Answer:
[tex]x=3, y=-1[/tex]
Step-by-step explanation:
[tex]3(3y+6)+2y=7 \\ \\ 9y+18+2y=7 \\ \\ 11y+18=7 \\ \\ 11y=-11 \\ \\ y=-1 \\ \\ \\ x=3(-1)+6=3[/tex]
Rosa is planting bulbs in her garden. She can plant 3 bulbs every 2 minutes. How long will it take her to plant 57 bulbs?
Answer: It would take her 38 minutes to plant 57 bulbs.
Step-by-step explanation:
please perform the following division !!
Answer:
[tex]\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{3}{a}+\frac{2}{b}}{\frac{5}{a^2}-\frac{2}{b^2}} \\ \\ =\frac{a^2 b^2 \left(\frac{3}{a}+\frac{2}{b} \right)}{a^2 b^2 \left(\frac{5}{a^2}-\frac{2}{b^2} \right)} \\ \\ =\frac{3ab^2 + 2a^2 b}{5b^2 - 2a^2}[/tex]
Two friends take a 4000-mile cross-country trip together, but they drive their own cars. Car A has a 10-gallon gas tank
and averages 30 miles per gallon, while car B has a 20-gallon gas tank and averages 20 miles per gallon. Assume
both drivers pay an average of $2.65 per gallon of gas.
a. What is the cost of one full tank of gas for car A? For car B?
b. How many tanks of gas do cars A and B each use for the trip?
c. About how much do the drivers of cars A and B each pay for gas for the trip
Answer:
a.
Car A: $26.50
Car B: $53.00
b.
Car A: 13 1/3
Car B: 10
c.
Car A: $353
Car B: $530
Step-by-step explanation:
Car A: 10 gal, 30 mpg
Car B: 20 gal, 20 mpg
a.
Car A: 10 gal × $2.65/gal = $26.50
Car B: 20 gal × $2.65/gal = $53.00
b.
Car A: 1 full tank will drive 10 gal × 30 mpg = 300 miles
4000 miles / 300 miles = 13 1/3
Car B: 1 full tank will drive 20 gal × 20 mpg = 400 miles
4000 miles / 400 miles = 10
c.
Car A: 13 1/3 × 10 gal × $2.65/gal = $353
Car B: 10 × 20 gal × $2.65/gal = $530
Using the slope formula, find the slope of the line through the points (0,0) and (5,10). Use pencil and paper. Explain how you can use mental math to find the slope of the line.
5. a rectangular plot of land is to be enclosed by fencing. one side is along a river and so needs no fence. if the total fencing available is 600 meters, fi d the dimensions of the plot to have maximum area.
Using basic geometry and applying the fence only on 3 sides, The required dimensions of the plot to have maximum area is 200 x 200.
What do you mean by geometry?A subfield of mathematics called geometry examines the dimensions, placements, angles, and sizes of objects.
What do you mean by dimensions of a figure?In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.
fence length available = 600m
We only need to fence 3 sides. So length in each side = 600/3
=200m
So, Final dimension = 200 x 200
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Sandy wants to graph the equation y=2x^2+4x-6. What set of key points can she use to graph the equation?
The key points of option (B) are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
What are graphs?Write the equation in the form y = MX + b to determine the slope m and the y-intercept.
This will allow you to graph the equation using the slope and y-intercept (0, b). The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, we have the equation:
y=2x^2+4x-6
Now, plot this equation in the graph as follows:
(Refer to the image attached below)
x-axis: (1, 0)
y-axis: (-3, 0)
Vertex: (-1, -8)
Therefore, the key points of option (B) which are the x-axis: (1, 0), y-axis: (-3, 0), and Vertex: (-1, -8) she can use to graph the given equation.
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What happens to y=x when the y-intercept is changed
Answer:
When the y-intercept of a line is changed, the line will shift up or down along the y-axis. The slope of the line will remain the same, but the point at which the line crosses the y-axis will change. This means that the position of the line on the graph will change, but the overall shape of the line will stay the same. For example, if the y-intercept of the line y=x is changed from (0,0) to (0,5), the line will shift up by 5 units and will now be represented by the equation y=x+5. This will cause the line to intersect the y-axis at the point (0,5) instead of (0,0).
A gold mine has two elevators, one for equipment and another for the miners. The equipment elevator descends 4 feet per second. The elevator for the miners descends 15 feet per second. One day, the equipment elevator begins to descend. After 27 seconds, the elevator for the miners begins to descend. What position of each elevator relative to the surface after 17 seconds? At that time, which elevator is deeper?
