What are the slope and the y-intercept of the line shown in the graph?
(A) y-intercept = 2 and slope = -3
(B) y-intercept = 2 and slope = 3
(C) y-intercept = 3 and slope = 2
(D) y-intercept = -3 and slope = 2
Answers
the slope is rise over run. Try to choose two points on the line that you can make out the location of like (0,2) and (1,-1) is close enough. Count rise down -3 over run right +1 = -3 slope
y-intercept = 2
slope = -3
let's take the 2 coordinates from the line.
(0, 2)(1, -1)
The y-intercept is when x = 0, When x = 0, y = 2 . This means the y-intercept is 2.
m = slope = -1 - 2 / 1 - 0 = -3 / 1 = -3
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Related Questions
Write the contrapositive of the statement below.
If a triangle is an obtuse triangle, then it has one angle with measure greater than 90°
A triangle has one angle greater than 90°.
A triangle is an obtuse triangle.
If a triangle is not an obtuse triangle, then it does not have one angle greater than 90°.
If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle.
Answers
Michael's score is 586. moises' score is 754. michael estimates he needs about 200 more points to reach moise' score. explain how michael came up up with his estimate what strategy did he use
Answers
The ________ is another term for the variance of the sample data. mean square between mean square total mean square within total sum of squares
Answers
The term 'mean square within' (MSwithin) refers to the sample variance in a set of data, which is computed by dividing the sum of squares within (SSwithin) by its degrees of freedom. This term is used in ANOVA to estimate how much variation within the sample data is due to chance.
Explanation:The term mean square within (MSwithin) is another term for the variance of the sample data. MSwithin represents the variance within groups.
To calculate this variance, the sum of squares within (SSwithin), which represents the variation within samples that is due to chance, is divided by its respective degrees of freedom.
The variance is a measure of how much the data points in a sample differ from the sample mean.
Variance is calculated by taking the mean of the squared deviations from the mean.
This calculation is often used to determine how spread out the values in a data set are.
In the context of an analysis of variance (ANOVA), the MSwithin is used in conjunction with mean square between (MSbetween), which represents the variance between groups, to calculate the F ratio used for testing the null hypothesis.
Write the conversion factor for converting meters to centimeters.
Answers
Therefore, centimeter/meter = 1/100, or 100*centimeter/meter = 1.
Thus, to convert "x" meters into centimeters, you write:
x meter = x*100*centimeter*meter/meter.
At this point, the "meter" cancel out, and you get:
x meter = 100*x centimeters.
This technique is called dimensional analysis, and it is very useful. All you are doing is multiplying by 1, and that takes care of the units.
Answer:
1 meter = 100 centimeter
Step-by-step explanation:
A conversion factor is a numerical value that we use to change one set of unit to another set by performing actions like multiplication or division. When we are converting something, we must use the appropriate conversion factor of an equal value. Few conversions are :
1 meter = 100 centimeter
1 kilometer = 1000 meter
1 foot = 12 inches
1 gallon = 4.54 liters
We want the conversion factor for converting meters to centimeters. this is 1 m = 100 cm.
The formula V = IR shows the relationship between voltage, current, and resistance. Solve this formula for R.
R = VI
R = V divided by I
R = V + I
R = V – I
Answers
This would look like:
V=IR
V/I=R/I
V/I=R
ANSWER
R=v divided by I
The formulae for resistance R is R = V/I
What is Ohm's Law ?
Providing that all physical conditions and temperatures are constant, Ohm's law says that the voltage across a conductor is directly proportional to the current flowing through it.
Ohm's law is given as :
V = IR
Now to find the value of R we divide both side by current I :
[tex]\begin{aligned}V&=IR\\R&=\frac{V}{I}\end{aligned}[/tex]
Therefore, the formulae for resistance R is R = V/I
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How many solutions does the equation have?
2x + 3 = 4x + 2
A. No solutions
B. One solution
C. Many solutions
Answers
The equation will have only one root.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" symbol and terms on both sides must always be present when writing an equation. Equal treatment should be given to each party. Multiple terms, operators, and variables are not required on each side of an equation.
