Answers
3x + 3 + 2x + 22 = 180
Combining like terms,
(3x + 2x) + (3 + 22) = 180
Simplifying,
5x + 25 = 180
Transpose the constants to only one side of the equation,
5x = 155
Divide the equation by 5.
x = 31
ANSWER: x = 31
Related Questions
The Kwon family has a rainwater catchment system they use to water their garden. After 3 days without rain, the depth of water in the tank is 63 inches. After 5 days, the depth is 57 inches. What will the depth of water in the tank be after 17 days?
Answers
if d = 3
f(d) = 72 -3d = 72 - 3(3) = 72 - 9 = 63 inches
if d = 5
f(d) = 72 -3d = 72 - 3(5) = 72 - 15 = 57 inches
so
if d = 17
f(d) = 72 -3d = 72 - 3(17) = 72 - 51 = 21 inches
answer
the depth of water in the tank will be 21 inches after 17 days
63-57 = 6 inches in 2 days
6/2 = 3 inches per day
17-5 = 12
12*3 =36 inches in 12 days
57-36 = 21 inches after 17 days
A rectangular garden has a length of 12 feet. You need 36 feet of fencing to enclose the garden. What is the width of the garden.
Answers
Equation and steps:
12+12+x+x=36 x= width of the garden
24+2x=36
2x=12
x=6
The width of the rectangular garden is 6 feet with a perimeter of 36 feet.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, A rectangular garden has a length of 12 feet.
Assuming the width of the garden to be x feet.
We know the perimeter of a rectangle is 2(length + width).
∴ 2(12 + x) = 36.
24 + 2x = 36.
2x = 12.
x = 6 Or the width is 6 feet.
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You place a cup of 200 degrees F coffee on a table in a room that is 67 degrees F, and 10 minutes later, it is 195 degrees F. Approximately how long will it be before the coffee is 180 degrees F? Use Newton's law of cooling: T(t)=T[a]+(T[o]-T[a])e^-kt A. 40 minutes B. 15 minutes C. 1 hour D. 35 minutes
Answers
195=67+133e^(-10k)
128=133e^(-10k)
128/133=e^(-10k)
ln(128/133)=-10k
k=-ln(128/133)/10
T(t)=67+133e^(tln(128/133)/10), if T(t)=180
180=67+133e^(tln(128/133)/10)
113=133e^(tln(128/133)/10)
113/133=e^(tln(128/133)/10)
ln(113/133)=tln(128/133)/10
10ln(113/133)=tln(128/133)
t=10ln(113/133)/ln(128/133)
t≈42.5 minutes...
t≈40 minutes (to nearest 5 minutes? :P)
short but other than that same as the the other guy
Regroup to express the number in a different way , please help
Answers
hope it helps
Use the direct variation equation y=x/4 to solve for x when y =60
Answers
60 = x / 4
or:
60 = x : 4
x = 60 * 4
Answer: x = 240
The first card selected from a standard 52-card deck was a king. if it is not returned to the deck, what is the probability that a king will be drawn on the second selection?
Answers
there would be 3 kings left and 51 cards left
so it would be a 3/51 which reduces to 1/17 probability
The probability of drawing a king from a 52-card deck on the second draw, given that a king was drawn on the first draw and was not replaced, is 1 in 17.
Explanation:The question pertains to the concept of probability, specifically with regards to sampling without replacement in a 52-card deck. First, let's identify the elements: there are 4 kings in a 52-card deck. When one king is drawn and not replaced, there are now 51 cards left with 3 kings.
The probability of drawing a king on the second draw, with the first king not replaced, is the number of favorable outcomes (drawing a king) divided by the total number of outcomes (total cards left). Hence, the probability is 3/51 = 1/17.
This means that there is 1 chance in 17 of drawing a king on the second draw if a king has been drawn on the first draw and not replaced.
