Answer:
r={21}
Step by Step Explanation:
PREMISES
Two times three plus a number, say, r=27
ASSUMPTIONS
Let r=the number
CALCULATIONS
The numerical expression “two times three plus a number r=27” can be denoted as:
(2×3)+r=27
6+r=27
6–6+r=27–6
0+r=27–6
r=21
PROOF
If r=21, then the equations
(2×3)+r=27
6+21=27 and
27=27 prove the root (zero) r=21 of the statement (2×3)+r=27
PREMISES
Two times three plus a number, say, r=27
ASSUMPTIONS
Let r=the number
CALCULATIONS
The numerical expression “two times three plus a number r=27” can be denoted as:
(2×3)+r=27
6+r=27
6–6+r=27–6
0+r=27–6
r=21
PROOF
If r=21, then the equations
(2×3)+r=27
6+21=27 and
27=27 prove the root (zero) r=21 of the statement (2×3)+r=27
Answer:
5 and 6
Step-by-step explanation:
let the 2 numbers be x and y , then
3x + 2y = 28 → (1)
2x + 3y = 27 → (2)
multiplying (1) by 2 and (2) by - 3 and adding will eliminate x
6x + 4y = 56 → (3)
- 6x - 9y = - 81 → (4)
add (3) and (4) term by term to eliminate x
0 - 5y = - 25
- 5y = - 25 ( divide both sides by - 5 )
y = 5
substitute y = 5 into either of the 2 equations and solve for x
substituting into (1)
3x + 2(5) = 28
3x + 10 = 28 ( subtract 10 from both sides )
3x = 18 ( divide both sides by 3 )
x = 6
The 2 numbers are 6 and 5
Pythagorean Theorem
(Rounding)
Find the length of the third side. If necessary, round to the nearest tenth.
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the answer is 3.5
Step-by-step explanation:
c² ::: a² + b²
(4)² ::: (2)² + b²
16 ::: 4 + b²
16-4 ::: b²
/12 ::: b2
b ::: 3.5
Which number is rational?
Ov2
M
O 10
O 16
O √2
O π
O √10
✔ O √16
rational numbers are decimals, whole numbers, fractions.
√16 = 4 || which is whole numberπ and √a for non whole numbers fall under irrational numbersA rental car costs $15 a day plus 25 cents for each mile driven. Which
expression shows the cost to rent a car for 1 week and drive 200 miles?
A. (15.25 x 7) + 200
B. (0.25 x 7) + (15 x 200)
C. (15 x 7) + (0.25 x 200)
D. 15 + (0.25 x 200
The expression that shows the cost to rent a car for 1 week and drive 200 miles is (15 × 7) + (0.25 × 200)
The problem can be modelled to a linear equation.
Linear equationLinear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
y = total cost of the rental
x = mile driven
Hence,
y = 0.25x + 15
Therefore, the expression that shows the cost to rent a car for 1 week and drive 200 miles is as follows:
(15 × 7) + (0.25 × 200)learn more on linear equation here: https://brainly.com/question/1550434
I also need help with these! It would mean a lot.
Please help me on this question
Answer:
V = £21,012.50
Step-by-step explanation:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of times periods elapsedGiven:
A = VP = £20,000r = 2.5% = 0.025n = 1t = 2Substituting given values into the formula:
[tex]\sf \implies V=20000(1+\frac{0.025}{1})^{(1 \times 2)}[/tex]
[tex]\sf \implies V=21012.5[/tex]
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4(2x)−8x+4
Answer:
4(2x) - 8x + 4
4 × 2x = 8x
8x - 8x + 4
= 4
Done!
Choose the line plot that correctly shows this data about the growth of bean plants:
1/2,3/4,1/2,1/4,1/2,1/4,3/4,3/4,1/2
Answer:
It is the first one
Step-by-step explanation:
Hi, it is the first one because there is 4 - 1/2 3 - 3/4 and 2 - 1/4
What is the value of the expression? Show your work.
Answer:
343
Step-by-step explanation:
Given :
[tex]\frac{7^{12}*7^{9} }{(7^{6})^{3} }[/tex]Numerator
7¹² × 7⁹7²¹Denominator
(7⁶)³7¹⁸Fraction
Numerator/Denominator7²¹/7¹⁸7³343Select all that apply.
The bar graph below represents the following table, but the graph has at least one mistake. Choose the statements that describe what is wrong with the graph.
Answer:
The labels are switched
The "cloudy" bar is the wrong length
The "party cloudy" bar is wrong length
I hope my answer helps you.
What is the value of "X"?
Answer:
6
Step-by-step explanation:
All triangles equal 180 degrees to this is what I did:
8x + 2 + 70 + 60 = 180
8x + 2 + 130 = 180
8x + 132 = 180
subtract 132 from each side
8x = 48
now divide each side by 8 to isolate the x
x = 6.
What is the polygon being Rotated to create the blue quilt block pattern
As shown, to obtain the blue quilt block pattern, we have to rotate the parallelogram.
