Equation of a line passing through the point (5, -6) and parallel to 3x + 5y = 7
First find the slope of the equation 3x + 5y = 7
Re-arrange
5y = -3x + 7
Divide through by 5
\(y=-\frac{3}{5}\text{x + }\frac{7}{5}\)compare the above with y = mx + b
slope (m) = -3/5
Parallel equations have same slope
The slope of the equatiion is -3/5
substitute
x₁ = 5 y₁=-6 m=-3/5 in the formula below
y- y₁ = m(x - x₁)
\(y+6=-\frac{3}{5}(x\text{ -5)}\)\(y\text{ + 6 =}\frac{-3}{5}x\text{ +3}\)\(\frac{3}{5}x\text{ + y = 3-6}\)\(\frac{3}{5}x+y=-3\)\(3x+\text{ 5y =-15}\)There is a mound of g pounds of gravel in a quarry. Throughout the day, 200 pounds of gravel is added to the mound. Two orders of 700 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel.
Answer:
\(\fbox {2,400 pounds}\)
Step-by-step explanation:
Information we have :
200 pounds is added2 orders of 700 pounds is removed1,200 pounds remainWhat we need to find :
Original amountSolving :
g + 200 - 2(700) = 1200g + 200 = 1200 + 1400g + 200 = 2600g = 2,400 pounds of gravelYou and your family go camping.
Your campsite is square. The area
of your campsite is 900 square
feet. What is the perimeter of the
campsite?
Answer:
The campsite would be 65 m by 65 m. 65 x 65 = 4,225. Another way to put it (and the way to figure it out) is that the square root of 4,225 is 65.
Step-by-step explanation:
What is the distance between the points (-2,1) and (5,-4)
Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
Distance between two pointsThe distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= \(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)
Distance between the points (-2,1) and (5,-4)In this case, you know:
(x1, y1): (-2,1)(x2, y2): (5,-4)Replacing in the definition of distance:
distance= \(\sqrt{(5-(-2))^{2} +(-4-1)^{2} }\)
distance= \(\sqrt{(5+2)^{2} +(-5)^{2} }\)
distance= \(\sqrt{7^{2} +(-5)^{2} }\)
distance= \(\sqrt{49+25 }\)
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
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consider the following formula used to estimate the height ,h, of a seedling after w weeks since planting:
Answer:
B
Step-by-step explanation:
solve for W
subtract 8/5 from both sides
then multiply by 5
hope this was helpful
Kelly wants to plant flowers on the edge of a circular flowerbed around a tree. If the radius of the flowerbed is 2 feet, and she wants to place the
plants approximately 3 feet apart. How many flower plants should she buy?
A
2 flowers
B
3 flowers
D
4 flowers
5 flowers
Answer:
Divide the given diameter by 2 to obtain the radius in feet.
Divide the radius in feet by 3 to obtain the radius in yards.
Square the radius and multiply the result by an approximation of suitable for your required level of precision. This calculation will provide you with the area of the circle in square yards.
Multiply the calculated area by 13 and round to the nearest whole number. (unless you think the hero of this story knows of a nursery that will sell him fractional parts of a plant)
Notes on approximation of for this problem. Either , , or any representation of to greater precision will result in the same number of plants after rounding to the nearest whole number of plants.
John
Step-by-step explanation:
Can y’all please help me with one of my problems
Answer:
x= -2
h(x)= 5/x+6
h(-2)= 5/-2+6
= 5/4
=1.25
Bill runs each lap in 5 minutes. He will run at most 10 laps today. What are the possible numbers of minutes he will run today?
Use t for the number of minutes he will run today.
Write your answer as an inequality solved for t .
Answer:
A possible number of minutes is 50
Step-by-step explanation:
5 x 10 = t
Answer:
10 x 5 equals 50mins in total. ^_^
Step-by-step explanation:
An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$5000 with a standard deviation of o-$250
distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses.
If we create a sampling distribution with a sample of 64 homeowners, what is the z-score that corresponds to a sample average of $5100?
Round to four decimals
Type your answer.
1 point
Answer:
To find the z-score, we use the formula:
z = (x - mu) / (sigma / sqrt(n))
where:
x = sample mean = $5100
mu = population mean = $5000
sigma = population standard deviation = $250
n = sample size = 64
Substituting the values, we get:
z = (5100 - 5000) / (250 / sqrt(64))
z = 2.56
Therefore, the z-score that corresponds to a sample average of $5100 is 2.56 (rounded to four decimals).
Step-by-step explanation:
I clicked on the black picture. thought is was the box to enter the answer.
Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The logarithm expression can be simplified to:
In(6x^9)-In(x^2) =7·ln(6x)
How to write this as a single logarithm?There are some logarithm properties we can use here.
log(a) - log(b) = log(a/b)
log(a^n) = n*log(a)
(these obviously also apply to the natural logarithm)
Now let's look at our expression, it says that:
In(6x^9)-In(x^2)
Using the first rule, we can rewrite this as.