Given equation:
2x + 3 = 4x + 2
On solving
2x - 4x = 2-3
-2x = -1
x= -1/(-2)
x= 1/2
Also, the equation as only one variable of degree one which implies that it will have only one solution.
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Guys please help! In triangle CDE, the measure of angle C is 90 degrees, side CD is 15 and DE is 3 more than CE. Find the length of the longest side of CDE.
Answers
your triangle is
CD=15=a
CE=?=b
DE=CE+3=b+3=c
and C=90°
-> insert those values, with c substituted with b+3 to remove c
c^2=a^2+b^2-2*a*b*cos(C)
(b+3)^2=15^2+b^2-2*15*b*cos(90)
cos(90)=0->
(b+3)^2=15^2+b^2
b^2+2*3*b+3^2=225+b^2
6b+9=225
6b=216
b=36=CE
DE=CE+3=36+3=39
Final answer:
Using the Pythagorean theorem, the length of the longest side of right-angled triangle CDE, which is the hypotenuse DE, is found to be 39 units.
Explanation:
In triangle CDE, angle C is given as 90 degrees, making this a right-angled triangle. According to the information provided, side CD is 15 units long, and side DE is 3 units more than side CE. We are asked to find the length of the longest side, which would be the hypotenuse in a right-angled triangle. To find the hypotenuse, which we'll designate as side DE, we must first establish the relationship between the sides. Let's call CE 'x'; therefore, DE will be 'x + 3'. Since we've established that the triangle is right-angled at C, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
So, the equation becomes CD² + CE² = DE², or 15² + x² = (x + 3)². If we solve for 'x' we have:
225 + x² = x² + 6x + 9216 = 6xx = 36As a result, CE = 36 units and DE, the longest side, equals 36 + 3, which is 39 units.
By applying the Pythagorean theorem correctly, we've found that the length of the longest side of triangle CDE is 39 units.
Consider the following expression.
9v+2u+1
select all the true statements below.
*9v is a coefficient
*v+2u+1 is is written as a sum of three terms
*9v and 1 are like terms
*9v is a factor
*1 is a constant
*None of these are true
Answers
They forgot the 9 in the second line false
9v and 1 are not like terms false
9v is not a factor false
1 is a constant TRUE
The statements that are true are: v+2u+1 is written as a sum of three terms, and 1 is a constant.
Explanation:Let's analyze each statement one by one:
9v is a coefficient: False. Coefficients are the numbers that multiply the variables. In this case, 9v is a term where 9 is the coefficient and v is the variable. v+2u+1 is written as a sum of three terms: True. The expression v+2u+1 can be separated into three terms - v, 2u, and 1. 9v and 1 are like terms: False. Like terms have the same variables raised to the same power. In this case, 9v and 1 are not like terms. 9v is a factor: False. Factors are multiplied together to get a product. In this case, 9v is not being multiplied by anything. 1 is a constant: True. Constants are terms that do not contain variables. In this case, 1 is a constant term. None of these are true: False. As we have identified, statement 2 and 5 are true. Learn more about Algebra here:
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Which statement is needed to fill in the blank in this syllogism?
If a polygon is a rectangle, then ____________________.
If a polygon has four sides, then it is a quadrilateral.
Therefore, if a polygon is a rectangle, then it is a quadrilateral.
a polygon has four sides
Not enough information.
a polygon is a quadrilateral
a polygon is a rectangle
Answers
The population in Utah was 2,763,888 in 2010. The number of people living in Utah in 2016 increased by 10.4% percent. What was Utah's approximate population in 2016?
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now, if 2,763,888 is the 100%, what is the 110.4% of it then?
[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2,763,888&100\\ x&110.4 \end{array}\implies \cfrac{2,763,888}{x}=\cfrac{100}{110.4} \\\\\\ \cfrac{2763888\cdot 110.4}{100}=x[/tex]
Describe two ways to solve the equation 2(4x-11)=10
Answers
List all of the number sets that contain the number 15.