What is parallelogram?A parallelogram is a quadrilateral consisting of pairs of parallel sides.
To obtain the blue quilt block pattern, we have to rotate the parallelogram. This rotation allows the parallelogram to take on a new orientation, and when it is positioned correctly, it creates the blue quilt block pattern. The process of rotating the parallelogram may seem simple, but it is a critical step in achieving the desired quilt design. It requires attention to detail and precision to ensure that the parallelogram is correctly rotated, and the resulting blue quilt block pattern is aligned correctly.
Moreover, the correct rotation of the parallelogram can significantly impact the overall appearance of the quilt, and even a slight misalignment can make a noticeable difference. Therefore, it is important to carefully follow the instructions to rotate the parallelogram to achieve the intended blue quilt block pattern.
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which recurring decimal is equivalent to the Fraction shown ? 9/11
equals a) 0.8 b) 0.18 c) 0.18 d) 0.18'
Using a calculator would show that
[tex]9/11 = 0.818181\ldots = 0.\overline{81}[/tex]
The horizontal line over top means the "81" repeats forever.
You can use long division as an alternative method to getting the answer above.
Jasmine's credit card has a $2,000 balance that she carried over from last month. assuming her credit card charges an 18 percent annual interest rate, how much will her interest charges be this month?
Using simple interest, it is found that her interest charge this month will be of $30.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of interest after t years in is modeled by:
I(t) = Prt
In which:
P is the initial amount.r is the interest rate, as a decimal.In this problem, considering the time in years, the parameters are:
[tex]P = 2000, r = 0.18, t = \frac{1}{12}[/tex]
Hence:
[tex]I(t) = 2000 \times 0.18 \times \frac{1}{12} = 30[/tex]
Her interest charge this month will be of $30.
More can be learned about simple interest at https://brainly.com/question/25296782
if ey/n + k = t, what is y in terms of e, n, k, and t?
1) y= tn+k/e
2) y= tn-k/e
3) y= n(t+k)/e
4) y= n(t-k)/e
Answer:
option 4
Step-by-step explanation:
To write in terms of y
Step 1: subtract k from both sides
[tex]\sf \dfrac{ey}{n} + k - k = t -k\\\\\\\dfrac{ey}{n}=t-k[/tex]
Step 2: Multiply the entire equation by n
[tex]\sf n*\dfrac{ey}{n}=n*(t-k)\\\\\\ey=n(t-k)[/tex]
Step 3: Divide the entire equation by 'e'
[tex]\sf \dfrac{ey}{e}=\dfrac{n(t-k)}{e}\\\\\\\boxed{y =\dfrac{n(t-k)}{e}}[/tex]
Annie's squirt gun holds two tanks one tank holds 968 ML and the other tank holds 784 ML how many liters does the squirt gun hold in total
ayo
968ml + 784ml = 1752ml or 1.752Liter
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Answer:
7.093 cm
Step-by-step explanation:
[tex]4.5^2+x^2=8.4^2[/tex]
[tex]20.25+x^2=70.56[/tex]
[tex]x^2=50.31[/tex]
[tex]\sqrt{50.31}= 7.093[/tex]
What is the radius and diameter of 13cm
Answer:
Radius = 6.5
diam = 13
Step-by-step explanation:
diameter is already stated
radius is half of the diameter
3(−2−3x)=−9x−4 how many solutions
Answer:
there are no solutions
Volume of cylinders, spheres, and cones word problems
A graduated cylinder is filled with 367 cm3 of liquid. The liquid is poured into a different cylinder that has a
radius of 3 cm.
What will the height of the liquid be in the new cylinder?
cm
Solve the triangle. Round to the nearest tenth.
In AABC, c = 9, b = 25, mZA = 113°
Answer:
28.5
Step-by-step explanation:
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marc had 6n marbles. he gave 9 marbles to each of his cousins and had 4n marbles left. find how many cousins marc had in terms of n.
Answer:
9c=2n
Step-by-step explanation:
6n-9c=4n.
9c=2n
n = 9/2c, my bad for the wrong answer at first.
A mobile set after allowing a discount of 10% on its marked price, was sold at a gain of 20%,Had it been sold after allowing 20% discount,there would have been a profit Rs.350. Find the cost price and marked price of the mobile set.
Answer:
Let x be the cost price.
Let y be the marked price
Gain = 20%
Then , sale price = 120/100 * x = 1.2x
Now , sale price is after 10% discount from marked price.
Hence , marked price, y = 1.2x/90 * 100 =
y * 0.9 = x * 1.2
Now, with 20% discount, sale price = y * 80/100 = 0.8y
Now, profit = 0.8y — x
Now, 0.8y — x = 350
0.8 * x * 1.2/0.9 — x = 350
1.0667x — x = 350
Hence, x = 350/0.0667= Rs.5250
Hence marked price = (5250 + 350) * 100/80 = Rs.7000
Cora works as a plumber and earns $50 per house call, plus $18 for every hour of work. She billed a customer $104, but forgot how long she worked. To solve for the number of hours, she subtracted 50 from 104 and then divided by 18.
