Ken earned $128 from his part-time job and spent 25% of it, leaving him with $96. He then donated 1/6 of the remaining money to charity, which equals $16.
Explanation:This problem is about percentages and fractions. Ken earned $128 from his part-time job and spent 25% of it on games, which equals <$128 * 25/100 = $32>. So after buying games, Ken is left with <$128 - $32 = $96>. Ken then decides to donate a fraction, 1/6 of the remaining money to charity. To figure out how much he donates, we multiply $96 by 1/6, which is <$96 * 1/6 = $16>. So, Ken donates $16 to charity from his summer job earnings.
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Given the net of the rectangular prism, what is its surface area?
96 m2
144 m2
160 m2
180 m2
Answer:
[tex]160\ m^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the rectangular prism is equal to the area of its six rectangular faces of the net
so
[tex]SA=2(2*4)+2(12*2)+2(12*4)\\ \\SA=16+48+96\\ \\SA=160\ m^{2}[/tex]
Answer:
160 m2
Step-by-step explanation:
The sum of the measures of angle M and angle R is 90 °
•the measure of angle M is (5x+10)°
•the measure of angle R is 55°
What is the value of x?
The value of x is 5.
Given:
angle M + angle R = 90°angle M = (5x+10)°angle R = 55°Recall:
Two angles that add up to give you 90°, is a complementary angle.Thus,
Since angle M and angle R sum up to give 90°, they are complementary angles.The following equation can be created to solve for the value of x:
[tex]m\angle R + m\angle M = 90[/tex]
Substitute[tex]55 + 5x+10 = 90\\[/tex]
Add like terms[tex]5x + 65 = 90[/tex]
Subtract 65 from both sides[tex]5x = 90 - 65\\\\5x = 25[/tex]
Divide both sides by 5[tex]x = 5[/tex]
Therefore, the value of x is 5
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I need help on this
Answer:
12 + 12 + 60 + 216 = 300 ft squared
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
First find the area of the rectangle which would be 18 times 12. This will give you 216 for the rectangle. To find the area of the trapezoid you would add the base of the trapezoid for top and bottom. 10+18. This will give you 28. Next divide it by 2. This will give you 14. Now multiply 14 by the height of the trapezoid which is 6. This will give you 84 for the trapezoid. Now add the rectangle and the trapezoid 84+216=300. The area of the figure is 300.
Suppose the probability of an event occurring is P(A), and the probability of the event not occurring is P(A'). If P(A) = m and P(A') = n, which of the following equations must be true?
A. m = 1 + n
B. n = 1 - m
C. n = m + 1
D. M =n -1
Answer:
B
Step-by-step explanation:
P(A)+P(A')=1
m+n=1
B is the only answer equal this if you add m to both sides.
Answer:
I got B! n=1-m
What is the effect on the graph of the parent function f(x)=x when f(x) is replaced with f(x-7)
Answer:
I think it shifts horizontally by 7 units to the right. Not completely sure though.
Step-by-step explanation:
Andy, David and Tim altogether have 180 stamps. Andy has 20 fewer than David, and Tim has 80% of the sum of Andy's and David's stamps.How many stamps does each of them have?
andy has 40
david has 60
tim has 80
Answer:
Step-by-step explanation:
Alright, lets get started.
Let Andy have A stamps.
Let David have D stamps.
Let Tim have T stamps.
Andy, David and Tim altogether have 180 stamps, means
[tex]A+D+T=180....................... equation 1[/tex]
Andy has 20 fewer than David, means
[tex]A+20=D...............................equation 2[/tex]
Tim has 80% of the sum of Andy's and David's stamps, means
[tex](A+D)*0.8=T........................equation 3[/tex]
Putting the value of D as A+20 in equation 1 and 3
[tex]A+A+20+T=180[/tex]
[tex]2A+T=160[/tex]........................equation 5
[tex](A+A+20)0.8=T[/tex]
[tex](2A+20)0.8=T[/tex]
[tex]1.6A+16=T[/tex] ....... equation 6
Plugging the value of T in equation 5
[tex]2A+1.6A+16=160[/tex]
[tex]3.6A=144[/tex]
[tex]A=40[/tex]
[tex]D = 40+20 = 60[/tex]
[tex]T=1.6*40+16[/tex]
[tex]T=64+16=80[/tex]
It means Andy has 40 stamps.
It means David has 60 stamps.
It means Tim has 80 stamps.
