Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
We have
[tex](-6,\ 3)\to x_1=-6,\ y_1=3,\ m=\dfrac{5}{2}[/tex]
Substitute:
[tex]y-3=\dfrac{5}{2}(x-(-6))\\\\y-3=\dfrac{5}{2}(x+6)[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
[tex]y-3=\dfrac{5}{2}(x+6)[/tex] use the distributive property
[tex]y-3=\dfrac{5}{2}x+\dfrac{5}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3[/tex]
[tex]y-3=\dfrac{5}{2}x+15[/tex] add 3 to both sides
[tex]y=\dfrac{5}{2}x+18[/tex]
Convert to the standard form:
[tex]Ax+By=C[/tex]
[tex]y=\dfrac{5}{2}x+18[/tex] multiply both sides by 2
[tex]2y=5x+36[/tex] subtract 5x from both sides
[tex]-5x+2y=36[/tex] change the signs
[tex]5x-2y=-36[/tex]
3 less than 7 times a number
Answer:
7-3n
Step-by-step explanation:
3 less than 7.................. 7-3
times a number ............ n
Together ......................... 7-3n
What is 12.5% written as a fraction in simplest form?
Answer:
1/8
Step-by-step explanation:
Check: 12.5 * 8 = 100
Answer:
1/8 is the simplest form
Step-by-step explanation:
12.5% = 12.5/100 = 125/1000
125/125 = 1
1000/125 = 8
= 1/8
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The system of equations is graphed on the coordinate plane.
y=x−1
y=−2x−4
A graph with a blue line passing through coordinates (-2, 0), (-1, -2) and (0, -4) and a red line passing through coordinates (-1, -2), (0, -1) and (1, 0).
Answer:
The solution of the system is the point (-1,-2)
Step-by-step explanation:
The question is
Enter the coordinates of the solution to the system of equations
we have
[tex]y=x-1[/tex] ----> red line
[tex]y=-2x-4[/tex] ----> blue line
Solve the system by graphing
Remember that the solution of the system of equations is the intersection point both graphs. The solution is a point that satisfy both equations
using a graphing tool
The intersection point is (-1,-2)
The intersection point satisfy both equations
therefore
The solution of the system is the point (-1,-2)
see the attached figure to better understand the problem
What is the fraction Simplify 300/220
Answer:
15/11
Step-by-step explanation:
Because the GCF is 20
Hope this helps:)
Answer:
15/11
Step-by-step explanation:
At a certain company, Joe sells 25% of the products, Cindy sells 40% of the products, and Jamie sells 35% of the
products. Which of the following graphs represents the sales of this company?
The graph that represents the sale of the company is the first graph as shown attached.
In the first pie chart, each salesperson's contribution is clearly depicted as a segment of the whole pie. Joe's 25%, Cindy's 40%, and Jamie's 35% are visually represented.
Pie charts are good for showing how much of something each person sells. They help us see who sells more without needing to do hard math.
With pie charts, it's easy to understand who sells the most just by looking at the colors and sizes of the slices. They make it simple to compare how much each person sells without having to do any fancy calculations.
hiro thinks -5 = -5 is hiro thinking correct
a machine can produce 6 yards of fabric in 2 minutes. how much fabric can the machine produce in 7 days?
Answer:
30,240 yards
Step-by-step explanation:
6*30 in an hour
6*30*24 in a day
6*30*24*7 in a week, solve for 30240
Determine the range of the function f(x)=x^2-2/2 when the domain is {0, 2}.
