Answers
x - y = -3 2x + y = 14
Solve using substitution.
First, isolate one variable.
x + y = 5
x = 5 - y
Then, plug its expression into the other equation and solve.
x - y = -3
5 - y - y = -3
5 - 2y = -3
-2y = -8
y = 4
Next, plug your new value into one of the original equations to solve for the second variable.
x + y = 5
x + 4 = 5
x = 1
Finally, check work with substitution.
x + y = 5 => 1 + 4 = 5 <--True
x - y = -3 => 1 - 4 = -3 <--True
Next.
y = 3x - 1
2x + y = 14
2x + y = 14
2x + (3x - 1) = 14
2x + 3x - 1 = 14
5x - 1 = 14
5x = 15
x = 3
y = 3x - 1
y = 3(3) - 1
y = 9 -1
y = 8
y = 3x - 1 => 8 = 3(3) - 1 => 8 = 9 - 1 <--True
2x + y = 14 => 2(3) + 8 = 14 => 6 + 8 = 14 <--True
Answer:
4.
x = 1
y = 4
5.
x = 3
y = 8
Related Questions
An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a cylinder, as shown below:
© 2011 Jupiterimages Corporation
Each cone of the hourglass has a height of 18 millimeters. The total height of the sand within the top portion of the hourglass is 54 millimeters. The radius of both cylinder and cone is 8 millimeters. Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second. How many seconds will it take until all of the sand has dripped to the bottom of the hourglass?
68.3
38.4
268.8
230.4
Answers
Explanation:
For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.
I have attached the figure for better understanding.
1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.
So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.
This is how you calculate the volume of the top portion:
1) The height of the cylinder is 54 mm - 18 mm = 36 mm
2) The formula for the volume of a cylinder is V = π (radius)^2 * height
radius = 8 mm
height = 36 mm
=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3
3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height
radius = 8 mm
height = 18 mm
V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3
4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:
Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3
5) To find the number of seconds it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:
time in seconds = total volume of sand / rate of dripping
time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s
That is the answer: 268.8 s
Write three functions.
In the first function, y should vary directly with x.
In the second function, y should vary inversely with x.
In the third function, the relationship between x and y should be neither inverse variation nor direct variation.
Describe the graph of each function and give a real-world example for each.
Answers
.. The volume of an ideal gas is directly proportional to its absolute temperature.
2) y = k/x . . . . for some constant k
.. The volume of an ideal gas is inversely proportional to its pressure.
3) y = 1.8x +32
.. Temperatures in degrees Fahrenheit are linearly related to those in degrees Celsius, but the relation is neither directly nor inversely proprotional.
Evaluate a/b for a= 1/2 and b= - 3/7
A) - 7/6
B) 3/14
C) - 3/14
D) - 32/21
Please explain your answers.
Thanks! : )
Answers
You are given that a is 1/2 and b is -3/7
Write this down...
Answer: -7/5
Substitute the value of the variable into the expression and simplify.
Exact Form: −7/6
BRAINLIEST!
A store manager wishes to investigate whether there is a relationship between the type of promotion offered and the number of customers who spend more than $30 on a purchase. Data will be gathered and placed into the two-way table below.
Answers
Answer:
D. The manager should check both relative frequencies by row and by column to look for an association.
Step-by-step explanation:
the correct answer would be D
Which relationship describes angles 1 and 2?
Select each correct answer.
supplementary angles
complementary angles
vertical angles
adjacent angles
Answers
Sammy is 5 feet 3 inches tall. He casts a shadow that is 31 feet 6 inches long. He is standing next to a stop sign that casts a shadow that is 40 feet 6 inches long. How tall is the stop sign in feet and inches.
Answers
[tex]\frac{378}{486}=\frac{63}{x}[/tex]. This comes because we compare corresponding sides of the similar triangles. 378 corresponds with 486, since they are the horizontal lengths of the shadows. 63 corresponds to x, since they are the heights of Sammy and the sign. Solving this by cross multiplication:
[tex]378*x=63*486 \\378x=30618[/tex]
Divide both sides by 378:
[tex]\frac{378x}{378}=\frac{30618}{378} \\x=81[/tex]
The sign is 81 inches tall. Converting this to feet and inches, divide by 12; this gives us 6.75. We have 6 feet and 0.75 feet. 0.75 feet * 12 inches per foot = 9 inches. The sign is 6 feet 9 inches tall.
How many drivers who start driving before they are 20 are convicted of a traffic violation within the first year of driving?
Answers
Hope this helped.
Solve for x
Please help quick
Answers
b and c are parallel meaning that the intersection of c and a is also perpendicular
11x - 9 = 90 degrees
solve
11x - 9 = 90
add 9 to both sides
11x = 99
divide both sides by 11
x = 9
Hope this helps
Evaluate the exponential expression. Write your answer as a fraction in simplest form.
