Answer:
49.8 degrees celcius
Step-by-step explanation:
Does a triangle with these side lengths exist?
28, 41, 13
Answer:
No
Step-by-step explanation:
it doesnt add up to 180 degrees
Use the triangle inequality theorem.
Add two sides together and see if it is greater than the length of the 3rd side:
28 + 41 = 69 which is greater than 13
41 + 13 = 54 which is greater than 28
28 + 13 = 41 this is equal to the 3rd side length of 41 and not greater than 41
Because 28 + 13 is not greater than 41 those 3 lengths cannot make a triangle.
Fourteen less children’s meals were served than adult meals at a barbecue. Children plate were 1.50 each and adult plates were 2.00 each . If the total amount of money collected was 441 , how much of each type of plate was served
Answer:
134 children and 120 adult plates were served
Step-by-step explanation:
let the children mean be x
Let the adult meal be y
If fourteen less children’s meals were served than adult meals at a barbecue, then;
y = x - 14 .... 1
IF Children plate were 1.50 each and adult plates were 2.00 each with a total of 441 in amount then;
1.5x + 2y = 441 .... 2
Substitute 1 into 2;
1.5x + 2(x-14) = 441
1.5x+2x-28 = 441
3.5x = 441+28
3.5x = 469
x = 469/3.5
x = 134
Recall that y = x - 14
y = 134-14
y = 120
Hence 134 children and 120 adult plates were served
Find the least common denominator for the following pair of rational expressions. 2/(k ^ 2 + 5k) and 8/(k ^ 2 + 2k - 15)
Answer:
\(k(k-3)(k+5)\)
Step-by-step explanation:
\(k^2+5k=k(k+5) \\ \\ k^2 + 2k-15=(k+5)(k-3)\)
So, the least common denominator is \(k(k-3)(k+5)\).
Simplify 4 square root of 72
Simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
As given in the question,
Given expression,
4 square root of 72
Prime factors of 72 are as follow:
72 = 2 × 2 × 2 × 3 × 3
Rewrite them into exponent form we get
72 = 2³ × 3²
Simplification of the given expression 4 square root of 72 is
4√72
= 4 × √ 2³ ×3²
= 4 × √ 2² × 2 × 3²
Calculate the square root
= 4 ×2 ×3 √2
= 24√2
= 24 ×1.414
= 33.94
Therefore, simplification of the given expression 4 square root of 72 is equal to 24√2 or 33.94.
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A company installs a rectangular septic tank 10 ft long by 15 ft wide and 8 ft deep. Calculate the capacity of the tank in gallons. (Use 1ft^3 = 7.48 gal.)The capacity of the tank is:enter your response here gallons. (Round to the nearest gallon as needed.)
To find the capacity in gallons we firs need to find the volume.
The volume is given by:
\(V=lwh\)Plugging the values given we have:
\(V=(10)(15)(8)=1200ft^3\)Now that we know that we need to convert it, to do this we multiply by the factor given:
\(1200(7.48)=8976\)Therefore the capacity of the tank is 8976 gal
The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. Which equation can be used to find the value of x?
Answer:
the equation is : 7x + 15 + 15 = 17xand x = 3Step-by-step explanation:
The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. Which equation can be used to find the value of x?
7x + 15 + 15 = 17x
30 = 10x
x = 3
--------------------
check
7×3+15+15=17×3
21 + 30 = 51
51=51
the answer is good
Answer:
17x=30+7x
Step-by-step explanation:
Find the area of the following figure. Explain how you got your answer.
Answer:
26.5
Step-by-step explanation:
cut the shape into 3 shapes
area of a retangle is = L*W= 5*4 = 20
Area of a triangle = a= h*b/2 = 3*3/2 = 4.5
Area of a triangle = a= h*b/2 = 2*2/2 =2
A minor league baseball park has 6800 seats. Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200. If the number of bleacher seats is 2 times the number of box seats, how many seats of each type are there?Box seats:_______ Grandstand seats:_______ Bleacher seats:______
Answer:
Step-by-step explanation:
Let us represent
The number of Box seats = x
The number of grandstand seats = y
The number of bleacher seats cost = z
A minor league baseball park has 6800 seats.
