"The product of a six and a number increased by four is equal to
the product of twelve and the same number decreased by twenty."
Answers
Answer:
[tex] 6x + 4 = 12x - 20 [/tex]
[tex] x = 4 [/tex]
Step-by-step explanation:
Let "x" be the number.
Product of 6 and x (6*x), increased by 4 = [tex] 6x + 4 [/tex]
Product of 12 and x, (12*x), decreased by 20 = [tex] 12x - 20 [/tex].
Set both expressions equal to each other and solve for x as shown below:
[tex] 6x + 4 = 12x - 20 [/tex] (equation)
Subtract 12 from both sides
[tex] 6x + 4 - 12x = 12x - 20 - 12x [/tex]
[tex] -6x + 4 = -20 [/tex]
Subtract 4 from both sides
[tex] -6x + 4 - 4 = -20 - 4 [/tex]
[tex] -6x = -24 [/tex]
Divide both sides by -6
[tex] \frac{-6x}{-6} = \frac{-24}{-6} [/tex]
[tex] x = 4 [/tex]
Related Questions
please answer this question
Answers
For the integral ∫asin(x)dx, use integration by parts ∫udv=uv−∫vdu.
Let u=asin(x) and dv=dx.
Then du=(asin(x))′dx=[tex]\rm \dfrac{dx}{ \sqrt{1 - {x}^{2} } } [/tex] and v=∫1dx=x
So,
[tex] \rm{\int{\operatorname{asin}{\left(x \right)} d x}}=\color{h}{\left(\operatorname{asin}{\left(x \right)} \cdot x-\int{x \cdot \frac{1}{\sqrt{1 - x^{2}}} d x}\right)}=\color{h}{\left(x \operatorname{asin}{\left(x \right)} - \int{\frac{x}{\sqrt{1 - x^{2}}} d x}\right)} \\ [/tex]
Let u=1−x2.
Then du=(1−x2)′dx=−2xdx and we have that xdx=−du/2.
The integral can be rewritten as
[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{g}{\int{\frac{x}{\sqrt{1 - x^{2}}} d x}} = x \operatorname{asin}{\left(x \right)} - \color{j}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} \\ [/tex]
Apply the constant multiple rule ∫cf(u)du=c∫f(u)du with c=-1/2 and f(u)=[tex] \frac{1}{ \sqrt{u} } [/tex]
[tex] \rm x \operatorname{asin}{\left(x \right)} - \color{h}{\int{\left(- \frac{1}{2 \sqrt{u}}\right)d u}} = x \operatorname{asin}{\left(x \right)} - \color{h}{\left(- \frac{\int{\frac{1}{\sqrt{u}} d u}}{2}\right)} \\ [/tex]
Apply the power rule
[tex] \rm\int u^{n}\, du = \frac{u^{n + 1}}{n + 1} \\ [/tex]
with n=−1/2
[tex] \rm x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\int{\frac{1}{\sqrt{u}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\int{u^{- \frac{1}{2}} d u}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\frac{u^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1}}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{j}{\left(2 u^{\frac{1}{2}}\right)}}{2}=x \operatorname{asin}{\left(x \right)} + \frac{\color{h}{\left(2 \sqrt{u}\right)}}{2} \\ [/tex]
[tex] \rm Recall \: that \: u=1− {x}^{2} [/tex]
[tex] \rm x \operatorname{asin}{\left(x \right)} + \sqrt{\color{re}{u}} = x \operatorname{asin}{\left(x \right)} + \sqrt{\color{rd}{\left(1 - x^{2}\right)}} \\ [/tex]
Therefore,
[tex] \rm\int{\operatorname{asin}{\left(x \right)} d x} = x \operatorname{asin}{\left(x \right)} + \sqrt{1 - x^{2}}+C \\ [/tex]
A machine fills 150 bottles of water every 8 minutes. How many minutes it takes this machine to fill 675 bottles?
Answers
Answer:
36 Minutes
Step-by-step explanation:
150/8=18.75
675/18.75=36
So hence, your answer is 36 Minutes
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You go to ice cream place for dessert one day. You can get vanilla, chocolate, or twist ice cream. You have a choice of rainbow sprinkles, chocolate sprinkles, or no sprinkles. You can get your ice cream in a cup or a cone and they each come in small, medium m, and large sizes. How many different combinations are there in all?