(2^3)^-2
Answers
(2^3)^-2
Multiply the powers.
2^-6
Put the negative on the bottom.
1/2^6
1/64= the equivalent fraction
I hope this helps!
~kaikers
If you answer (making sense) and explain (so I can understand) you will be awarded! Please help ASAPA
Answers
The manager of a convenience store wishes to determine how many cartons of eggs are damaged in shipment and delivery. For ten shipments of 1000 cartons of eggs, she examines every 50th carton to see how many cartons contain cracked eggs.
Identify the population and the sample
a.
population: 1,000,000 cartons of eggs
sample: every 50th carton in each shipment
c.
population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment
b.
population: 1,000,000 cartons of eggs
sample: the 50th carton of eggs
d.
population: 10 shipments of 1000 cartons of eggs
sample: the 50th carton of eggs
Answers
Answer:
Option c. Population: 10 shipments of 1000 cartons of eggs
sample: every 50th carton in each shipment.
Step-by-step explanation:
First we find out population :
For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.
Therefore, 1000 × 10 = 10,000 cartons of eggs.
Population : 10,000 cartons of eggs
Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.
Hence, Sample would be every 50th carton in each shipment.
In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs
Therefore, option c would be correct.
Help please!
The length of a football field is 67 yards greater than the width the perimeter of the field is 346 yard. Find the length and width of the football field.
Answers
In order for us to solve this question, we will need to set up an equation with an unknown variable. We will then solve for it, thus receiving everything we need for the width and length of the football field. I will also be attaching an image with all the work shown, so make sure to take a look at it.
First of all, let's identify our total in the equation. In this case, if we add both length and width together, we will get one half of 346 - the perimeter due to the fact that perimeter calls for both widths, and both lengths of a rectangle.
Let's form the equation which we will then solve.
[tex]2[x+(x+67)]=346[/tex]
In this equation, x stands for the width. You can also see "x+67", which is the length of the rectangle. Both these values are added together, and multiplied by two. Let's start solving.
Let's simplify this equation.
[tex]4x+134=346[/tex]
As you can see, we have multiplied the sum of all these numbers by two. Now, let's get rid of 134 on both sides.
[tex]4x=212[/tex]
In that step, I have deducted 134 from both sides. Now, let's get rid of four on both sides by dividing it.
[tex]x=53[/tex]
Awesome! As we know, "x" is the width. Now, knowing the width, we can find the length simply by adding 67 to the variable x since length is 67 yards longer than the width.
[tex]53+67=120[/tex]
Great! Our answer is formed.
Answer: Length of the rectangle is 120 yards, and width of the rectangle is 53 yards.
A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone?
Answers
Cylinder Volume = 3.14159 * 1 * 21
Cylinder Volume = 65.97 cc
Volume Cone = [PI * radius^2 * height] / 3
radius^2 = 3 * 65.97 / (3.14159 * 7)
radius^2 = 9
radius = 3 centimeters
Zaira spent 55 hours in 2 weeks working on a science project. she worked 32 hours the first week. Write and solve an addition equation to find the amount of time she spent working the second week.
Answers
55 hours in 2 weeks
32 hours in the first week
So, 32 plus the amount of time she worked on the project the second week adds up to 55.
32 + x = 55
Now, simply solving! What you do to one side, you do to the other in order to isolate the variable
(32 - 32) + x = (55 - 32)
x = 23
She worked 23 hours on the project during the second week!
Which of these numbers is an irrational number? of these numbers is an irrational number? 3⁄5, Square root of 4, Square root of 25, Square root of 20, 5/3
Answers
Information is given about a polynomial f left parenthesis x right parenthesisf(x) whose coefficients are real numbers. find the remaining zeros of f. degree 3; zeros: negative 8 comma negative 3 minus i−8, −3−i enter the remaining zeros of f.
Answers
The remaining zero of f(x) is -3+i.
Which of these states had a flat state income tax in 2009
Apex
A.Michigan
B.New Hampshire
C.South Carolina
D.Georgia
Answers
Answer:
The correct answer is:
Michigan.
Michigan is the state that had a flat state income tax in 2009.
Step-by-step explanation:
A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.
Flat tax benefits higher income brackets progressively due to decline in marginal value.
The state that had a flat state income tax in 2009 is:
Michigan.
Michigan is a flat-tax state that levies a state income tax of 4.25%
How long will it take for 750 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 68 mg?
