Answer:
x=2, y=8. (2, 8).
Step-by-step explanation:
y-2x=4
2x+3y=28
----------------
y=2x+4
2x+3(2x+4)=28
2x+6x+12=28
8x+12=28
8x=28-12
8x=16
x=16/8
x=2
y-2(2)=4
y-4=4
y=4+4
y=8
Lydia is taking a test. It has four multiple choice questions, each with three options to choose from, and five True/False questions. If Lydia guesses on each question, what is the probability she will earn 100%
Answer: 50%
Step-by-step explanation:
Devaughn is 15 years younger than Sydney. The sum of their ages is 25. What is Sydney's age?
Answer:
20
Step-by-step explanation:
Let Sydney's age be represented by s. Then the sum of the two ages is ...
s + (s-15) = 25
2s = 40 . . . . . . add 15
s = 20 . . . . . . . divide by 2
Sydney's age is 20.
denise is using a ladder to clean the outside of her second story windows. the ladder she is using is 24 feet long and she puts the base of the ladder 13 feet away from the house in order to avoid her flower gardens. how high up the side of her house does the ladder reach? round to the nearest tenth, if necessary
Answer:
20.2 ft
Step-by-step explanation:
First, always draw a diagram to help you solve the problem. (See the picture below). The situation forms a right triangle. We can assume the ground and the house and perpendicular, creating the 90° angle. The ladder is the hypotenuse.
Since we have a right triangle, and we have one missing side, we can solve the problem using the Pythagorean Theorem, which is a² + b² = c². "a" and "b" are the perpendicular sides and the "c" is the hypotenuse.
Assign a variable for the missing side (not the hypotenuse!)
let "b" represent the height the ladder reaches on the house
Use the formula and substitute the other known values. Then, isolate 'b' to solve by doing the reverse operations in the reverse order of BEDMAS.
a² + b² = c²
13² + b² = 24² Substitute the two known sides.
13² - 13² + b² = 24² - 13² Subtract 13² from both sides
b² = 24² - 13² Cancelled out positive 13² on the left side
√b² = √(24² - 13²) Square root both sides
b = √(24² - 13²) "b" is isolated because √ and ² are reverse operations
b = √(576 - 169) Square the numbers inside the bracket. Subtract.
b = √407 Find the square root
b = 20.174241 Round this number to nearest tenth
b ≈ 20.2 Answer in feet units
Remember when rounding, you round either up or down depending on the digit to the right of what you are rounding to.
"The nearest tenth" is rounding to the first decimal. To the right of the first decimal is '7'. Since '7' is "5 or greater" you round up. If '7' was "4 or less", you would round down.
Therefore, the ladder reaches 20.2 feet up the side of the house.
Using the Pythagorean theorem, we find that the ladder reaches approximately 20.2 feet up the side of Denise's house when the base is placed 13 feet away from the building.
Denise is using a 24-feet long ladder and placing the base of the ladder 13 feet away from her house. To calculate how high up the side of her house the ladder reaches, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, the hypotenuse is the ladder, one side is the distance from the house, and the other side is the height the ladder reaches up the house.
To find the height (h), we can set up the equation: h^2 + 13^2 = 24^2. Calculating further, we get h^2 = 24^2 - 13^2, which simplifies to h^2 = 576 - 169. This gives us h^2 = 407. Taking the square root of both sides, we find that h is approximately 20.2 feet when rounded to the nearest tenth.
URGENT!!!!
Determine whether each number could be the probability of an event. Explain your reasoning.
1.5
1
Answer:
1.5--> Not a probability
1---> Can be a probability
Step-by-step explanation:
The range of the probability of an event is given by 0≤P(E)≤1
The probability of an event E, P(E) cannot be greater than 1.
This means P(E)≠1.5
P(E)=1 could be a probability of an event because it falls within the range.
Probability of an event being 1, means the event is certain to happen.
What fraction of an hour is 50 minutes?
Give your answer in its simplest form.
Answer:
Step-by-step explanation:
1 hour=60 mins, 50/60=5/6
The answer is 5/6
Answer:
[tex]\frac{5}{6}[/tex]
Step-by-step explanation:
The fraction is expressed as 50 over the number of minutes in an hour.
note 1 hour = 60 minutes, thus
fraction = [tex]\frac{50}{60}[/tex] ← divide (cancel ) 50 and 60 by 10
fraction = [tex]\frac{5}{6}[/tex] ← in simplest form
Amelia need 1/2 stick of butter to make cornbread he also needs one fourths stick butter to make apple muffins what fraction of a stick of butter does he need in all
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Step-by-step explanation:
Given,
Stick of butter needed to make cornbread = [tex]\frac{1}{2}[/tex]
Stick of butter needed to make apple muffins = [tex]\frac{1}{4}[/tex]
Total stick of butter needed = Cornbread + Muffins
Total stick of butter needed = [tex]\frac{1}{2}+\frac{1}{4}[/tex]
Total stick of butter needed = [tex]\frac{2+1}{4}[/tex]
Total stick of butter needed = [tex]\frac{3}{4}[/tex]
Amelia needs [tex]\frac{3}{4}[/tex] stick of butter to make cornbread and apple muffins.
