Answer:
34 years
Step-by-step explanation:
f = s + 28 Eq. 1
f+8 = 3(s+8) Eq. 2
f = father age
s = son age
replacing Eq. 1 on Eq. 2
(s+28) + 8 = 3(s+8)
s + 36 = 3*s + 3*8
s + 36 = 3s + 24
36 - 24 = 3s - s
12 = 2s
12/2 = s
s = 6
from the Eq. 1
f = 6 + 28
f = 34
Check
from the Eq. 2
34+8 = 3(6+8)
42 = 3*14
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to the following linear inequality in the coordinate plane.
5x - y > -3
27
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
10
8
6
The solution to the inequality 5x - y > -3 is shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An inequality shows the non equal comparison of two or more variables and numbers.
The solution to the inequality 5x - y > -3 is shown in the graph.
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A thin silver disc of diameter 10 cm costs # 3 300. What is the cost per m²
Answer:
The diameter is 10 cm. the radius is 5 cm. the area is πr² = π x 5² = 78.5 cm².
1 m² = 10,000 cm².
78.5/10,000 = 3,300/n n is the cost per square meter.
78.5n = 10,000 x 3300
n = 420,382.1656
The cost per square meter is $420,382.17.
\In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur. The climate in which these mice live has slowly gotten colder.
How will this change in the environment most likely affect the mouse population?
The adaptation of thinner fur will be selected over thicker fur, and the population will remain unchanged.
The adaptation of thicker fur will be selected over thinner fur, and the population will remain unchanged.
The adaptation of thinner fur will be selected over thicker fur, and the population will evolve.
The adaptation of thicker fur will be selected over thinner fur, and the population will evolve.
The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.
The climate in which these mice live has slowly gotten colder.
The change in the environment most likely affect the mouse population will be
The adjustment of thicker fur will be selected over thinner fur, and the population will develop.
Then the correct option is D.
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Find (f • g) (x) Assume x>0
Answer:
[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]
[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]
[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]
Rewrite 100 as 10²:
[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]
[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies (f \cdot g)(x)=10x[/tex]
Fill in the table with the appropriate value to describe the amount of hot dogs eaten at a hot dog eating contest.
Which value should be placed in the empty space in the table?
A. 1/6
B. 1/4
C. 1/12
D. 1/8
20 hot dogs was eaten by the 10 people who attended the hot dog eating contest.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let us assume that there were 10 people at the hot dog eating contest. If each person eats 2 hot dog, hence:
Number of hot dogs eaten = 2 hot dog per person * 10 people = 20 hot dogs.
20 hot dogs was eaten by the 10 people who attended the hot dog eating contest.
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Solve for x.
log x = 3
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 1000}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{log(x) = 3}[/tex]
Find: [tex]\textsf{The value of x}[/tex]
Solution: In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base. When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.
Get rid of log
[tex]10^{\textsf{log}_{10}\textsf{(x)}}} = 10^{\textsf{3}}[/tex][tex]x = 10^{\textsf{3}}[/tex][tex]x = 1000[/tex]Therefore, the final answer would be that x is equal to 1000.
edg vector operations, any help appreciated!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Add \:\: -6 \hat i - 6\hat j \:\:with \:\; Vector \:\; c[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Vector d can be represented as :
[tex]\qquad \tt \rightarrow \: - 2 \hat i - 2 \hat j[/tex]
Vector c can be represented as :
[tex]\qquad \tt \rightarrow \: 4 \hat i + 4\hat j[/tex]
we have to create vector d from vector c
So, let's assume a vector x, such that sum of vector x and vector c equals to vector d
[tex]\qquad \tt \rightarrow \: x + ( 4 \hat i + 4 \hat j) = - 2 \hat i - 2 \hat j[/tex]
[tex]\qquad \tt \rightarrow \: x = - ( 4 \hat i + 4 \hat j) - 2 \hat i - 2 \hat j[/tex]
[tex]\qquad \tt \rightarrow \: x = (- 4 \hat i - 2 \hat i) + ( - 4 \hat j - 2 \hat j)[/tex]
[tex]\qquad \tt \rightarrow \: x = - 6 \hat i -6 \hat j[/tex]
Henceforth, in order to get vector d, we need to add (-6i - 6j) in vector c
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
simplify (3+√5)(3+√2)
When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
Surd operationa√b × c√d = (a × c)√(b × d)
How to simplify (3 + √5)(3 + √2)(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
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Need help urgently please
Which expression has a value of 16 when n = 5?