HELP
The range of function is { -1, 1 }
Solution:
Given that, the function is:
[tex]f(x) = \frac{x^2-2}{2}[/tex]
Domain is {0, 2 }
We have to find the range of function
The domain refers to the set of possible input values
The range is the set of possible output values
Here domain is x = 0 and x = 2
Substitute x = 0 in given function
[tex]f(0) = \frac{0-2}{2}\\\\f(0) = \frac{-2}{2}\\\\f(0) = -1[/tex]
Substitute x = 2 in given function
[tex]f(2) = \frac{2^2-2}{2}\\\\f(2) = \frac{4-2}{2}\\\\f(2) = \frac{2}{2} = 1[/tex]
Thus the range of function is { -1, 1 }
What fraction of 56 is 21
Answer:
[tex]\frac{8}{3}[/tex]
Step-by-step explanation:=
= [tex]\frac{56}{21}[/tex] ( Divide both sides by 7)
= [tex]\frac{8}{3}[/tex]
21 is 3/8 fraction of 56.
What is fraction?A fraction describes a part of a whole. For example, one slice of a pizza is a fraction of the whole pizza.
Given that, what fraction of 56 is 21,
Finding the fraction, we get,
21 / 56 = 7(3) / 7(8)
= 3 / 8
Hence, 21 is 3/8 fraction of 56.
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Joyce lost 26 lbs on her diet. During vacation she gained 4 lbs. How much was her overall loss?
Complete the conversion. 104 km = ______ m A. 10.4 m
B. 104 m
C. 10,400 m
D. 104,000 m
Answer:
The area of a the parallelogram is 88meers squared
Find the value of k so that the point A lies on the line given by equation.
A(2, 2), kx+(k+1)y=2
Answer:
k = 0
Step-by-step explanation:
Explanation:-
given straight line equation is k x+(k+1)y=2......(1)
The point A(2,2) lies on the equation is
substitute x = 2 and y=2
k(2) + (k+1)(2) =2
now simplify 2 k+2 k+2 = 2
subtracting '2' on both sides , we get solution is
4 k +2 -2 = 2-2
4 k =0
k = 0
Answer:
k = 0
Step-by-step explanation:
kx + (k + 1)y = 2
2k + 2(k + 1) = 2
2k + 2k + 2 = 2
4k + 2 = 2
4k + 2 - 2 = 2 - 2
4k = 0
4k ÷ 4 = 0 ÷ 4
k = 0
In circle A, ZBAE = ZDAE.
What is the length of BE?
O
O
14 units
17 units
27 units
34 units
V
3x-24
Incomplete question the complete question with the diagram is given below.
Answer:
The Correct option is second one 17 units.
Therefore the Length of BE is 17 units.
Step-by-step explanation:
Given:
∠BAE = ∠DAE
BE = 3x - 24
DE = x + 10
To Find :
Length of BE = ?
Solution:
∠BAE = ∠DAE .........Given:
As Chords that subtend congruent angles are congruent. That is equal angles subtends equal chords.
So , the chord BE and DE are equal
Substituting the values we get
[tex]BE=DE\\3x-24=x+10\\2x=34\\\\x=\dfrac{34}{2}=17\\\\x=17\ units[/tex]
Therefore the Length of BE is 17 units.
Answer:
Answer is C
Step-by-step explanation:
edge 2021
Is the following shape a parallelogram? If so, which condition proves it ?
A. Both pairs of opposite sides are parallel ( definition )
B. One pair of opposite sides are parallel and congruent
C. Both pairs of opposite sides are congruent
D. Both pairs of opposite angles are congruent
E. One angle is supplementary of both sides of its consecutive angles
F. The diagonals bisects each other
Answer:
B and F
Step-by-step explanation:
Option A is false, there is no information whether opposite sides are parallel.
Option B is true because of following parallelogram theorem.
Parallelogram theorem: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram.
Option C is false, there is no information about any angles.
Option D is false, there is no information about any angles.
Option E is false, there is no information about any angles.
Option F is true because of following parallelogram theorem.
Parallelogram theorem: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram.