Answer:
Cora worked 3 hours
Step-by-step explanation:
104 = 18x + 50 ( x = # of hours worked)
54 = 18x ( subtracted 50 from both sides)
3 = x ( divided both sides by 18)
Fran is going to transfer her credit card balance over to a new card. she has an existing balance of $752.69. her current card charges her a transfer fee of 12.5%, added to her balance, for transferring her debt. the new card has an opening fee of $50, which is also added to her balance. she will also have to make an immediate minimum payment, which is 3.35% of her total balance. how much will her balance be after she makes this payment, assuming that she pays the minimum amount? round all dollar values to the nearest cent. a. $866.74 b. $868.40 c. $818.41 d. $926.82 please select the best answer from the choices provided a b c d
The Fran's balance will be $866.73.
She has an existing balance of $752.69
Her current card charges her a transfer fee of 12.5%, added to her balance, for transferring her debt.
What is the meaning of balance?An even distribution of weight enabling someone or something to remain upright and steady.
Which is given by,
[tex]0.125\times 752.69=94.04[/tex]
The total is given by,
[tex]752.69+94.04=846.77[/tex]
The new card has an opening fee of $50, which is also added to her balance.
This becomes now = [tex]846.77+50=896.77[/tex]
She also have to make an immediate minimum payment, which is 3.35% of her total balance.
This amount is = [tex]0.0335\times 896.77=30.04[/tex]
Now balance in her account is = [tex]0.0335 \times 896.77=30.04[/tex]
Therefore, Fran's balance will be $866.73.
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An isosceles right triangle has a hypotenuse of 16mm what would the area of the triangle be
Answer: 64 square mm
Step-by-step explanation:
2x + y - 3z , x = 2/5 , y = 2/3 , z = 1/6 what does it equal
29/30
2x + y - 3z
2 x 2/5 + 2/3 - 3x1/6
4/5 + 2/3 - 3/6
x 3 x 5
12/15 + 10/15 - 3/6
22/15 - 3/6
x2. x5
44/30 - 15/30
= 29/30
Hope this helps!
Find the slope and the y-intercept of the line.
Y=2-1/3x
Slope:- -1/3
y-intercept:- 2
Solution:-The equation of the line is written in slope-intercept form, which looks like this:- y=mx+b.In this formula, m stands for the slope, and b stands for the y-intercept of the line.In this case, the equation looks like this:- y=b+mxHowever, it does not matter. m is still the slope and b is still the y-intercept.Also, you should notice that the slope is the coefficient of x (the number next to x) and b is the constant (a number added/subtracted to/from the slope)Therefore, the slope of the line is equivalent to:--1/3And the y-intercept is equivalent to the following:-2Hope it helps.
Do comment if you have any query.
Answer:
Slope: -1/3
Y-intercept: 2
Explanation:
The equation y = 2 - 1/3x is in slope-intercept form.
The format of slope intercept is y = mx + b, where m = slope and b = y-intercept.
The slope is the coefficient of x.
Hence, the slope of y = 2 - 1/3x is -1/3.
As for the y-intercept, that is the constant.
The constant in y = 2 - 1/3x is 2. Hence, the y-intercept is 2.
3a^2 X b/c divided by (3ab)^2
Answer: 1/3cb
Step-by-step explanation:
i hope this helps
Answer:
[tex] {Answer \: is \: }\frac{1}{3bc} [/tex]
Step-by-step explanation:
[tex]Divide \: 3 {a}^{2} \times \frac{b}{c} = 3 {ab}^{2} [/tex]
[tex] \frac{3 {a}^{2} \cdot \frac{b}{c}}{{(3ab)}^{2} } \\ \frac{3 {a}^{2}{b }}{{(3ab)}^{2}c} \\ \frac{3 {a}^{2} b}{9 {a}^{2} {b}^{2}c } \\ \frac{\not3 {a}^{2} b}{\not9 {a}^{2} {b}^{2}c } \\ \frac{ {a}^{2} b}{3 {a}^{2} {b}^{2}c } \\ \frac{ \not{a}^{2} b}{3 \not{a}^{2} {b}^{2}c } \\ \frac{\not{b}}{3 \not{b}^{2}c } \\ \frac {1}{3bc}[/tex]
[tex] {Answer \: is \: }\frac{1}{3bc} [/tex]
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Calculate the side lengths using the given scale.
Someone please help me!!
Answer:
x = 12 cm
y = 2 cm
Step-by-step explanation:
Length is G are 3 times the lengths in H.
Lengths in H are 1/3 the lengths in G.
x = 3 × 4 cm = 12 cm
y = 6 cm / 3 = 2 cm
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Answer:
2,250 yd^3
Step-by-step explanation:
formula for pyramid is lwh/3
