance of Mercury from the Sun?
O 5.2. 107 kilometers
O 4.7. 108 kilometers
O 5.2. 108 kilometers
O 5.7. 109 kilometers
Properties and characteristics of sum and difference of two cubes.
Answer:
The properties and characteristics of the sum of two cubes
1) In the sum of two cubes, the middle sign of the binomial factor on the right hand side of the equation is positive
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the sum of two cubes
The properties and characteristics of the difference of two cubes
1) In the difference of two cubes, the middle sign of the binomial factor on the right hand side of the equation is always negative
2) The trinomial factor has a middle sign that is opposite to the middle sign in the question on the difference of two cubes
Step-by-step explanation:
The sum and difference of two cubes are;
a³ + b³, and a³ - b³
Factorizing the expressions for the sum and difference of two cubes can be shown as follows;
Sum of two cubes; a³ + b³ = (a + b) × (a² - a·b + b²)
Difference of two cubes; a³ - b³ = (a - b) × (a² + a·b + b²).
A pair of dice is rolled. What is the probability that the sum of the two dice will be greater than 8 given that the first die rolled is a 5?
Answer:
1/2
Step-by-step explanation:
First die rolled 5
Second die can roll 1, 2, 3, 4, 5, 6
Only if the second die rolls 4, 5, 6 will the sum be greater than 8.
p(sum > 8) = 3/6 = 1/2
Answer: 1/2
Step-by-step explanation:
First die rolled 5
Second die can roll 1, 2, 3, 4, 5, 6
Only if the second die rolls 4, 5, 6 will the sum be greater than 8.
p(sum > 8) = 3/6 = 1/2
SOMEBODY HELP PLEASE! ACME Hardware is introducing a new product called Greener Cleaner. Complete the table by finding the cost per milliliter for each size based on the sales price. One liter is 1,000 milliliters. (Answer the questions too, please!)
Answer:
Kindly check explanation
Step-by-step explanation:
SMALL SIZE :
AMOUNT OF LIQUID = 250 milliliters
Sales price = $4.50
Cost per milliliter :
Sales price / amount of liquid
$4.50 / 250 = $0.018
MEDIUM SIZE :
AMOUNT OF LIQUID = 500 milliliters
Sales price = $9.95
Cost per milliliter :
Sales price / amount of liquid
$9.95 / 500 = $0.0199
= $0.020 ( 3 decimal places)
LARGE SIZE :
AMOUNT OF LIQUID = 1 LITRE = 1000 milliliters
Sales price = $16.95
Cost per milliliter :
Sales price / amount of liquid
$16.95 / 500 = $0.0199
= $0.01695
= $0.017 ( 3 decimal places)
A) LARGE < SMALL < MEDIUM
B) LEAST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
1 large size + 2 small sizes
$16.95 + 2($4.50)
$16.95 + $9.00
= $25.95
C.) MOST EXPENSIVE WAY TO BUY 1500 milliliters of green cleaner :
3 medium sizes
3 * ($9.95)
$29.85
Covert the verbal expression into an algebraic expression.
The product of 23 and a number x
Answer:
23×x
=23x
Hope it helps
Answer:
23x
Step-by-step explanation:
"The product of" indicates that we will be multiplying the two quantities. 23 multiplied by x can be written as 23 * x which simplifies to 23x.
HELLLLLPPPPP FASTTTT
What is the best estimate for the value of the expression? (StartFraction 34 over 8 EndFraction minus StartFraction 16 over 3 EndFraction) minus StartFraction 14 over 9 EndFraction Negative 3 Negative 2 and one-half 7 7 and one-half
Answer:
The best estimated value of the expression is negative 3
Step-by-step explanation:
What is the best estimate for the value of the expression? (StartFraction 34 over 8 EndFraction minus StartFraction 16 over 3 EndFraction) minus StartFraction 14 over 9 EndFraction
Solution
(34 / 8) - (16 / 3) - (14 / 9)
= 34/8 - 16/3 - 14/9
Find the sum
= 306 - 384 - 112 / 72
= -190 / 72
= -2 46 / 72
= -2 23 / 36
= -2.6389
Approximately -3
The best estimated value of the expression is negative 3
Answer:
The answer is -2 1/2,
Step-by-step explanation:
1. Is the function g(x) increasing or decreasing over the interval -2 < x <-1?
2. the function h(x) increasing or decreasing over the interval -2 < x <-1?
Answer:
g(x) increasing
h(x) decreasing
Step-by-step explanation:
Since the value of y gets larger as the value of x increases over the interval -2 <x<-1 for the function g(x), the function is increasing
Since the value of y gets smaller as the value of x increases over the interval -2 <x<-1 for the function h(x), the function is decreasing
For the function f(x) = 3(x − 1)2 + 2, identify the vertex, domain, and range.
Answer:
Ok, our function is:
f(x) = 3*(x - 1)^2 + 2.
First, domain:
We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.
In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)
Then the domain is the set of all real numers.