Hope it will help :)
Find all solutions for a triangle with A=40 degrees , B=60 degrees and c = 20.
Answer: 40 +60+20= 120
Step-by-step explanation:
Answer:
A = 40 degrees
B = 60 degrees
C = 80 degrees
a = 13.1
b = 17.6
c = 20
Step-by-step explanation:
They give us A = 40 degrees and B = 60 degrees and in one triangle the sum of the angles should be 180, so you add 40 and 60, and then subtract that value by 180.
40 + 60 = 100
180 - 100 = 80
C = 80 degrees
From here you use the law of sines
20/sin(80) = a/sin(40)
when you cross multiply them you should get this:
20 * sin(40) = sin(80)*a
Simplify them
12.9 = sin(80) * a
Divide them to isolate the variable
12.9/sin(80) = a
a = 13.1
To find side length b you use law of sines again
20/sin(80) = b/sin(60)
Cross multiply
20 * sin(60) = sin(80) * b
Simplify
17.3 = sin(80) * b
Divide to isolate the variable
17.3/sin(80) = b
b = 17.6
Which is the answer
Answer:
Inverse property
Step-by-step explanation:
The definition of the inverse property is to add to get a result of zero. Since we are adding the inverse of each term to get a result of zero each time, we are using the inverse property.
PLEASE HELP!!!!!!!!! The scale on a map shows that 5 centimeters = 2 kilometers. What number of centimeters on the map represents an actual distance of 5 kilometers?
Answer:
12.5 cm
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
5 cm = 2 km
? cm = 5 km
5 cm = 2 km
( ÷ 2 )
2.5 cm = 1 km
( × 5 )
12.5 cm = 5 km
What is the length of BC round to the nearest 10th of a unit
Answer:
8.6 units
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = B(1, 6) and (x₂, y₂ ) = C(8,1)
d = [tex]\sqrt{(8-1)^2+(1-6)^2}[/tex]
= [tex]\sqrt{7^2+(-5)^2}[/tex]
= [tex]\sqrt{49+25}[/tex]
= [tex]\sqrt{74}[/tex] ≈ 8.6
Given the functions: f(x) = 7x + 10 and g(x) = 1.75x + 10. Make a table of values for each function to determine which value of x is closest to where g(x) begins to exceed f(x). A) x = 5 B) x = 6 C) x = 7 D) x = 8
Your answer Would be c
Your answer will be C
Find all of the polar coordinates of point P if p=(1,-pi/6)
Answer:
The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n).
Step-by-step explanation:
The polar coordinates can be written as (r,Ф)= (r,Ф+2nn) or (r,Ф) =(-r,Ф+(2n+1)n) and n is any integer value.
We are given p=(1,-pi/6)
P(r,Ф), then r = 1 and Ф = -pi/6
The polar coordinates will be
P(r,Ф)= (r,Ф+2nn) = (1 , -pi/6 + 2nn) and n is any positive integer and the value of r is positive.
P(r,Ф) =(-r,Ф+(2n+1)n) = (-1, -pi/6+(2n+1)n) and n is any positive integer and the value of r is negative.
The all polar coordinates of point P are (1 , -pi/6 + 2nn) and (-1, -pi/6+(2n+1)n)
B
=
Round your answer to the nearest hundredth.
The measure of B is 51.06°
From pythagoras;
sinθ = opposite / Hypotenus opposite = 7Hypotenus = 9Substituting into the relation;
Sin(B) = 7/9
Sin(B) = 51.057
To the nearest hundredth , we have ; 51.06
solve the inequality 5x+3 ≥48
Answer:
x≥9
Step-by-step explanation:
First you need to take 3 from both sides.
5x + 3 -3 ≥ 48 -3 which is 5x ≥ 45
Then you need to divide both sides by 5.
5x÷5 ≥ 45÷5 with gives the answer x ≥ 9
The solution to the given inequality (5x+3 ≥48) is x ≥ 9
To solve an equation or an inequality, we will determine the value of the variable in the equation or inequality.
From the question,
To solve the given inequality 5x+3 ≥48
We will determine the value of the variable x, that satisfies the inequality.
Now, to do this
First, subtract 3 from both sides, that is
[tex]5x+3-3 \geq 48-3[/tex]
We get
[tex]5x \geq 45[/tex]
Now, divide both sides by 5
[tex]\frac{5x}{5} \geq \frac{45}{5}[/tex]
[tex]x\geq 9[/tex]
Hence, the solution to the given inequality is x ≥ 9
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Solve for x in the equation x^2-14x+31=63.