Keywords: fraction, addition
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Round to estimate the quotient
199,988 ÷17
Answer:
11764
Step-by-step explanation:
199,988 ÷17 = 11764
3.4.13
E Question Help
Scott invested a total of $5900 at two separate banks. One bank pays simple interest of 12% per year while the other pays simple interest at a rate of 6% per year. If
Scott earned $540.00 in interest during a single year, how much did he have on deposit in each bank?
Scott had $ 2,800 on deposit at the bank that payed 12% interest.
Answer:
$3100 at 12%$2800 at 6%Step-by-step explanation:
Let x represent the amount on deposit at 12%. Then 5900-x is the amount deposited at 6%, and the total interest earned is ...
12%·x +6%·(5900 -x) = 540
0.06x + 354 = 540 . . . . . . . . eliminate parentheses
0.06x = 186 . . . . . . . . . . . . . . subtract 354
x = 3100 . . . . . . . . . . . . . . . . . divide by 0.06
Scott invested $3100 at 12% and $2800 at 6%.
_____
Quick sanity check
The average interest earned is $540/$5900 ≈ 0.0915 ≈ 9.15%. This is more than the average of 12% and 6%, which is (12+6)/2 = 9 percent. Hence more than half of the money must be deposited at 12%.
What is the solution to the system of equations below?
y=-3/4x+3 and y = -12
(20,–12)
(12, -12)
(6, -12)
(-12, 12)
Answer:
X = 20
Y = -12
so option A is correct
Step-by-step explanation:
since Y value is already given which is
Y = -12 so put in equation
Y = -3/4 x +3
-12- 3 = -3/4 x
-15 = - 3 / 4 x
X= -15 × - 4/ 3
X = -5 × -4
X = 20
Answer:
20,-12 aka (A)
Step-by-step explanation:
Use a fraction (in simplest form) to describe the shaded amount.
Answer:
If you have four parts. And if 3 are shaded than you answer is 3/4 are shaded. Or maybe 1/4 is not shaded.
Step-by-step explanation:
I REALLY NEED HELP!!!! WILL MAKE BRAINLIEST!!!!!!!!!!!
Two ninths of the eighteen people are eating cookies how many people are eating cookies
Answer:
4 people were eating cookies.
Step-by-step explanation:
2/9 of 18 people are eating cookies
= 2/9 × 18
= 2 × 2
=4 people
Therefore 4 people were eating cookies.
Answer:
4
Step-by-step explanation:
2/9=.222222222222 18*.222222222222=4
An equation is shown below.
3(x-2)+7x=1/2(6x-2)
How many solutions, if any, does the equation have?
Answer:
x=5/7
Step-by-step explanation:
3(x-2)+7x=1/2(6x-2)
3x-6+7x=6/2x-2/2
10x-6=3x-1
10x-3x-6=-1
7x-6=-1
7x=-1+6
7x=5
x=5/7
What is 25x^2 above 5x
Answer:
[tex] \frac{25 {x}^{2} }{5x} \\ = \frac{5 \times 5 \times x \times x}{5 \times x} \\ = 5x[/tex]
Find the area of the triangle. Show as much work as possible for full credit.
The area of a triangle is 1/2*b*h so you should be able to do it on your own now
Answer:
[tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]
Step-by-step explanation:
Area = (base*height)/2
Base = [tex]\frac{5}{6}[/tex] X
Height = X
Area = (X * [tex]\frac{5}{6}[/tex]X)/2 = [tex]\frac{5}{12}[/tex] [tex]x^{2}[/tex]
A 24 ounce mocha beverage with whipped cream has 25% of the calories allowed on a 2000 per day diet. What percentage of a 2500 calorie per day diet would this same drink constitute?
Answer:
the answer is 20 percent
Answer:
the answer would be c) 20‰
Step-by-step explanation:
Sam answered 36 questions correctly out of 60. Express his score as a percentage.
Answer:
60%
Step-by-step explanation:
36 / 60 = .6
We turn .6 into an percentage which gives 60%
Answer:
60
Step-by-step explanation:
because thunk of 30/60 that is 50 percent then at 6 and you get 60
The quotient of a number and -7 decreased by 2 is 10. find the number
Answer:
12/7
Step-by-step explanation:
2
[tex]2)x - 5) + 2 - 3(5 - 2x) = 16[/tex]
Answer:
Step-by-step explanation:
2(x-5)+2-3(5-2x)=16
2x-10+2-15+6x =16
8x-23 =16
8x =39
x = 39/8
Write the inequality that represents the sentence. The product of 7 and a number is at least 30.
seven is greater than or equal to 30
The probability that an event will happen is P(E)=
23/37. Find the probability that the event will not happen,
The probability that the event will not happen is
Answer:
14/37
Step-by-step explanation:
P(E) = 23/37
P(not E) = 1 − P(E)
P(not E) = 1 −23/37
P(not E) = 14/37
The probability that the event will not happen is approximately 0.3784 or 37.84%, calculated by subtracting the probability of the event from 1.
