Answer:
y = x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 1 , then
y = x + c ← is the partial equation
to find c substitute (2, - 1 ) into the partial equation
- 1 = 2 + c ⇒ c = - 1 - 2 = - 3
y = x - 3 ← equation of line
A parasail is $\frac{3}{100}$
mile above the water. After 5 minutes, the parasail is $\frac{1}{50}$
mile above the water. Find the change in height of the parasail.
The change is height is
mile.
The change in height of the parasail = 1/100.
What is height?Height of defined as the measurement that is taken for an object which starts from its base to the topmost point. This is usually measured in meters.
From the question,
The height of the parasail above the water level= 3/100
The height of the parasail above the water level after 5 minutes= 1/50
The change in height of the parasail is determined by finding the difference between the two heights.
That is, = 3/100 - 1/50
= 0.03- 0.02 = 0.01
When changed to fraction is = 1/100
Therefore, the change in height after 5 minutes is = 1/100
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For each ordered pair, determine whether it is a solution to y=3x-6
-4,18
5,24
7,-45
-8,-30
The point (-8,-30) is ordered pair which is the correct solution to y=3x-6.
What is ordered pair?The position of a point on the coordinate plane with respect to the origin is represented by an ordered pair in coordinate geometry. Two parallel intersecting lines, with one line being the x-axis and the other being the vertical, form a coordinate plane (y-axis).
The origin is the place where the two axes meet. An ordered pair (x, y), where x is known as the x-coordinate and y is known as the y-coordinate, is used to represent each point on the coordinate plane.
To find the solution of the y = 3x - 6 we will simply use the trial and error method to find if the given the ordered pair are correct or incorrect.
(-4,18)
y = 3x - 6
18 = 3(-4) - 6
18 = -12 - 6
18 = -18
Incorrect solution
(5,24)
y = 3x - 6
24 = 3(5) - 6
24= 15 - 6
24= 9
Incorrect solution
(7,-45)
y = 3x - 6
-45 = 3(7) - 6
-45 = 21 - 6
-45 = 15
Incorrect solution
(-8,-30)
y = 3x - 6
-30 = 3(-8) - 6
-30 = -24 - 6
-30 = -30
Correct solution
Thus, The point (-8,-30) is ordered pair which is the correct solution to y=3x-6.
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Giorgio used all the vegetables shown in the table above for his dinner.
a. How much money did his meal cost?
Considering the cost of 3 bell peppers are $2.05, 4 tomatoes are $1.09, 2 onions are $0.65 and 5 potatoes are $0.33, and Giorgio used all these vegetables for his dinner, then his meal costed a total amount of $4.45.
As per the question statement, no information about the vegetables Gorgio used for his dinner or their prices are provided in the question statement, and thus we are considering that, Gorgio used 3 bell peppers that costed $2.05, 4 tomatoes at $1.09, 2 onions at $0.65 and 5 potatoes at $0.33 in his dinner recipe.
We are required to calculate how much does Gorgio's dinner meal cost.
To solve this question, we simply have to add up the prices of the ingredients and we will obtain our desired answer.
That is, Gorgio's meal costed a total amount of $(2.05 + 1.09 + 0.65 + 0.33)
= $4.45
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Can you please give me the name of the Math book that has this problem solving question below?
Nick's bank account balance was $21. if he writes a check for $30 and his bank charges him $35 for overdrawing his account, find his account balance
Answer:
not sure but I know the answer
Step-by-step explanation:
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HELP ME PLEASE DONT MIND THE DRAWING
1. Point slope form
2. y = -2x + 25
The formula for point slope form is:
y − y1 = m(x − x1), which is exactly what y-7=-2(x-9) is, as y1 is 7, m is -2 and x is 9.
To get this into slope intercept form, we have to solve for y/ isolate it.
y - 7 = -2 (x-9)
First, distribute the -2.
y - 7 = -2x + 18
Then add 7 on both sides to get rid of the -7.
