[tex]\text{Use}\ (a+b)^2=a^2+2ab+b^2\\\\x^2+4x+4=25\\\\x^2+2(2)(x)+2^2=25\\\\(x+2)^2=25\iff x+2=\pm\sqrt{25}\\\\x+2=-5\ \vee\ x+2=5\qquad\text{subtract 2 from both sides}\\\\\boxed{x=-7\ \vee\ x=3}[/tex]
Other method:
[tex]x^2+4x+4=25\qquad\text{subtracr 25 from both sides}\\\\x^2+4x-21=0\\\\x^2+7x-3x-21=0\\\\x(x+7)-3(x+7)=0\\\\(x+7)(x-3)=0\iff x+7=0\ \vee\ x-3=0\\\\x+7=0\qquad\text{subtract 7 from both sides}\\\boxed{x=-7}\\\\x-3=0\qquad\text{add 3 to both sides}\\\boxed{x=3}[/tex]
Mark and Bonnie both make $11 per hour working for their parents. If they combine their efforts and work for the same amount of hours, which expression would NOT show their total combined earning
what is definition of equivalent fractions
Equivalent fractions are fractions that are equal to each other.
So they might have different denominators
and different numerators but they're
going to be equal fractions.
recursive formula 2,5,11,23
Answer:
The first few Thabit numbers are: 2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ... (sequence A055010 in the OEIS)
Step-by-step explanation:
19. Describe how the graphs of y = |x| and y = |x + 5| are related. (1 point)
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is
5.
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is
–5.
The two graphs are the same.
The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is
5.
Answer:
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is 5.
Step-by-step explanation:
When we add the 5 inside the absolute value, we shift the graph to the left 5 units. The y intercept of abs (x) is 0 and the y intercept of y = abs(x+5) is 5 . The x intercept of y =abs (x) is 0 and the x intercept of y =abs(x+5) is -5. The graph has the same shape
If you have a two- digit divisor and a three- digit dividend, does the quotient always have the same number of digits? Please help ASAP!!!
Find the correct solution graph for inequality?
a math club earns $2,080 from selling 62 floor seats and 120 Stadium seats to a lip sync Talent competition at the floor seats cost twice as much as Stadium seats find the price of each ticket
Answer:
Price of floor seat =$ 17 and
Price of stadium seats = $8.5
Step-by-step explanation:
Let x represents the cost of floor seats and y represents the cost of stadium seats.
Then, from the given condition, we have;
Total cost for selling floor seats = 62x and the total cost for stadium seats = 120y.
Since, a math club earn $2,080.
⇒ 62x + 120y = 2080 .....[1]
Also, it is given that the floor seats cost twice as much as Stadium seats.
⇒ x = 2y .....[2]
Substitute this equation [2] in [1] we get;
[tex]62(2y) + 120y = 2080[/tex]
Simplify:
124y + 120y =2080
Combine like terms;
244y =2080
Divide both sides by 144 we get;
[tex]y = \frac{2080}{144} = 8.5[/tex]
⇒y = $8.5
Substitute this in [2] we get x;
x = 2(8.5) = 17
i.e, x = $ 17
Therefore, the price of floor seat is, $ 17 and the price of stadium seats is, $8.5
Find the equivalent expression using the same basis (34•84)^3
Answer:
(2)^9•(3)^3•(7)^3•(17)^3
Step-by-step explanation:
(34•84)^3
=(34)^3•(84)^3
=(2•17)^3•(2•2•3•7)^3
=(2)^3•(17)^3•(2)^3•(2)^3•(3)^3•(7)^3
=(2)^(3+3+3)•(17)^3•(3)^3•(7)^3
=(2)^9•(3)^3•(7)^3•(17)^3
Answer:
The answer is 2^9•3^3•7^3•17^3
Step-by-step explanation:
First, we simplify the expression inside bracket
34•84
= (2•17)•(2•42)
= (2•17)•(2•2•21)
= (2•17)•(2•2•3•7)
= 2^3•3•7•17
Substituting back
(34•84)^3
= (2^3•3•7•17)^3
= 2^9•3^3•7^3•17^3
|60| ___ |-60|
1. =
2. <
3. >
Answer:
1. =
Step-by-step explanation:
Absolute value means always positive
so
|60| ___ |-60|
60 _____ 60
They are equal
-8 + (+7)= add. need help
Question
-8 + (+7)=
Answer:
-1Step-by-step explanation:
the expression -8 +(+7) is equal to 7 - 8 (commutative property)
7 - 8 = -1
Use the Counting Principle to find the probability of rolling a 4 on each of 3 number cubes
Answer:
[tex]\frac{1}{216}[/tex]
Step-by-step explanation:
We have been given that three cubes are being rolled and we are required to find the probability of getting 4 on each of the three cubes.