A.
rational numbers and integers
B.
rational numbers, integers, and natural numbers
C.
rational numbers, integers, and whole numbers
D.
rational numbers, integers, natural numbers, and whole numbers
Answers
Final answer:
The number 15 belongs to several sets of numbers: it is a rational number, an integer, a whole number, and a natural number. Therefore, the correct answer to which sets contain the number 15 is D. Rational numbers, integers, natural numbers, and whole numbers.
Explanation:
Number sets form a hierarchy where certain numbers fit into multiple categories based on their characteristics. Starting from the broadest categories, we have complex numbers, which include all numbers with a real and imaginary part. However, the number 15 does not have an imaginary part, so we look to smaller sets.
The real numbers include all the values that can be found on the number line, which includes rational numbers (like fractions), irrational numbers (like √2), integers, whole numbers, and natural numbers. The number 15 is a real number because it can be found on the number line, but it is also specifically a rational number, an integer, a whole number, and a natural number because:
As a rational number, it can be expressed as the ratio of two integers, specifically 15/1. As an integer, it is a whole number and does not have a fractional or decimal part. As a whole number, it is a non-negative integer, starting from 0 and moving upwards. As a natural number, it is a positive integer used for counting (1, 2, 3, ...).
Therefore, the correct answer to the question is D. Rational numbers, integers, natural numbers, and whole numbers all contain the number 15.
what is 71/50 as a percentage
Answers
a rectangular flower bed is five feet longer than it is wide. its area is eighty-four square feet.
What are its dimensions?
Show all work using an equation
Answers
The length of the of the flower bed is (w+5) and the width is w.
To find the area we need to multiply the length(w+5) by the width(w) and set it equal to 84,
(w+5)(w)=84
w^2 +5w=84
Using the quadratic equation you get the solutions of 7 and -12. Since 7 is positive it is our width. Our length is 7+5 or 12.
How do you do 6p-(5p+5)=-8-2(p+12)
Answers
6
p
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5
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Step 1: Simplify both sides of the equation.
6
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6
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(Distribute the Negative Sign)
6
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5
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6
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6
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(Distribute)
6
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(Combine Like Terms)
p
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32
p
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Step 2: Add 2p to both sides.
p
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Step 3: Add 5 to both sides.
3
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32
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=
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27
Step 4: Divide both sides by 3.
3
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=
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27
3
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9
What is the slope of a line parallel to the line 4x - 7y = -14?
Answers
4x - 7y = -14
Subtract 4x from both sides of the equation.
-7y = -4x - 14
Divide all terms by -7.
y = 4/7x + 2
Solution: The slope of a line parallel to 4x - 7y = -14 is positive 4/7.
Final answer:
The slope of a line parallel to the line 4x - 7y = -14 is determined by converting the equation to slope-intercept form, revealing that the slope is 4/7. Thus, any line parallel to it will have the same slope of 4/7.
Explanation:
The slope of a line parallel to the line 4x - 7y = -14 is first determined by rewriting the given line in slope-intercept form (y = mx + b), where m represents the slope. For the line 4x - 7y = -14, we can solve for y to find the slope:
Add 7y to both sides: 4x = 7y - 14.
Then add 14 to both sides: 4x + 14 = 7y.
Finally, divide every term by 7 to solve for y: (4/7)x + 2 = y.
The slope of the line is 4/7. Since parallel lines have equal slopes, any line parallel to the given line will also have a slope of 4/7.
A scientist has a 120 mg sample of an unstable isotope. The amount of the substance remaining in the sample decreases at a rate of 16% each day. At the end of t days, there is less than 30 mg of the substance remaining. Which inequality represents this situation, and after how many days will the sample size remaining be less than 30 mg?
