i need help with understand how to solve literal equations,this one in particular
Answers
The given equation is
\(-12x+8y=-48\)The equation has 2 variables (x and y)
To solve it, we have to assume a value of x and get its corresponding value of y
Let x = 1, then substitute it in the equation and solve it to find y
\(\begin{gathered} x=1 \\ -12(1)+8y=-48 \\ -12+8y=-48 \end{gathered}\)Add 12 to both sides
\(\begin{gathered} -12+12+8y=-48+12 \\ 0+8y=-36 \\ 8y=-36 \end{gathered}\)Divide both sides by 8
\(\begin{gathered} \frac{8y}{8}=\frac{-36}{8} \\ y=-4.5 \end{gathered}\)At x = 1, y = -4.5
Then one solution of the equation is (1, -4.5)
Related Questions
a line with y-intercept (0,1) which passes for thought the point (1,1)
Answers
Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.
The template: y = mx + b
b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:
y = mx – 2
Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.
So, taking your two points, you calculate the slope, m, in the following way:
(x1,y1) = (0,–2)
(x2,y2) = (5,1)
y2 – y1 1 – (–2) 1 + 2 3
m = ________ = ________ = ________ = ____
x2 – x1 5 — 0
Step-by-step explanation:
Question 2
A box contains 22 coloured pencils.
6 pencils are pink, 9 pencils are blue and 7 pencils are yellow.
Write down the ratio pink pencils : not pink pencils.
Give your answer in its simplest form.
Answers
Answer:
3/8 or 3:8
Step-by-step explanation:
pink : not pink
6 : 16
Think of it as a fraction. Simplify it in the same way.
6/16 simplifies to 3/8
So the pink:notpink ratio is 3/8 or 3:8
when simplified it becomes 3:8
Pls help its urgent
Question 1:
In my backyard there are chickens and cows (no other animals). Among them there is a total of 366 eyes and 558 legs. How many chickens do I have in my backyard?
Answers
The total animals = 139, and we can substitute this value into equation (3) to obtain:x = 2(139) - 279 => x = -1This doesn't make sense since we can't have negative chickens.
Let the number of chickens be x and the number of cows be y in the backyard. We can create two equations based on the given information:The total number of animals is x + y = total animals ...
(1)The total number of eyes and legs can also be expressed as 2x + 2y = 366 (since each animal has two eyes) and 2x + 4y = 558 (since each chicken has 2 legs and each cow has 4 legs).
Simplifying the equations, we get:x + y = total animals ... (1)x + 2y = 279 ... (2)From equation (1),
we can substitute y = total animals - x in equation (2) to obtain:x + 2(total animals - x) = 279 => 2total animals - x = 279 => x = 2total animals - 279 ... (3)We also know that x + y = total animals, so y = total animals - x.
Substituting equation (3) into this expression, we get:y = total animals - (2total animals - 279) => y = 279 - total animals ... (4)
To find the value of x, we need to know the value of total animals. We can obtain this value by adding equations (1) and (4):x + y + (279 - total animals) = total animals => x + y = 279/2 => x + y = 139.5
Since x and y are both whole numbers, they must add up to an even number. The only possible value is 70 + 69 = 139. Therefore, there must be a mistake in the problem statement or calculations.
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What is the total capacity of all the servings that are two and two fourths cups? A line plot titled Servings of Lemonade. The bottom label is Capacity in cups. There is a number line from 1 to 2 and 2 fourths, partitioned into fourths. There is one mark above 1. There are 4 marks above the first tick mark after 1. There is 1 mark above the second tick mark after 1. There are 2 marks above the third tick mark after 1. There are 3 marks above the first tick mark after 2. There are 2 marks above the second tick mark after 2. three and three over four cups 4 cups four and three over four cups 5 cups
Answers
The correct answer is option D. 250 milliliters, is the capacity of a small cup.
It is given that, the total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters.
