Step-by-step explanation:
the slope of a line is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
a slope = 0 means that the y coordinate change is always 0, so y does not change anywhere on the line.
that makes y a constant c, and x can be any value completely independent of y.
the line is the summary of all points that have c as their y coordinate.
so, the general equation for such a line is simply
y = c
what is c ?
as we have one point on the line, remember the statement above : the line is the summary of all points that have c as their y coordinate.
that means (3, -4) must have the same y coordinate.
so, c = -4.
the equation of the line is therefore
y = -4
what is 7.25 converted as a fraction
Submit
Submit
Submit
7.25 would be 7 1/4 or 29/4
What does K =
2(k-3)/k+9 = 3/5
The value of k in the equation is 6.
How to solve equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Therefore, the equation can be solved as follows;
[tex]\frac{2k-3}{k+9}=\frac{3}{5}[/tex]
cross multiply
5(2k - 3) = 3(k + 9)
10k - 15 = 3k + 27
add 15 to both sides of the equation
10k - 15 = 3k + 27
10k - 15 + 15 = 3k + 27 + 15
10k = 3k + 42
subtract 3k from both sides of the equation
10k = 3k + 42
10k - 3k = 3k - 3k + 42
7k = 42
divide both sides by 7
k = 42 / 7
k = 6
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peter deposited $7,790 into an account that earns 4 5/8% interest, compounded annually. calculate the interest peter will earn after 42 months. how much will peter have in his account after 42 months?
The interest earned by Peter after 42 months is $1,335.60 and the total amount in his account is $9,125.60.
How to determine the accrued ( A ) and interest ( I ) amount in a compound interest?The formula for compound interest is expressed as;
A = P(1 + r/n)^nt
Where A is accrued amount, P is principal, r is interest rate, n is compound, and t is time period.
Given the data in the question;
Principal P = $7,790Annual interest r = 4 5/8%Compounded annually n = 1Time t = 42 monthsAccrued amount A = ?Interest I = ?First, convert the interest rate to decimal.
Rate r = 4 5/8% = (4×8 + 5 )/8%
Rate r = 37/8%
Rate r = 4.625%
Rate r = 4.625/100 = 0.04625 per pear
Next, convert time from months to years
Time t = 42 month = ( 42/12 )years
Time t = 3.5 years
To determine the accrued amount, plug the given values into the compound interest formula and solve for A.
A = P(1 + r/n)^nt
A = $7,790(1 + 0.04625/1)^( 1 × 3.5 )
A = $7,790(1 + 0.04625 )^( 3.5 )
A = $7,790(1.04625 )^( 3.5 )
Accrued amount A = $9,125.60
Note that; Accrued amount A = Principal P + Interest I
Hence;
Interest I = A - P
Interest = $9,125.60 - $7,790
Interest = $1,335.60
Amount in the account after 42 months is the same as the accrued amount A, this is $9,125.60.
Therefore, the interest earned is $1,335.60 and the accrued amount is $9,125.60.
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Two pieces of metal measure 1 1/6 and 3/12 yards each. Three times the amount of metal is needed for a project. How many yards total of medal is needed?
I’ll give brainliest!
By working with the given mixed numbers, we will get that for the project they need (4 + 1/4) yards of metal.
How many yards of metal are needed?At this point, we have two pieces that measures (1 + 1/6) yd and (3/12) yd, adding that length we get a total length:
L = (1 + 1/6) yd + (3/12) yd = (1 + 2/12) yd + 3/12yd = (1 + 5/12) yd
Now we know that we need 3 times that amount of metal for the project, then the total amount of metal that we need is:
3*L = 3*(1 + 5/12) yd = (3 + 15/12) yd
We can write this as a mixed number as:
(3 + 12/12yd + 3/12yd) = (4 + 3/12)yd = (4 + 1/4) yd
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joseph can ride his bike 32 miles in 5 hours. kyle can ride his bike 20 miles in 3 hours who would ride farther in 15 hours explain .
