Five years ago, Victor was twice as old as his daughter Anika. In 10 years, the sum of their ages will equal 90. Find their ages now.
Answer: 45 and 25
Step-by-step explanation:
Given
Five years ago victor was twice as old as his daughter
Suppose the current age of victor and his daughter are x and y
For five years ago
[tex]\Rightarrow (y-5)=2(x-5)\\\Rightarrow y-5=2x-10\\\Rightarrow y=2x-5\\\Rightarrow 2x-y=5\quad \ldots(i)[/tex]
In 10 years sum of their ages is 90
[tex]\Rightarrow (y+10)+(x+10)=90\\\Rightarrow x+y=70\quad \ldots(ii)[/tex]
On solving (i) and (ii) we get
[tex]\Rightarrow x=25,y=45[/tex]
So, the current age of victor is 45 and his daughter is 25
Answer:
45 , 25
Step-by-step explanation:
Write an equation that is parallel to the line y = x-5 and
passes through the point (1, -2)
Select one:
a: y = -3x + 1
b.y = 3x + 1
c. y = x + 1
d. y = x-3
Answer:
D. y = x - 3
Step-by-step explanation:
A parallel line will have the same slope, so the line will also have a slope of 1.
Plug in the slope and the given point into y = mx + b, and solve for b:
y = mx + b
-2 = 1(1) + b
-2 = 1 + b
-3 = b
Plug in the slope and b into y = mx + b:
y = mx + b
y = x - 3
So, the equation is D. y = x - 3
Bart is going to paint his bedroom. His uncle told him that a gallon of paint would cover a surface of approximately 40 square feet. He knew that the ceiling in his room was 9 feet high and the paint was $22 a gallon. He also had to buy brushes, a drop cloth, and a ladder. How many gallons of paint should he buy to paint the walls in his bedroom
Answer:
The measurement for the length of the walls.
Step-by-step explanation:
Given
[tex]Cost = \$22[/tex] per gallon
[tex]Height = 9ft[/tex]
[tex]1\ gallon = 40ft^2[/tex]
See comment for complete question
Required
The additional information needed to solve the question
First, we need to calculate the area of the walls of the bedroom.
The height of the ceilings represents the length/width of the walls; so, we need the width of each side of the bedroom.
Since the width is not given, then we can conclude that the additional information needed is the length/width of the walls.
help me plsssssssssssss
Answer:
bro the co ordinates are in the picture itself
Answer:
A'(-3,0) ; B'(0,0); C'(3,6) ; D'(-3,6)
Step-by-step explanation:
O(-6,-6)
A( -5 , -4) = A( -6+1 , -6 + 2)
A'(-6+3 ,-6+6) = A'(-3,0)
B(-4,-4) = B(-6+2 , -6+2)
B'(-6+6,-6+6)= B'(0,0)
C(-3,-2) = C(-6+3, -6+4)
C'(-6+9 , -6+12) = C'(3,6)
D(-5 , -2) = D(-6+1 , -6 +4)
D'(-6+3, -6+12)=D'(-3,6)
HELPPP PLSS 10 POINTS.
Identify the coefficient of term g2 in the expression:
2f + 9g + 4g2 - 3h
plss answer
plss answer
AYou need soneolper...
Step-by-step explanation:
Op in the chgat
1. In the figure below, PU = 12, VT = 5, and VQ = 6. Which of the following is FALSE?
Answer:
for 1 its a and for 2 its c...
A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 10 drivers living on one particular street, 3 were involved in a car accident last year. If 10 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?
Answer:
The correct answer: 0.05404
Step-by-step explanation:
Given:
Binomial distribution = x
n = 10
and p = 0.09
solution:
P(X=x) =1 0Cx*(0.09^x)*((1-0.09)^(10-x)) for x=0,1,2,...,10
So the probability is calculated by the Formula:
P(X>=3) = 1-P(X=0)-P(X=1)-P(X=2)
putting the given values in the formula
= 1-10C0*(0.09^0)*((1-0.09)^(10-0))-...-10C2*(0.09^2)*((1-0.09)^(10-2))
= 0.0540400
Thus, the correct answer: 0.05404
ugh ,, im stuck again :( someone please explain this !!!
Answer:
63cm²
Step-by-step explanation:
Area of the shaded region = Area of the rectangle - Area of the two triangles
Area of the rectangle = 6(3+14)
Area of the rectangle = 6 * 17
Area of the rectangle = 102cm²
Area of the smaller triangle = 1/2 * 3 * 6
Area of the smaller triangle = 18/2 = 9cm²
Area of the larger triangle = 1/2 * 6 * (17-7)
Area of the larger triangle = 1/2 * 6 * 10
Area of the larger triangle = 60/2 = 30cm²
Area of the shaded part = 102 - (9+30)
Area of the shaded part = 102 - 39
Area of the shaded part = 63cm²
!!!!!!URGENT!!!!!
