Answer:
y = 5x + 11
Step-by-step explanation:
We are given that a line passes through (-2, 1) and also it contains a slope of 5
We want to write the equation of this line in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y axis
As we are already given the slope, we can immediately substitute it into the formula
Replace m with 5 in y=mx+b:
y = 5x + b
Now we need to find b
As the equation passes through the point (-2, 1), we can use its values to help solve for b.
Substitute -2 as x and 1 as y:
1 = 5(-2) + b
Multiply
1 = -10 + b
Add 10 to both sides
11 = b
Substitute 11 as b in the equation
y = 5x + 11
Topic: finding the equation of the line
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If f(x) = |x| + 9 and g(x) = –6, which describes the range of (f + g)(x)?
(f + g(x)>3 for all values of x
(f + g)(x)<3 for all values of x
(f + g)(x)>6 for all values of x
(f + g)(x)<6 for all values of x
Answer: for all values of x
Step-by-step explanation:
[tex](f+g)(x)=|x|+9-6=|x|+3[/tex]
Since the range of y = |x| is [tex]y \geq 0[/tex], adding 3 to this shifts the graph 3 units up, giving us that [tex](f+g)(x) \geq 3[/tex] for all values of x.
Help asap please I need it
Answer: 8x+70
Step-by-step explanation:
[tex]\sum^{5}_{n=2} (2x+5n)=(2x+10)+(2x+15)+(2x+20)+(2x+25)=\boxed{8x+70}[/tex]
which set of ordered pairs corresponds to the graph ?
Answer:
Let first check the coordinates of the points
A = (1 , -6)
B = (2 , -4)
C = (2, -2)
D = (4, -2)
E = ( 6, 0)
Option 4 is correct..
Explanation -
to find the coordinates we have to find the distance of that point from x Axis and then y axis. from origin.
(x-8)^2 i need step by step please like eveyone gets x2 -16x +64 i dont get
how
Answer:
x²-16x+64
use formula =a²-2ab+b²x²-2.x.8+8² (for knowledge 2 × 8 = 16)x²-16x+64Answer:
(x -8)² = x² -16x +64
Step-by-step explanation:
A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.
All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.
__
expanding a product of binomialsOne of the patterns that is used with quadratics is the square of a binomial.
(a - b)² = a² -2ab +b²
This is the result of applying the distributive property several times.
First of all, the exponent indicates repeated multiplication:
(a -b)² = (a -b)×(a -b)
The distributive property tells you each term outside parentheses multiplies each term inside:
= a×(a -b) -b×(a -b)
= a·a -a·b -b·a +b·b . . . . . and again
Now, we collect terms, recognizing that ab=ba.
= a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication
So, the pattern for the square of a binomial is ...
(a -b)² = a² -2ab +b²
__
using the patternFor your specific case, ...
a = xb = 8(x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern
(x -8)² = x² -16x +64
_____
Additional comment
If you want to do this without using the pattern, just make use of the distributive property:
[tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]
__
While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:
(x -8)(x -8) -- First: x·x = x²(x -8)(x -8) -- Outer: x·(-8) = -8x(x -8)(x -8) -- Inner: (-8)·x = -8x(x -8)(x -8) -- Last: (-8)(-8) = 64Then the product is ...
(x -8)² = x² -8x -8x +64 = x² -16x +64
__
Of course, the distributive property is involved in what we call "collecting terms."
-8x -8x = (-8-8)x = -16x
The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.
evaluate 7/8+1/4÷6/7
Step-by-step explanation:
[tex] = \frac{7}{8} + \frac{1}{4} \div \frac{6}{7} [/tex]
[tex] = \frac{7}{8} + \frac{1}{4} \times \frac{7}{6} [/tex]
[tex] = \frac{7}{8} + \frac{7}{24} [/tex]
[tex] = \frac{7 \times 3}{8 \times 3} + \frac{7}{24} [/tex]
[tex] = \frac{21}{24} + \frac{7}{24} [/tex]
[tex] = \frac{28}{24} [/tex]
[tex] = \frac{7}{6} [/tex]
7/8+(1/4÷6/7)
1/4 ÷ 6/7 = 7/24
7/8 + 7/24 = 7/6 = 1 1/6
Bayes' rule combines accuracy, false positives, and _____ to determine the probability of a result.
