what is the slope of the line
Answer:
4/5
Step-by-step explanation:
Because slope=rise/run.
Answer: slope = [tex]\frac{5}{6}[/tex]
Step-by-step explanation:
The formula for finding slope is given by
slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
From the graph give :
[tex]x_{1}[/tex] = -3
[tex]x_{2}[/tex] = 3
[tex]y_{2}[/tex] = 4
[tex]y_{1}[/tex] = -1
substituting into the formula , we have
slope = [tex]\frac{4-(-1)}{3-(-3)}[/tex]
slope = [tex]\frac{4+1}{3+3}[/tex]
slope = [tex]\frac{5}{6}[/tex]
Find the number, if 1.5 of it is 30
Answer is 30
Step-by-step explanation:
1.5 of X = 30
1.5*X = 30
X = 30/1.5
= 20
Answer:
20
Step by step explanation:
30/1.5
=20
y=x^(2)-12x+40 in vertex form
Answer:
[tex]y=(x-6)^2+4[/tex]
Step-by-step explanation:
Vertex Form Of The Parabola
The equation of a parabola can be expressed in either standard or vertex form. The standard form is
[tex]y=ax^2+bx+c[/tex]
and the vertex form is
[tex]y=a(x-h)^2+k[/tex]
Where (h,k) it the vertex of the parabola
Transforming one into the other form is easily achieved by applying simple algebra .
Our function is
[tex]y=x^2-12x+40[/tex]
Completing squares, we have
[tex]y=x^2-12x+36+40-36[/tex]
Reducing
[tex]\boxed{y=(x-6)^2+4 }[/tex]
The vertex of the parabola is the point (6,4)
Final answer:
To convert the quadratic equation y = x^2 - 12x + 40 into vertex form, the completing the square method is employed, resulting in y = (x - 6)^2 + 4, showing the vertex at (6, 4).
Explanation:
Converting a Quadratic Equation to Vertex Form
The question asks how to convert the quadratic equation y = x2 - 12x + 40 into its vertex form. The vertex form of a quadratic equation is y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. To convert the given quadratic equation into vertex form, we'll use completing the square method.
Start with the original equation: y = x2 - 12x + 40.Factor out the coefficient of x2, which is 1 in this case, so this step doesn't change the equation.Rewrite the equation focusing on the x-terms: y = (x2 - 12x) + 40.To complete the square, take half of the coefficient of x (which is -12/2 = -6), square it (-62 = 36), and add and subtract it inside the parenthesis: y = (x2 - 12x + 36) - 36 + 40.Simplify and rewrite: y = (x - 6)2 + 4.This shows the quadratic equation in vertex form with the vertex at (6, 4).
Evaluate
c
2
−
3
+
6
d
2
c
−3+
d
6
start fraction, c, divided by, 2, end fraction, minus, 3, plus, start fraction, 6, divided by, d, end fraction when
c
=
14
c=14c, equals, 14 and
d
=
3
Answer:
The answer = 6
Step-by-step explanation:
Given expression:
[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]
To evaluate the given expression, when [tex]c=14[/tex] and [tex]d=3[/tex]
Solution:
We have:
[tex]\frac{c}{2}-3+\frac{6}{d}[/tex]
Plugging in [tex]c=14[/tex] and [tex]d=3[/tex] in the given expression, to evaluate.
⇒ [tex]\frac{14}{2}-3+\frac{6}{3}[/tex]
Evaluating:
⇒ [tex]7-3+2[/tex]
⇒ 6 (Answer)
Answer:
hmm 6
Step-by-step explanation:
The equation of a line is x + 3y = 14. What is the y-intercept of the line?
Answer:
To find the y-intercept of a line you need to first put it into the equation y=mx+b
x+3y=14 (minus x from each side)
3y=-x+14 (divide both sides by 3)
y=-1/3x+14/3
Your y-intercept is the b in the formula above, so your y-intercept would be 14/3
Hope this helps ;)
Use the given information to write the equation of each line
Passing through (1,-4) and (-2,5)
Answer:
y = -3x - 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (1, -4) and (-2, 5).
Substitute:
[tex]m=\dfrac{5-(-4)}{-2-1}=\dfrac{5+4}{-3}=\dfrac{9}{-3}=-3[/tex]
Substitute the value of a slope and the coordinates of the point (1, -4) to the equation of a line:
[tex]-4=-3(1)+b[/tex]
[tex]-4=-3+b[/tex] add 3 to both sides
[tex]-4+3=-3+3+b[/tex]
[tex]-1=b\to b=-1[/tex]
Finally:
[tex]y=-3x-1[/tex]
What is the sum of 1 7 10 and 3 3 5 ? Use the fraction strips to help.