Answers
The inequality is 120*0.84^t < 30
120*0.84^t < 30
0.84^t < 30/120 < 0.25
t * ln 0.84 < ln 0.25
t < ln 0.25 / ln 0.84
t < 7.95
Answer = 8 days
Answer:
Step-by-step explanation:
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The volume of a rectangular prism is measured in cubic iscubic inches. WhatWhat units will the length, width, and height of the prism be measured in?
A. Inches
B. square inches
C. cubic inches
D. feet
Answers
given unit is inch
so the answer is A. inches
by graphing the system of constraints find the values of x and y that maximize the object function.
Answers
Answer with Step-by-step explanation:
The solution of system of equations is all those values of x and y which satisfy both the inequalities or the points which lie in the region common between both the inequalities.
N=100x+40y
The optimal solution will be find from the points which lie on the extreme end of the region common between the inequalities i.e. (2,6), (0,8) or (5,0)
(x,y)=(2,6)
N=100×2+40×6
N= 200+240
N=440
(x,y)=(0,8)
N=100×0+40×8
N= 0+320
N=320
(x,y)=(5,0)
N=100×5+40×0
N= 500+0
N=500
Hence, optimal solution is:
(5,0)
2x + 12 - 7x = -2 for x
leave your answer as an improper fraction or convert to a decimal
Answers
2x+12-7x=-2
-5x+12=-2
-5x=-14
x=14/5
geometry help will give brainliest
Answers
=========
Write an equation for line passing through (8,12) that is perpendicular to
y = (4/3)x - 5
Note:
When two lines are perpendicular, the product of their slopes is -1.
The slope of the given line is 4/3.
Therefore the slope of the perpendicular line is -3/4.
Let the equation of the perpendicular line be
y = -(3/4)x + c
Because the line passes through (8,12), therefore
-(3/4)*8 + c = 12
-6 + c = 12
c = 18
The equation is y = -(3/4)x +18
Answer: [tex]y= -\frac{3}{4} x + 18[/tex]
Problem 2
=========
Write an equation for a line passing through (-30,7) that is perpendicular to
y = -3x - 5.
The perpendicular line will have a slope of 1/3. Let its equation be
y = (1/3)x + c
Because the line passes through (-30,7), therefore
(1/3)*(-30) + c = 7
-10 + c = 7
c = 17
The equation is y = (1/3)x + 17
Answer: [tex]y = \frac{1}{3} x + 17[/tex]
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
Answers
a computer code is based on the prime factorization of 160. Find the prime factorization of 160
Answers
Answer:
[tex]2\times 2\times 2\times 2\times 2\times 5[/tex]
Step-by-step explanation:
We have been given that a computer code is based on the prime factorization of 160. We are asked to find prime factorization of 160.
We know that prime factorization of a number is writing the prime factors of a number such that their product gives the original number.
To find prime factors of 160, we will divide 160 by 2 for 5 times and then divide by 5.
Prime factorization of 160: [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].
Therefore, the prime factorization of 160 is [tex]2\times 2\times 2\times 2\times 2\times 5[/tex].
What's the sum of 2⁄5 and 2⁄4?
Answers
2/5=8/20
2/4=10/20
sum is 8/20+10/20=18/20 = 9/10
You need to have the same denominator in order to add
The least common multiple of 4 and 5 is 20
[tex] \frac{2}{5} [/tex] multiplied by 4 on the numerator and the denominator
[tex] \frac{2}{4} [/tex] multiplied by 5 on the numerator and the denominator
Giving us:
[tex] \frac{8}{20} [/tex] + [tex] \frac{10}{20} [/tex]
= [tex] \frac{18}{20} [/tex]
It can further be simplified into:
[tex] \frac{9}{10} [/tex]
Find the measure of angle Q
Answers
The value of ∠Q in the figure is 146⁰.
How to determine the value of The value of ∠Q in the figure.