To find the capacity of a small cup
Let small cup capacity be 's' and large cup capacity be 'l'
From the given information we can write,
2l + 2s = 1500
Then l + s = 750
one large cup and two small cups is 1,000 milliliters.
l + 2s = 1000
l + s + s = 1000
(l + s) + s = 1000
750 + s = 1000
s = 1000 - 750 = 250
The correct answer is option D. 250 milliliters
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complete question:
The total capacity of two large cups and two small cups is 1,500 milliliters. If the total capacity of one large cup and two small cups is 1,000 milliliters, what is the capacity of a small cup?
A. 375 milliliters
B. 200 milliliters
C. 500 milliliters
D. 250 milliliters
Which inequality is equivalent to 2/3 X-5 < 11
Answers
Answer:
2/3 x - 5 < 11
2/3 x < 16 (add 5 to both sides)
x < 16 * 3/2 (multiply both sides by 3/2)
x < 24
Step-by-step explanation:
The cost C (in dollars) of making n watches is represented by C=15n+85. How many watches are made when the cost is $385?
Answers
Answer:
20=n
Step-by-step explanation:
Take 385 and subtract 85. You get 300. Divide 300 by 15n. You get 20.
20=n
If you want to double check, replace n with 20 so the equation is
C=(15x20)+85
Hope I help!
how can i solve this problem if its congruent or not
Answers
9514 1404 393
Answer:
∆BCR ≅ ∆BAR
x = 6
Step-by-step explanation:
For congruence, define point R where the altitude line meets segment AC.
The diagram shows you AR ≅ RC. You know BR ≅ BR by the reflexive property, and you know that ∠BRC ≅ ∠BRA = 90°. You can therefore claim ...
∆BCR ≅ ∆BAR . . . . by the SAS congruence postulate
__
To solve for x, you don't need to show congruence of the right triangles. You only need to realize that the markings on segment AC show the left half is the same length (x) as the right half. The Pythagorean theorem is used to find x.
x² +8² = 10²
x² = 100 -64 = 36
x = √36 = 6
The length of x is 6 units.
_____
As you can see here, an altitude that is a median divides the isosceles triangle into two congruent right triangles. (That altitude also bisects angle B.)
You may recognize that the side ratios in the right triangle are 8:10 = 4:5. The missing side completes the Pythagorean triple 3:4:5, so is 2·3 = 6 = x.
Ria was given $42.30 to babysit for 2.5 hours. How much did she get for one hour?
Answers
Answer:
$16.92
Step-by-step explanation:
Just divide 42.30 by 2.5 and it will give you the answer
The owner of a small store buys coats for 55.00 each
He sells the coats for 66.00 each
Answers
he must buy 24 jackets to get atheist 260 dollars
Two regular 6-sided dice are tossed. Compute the probability that the sum of the pops on the upward faces of the 2 dice is the following. 1
Answers
Answer: 0
Step-by-step explanation:
Select the expression that has a quotient greater than 1. Explain your reasoning PLEASE ANSWER THIS
1. 4 2/3 ÷ 5 1/4
2. 3 1/8 ÷ 2 2/5
3. 1 6/7 ÷ 2 1/3
4. 5 3/4 ÷ 7 3/8
Answers
Define a variable, used let statements, set up an equation, then solve. Morgan is making two cookie recipes. Recipe A calls for one-third third less than twice the number of cups of sugar that Recipe B calls for. If she needs four and one-sixths cups of sugar in all, how many cups will she need for Recipe A?
Answers
EXPLANATION
Let's see the facts:
-Morgan is making ----------------> 2 cookie recipes.
Recipe A ---> A = 2RecipeB -(1/3) 2RecipeB
-She needs-----------> Recipe A + Recipe B = 4 1/6 cups of sugar
Now, we have a system of equations:
(1) A = 2B -(1/3)2B
(2) A + B = 4 1/6
Multiplying both sides of (1) by 3:
3A = 6B - B
Simplifying:
3A = 5B
Isolating B:
B = 3/5 A
Substituting B-value in (2)
\(A\text{ + }\frac{3}{5}A\text{ = 4}\frac{1}{6}\)Reordering:
\(A+\frac{3}{5}A=\text{ }\frac{25}{6}\)Multiplying both sides by 30:
\(30A\text{ + 18A = 25}\cdot5\)\(48A\text{ = 125}\)Dividing both sides by 48:
\(A\text{ = }\frac{125}{48}\)Representing as mix fraction and rounding:
\(A=\text{ 2}\frac{2}{3}\)ANSWER: She will need two and two-thirds cups of Recipe A.