Answer: [tex]5\frac{3}{10}[/tex]
We first write them as improper fraction.
[tex]1\frac{7}{10}=\frac{17}{10}[/tex]
[tex]3\frac{3}{5}=\frac{18}{5}[/tex]
Then we find the LCM of the denominators. That is 10.
Using LCD we find the sum:
[tex]1\frac{7}{10}+3\frac{3}{5}\\=\frac{17}{10}+\frac{18}{5}\\=\frac{17}{10}+\frac{36}{10}\\=\frac{53}{10}\\=5\frac{3}{10}[/tex]
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The sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]
To find the sum of the fractions [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \)[/tex], let's first convert them to a common denominator.
The least common denominator for 7, 3, and 5 is 105 (since it's the smallest number divisible by all three denominators).
So, we need to express each fraction with a denominator of 105:
[tex]- \( \frac{1}{7} \) becomes \( \frac{15}{105} \) (multiplied by 15)[/tex]
[tex]- \( \frac{10}{3} \) becomes \( \frac{350}{105} \) (multiplied by 35)[/tex]
[tex]- \( \frac{3}{5} \) becomes \( \frac{63}{105} \) (multiplied by 21)[/tex]
Now, we add these fractions:
[tex]\( \frac{15}{105} + \frac{350}{105} + \frac{63}{105} = \frac{15 + 350 + 63}{105} = \frac{428}{105} \)[/tex]
So, the sum of [tex]\( \frac{1}{7} \), \( \frac{10}{3} \), and \( \frac{3}{5} \) is \( \frac{428}{105} \).[/tex]
What is the slope of the line that passes through the points (-7, -7) and (-7, 1)? Write your answer in simplest form.
Answer:
undefined, stays on x so straight vertical - vertical line is undef slope
Answer: The slope is undefined
Step-by-step explanation:
The slope of a line is calculated using the formula :
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = -7
[tex]x_{2}[/tex] = -7
[tex]y_{1}[/tex] = -7
[tex]y_{2}[/tex] = 1
Substituting the values into the formula , we have :
m = [tex]\frac{1-(-7)}{-7-(-7)}[/tex]
m = [tex]\frac{8}{0}[/tex]
m = undefined
20-8 divided by 2 to the second powerX3
Answer:
6
Step-by-step explanation:
20-8=12
12÷2=6
6x6=36
Answer:
Step-by-step explanation:
Please help me solve these three interval notations!!!!
Answer:
i) [0,4)
ii) [-2,-10]
iii) (-6,-4)
Step-by-step explanation:
i) the interval notation shown in the figure for the first option is [0,4) . Square bracket is used when an end value is included in the range as indicated by the black circle and a normal bracket is used to indicate when the end value is not included in the range as indicated by the white circle.
ii) the interval notation for the second option is given as [-2, 10].
iii) the interval notation for the third option is given by (-6, -4)
Which statement about the following system is correct?
Y=x-6
Y=-x-2
A. The equations are independent because the lines intersect in one point.
B.The equations are independent because the equations represent parallel lines.
C.The equations are dependent because the lines are the same line.
D.The equations are dependent because the lines do not intersect.
The correct statement about the system of equations y = x - 6 and y = -x - 2 is that the equations are independent because the lines intersect at one point, as they have different slopes.
Explanation:The student is asking which statement about the system of equations is correct. The equations given are:
y = x - 6y = -x - 2Let's analyze both equations:
Since the two lines have different slopes, they are not parallel and will intersect at a single point, making the system consistent and independent. Therefore, the correct answer is:
A. The equations are independent because the lines intersect in one point.
g(x) = -x2 + 12x - 32
In vertex form
Answer: g(x) = -(x - 6)² + 4
Step-by-step explanation:
g(x) = -x² + 12x - 32
g(x) = -(x² - 12x) - 32
g(x) = -(x² - 2 × x × 6 + 6² - 6²) - 32
g(x) = -[ (x - 6)² - 36 ] - 32
g(x) = -(x - 6)² + 36 - 32
g(x) = -(x - 6)² + 4
Here, (6,4) is vertex.
Given the following functions f(x) and g(x), solve (f+g)(2) and select the correct answer below:
f(x) = 6x - 2
g(x) = x - 1
A. 13
B. 11
C. 24
D. 30
Answer:
B
Step-by-step explanation:
In the picture above
Hope this helps.
Pick the correct equation for the line below:
y=x^2 y + 90
y=3x + 90
y = 90x - 10
y = -10x + 90
Answer:
none of above because the correct equation is y= -3x+90
In the equation below, for what value of c does x = 4?