Vertex:
Let's expand our function:
f(x) = 3*x^2 - 3*2*x + 1 + 2
f(x) = 3*x^2 -6*x + 2
The vertex of a quadratic function:
a*x^2 + b*x + c is at:
x = -b/2a
here we have:
a = 3 and b = -6
x = 6/2*3 = 6/6 = 1.
And the value of y at that point is:
f(1) = 3*(1 - 1)^2 + 2 = 2
Then the vertex is at: (1, 2)
Range:
The range is the set of all the possible values of y.
Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.
Then the minimal value of our quadratic function is the value at the vertex, y = 2.
This means that the range can be written as:
R = y ≥ 2
So the range is the set of all real numbers that are larger or equal than 2.
Find the area of a circle with a diameter of 4.
Either enter an exact answer in terms of it or use 3.14 for 7 and enter your answer as a decimal.
units?
area of circle =22/7×4=12.56
Gamal is buying ham and turkey to make sandwiches for a party. At most, he can spend $50, and he must buy more than 8 pounds of meat to make enough sandwiches. The ham costs $6 per pound, and the turkey costs $7 per pound. He writes the system of inequalities shown to model h, the number of pounds of ham, and t, the number of pounds of turkey, he can buy.
Inequality 1: h + t > 8
Inequality 2: 6h + 7t ≥ 50
Which inequality did Gamal write incorrectly, and how can it be corrected?
Inequality 1 is incorrect; it should be h + t ≤ 8.
Inequality 1 is incorrect; it should be h + t > 50.
Inequality 2 is incorrect; it should be 6h + 7t ≤ 8.
Inequality 2 is incorrect; it should be 6h + 7t ≤ 50.
Answer:
its d
Step-by-step explanation:
6h + 7t should be less than or equal to 50 because that is all the money he has to spend
Answer:
Inequality 2 is incorrect; it should be 6h + 7t ≤ 50.
Step-by-step explanation:
Inequality 1: h + t > 8 this is correct we need more than 8 lbs of meat
Inequality 2: 6h + 7t ≥ 50
This is incorrect. This states he must spend 50 or more dollars
6h + 7t ≤ 50
This is 50 or less dollars being spent
Use the quadratic formula to solve for the roots of the following equation.
x2 - 4x + 13 = 0 x=____a0 +- ______a1 I
2+3i, x=2−3
Explanation:
what is happening to this graph when the x vaules -1 and 1
Answer:
c.
Step-by-step explanation:
Answer:
Hey there!
The graph is decreasing when the x values are between -1 and 1.
Let me know if this helps :)
What x value solves the equation? 3x – 5 = 1 x =
Answer:
x = 2
Step-by-step explanation:
3x - 5 = 1
Adding 5 to both sides gives us:
3x - 5 + 5 = 1 + 5
3x = 6
Dividing the equation by 3 gives us:
3x / 3 = 6 / 3
x = 2
Answer:
x = 2 Hfizfifsits96eotst9s
PLEASE HELP QUICK A prism has 2 congruent hexagonal bases like the one shown. Each hexagon is made from 2 congruent isosceles trapezoids. The volume of the prism is 234 cubic units. What is the height of the prism? 3 units 4 units 6 units 8 units
==========================================================
Explanation:
Let's find the area of the hexagon. It's composed of two identical (aka congruent) trapezoids.
Each trapezoid has two parallel bases of 4+4 = 8 and 5 units. The height is 3. The area of one trapezoid is
area = height(base1+base2)/2
area = 3*(8+5)/2
area = 19.5
which doubles to 2*19.5 = 39 to represent the area of the entire hexagon
--------------------------------
The volume of any prism is found through this formula
volume = (area of base)*(height of prism)
We just found the area of the base to be 39. The height is unknown, so we'll call it h. The volume is given to be 234.
We end up with this equation
234 = 39h
which solves to h = 6 after dividing both sides by 39. This prism has a height of 6 units.
The height of the prism is 6 units
What is Hexagonal prism?The hexagonal prism is a prism with hexagonal base.
What is isosceles trapezoid?An isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides.
What is Volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Given,
Each hexagon is made from two congruent isosceles trapezoids
Therefore
Area of one isosceles trapezoids = [tex](a+b).(\frac{h}{2} )[/tex]
where,
a =4+4 = 8 units
b = 5 units
h = 3 units
Area of one isosceles trapezoids =[tex](8+5)(\frac{3}{2} )[/tex] =19.5 unit square
Area of the hexagon = Area of two isosceles trapezoids
Area of hexagon = 2× 19.5 = 39 unit square
We know that,
Volume = Base area × Height
Volume = 234 cubic units
234 = 39 × h
h = [tex]\frac{234}{39}[/tex] = 6 units
Hence, the height of the prism is 6 units
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37. What is the slope of the equation ?
-3
y = x + 2
HELP! answer if you can!