Answers
A bag contains 8 red marbles, 6 blue marbles and 3 green marbles. If three marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that all three marbles drawn will be blue?
Answers
Answer: 0.29
Step-by-step explanation:
The probability of the first being blue is 6/17, the second is 5/16 and the third is 4/15. Multiply these together to get the total probability:
6/17 x 5/16 x 4/15 = .029
Farmland A farmer has a rectangular plot of land shaped like the figure in the graph. There is another identical plot of land 100 yards east and 120 yards north of the original plot. Graph both plots of land. Then find the combined area of the two plots of land
Answers
The graph of both plots would be the one graph in option C.
Combined area = 2(area of one rectangular plot) = 720 sq. yds.
What is the Area of a Rectangular Shape?Area of a rectangular shape = length × width
From the graph given, 1 unit represents 20 yards. Therefore:
100 yards east of the original plot is going to be 5 units to the left on the x-axis.120 yards north of the original plot would be 6 units upwards on the y-axis.Therefore, the graph of both plots would be the one given in option C.
The plot is rectangular in shape having 60 yards × 60 yards. Therefore:
Area of 1 plot = length × width = 60 × 60 = 360 square yards.
Combined area = 2(area of one rectangular plot) = 2(360) = 720 sq. yds.
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14:56 as a simplified ratio
Answers
Answer:
1:4
Step-by-step explanation:
To represent 14:56 as a simplified ratio, we need to reduce it by finding the GCF (greatest common factor) and dividing it by both terms.
The GCF of 14 & 56 is 14.
14 / 14 = 1
56 / 14 = 4
Thus we are left with our new simplified ratio, 1:4.
How is each one determined?
Answers
Answer:
I don't know-how to answer that
What is the slope of a line that is perpendicular to the
line y = -1/2X + 5?
Answers
Answer:
the slope is −12
Step-by-step explanation:
The equation of a perpendicular line to y=−x2+5 y = - x 2 + 5 must have a slope that is the negative reciprocal of the original slope.
Hope it helps!!!Brainliest pls!!!-1/2
That would be the answer
A running shoe store mounts a new promotional campaign. Purchasers of new shoes may, if dissatisfied for any reason, return them within 7 days of purchase and receive a full refund. The cost to the dealer of such a refund is $105. The dealer estimates that with an 11% probability each purchaser, for whatever reason, will return their pair of shoes and obtain refunds. Suppose that 120 pairs of shoes are purchased during the campaign period. Clearly the exact number of purchasers who return their product is unknown. Answer the following questions:
a. Describe the probability distribution of the number of pairs of shoes that will be returned for refunds.
b. What is the mean and standard deviation of the number of pairs of shoes that will be returned for refunds.
c. What is the mean and standard deviation of the total refund costs that will accrue as a result of these refunds.
Answers
Answer:
a
[tex]P(K = k ) = \ ^nC_x * p^k * (1-p)^{n-k}[/tex]
Here k is the random number of number of pairs of shoes that will be returned for refund, which can be k = 0,1 ,2,3,4 ..., 120
b
The mean is [tex]E(K) = np = 13.2[/tex]
The standard deviation is [tex]\sigma = 3.43[/tex]
c
The mean is [tex]E(C) = E(105 K) = 1386[/tex]
The standard deviation is [tex]\sigma = 381.48 [/tex]
Step-by-step explanation:
From the question we are told that
The cost to dealer for each refund is [tex]C = \$105[/tex]
The probability that a shoe will refunded is [tex]P(x) = 0.11[/tex]
The number of shoes purchased is n = 120 pairs
Generally the probability distribution of the number of pairs of shoes that will be returned for refunds is
[tex]P(K = k ) = \ ^nC_x * p^k * (1-p)^{n-k}[/tex]
Here k is the random number of number of pairs of shoes that will be returned for refund, which can be k = 0,1 ,2,3,4 ..., 120
Generally the mean is mathematically represented as
[tex]E(K) = np = 120 * 0.11[/tex]
=> [tex]E(K) = np = 13.2[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ n* p (1-p)}[/tex]
=> [tex]\sigma = \sqrt{ 120* 0.11 (1-0.11)}[/tex]
=> [tex]\sigma = 3.43[/tex]
Generally the total refund cost is mathematically represented as
[tex]C = 105 K[/tex]
Here K denotes the number of shoes returned
Generally the mean of the total refund cost is mathematically represented as
[tex]E(C) = E(105 K) = 105 E(K)[/tex]
=> [tex]E(C) = E(105 K) = 105 * 13.2[/tex]
=> [tex]E(C) = E(105 K) = 1386[/tex]
Generally the variance of the total refund cost is mathematically represented as
[tex]Var(K) = 105^2 * E(K)[/tex]
=> [tex]Var(K) = 105^2 * 13.2[/tex]
=> [tex]Var(K) = 145530[/tex]
=> [tex]\sigma = \sqrt{145530 }[/tex]
=> [tex]\sigma = 381.48 [/tex]
Between 0 and 1
Between 2 and 3
Between 5 and 6
Between 7 and 8
Answers
the square root of seven is 2.6 !