1 / (2x + 4) = 3x-c
Answer:
Option D.
Jenn's answer is not correct. She got it substituting [tex]c=4[/tex] into the equation and solving for "x".
Step-by-step explanation:
Given the following equation:
[tex]\frac{1}{2}(2x + 4) = 3x-c[/tex]
Since you need that [tex]x=4[/tex], you hace to substitute that value into the equation:
[tex]\frac{1}{2}(2(4) + 4) = 3(4)-c[/tex]
Now you need to solve for "c":
[tex]\frac{1}{2}(8 + 4) = 12-c\\\\\frac{12}{2}= 12-c\\\\6=12-c\\\\c+6=12\\\\c=12-6\\\\c=6[/tex]
Therefore for a a value of [tex]c=6[/tex], you get [tex]x=4[/tex]
Then, the you can identify that the correct answer is the one given in the Option D.
Jenn made a mistake, because she substituted [tex]c=4[/tex] into the equation and then solve for "x":
[tex]\frac{1}{2}(2x + 4) = 3x-(4)\\\\x+2=3x-4\\\\2+4=3x-x\\\\6=2x\\\\\frac{6}{2}=x\\\\x=3[/tex]
To determine the value of c when x equals 4 in the given equation, substitute x with 4 and solve for c. The resulting value of c is approximately 11.9167.
Explanation:To find the value of c for which x = 4 in the equation 1 / (2x + 4) = 3x - c, we start by substituting x with 4:
1 / (2×4 + 4) = 3×4 - c
1 / (8 + 4) = 12 - c
1 / 12 = 12 - c
Now we solve for c:
1 / 12 = 12 - c
c = 12 - 1 / 12
c = 12 - 0.0833
Finally, we find the value of c:
c = 11.9167
Therefore, for x = 4, the value of c is approximately 11.9167.
11. Given: TQ bisects ZRTP, QS || PT
RT = 30. Find QP, RS and QS
QP=24 cm
RS=11.25 cm
QS=18.75 cm
Explanation:
Given that TQ bisects <RTP
[tex]therefore <QTP=<QTR\\[/tex](1)
consider ΔRQS and ΔRPT
QS||PT,RP and RT are transversals
[tex]<SQT=<QTP[/tex](alternate angles)(2)
comparing (1) and (2)
[tex]<SQT=<STQ[/tex] and triangle SQT is isocelus
Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle)
Therefore <RQS=<RPT(corresponding angles)
<RSQ=<RTP(corresponding angles)
therefore by AA criterion for similarity
ΔRQS~ΔRPT
According to the property of similar triangles
[tex]RQ/RP=RS/RT=QS/PT[/tex][tex]9/RP=X/30=QS/50\\9/RP=X/30=(30-X)/50\\X/30=(30-X)/50\\50X=30(30-X)\\50X=900-30X\\50X+30X=900\\80X=900\\X=900/80=11.25\\RS=11.25 cm\\QS=30-X=30-11.25\\QS=18.75 cm\\9/RP=X/30\\9/RP=11.25/30\\9*30/11.25=RP\\RP=24 cm[/tex]
The capacity of a backyard pool would most
likely be measured in which unit?
Answer:
I would use cubic meters :)
Step-by-step explanation:
Final answer:
The capacity of a backyard pool is commonly measured in gallons in the United States, or liters and kiloliters in countries using the metric system, due to the large volume of water pools can hold.
Explanation:
When considering the capacity of a backyard pool, we're dealing with a fairly large volume of water that needs to be measured. In the United States, the most common unit of measure for this purpose would be gallons, as it is a large unit for capacity suitable for measuring significant amounts of liquid like the volume of water in a swimming pool. Elsewhere, where the metric system is more common, one would likely use liters or kiloliters to quantify the capacity of a backyard pool.
For example, a typical backyard pool may contain about 15,000 gallons of water, which is significantly larger than quantities we would measure in smaller units such as milliliters or ounces. When discussing such large volumes, it's essential to use a unit of measure that appropriately represents the size of the container or space, hence gallons or liters are most suitable for the situation.
Which set of sides will make a triangle?
6 cm, 15 cm, 6 cm
13 cm, 7 cm, 6 cm
10 cm, 9 cm, 9 cm
4 cm, 8 cm, 14 cm
Answer:
(c) 10 cm, 9 cm, 9 cm
Step-by-step explanation:
You want to identify the set of side lengths that can form a triangle.
Triangle inequalityThe triangle inequality requires a + b > c, for any assignment of a, b, c to side lengths. In effect, the sum of the two shortest sides must exceed the length of the longest side.