1. The position (distance covered) of each elevator relative to the surface after additional 17 seconds is as follows:
The equipment elevator descended 176 feet from the surface.The miners' elevator descended 255 feet from the surface.2. After 17 seconds, the miners' elevator is deeper by 79 feet than the equipment elevator.
How are the distances computed?Distance is a function of speed and time.
This implies that distance is the product of speed and time.
The descent speed of the equipment elevator = 4 feet per second
The total time in seconds the equipment elevator descended = 44 seconds (27 + 17)
The descent distance covered in 44 seconds = 176 feet (44 x 4)
The descent speed of the miners' elevator = 15 feet per second
The total time in seconds the miners' elevator descended = 17 seconds
The descent distance covered in 17 seconds = 255 feet (17 x 15)
Thus, the difference in the descent distance between the equipment elevator and the miners' is 79 feet (255 - 176).
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Which of these statements is FALSE? a.) A data set is a characteristic of an individual member of the population that can be measured. b.) The distribution describes what values the variables take and how often they take those values. c.) A data set is a list of numbers that is associated with context. d.) The distribution can be summarized by a frequency table.
The statement A ie A data set is a characteristic of an individual member of the population that can be measured is false
What is statement ?
Depending on the context, the term "statement" in logic can refer to either a proposition or a coherent declarative utterance that can be true or false. Which is the claim a true or false declarative phrase makes.
A sentence that asserts something to be true is called a statement. In the fields of law, banking, and government, there are more types of statements. Every statement makes a claim or a point. If you see an accident, you have to tell the police what you observed in a statement.
A statement is a directive issued to the computer that tells it to carry out a specific task, like display something on the screen or gather input. A succession of assertions make up a computer program.
When It applies to the whole population, in general
The statement that is false is A data set is a characteristics of an individual member of the population that can be measured
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Help ASAP FIRST CORRECT ANSWER GET BRAINLY ANSWER
Diane holds an accounting degree what company might be interested in hiring Diane
Answer: EY
Step-by-step explanation:
Ey is a business' that need people with an accounting degree
Answer:
meaningfulness
Step-by-step explanation:
in psychology, is described as a process through which the high degree of salience or significance of a particular piece of information is being reflected. Information that encompasses meaning related to an individual is described as meaningful. However, meaningfulness is highly dependent on the understanding or comprehension of a particular meaning.
Suppose that 18 inches of wire costs 72 cents.
At the same rate, how much (in cents) will 39 inches of wire cost?
Answer:
39 inches of wire would cost 156 cents
Step-by-step explanation:
1) Make an Equation
18x = 72
2) Solve for x to determine cost per inch of wire
x = 72/18
x = 4
3. Multiply x value by 39 to get the cost for 32 inches of wire (c)
39x = c
39 (4) = c
156 = c
4) Find 14.56 ÷ 2.8.
First, find an equivalent expression with a
whole number divisor.
1.456 = 28
14.56 28
145.628
1,456 ÷ 28
The value of the expression is 5.2.
The equivalent expression with a whole number divisor is 145.6/28.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
14.56 ÷ 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
= 145.6 / 28
= 5.2
Thus,
The value of the 14.56÷ 2.8 is 5.2.
The equivalent expression is 145.6/28.
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Answer:
The expression answer is 5.2.
145.6/28 is the equivalent expression using a whole number divisor.
Explanation:
For the time being, we have:
14.56 2.8
= 14.56 / 2.8
= 14.56 x 10 / 28
For the time being, we have:
As a result, the value of 14.56 2.8 is 5.2.
145.6/28 is an equivalent expression.
Please help I need it please hrlpppp
The composition of the two functions g of x and f of x is:
(g o f)(x) = 3x² - 15x + 1
How to find the composition of functions?Here we have three known functions, these are:
f(x) = x² - 5xg(x) = 3x + 1h(x)= (x - 1)/xAnd we want to find the composition of functions:
(g o f)(x)
That means that we need to evaluate the function g(x) on f(x), so we will get:
(g o f)(x) = g( f(x))
Then we will get:
g( f(x)) = 3*f(x) + 1
Now we can replace the actual function f(x) there, so we will get:
g( f(x)) = 3*f(x) + 1
g( f(x)) = 3*(x² - 5x) + 1
Now we can simplify that:
g( f(x)) = 3*(x² - 5x) + 1
g( f(x)) = 3*x² - 3*5x + 1
g( f(x)) = 3x² - 15x + 1
Then the composition of functions is:
(g o f)(x) = 3x² - 15x + 1
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Find the slope for the answer
The Equation for the given line in the graph is x+ y = 3.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
From the Graph take two points (0, 3) and ( 3, 0)
So, slope for the line
= ( 0-3 ) ( 3-0)
= -3/3
= -1
So, the Equation of line is
y[tex]- y_1[/tex] = m(x[tex]-x_1[/tex])
y- 3 = (-1)(x- 0)
y- 3 = -x
y+ x = 3
x+ y = 3
Hence, the Equation line is x+ y= 3.