We know the probability of rolling a 4 on one cube will be [tex]\frac{1}{6}[/tex]. Since there are 3 cubes, the probability of rolling 4 in each of the individual cubes will be [tex]\frac{1}{6}[/tex].
But we want 4 to be rolled on all three cubes at once, in order for that to happen, we need to get a four on first cube AND second cube AND third cube. Since there is AND between the events, we will multiplied their probabilities as per counting principle. Thus, the required probability of rolling 4 on each of the three cubes is [tex]\frac{1}{6}\cdot\frac{1}{6}\cdot\frac{1}{6}[/tex] which simplifies to [tex]\frac{1}{216}[/tex].
Michael and Imani go out to eat for lunch.
Part A
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill?
Part B
If Michael and Imani add an 18% tip to the bill, what does their lunch cost in total?
Answer:
Part A: $27.32
Part B: $32.24
Step-by-step explanation:
Part A:
$25.30 is the cost, since we are increasing it by the 8% meals tax, we are going to do 25.3 * the decimal form of 8%, or 0.08, plus one so that we already have our 25.3 factored in. Which equals 25.3 * 1.08, which equals 27.324, which we round to $27.32.
Part B:
We take our $27.32 and we times it by 1.18 for the reason stated above, which equals 32.2376, which is rounded to $32.24.
Your housing and fixed expenses are $685.70/month. If they are 33% of your realized income, how much is your realized income per month?
a) $2,077.88
b) $2,790.55
c) $2,219.91
d) $2,488.16
Answer:
Option a. $2077.88 is the correct answer.
Step-by-step explanation:
Your housing and fixed expenses are $685.70 per month.
If they are 33% of your realized income.
Let your realized income per month be x
33% of x = $685.70
[tex]\frac{33}{100}[/tex] of x = 685.70
0.33x = 685.70
x = 685.70 ÷ 0.33 = 2,077.8787 rounded to $2,077.88
Your realized income per month would be $2,077.88.
PLEASE ANSWER 30 POINTS!
To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. How many deer are in the forest?
Answer:
2520
Step-by-step explanation:
There are 405 deer per 45 tags.
The ranger tagged 280 deer.
No. of deer = 280 × 405/25
No. of deer = 280 × 9
No. of deer = 2520 deer
There are 2520 deer in the forest
Answer:
Total deers in the forest is 640
Step-by-step explanation:
Since the Number of tagged deer is 280
the number of caught deer is 405 after all tagged deers were released
Surprisingly 45 of 280 of tagged deer was found hence the remaining tagged deer has exscaped in to the forest
The number of deers in the forest is
405-45+250=640
The remaining tagged deer that did not return is
280-45= 235
This table represents a function. Plot points to represent the function as a graph.
X Y
-4 10
0 8
4 6
10 3
Answer:
it says it already a function so your just plotting (-4,10) (0,8) (4,6) (10,3) on a graph, there isnt a graph to do it for you. Sorry if im reading this wrong :(
Step-by-step explanation:
Answer:
The points represent a linear function (first-order polynomial).
Step-by-step explanation:
The points are included in the attached image, which depicts a constant slope and, consequently, represents a linear function (first-order polynomial).
To convert 3 square feet to square centimeters, multiply 3 by 9.29 × 10-2
True
False
Final answer:
To convert 3 square feet to square centimeters, multiply by the correct conversion factor of 9.29 × 10⁻².
Explanation:
To convert square feet to square centimeters, you need to understand the conversion factor between these two units. Since 1 foot is equal to 30.48 centimeters and area is defined as the product of the two dimensions, you need to square the conversion factor of 30.48 to convert square feet to square centimeters.
So, the correct conversion factor is (30.48 cm/1 ft)².
