The value of b of the equation is -9/5
How to find the value of b with the equation in slope-intercept form?Given that: line JK passes through points J(-4,-5) and K(-6,3) and if the equation of the line is written in slope-intercept form, y=mx+b
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system
Using the y-y₁/y₂-y₁ = x-x₁/x₂-x₁
where (x₁, y₁) = (-4,-5) and (x₂, y₂) = (-6,3), the equation is:
y-(-5) / 3-(-5) = x-(-4)/-6-(-4)
y+5 / 3+5 = x+4 /6+4
(y+5)/8 = (x+4)/10 cross multiply:
10(y+5) = 8(x+4)
10y + 50 = 8x + 32
10y = 8x +32 - 50
10y = 8x - 18
y = 8x/10 - 18/10
y = 4x/5 - 9/5
Comparing y = 4x/5 - 9/5 with y=mx+b
b = -9/5
Therefore, the value of b is -9/5
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What’s 1,598 fewer then 25,876
Answer:
24,278
Step-by-step explanation:
What is the slope of the line?
Answer:
8/2 or 4/1
Step-by-step explanation:
To find the slope, you simply count how high up one point is from another (0,0 to 2,8) and then how far over. Since 2,8 is 8 points up from 0,0 the numerator of our slope would be 8; and since 8,2 is two over from 0,0 the denominator is 2. Simplify this to 4/1.
Make d the subject of the formula h=d/3+2
Answer:
d = 3h - 6
Step-by-step explanation:
h = [tex]\frac{d}{3}[/tex] + 2 ( multiply through by 3 to clear the fraction )
3h = d + 6 ( subtract 6 from both sides )
3h - 6 = d
There are 15 plates in a kitchen cabinet. the diameter of each plate is either 7 inches or 12 inches. the diameter of all 15 plates combined is 140 inches. which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?
The system of linear equations which is used to find number of 7 -inch plates ,x and 12- inch plates y is
x+y = 15 ---(1)
7x+12y = 144 ---(2)
In the given question we have following informations,
total number of plates in kitchen cabinet = 15
diameter of each plate either 7-inch or 12-inch.
let the number of plates in kitchen cabinet with Diameter 7-inch = x
and number of plates in kitchen cabinet with Diameter 12-inch = y
the diameter of all 15 plates combined = 144 inches
from the above details we can make a system of linear equations for two variables say x and y
x + y = 15 -----(1)
7x + 12y = 144 ---(2)
equation (1), (2) made the required system of equations.
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Find the solution for −0.5x − 3.69 = x − 1.9 − 2.39. x = 0.4 x = −0.4 x = 2.5 x = −2.5
The solution for the given expression -0.5x-3.69=x-1.9-2.3 is x= 0.34
The given problem is related to an algebraic expression which is the thought of expressing numbers utilizing letters or letter sets without indicating their real values, which is made up of factors and constants, at the side of logarithmic operations (expansion, subtraction, etc.). Expressions are made up of terms.
since the given expression is :
-0.5x-3.69=x-1.9-2.3
=>-0.5x-x=-1.9-2.3+3.69
=>-1.5x=-0.51
=>x=0.34
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Write an equation in slope-intercept form of the line that passes through the given points.
Equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.
Given points:
(1, 1.5) and (2, 3.5)
slope m = 3.5 - 1.5 / 2 - 1
= 2/1
m = 2
substitute m and (1,1.5) in y = mx + c
1.5 = 2*1 + c
1.5 - 2 = c
c = -0.5
c = -1/2
y = mx + c
y = 2x - 1/2.
Therefore equation in slope-intercept form of the line that passes through the given points is y = 2x - 1/2.
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Write an equation of the line, in point-slope form, that passes through the two given points.
points: (-9,5), (17,-8)
The required equation of the line is y = -(1/2)x + 1/2 which passes through the points (-9,5), (17,-8).
What is the slope of the line?The slope of a line is expressed as the gradient of the line.
Given that line passes through the points (-9,5), (17,-8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -9, y₁ = 5
x₂ = 17, y₂ = -8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 5 = (-8- 5)/(17-(-9))[x -(-9)]
⇒ y - 5 = (-13)/(26)[x +9]
⇒ y - 5 = -1/2(x +9)
⇒ y = -(1/2)x - 9/2 + 5
⇒ y = -(1/2)x + 1/2
Therefore, the equation of the line is y = -(1/2)x + 1/2 which passes through the points (-9,5), (17,-8).