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a pentagon is made up of an equilateral triangle abc of side length 2 on top of a square bcde. circumscribe a circle through points a, d and e. what is the radius of the circle
An equilateral ABC with a side length of 2 cm is placed on top of a square to form a pentagon. BCDE Draw a circle around points A, D, and E. The circle's diameter is: A 1+ 2 3
How many sides are there in a pentagon?An equilateral pentagon is a polygon in the Euclidean plane in geometry that has five equal-length sides. It may create a family of pentagons because the five of its vertex angles can take on a variety of sets of values.
An equilateral pentagon is what?An equilateral pentagon is a polygon with five equal sides in geometry. In turn, its five internal angles may accept a variety of sets of values, allowing it to create a family of pentagons. It is necessary for all angles to sum up to 540 degrees and fall within the range of 0 to 360 degrees.
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Marcus has $400 in his savings account.
He decides that he will put a fixed
amount of money into his account every
month. His goal is to save $1,000.
A formula describing this scenario is:
1000=400+ xm
where
x = amount saved each month
m = number of months
To reach his goal, Marcus will have to save $(600/m) each month.
What is a mathematical equation and expression?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that Marcus has $400 in his savings account. He decides that he will put a fixed amount of money into his account every month. His goal is to save $1,000.
The formula describing the Marcus saving's scheme is -
1000 = 400 + xm.
where -
[x] - amount saved per month
[m] - number of months
Solving the equation further to find the amount saved per month is -
1000 = 400 + xm
1000 - 400 = xm
600 = xm
x = (600/m)
Therefore, Marcus will have to save $(600/m) each month to reach his goal.
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Approximate -12+√32 to the nearest tenth.
-6.3
-5.7
5.7
6.3
The approximate value of -12 + [tex]\sqrt{32}[/tex] is option (A) -6.3
The given expression is
-12 + [tex]\sqrt{32}[/tex]
First find the value of [tex]\sqrt{32}[/tex]
Prime factorization of 32
Prime factorization is defined as the method of expressing a number as a product of its prime factors
32 = 2 × 2 × 2 × 2 × 2
Therefore,
[tex]\sqrt{32}[/tex] = 2 × 2[tex]\sqrt{2}[/tex]
Multiply the numbers
[tex]\sqrt{32}[/tex] = 4[tex]\sqrt{2}[/tex]
The value of [tex]\sqrt{2}[/tex] = 1.414
The the value of 4[tex]\sqrt{2}[/tex] = 4 × 1.414
Multiply the numbers
= 5.656
The value of the expression
-12 + [tex]\sqrt{32}[/tex] = -12 + 5.656
Add the numbers
= -6.344
Approximate value will be
≈ -6.3
Therefore, the result of the expression -12 + [tex]\sqrt{32}[/tex] is -6.3
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Regina ran 31 miles last week. This week, she ran 42.5 miles. What is her percent increase to the nearest tenth?
Answer:
36.8%
Step-by-step explanation:
PLEASE MARK BRAINLIEST
42.5-31=11.4
11.4/31 is approx 0.367741935 , or 36.7741935 %.
Rounding it to the nearest tenth gives you 36.8%.
how do i simplify 3(8x-4)-6x+6?
Answer:
18x−6
Step-by-step explanation:
Distribute
If random samples are drawn from two independent populations where we draw samples of size 51 from population A which has mean 20.1 and standard deviation 5.49, and samples of size 76 are drawn from population B with mean 27.3 and standard deviation 5.06, what is the standard error for the sampling distribution? Round to four decimal places.
the required standard error is 6.9 for the sampling distribution.
The standard error of the sampling distribution is given by the formula SE = sqrt( (SD1² / n1) + (SD2² / n2) )
As per the question, we are given that samples of size 51 are drawn from population A with a standard deviation of 5.49, and samples of size 76 are drawn from population B with a standard deviation of 5.06.
Substituting these values into the formula, we get:
SE = √( (5.49² / 51) + (5.06² / 76) )
SE = √( (30.11) + (17.93) )
SE = √(48.04)
SE = 6.9
Therefore, the required standard error is 6.9 for the sampling distribution.
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6. Which of the following strategies can
help you solve 4 x 6? Select all that
apply.