StartFraction 25 Over n EndFraction + 7
30 minus 3 n
7 + StartFraction 45 Over n EndFraction
n cubed minus 114
Answer:
7+45/n or 5
Step-by-step explanation:
45 divided by n or technically 5 is 9 plus 7 is 16 :)
Answer:7+45/n or 5
Step-by-step explanation:
Someone please help with this!!
Answer:
A
Step-by-step explanation:
Comment (and answer)
Both start with the plus x axis as one of the arms. The other arm of 110o goes anti clockwise until it is 30 degrees into the second quadrant.
The answer can be found by using 110 - 360 = negative angle.
So 110 - 360 = - 250 which goes clockwise from the plus x axis. The answer must be A.
Make sure you understand the concept of clockwise and anti clockwise. If you don't know, ask your teacher, write it down, and try not to forget it. The distinction comes up a lot.
write the faction in the simplest form 28/36
Answer:
7/9
Step-by-step explanation:
Divide the numerator and denominator by 4.
28/36 = 7/9
Answer:
7/9
Step-by-step explanation:
28 and 36 are both divisible by 4.
28÷4 is 7 and
36÷4 is 9
28/36 = 7/9
What is the solution of the inequality sh
below?
9+b≤2
Answer:
b≤-7Step-by-step explanation:
b+9≤2
Subtract 9 from both sides:
b+9-9≤2-9b≤-79+b≤2
subtract 9 on each side which will be -7
the answer will be b≤-7
Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12 per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations
Answer:
P =2(x+ y) [tex]ft[/tex].
A =xy [tex]ft^{2}[/tex]
Step-by-step explanation:
perimeter of rectangle (P)= 2(L+B
Area of rectangle (A) = L×B
Given,
width = 'x'
length = y = x+20
therefore using above formula
P = 2(x+20 + x) = 2(2x+20)
A = (x+20)(x)
cost of land per square foot = $12
cost of land per linear foot = $8
total cost of land = $10560
now,
P×8 + A×12 = 10560
2(2x+20)×8 + (x+20)(x)×12 = 10560
32x + 320 + 12x²+ 240x = 10560
12x² + 272x = 10240
12x² + 272x - 10240 = 0
solving this quadratic equation using Discriminant method
x = [-b ±√(b² - 4ac)]/2
where b is the coefficient of x
a is the coefficient of x²
and c is the constant term
by replacing values in the above formula
x = 19.5 , x = -42.24
as the area cannot be negative therefore -42.24 is neglected
hence x = 19.5ft
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The Great Pyramid of Giza in Egypt is a square pyramid. The height is approximately 450 feet, and the side length of the base is approximately 750 feet. What is the lateral surface area of the pyramid rounded to the nearest thousandth?
The lateral surface area of the Pyramid will be 850547 square feet.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called as the area of the circle.
The lateral surface area will be calculated as:-
A = [tex]= l\sqrt{(\dfrac{w}{2})^2+h^2} + w\sqrt{(\dfrac{l}{2})^2+h^2}[/tex]
A = [tex]= 750\sqrt{(\dfrac{750}{2})^2+450^2} + 750\sqrt{(\dfrac{750}{2})^2+450^2}[/tex]
A = 750 √321525 + 750 √321525
A = 150 √√321525
A = 1500 x 567.031
A = 850547 square feet
Therefore the lateral surface area of the Pyramid will be 850547 square feet.
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Two gymnasts are running toward each other in a floor routine, and they plan to precisely time a flip to stay synchronized for the audience. The path of the gymnasts is parabolic and modeled by the following equations, where y is the height of the flip and x is the time in seconds:
Answer:
4 secs
Step-by-step explanation:
Since they have to be synchronized, their parabolic equations must be equal to one another
3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0
2t^2 - 9t + 4
(2t - 1)(t - 4) = 0
t = 1/2, 4
From the options, the answer is 4
The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
so, correct option is: C.
Here, we have,
To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.
The given equations are:
y = –(x – 5)² + 3
y = –3(x – 3)² + x + 1
Setting the two equations equal, we have:
–(x – 5)² + 3 = –3(x – 3)² + x + 1
Expanding the squared terms:
–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1
Simplifying the equation:
–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1
Combining like terms:
–x² + 10x – 22 = –3x² + 19x – 26
Rearranging the equation:
2x² - 9x + 4 = 0
To solve this quadratic equation, we can factor it:
(2x - 1)(x - 4) = 0
Setting each factor equal to zero:
2x - 1 = 0 or x - 4 = 0
Solving for x:
2x = 1 or x = 4
Dividing by 2:
x = 1/2 or x = 4
Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.
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Which expressions are equivalent to the one below? Check all that apply.
In (e^2)
Possible Answers Below:
A.)2•In e
B.) 2
C.) 2e
D.) 1
Answer:
a and b
Step-by-step explanation: you can move the exponent to the front and lne is also equal to one times 2 = 2
Camille bought 120 doughnuts for $60. Her profit was $48 once she sold 80 doughnuts. Write an
equation that represents Camille's profit P, as a function of the number of doughnuts sold, n.
PLEASE HELP WITH SHOWED WORK!!!
The equation that represents Camille's profit p as a function of the number of doughnuts sold, n is P = 1.35n - 60
How to represent an equation ?She bought 120 doughnuts for $60.
Therefore,
cost = $60
Her profit was $48 once she sold 80 doughnuts.
p = profit
n = number of doughnuts sold.
Therefore,
let
x = amount she is selling each doughnuts
p = nx - 60
Using the information given we have:
48 = (80x) - 60
Therefore,
x = $1.35
Hence, for any number of doughnuts then, we have the profit equation as follows:
P = 1.35n - 60
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You can walk over the mountains to
your campsite or take a safer, easier trip around the mountains. You
are on the ground at P(0, 0) and the campsite is at C(-2, 7). You
travel around the mountain by going to A(2, 5). The coordinate
system is measured in meters. Draw a diagram of the situation.
Find PA and AC.
Answer:
PA = [tex]\sqrt{29}[/tex]
AC =[tex]\sqrt[2]{5}[/tex]
Step-by-step explanation:
distance formula : if [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] are two points on a line segment then distance between both the points is given by distance formula.
[tex]d = \sqrt{[(x_{2} - x_{1} )^2 +(y_{2} - y_{1})^2]}[/tex]
therefore ,
given points are , A(2, 5), P(0, 0), C(-2, 7).
so PA = [tex]\sqrt{[({2} - {0} )^2 +({5} - {0})^2]} = \sqrt{({2} )^2 +({5} )^2}[/tex]
PA = [tex]\sqrt{\229}[/tex]
similarly,
AC = [tex]\sqrt{[({-2} - {2} )^2 +({7} - {5})^2]} = \sqrt{({4} )^2 +({2} )^2}[/tex]
AC = [tex]\sqrt{20} = \sqrt[2]{5}[/tex]
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Which statements describe a triangular prism? Select three options. It has one base. It has two bases. It has three lateral faces. It has four lateral faces. Its lateral faces are rectangular.
The statements that describe a triangular prism are:
It has one base. It has three lateral faces. Its lateral faces are rectangular.What is a triangular prism?A triangular prism is a three-dimensional object that is made up of one base that has the shape of a triangle and three lateral sides that have the shape of a rectangle. A triangular prism has 5 faces, 9 edges and 6 vertices.