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A company orders 11 boxed lunches from a deli for $84.15. If each boxed lunch costs the same amount, how much do 14 boxed lunches cost?
The cost for 14 boxed lunches is $107.10.
How to calculate the price?From the information, the company orders 11 boxed lunches from a deli for $84.15. Therefore, we need to calculate the unit price and this will be:
= Total amount / Number of orders
= $84.15 / 11
= $7.65
Therefore, the value for 14 boxes will be:
= Unit price × Number of orders
= $7.65 × 14
= $107.1
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math problem - help i need the answer for this, im very desperate for an answer.
Answer:
(x+10,y+8)
Step-by-step explanation:
If you look at the point (0,2) and it image (10,10) To go from 0 to 10 you must move 10 spaces to the right. That would be x + 10.
If you look at the same two points. You would have to move up 8 spaces to go from 2 to 10. That would be y + 8.
The same thing is true with the second two points given.
Jonathan earned the following scores on his math test 82,79,85,100,46,92,88 what is his mean test score?
Answer:
496.5714285714
Step-by-step explanation:
82+79+85+100+46+92+88
7
=496.5714285714
What is the answer to x - 5 > 12?
Answer:
x > 17
Step-by-step explanation:
x - 5 > 12 ( isolate x by adding 5 to both sides )
x > 17
-------------- from your comment
x - (- 5) > 12 , that is
x + 5 > 12 ( subtract 5 from both sides )
x > 7
a set of bivariate data was used to create a least-squares regression line. which of the following is minimized by the line? responses the sum of the residuals the sum of the residuals the sum of the squared residuals the sum of the squared residuals the sum of the absolute values of the residuals the sum of the absolute values of the residuals the influence of outliers the influence of outliers the slope
The only correct option that is minimized by the least squares regression line is. Option B the sum of the squared residuals.
lets check all the option -
Option A - This claim is untrue because the residuals' summation would provide a value of 0.
Option B - Because error must be kept to a minimum, the residuals must sum to zero and the line must be as close to the points as possible. Prior to summing them, we must first square the residuals, which will always result in a positive value. This option is accurate since the Least Square Regression Line minimizes the total of residuals.
Option C - This choice is incorrect because the least squares regression line cannot be created by adding the absolute values of the residuals.
Option D - This alternative is incorrect since the influence of outliers has nothing to do with the subject at hand.
Option E - Due to slope's lack of relevance to the subject at hand, this choice is also incorrect.
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Can someone answer this?
The values indicated trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
How to find the trigonometric functions?Trigonometric functions are the periodic functions that denote the relationship between angle and sides of a right-angled triangle e.g sine, cosine, tangent, etc.
Given: tan(β) = 7
Thus, β = arc tan 7 = 81.87
(a) cot(β) = 1/tan(β) = 1/7 = 0.14
(b) cos(β) = cos 81.87 = 0.14
(c) tan(90-β) = tan(90-81.87) = tan 8.13 = 0.14
(d) csc(β) = 1/sinβ = 1/sin(81.87) = 1.01
Therefore, the value of the trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) = 0.14 and csc(β) = 1.01
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. Identify the key features of g(x) = x², including the domain, range, x and y intercepts, and
intervals of increase and decrease.
The required key features of [tex]g(x) = x^{2}[/tex] including domain is (-∞, ∞) (i.e. all real values), range = [0,∞), x-intercept = (0,0), y-intercept = (0,0), interval of increasing = (0,∞) and interval of decreasing = (-∞, 0)
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function.
The graphs of quadratic functions are frequently curved or nonlinear. A parabola, a kind of U-shaped curve, is the particular type of curve that makes up the graph of a quadratic function.
Given, [tex]g(x) = x^{2}[/tex]
The graph of the given function is given below:
From the graph,
Domain = (-∞, ∞) (i.e. all real values)
Range = [0,∞)
x-intercept = (0,0)
y-intercept = (0,0)
Interval of increasing = (0,∞)
Interval of decreasing = (-∞, 0)
Hence, these are the required key features of [tex]g(x) = x^{2}[/tex].
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Write and graph linear equations
The equation of linear equation is y = -5x +3.
What is equation of linear equation?
A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.
The standard form or the general form of linear equations in one variable is written as, Ax + B = 0; where A and B are real numbers, and x is the single variable. The standard form of linear equations in two variables is expressed as, Ax + By = C; where A, B and C are any real numbers, and x and y are the variables.
The slope intercept form of linear equation is
y = mx + b
where m is the slope.
Given,
The slope = -5
and the points are (4, -17)
y = -17, x = 4, m = -5
-17 = -5(4) + b
-17 = -20 + b
-17 + 20 = b
b =3
The equation of linear equation is y = -5x + b
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5x+13≥−37. find for x
Answer:
x ≥ -10
Step-by-step explanation:
Given equation,
→ 5x + 13 ≥ -37
Now the value of x will be,
→ 5x + 13 ≥ -37
→ 5x ≥ -37 - 13
→ x ≥ -50/5
→ [ x ≥ -10 ]
Hence, the value of x is -10.
Express your answer as a polynomial in standard form.
f(x)= -3x+5
g(x)=x^2+2x+15
Find: (g∘f)(x)
Answer: [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
=====================================================
Explanation:
The notation (g∘f)(x) is the same as g(f(x))
We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.
This is what the steps look like
[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]
Therefore,
[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]
You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.
on the grid,draw the graph of y=2x-3 for values of x from -3 to 5
The graph of the equation y = 2x - 3 at the interval of -3 to 5 is attached below.
Graph:
Graph means the diagram that shows the variation of a variable in comparison with that of one or more other variables.
Given,
Here we have the equation y = 2x - 3
Now, we need to plot the graph of the given equation at the interval of -3 to 5..
To plot the graph for the given function,
The given interval is taken as the value of x and we have to calculate the value of y from it,
Now, we have to take the given interval -3, -2, -1, 0, 1, 2, 3, 4, 5 are the samples value for x.
So, we have to apply the values on the equation,
Then we get the value of the function as,
x = -3 => y = 2(-3) - 3 = -6 - 3 = 9
x = -2 => y = 2(-2) - 3 = -4 - 3 = -7
x = -1 => y = 2(-1) - 3 = -2 - 3 = -5
x = 0 => y = 2(0) - 3 = 0 - 3 = -3
x = 1 => y = 2(1) - 3 = 2 - 3 = -1
x = 2 => y = 2(2) - 3 = 4 - 3 = 1
x = 3 => y = 2(3) - 3 = 6 - 3 = 3
x = 4 => y = 2(4) - 3 = 8 - 3 = 5
x = 5 => y = 2(5) - 3 = 10 - 3 = 7
The completed table is attached below.
Now, we have to plot the graph through the derived table, then we get the graph like the following.
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The football team played 10 games and won 7 games. What was its winning percentage?
Answer:
70%
Step-by-step explanation:
"6 more than 7 times the amount of 10"
Answer: 76
Step-by-step explanation:
Based on the given conditions, formulate: 6+10*7
Calculate the product or quotient: 6+70
Calculate the sum or difference: 76
for a lower tail test, the test statistic z is determined to be zero. what is the p-value for this test?
0.5 is the p-value for this Z -test .
What is the Z test's p-value?
For each test, the p-value is the likelihood that the null hypothesis will be correct, which is expressed as the probability of receiving a z-value . an absolute value at least as great as the one we actually observed in the sample data.P-value, or probability value, is the likelihood that a statistic will be at least this distant from the mean if the null hypothesis is assumed to be true. So it can be thought of as a conditional probability, to put it another way.For a lower tail test, the test statistic z is determined to be zero that means
P(z<0)
Then p-value is
p-value = P(z<0) = 0.5 (From z score table )
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the sample regression line a. is estimated by the population regression line. b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line. c. shows the actual (or true) relation between the dependent and independent variables. d. is used to estimate the population regression line. e. connects the data points in a sample.
The simple regression line is used to estimate the population regression line.
We are asked about, the simple regression line
We have options:
a. is estimated by the population regression line.
b. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.
c. shows the actual (or true) relation between the dependent and independent variables.
d. is used to estimate the population regression line.
e. connects the data points in a sample.
From the above options, Option (d) is the correct one i.e. is used to estimate the population regression line.
The simple regression line is used to estimate the population regression line.
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Find the product. (a2)(2a3)(a2 â€"" 8a 9) 2a7 â€"" 16a6 18a5 2a7 â€"" 16a6 â€"" 18a5 2a8 â€"" 16a7 18a6 2a12 â€"" 16a7 18a6
The price of a movie ticket at the theater is $7 for students.
The price is higher for adults.
A group of 4 students and 3 adults paid $64 in all for movie tickets.
How much does each adult ticket cost?
Each adult tickets costs
The cost of each adult ticket for watching movie at the theatre equals to $12.
How do we derive the cost of each adult ticket?Given data:
Student ticket price = $7
Group of 4 students and 3 adults paid $64 in all for movie tickets.
The computation of each of the adult ticket cost is as follows:
Let x be the cost of each adult ticket.
Then, cost of 3 adult tickets = 3x.
Now:
The cost of 1 student ticket = $7
The cost of 4 student ticket = $7(4)
Then, we get the following equation:
7(4) + 3x = 64
18 + 3x = 64
3x = 64 - 18
3x = 36
x = 12
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Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries
sells for $1.50 and each pound of grapes sells for $2.75. Arun made $130.25 from
selling a total of 66 pounds of raspberries and grapes, Determine the number of
pounds of raspberries sold and the number of pounds of grapes sold.
Answer:
41 pounds of raspberries and 25 pounds of grapes
Step-by-step explanation:
x = pounds of raspberries
y = pounds of grapes
1.50x + 2.75y = 130.25
x + y = 66 --> y = -x + 66
Substitute and solve for x:
1.50x +2.75(-x +66) = 130.25
1.50x - 2.75x + 181.5 = 130.25
150x - 275x + 18150 = 13025
-125x +18150 = 13025
-125x = -5125
x = 41
Substitute x to find y:
41 + y = 66
y = 25
Answer:
There were 41 pounds of raspberries sold and 25 pounds of grapes sold.
Step-by-step explanation:
Refer to the figure below. M
The measure of the angle ∠C is 17°.
The angle having a measure equal to 32° and the angle ∠B form a linear pair. They are supplementary angles. When two lines cross, they generate a pair of neighbouring angles called a linear pair. A linear pair's two angles are always supplementary, which means their measurements add up to 180 degrees. The sum must be equal to 180°.
32° + ∠B = 180°
∠B = 180° - 32° = 148°
Now, we will use the angle sum property of a triangle. The sum of all the angles in a triangle is equal to 180°.
∠B + ∠C + 15° = 180°
148° + ∠C + 15° = 180°
∠C + 163° = 180°
∠C = 180° - 163° = 17°
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There are 95 males and 125 females participating in a marathon. What
percent of the participants are female? Round your answer to the nearest
hundredth.
Answer: 55.56%
Step-by-step explanation:
To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.
The dot plot shows 20 students' scores on a quiz
in English class.
Quiz Scores
If one student from the class is chosen at
random, what is the probability that he or she
scored MORE than 15 points on the quiz?
Answer:
Probability = A. 2 / 5
Step-by-step explanation:
Probability = ( Number of Favorable Outcomes ) / (Total Number of Outcomes )
So the Total Number of Students = 20
Number of Students ( Dots ) scored more than 15 = 3+2+1+2 = 8
Probability = 8 / 20 = 2 / 5
Glad to Help
Answer: 12/20= 3/5
Step-by-step explanation:
you have to count all the dots on the dot plot to find your denominator which is 20.
then you count all the dots that are fifteen or more and there are 12 so 12/20 is the probability which is simplified into 3/5.
if we want to create a 95% confidence interval for a population proportion with a margin of error (m) of 0.099, what sample size is necessary? use the simplified formula (n
For the specified requirements, 97 sample size are required.
Given that,
Confidence Interval = 95
Margin of error (m) =0.099
We know , to find Sample size for estimating a population proportion
n = (Z*/m)² P(1-P)
where , m is margin of error
P is estimated proportional value.
If we have no preconceived of the value of the population proportion
, then we use P= 0.50 because it is most conservative and it will give use the largest sample size calculation.
for a 95% confidence interval ,
Z* = 1.960 , m=0.099
Using equation we get
n = (1.96/0.099)²(0.5)( 1 - 0.5 )
By solving,
n = 97.02≅ 97
The necessary sample size is 97
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Sean drew a vertical line segment and labeled the top endpoint W and the other endpoint X.
He then found the midpoint of WX and labeled it Y. Starting at Y and moving to the right, he
drew a line segment of length WY perpendicular to WX, and he labeled the new endpoint Z.
Finally, he drew a line segment parallel to YZ, also of length WY, starting at W and moving to
the right.
What letter did Sean draw?
E
F
L
T
PLEASE HELP
Sean drew a letter (b)F.
What is Geometry construction?
Drawing precise shapes, angles, or lines is referred to in geometry as "construction." These structures only require a compass, a straightedge (a ruler), and a pencil.
according to the question, WX is a straight line having a midpoint at Y.
YZ is drawn perpendicular to WX. And parallel to YZ a line segment is drawn After this Geometrical construction, a letter is drawn which is F.
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