(6x6) + (6 x 6)
(4 x 3) + (4 x 3)
(5x5)+(4x 1)
(5x4) + (1x4)
(2x4) + (2x6)
Answer:
(4x3) + (4x3) and (5x4) + (1x4)
Step-by-step explanation:
When you multiply 4 by 3 you get 12. And 12 + 12 is 24. 4 x 6 is 24 so then that is an answer. And 5 by 4 is 20 and 1 x 4 is 4 you add them you get 24.
:)):))):)/):)::!:&’s
Answer:
ASA
Step-by-step explanation:
Drag the operation signs to make the equation true. A
not at all
12
x
+
(74) + 5
3 = 19
Answer: 12 / (7-4)+5 x 3=19
the / is the same as the dividing sign
Step-by-step explanation:
12 / (7-4)+5 x 3=19
12/3+15=19
4+15=19
19=19
Which number doesn’t share the same pattern as 2, 20, 4, 8, 300
Answer: 3
The full question is: Consider the numbers [2, 20, 4, 8, 300]. Which of the following options does not share the same pattern? Choices: 3, 4, 22, 600, 602, 1994
Step-by-step explanation:
The answer is 3 because all of the other number choices are even.
In the data set below, what is the value of the 1st quartile?
(6,7,8,9,10,12,14)
Answer: 7 is the first quartile
Step-by-step explanation:
method to find quartile
Order your data set from lowest to highest values
Find the median. This is the second quartile Q2.
At Q2 split the ordered data set into two halves.
The lower quartile Q1 is the median of the lower half of the data.
The upper quartile Q3 is the median of the upper half of the data.
If the size of the data set is odd, do not include the median when finding the first and third quartiles.
If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q2.
This is due tomorrow please help
The two solutions are (0, 1) and (-4, 0)
Increasing graphx-intercept= -4 and y-intercept = 1The slope of the graph is 0.25Two solutions on the lineFrom the question, we have the following parameters that can be used in our computation:
Graph of a linear relationship
From the graph of the linear relationship, we have the following points on the line
(0, 1) and (-4, 0)
Hence, the solutions are (0, 1) and (-4, 0)
Increasing or decreasingOn the graph, we can see that as x increases, the y value increases
This means that the graph is an increasing graph
The interceptsIn (a), we have
(0, 1) and (-4, 0)
These points represent the intercepts
So, we have
x-intercept= -4
y-intercept = 1
The slope of the lineThe slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (0, 1) and (-4, 0)
Substitute the known values in the above equation
So, we have the following equation
Slope = (0 - 1)/(-4 - 0)
Evaluate
Slope = 0.25
Hence, the slope of the line is 0.25
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6. Rachel has a $10,000, three-year loan with an APR of 7.25%.
a. What is the monthly payment?
b. What is the total amount of the monthly payments?
c. What is the finance charge?
a) Rachel's monthly payment for the $10,000 three-year loan with an APR of 7.25% is $309.92.
b) The total amount of the monthly payments is $11,157.12.
c) Rachel's finance charge for the loan is $1,157.12.
What is the finance charge?The finance charge is the interest and other fees paid for a loan or credit.
The finance charge is based on the annual percentage rate (APR).
The monthly payments, total monthly payments, and the finance charge can be determined using an online finance calculator as follows:
N (# of periods) = 36 months (3 years x 12)
I/Y (Interest per year) = 7.25%
PV (Present Value) = $10,000
FV (Future Value) = $0
Results:
Monthly Payment (PMT) = $309.92
Sum of all periodic payments = $11,157.12 ($309.92 x 36)
Total Interest (finance charge) = $1,157.12
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Container A has 300 liters of water, and is being filled at a rate of 6 liters per minute. Container B has 900 liters of water, and is being drained at 2 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
It will take 150 minutes for the two containers to have the same amount of water.
To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:
m = |A - B| / (a - b)
where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.
In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:
m = |300 - 900| / (6 - 2)
m = |-600| / 4
m = 600 / 4
m = 150 minutes
Therefore, it will take 150 minutes for the two containers to have the same amount of water.
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Write the equation of the line in fully simplified slope-intercept form.
The equation of the line in slope intercept form is y = 1 / 5 x + 7.
How to represent equation in slope intercept form?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's find the slope of the line as follows:
using (0, 7) and (5, 8)
m = 8 - 7 / 5 - 0
m = 1 / 5
m = 1 / 5
Therefore, let's find the y-intercept using (0, 7).
Hence,
y = 1 / 5 x + b
7 = 1 / 5 (0) + b
b = 7
Therefore, the equation of the line is y = 1 / 5 x + 7
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A crew of highway workers paved
mile in minutes. If they work at the same rate, what portion of a mile will they pave in one hour?
I don't know .............