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Add or subtract the following mixed numbers using the first method. Be sure your answers are in mixed number format and reduced to lowest terms. 3 3/8 + 2 1/6 =
Answers
by using the first method,
multiplying 3/8 with 3/3 and 1/6 with 4/4 we get 9/24 and 4/24 so,
3 9/24 + 2 4/24 = (3+2) and (9/24 + 4/24)
when adding 3 and 2 we get 5 and adding 9/24 and 4/24 we get 13/24
so the answer is 5 and 13/24
You have just purchased a 10-year, $1,000 par value bond. the coupon rate on this bond is 8 percent annually, with interest being paid each 6 months. if you expect to earn a 10 percent simple rate of return on this bond, how much did you pay for it?
Answers
I=(1000×0.08)/2=40
(PVIFA kd, n)=((1−(1+0.1÷2)^(−2×10))
÷(0.1÷2))
Mv =1000
(PVIF kd, n) =1÷(1+0.1÷2)^(2×10))
So the answer is
V=40×((1−(1+0.1÷2)^(−2×10))
÷(0.1÷2))+(1,000÷(1+0.1÷2)^(2×10))
=875.38...answer
Tommy has a piece of toast that has butter on one side, and he dropped it twice. Both times, it landed with the butter side up. If he drops it two more times, what is the probability that it will have landed butter side up a total of three times?
Answers
Answer: The required probability is 50%.
Step-by-step explanation: Given that Tommy has a piece of toast that has butter on one side.
The first two times dropped the piece, it landed with the butter side up.
We are to find the probability that the piece will have landed butter side up a total of three times, if he drops it two more times.
For the butter side to be landed up three times, one of the last two drops must land butter side up.
Let, 'S' denotes the sample space for the experiment of dropping the piece for the last two times, then
n(S) = 2.
Let, 'B' be the event of getting one of the last two drops landed butter side up, then
n(B) = 1.
Therefore, the probability of getting one of the last two drops landed butter side up will be
[tex]P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{2}=50\%.[/tex]
Thus, there is 50% probability of landing butter side up a total of three times.
Evaluate the limit, if it exists. (if an answer does not exist, enter dne.)lim h → 0 (x + h)3 − x3h
Answers
[tex]\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h[/tex]
Now, if you're familiar with the definition of the derivatives, you'll notice that this is the limit form of the derivative of the function [tex]f(x)=x^3[/tex], which you may also know to be [tex]3x^2[/tex]. But let's assume you don't know that just yet, and that it's actually the result you intend to find.
Expand the numerator:
[tex]\dfrac{(x+h)^3-x^3}h=\dfrac{(x^3+3x^2h+3xh^2+h^3)-x^3}h=\dfrac{3x^2h+3xh+h^3}h[/tex]
Now, when [tex]h\neq0[/tex], we can divide through by the lowest power of [tex]h[/tex]. We can do this because we're considering the limit as [tex]h[/tex] is *approaching* 0, and not when it actually takes on the value of [tex]h=0[/tex].
[tex]\dfrac{(x+h)^3-x^3}h=3x^2+3xh+h^2[/tex]
Now, as [tex]h\to0[/tex], we can see only the leading term remains, so that
[tex]\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h=3x^2[/tex]
as expected.
To evaluate the limit of (x + h)³ - x³h as h approaches 0, we can expand the expression using the binomial theorem and simplify. The resulting expression can be factored to show that as h approaches 0, the entire expression becomes 0. Therefore, the limit is 0.
Explanation:To evaluate the given limit, we can start by expanding the expression (x + h)³ using the binomial theorem. This gives us (x³ + 3x²h + 3xh² + h³) - x³h. Simplifying further, we can cancel out the x³ terms and obtain 3x²h + 3xh² + h³ - x³h. Now, we can factor out h from the expression to get h(3x² + 3xh + h² - x³). As h approaches 0, the entire expression becomes 0, since h is being multiplied by a polynomial that does not contain h. Therefore, the limit is 0.