In finding the solution of the equation: 5 - 3x = 2 + 9, 3x is added to both sides of the equation first. Which of the following should be done next?
add -9
add -5
add -2x
The next step in solving the equation 5 - 3x = 2 + 9 is (a) add -9
How to determine the first step?From the question, we have the following equation that can be used in our computation:
5 - 3x = 2 + 9
When 3x is added to both sides, the equation becomes
5 = 2 + 9 + 3x
The next step is to eliminate 9 or 2 from the variable term
This can be done by adding -9 to both sides
So, we have:
-9 + 5 = 2 + 3x
Hence, the next step is (a) add -9
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A sprinter completed a 100 m run with
a time of 12.31 seconds.
Her time, t, has been truncated to a
hundredth of a second.
Write the error interval fort in the form
a ≤ t
The error interval is 12.305 ≤ t < 12.315 (by using rounding rules)
What is rounding rules?
Round the number up if 5, 6, 7, 8, or 9 follow the number you are rounding.
Round the number down if the rounded number is followed by a 0, 1, 2, 3, or 4. for e.g, 1.205 becomes 1.21 (rounding up) and if 1.21 (round the number down) then it will be 1.2.
In this question :
- Time = 12.31 seconds
- if we consider the thousandth digit then the times of 12.305 or greater and less than 12.315 are rounded to 12.31.
Therefore, the interval is 12.305 ≤ t < 12.315.
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HELP ASAP PLS I'LL GIVE BRAINLIEST..!
The average of the fraction of students on both classes who went on the field trip is; 13/20.
What is a fraction?A fraction represents a part of a number or any number of equal parts. A fraction is a ratio of two integers called the numerator and denominator.
Given that the sum of the fraction of both students in the two classes is;
3/5 + 7/10
We know that the LCM of the denominators which are 5 and 10 is 10
Therefore, the sum of both fractions = 6/10 + 7/10 = 13/10
The average = 13/10 /2 = 13/10 x 2
The average = 13/20
Therefore, the average of the fraction of students on both classes who went on the field trip is; 13/20.
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-6(x)² + y³ - 8.
For x = 3
For y = 2
Answer:
- 54
Step-by-step explanation:
substitute x = 3 , y = 2 into the expression
- 6x² + y³ - 8
= - 6(3)² + 2³ - 8
= - 6(9) + 8 - 8
= - 54 + 0
= - 54
Solve the formula A=yn+y for n
Solving for n for n in the formula A = yn + y is expressed as: n = A/y - 1.
How to Solve for the Formula for a Variable?
Solving for the formula for a variable, means we should make the variable the subject of the formula by isolating the variable to one side of the equation to determine its value.
Given the equation of the formula, A = yn + y, to solve for n, follow the steps below:
A = y(n + 1)
Divide both sides by y:
A/y = y(n + 1)/y [division property of equality]
A/y = n + 1
Subtract 1 from both sides:
A/y - 1 = n + 1 - 1 [subtraction property of equality]
A/y - 1 = n
n = A/y - 1
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x+y+z=3000
5x-3y=0
x-10.5y-z=0
The value of x, y, z is -18000/83, -30000/83, 297000/83 respectively.
This problem is solve by substitution method.
what is substitution method?
Substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Given,
x+y+z=3000
5x−3y=0
x−10.5y−z=0
Solve x+y+z=3000 for x.
x=−y−z+3000
Substitute −y−z+3000 for x in the second and third equation.
5(−y−z+3000)−3y=0
−y−z+3000−10.5y−z=0
Solve these equations for y and z respectively.
y=1875−5/8z
z=1500-23/4y
Substitute 1875−5/8z for y in the equation z=1500−23/4y
z=1500−23/4(1875-5/8z)
z= 297000/83
put this value in y = 1875- 5/8z
y= -30000/83
substitute the value of y and z in equation one
x= -18000/83
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What is the remainder of the quantity 4 x cubed minus 20 x minus 50 end quantity divided by the quantity x minus 3 end quantity? Show all necessary steps.
Please show me step by step tysm^^
=
#1
When a skydiver opens their parachute, they descend at a
rate of 3 m/s. If a skydiver is 1200 meters up in the air, then
how long will it take for them to reach the ground?
Time before reaching the ground?