Choices6+6 = 12 < 15 . . . . not a triangle
6+7 = 13 . . . . . . . . not greater; not a triangle
9+9 = 18 > 10 . . . . forms a triangle
4+8 = 12 < 14 . . . . not a triangle
The set of sides that will make a triangle is {10 cm, 9 cm, 9 cm}.
__
Additional comment
The semiperimeter (half the sum of side lengths) is always greater than any side length in a triangle. For example, if the perimeter is 20, the longest side must be less than 10.
By applying the Triangle Inequality Theorem, we find the only set of sides that could make a valid triangle is 10 cm, 9 cm, 9 cm.
Explanation:The question is asking to identify which set of given lengths could make a valid triangle. To answer this question, it's important to remember the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this concept to each option.
6 cm, 15 cm, 6 cm: The sum of the two shorter sides (6 + 6 = 12 cm) is not greater than the longest side (15 cm), so this cannot form a triangle. 13 cm, 7 cm, 6 cm: The sum of the two shorter sides (7 + 6 = 13 cm) equals to the longest side, which also violates the triangle inequality, so this cannot form a triangle. 10 cm, 9 cm, 9 cm: The sum of the two shorter sides (9 + 9 = 18 cm) is greater than the longest side (10 cm), so this can form a triangle. 4 cm, 8 cm, 14 cm: The sum of the two shorter sides (4 + 8 = 12 cm) is not greater than the longest side (14 cm), so this cannot form a triangle.
Therefore, the only set of lengths that could make a valid triangle is 10 cm, 9 cm, 9 cm.
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Name 6 kingdoms and give an example of each
Answer:
Step-by-step explanation:
1. animals - rabbit
2. plants - moss, flowers etc .
3. fungi - mushroom
4. protista - giant kelp
5. eubacteria - thermus
6. archaebacteria - euryarchaeota
At West Painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write
up an estimate for the cost of a job, they need to know how much paint a job will take. If they average painting of a room with
5 of a gallon of paint, then they can paint, on average, 4 rooms per gallon
Answer:
West Painting can paint, on average, 1 7/8 rooms per gallon of paint
Complete statement and question:
At West painting, they get about three calls a day asking for an estimate of the cost for having the interior of a house painted. To write up an estimate for the cost of a job, they need to know how much paint a job Will take. If they average painting 3/4 of a room with 2/5 of a gallon of paint, then they can paint, on average ______ rooms per gallon.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Amount of paint needed to paint 3/4 of a room = 2/5 of a gallon
2. They can paint, on average how many rooms per gallon?
Let's use the Rule of Three Simple to answer this question, this way:
Paint Rooms
2/5 gallon 3/4
1 gallon x
x = Number of rooms on average painted with one gallon of paint
x * 2/5 = 3/4 * 1
x = 3/4 / 2/5
x = 3/4 * 5/2 = 15/8 = 1 7/8
West Painting can paint, on average, 1 7/8 rooms per gallon of paint
15. At a school for, 70% of the people are under 16 years old. One of the people rema
there are 21 teachers at the fair how many people are there at the far total
h. 125
Answer:
210 people are there at the fair
Step-by-step explanation:
Let the total number of people at the fair = X
People under 16 years old = 70% of X = 0.7 X
People remaining = Total number of people - Under 16 years
= X - 0.7X = 0.3X
The number of teachers = 1/3 of People remaining = 1/3 of 0.3X
Since there are 21 teachers
1/3 of 0.3X = 21
1/3 x 0.3X = 21
0.1X = 21
Divide both sides by the coefficient of X
0.1X/0.1 = 21/0.1
X = 210
That is 210 people are there at the fair
Compare |− 4 25 | and |− 7 20 |.
Answer:
Step-by-step explanation:
| - 425 |=425
| - 720 |=720
Beacause 720>425=>| - 720 |>| - 425 |
6 x 4237 solve using distributive property
Answer:
25422
Step-by-step explanation:
Paul was asked to use the elmination to find the solution to the system of linear equations
5x + 4y = 1
−2x − 8y = −26
What are the missing steps in his work below?
5x + 4y = 1 −2x − 8y = −26
10x + 8y = 2 + (−2x −8y = −26) 8x + 0y = −24 8x = −24 x = −3 5x + 4y = 1 5(−3) + 4y = 1 −15 + 4y = 1 4y = 16
y = 4 Select one: A. 5x + 4y = 1 + (−2x − 8y = −26)
B. 2⋅[5x + 4y = 1] 10x + 8y = 2
C. 5x + 4y = 1 − (−2x − 8y = −26)
D. −5⋅[−2x − 8y = −26] 10x + 40y = 130
Answer:
Option B is correct.