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Round to the nearest while decimal 6.7
Answers
Then, [tex]six [/tex] is rounded [tex]1ten[/tex] & [tex]seven[/tex] is rounded to [tex]ten [/tex]
Your answer: [tex]7[/tex]
[tex]good\\luck \\ on \\ your \\ assignment \\ \\ \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ \\ \\ MeIsKaitlyn :)[/tex]
-1/9 - (-2/15)
write in simplest form
Answers
= -1/9 +2/15
= -5/45 + 6/45
= 1/45
What is the cube root of 0?
Answers
The cube root of 0 is 0; this is because 0 multiplied by itself three times is 0.
The cube root of 0 is simply 0. This is because any number, when multiplied by itself three times, which is what we are doing when we take the cube of a number, that results in 0, must have been 0 to start with. The cube root operation is asking us what number, when cubed, gives us the original number, and in the case of 0, 0³ equals 0. Therefore, the cube root of 0 is 0.
Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $500 item is $30, what is the sales tax on a $900 item?
Answers
cross multiply
(500)(x) = (900)(30)
500x = 27000
x = 27000/500
x = 54 <===
Answer: $54
Step-by-step explanation:
The equation to show the direct variation in two quantities x and y is given by :-
[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]
The tax on a $500 item is $30.
Let 'x' be the sales tax on a $900 item.
Then , we have the following equation:-
[tex]\dfrac{x}{900}=\dfrac{30}{500}\\\\\Rightarrow\ x=\dfrac{900\times30}{500}\\\\\Rightarrow\ x=54[/tex]
Hence, the sales tax on a $900 item = $54
Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.
Answers
A farmer is going to plant carrots on 5 3/14 acres, corn on 4 23/42 acres and peppers on 2 5/21 acres. If each acre requires 6 bags of fertilizer, how many bags of fertilizer does the farmer need to plant all the acres?
Answers
so
[tex]\bf 5\frac{3}{14}\implies \cfrac{5\cdot 14+3}{14}\implies \cfrac{73}{14} \\\\\\ 4\frac{23}{42}\implies \cfrac{4\cdot 42+23}{42}\implies \cfrac{191}{42} \\\\\\ 2\frac{5}{21}\implies \cfrac{2\cdot 21+5}{21}\implies \cfrac{47}{21}\\\\ -------------------------------\\\\ \cfrac{73}{14}+\cfrac{191}{42}+\cfrac{47}{21}\impliedby \textit{our LCD is just 42}\implies \cfrac{3\cdot 73+1\cdot 191+2\cdot 47}{42} \\\\\\ \cfrac{219+191+94}{42}\implies \cfrac{504}{42}\implies \cfrac{12}{1}\implies 12[/tex]
now, that's how many acres the farmer has in total
now, if each acre takes 6 bags of fertilizer, well, you surely know how much that is.
How much water should be added to 14 mL of 15% alcohol solution to reduce the concentration to 7%?
Answers
To decrease the concentration of a 15% alcohol solution to 7%, 16 mL of water needs to be added to the original 14 mL solution.
Explanation:The problem involves using the concept of concentration dilution that is C1V1 = C2V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
First, we need to convert the percentage to decimal so, C1=0.15 (15% as a decimal) and C2=0.07 (7% as a decimal). We know V1=14 mL (the starting volume of the 15% alcohol solution) and we are solving for V2.
Insert the known values into the equation and solve for V2: (0.15)(14) = (0.07)(V2). After calculation, V2 is approximately 30 mL.
To figure out how much water should be added to reduce the concentration from 15% to 7%, subtract the initial volume from the final volume: 30 mL - 14 mL = 16 mL.
So 16 mL of water needs to be added to the 15% alcohol solution to reduce the concentration to 7%.
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this figure is a regular 12 sided polygon and measure of a angle is 4
Answers
What percent of 28.8 is 3.6?
Answers
divide them:
3.6/28.8 = 0.125
0.125 = 12.5%
16 less than one-fourth of some number, w" can be expressed algebraically as
Answers
"one-fourth some number w"= w/4
So together
w/4-16
Find the value of y, rounded to the nearest tenth. Please help me, I'd appreciate it!!