Super Painters charges $1.00 per square foot
plus an additional fee of $25.00 to paint a
living room. If x represents the area of the
walls of Francesca's living room, in square
feet, and y represents the cost, in dollars,
which graph best represents the cost of
painting her living room?
Answers
You circled b and i would agree. Because Francesca is doing a living room, it would natuarly start at $25. So it cant be c. And Because x represents the walls, the graph would be a possitive corrolotion so i would say it is b
The graph b shows the adequate information for painting cost of living room. Option b is correct.
Graph that shows adequate information for cost of painting for living room to be determine.
What is graph?The graph is a demonstration of curves which gives the relationship between x and y axis.
Here, equation for the painting of living room can be given as y = 1x+25.
This relation ship clearly seen in graph b.
Thus, the graph b shows the adequate information for painting cost of living room.
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I’m asking a lot of questions sorry anyone???
Answers
Answer:
For number question #8 its 8/3
Step-by-step explanation:
One way i do is multiply the denominator by the whole number and then add the numerator . For example 2 2/3
2x3=6 6+2=8
Do NOT change the numerator, it stays the same.
solve -36 4/9 - (-10 2/9) - (18 2/9)
Answers
Answer:
=−148
3
(Decimal: -49.333333)
Step-by-step explanation:
−364
9
−(
−102
9
)−
182
9
14 f ( x ) = √ 7 + x range
Answers
[tex]f(x) = \sqrt{7 + x} [/tex]
We know that anything underneath a square has to be positive. so accordingly[tex]7 + x \geqslant 0[/tex]
[tex]x \geqslant - 7[/tex]
[tex]domain \: - 7 \leqslant x \leqslant \infty [/tex]
The answer to any value of x that that you plug, between -7 & ∞ will be between 0 & infinity.[tex]range \: \: 0 \leqslant f(x) \leqslant \infty [/tex]
A US nickel has a mass of 5.00 g a US penny has a mass of 2.50 g what is the mass in kilograms of the coins in the
bag contending 186 nickels in 72 pennys
Answers
Answer:
1110 g
Step-by-step explanation:
Here is the fastest way to solve this problem: (5 x 186) + (2.5 x 72)
However, if you want a step-by-step explanation, here it is:
The total mass of the coins in the bag is the mass of the nickels plus the mass of the pennies.
Let's start by finding the mass of the nickels in the bag.
We know that one nickel has a mass of 5 g, and that there are 186 nickels. So, the total mass of all the nickels in the bag will be 186 x 5 = 930 g.
Now, let's find the mass of the pennies in the bag.
We know that one penny has a mass of 2.5 g, and that there are 72 pennies in the bag. So, the total mass of all the pennies in the bag will be 2.5 x 72 = 180.
We now add these two masses (930 + 180) to get our final answer, 1110 g.
pls help. i know the formulas, but i messed up my math.