Two similar rectangles have a proportional coefficient of 1:2, and the perimeter of the smallest one is 80 m, find the
perimeter of the small rectangle
Answer:
160m
Step-by-step explanation:
Since the rectangles are similar and we have their proportion of coefficient, the larger rectangle is twice the smaller rectangle.
Furthermore, the ratio of two longer sides should equal the ratio of the two shorter sides.
Therefore, for our case, we multiply the smaller rectangle by 2.
Hence;
(80 × 2)m
= 160 m
NB:
The ratio of the areas of two similar shapes or figures is equivalent to the square of the corresponding sides.
can i gets help with this 2x^2 – 9x + 2 = –1
box plots! pls help!
Answer:
the answer is b i thinkk.
I need helppppppppppppppppppppppppppppppppppppppppppppp nowwwwwwwwwwwwwwww i am desperate
Answer: 14 2/3
This is the same as saying [tex]14\frac{2}{3}[/tex] which is the mixed number 14 and 2/3
whole part = 14
fractional part = 2/3
==================================================
Explanation:
To find the volume of a prism, we multiply the base area by the height.
The base area is shown in green as 7 1/3 square units.
This multiplies with the height 2 to get
2*(7 1/3) = 2*(7 + 1/3) = 2*(7) + 2*(1/3) = 14 + 2/3 = 14 2/3
As alternative notation, you can write 14 2/3 as 14 & 2/3.
Or you could write [tex]14 \frac{2}{3}[/tex]. Keep in mind that this does not mean 14 times 2/3.
A line passes through the points(8,2) and (10,3) What is its equation in slope intercept form
Answer: y = ½x - 2
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1}} =\frac{3-2}{10-8} =\frac{1}{2}[/tex] b = y-intercept ⇒ Substitute in a given point to the function to find by = ½x + b
2 = ½(8) + b
2 = 8/2 + b
2 = 4 + b
2 - 4 = b
b = -2
y = ½x - 2
Find the value of z such that 0.04 of the area lies to the left of z. Round your answer to two decimal places.
Answer: The value of z is -1.75.
Step-by-step explanation:
Given: P(Z<z)=0.04
To find the value of z such that 0.04 of the area lies to the left of z.
We will use z-score table to get the value of z here.
IN z-score table, we have
For P(Z<-1.7507)=0.04
Hence, the value of z is -1.7507.
Its approximate value is -1.75
So the final answer is z=-1.75.
please help me with this problem !
Answer:
a you cant add if they are not the same denominator
Answer:
Finding the least common denominator[tex]Answer: A[/tex]
------------------------
Hope it helps...
Have a great day!!
2x times -y or (2x)(-y)
Answer:
(2x)(-y)
Step-by-step explanation:
Both are technically correct, but (2x)(-y) is more professional. You can also say 2x * -y.
Hope this helps!
Consider functions p and q.
On which interval are both functions increasing?
(See Below)
Answer:
(-2, 3)
Step-by-step explanation:
Function given in the graph 'p' is increasing from x = -2 to x = ∞.
Another function 'q' represented by the equation is,
q(x) = -|x - 3| + 4
By using graphing utility, graph of the function will be as shown in the attachment.
Graph of the function 'q' will be increasing from x = -∞ to x = 3
Therefore, common domain in which both the function are increasing is (-2, 3)
Answer:
(-2, 3)
Step-by-step explanation:
PLATOO
what is the correct answer for this question ?
Answer:
[tex]b)\ 61m[/tex]
Step-by-step explanation:
The given triangle is a right triangle. This means that one can use right-angle trigonometry to solve the triangle. The right angle trigonometric ratios are a set of ratios that relate the sides and angles of a triangle. These ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Bear in mind, the names (opposite) and (adjacent) change depending on the angle of reference. However, the side (hypotenuse) refers to the side opposite the right angle, this side doesn't change depending on the reference angle.
In this problem, one is given the measure of an angle, and the measure of the hypotenuse, the problem asks one to solve for the side opposite the given angle measure. It would make the most logical sense to use the ratio of sine (sin) to do this.
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(56)=\frac{h}{73}[/tex]
Inverse operations,
[tex]sin(56)=\frac{h}{73}[/tex]
[tex]73(sin(56))=h[/tex]
[tex]60.519\approx h[/tex]
the polygons in each pair are similar. Find the missing side length
Answer:
Since they are similar, 45/27=30/18=x/24. x=40
Solve for x.