Which descriptions can describe more than one triangle? Select two options.
side lengths of 6 ft, 8 ft, and 10 ft
angle measurements of 35, 35, and 110°
angle measurements of 30°, 40, and 50°
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Answer:
angle measurements of 35, 35, and 110°
angle measurements of 40°, 60°, and 80°
Step-by-step explanation:
we know that
The length sides of a triangle must satisfy the Triangle Inequality Theorem and the sum of their interior angles must be equal to 180 degrees
Remember that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means, I can have more than one triangle with the same internal angles
so
Verify each description
case 1) side lengths of 6 ft, 8 ft, and 10 ft
Remember that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the triangle inequality theorem
1) 6+8 > 10 ---> is true
2) 6+10 > 8 ---> is true
3) 8+10 > 6 ---> is true
therefore
The description describe only one triangle
case 2) angle measurements of 35, 35, and 110°
The sum of the interior angles is equal to 180 degrees
therefore
The description can describe more than one triangle, by similar triangles
case 3) angle measurements of 30°, 40, and 50°
The sum of the interior angles is not 180 degrees
therefore
The description is not a triangle
case 4) angle measurements of 40°, 60°, and 80°
The sum of the interior angles is equal to 180 degrees
therefore
The description can describe more than one triangle, by similar triangles
case 5) side lengths of 4 cm, 6 cm, and 9 cm
Remember that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the triangle inequality theorem
1) 4+6 > 9 ---> is true
2) 4+9 > 6 ---> is true
3) 6+9 > 4 ---> is true
therefore
The description describe only one triangle
Answer:
Angle measurements of 35, 35, and 110°
Angle measurements of 40°, 60°, and 80°
Step-by-step explanation:
took a test got the answer correct
Write an algebraic expression for the phrase.
7 inches shorter than 6 times the length x of a table in inches
7x + 6
6x + 7
7x – 6
6x – 7
Step-by-step explanation:
To find, an algebraic expression for the given phrase = ?
6 times the length x = 6x
and
7 inches shorter than 6 times the length x
= 6x - 7
∴ 7 inches shorter than 6 times the length x of a table in inches = 6x - 7
Hence, the required "option d) 6x – 7" is correct.
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Write as a product of two polynomials.
x(y–5)–y(5–y)
Final answer:
The expression x(y-5) - y(5-y) can be rearranged and factored into (y - 5)(x + y), which is the expression written as a product of two polynomials.
Explanation:
To write the expression x(y-5) - y(5-y) as a product of two polynomials, we first distribute the variables across each term:
x(y-5) = xy - 5x
-y(5-y) = -5y + y²
Now, combining like terms:
xy - 5x - 5y + y²
This expression can't be factored as is, since it cannot be represented by the product of two simpler polynomials with real coefficients. However, we can rearrange the terms:
(xy - 5y) + (y² - 5x) = y(x - 5) + y(y - 5)
Here we can see a common factor of (y-5):
(y - 5)(x + y)
This is the expression written as a product of two polynomials.
What is the answer to (20÷4)-3
Answer:
2
Step-by-step explanation:
(20÷4)-3
20÷4=5
5 x -3= 2
Answer:
2
Step-by-step explanation:
20 /4=5
5-3=2
In a town there are 1349 families. If there are on average two children attending elementary school from each family and each school can accommodate 220 children, the minimum number of elementary schools need in the region is?
Answer:
13
Step-by-step explanation:
First find the number of children attending elementary school
= 1349*2
= 2698 children
Now each school can accommodate 220 children so divide the number of children by 220
=
= 12.26 which is the closest to 13 in the options so the answer is 13
Step-by-step explanation:
Li’s garden is shaped like a rectangle. The area of the garden is 232 meters. If the length is 8 meters, what is the perimeter?
16 m
29 m
58 m
74 m
Answer: 29 m
Step-by-step explanation: First find the width
Since Area = Length x Width
Width = Area/Length = 232/8 = 29
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Suppose that a randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 60%. Which of these groups of numbers could represent a success?
A. 0, 1, 2, 3, 4, 5, 6
B. 0, 1, 2, 3, 4, 5, 6, 7
C. 0, 1, 2, 3, 4, 5, 6, 7, 8
D. 0, 1, 2, 3, 4, 5
Answer:
.0,1,2,3,4,5,6,7,8
The group which represents a success is D. 0, 1, 2, 3, 4, 5.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
a randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 60%.