Answers
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Given :-Here, we have composite figure which is composed of 2 cuboids. The dimensions of larger cuboid is 12cm, 7cm, 7cmThe dimensions of smaller cuboid is 7cm, 2cm , 2cmTo Find :-We have to find the total surface area of the composite figure Let's Begin :-Here,
The dimension of larger cuboid are
Length = 12cmBreath = 7 cmheight = 7 cmWe know that,
Lateral surface area of cuboid
[tex]\bold{\red{ = 2( lb + bh + hl)}}[/tex]
Subsitute the required values,
[tex]\sf{ = 2[(7)(7) + (7)(12) +(7)(12) ]}[/tex]
[tex]\sf{ = 2[ 49 + 84 ]}[/tex]
[tex]\sf{ = 2[ 49 + 168 ]}[/tex]
[tex]\sf{ = 2[ 217 ]}[/tex]
[tex]\bold{ = 434 cm^{2}}[/tex]
Now,We have to find the lateral surface area of smaller cuboid
The dimensions of smaller cuboid are 7cm, 2cm and 2cmTherefore,
Lateral surface area of smaller cuboid
[tex]\sf{ = 2[(2)(7) + (7)(2) +(2)(2) ]}[/tex]
[tex]\sf{ = 2[ 14 + 14 + 4 ]}[/tex]
[tex]\sf{ = 2[ 28 + 4 ]}[/tex]
[tex]\sf{ = 2[ 32]}[/tex]
[tex]\bold{ = 64 cm^{2}}[/tex]
The common base area of both the cuboids
[tex]\sf{ = lb }{\sf{ + lb}}[/tex]
[tex]\sf{ = 14 + }{\sf{ 14}}[/tex]
[tex]\bold{ = 28 cm^{2}}[/tex]
Now,The total surface area of the given composite figure
= SA of larger cuboid + SA of smaller cuboid - common base area
Subsitute the required values,
[tex]\sf{ = 434 + 64 - 28 }[/tex]
[tex]\sf{ = 498 - 28 }[/tex]
[tex]\bold{ = 470cm^{2}}[/tex]
Hence, The surface area of composite figure is 470 cm² .
Answer:
470cm²
Step-by-step explanation:
SA= (12*7)*4+(7*7)*2+(2*2)*2+(7*2)*2
=336+98+8+28
= 470 cm²
Therefore, the surface ares is 470 cm².
~
The angles opposite the congruent sides of an isosceles triangle are congruent. Find the value of x in the triangle. Show all your work.
The figure shows a triangle with 2 congruent sides. The angle between the congruent sides measures x degrees and a different angle measures 70 degrees.
Answers
Answer:
40
Step-by-step explanation:
Angles opposite congruent sides in a triangle are congruent, so the other base angle is also 70 degrees.
This means that the interior angles are 70, 70, and x
Since the sum of the measures of the angles of a triangle is 180 degrees,
70+70+x=180
140+x=180
x=40
Drag each volume of a prism to match a rectangular prism
on the left with the given dimensions.
54 cu. in.
72 cu. in.
36 cu. in.
80 cu. in.
Dimensions of
Rectangular Prism
Volume of Rectangular
Prism
4 in., 3 in., 6 in.
6 in., 3 in., 2 in.
4 in., 5 in., 4 in.
2 in., 9 in., 3 in.
Answers
The volume of the rectangular prism with the dimensions given are as follows:
v = 72 inches³
v = 36 inches³
v = 80 inches³
v = 54 inches³
Volume of a rectangular prismv = lwhwhere
l = length
w = width
h = height
Therefore,
a.
v = 4 × 3 × 6 = 72 inches³b.
v = 6 × 3 × 2 = 36 inches³c.
v = 4 × 5 × 4 = 80 inches³d.
v = 2 × 9 × 3 = 54 inches³learn more on rectangular prism here: https://brainly.com/question/13512346
10. A parabola has an axis of symmetry x = 2 and one of the x-intercepts is x =5. Where is the
other x-intercept?
Answers
Answer:
-1
Step-by-step explanation:
5-2=3
2-3=-1
Large Reusable bottles cost four dollars more than small ones eat large bottles cost $24 less than small ones how much does one small bottle cost
Answers
Answer:
$20
Step-by-step explanation:
The large ones cost $4 more so what you would do is to subtract that $4 from the $24.
24-4=20
Just provide answers please... thank you!