Philip has been experimenting with new recipes at his bakery for the past 8 months. This month, he tried a recipe for lavender vanilla muffins and gave samples to his customers. He asked them to rate the muffins on a scale of 1 to 10 stars. The median rating was 7 stars, and the interquartile range was 4 stars. ) What can you conclude from these data and statistics? Select all that apply. () No customer gave the muffins fewer than 8 stars. A typical rating for the muffins was 7 stars. The middle 50% of customer ratings had a range of 4 stars. Submit
Answers
- A typical rating for the muffins was 7 stars, since the median rating was 7 stars.
- The middle 50% of customer ratings had a range of 4 stars, since the interquartile range was 4 stars.
- We cannot conclude that no customer gave the muffins fewer than 8 stars, as the median is not necessarily equal to the mean, and it is possible that some customers rated the muffins below 8 stars. Therefore, this statement is not necessarily true.
A cone has a volume of 6 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? (1 point)
Answers
Answer:
18 cubic inches
Step-by-step explanation:
The formulas for the volumes of a cone and a cylinder can be used to answer this question.
Volume formulasThe volume of a cone is given by ...
V = 1/3πr²h . . . . . volume of cone with radius r and height h
The volume of a cylinder is given by ...
V = πr²h . . . . . volume of a cylinder with radius r and height h
Relation between volumesComparing the formulas, we see that the volume of a cone is 1/3 the volume of a cylinder with the same radius and height.
(cone volume) = 1/3(cylinder volume)
Multiplying this equation by 3 gives ...
3×(cone volume) = (cylinder volume)
Using the given value for cone volume, we have ...
cylinder volume = 3×(6 in³) = 18 in³
The volume of the cylinder is 18 cubic inches.
someone please answer this its confusing me
Answers
the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9
line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12
Im desperate like most of my question-
The original price of a T-shirt is $15. The sale price includes a 35% discount. What is the sale price?
Thank you
Answers
===========================================================
Explanation:
There are two ways to solve this problem.
Method 1:
35% = 35/100 = 0.35
35% of 15 = 0.35*15 = 5.25
So you save $5.25, which is the discount amount.
The sale price is 15 - 5.25 = 9.75 dollars
---------------
Method 2:
If you save 35%, then you still need to pay the remaining 65%
35% + 65% = 100%
The sale price is 65% of original price
sale price = 65% of original price
sale price = 0.65*15
sale price = 9.75 dollars
---------------
Extra info (optional section)
The benefit of method 2 is that we can chain multiple discounts together. Consider that on top of the 35% discount, the store then decides that members (people who pay monthly) will get an extra 10% off. The natural thinking is that the total discount is 35%+10% = 45% off, but that's not correct.
We can see this if we say that the original price is say $100 and 35% off would lead to a price of 0.65*100 = 65 dollars. Then an extra 10% off means we pay 90% of that new price (65 dollars) to get 0.90*65 = 58.50
As a shortcut, we can just multiply the values of 0.65*0.90 = 0.585
Then note how 100*0.585 = 58.50 showing us a fairly fast way to compute the final sale price even if multiple discounts are applied. This can be extended to more discounts. Again, we do not add the percentages when it comes to figuring out how much the total discount percentage would be.
Since the item was $100 but now it's 58.50, this means we saved 100-58.50 = 41.50 dollars. The discount is therefore 41.50/100 = 41.50% which is close to the 45% calculated earlier, but not quite there.
Answer:
$5.25
Step-by-step explanation:
12 x 12 / 12 x 12 x 12 x 12 - 777 + 21 x 12 x 12 / 12 = ?
Answers
Answer:
116,031 about
Step-by-step explanation:
Answer:
20,211
Step-by-step explanation:
Use the correct order of operations, and do one step at a time.