The blank space in the task content should be filled with; false negatives.
What is Baye's rule?Baye's theorem can be used to correct measurement errors provided the real probabilities, the chance of a false positive and the chance of a false negative is known.
Hence, it follows from the methodology above that the Baye's rule combines accuracy, false positives and false negatives in a bid to determine the probability of a result.
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Skylar models the volume of a popcorn box as a right rectangular prism and the box can hold 69 cubic inches of popcorn when it is full. Its width is 33 in and its height is 5 3/4 in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer:
4/11 of an inch (about .4 of an inch)
Step-by-step explanation:
[tex]l \times 33 \times 5.75 = 69[/tex]
[tex]189.75l = 69[/tex]
[tex]l = \frac{69}{189.75} = \frac{4}{11} = .3636[/tex]
So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.
A rectangular room is 1.2times as long as it is wide, and its perimeter is
30 meters. Find the dimension of the room.
The length is :
meters and the width is
___meters.
The length is 6.8 meters and the width is 8.2 meters.
How to determine the dimension of the room?Represent the length and the width with x and y
So, we have:
y = 1.2x
P = 2(x + y)
The perimeter is 30.
So, we have:
2(x + y) = 30
Divide by 2
x + y = 15
Substitute y = 1.2x
x + 1.2x = 15
This gives
2.2x = 15
Divide by 2.2
x = 6.8
Substitute x = 6.8 in y = 1.2x
y = 1.2 * 6.8
Evaluate
y = 8.2
Hence, the length is 6.8 meters and the width is 8.2 meters.
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Can someone tell me why this wrong please
Answer:
4,051,500
Step-by-step explanation:
You have 7.3 % that are one native one foreign
Multiply that by the number of households
.073 * 55,500,000
4,051,500
Part A
Which shapes can you use to model the log and the board?
Answer:
A cylinder
Step-by-step explanation:
Hope this helps :)
These expressions represent four numbers. The value of the median of the expressions is 12.
Answer:
Try retyping ,which expressions ..?? Maybe it didn't come out
Answer:
15
Step-by-step explanation:
Actual Question:
These expressions represent four numbers. The value of the median of the expressions is 12.
x , 2x, 6x, 11x
Work out the value of the mean of the expressions.
_____________________________________________
See the attachment for steps.
which number is the
same distance away from -12 as 2?
Answer:
-26
Step-by-step explanation:
2 is 14 away from -12. The other number that is 14 away from -12 is -26.
-12 + x = 2
x = 14
-12 - 14 = -26
Find the average rate of change of the function on the interval specified.
g(x) = 7x3 − 4
on
[−3, 3]
The average rate of change of the function will be 63.
The average rate of change of the function is used to find the slope of the graphed function which can be calculated by the change in y value divided by the change in x value.
The average rate of change of function f(x) in the interval [a,b] can be calculated as avearge rate of change= (f(b)- f(a))/(b-a)
Here given function is g(x) = 7x³-4
which is defined in the interval [-3,3].
So using the defination of the average rate of change, The average rate of change= (g(3)-g(-3))/(3-(-3))
= {(7(3³)-4)-(7*(-3)³-4)}/(3-(-3))
= {(189-4)-(-189-4)}/(3+3)
= (185-(-193))/6
= (185+193)/6
= 378/6
= 63
Therefore the average rate of change of the function will be 63.
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Jared made sixty dollars mowing lawns over the summer. If he spent thirty-nine dollars buying new mower blades, how many seven-dollar games could he buy with the money he had left?
Answer:
three
Step-by-step explanation:
60 - 39 = 21
21/7 = 3
What is the semiannual interest payments of a 30 year bond with a face value of $50 million and a stated annual interest rate of 4 percent?
Based on the stated annual interest rate and the face value of the bond, the semiannual payments will be $1,000,000.
How can the semiannual interest payment be found?The formula to find the semiannual payment is:
= (Face value x Stated annual interest rate) / 2 semi-annual periods per year
Solving gives:
= (50,000,000 x 4%) / 2
= 2,000,000 / 2
= $1,000,000
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A fire fighter sees a woman trapped in the building 81 feet up from the bottom floor. If the firetruck is parked 41 feet away from the bottom of the building, at what angle of elevation, to the nearest degree, shut the fire fighter extend the ladder to reach the woman?
Which angles would the consecutive interior angles theorem state are supplementary?
Answer:
<3 and <5<4 and <6
Step-by-step explanation:
Now that we know how to identify consecutive interior angles, let’s talk about the theorem. The consecutive interior angles theorem states that when the two lines are parallel, then the consecutive interior angles are supplementary to each other. Supplementary means that the two angles add up to 180 degrees.
There were 582 students enrolled in a freshman-level chemistry class. By the end of the semester, the number of students who passed was 5 times the number of students who failed.
Answer:
let the no. of students who failed the examination be X
therefore, no. of students passed = 5x
total no. of students = 582
5x + X = 582
6x = 582
x = 97
no. of students failed the examination = 97
no. of students passed = 97*5 = 485
PLEASE HELP!!!!!!!!!
The equivalent expression to ∑n(n+1) is ∑n²+∑n.
What is Equivalent expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression;
∑(n(n+1))
= ∑ (n² + n)
= ∑n²+∑n
Thus, the equivalent expression to ∑n(n+1) is ∑n²+∑n.
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Express verbal statement in algebraic form.
The cost to rent a sailing boat at Catalina Island is $370 per day
plus $80 for every hour of use. What is the maximum number of
hours the sail boat can be rented for each day, if the rental cost is
not to exceed $1090 per day?
Answer:
370 + 80x ≤ 1090
Step-by-step explanation:
By using letter variables for the unknown numbers, we can break down the question into mathematical terms:
If the cost is $370 per day and the number of days is unknown, we can substitute the number of days with a placeholder. In this case, it'll be a variable such as x. So the cost can be represented by $370y.
If the cost is $80 per hour and the number of hours is unknown, we can substitute the number of hours with a placeholder. In this case, it'll be a variable such as y. So the cost can be represented by $80x.
The questions asks for the total cost not to exceed $1090 per day. This means that we know that the number of days is 1. We're trying to find the maximum number of hours, so our equation will combine the costs of both day costs and hour costs:
$370 (1 day) + $80 (x hours) ≤ $1090 per day
The symbol is the equal to or less than symbol, meaning the combined total costs is either equal to $1090 or less than it.
To simplify this, we can rewrite it as:
370 + 80x ≤ 1090
What is the measure of complemnt angle 42
Answer:
Complemetry angle = 90° - 40°
= 50°
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex]
Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complement of 90 by setting up an equation; (let x be the unknown angle).
[tex]\implies[/tex] 42+x=90
Subtract 42 from both sides
x=48
--
Hope that this helped! Best wishes.
--
can someone show me the steps to solve #83 please?
Answer:
18π ≈ 56.5 meters
Step-by-step explanation:
The length of the arc of a circle is given by the formula ...
s = rθ . . . . where r is the radius, and θ is the central angle in radians
ApplicationYou are given the values of r and θ, so you only need to put them into the formula and simplify.
s = (27 m)(2π/3) = 18π m
The length of the arc is 18π meters, about 56.5 meters.
Given the diagram below, what is cos(45)?