Step-by-step explanation:
Paul was asked to use the elmination to find the solution to the system of linear equations
What are the missing steps in his work below?
So, the step missing is multiplying equation 1 by 2 i.e
So, Option B is correct.
How can you compare 5/8 and 1/2
PLEASE ANSWER!! :)
Answer:
see attached work shown
by Thursday the Cutters and sewers in a clothing Factory had made 280 jackets. This is 87 1/2 % of the total number of jackets they were expected to make for the week. What is the total number of jackets the workers had to make that week?
Answer:
320
Step-by-step explanation:
87 1/2% (same as 87.5%) " of " the total jackets " is" 280
let j represent the total jackets
turn ur percent to a decimal....87.5% = 0.875
" of " means multiply , " is " means equals
0.875j = 280
j = 280 / 0.875
j = 320 <====== ur answer
Final answer:
The workers at the clothing factory were expected to make a total of 320 jackets for the week, as 280 jackets represented 87.5% of their weekly target.
Explanation:
To find the total number of jackets the workers were expected to make for the week, we'll set up a proportion where 87.5% corresponds to the 280 jackets they had made by Thursday. We know that 87.5% can also be expressed as the fraction 7/8. Therefore, if 7/8 of the total is 280 jackets, we need to divide 280 by 7 and then multiply by 8 to find the total number of jackets.
First, calculate the number of jackets corresponding to 1/8 of the total:
280 jackets
7 (parts) = 40 jackets
Next, multiply the value of 1/8 of the total by 8 to get the full 100%:
40 jackets
8 (parts) = 320 jackets
So, the workers were expected to make a total of 320 jackets for the week.
(5X+7)+(X+2) add linear expressions
Answer:
6x+9
Step-by-step explanation:
add like terms
5x+x=6x
7+2=9
5x+7+x+2=6x+9
please help me with missing angles
Answer:
u = 40° , v = 40° and x = 100°
Step-by-step explanation:
i) from the rule of triangle we know that the sum of all three angles = 180°
ii) 100° + 40° + y = 180°. Therefore y = 40°. where y is the angle adjacent to v.
iii) from theorem on parallel lines we can say that u = y =40°
iv) from the properties of parallel lines we get v = 40° as interior alternate angles are equal.
v) again from the properties of parallel lines we get u = 40°
vi) using the triangle property as in i) we can see that u + v + x =180° therefore 40° + 40° + x = 180°. Therefore x = 100°.
vii) Therefore u = 40° , v = 40° and x = 100°
Find the measure of y.
this has 129, 116, 120,130, 135, 125v and y
I NEEEDDD TO KNOWW WHAT IS (Y)
134°
130°
129°
145°
The measure of angle y in the heptagon is 145 degrees.
What is a polygon?In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and a finite number of sides. Additionally, some examples of a polygon include the following:
• Triangle
• Quadrilateral
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
To find the measure of angle y in a heptagon, we can use the formula for the sum of the interior angles of a polygon, which is:
Sum of interior angles = (n-2) x 180 degrees
where n is the number of sides of the polygon.
For a septagon (a polygon with seven sides), we can substitute n=7 into the formula:
Sum of interior angles = (7-2) x 180 degrees = 5 x 180 degrees = 900 degrees
We can now find the value of angle y by adding up the measures of all the given angles and subtracting the sum from the total sum of the interior angles:
y = 900 - (129 + 116 + 120 + 130 + 135 + 125) = 145 degrees
Therefore, the measure of angle y in the Heptagon is 145 degrees.
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Complete question:
At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today. How much more did it snow yesterday than today?
It snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today
Solution:
Given that, At the Butler Ski Resort, it snowed 1/2 of a foot yesterday and 1/5 of a foot today
From given information,
[tex]\text{Snowed yesterday } = \frac{1}{2} \text{ foot }\\\\\text{Snowed today } = \frac{1}{5} \text{ foot }[/tex]
To find: how much more did it snow yesterday than today
So we have to find the difference between snowed yesterday and today
[tex]\text{Difference} = \text{Snowed yesterday } - \text{ snowed today }\\\\\text{Difference} = \frac{1}{2} - \frac{1}{5}\\\\\text{Difference} = \frac{1 \times 5}{2 \times 5}-\frac{1 \times 2}{5 \times 2}\\\\\text{Difference} = \frac{5}{10}-\frac{2}{10}\\\\\text{Difference} =\frac{3}{10}[/tex]
Hence it snowed [tex]\frac{3}{10}[/tex] foot more yesterday than today