A. ≈ 50 days
B. ≈ 54 days
C. ≈ 48 days
D. ≈ 52 days
Answers
y = A (b) ^ t
Where,
A: initial amount
b: decrease rate
t: time
Substituting values:
y = 750 (0.5) ^ ((1/15) * t)
The number of days to reach 68 mg is:
68 = 750 (0.5) ^ ((1/15) * t)
Clearing t:
(0.5) ^ ((1/15) * t) = (68/750)
log0.5 ((0.5) ^ ((1/15) * t)) = log0.5 (68/750)
(1/15) * t = log0.5 (68/750)
t = 15 * log0.5 (68/750)
t = 51.94
Rounding:
t = 52 days
Answer:
D. ≈ 52 days
Answer:
52 Days
Step-by-step explanation:
help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.
A. x=2, y=1
B. x=3, y=2
C. x=1, y=2
D. x=2, y=3
Answers
well it means that 3y = x + 3, and that y + 1 = x, when does that happen anyway? let's see,
[tex]\bf \begin{cases} 3y=x+3\\ y+1=\boxed{x} \end{cases}\implies 3y=\boxed{y+1}+3\implies 3y=y+4 \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2\\\\ -------------------------------\\\\ \textit{and since we know that }y+1 =x\implies (2)+1=x\implies 3=x[/tex]
abcd is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC s 4y-6 and the length of CD is 8y-18, find the value of y. 30 points for brainliest!
Answers
AB = 7y - 4
CD = 8y - 18
In any isosceles trapezoid, the two legs are of equal length.
Therefore, AB = CD
⇒ 7y - 4 = 8y - 18
Add 18 to both sides of the equation
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Subtract 7y from both sides of the equation
7y - 7y + 14 = 8y - 7y
14 = y
⇒ y = 14
The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.
Given :
ABCD is an isosceles trapezoid with legs AB and CD and base BC.If the length of AB is (7y - 4), the length of BC s (4y - 6) and the length of CD is (8y - 18).The two legs are of equal length In any isosceles trapezoid that means:
7y - 4 = 8y - 18
Add 18 on both sides in the above equation.
7y - 4 + 18 = 8y - 18 + 18
7y + 14 = 8y
Now, subtract 7y on both sides in the above equation.
7y + 14 - 7y = 8y - 7y
Simplify the above expression in order to get the value of 'y'.
y = 14
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Assume that the grasshopper in the food pyramid above must eat half its body weight in grass each day. If an average-size grasshopper weighs 2 grams, and 1 blade of grass weighs 0.1grams (one tenth of a gram), how many blades of grass does the grasshopper need to eat each day?
Answers
We have:
"must eat half its body weight in grass each day":
(2 grams) * (1/2) = 1 gram
Then,
"1 blade of grass weighs 0.1grams"
Then the amount you need to eat is given by:
N = (1) / (0.1)
N = 10 blades of grass
Answer:
the grasshopper needs to eat 10 blades of grass each day
Answer:
The grasshopper needs to eat 10 blades of grass each day.
Step-by-step explanation:
The grasshopper in the food pyramid above must eat half its body weight in grass each day.
The average weight of the grasshopper is 2 grams.
The weight of one blade of grass is 0.1 grams.
Now,
The weight of grass eating by the grasshopper per day is 1 gram.
Let us assume that the grasshopper eats the "n" number of blades of the grass.
Therefore,
[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]
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determine if the number is written in scientific notation. if not explain 5.6 x 10^12
A. no its not written as a power of 10
B.no the first factor is not a number between 1 and 10
C. yes the number is written in scientific notation
Explain your answer please
Answers
Explanation:
In scientific notation, we have a decimal number multiplied by a power of 10. The decimal number has the decimal point behind the first non-zero digit, and the exponent on the power of 10 tells us how many places to move the decimal.
In this problem, we have 5.6, which has the decimal after the first non-zero digit. We also have 10¹², which tells us to move the decimal 12 places.
This is in scientific notation.
Answer:
C. Yes, the number is written in scientific notation.
Step-by-step explanation:
We have been given a number [tex]5.6\times 10^{12}[/tex]. We are asked to determine whether our given number is written in scientific notation or not.
We know that when a number greater than 1 and less than 10 is multiplied by a power of 10, then the number is written in scientific notation.
Upon looking at our given number we can see the number 5.6 is between 1 and 10. In addition, 5.6 is being multiplied by 10 to the power 12.
Therefore, our given number is written in scientific notation and option C is the correct choice..
true or false 120% of a whole number is always greater than the number? and why?
Answers
100% = [tex] \frac{100}{100}[/tex]
percent means per 100.
so 120% = 120/100 = 1.2
120% of a whole number. For example 120% * 10 = [tex] \frac{120}{100} * 10 [/tex] = 12
is it greater than 10.
20 Points!!!
For working 13 hours you earned $45.50 and $94.50 for 27 hours. What is your rate of pay in dollars per hour? a. 14 dollars per hour b. 3.50 dollars per hour c. 6.50 dollars per hour d.2.07 dollars per hour
Will give branliest!!!