The time taken for them to reach the ground is 0.305s.
What are the equations of motion?
Kinematics equations of motion define the fundamentals of an object's motion, such as its position, velocity, or acceleration over time. These three equations of motion control how an item moves in one, two, and three dimensions. It is possible to determine components like displacement(s), velocity(initial and final), time(t), and acceleration(a) using one of three equations of motion (a). The three equations of motion are as follows:
First equation: v = u + at
Second equation: s = u*t + 0.5t²
Third equation: v² = u² + 2as
Given, the initial velocity of the skydiver = 3 m/s
Height of fall for the skydiver = 1200 m
Also, after reaching ground, final velocity of the skydiver = v = 0 m/s
Let the time taken to reach the ground be = t
Therefore, using the first equation, we have
0 = 3 + (-9.81)t ⇒ t = -3/-9.81 = 0.305 s
Thus, time taken for them to reach the ground is 0.305s.
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2(3v + 8) = 70 solve for v simplify your answer as much as possible
Answer:
v = 9
Step-by-step explanation:
2(3v + 8) = 70 Distribute the 2
2(3v) + 2(8) = 70
6v + 16 = 70 Subtract 16 from both sides
6v = 54 Divide both sides by 6
v = 9
Question 8 of 8 Pls answer quickly pls and thank you
What are all the possible ways to classify the following shape?
shape
A. polygon, quadrilateral, trapezoid
B. polygon, quadrilateral, parallelogram, trapezoid
C. quadrilateral, trapezoid
A polygon is a flat shape that is encircled by lines known as edges. It has a two-dimensional appearance. As a result, all of the shapes in sections a, b, and c are polygons.
A. Trapezoid, Quadrilateral - A trapezoid always forms a quadrilateral since it is a regular polygon having four sides. A trapezoid is a quadrilateral with opposing parallel sides. A right angle, also known as a right trapezoid, can have congruent sides, which are referred to as isosceles.
B. Polygons, quadrilaterals, parallelograms, and trapezoids - A quadrilateral is a four-sided shape. A parallelogram is a form with four parallel and equal-length sides. A parallelogram's area is equal to the base multiplied by the height. A trapezoid is a shape that has at least one set of opposite ends that are parallel.
C. quadrilateral, trapezoid - A trapezoid is a quadrilateral with several parallel opposed sides. Although the right angles of square trapezoids and isosceles triangles can be included which is an isosceles quadrilateral.
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A uniform continuous distribution has a maximum of 14 and a minimum of 2. Samples of size 36 are drawn from the distribution. What is the variance of the sample means?.
The variance of the sample means will be 0.3428.
What is Variance of sample means?
The variance of the sampling distribution of the mean is the population variance divided by the sample size.
Given that;
A uniform continuous distribution has a maximum of 14 and a minimum
of 2.
Samples of size 36 are drawn from the distribution.
Now,
The population variance = 14 - 2
= 12
And, Sample size = 36
Since, The variance of the sample means is defined as;
= Population variance / Sample size
Substitute all the values, we get;
= 12 / 35
= 0.3428
Thus, The variance of the sample means will be 0.3428.
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write as a single fraction:
2/x+2 + 3/2x+1
Answer:
3x2+6x+4 2x
hope this helps !!
HAVE A AMAZING DAY
Answer:
(6x+7)/2x
Step-by-step explanation:
2/x+2 + 3/2x+1
2/x+2x/x + 3/2x+x/x [Convert the bolded numbers into fractions with x in the denominator.
2/x+2x/x + 3/2x + x/x [Convert the bolded numbers so that the denominator becomes 2x]
4/2x+4x/2x + 3/2x + 2x/2x
4/2x+4x/2x + 3/2x + 2x/2x [Now that all numbers have the same denominator, we can add the numerators]
(4+4x + 3 + 2x)
(6x+7)
(6x+7)/2x [Place the denominator, 2x, back into the fraction]
is y=1000x proportional?
Answer:
has a proportional relationship with a constant of proportionality of 1000.c
Step-by-step explanation:
y=1,000x,y=1,000x
Y-intercept = 4 Slope = 2
Answer:
y=2x+4
Step-by-step explanation:
Guessing you need an equation?
(Writing Two-Step Equations HC) Given the equation 4x + 12 = 64: Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points) Part B: Solve the equation showing all work. (4 points) Part C: Explain what the value of the variable represents. (2 points)
PLEASE HURRY IM IN A EXAM LIKE WHYYYYYY :'), I WILL GIVE 20 POINTS OR MORE JUST ANSWER
Considering the expression 4x + 12 = 64, it is found that:
A. The problem is that you purchased x fried pastry, costing $4, plus a chocolate and a soda, costing $12, and the total purchase cost was of $64.
B. The solution is x = 13.
C. The solution means that you purchased 13 fried pastry.
Expression
The expression is presented as follows:
4x + 12 = 64.
A possible context for this problem is:
x fried pastry are purchased, each costing $4, hence 4x.A chocolate and a soda purchased, costing a total of 12, hence 4x + 12.The total cost of the purchase was of $64, hence 4x + 12 = 64.The number of fried pastry purchased is the solution to the equation, calculated as follows:
4x + 12 = 64
4x = 52
x = 52/4
x = 13 -> 13 fried pastry were purchased.
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I need help with the following question.
Answer:
A
(Look at the screenshots below)
1st screenshots shows the "moved down to two units"
2nd screenshot shows the"flipped over a vertical line that lines halfway between the two triangles"
pleaseeeee i need help before school tomorrow thanks :)
Answer:
You need to know that not a cheat
Solve for variable c
6c x 88 - 93 = 67
6c X 88 = 93+67
528c=160
C=0,303030303030303
Could someone please answer this?
Cost of total 12 chocolate crackle is $8.875
What is multiplication and division?
Multiplication and division are two of the basic arithmetic operations . in multiplication we find the product of two numbers. And division is splitting a number in equal given part.
We are given cost of 24 chocolate crackel
The total cost comes out to be $17.75
a) To make 12 chocolate crackle we require material of exactly half cost
Which will be $8.875
b) To make 6 chocolate crackle we will require material of exactly one fourth of the cost which will be $4.435
c) To make 36 chocolate crackle we will require material of exactly one and half cost
Which will be $26.625
d) To find the cost of one chocolate we divide the cost of 24 chocolate Crackle by 24 we get the cost of 1 chocolate crackel as $0.739
e) The cost of one chocolate crackel in cents is $74 cents
Hence, Cost of total 12 chocolate crackle is $8.875
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A plant is already 51 centimeters tall, and it will grow one centimeter every month. The plant's height, H (in centimeters), after
m months is given by the following function.
H(m)=51+m
What is the plant's height after 33 months?
Answer:
84 cm
Step-by-step explanation:
H=51+m
m=months, substitute m for 33 months
H=51+33
H=84
The plant's height will be 84 cm after 33 months
I don't understand this: beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet. how many cans will beth need to buy?
The required number of cans would be 2 for painting a circular tabletop that has a radius of 3 feet.
What is the area of the circle?The area of the circle is equal to the product of the square of the radius of the circle and pi.
A = πr²
where 'r' is the radius of the circle
We have been given that beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet.
Firstly, we need to calculate the area of a given circular tabletop which is equal to the area of a circle with a radius of 3 feet.
area of the circular tabletop = the area of a circle
area of the circular tabletop = π r²
Here r = 3 feet
area of the circular tabletop = π (3)²
area of the circular tabletop = 9π
area of the circular tabletop = 28.27 square feet
Required number of cans = 28.27 / 15
Required number of cans = 1.88 ≈ 2
Therefore, the required number of cans would be 2.
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given f(x)=4x+1 describe how the graph of g compares with the graph of f. g(x)=(4x+1)+3
The description of the graph of function g(x) is 3 units translation up
How to describe the graph of function g(x)?The equations of the functions are given as
f(x) = 4x + 1
g(x) = (4x + 1) + 3
Substitute f(x) = 4x + 1 in the equation g(x) = (4x + 1) + 3
So, we have
g(x) = f(x) + 3
The above rule implies that:
The function g(x) is a translation of the function f(x)
The unit of the translation is 3 and the direction of the translation is up
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Find the quotient of the given fractions below. Write your solution in your notebook.↑
Pa help please with solution!