Explanation:In probability, the likelihood of an event occurring and not occurring always adds up to 1. This principle is called the Law of Total Probability.
Given the probability that the event will happen is P(E)= 23/37. To find the probability that the event will not happen, you need to subtract the probability of the event occurring from 1.
So, the probability that the event will not happen, often written as P(E') or P(not E), is calculated as follows:
First convert the fraction 23/37 to a decimal. This equals approximately 0.6216.Then, subtract this decimal from 1. This equals approximately 0.3784.Therefore, the probability that the event will not happen is approximately 0.3784 or 37.84%.
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what is 0.8 written as a decimal?
Answer:
8/10
Step-by-step explanation:
I think that you are probably looking for 0.8 as a fraction because it is a decimal already.
So, 0.8 means %80 such as 8 points out of 10 points
This can be represented as 8/10
There are also many other ways to write it, but it will always simplify down to 4/5. Example: 8/10, 16/20, 24/30
Answer:0.008
Step-by-step explanation:
does Y-9 equal 6+x. Why or why not
Answer: NO
Step-by-step explanation:
it is not because they have two different variables x and y
and has different constant values +6 and -9
Height:10
radius: 3
What is the volume of the cone to the nearest whole number?
A) 31 m3
B) 94 m3
C) 188 m3
D) 283 m3
Answer:
It is 94
Step-by-step explanation:
The volume of a cone with a height of 10 meters and a radius of 3 meters is
94 m³.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, A cone has a radius of 3 meters and a height of 10 meters.
Therefore, The volume of this cone is,
= (1/3)π(3)²×10 m³.
= 30π m³.
= 30×3.14 m³.
= 94.2 m³ or 94 m³.
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A town’s population of children increased from 376 to 421 during the past year.
Which equation shows how to find the percent increase?
A. p=421−376
376
B. p=421−376
421
C. p=376
421−376
D. p=376+421
376
The equation shows how to find the percent increase:
[tex]Percent\ increase = \frac{421-376}{376} \times 100[/tex]
Solution:
Given that,
A town’s population of children increased from 376 to 421 during the past year
To find: percent increase
The percent increase is given by formula:
[tex]\text{Percent increase} = \frac{\text{Final value - initial value}}{\text{initial value}} \times 100[/tex]
From given,
Initial value = 376
Final value = 421
[tex]Percent\ increase = \frac{421-376}{376} \times 100\\\\Percent\ increase = \frac{45}{376} \times 100\\\\Percent\ increase = 11.968 \%[/tex]
Thus the equation is found and solved
Answer: b. 2+2=+=./.'+2009+4=69
Step-by-step explanation:
am pro
can someone help me??
Answer:
1st option: 60°
Step-by-step explanation:
Please see attached picture for full solution.
Answer:
1st option: 60°
Step-by-step explanation:
Please see attached picture for full solution.
Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.
a) Who is correct, Aaron or Blake?
b) Cite evidence to support your claim.
c) Explain your thinking.
Answer:
a) I think Aaron is correct.
Step-by-step explanation:
Aaron and Blake are having a disagreement during math class. Aaron says 0.3838 is a terminating decimal while Blake says it's a repeating decimal.
a) I think Aaron is correct.
b) If we convert the decimal into fraction then this will give
[tex]0.3838 = \frac{3838}{10000} = \frac{1919}{5000}[/tex]
c) So the fraction [tex]\frac{1919}{5000}[/tex] has an exact value of 0.3838 and this does not repeat. Hence, this is a terminating decimal. (Answer)
form the intersection for the followng set
X={0,10,100,1000}
Y={100,1000}
X ∩ Y =
Answer:
x=0
Step-by-step explanation:
The radius of a circle is 4 yards. What is the circle’s circumference?
Answer:
25.13
Step-by-step explanation:
The formula of a circumference of a circle is C= 2x π x r
c = 2x π x 4 yards
c= 25.13 yards
The table shows equivalent ratios. Find the missing numbers in the table.
x y
2
4 16
6 24
8
Answer:
(2,8) and (8,32)
Step-by-step explanation:
ratios can be written as x:y or x/y
so look at what is given
(4,16)....4/16 reduces to 1/4
(6,24)...6/24 reduces to 1/4
so the pattern is ur either dividing y by 4 and getting x....or ur multiplying x by 4 and getting y
and since ur other 2 points given dont have y, we will multiply x by 4 to get y.
(2,y).....lets multiply x, which is 2, by 4......2 * 4 = 8
so ur point is (2,8)
(8,y).....multiply x, which is 8, by 4.....8 * 4 = 32
so ur point is (8,32)