12 x 12/12 x 12 x 12 x 12 - 777 + 21 x 12 x 12/12 =
= 144/12 x 12 x 12 x 12 - 777 + 252 x 12/12
= 12 x 12 x 12 x 12 - 777 + 3024/12
= 144 x 12 x 12 - 777 + 252
= 1728 x 12 - 777 + 252
= 20,736 - 777 + 252
= 19,959 + 252
= 20,211
Ricardo can complete 4 laps around a track in 10 minutes. Create a graph that has a slope that represents the
number of laps Ricardo can run per minute.
Select two points on the coordinate grid. A line will connect the points.
HELP !!
Answers
The graph is attached below.
The number of laps completed by Ricardo in 10 minutes is 4.The number of laps completed by Ricardo in 1 minute is 4/10.Thus, slope is 0.4.We can form a linear function.The function "y" equals 0.4x.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.y = 0.4xNow, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that has a positive slope of magnitude 0.4 and passes through origin.To learn more about functions, visit :
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Amir is in charge of getting oranges for today's soccer game. He buys 2 bags with
6 oranges in each bag. He also buys 4 loose oranges.
Choose all the expressions that can be used to find the number of oranges Amir gets
in all.
Answers
The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all
What is linear expressions?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.
Let's represent the total no of oranges by x.
Therefore ,
2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.
an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x
x = 12+4 or x-12 = 4
= 16
therefore amir got 16 oranges in all
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Answer the problem 1010+3839
Answers
Answer:
4,849
Step-by-step explanation:
1010+3839=4849
Answer:
4,849
Step-by-step explanation:
Brainliest please
Triangle BCD has the following side lengths: BC = 60, CD = 50
Triangle RST has the following side lengths: RS: 11x-4, ST = 70
What is the value of x?
What is the length of side RS?
Answers
The value of x is 11 and the length of side RS is 117
How to determine the value of x?The given parameters are
BC = 60 and CD = 50
RS = 11x - 4 and ST = 70
Express as a ratio
BC : CD = RS : ST
So, we have
60 : 50 = 11x - 4 : 70
Express as fraction
60/50 = (11x - 4)/70
Cross multiply
50 * (11x - 4) = 70 * 60
Divide both sides by 50
11x - 4 = 84
This gives
11x = 88
Divide
x = 11
Substitute x = 11 in RS = 11x - 4
RS = 11 x 11 - 4
Evaluate
RS = 117
Hence, the value of x is 11 and the length of side RS is 117
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 72 stocks traded on the NYSE that day showed that 29 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of a = 0.02.
What is the test statistic for this sample?
Use p rounded to 4 decimal places. (Report answer accurate to 4
decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =
The p-value is either less than (or equal to) or
greater than?
This p-value leads to a decision to...
reject the null or accept the null or fail to reject the null?
As such, the final conclusion is that... (select a letter)
A) There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went
up is is more than 0.3.
B) There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that
went up is is more than 0.3.
C) There is sufficient evidence to support the claim that the proportion of stocks that went up is is more
than 0.3.
D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
Answers
The test statistic and the p-value of the research are respectively z = 1.9072 and p-value = 0.0283 and the conclusion is that; D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.
How to find the p-value from the research?Let us first of all define the hypotheses;
Null Hypothesis; H₀: p ≤ 0.3
Alternative Hypothesis; Hₐ: p > 0.3
Sample proportion is;
p^ = 29/72 = 0.403
The formula for the test statistic is;
z = (p^ - p)/(√(p(1 - p)/n))
Plugging in the relevant values gives;
z = (0.403 - 0.3)/(√(0.3(1 - 0.3)/72))
z = 1.9072
From p-value from z-score calculator, we have that;
p-value = 0.0283
p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
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PLEASE ANSWER QUICKLY!!!!
10.A school purchases boxes of candy bars.
- Each box has 50 candy bars
- Each bos costs $30
How much does the school have to charge for each candy bar to make a
profit of $10 per box?
Answers
9514 1404 393
Answer:
$0.80
Step-by-step explanation:
The cost of each box is $30. To make a profit of $10, the 50 candy bars must be sold for a price that will generate $30 +10 = $40 in revenue:
$40/(50 bars) = $(4/5)/bar = $0.80 per bar
The school must charge $0.80 for each candy bar to make a profit of $10 per box.