Hence,
x + y + z = 6800
Box seats cost $19, grandstand seats cost $9, and bleacher seats cost $4. When all seats are sold, the revenue is $61200.
Hence:
$19 × x + $9 × y + $4 × z = $61200
19x + 9y + 4 z = 61200
If the number of bleacher seats is 2 times the number of box seats
z = 2x
Hence we substitute
x + y + z = 6800
x + y + 2x = 6800
3x + y = 6800.... Equation 3
y = 6800 - 3x
For Equation 2, substituting 2x for z
19x + 9y + 4z = 61200
19x + 9y + 4(2x) = 61200
19x + 9y + 8x = 61200
27x + 9y = 61200...... Equation 4
Combining Equation 3 and 4
3x + y = 6800.... Equation 3
27x + 9y = 61200...... Equation 4
Note that:
y = 6800 - 3x
We substitute the above in Equation 4
27x + 9(6800 - 3x) = 61200
27x + 61200 - 27x = 61200
Box seats:_______ Grandstand seats:_______ Bleacher seats:______
Marcus has a life insurance policy that will pay his family $35,000 per year if
he dies. If interest rates are at 2.5% when the insurance company has to pay,
what is the amount of the lump sum that the insurance company must put
into a bank account?
O
A. $1 million
O
B. $350,000
O
C. $1.4 million
O
D. $3.5 million
The correct answer is $1.4 million
The insurance company must put $1.4 million into a bank account.
What is insurance?Insurance is a way to manage your risk. When you buy insurance, you purchase protection against unexpected financial losses. The insurance company pays you or someone you choose if something bad happens to you.
Given that, Marcus has a life insurance policy that will pay his family $35,000 per year if he dies. the interest rates are at 2.5%, we need to find the amount of the lump sum that the insurance company must put into a bank account,
Considering that the interest is Simple interest,
So, SI = PRT / 100
Here, the interest is 35000, P we need to find, r = 2.5 and T = 1
35000 = 2.5P/100
3500000 = 2.5P
P = 1400000
P = 1.4 millions
Hence, the insurance company must put $1.4 million into a bank account.
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Find x in this equation
Answer:
5
Step-by-step explanation:
\(\triangle HBK \cong \triangle NBK\) by SAS. Using CPCTC, \(3x=x+10 \implies 2x=10 \implies x=5\).
A tank that is 40% full contains 640 gallons of water. What it's full capacity?
Answer:
1,600
Step-by-step explanation:
a container of water has 1/4 water and 1/3 oil. how much is the fraction of the empty space
The Fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.
The container is made up of two substances: water and oil. We know that the container has 1/4 water and 1/3 oil. This means that the remaining space in the container is made up of neither water nor oil, i.e., empty space.
To find the fraction of empty space, we need to add the fractions of water and oil together and subtract them from 1. This is because the sum of the fractions of water, oil, and empty space must equal 1, which represents the total volume of the container.
The fraction of water in the container is 1/4, and the fraction of oil is 1/3. Therefore, the fraction of the container that is not empty is:
1/4 + 1/3 = 3/12 + 4/12 = 7/12
To find the fraction of empty space, we subtract this fraction from 1:1 - 7/12 = 5/12
Therefore, the fraction of empty space in the container is 5/12. This means that 5/12 of the container is not filled with water or oil, and is instead empty.
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756 divided by 36
plz need help
Answer:
21
Step-by-step explanation:
I did the math.
Answer:
756 divided by 36 = 21
half of the quantity of 6 less than a number f is 4
Answer:
I believe 10
Step-by-step explanation:
the reason I believe it is 10 is because that is the main mathematical explanation for this equation
If x < 0 and y > 0, where is the point (x, y) located?
Answer:
(x,y) is in the Quadrant II.
Step-by-step explanation:
The Quadrant II contains the x-values that are less than 0 (negative x-values), while the y-values are greater than 0 (positive y-values). Therefore, if x < 0 and y > 0, then point (x, y) must be somewhere in Quadrant II of the Cartesian Plane.