Help ASAP.
Answers
Answer:
$3.50 per hour
Step-by-step explanation:
Given : For working 13 hours you earned $45.50 and $94.50 for 27 hours
To Find :What is your rate of pay in dollars per hour?
Solution :
Pay for 13 hours = $45.50
So, Pay for 1 hour = [tex]\frac{45.50}{13}[/tex]
Pay for 1 hour = [tex]3.50[/tex]
So, rate is $3.50 per hour
So, Option B is true
Hence rate of pay in dollars per hour is $3.50 per hour
Find the function rule.
X: -2, -1, 0, 1, 2
Y: 9,4, -1, -6, -11
Answers
The function rule is y = -5x - 1 , obtained by observing the linear relationship where y decreases by 5 as x increases by 1.
To find the function rule that relates the values of x to y , let's first observe the pattern in the given data:
[tex]x & y \\-2 & 9 \\-1 & 4 \\0 & -1 \\1 & -6 \\2 & -11 \\[/tex]
Notice that as x increases by 1, y decreases by 5. This suggests a linear relationship between x and y , where the slope of the line is -5.
The general form of a linear function is ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
To find the y-intercept, let's pick any point from the table, for example, when ( x = 0 ), ( y = -1 ).
So, we can plug the values of ( x ) and ( y ) into the linear function formula:
[tex]\[-1 = (-5)(0) + b\][/tex]
[tex]\[-1 = 0 + b\][/tex]
[tex]\[b = -1\][/tex]
Now we have the slope (( m = -5 )) and the y-intercept (( b = -1 )), so the function rule is:
[tex]\[ y = -5x - 1 \][/tex]
Now, let's verify this function rule with another point from the table, for example, when ( x = 2 ):
[tex]\[ y = -5(2) - 1 \][/tex]
[tex]\[ y = -10 - 1 \][/tex]
[tex]\[ y = -11 \][/tex]
This matches the value of ( y ) in the table, confirming that our function rule is correct.
The radius of a cylinder is increased by a factor of 5. The height is not changed.
What is the effect of the increase on the volume of the cylinder?
A) The volume of the cylinder increases by a factor of 5.
B) The volume of the cylinder increases by a factor of 25.
C) The volume of the cylinder increases by a factor of 15.
D) The volume of the cylinder increases by a factor of 10.
Answers
When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.
Explanation:The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.
Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.
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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]
Let's analyze the relationship between the volume of a cylinder and its dimensions.
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
[tex]\( r \)[/tex] is the radius of the cylinder,
[tex]\( h \)[/tex] is the height of the cylinder.
Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]
Now, let's compare the volumes before and after the increase in radius:
1. Original Volume [tex](\( V_{\text{original}} \))[/tex]
[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]
2. New Volume [tex](\( V_{\text{new}} \))[/tex]
After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].
[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]
Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]
[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]
45% of 40 is 18% of what number?
Answers
Answer:
45% of 40 is 18% of 100
Step-by-step explanation:
45% of 40 is 18% of what number
First we find out what is 45% of number 40
45% times 40
[tex]\frac{45}{100} * 40= 18[/tex]
Now we find
18 = 18% of what number
Let the unknown number be x
18 = 18% * x
[tex]18= \frac{18}{100} * x[/tex]
18 = 0.18 * x
Divide by 0.18 on both sides
100= x
So 45% of 40 is 18% of 100
The complete statement is 45% of 40 is 18% of 100
How to determine the number that completes the statementFrom the question, we have the following parameters that can be used in our computation:
45% of 40 is 18% of what number
Represent the number with x
So, we have
45% of 40 is 18% of x
Express as an equation
45% of 40 = 18% of x
Next, we have
18 = 0.18x
Divide through by 0.18
x = 100
Hence, 45% of 40 is 18% of 100
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HELP ASAP!!!!!!!!!!!!!!!!!!!!
a. 49
b. 12
c. 7
d. 1
Answers
you know a and c
a=24
c=25
24 squared + x squared = 25 squared
576+x squared =625
subtract 576 from both sides
x squared = 49
square root x and 49
x=7
C is the answer
A flower garden is in the shape of a right triangle. One leg of the triangle is 6 ft long and the hypotenuse is 12 ft long. What is the length of the other leg?
answers
A. 10.4ft
B.12.8ft
C13ft
D14.6ft
Answers
If this answer helped you and was correct you can name me "Brainliest." ty :)
Which of the following is a cubic binomial
A.w^3-6w^2+9
B.7a^3+4a^-2
C.-y^3+3y^5
D.x^2-2x^3
Answers
this is because it has two terms, and the first term has a power of 3