To convert 3 square feet to square centimeters, you can use the conversion factor as follows:
(3 ft²) × (30.48 cm/1 ft)² = 274.32 cm²
Therefore, the statement is True as multiplying 3 by the correct conversion factor of 9.29 × 10⁻² will indeed give you the value of 274.32 square centimeters.
can someone please help me look for x and y, in the equations
2x= 4y-16
2x- y=-7
Answer:
y = 3 and x = -2 PLEASE GIVE BRAINLIEST
Step-by-step explanation:
Solve for y
4y - 2x = 16
-y + 2x = -7
3y = 9
y = 9 ÷ 3
y = 3
Input y to find x
2x = 4(3) - 16
2x = 12 - 16
2x = -4
x = -4 ÷ 2
x = -2
Input both x and y to see if it works
2(-2) = 4(3) - 16 2(-2) - 3 = -7
-4 = 12 -16 -4 -3 = -7
-4 = -4 -7 = -7
The solution to the system of equations is [tex]x = -2[/tex] and [tex]y = 3[/tex].
To solve the system of equations given by
[tex]2x = 4y - 16[/tex][tex]2x - y = -7[/tex]Here is a step-by-step guide on how to solve for [tex]x[/tex] and [tex]y[/tex].
Step 1: Simplify the first equation
Start by rearranging the first equation to express it in terms of one variable. We can isolate [tex]y[/tex]:
[tex]2x = 4y - 16[/tex]
[tex]4y = 2x + 16[/tex]
[tex]y = \frac{2x + 16}{4}[/tex]
[tex]y = \frac{x}{2} + 4[/tex]
Step 2: Substitute [tex]y[/tex] in the second equation
Now, we can substitute [tex]y[/tex] in the second equation:
[tex]2x - \left(\frac{x}{2} + 4\right) = -7[/tex]
Step 3: Solve for [tex]x[/tex]
Distributing the negative and simplifying:
[tex]2x - \frac{x}{2} - 4 = -7[/tex]
Multiply every term by 2 to eliminate the fraction:
[tex]4x - x - 8 = -14[/tex]
This simplifies to:
[tex]3x - 8 = -14[/tex]
[tex]3x = -14 + 8[/tex]
[tex]3x = -6[/tex]
[tex]x = -2[/tex]
Step 4: Substitute [tex]x[/tex] back to solve for [tex]y[/tex]
Now substitute [tex]x = -2[/tex] back into the equation for [tex]y[/tex]:
[tex]y = \frac{-2}{2} + 4[/tex]
[tex]y = -1 + 4[/tex]
[tex]y = 3[/tex]
there are 54 girls in a bowling league. there are 2 girls for every boy in the league. how many boys are in the league?
Answer:
27 boys
Step-by-step explanation:
1. divide 54 by 2
the answer will come up to 27.
to check your work you can do 27 times 2
27 × 2 = 54
Given the height,h, and the volume v of a certain cylinder. Alex uses the formula
r= √v/πh to compute its radius r, to be 10 meters.
A second cylinder has the same volume as the first cylinder, but it is 25 times taller. What is the radius of the second cylinder?
Answer:
A = 2/5
Step-by-step explanation:
r = sqrt(v) / (pi*h)
10 = sqrt(v) /(pi * h)
Solve for the volume by multiplying by pi * h on each side
10 * pi * h = sqrt(v)
Now square each side
(10*pi* h) ^2 = v
Now we have a second cylinder with a height that is 25 times the height of the other cylinder but the same volume. Solving for volume, we will multiply by
r = sqrt(v) / (pi*h)
r = sqrt(v) /(pi *25h)
r* pi * 25h = sqrt(v)
Now square each side
(r*pi*25h) ^2 = (sqrtv) ^2
(r*pi*25h)^2 = v
The problem states the the 2 cylinders have the same volume
(10 * pi * h) ^2 = ( r * pi * 25h) ^2
Take the square root of each side
10*pi*h = r*pi * 25h
Divide each side by pi and h
10 = 25r
Divide by 25
10/25 =r
2/5 =r
The figure shows five points. A point has been translated right and up
A point has been translated right and up from point D could be the image of B.
It indicates that a point was translated right and up.
As a result, any point existing on the rightmost side cannot be the translated point.
As a result, points E and D are ruled out.
There is no point that is higher than point A.
As a result, no "up" translation is available for point A.
Only points C and B are capable of "right and up" movement.
As a result, the first option "Point D could be the image of B" is correct.
what number multipled by its self equals 3600
Answer: The answer is 60.
Step-by-step explanation: To determine this, we need to square root the number in question. In this case, that’s 3600.
The square root of 36 is 6, so the square root of 3600 is 60, following the rules of zeros.