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area = ft
help me please ty:)
find the length using the Pythagorean theorem.
Length = sqrt(20^2 - 12^2)
Length = 16 feet
area = 12 x 16 = 192 square feet
The x-coordinate of the point (50, 55) is ___________.
The x-coordinate of the point (50, 55) is 50
What is graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
The distance of point (50, 55) perpendicular to y-axis
Thus, perpendicular distance = 50 units
The x-coordinate of the point (50, 55) is 50
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Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below. A graph represents the water level to fill the tank on Y-axis per time on X-axis. Segments A, B, and C fill the tank from 10 to 60, 60 to 80, and 80 to 110 centimeters in the first 2, next 4, and last 3 minutes. Place the segments in the correct order from the least to the greatest rate of increase in the water level. B A C , ,
The least to greatest slope, the segments are B, C and A.
Given that,
Segments A, B, and C on the graph below represent the water level of the tank every minute since it started filling.
A graph shows the water level needed to fill the tank on the y axis per unit of time on the x axis.
The segment's slope indicates how quickly the water level is rising. The slope, which is determined by the segment's angle with the positive x axis, is the ratio of rise to run.
slope of segment A = 60₋10/2 = 25
slope of segment B = 80₋60/4 = 5
slope of segment C = 110₋80/3 = 10
We can see that section B has the least slope, followed by segment C, and then segment A, which has the greatest slope.
B, C, and A are the segments in descending order of least to greatest slope.
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I'm having trouble with inequalities, any help will be appreciated, thanks.
Answer:
-3/2 ≤ x < 5
Decimal form:
-1.5 ≤ x < 5
(hope this helps)
A laptop costs £600
Students get a 5% discount.
How much discount will a student get?
Answer:
cost price = £ 600
discount = 5%
selling price =
5/100 * 600.
5 * 6
30 £
price = 600 - 30
= 570
The length of a rectangle is 7 inches and the width is 42 inches. What is the ratio,
using whole numbers, of the length to the width?
Answer:
6 : 1
Step-by-step explanation:
The length is the longer side compared to the width.
Hence, the length is 42 inches and width is 7 inches.
Taking the ratio :
Length : Width42 : 77 x 6 : 76 : 1Answer:
1 : 6
Step-by-step explanation:
42 /7 = 6
We will have to simply the ratios in order to get the answer.
Can You Please Help Me, I Would Really Appreciate It!!
Let's take this problem step by step:
To find the ordered pair of the system:
⇒ must set both equations equal to each other
⇒ solve for 'x'
Let's solve:
[tex]x^2-2x+3=-2x+12\\x^2-2x+2x+3-12\\x^2-9=0\\(x+3)(x-3)=0[/tex]
Let's find the x-values:
[tex](x+3)=0\\x=-3\\\\(x-3)=0\\x+3[/tex]
Let's find f(x)'s value for each 'x':
[tex]x=-3\\f(-3)=-2(-3)+12=6+12=18\\\\x=3\\f(3)=-2(3)+12=-6+12=6[/tex]
Answer: (3, 6), (-3,18)
Hope that helps!
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Marcela was assigned some math problems for
homework. She answered half of them in study hall.
After school she completed seven more. If she still
has 11 problems to do, how many problems were
assigned?
Answer:
36 problems
Step-by-step explanation:
so let's say x = how many problems Marcela was assigned
she completed half of them so the amount of problems left is x/2
She then completed 7 more so now we can subtract 7. We then set this to 11 to solve for x
x/2 - 7 = 11
x/2 = 18
x = 36
What is the equation of the quadratic function shown in the graph?
Answer: f(x) = -2 (x+3) (x-1)
Step-by-step explanation: See Attachment
Convert the angle from radians to degrees: [tex]\frac{5}{6}\pi[/tex] with working