In(6x^9)-In(x^2) = ln(6x^9/x^2)
Now solving the quotient in the argument:
ln(6x^9/x^2) = ln(6x^7) = 7·ln(6x)
That is the expresison simplified.
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Ayesha is the marketing manager for Superior Stationery Suppliers, a company that supplies a variety of stationery items to its customers, mostly businesses. Ayesha has started a process to understand the key buying motivations for customers. Ayesha must consider each of the following variables in the process, except...
risms
gure.
The rectangular prism has
✓ lateral faces.
The rectangular prism has a surface area of
square inches.
Answer:
4 lateral faces
254 square inches
Answer:
The one above is right just did it on edge.
Step-by-step explanation:
Make a equation for the scatter plot line
Answer:
y = -7.2x + 540
Step-by-step explanation:
to find the slope I used the x-and-y intercepts: (0, 540) and (75, 0)
slope = 540/-75 or -7.2
Find the measure of ACD
A - 36 degrees
B - 126 degrees
C - 162 degrees
D - 216 degrees
Answer:
C
Step-by-step explanation:
i assume its
C.
Which graph represents 12 = 3x + 4y line a, line b, line c
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
Which statement applies to the transformed function f(x)−4
?
The function is odd, and the graph would be shifted downward. option(2)
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units.
The statement "f(x) - 4" represents a transformation applied to the original function f(x). This transformation involves subtracting 4 from the values of the function f(x) for all x. In other words, it shifts the entire graph of f(x) downward by 4 units along the y-axis.
Specifically, each y-value of the original function f(x) is reduced by 4. For example, if the original function had a point (x, y), the transformed function f(x) - 4 would have the corresponding point (x, y - 4). This means that every point on the graph is shifted downward by 4 units.
This transformation affects the overall shape, position, and properties of the function. The new graph will have the same general shape as the original, but it will be translated downward. If there were any intercepts or turning points in the original function, they will also be shifted downward by 4 units. Option(2)
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Pls answer this fast
Answer: C
Step-by-step explanation:
1. divide 3 by 2 to find out how many pounds of blueberries she picked each day. 3/2 is 1.5
2. multiply 1.5 by 16 to convert to ounces. 1.5x16 is 24.
3. she picked 24 ounces of blueberries each day.
3/8 of {38/5-1/3{5/4+10/3}×12/5
Answer:
1863/275=6.7745recurring
Step-by-step explanation:
Dont u have a calculator
¿De qué número 64 es el 80%?
If 20 articles cost ₹ 90, then the cost of 9 articles is
Answer:
₹ 40.50
Step-by-step explanation:
Cost of 20 articles = ₹ 90
Cost of 1 article = ₹ 90/20
Cost of 9 article = 9 x 90/20 = ₹ 40.50
If (x - 3)2 = 5, what values of x make the quadratic equation TRUE?
O A
15
+
3
O B. 3+15
O C. --J5+ 3
D. -3+15
Answer:
I need Help on this one too.
Step-by-step explanation:
please help
Answer: Its b
Step-by-step explanation:
Marcia is building a doghouse and needs to cut plywood for the roof. Plywood comes in sheets that are 48
square feet. Marcia needs two squares that are each 12 square feet. How much plywood is left over?
A) 24ft
B) 12ft
C)60ft
D) 36ft
Answer:
A,24ft
Step-by-step explanation:
you have 48^2ft and Marcia needs two squares that are each 12^2ft,
12+12=24
48-24=24
answer=24ft
Moe puts $1500 in a bank certificate that pays an annual rate of 4.5% compounded annually. No withdrawals or deposits are made. How much will the certificate be worth (to the nearest dollar) at the end of 7 years?
Answer:
FV= $2,041.29
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $1,500
Number of periods (n)= 7 years
Interest rate (i)= 4.5% = 0.045
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
FV= 1,500*(1.045^7)
FV= $2,041.29
Someone help me with this!!!!.... Given f(x)=x^2−3x−4
and g(x)=|x+3|−2, which value is a solution to the equation f(x)=g(x) ?
A
−4
B
−3
C
−1
D
4
Answer:
C -1
Step-by-step explanation:
in such a case the simplest way is to simply try the 4 numbers and see :
x² - 3x - 4 = |x + 3| - 2
x² - 3x - 2 = |x + 3|
A x = -4
(-4)² - 3×-4 - 2 = |-4 + 3|
16 + 12 - 2 = 1
26 = 1
wrong.
B x = -3
(-3)² - 3×-3 - 2 = |-3 + 3|
9 + 9 - 2 = 0
16 = 0
wrong.