Answer:
-2; 16
Step-by-step explanation:
Rewrite the equation [tex]x^2-14x+31=63[/tex] as:
[tex]x^2-14x+31-63=0\\ \\x^2-14x-32=0[/tex]
Now use the quadratic formula:
[tex]D=b^2-4ac\\ \\D=(-14)^2-4\cdot 1\cdot (-32)\ \ [a=1,\ b=-14,\ c=-32]\\ \\D=196+128=324=18^2[/tex]
Now
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{D}}{2a}\\ \\x_{1,2}=\dfrac{-(-14)\pm\sqrt{18^2}}{2\cdot 1}=\dfrac{14\pm18}{2}=\dfrac{-4}{2},\ \dfrac{32}{2}=-2,\ 16[/tex]
Answer:
x = 16 or x = -2
Step-by-step explanation:
Points to remember
Solution of a quadratic equation ax² + bx + = 0 is given by
x = [-b ± √(b² - 4ac) ]/2a
To find the solution of equation
We have x² - 14x + 31 = 63
x² - 14x + 31 - 63 = 0
x² - 14x - 32 = 0
a = 1, b = -14 and c = 32
x = [-b ± √(b² - 4ac) ]/2a
= x = [- -14 ± √((-14)² - 4*1 * (-32)) ]/2*1
= [14 ± √324]/2
x = -2 or x = 16
heeeeeeeellllllllpppppppppp
Answer:
False
Step-by-step explanation:
To be a function each x can only go to one y
The number 5 goes to both 2 and 1, which violates the rule
Therefore, this is a relation, not a function
asap!!
85=2x(x^2+3)(2x+5) use quadratic equation
Answer:
Step-by-step explanation:
85=2x(x^2+3)(2x+5)
85=2x(2x^3+5x^2+6x+15)
85=4x^4+10x^3+12x^2+30x
4x^4+10x^3+12x^2+30x-85=0
2x^2(2x^2+5x+6)+30x-85=0
shoot, this isn't possible with quadratic, maybe you can get somewhere from here
The humpback whales traveled 2240 miles in 28 days. The gray whales traveled 2368 miles in 32 days. If the humpback whales had traveled at the same rate for 32 days how many more miles would they have to travel
Answer:
192
Step-by-step explanation:
32 days would be 80×32=2560
and 2560-2368= 192
So if the humpback were to travel for 32 days it would travel 192 miles more than the gray whale.
What is x for the following:
|x-1/x-1|=1
and...
x-1/x-1
Answer:
2, or any negative number
Step-by-step explanation:
For the first one x=2
The volume of a box with height x, length x-1, and width 2x+2 is given by the binomial 2x^3-2x. What is the volume of the box if it’s height is 4 feet?
Height = x
Length = x - 1
Width = 2x + 2
And it's said that height = 4 feet
So, x = 4
Then:
H = 4
L = 4 - 1 = 3
W = 2.4 + 2 = 10
The volume is:
V = 4 . 3 . 10
V = 120 ft³
What is the height of the triangular prism? Where it says C, what's the height?
Answer:
√7 ≈ 2.646
Step-by-step explanation:
The triangle apparently has two sides of length 4 and a third side of length 6. The altitude of the triangle will divide the long side in half, making that half one leg of the right triangle with hypotenuse 4.
The altitude of interest is then the length of the other leg:
√(4² -3²) = √7 ≈ 2.646
Susan walks 10 feet in 4 steps at this rate how many steps will it take her to walk 1 mile
Answer:
2112 Steps
Step-by-step explanation:
It would take her 2112 step to walk for 1 mile
The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. What is the probability that a person chosen at random from this group has brown or green eyes?
Answer: 13/25
Step-by-step explanation:
The probability that a person chosen at random from this group has brown or green eyes is 0.52.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
The table of the number of people and the colour of their eyes colour is given as,
Colour of Eyes Number of People
Brown 20
Green 6
Blue 17
Hazel 7
According to the table, the total number of people who participated in the survey is 50. Therefore, the probability that a person chosen at random from this group has brown or green eyes can be written as,
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
[tex]\rm Probability=\dfrac{\text{Number of people with brown and green eyes}}{\text{Total number of people who participated in the survey}}[/tex]
[tex]\rm Probability=\dfrac{20+6}{50}=\dfrac{26}{50} = 0.52[/tex]
Hence, the probability that a person chosen at random from this group has brown or green eyes is 0.52.