I hope this helps!
After a 15% off sale, a pair of Levi jeans were $11.50. How much was the original price of the Levi jeans?
What is 1 1/4 + 1 1/8?
Answer:
2 3/8
Step-by-step explanation:
1 1/4 + 1 1/8
We need to get a common denominator to add the fractions. The common denominator is 8
1 1/4 *2/2 + 1 1/8
1 2/8 + 1 1/8
2 3/8
An amusement park sold a total of 86 tickets. 34 of the tickets were child tickets, and the rest were adult tickets. What is the ratio of the number of adult tickets to the total number of tickets?
Answer:
51,400 thats my answer hope it helps!
A pole has a shadow that is 15 feet long.Mary is 4 feet tall and her shadow is 10 feet tall.how tall is the pole? ☹
ASAP
PLEASE HELP!
ANYONE HELP
ASAP
FAST
Answer:
The pole is 6 ft tall
Step-by-step explanation:
We can solve this using ratio's
4ft tall Mary x ft tall pole
----------- = -------------------
10 ft shadow 15 ft shadow
Using cross products
4 * 15 = 10 x
60 = 10x
Divide by 10
60/10 = 10x/10
6 =x
The pole is 6 ft tall
Answer:
it is 6 feet
Step-by-step explanation:
i dont have much of an explaination except that you have to draw a diagram inorder not tom get confused.
hope it helps.
I just need the answers for 10 and 12
Answer:
10.) y = -5x + 7
12.) y = 3/2x - 8
Step-by-step explanation: Since you have to create a new line that us parallel, the slopes will be equivalent. So the mx value will not change. Now we can plug in the coordinates to find the value of b.
10.)
2 = -5(1) + b.
2 = -5 +b
b = 7
therefore...
y = -5x + 7
12.)
2(-5) = 3(2) + b
-10 = 6 + b
b = -16
therefore...
2y = 3x - 16
simplified:
y = 3/2x - 8
[tex] {x}^{2} = \frac{121}{196} [/tex]
[tex]x^2=\dfrac{121}{196}\iff x=\pm\sqrt{\dfrac{121}{196}}\\\\x=-\dfrac{\sqrt{121}}{\sqrt{196}}\ \vee\ x=\dfrac{\sqrt{121}}{\sqrt{196}}\\\\\boxed{x=-\dfrac{11}{14}\ \vee\ x=\dfrac{11}{14}}\\\\\sqrt{a}=b\iff b^2=a\\\\\sqrt{121}=11\ \text{because}\ 11^2=121\\\\\sqrt{196}=14\ \text{because}\ 14^2=196[/tex]
There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 6 or a multiple of 4?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
BOLD number are multiples of 4 or 6
4 out of the 15 numbers are a multiple of either 4 or 6,
so the probablilty would be 4/15 or a 26.6% chance.
The probability that the result is a multiple of 6 or a multiple of 4 is 4 /15.
The spinner has 15 equal areas numbered 1 through 15.
If the spinner is spun one time the probability of getting a multiple of 6 or a multiple of 4 can be calculated below;
The numbered side are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15.
multiple of 6 are 6 and 12.
multiple of 4 are 4, 8 and 12
union of the set = 4, 6, 8, 12
number of acceptable value = 4
The probability of getting a multiple of 6 or a multiple of 4 = number of acceptable value / number of possible value
probability of getting a multiple of 6 or a multiple of 4 = 4 / 15 = 4 / 15
learn more: https://brainly.com/question/19217522?referrer=searchResults
16.45 markdown 33% what’s the anwser
dude, use a calculator
Step-by-step explanation:
Answer:
= 11.02
Step-by-step explanation:
Firstly, we need to find the percentage of the amount left first. This can be done by subtracting the percentage from 100:
100 - 33 = 67
To find the percentage of something, you need to use the following equation:
Amount x [tex]\frac{percentage}{100}[/tex]
Simply plug the given values in:
16.45 x [tex]\frac{67}{100}[/tex] = 11.02
So the answer is 11.02!
a) 1
b) -20
c) 20
d) 7
[tex]f(x)=x^2;\ g(x)=x-3\\\\(g\ \circ\ f)(x)=(x^2)-4=x^2-3\\\\\text{Put x = -2 to the equation}\\\\(g\ \circ\ f)(-2)=(-2)^2-3=4-3=1\to\boxed{a)}[/tex]