Answer:
Slope =1Step-by-step explanation:
Method 1 : Standard form method
[tex]y = x + 2\\\mathrm{Convert\:to\:standard\:form}:\quad x-y=-2\\\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\\\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\\\mathbf{A}=1,\:\mathbf{B}=-1\\m=-\frac{1}{-1}\\m=1[/tex]
Method 2 : Slope -intercept Form
[tex]\mathrm{Slope\:of\:}y=x+2:\\\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:} :\\\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\\\m=1[/tex]
multiple choice
a. 12 pie cm
b. 21 pie cm
c. 35 pie cm
Answer:
The correct option is;
a. 12 pie cm
Step-by-step explanation:
Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;
Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same
The volume of the square based prism = 452 cm³
Therefore, the volume of the cylinder (of equal base area) = 452 cm³
The formula for the volume of square based prism = Area of base × Height
∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm
Which gives;
Area of the base of the square based prism = 452/4 = 113 cm²
The area of the base of the cylinder [tex]A_c[/tex] = The area of the base of the square based prism = 113 cm²
The area of the base of the cylinder,[tex]A_c[/tex] is given by the following equation;
[tex]A_c[/tex] = π×r² = 113 cm²
r = √(113/π) = √35.97 ≈ √36 = 6 cm
The circumference of the base of the cylinder,[tex]C_c[/tex] is given by the following equation
[tex]C_c[/tex] = 2×π×r ≈ 2×π×6 = 12×π cm
The correct option is 12 pie cm.
If the area of the rectangle shown below is given by the expression 3x2 + 7x – 6,
and the width is (x + 3), which of the following could represent the length?
Answer:
Step-by-step explanation:
3x² + 7x - 6 = 3x² + 9x - 2x - 2*3
= 3x (x + 3) - 2(x +3)
= (3x - 2)(x + 3)
Area of the rectangle = 3x² + 7x - 6
length * width = 3x² + 7x - 6
length * (x + 3) = (3x -2)(x +3)
length = [tex]\frac{(3x-2)(x+3)}{(x+3)}[/tex]
length = (3x - 2)
ASAP how many solutions are there for the system of equations shown on the graph?
Answer: Infinitely many solutions
Step-by-step explanation:
The lines is on top of each other so this makes it many solution.
It can't be NO solution because the lines are not parallel to each, which means they will not intersect.
It can't be one solution because the lines doesn't intersect.
It can't be two solutions because the lines never intersect and they never intersect twice either.
Kia was 200 m north of the Liebrary when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes cost round-trip
Answer:
His speed is 2 m/s
His velocity is 0 m/s
Step-by-step explanation:
I'll assume the question is
Kia was 200 m north of the Library when he remembered he had to return some books to the library it took him to 200 seconds to do the round-trip which best describes hist round-trip.
Kia's distance from the Library is 200 m
the round-trip took him 200 s
The total distance for the round trip = 200 x 2 = 400 m
His displacement for the round trip = 0 m (since he returns to his original position)
His speed = distance/time = 400/200 = 2 m/s
His velocity = displacement/time = 0/200 = 0 m/s
Translate this into an equation 4 times a number divided by eight is three
Answer:
Here is the equation 4x6/8=3
Answer:
4 x q ÷ 8 = 3
4 x 6 ÷ 8 = 3
(24) ÷ 8 = 3
Find four consecutive integers such that twice the 3rd number decreased by the second number
is 8
Answer:
5, 6, 7, 8
Step-by-step explanation:
Let x represent the 2nd number. Then x+1 represents the third number, and the given relation is ...
2(x+1) -x = 8
x +2 = 8
x = 6
So, the numbers are 5, 6, 7, 8.
_____
Check
2(7) -6 = 8 . . . . true
a cone with base radius 7 cm has a volume of 308 cm cube find the vertical height of the cone take π 22/7
pls now
Answer:
h=6.003 cm
Step-by-step explanation:
[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]
1/3×22/7×7×7×h=308
h=308/51.3
Answer:
h = 6 cm
Step-by-step explanation:
r = 7 cm
Volume of cone = 308 cm³
[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]
h = 6 cm
factorize 12p2q -9q2
Answer:
[tex] \boxed{3q(4 {p}^{2} - 3q)}[/tex]Step-by-step explanation:
[tex] \mathsf{ 12 {p}^{2} q - 9 {q}^{2} }[/tex]
In such an expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor.
Factor out 3q from the expression
[tex] \mathsf{ = 3q(4 {p}^{2} - 3q)}[/tex]
Hope I helped!
Best regards!
Factorization of 12p²q-9q² is 3q(4p²-3q).
What is Factorization?Factorization is defined as breaking an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here, given expression is, 12p²q-9q²
Now, by factorizing this we get,
3q(4p²-3q)
Hence, required factorization is 3q(4p²-3q)
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Find the difference of functions s and r shown
below.
r(x) = -x2 + 3x
s(x) = 2x + 1
(s - r)(x) =
Answer:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]
And we want to find:
[tex]\displaystyle (s-r)(x)[/tex]
This is equivalent to:
[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]
In conclusion:
[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]
The sum of the cubes of 3 numbers which are in the ratio 1:2:3 is 7776. Find the numbers
the numbers - [tex]x,2x,3x[/tex]
[tex]x^3+(2x)^3+(3x)^3=7776\\x^3+8x^3+27x^3=7776\\36x^3=7776\\x^3=216\\x=6\\2x=12\\3x=18[/tex]
6,12,18