From the figure
Given
∠P = 2x + 10
∠R = 6x - 4
In ∆PQR
∠P + ∠Q + ∠R = 180⁰(sum of angles in triangle)
Substitute
2x + 10 + ∠Q + 6x - 4 = 180
8x + 6 + ∠Q = 180
But m∠P = m ∠R(base angles of issoceles triangle)
2x + 10 = 6x -4
-4x = -14
x = 7/2
Substitute into 8x + 6 + ∠Q = 180
8(7/2) + 6 + ∠Q = 180
28 + 6 + ∠Q = 180
34 + ∠Q = 180
∠Q = 180 - 34
= 146⁰
The value of ∠Q is 146⁰
A travel bureau estimates that when 20 tourists go to a resort with ten hotels. find the probability that no hotel is left vacant when the first group of 20 tourists arrives.
Answers
The solution for this problem is:
One way to solve is to using the "stars and bars" approach, but this could be the other one:
x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 = 20
then use (20+10-1) C(10-1), this will
result to 29C9.
Then find the way to distribute x
as a result, (20-10+10-1) C (10-1) = 19C9
Thus, the probability is 19C9/29C9 or 0.0093
Your company purchased 23 computers for $29,803.86. How much will it cost to buy 15 more of the same computer?
Answers
so 15 more computers would cost : 1295.82 * 15 = 19437.30 <==
The line passes through the points ( 7, -7) and ( 6, -5) a. y = -2x + 7 c. y = -2x - 7 b. y = 2x - 21 d. y = 2x - 7
Answers
y = mx + b
b = y - mx
b = -7 - (-2)(7)
b = -7 + 14
b = 7
equation
y = -2x + 7
answer
a. y = -2x + 7
Final answer:
The equation of the line passing through the points (7, -7) and (6, -5) is determined by finding the slope, which is -2, and then using the point-slope formula. However, the correct equation y = -2x + 21 is not listed among the student's provided options.
Explanation:
The student's question asks for the equation of a line that passes through two given points: (7, -7) and (6, -5). To find the equation of the line, we first need to determine its slope.
We use the formula for slope which is (change in y) / (change in x), often written as (y2 - y1) / (x2 - x1)
Slope = (-5 - (-7)) / (6 - 7) = 2 / -1 = -2. Therefore, the slope (m) is -2.
With the slope known, the next step is to use the point-slope form of the line equation, which is y - y1 = m(x - x1). Substituting one of the points and the slope, we get y - (-7) = -2(x - 7). Simplifying this gives us y = -2x + 14 + 7, which simplifies further to y = -2x + 21.
Therefore, among the options provided by the student, none of the equations match precisely, which means either there is a mistake in the question's options or in the calculation. However, the closest match, by the slope, would be option y = -2x - 7, considering only the slope and not the intercept.
Simplify 8(xy + 8) + 1
Answers
Final answer:
The expression 8(xy + 8) + 1 simplifies to 8xy + 65 by applying the distributive property and combining like terms.
Explanation:
The question asks to simplify the expression 8(xy + 8) + 1.
To simplify this expression, we need to apply the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. Hence, we distribute the 8 across the terms inside the parentheses:
8 × xy = 8xy8 × 8 = 64After distributing we combine the like terms:
8xy + 64 + 1
Then we combine the numerical terms:
8xy + 65
So, the expression simplifies to 8xy + 65. This is the final simplified form of the given expression.
Solve this quadratic equation using the quadratic formula.
x2 - 6x + 6 = 0
Answers
The solutions of the quadratic equation are 3 ± √3.
What are Quadratic Equations?Quadratic equations are defined as the polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is x² - 6x + 6 = 0.
The solutions of a quadratic equation ax² + bx + c = 0 can be found using the quadratic formula,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex] ] / 2a
From the given equation,
a = 1, b = -6 and c = 6
Substituting in the quadratic formula,
x = [-(-6) ± [tex]\sqrt{(-6)^2-(4*1*6)}[/tex] ] / [2 × 1]
= [6 ± [tex]\sqrt{36-24}[/tex]] / 2
= [6 ± [tex]\sqrt{12}[/tex]] / 2
= [6 ± 2√3] / 2
= 3 ± √3
Hence the solutions of the given quadratic equation are 3 + √3 and 3 - √3.
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