Please mark my answers as the Brainliest if my explanations were helpful :)
Find the 52nd term of the sequence
3,7,11,15
Answer: 3,7,11,15
Step-by-step explanation: Not the right explanation and answer.
What is 43% as a decimal
Answer:
The answer to the question provided is
.43
➼ Move the decimal two places over to the right.
three cards are drawn from an ordinary desk and not replaced
find probability a.getting 3 jackets
Answer:
Assuming you meant three jacks:
1 in 5525 or else 1/5525.
Step-by-step explanation:
You start with a full deck of 52 and 4 jacks. After each draw, you reduce both the jacks and total deck by one. Your first draw would be 4/52. The next would be 3/51. The final draw would be 2/50. You multiply each fraction together as you need all of them to happen, and that is your odds of drawing 3 jacks in a row without replacement.
Tiana is looking up her county's census data for a school project. Her county conducts a census every decade. She finds that the population was about 641,000 the year she was born, and that it had decreased to about 634,590 a decade later. Tiana reads that the population of the county is expected to continue decreasing each decade.
Write an exponential equation in the form y=a(b)x that can model the county population, y, x decades after Tiana was born.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How many decades after Tiana was born will the county population fall below 600,000?
decades
The exponential function that can model the county population, y, x decades after Tiana was born, is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 in 6.6 decades after Tiana was born.
What is an exponential function?The definition of the exponential function is presented as follows:
\(y = a(b)^x\)
In which the parameters of the exponential function are presented as follows:
a is the initial value.b is the rate of change.In the context of this problem, the values of these parameters are given as follows:
a = 641000, which is the initial population.b = 634590/641000 = 0.99.Hence the function is:
\(y = 641000(0.99)^x\)
The population will fall below 600,000 when y = 600000, hence:
\(y = 641000(0.99)^x\)
\(600000 = 641000(0.99)^x\)
\((0.99)^x = \frac{600000}{641000}\)
\(\log{(0.99)^x} = \log{\left(\frac{600000}{641000}\right)}\)
\(x\log{0.99} = \log{\left(\frac{600000}{641000}\right)}\)
\(x = \frac{\log{\left(\frac{600000}{641000}\right)}}{\log{0.99}}\)
x = 6.6 decades.
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roman spent $24 of the $30 in his wallet. What percent represents the fraction of $30 james spent
This year, the ratio of Alan's age to Bernice's age is 1:2. Four years ago, the total age of Alan and Bernice was 55 years. How old is Alan this year?
Answer:
21 years old
Step-by-step explanation:
Set Alan's age as x, Bernice's age as y
2x=y
x-4+y-4=55
x+y=63
3y=63
x=21
y=42
Is 8/18 closer to 0 1/2 or 1
Answer:
Closer to 1\2
Step-by-step explanation:
half of 18 is 9 and if you add 1 to 8 you get 9 so 8\18 is closer to 1\2
Hope it helps!
Solve for x and graph the answer on a number line
2
The solution to the system of inequalities in interval notation is [-2, 1].
How to solve the system of inequalities?Based on the information provided in the image below, we have the following system of inequalities;
-12 < 3x - 6
-3 ≥ 3x - 6
By adding 6 to both sides of the equation (inequality), we have;
-12 < 3x - 6
-12 + 6 < 3x - 6 + 6
-6 < 3x
-2 < x
x > -2 (flip)
-3 ≥ 3x - 6
-3 + 6 ≥ 3x - 6 + 6
3 ≥ 3x
1 ≥ x
x ≤ 1
Therefore, the solution to the system of inequalities is given by:
-2 < x ≤ 1
In interval notation, we have [-2, 1].
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
9(2n+1) help please brooooooo
Answer:
18n + 9
Step-by-step explanation:
Distribute 9 into the expression.
9*2n = 18n
9*1 = 9
18n + 9
in a typical bag of skittles, the ratio of red to yellow skittles is 3 to 7. If there are 40 skittles altogether, how many red skittles are there?