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Celia uses the steps below to solve the equation -3:8(-8-16d)+2d+24
Answer: i think it’s the last one
Step-by-step explanation:
A deep-sea exploring ship is pulling up a diver at the rate of 25 ft./min. the driver is 200 feet below sea level how deep it was the diver 10 minutes ago show your thinking
Answer:
Ten minutes ago, the diver was 450 feet below sea level.
Step-by-step explanation:
Since the diver is being pulled up, measuring his movement for the past 10 minutes requires that we use −25 for the movement over those 10 minutes. So, his depth 10 minutes ago is given by the expression
−200−25(10)
−200
−250
−450
So, 10 minutes ago, the diver was 450 feet below sea level.
Answer:
The diver 450 feet deep into sea 10 minutes ago.
Step-by-step explanation:
At present position ,depth at which diver was = 200 feet
Rate at which diver is pulled up = 25 ft/min
Let the depth of the diver 10 minutes ago be x
The depth of the diver 10 minutes ago will be sum of present position and distance covered by exploring ship by pulling diver in a 10 minutes.
x = 200 + 25ft/min × 10 = 200 ft + 250 ft = 450 ft
The diver 450 feet deep into sea 10 minutes ago.
For the following question, what is the value of x to the nearest tenth?
Answer:
I believe it is 11.5 but I’m not 100% sure
Step-by-step explanation:
Write a quadratic equation in factored form whose solutions are 7 and -5
[tex]\bf \stackrel{~~ solutions~\hfill }{ \begin{cases} x=7\implies &x-7=0\\ \cline{1-2} x=-5\implies &x+5=0 \end{cases}}\qquad \implies \stackrel{\textit{factored form}}{y=(x-7)(x+5)}[/tex]
Answer:
y = (x - 7)(x + 5)
Step-by-step explanation:
Given the solutions are x = 7 and x = - 5 then the factors are
(x - 7) and (x + 5)
The quadratic equation is the product of the factors
(x - 7)(x + 5) = 0 ← in factored form
finding the solutions of inequality
-7x+14>-3x-6
Answer:
x < 5
Step-by-step explanation:
- 7x + 14 > - 3x - 6
14 > 4x - 6
20 > 4x
x < 5
Answer:
x>5
Step-by-step explanation:
-7x+14>-3x-6
-4x+14>-6
-4x>-20
-x>-5
x>5
which of the symbols correctly relates the two numbers below? check all that apply 13?13
Answer:
Correct symbol is = .
Step-by-step explanation:
Given statement is : 13?13
Now we need to find about which of the symbols correctly relates the two numbers 13?13.
When we compare two numbers then there are only three cases possible.
First number is less than ( < ) second number.
First number is greater than ( > ) second number.
First number is equal to ( = ) the second number.
we see that both numbers 13 and 13 are equal so we will use = symbol.
Hence correct symbol is = .
Final answer:
The correct symbol to relate two identical numbers, such as 13 and 13, is the equals to (=) symbol.
Explanation:
The question asks which symbols correctly relate the two numbers 13 and 13. In mathematics, numbers can be compared using different symbols to show their relationship. These symbols include equals to (=), greater than (>), less than (<), greater than or equal to (>=), and less than or equal to (<=). When two numbers are identical, the correct symbol to relate them is the equals to (=) symbol because they have the same value.
Write the equation -3x+2y=7 in slope intercept form.
Answer:
[tex]y=\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
Slope-intercept form is given by y = mx + b
We need to re-arrange the equation given to have y to the left side of the equal sign (in other words, solve for y). Steps are shown below:
[tex]-3x+2y=7\\2y=3x+7\\y=\frac{3x+7}{2}\\y=\frac{3x}{2}+\frac{7}{2}\\y=\frac{3}{2}x+\frac{7}{2}[/tex]
the last answer is correct.
For this case we have that the line equation of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
We have the equation:
[tex]-3x + 2y = 7[/tex]
By adding 3x to both sides of the equation we have:
[tex]-3x + 3x + 2y = 7 + 3x\\2y = 3x + 7[/tex]
Dividing between 2 on both sides of the equation:
[tex]\frac {2y} {2} = \frac {3x} {2} + \frac {7} {2}\\y = \frac {3x} {2} + \frac {7} {2}[/tex]
ANswer:
Option D