Answers
Answer:
Probability of drawing a yellow candy: 10/36= 5/18
Something besides a yellow candy: for ecample: the red candies: 8/36= 2/9
Step-by-step explanation:
Probability of drawing yellow candies equals the sum of candies over yellow candies.
I’ve been stuck on this question for a while can someone help please
Answers
∠A and ∠B are supplementary. m∠A = (6x + 5), m∠B = (2x + 15). Find the measure of each angle.
Answers
Answer:
125 and 55
Step-by-step explanation:
180=8x+20
160=8x
x=20
6(20)+5 2(20)+15=
120+5=125 degrees 40+15=55 degrees
What is the volume of the triangular prism? *
Pleaseeeee answer
Answers
Answer:
360 ft³Step-by-step explanation:
The formula for calculating the volume of a right triangular prism is:
(1/2 x b x h) x lLet's use the formula to calculate the volume of the right triangular prism.
(1/2 x 15 x 6) x 8⇒ (15 x 3) x 8⇒ 45 x 8⇒ 360 ft³Choose all the constant terms in the expression. 12+15x-16-4x-10
Answers
The constant terms are 12, -16, -10.
Look at the attached image for an example of how to identify constants!
Hope that helped!
Answer:
[tex]\huge\boxed{\sf{12, -16, -10}}[/tex]
Step-by-step explanation:
Hello.
Please remember that a constant is a number without any variables next to it.
Let's search for constants in this expression.
The first term is 12. It has no variables, thus, it's a constant.
The second term is 15x. It does have a variable, thus, it's not a constant.
The third term is -16. It has no variables, thus, it's also a constant.
The 4th term is -4x (not a constant)
The last term is -10 (a constant)
I hope it helps & have an outstanding day.
[tex]\boxed{imperturbability}[/tex]
Please help me xx this is what I really need to finish
Answers
Answer:
bjc hnfj yn yt NV ubf. giving! y NV,
Answer:
x= 45°
x+10=55°
2x-10=80°
Step-by-step explanation:
According to ASP,
x+x+10+2x-10=180°
4x=180°
Therefore, x=180/4
=45°
x+10=45+10
=55°
2x-10=90-10
=80°
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Solve for x in the proportion below be sure to show work 5/x=25/6
Answers
Answer:
I think it is x is equals to 5/6.
Step-by-step explanation:
5/x = 25/6
x/5 * 5/x = 25/6 * x/5
x = 5/6
▪ Answer:
x = 5/6
▪ Step-by-step explanation:
Hi there !
5/x = 25/6
x = 5×6/25
x = 30/25
simplist 5
x = 6/5
Good luck !
First, rewrite 5/7 and 8/11 so that they have a common denominator.
Answers
common denominator = 7x11 = 77
5/7 = (5x11) / (7x11) = 55/77
and
8/11 = (8x7) / (11x7) = 56/77
5/7 and 8/11 can be rewritten as 55/77 and 56/77, respectively, so that they have a common denominator of 77.
What is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
To rewrite 5/7 and 8/11 with a common denominator:
We can find the least common multiple (LCM) of the denominators 7 and 11, which is 77.
Then, we can multiply each fraction by the appropriate form of 1 so that the denominators are equal to 77.
Here are the steps:
5/7 = (5/7) x (11/11) = 55/77 (multiply the numerator and denominator of the first fraction by 11)
8/11 = (8/11) x (7/7) = 56/77 (multiply the numerator and denominator of the second fraction by 7)
Therefore, 55/77 and 56/77 are the required fractions.
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Using the Pythagorean Theorem:
Mary drove 60 miles east and then 20 miles north. How many miles would
Mary
have driven if she could have gone directly from her starting point to her ending
point? (Use a calculator to find the square root, and round the answer to the nearest
tenth.)
She would have driven
miles.
Answers
Answer:
60
Step-by-step explanation:
east and north are two axis that are perpendicular to each other, so if we use Pythagorean rule, sqr60^2+20^2=20sqr10, approximately 63.24555
A plane travels a distance of 5,000 km in a time of 5.6 hours.
What is its average speed rounded to the nearest whole number?
Answers
5000/5.6 = 893 km/h
Good Luck.