Answers
y² = 7(15+7)
y² = 7*22
y² = 154
y = √154
y = 12.4 ← to the nearest tenth
A total of 634 tickets were sold for the school play. They were either adult tickets or student tickets. There were 66 fewer students tickets sold than adult tickets. Him many adult tickets were sold?
Answers
y= adult tickets
x+y=634
y=x-66
x+y=634 x-y=66 2x=700 x=350
350+y=634 y=284
So say adult sold would be x, then student sold would be x-66
add them
x+x-66=634 solve for x
2x=700 divide each side by 2
x=350
so 350 adult and 350-66=284 student
Suppose y varies directly with x, and y = 8 when x = –6. What direct variation equation relates x and y? What is the value of y when x = –2?
Answers
Answer:
Direct variation states that the relationship between two variables in which one is a constant multiple of the other one.
In other words, when one variable changes the other one changes in proportion to the first.
i.e, if y is directly proportional to x then, the equal will be of the form is, y= kx where k is the constant of variation.
Given: y varies directly with x, and y = 8 when x = –6
By definition of direct variation,
y = kx
Substitute the values of x = -6 and y=8 to solve for k;
8 = -6k
Divide both sides by -6 we get;
[tex]k = -\frac{8}{6} = -\frac{4}{3}[/tex]
Now, to find the value of y when x = 2 we have;
[tex]y = -\frac{4}{3}x[/tex]
Substitute the given value of x =-2 we have;
[tex]y = -\frac{4}{3} \cdot -2 = \frac{8}{3}[/tex]
Therefore, the direct variation related x and y is, [tex]y = -\frac{4}{3}x[/tex]
and the value of [tex]y =\frac{8}{3}[/tex] when x = -2
I really suck at math. please help =)
Answers
How many millimeters are there in 5 meters?
Answers
1 meter = 1000 mm
so 5 meters = 5 x 1000 = 5,000 millimeters
james put $1000 in a 2-year CD paying 7% interest, compounded monthly.
Answers
A=p (1+r/k)^kt
A future value?
P present value 1000
R interest rate 0.07
K compounded monthly 12
T time 2 years
A=1,000×(1+0.07÷12)^(12×2)
A=1,149.81
Answer with explanation:
Principal = $ 1000
Time = 2 years
Rate of Interest = 7 %
Since of rate of interest is compounded monthly,
then, [tex]R=\frac{7}{12}\\\\T=2 \times 12 =24[/tex]
Amount after 2 years
[tex]=P\times [1 +\frac{R}{100}]^T\\\\=1000 \times [1+\frac{7}{1200}]^{24}\\\\=1000 \times [\frac{1207}{1200}]^{24}\\\\=1000 \times (1.00583)^{24}\\\\=1000\times 1.14972\\\\=1149.72[/tex]
Amount after 2 years, when rate of interest, is compounded monthly=$ 1149.72
In a study of blood donors, 200 were classified as group O and 250 had a classification other than group O. What is the probability that a person will have group O blood? (Enter your answer as a fraction.)
Answers
It always works like this.
P(O) = 200/450 = 4/9
24x2+25x−47=(−8x−3)(ax−2)−53
Answers
the question is : find : a
24x²+25x−47=(−8x−3)(ax−2)−53
= -8ax²+16x-3ax +6-53
= -8ax²+16x-3ax - 47
24x²+25x−47= -8ax² + (16-3a)x -47
so : -8a = 24
16-3a =25
a = 24/-8 = -3
16-3(-3) =25...right
conclusion : a = = -3
Help!
During exercise, the recommended maximum heart rate in beats per minute is modeled by the formula, M = 176 – 0.8A, where M is the maximum heart rate and A is the person’s age. Solve the formula for A. At what age would you have a recommended maximum heart rate in beats per minute of 140?
A) 40 years
B) 50 years
C) 25 years D)
45 years
Answers
140= 176-0.8A
+.8A. +0.8A
140 + .8A = 176
-140. -140
.8A= 36
/.8. /.8
A = 45
18000 decrease by 15% every year for 3 years
Answers
2nd year= 15300 x 0.85 = 13005
3rd year= 13005 x 0.85= 11054.25