Solve for xx. Round to the nearest tenth of a degree, if necessary.
Answers
For more explanation, please see the attachment
what is the answer to this?? lmk asap pls and i need the right answer
Answers
Answer: no, no, no, yes
Step-by-step explanation:
Hello!
Just take each value of "u" and multiply it by 4. If the answer is smaller than 32, it is a solution. If not, it isn't a solution.
Stainless steel contains at least 10.5% chromium. If a steel container that weighs 40 grams contains 5 grams of chromium, does it meet the standard for stainless steel?
Answers
The steel container meet the standard for stainless steel because it contains 12.5% of chromium.
What is an equation?An equation is an expression showing the relationship between numbers and variables.
Stainless steel contains at least 10.5% chromium.
We need to determine if a steel container that weighs 40 grams contains 5 grams of chromium is stainless steel.
Therefore:
Percentage of chromium in the steel container = (5 grams / 40 grams) * 100% = 12.5%
12.5% > 10.5%, hence the steel container meet the standard for stainless steel
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Helppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
2
Step-by-step explanation:
( \(\frac{1}{2}\) × 4 ) × 5 - 2³ = 10 - 8 = 2
The ordered pair (2, 10) is a point on a direct variation equation. Write the direct variation equation.
Answers
Answer:
Y=KX so its 10=K2
Step-by-step explanation:
Plug in the Number OR K=y/x
Marisa was tracking the diving speed of a bird. The average speed was 108 miles per hour. That means in one hour, the bird would travel 108 miles at that speed. However, these dives last far less than an hour, so Marisa needs to convert this to feet per second
Answers
By a change of units, we will get that 108 mi/h = 158.4 ft/s
Here we want to transform 108 mi/h to feet per second.
Then we will use two relations:
1 mi = 5,280 ft1 h = 3,600 sThen we can just transform as:
108mi/h = (108*5,280 ft)/h = 570,240 ft/h
570,240 ft/h = 570,240 ft/(3,600 s) = 158.4 ft/s
So we have:
108 mi/h = 158.4 ft/s
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Find three positive numbers whose sum is 100 and whose product is a maximum.
Answers
Answer:
The numbers are;
x = 100/3, y = 100/3, z = 100/3
Step-by-step explanation:
Given the data in the question;
so let the numbers be; x , y and z
so
x + y + z = 100
now
G(x,y,z) = x + y + z - 100
F(x,y,z) = xyz
Fx = yz, Gx = 1
Fy = xz, Gy = 1
Fz = xy, Gz = 1
Fx = λ × Gx
yz = λ
Similarly, xz = lambda
And xy = lambda
From above clearly, x = y = z
x + y + z = 100
so
3x = 100
x = 100/3
since, x = y = z therefore, each number is equal to 100/3
x = 100/3, y = 100/3, z = 100/3
We want to find 3 positive numbers such that their sum is 100 and the product is maximum.
The maximum product is P = 37,025.93
Let's say that our 3 numbers are:
A, B, and C.
We must have:
A + B + C = 100
The product of these 3 numbers is:
P = A*B*C
For the restriction, we can write:
A = 100 - B - C
Now we can replace that in the product equation to get:
P = (100 - B - C)*B*C
P = 100*B*C - C*B^2 - B*C^2
Now we want to maximize this, to do it, we need to find the zeros of the derivate of the function. This is a two-variable function, but the dependence on C is exactly the same as the dependence on B, so we can find the zero of deriving with respect to one of these only.
dP/dB = 100*C - 2*C*B - C^2 = 0
C*(100 - 2*B - C) = 0
One solution is C = 0, the other is:
C = 100 - 2*B
And from the first restroctopm:
A + B + C = 100
we can get:
C = 100 - A - B
Then:
100 - A - B = 100 - 2*B
Then we get A = B
And if we derive the equation for C instead of B, we will get similar results that will lead to:
A = B = C.
This is what maximizes the product, then we have:
A + B + C = 3*A = 100
A = 100/3 = 33.33
P = (33.33)^3 = 37,025.93
This is the maximum product.
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