A. √2
B.1/√2
C. 3√2
D. 1/√3
Using the cosine ratio, the value of cos(45) in the diagram is: B. 1/√2.
How to Find the Cosine Ratio?Cosine ratio is, cos ∅ = adjacent length/hypotenuse length of a right triangle.
The triangle is a 45-45-90 triangle, thus, the two legs will be the same length, which is: 9 units each.
Hypotenuse = √(9² + 9²) = √162 = 9√2 units
∅ = 45°
Adjacent = 9 units
cos 45 = 9/9√2 = 1/√2
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Use the interactive to make a line that passes through the points 3'2 and -1'-1 slope
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
Equation of a lineThe standard equation of a line is expressed as y= mx + b
where
m is the slope
b is the y-intercept
Given the coordinate points on a line (3, 2) and (-1, -1)
Slope = -1-2/-1-3
Slope = 3/4
Determine the y-intercept
2 = 3/4(3) + b
2 = 9/4 + b
b = 2 - 9/4
b = -1/4
The required equation of the line passing the coordinates will be y = 3/4x - 1/4
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The larger of two consecutive integers is 7 greater than twice the smaller. Find the integers. ( 4, 5)( -8, -9)(-5, -6)
Answer:
(-5, -6)
Step-by-step explanation:
The smaller integer is x.
The larger integer is x + 1.
x + 1 = 7 + 2x
-x = 6
x = -6
x + 1 = -6 + 1 = -5
Answer: (-5, -6)
Find the quotient: (9mn2)(−3m6n)33m10n3
The quotient is -27m/ 55.
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
(9mn²)(−3m*6n)÷33m*10n³
=9mn² *(-18mn) / 330mn³
= -162m²n³/ 330mn³
= -27m/ 55
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Gianna is constructing a circle that passes through all three vertices of the triangle shown.
Where will the center of the circle be located?
OA. on a vertex of the triangle
OB. inside the triangle
OC. on a side of the triangle
OD. outside the triangle
B
Based on the definition of a circumcircle, the center of the circle as shown in the image below is located: B. inside the triangle.
What is a Circumcircle?A circumcircle, as shown in the diagram attached below, is a circle that is drawn so that all the vertices of a triangle touches the circumference of the circle.
Thus, as shown in the image attached below, the center of the circle is located: B. inside the triangle.
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Answer: OUTSIDE THE TRIANGLE
Step-by-step explanation: ANSWER ON EDMENTUM/PUTO
the answer to this question
solve the following inequality
The solution set of the inequality is:
w ∈ (-∞, -1] U [3, ∞)
How to solve the given inequality?
The graphed parabola is f(w), and we have the inequality:
f(w) ≤ 0.
So we need to identify the intervals such that the parabola is below the horizontal axis. By looking at the graph, we can see that the two intervals are:
Left side:
(-∞, -1]
Right side:
[3, ∞)
Where the brackets are used because points x = -1 and x = 3 are solutions.
Then the solution set of the inequality is:
w ∈ (-∞, -1] U [3, ∞)
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The point A(0,3) and point B(4,19) lie on the line L.
Find the equation of line L
Answer: The equation is y = 4x+3
Slope = 4
y intercept = 3
========================================================
Explanation:
Let's start off by finding the slope.
[tex]A = (x_1,y_1) = (0,3) \text{ and } B = (x_2,y_2) = (4,19)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{19 - 3}{4 - 0}\\\\m = \frac{16}{4}\\\\m = 4\\\\[/tex]
The slope is 4.
The y intercept is 3 because of the point (0,3)
We go from y = mx+b to y = 4x+3
m = slope
b = y intercept
---------------
Check:
Plug in x = 0 and we should get to y = 3
y = 4x+3
y = 4(0)+3
y = 0+3
y = 3
That works out. Now try x = 4. It should lead to y = 19
y = 4x+3
y = 4(4)+3
y = 16+3
y = 19
The answer is confirmed.