Total outcomes which are numbers from 0 to 9 = 10
If the probability of success is 60%,
P(success) = 60/100 = 6/10
That is, 6 numbers out of 10 are the outcomes which leads to success.
The correct option is D. 0, 1, 2, 3, 4, 5, which is the only option containing 6 numbers.
Hence the correct option is D.
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9.360 seconds= How many hours?
Answer:
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Step-by-step explanation:
Answer:
2.6 hours
Step-by-step explanation:
9360 second divide by 60 to get minutes
156 minutes divided by 60 to get hours
2.6 hours
Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 5 L, the pressure is 304 kPa (kilopascals). What is the volume when the pressure is 80 kPa ?
Answer:
19 L
Step-by-step explanation:
Given that the volume (V) varies inversely with the pressure (P) then the equation relating them is
V = [tex]\frac{k}{P}[/tex] ← k is the constant of variation
To find k use the condition V = 5 when P = 304
k = VP = 5 × 304 = 1520
V = [tex]\frac{1520}{P}[/tex] ← equation of variation
When P = 80, then
V = [tex]\frac{1520}{80}[/tex] = 19 L
A triangle has an angle that measures 110°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?
Answer:
20 and 50
Step-by-step explanation:
the angles of a triangle add up to 180 degrees.
so if 1 angle is 110, then the other two angles combined, add up to (180 - 110) = 70.
the other two angles are in a ratio of 2:5....added = 7
meaning 1 angle is 2/7 of total measure and the other angle is 5/7 of the measure
so one angle is : 2/7 of 70 = 2/7 * 70 = 140/7 = 20 <==
and the other one is 5/7 of 70 = 5/7 * 70 = 350/7 = 50 <==
Change 6 1/8 into an improper fraction.
Step-by-step explanation:
To find a improper fraction, you must multiply the denominator by the whole number, then add the numerator to the product.
6 x 8 = 48 + 1 = 49.
Our numerator for the improper fraction is 49, we keep the denominator as the same as the whole number fraction, which is 8.
Therefore, your improper fraction is 49/8.
The improper fraction equivalent of 6 1/8 is 49/8.
Given that a mixed fraction 6 1/8, we need to convert it into improper fraction,
To change a mixed number like 6 1/8 into an improper fraction, you need to convert the whole number and the fraction into a single fraction.
Step 1: Multiply the whole number by the denominator of the fraction.
6 x 8 = 48
Step 2: Add the product from Step 1 to the numerator of the fraction.
48 + 1 = 49
Step 3: Write the result from Step 2 over the original denominator.
The original denominator is 8.
Therefore, the improper fraction equivalent of 6 1/8 is 49/8.
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how to do multiplication
Context?
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What is the final elevation if a butterfly starts at 20 m and changes -16 m
Answer:
Therefore the final elevation of the butterfly is 4 m.
Step-by-step explanation:
i) initial elevation = 20 m
ii) change in elevation = -16m
iii) therefore final elevation = initial elevation + change in elevation
= 20 m + (-16 m)
= (20 - 16) m
= 4 m
Therefore the final elevation of the butterfly is 4 m.
Answer:
4
Step-by-step explanation:
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The hypotenuse length is D. 2√29
Step-by-step explanation:
Here apply the Pythagorean relationship were the sum of squares of the sides equals the square of the hypotenuse.
Mathematically,
a²+b²=c²
a=10 ,b=4 ,c=hypotenuse
10²+4²=c²
100+16=c²
116=c²
√116=c
√4*29=c
√4 *√29=c
2√29 =c
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How to complete a square
Answer: Step 1. Divide all terms by a (the coefficient of x2).
Step 2. Move the number term (c/a) to the right side of the equation.
Step 3. Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
Step-by-step explanation:
Convert the decimal to a fraction.
0.6 repeating
Answer: 2/3
Step-by-step explanation: