Answer:
20
Step-by-step explanation:
Let father's age be x
let son's age be y
x + y = 60 - (eq 1)
Six years ago,
(x - 6) = 5(y - 6) -(eq 2)
From (1)
x = 60-y
Therefore, 60-y - 6= 5y - 30
y = 14
in six years, y = 20
a solid has volume 2 cubic units and surface area 10 square units. The solid is dilated, and the image has a volume 128 cubic units. What is the surface area of the image?
Step-by-step explanation:
the answer is 640. Hope this helps
The side length of dilated cubes is 10.08 units. Then the surface area of the dilated cube is 609.6384 square units.
What is dilation?Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
A solid has a volume of 2 cubic units and a surface area of 10 square units.
The solid is dilated, and the image has a volume of 128 cubic units.
Let the original side length of the cube be a and dilated length of the cube be b.
The value of a will be
[tex]a^3 = 2\\\\a \ = 1.26[/tex]
Then the ratio of their volume will be
[tex]\rm \dfrac{b^3}{a^3} = \dfrac{Dilated \ volume }{Original \ volume }\\\\\\\dfrac{b^3}{a^3} = \dfrac{128}{2}\\\\\\\dfrac{b^3}{a^3} = 64\\\\\\\dfrac{b}{1.26} = 8\\\\\\b \ = 10.08[/tex]
Then the surface area of the dilated cube will be
[tex]\rm Dilated \ surface \ area = 6 *10.08^2\\\\Dilated \ surface \ area = 6*101.6064\\\\Dilated \ surface \ area = 609.6384 \ square \ units[/tex]
More about the dilation link is given below.
https://brainly.com/question/2856466
Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.
1. 4
2. 1/4
3. -1/4
4. −4
Please help!!
Answer:
1. 4
Step-by-step explanation:
the slope of:
f(x) = 10/2=5
g(x) = 10/½=20
so, g(x) = f(4.x)
=> k = 4
An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.:
Car
Compact Intermediate Full Size
Analyzer Computerized 50 55 63
Electronic 42 44 46
The following regression model can be used to analyze the data for a randomized block design involving two treatments and three blocks.
E(y) = 0 + 1x1 + 2x^2 + 3x^3
Show the values of the variables below.
Analyzer x1
Computerized __________
Electronic 1
Answer:
the value of the variable is 10
Y=x^3/2(x^2+1) I need the steps.
Answer:
0
Step-by-step explanation:
If you are looking for the x- intercept image is below
if you are looking for the y- intercept its the same as the x. Image is below
Pls answer will mark as brainliest
Answer:
[tex]\theta = 64.8^o[/tex]
Step-by-step explanation:
Given
[tex]h = 500m[/tex] --- altitude
[tex]x = 235m[/tex] --- horizontal distance
Required
The angle of elevation [tex]\theta[/tex]
The question is illustrated with the attached image.
From the attachment,
[tex]\tan(\theta) = \frac{h}{x}[/tex]
This gives:
[tex]\tan(\theta) = \frac{500m}{235m}[/tex]
[tex]\tan(\theta) = 2.128[/tex]
Take arctan of both sides
[tex]\theta = \tan^{-1}(2.128)[/tex]
[tex]\theta = 64.8^o[/tex]
Solve the inequality -6c< -12
Answer: c<2
Step-by-step explanation:
-6c<-12
c<-12/-6
c<2
A group of campers is going to occupy 6 campsites at a campground. There are 16 campsites from which to choose. In how many ways can the campsites be chosen?
Answer:
The campsites can be chosen in 5,765,760 different ways.
Step-by-step explanation:
Given that a group of campers is going to occupy 6 campsites at a campground, and there are 16 campsites from which to choose, to determine in how many ways the campsites can be chosen, the following calculation must be performed:
16 x 15 x 14 x 13 x 12 x 11 = X
240 x 182 x 132 = X
240 x 24,024 = X
5,765,760 = X
Therefore, the campsites can be chosen in 5,765,760 different ways.
What are the four answers?
Answer:
CLAE
Step-by-step explanation:
1=43
2=28
3=24
4=83
en un bolillero hay 10 bolitas iguales numeradas del 0 al 9 ¿cual es el espacio muestral?
What is the y-intercept of the quadratic function below?
There is no y-intercept
(0, -1)
(-4, 0)
(-2, 3)
Please help ,cant figure it out.
Answer:
B. √2^5
Step-by-step explanation:
(2^½. 2^¾)²
= 2¹ . 2^(1½)
= 2^(2½)
= 2^(5/2)
=√2^5
6. There were 900 sweets in 3 boxes, A, B and C. 18 sweets were transferred from A to B and 5
sweets were transferred from B to c. of the sweets in C were then transferred to A. There were
then an equal number of sweets in all 3 boxes. How many sweets were there in each box at first?
28
Answer: a=168, b=287, c=445
Step-by-step explanation:
Area of a trapezoid
Find the area of this trapezoid. Be sure to include the correct unit in your answer.
6 cm
0
10 cm
8 cm
12 cm
Answer:
h
Step-by-step explanation:
h
mnv
[tex]2 \times \frac{7}{?} = 4[/tex]
Answer:
? = 7/2
Step-by-step explanation:
? = x
a denominator can’t be equal to 0
x ≠ 0
14/x = 4
14 = 4x
x = 7/2
d. Pic
d. Z-a
PART II. ACTIVITIES
. Encircle the letter of the correct answer.
1. It contains two related data. It has horizontal axis and vertical axis.
a. Pie Graph
b. Bar Graph c. Line Graph
2. What do you call the horizontal axis of the line graph?
a. w-axis
b. x-axis
c. y-axis
3. What do you call the vertical axis of the line graph?
a. w-axis
b. x-axis
c. y-axis
4. Which of the following is not a step in making line graph?
a. Put a title on the line graph.
b. Connect the points with a line.
Draw the line for the x-axis and the z-axis.
d. Plot the points that correspond to each variable in the table,
5. It is shown just above the table or a line graph.
b. body
d. z-a
a, title
c. table
d. n
3. Directions: Study the line graph below. Encircle the letter of the corr
What are elliptic and hyperbolic geometries? Why were they developed?
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
The key fact that makes elliptic and hyperbolic geometries different from Euclidean geometry is the consideration of curvature in spaces.
In this case, Euclidean geometry considers only spaces with no curvatures, whereas elliptic geometry considers spaces with a constant negative curvature and hyperbolic geometry makes with spaces with a constant positive curvature.
The elliptic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant negative curvature.
The hyperbolic geometry is a formal geometric system which satisfies the first four Euclidean postulates and considers solely spaces with a constant positive curvature.
These formal systems were developed to demonstrate the possibility of the existence of geometries in which the fifth Euclidean postulate is not observed.
We kindly invite to check this question on non-Euclidean geometry: https://brainly.com/question/16972917
The perimeter of a triangle is 57 inches. Twice the length of the longest side minus the length of the shortest side is 22 inches. The sum of the length of the longest side and twice the sum of both the other side lengths is 94 inches. Find the side lengths
[tex]\begin{cases} a = shortest\\ b = medium\\ c = longest \end{cases} \begin{array}{llll} \stackrel{\textit{perimeter is 57}~\hfill }{a + b + c = 57}~\\\\\stackrel{\textit{twice longest minus shortest}}{2c-a=22~\hfill }\\\\ \stackrel{\textit{longest plus twice others}}{c + 2(a+b) = 94~\hfill } \end{array} \\\\[-0.35em] ~\dotfill\\\\ 2c-a=22\implies 2c=a+22\implies \boxed{2c-22=a} \\\\\\ \stackrel{\textit{we know that}}{c+2(a+b)=94}\implies c+2a+2b=94\implies c+2(2c-22)+b=94[/tex]
[tex]c+4c-44+2b=94\implies 5c-44+2b=94\implies 5c+2b=138 \\\\\\ 2b=138-5c\implies \boxed{b = \cfrac{138-5c}{2}} \\\\\\ \stackrel{\textit{we know the perimeter is}}{57=a + b + c}\implies 57 = \stackrel{a}{(2c-22)}+\stackrel{b}{\cfrac{138-5c}{2}}+c \\\\\\ 57=2c-22+\cfrac{138}{2}-\cfrac{5c}{2}+c\implies 57=3c-22+69-\cfrac{5c}{2} \\\\\\ 57=3c-47+\cfrac{5c}{2}\implies 10=3c-\cfrac{5c}{2}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{2}}{20=6c-5c}[/tex]
[tex]\blacktriangleright 20=c \blacktriangleleft \\\\\\ \boxed{2c-22=a}\implies 40-22=a\implies \blacktriangleright 18=a \blacktriangleleft \\\\\\ \boxed{b = \cfrac{138-5c}{2}}\implies b=\cfrac{138-5(20)}{2}\implies b=\cfrac{38}{2}\implies \blacktriangleright 19 \blacktriangleleft[/tex]
A person invests $3,500 in an account that earns 7.5% interest compounded continuously. What is the value of the investment after 4 years?
I think it's: 4,674.14$
Answer:
A = $4724.36
Step-by-step explanation:
P = $3500
r = 7.5% = 0.075
t = 4years
n = 365
[tex]A = P(1 + \frac{r}{n})^{nt}\\\\[/tex]
[tex]=3500(1 + \frac{0.075}{365})^{365 \times 4}\\\\=3500(1.00020547945)^{365\times4}\\\\= 3500 \times 1.34981720868\\\\= 4724.36023037\\\\= \$ 4724.36[/tex]
Which graph shows the line y = 2x + 3?
C
НА
A
D
B
A. Graph A
Ο Ο
B. Graph D
C. Graph B
D. Graph C
the answer is letter B.graph D
Pls I’m confusedddddddddddd
Answer:
[tex]{ \bf{area = \pi {r}^{2} }} \\ { \tt{ = 3.14 \times {( {3.82}) }^{2} }} \\ { \tt{ = 45.8 \: {m}^{2} }}[/tex]
1 +3 = ????????????????
One and three are both numbers. We can add the, together and get another number. The fact that these two numbers should be added is shown by the symbol between them. Adding 1 to 3 equals to 4.
Factor completely, then place the factors in the proper location on the grid. a8 - 12a4 + 36
Answer:
[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]
what would it look like?
x^2 + y^2 = 12.25
The above equation is the equation for a circle. The formula for the equation of a circle is (x - h)^2 + (y - k)^2 = r^2.
Looking at the given equation, x and y, otherwise known as the center, are not shifted at all. This mean that the center of our circle is at (0,0).
To find the radius, we take the square root of 12.25, which is 3.5. Therefore, go 3.5 units up, down, left, and right (to make a + sort of shape) from the center and then connect the points to make the circle.
Hope this helps!! :)
Answer:
Step-by-step explanation:
The graph of x^2 + y^2 = 12.25 will be a circle with centre at (0, 0) and radius will be √12.25 = 3.5.
2x + y = 1 is a straight line
y = -2x + 1 so it will pass through the y axis at y = 1 and also through the point
(-1/2, 0).
Where the line passes through the circle will be the solutions to the system.
Y=4x pls help pls help
Answer:
(1,4) , (3,12) , (5,20)
Step-by-step explanation:
You should put the first number in X and find the second number from equation.
Alex drives at an average speed that is
1
5
of the average speed that Roy's train travels.
Alex takes 15 minutes to travel 12 km in her car.
Roy travels for 1 hour and 20 minutes on his train.
How far does Roy travel to 2 dp?
plz i need asap
Answer:
ayy sensya na po Yan din po hanap Kong answer
Pls help its due at 11:10
Answer:
firstly
we all know that the angles of a triangle they all add up to 180° meaning when you add them all they must give you 180°
88°+33°+L = 180° ( sum of angle in a ∆)
121° + L = 180°
L = 180° - 121°
L = 59°
Step-by-step explanation:
first you you must add all your angles and all equal to 180°
that you add the like terms
than you transpose 121° to the right hand side
Write a system of equations to describe the situation below, solve using substitution, and fill in the
blanks.
Peter is going to send some flowers to his wife. Cedarburg Florist charges $3 per rose, plus $21 for
the vase. Sally's Flowers, in contrast, charges $2 per rose and $26 for the vase. If Peter orders the
bouquet with a certain number of roses, the cost will be the same with either flower shop. How
many roses would there be? What would the total cost be?
If the bouquet contains
roses, it will cost $
My
Answer:
R=5
Step-by-step explanation:
3r+21
2r+26
3r+21=2r+26
r=5
If angles of measures (x - 2) and (2x + 5) are a pair of supplementary angles, find the measures of those angles
Answer:
Solution: Since (x - 2)° and (2x + 5)° represent a pair of supplementary angles, then their sum must be equal to 180°. Therefore, the two supplementary angles are 57° and 123
which symmetry does y= -x^2-2x have? x-axis symmetry, y-axis symmetry, origin symmetry, or no symmetry?
Answer:
Step-by-step explanation:
The curve is symmetric about x = 1
so does not qualify for y-axis symmetry, nor the others.
NO LINKS!! Stat whether A and B are independent or dependent. Part 2
Answer:
Step-by-step explanation:
A). "If you do not study and fail the next test"
Two statements are combined in the given statement.
"If you don't study" and "fail the next test"
Second statement is the consequence of the first statement.
Therefore, events are dependent.
B). If you select a card from a deck and without replacing it, you select another card.
Here, selection of a card from a deck without replacing it doesn't affects the selection of another card.
Therefore, both the events are independent.