Answer:
I love Skittles
what's your favorite color?
Customers blah blah blah blah
Answer:
blah
Step-by-step explanation:
blah + blah = blah
blah x blah = blah
blah / blah = blah
blah - blah = blah
Find the value of x
Answer: 11
Step-by-step explanation:
By the angle bisector theorem,
\(\frac{3x-3}{5x}=\frac{24}{44}\\\\44(3x-3)=24(5x)\\\\132x-132=120x\\\\12x-132=0\\\\ 12x=132\\\\x=\boxed{11}\)
Which expressions are polynomials?
Select each correct answer.
2 + s
4x^3 + y
x^2 - x squared + 2
y
Answer:
The third one
Step-by-step explanation:
A line is represented by the equation y/x−2=3/11 . Select all the coordinates of points that lie on the line.
Select one or more:
a. (2, 0)
b. (-16/3, -2)
c. (8, 5/2)
d. (0, 0)
e. (1, 2)
f. (5, 9/11)
The coordinate of the point that lies on the line is (2,0)
How to determine the coordinates of points on a line?Given y/x−2=3/11
In order to find the coordinates of points that lie on the line:
First, find the value of x when y = 0:
y/x−2=3/11, when y = 0:
0/x−2=3/11
3(x-2) = 0
3x -6 = 0
3x = 6
x = 6/3 = 2
Also, find the value of y when x = 0:
y/x−2 = 3/11 when x = 0:
y/0−2 = 3/11
y/-2 = 3/11
11y = -6
y = -6/11
Since the coordinates of the two points are (2,0) and (0,-6/11 ). Therefore, option a with the coordinate (2,0) is the answer.
Therefore, the values to be plotted on our graph are (0, 1) and (-0.2, 0). The image of the graph is attached
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consider the following graph. the x y coordinate plane is given. the curve begins at the origin, goes up and right becoming less steep, the curve changes direction at (1, 3), goes down and right becoming more steep, passes through (2, 2), goes down and right becoming less steep, changes directions at (3, 1), goes up and right becoming more steep, passes through the point (4, 3), goes up and right becoming less steep, passes through (5, 4) almost horizontally, goes up and right becoming more steep, passes through the approximate point (6, 4.2) and ends at (7, 6). (a) find the interval(s) on which f is increasing. (enter your answer using interval notation.) (b) find the interval(s) on which f is decreasing. (enter your answer using interval notation.) (c) find the interval(s) on which f is concave upward. (enter your answer using interval notation.) (d) find the interval(s) on which f is concave downward. (enter your answer using interval notation.) (e) find the coordinates of the inflection point(s). (order your answers from smallest to largest x, then from smallest to largest y.) (x, y)
(a) The function f is increasing on the intervals [0,1) and (3,7].
(b) The function f is decreasing on the interval [1,3].
(c) The function f is concave upward on the intervals [0,1) and (4,7].
(d) The function f is concave downward on the intervals [1,4].
(e) The inflection points occur at (1,3) and (4,3).
(a) The function f is increasing on the intervals where its slope is positive.
Based on the description of the graph, f is increasing on the following intervals: (0, 1) and (3, 7).
So, in interval notation, the answer is: (0, 1) ∪ (3, 7).
(b) The function f is decreasing on the intervals where its slope is negative.
Based on the description of the graph, f is decreasing on the following interval: (1, 3).
So, in interval notation, the answer is: (1, 3).
(c) The function f is concave upward on the intervals where its second derivative is positive.
Based on the description of the graph, f is concave upward on the following intervals: (0, 1) and (3, 5).
So, in interval notation, the answer is: (0, 1) ∪ (3, 5).
(d) The function f is concave downward on the intervals where its second derivative is negative.
Based on the description of the graph, f is concave downward on the following interval: (1, 3) and (5, 7).
So, in interval notation, the answer is: (1, 3) ∪ (5, 7).
(e) Inflection points occur where the function's concavity change.
Based on the description of the graph, there are three inflection points: (1, 3), (3, 1), and (5, 4).
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