Pamapasa na bukas!
The quotient of [tex]12\frac{3}{8}[/tex] ÷ [tex]2\frac{3}{4}[/tex] is 4 1/2.
The quotient of [tex]9\frac{2}{5}[/tex] ÷ [tex]1\frac{3}{10}[/tex] is 7 3/13
The quotient of [tex]7\frac{1}{4}[/tex] ÷ [tex]1\frac{7}{8}[/tex] is 1 13/15
The quotient of [tex]8\frac{5}{6}[/tex] ÷ [tex]2\frac{1}{4}[/tex] is3 25/27
The quotient of [tex]5\frac{4}{7}[/tex] ÷ [tex]2\frac{10}{21}[/tex] is 2 1/4
The quotient of [tex]12\frac{5}{8}[/tex] ÷ [tex]3\frac{19}{24}[/tex] is 3 30 / 91
The quotient of [tex]7\frac{5}{6}[/tex] ÷ [tex]3\frac{1}{2}[/tex]is 2 5/21
The quotient of [tex]14\frac{2}{3}[/tex] ÷[tex]2\frac{2}{9}[/tex]is 6 3/5
What are the quotients?A quotient is the result of a division process. Division is the mathematical operation that is used to part a number into equal groups using another number. The sign that is used to represent division is ÷.
A mixed number is a fraction that is made up of a whole number and a proper fraction. An example of a mixed number is 1 1/2.
[tex]12\frac{3}{8}[/tex] ÷ [tex]2\frac{3}{4}[/tex]
99 / 8÷ 11/4
99 / 8 x 4/11 = 9/2 = [tex]4\frac{1}{2}[/tex]
[tex]9\frac{2}{5}[/tex] ÷ [tex]1\frac{3}{10}[/tex]
47 / 5 ÷ 13/10
47 / 5 x 10/13 = 94 / 13 = 7 3/13
[tex]7\frac{1}{4}[/tex] ÷ [tex]1\frac{7}{8}[/tex]
29 / 4 ÷ 15/8
29 / 4 x 8/15 = 58 / 15 = 1 13/15
[tex]8\frac{5}{6}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
53 / 6 ÷ 9/4
53 / 6 x 4/9 = 106 / 27 = 3 25/27
[tex]5\frac{4}{7}[/tex] ÷ [tex]2\frac{10}{21}[/tex]
39 / 7 ÷ 52/21
39 / 7 x 21/52 = 117 / 52 = 2 1/4
[tex]12\frac{5}{8}[/tex] ÷ [tex]3\frac{19}{24}[/tex]
101 / 8 ÷91 / 24
101 / 8 x 24/91 = 303 / 91 = 3 30 / 91
[tex]7\frac{5}{6}[/tex] ÷ [tex]3\frac{1}{2}[/tex]
47 / 6 ÷ 7/2
47 / 6 x 2/7 = 47 / 21 = 2 5/21
[tex]14\frac{2}{3}[/tex] ÷[tex]2\frac{2}{9}[/tex]
44 / 3 ÷ 20/9
44 / 3 x 9/20 = 33/5 = 6 3/5
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g(x) = -3x - 5, find g(4).
Step-by-step explanation:
putting the value of x in -3x-4 where x is 4 so the ans is -17
Let f(x) = 2x+4. If f(x) = 16, find x.561024
Solution
Let f(x) = 2x+4. If f(x) = 16, find x.
[tex]\begin{gathered} f(x)\text{ =16} \\ f(x)=2x+4 \\ \text{Let's replace f(x) with 16} \\ 16=\text{ 2x+4} \\ \text{collect the like terms} \\ 16-4=2x \\ 12=2x \\ \text{Divide both sides by 2} \\ x=6 \end{gathered}[/tex]Answer:
x=6
Step-by-step explanation:
Substitute f(x)=16 into the equation:
16=2x+4
Get x by itself:
2x=12
Divide both sides by 2:
x=6