C x = -1
(-1)² - 3×-1 - 2 = |-1 + 3|
1 + 3 - 2 = 2
2 = 2
correct.
D x = 4
4² - 3×4 - 2 = |4 + 3|
16 - 12 - 2 = 7
2 = 7
wrong.
What is the answer please help if you put a link I will report
Answer:
true.
Step-by-step explanation:
Provide the Domain and range.
Answer:
domain is like the membrane
Step-by-step explanation:
domain
If log₂(4x + 6) = 4, then x = ____
You may enter the exact value or round to 4 decimal places.
Answer: -1/2
Step-by-step explanation: To solve this problem, we can use the properties of logarithms to isolate the variable x on one side of the equation. The properties of logarithms tell us that the logarithm of a product is the sum of the logarithms of the factors, and that the logarithm of a power is the exponent times the logarithm of the base.
If log₂(4x + 6) = 4, we can rewrite the left side of the equation as follows: log₂(4x + 6) = log₂(2^4 * (2x + 3))
Then, using the property of logarithms that the logarithm of a product is the sum of the logarithms of the factors, we can simplify the equation as follows: log₂(4x + 6) = 4 + log₂(2x + 3)
Now, we can use the property of logarithms that the logarithm of a power is the exponent times the logarithm of the base to simplify the equation even further: log₂(4x + 6) = 4 + 1 * log₂(2x + 3)
Since the logarithm of a power is the exponent times the logarithm of the base, this means that the logarithm of a number is the logarithm of that number divided by the logarithm of the base. Therefore, we can divide both sides of the equation by log₂ to isolate the variable x on one side of the equation:
log₂(4x + 6) / log₂ = 4 + 1 * log₂(2x + 3) / log₂
(4x + 6) / 1 = 4 + (2x + 3) / 1
4x + 6 = 4 + 2x + 3
4x + 6 = 2x + 7
2x = -1
x = -1/2
Therefore, if log₂(4x + 6) = 4, then x = -1/2.
17. You want to test a new athlete's-foot treatment. You test men and women separately, randomly dividing them into treatment and control groups. The treatment groups receive the new treatment and the control groups receive an inert powder that resembles the treatment. Neither the subjects nor the test administrators know which groups receive the treatment and which groups receive the inert powder. At the end of the experiment, all subjects are asked to rate their degree of relief from athlete's foot. These scores are compared between groups. Which of the following groups of elements were present in this study?
a. Randomization, blocking, placebo, comparative, double-blind
b. Comparative, randomization, placebo, blind
c. Double-blind, randomization, comparative, placebo
d. Randomization, stratified sample, placebo, blind, treatment
e. Double-blind, control, observational, blocking
Answer:
a. Randomization, blocking, placebo, comparative, double-blind
Step-by-step explanation:
1. Randomization is the process of assigning the subjects in an experiment to any of the treatment groups. This was applied in this experiment when the researcher randomly divided the men and the women into treatment and control groups.
2. Blocking is introduced in an experiment in order to remove nuisance factors. The researcher introduced blocking in this experiment when he divided the men and women on the basis of gender.
3. The Placebo is the inert powder that was given to a group. It has no effect on the participants who receive it.
4. Comparative research compares the result from two groups. This is seen in this research hen the researcher compares the scores between the groups.
5. A double-blind experiment is one where neither the subjects nor the test administrators know which groups receive a treatment. This factor is present in this test.
Ryan earns $85.00 for babysitting each week. How many weeks will he need to babysit in order to buy airpods for $179.00?
Answer:
3 weeks
Step-by-step explanation:
85 + 85 = 170
But thats not enough so he needs to work another week to get the other $9 to afford the airpods.
So . 85 + 85 + 85 = 255
Can the following quadrilateral be proven to be a parallelogram based on the given information? Explain.
(picture shown below)
A.) No. It cannot be proven because at least two of the adjacent angles are not congruent to each other
B.) Yes. It can be proven because both pairs of opposite sides are congruent.
C.) No. It cannot be proven because it does not have an angle that is supplementary to both of its consecutive angles.
D.) Yes. It can be proven because both pairs of opposite angles are congruent.
Answer:
Step-by-step explanation:
The answer is, no!
Step-by-step explanation:
The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.
So, here is the given information on what we need to classify a shape as a parallelogram:-
1) Parallel Sides
2)Opposite Sides are equal.
3) Adjacent sides are not equal.
4) Opposite angles are equal.
5)Adjacent angles are not equal.
Based on this, we can classify a shape as a parallelogram.
Hope, this answer helps!
x - 2y = - 7
3x + 2y = 3
Answer:
1. x = − 7 + 2 y
2. x = 1 − 2 y /3
Step-by-step explanation:
Answer: [1] x + 2y = 7
[2] 3x - 2y = -3