4(x + 3) = x +42
x = [?]
Answer: x=10
Step-by-step explanation:
[tex]4(x+3)=x+42\\4x+12=x+42\\4x-x=42-12\\3x=30\\x=10[/tex]
if x=(a+4 and y=(a-4),show that xy=a square -16
(a+4) (a-4)
according to formula,
x square - y square : (x+y) (x-y)
(a+4) (a-4)
xy : a square - 4
The places X and Y are 76km apart on a highway one car starts from Y and other from X at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars?
Answer:
Fast car = 45.6
Slower car = 30.4
Step-by-step explanation:
Let the speed of the first car = x
Let the speed of the second car = y
Travelling towards each other.
x *1 + y*1 = 76 miles
x*5 - y*5 = 76 miles. This is kind of tricky. You have to understand that the first car that is 76 miles from the second car and makes up that 76 in 5 hours. The distance they both travel is subtracted out.
Divide by 5
x - y = 76/5
x - y = 15.2 The speeds differ by 15.2
x + y = 76
x - y = 15.2
2x = 91.2
x = 45.6
y = 76 - 45.6 = 30.4
When the two vehicles speeds are multiplied by 5, the difference is 76 km
Please find attached herewith the solution of your question.
If you have any query, feel free to ask.
PLEASE HELP!! i dont understand it
Answer:
a. y^ -1 = e^x +2
Step-by-step explanation:
y = ln (x-2)
Exchange x and y
x = ln (y-2)
Solve for y
Raise each side with a base of e
e^ x = e^(ln(y-2)
e^x = y-2
Add 2 to each side
e^x +2 =y
Help I don’t understand this
CAN SOMEONE HELP ME PLEASE
Answer:
.54 (54%)
Step-by-step explanation:
find the area of this circle
Radius: 7ft
Area of circle =153.86ft²
Answer:
Solution given;
Radius[r]: 7ft
To find;
Area of circle;
Step-by-step explanation:
use formula:
Area of circle =πr²
Calculation:
Area of circle =πr²
substitute value
.Area of circle =3.14*7²=153.86ft²
Identify the dependent variable: the time it takes to make rag dolls for a mission in Africa and the number of people working on the dolls the distance travelled while walking and the time taken the cost of an end of year grade 9 party and the number of people attending
Answer:
The time it takes to make rag dolls for a mission in Africa.
The time taken.
The cost of an end year party.
Step-by-step explanation:
The dependent variable refers to the variable which is predicted or measured in an experiment , the value of the dependent variable relies on the variation in the independent or predictor variable.
The time it takes to make rag dolls for a mission in Africa and the number of people working on the dolls ;
DEPENDENT VARIABLE = The time it takes to make rag dolls for a mission in AFRICA. This is because time taken will depend on the number of people working.
The distance travelled while walking and the time taken ;
DEPENDENT VARIABLE = THE time taken
The time taken will depend on distance traveled.
The cost of an end of year grade 9 party and the number of people attending ;
DEPENDENT VARIABLE = The cost of an end year party.
Cost of partybwill depend on the number of people attending.
Omggg guys please help me find those two boxes
Answer:
Both boxes are -20.25
Step-by-step explanation:
The y-value for the vertex is when you plug in the x-value of the vertex in. The vertex is at (2.5, -20.25). SInce the vertex is the lowest or highest point on a parabola, the range is y>=-20.25.
Given an aritmetic progression 2,6,10,14.. find the smallest value of n such that the sum of the first n terms is greater than 200.
Answer:
Without thinking too hard, by adding the progression of number until we reach >200 and counting what n value we have we can solve this question.
The rule of this progression is to + 4 every time.
2 + 6 + 10 + 14 + 18 + 22 + 26 + 30 + 34 + 38 + 42
This will give us 242, which is greater than 200. There are 11 numbers here, so the n value is 11.
Answer:
Hello,
Step-by-step explanation:
Using n terms, the arithmetic sequence will be:
2,6,10,14,...,?
=0*4+2,1*4+2,2*4+2,3*4+2,...,(n-1)*4+2
s=(0*4+2)+(1*4+2)+(2*4+2)+(3*4+2)+...+(n-1)*4+2 >200
(2+2+2+...+2)+4(0+1+2+...+(n-1)) > 200
2*n+4*(0+(n-1))*n/2 >200
2n+2(n²-n) > 200
2n² >200
n² > 100
n >10
the smallest value of n is 11.
11 th term is (11-1)*4+2=42
sequence={2,6,10,14,...,42} which sum is 2*11²=242