+ 7 + 7
y = -2x+25
evaluate the function when x=3 h(x) = -x + 5
Answer:
2
Step-by-step explanation:
substitute x = 3 into h(x)
h(3) = - 3 + 5 = 2
use a table, an equation, and a graph to represent:sue swims 1.5 laps per minute
Represent the situation by using a function. If Sue swims 1.5 laps per minute, the equation that represents this situation is
[tex]y=1.5x[/tex]Where y is the number of laps and x is the time in minutes
With this equation you can make a table
Finally, make the graph
the length of two sides of the right triangle ABC shown in the illustration are given. I have to find the length of the third side in centimeters. a= 7 cm and b= 24 cm
we have that
Applying the Pythagorean Theorem
c^2=a^2+b^2
substitute given values
c^2=7^2+24^2
c^2=49+576
c^2=625
c=25 cmDetermine whether each graph represents a function explain
The correct statement regarding whether each graph represents a function is given as follows:
a. Represents a function, as each input is mapped to only one output.
b. Does not represent a function, as there are inputs mapped to two outputs.
When does a graph represents a function?A graph will represent a function if the graph contains no vertically aligned points, that is, each value of x is mapped to only one value of y.
Vertically aligned points mean that a value of the input x is mapped to multiple values of the output y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.
In the context of this problem, we have that:
In the discrete graph a, each value of x, x = 1, x = 2, x = 3, x = 4 and x = 5, is mapped to only one value of y, hence the graph is a function.In the continuous graph b, there are values of x mapped to two values of y, hence it is not a function.On the continuous graph, a vertical line is drawn and shown at the end of the answer, representing visually when does a graph does not represent a function, as the vertical line crosses the function at multiple points.
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Determine the value for x in the equation x over 5 and 7 tenths equals 2 and 3 tenths.
3.4
8.0
11.4
13.11
Answer:
d. 11.4, 3.4
Explanation:
Given
Required
Determine the zeros
The best way to solve this is to apply the graphical method.
First, we plot the graph of:
See attachment
Next, we write out all values of x when the line crosses the y-axis.
From the attached graph, the points are (approximately):
Option (d) is the closest to the above values.
Hence, the zeros are: -1.4 and 3.4
active attachment
Answer:
13.11
Step-by-step explanation:
[tex]\frac{x}{5\frac{7}{10} }[/tex] = 2 [tex]\frac{3}{10}[/tex] ( multiply both sides by 5 [tex]\frac{7}{10}[/tex] to clear the fraction
x = 5 [tex]\frac{7}{10}[/tex] × 2 [tex]\frac{3}{10}[/tex] = 5.7 × 2.3 = 13.11
Tom says he is comparing banks to see what interest rates they offer on savings accounts. Explain how Tom should use the information he gets to decide which bank to open a savings account with.
Tom should choose the bank that gives the highest interest rate on savings accounts
What is interest rate?The amount a lender charges a borrower is called an interest rate, and it is expressed as a percentage of the principal, or the loaned amount. Typically, a loan's interest rate is expressed as an annual percentage rate, or APR.
A savings account or certificate of deposit earnings at a bank or credit union may also be subject to an interest rate (CD). The interest received on these deposit accounts is measured in annual percentage yields. In this case, the one that gives the best rate is the best option to choose.
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Answer:
Tom should choose the bank that offers the highest interest rate on savings accounts. Since the principal and time would be the same for each bank, the higher the interest rate, the more money Tom would earn.
Step-by-step explanation:
this was the sample answer on edge. I hate edge
2m ÷8m in standard form
Answer:
1/4
Step-by-step explanation:
2m/8m = 1/4
Answer:
1/4
Step-by-step explanation:
2m ÷8m
Divide
2m
----
8m
Cancel like terms
2
---
8
Divide the top and bottom by 2
2/2
------
8/2
1
-----
4
An international company has 15,900 employees in one country. If this represents 34,6% of the company's employees, how many employees does it have in total?
Using percentage, we calculated that the total number of employees in the company equals 45954.
How do we express Percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means.
Given,
34.6% of the employees in the company equals 15,900
Let the total number of employees in the company = x
According to the given question,
34.6 / 100 × x = 15,900
⇒ x = 15900 × 1000 / 346
⇒ x = 45954
∴ Total employees in the company equals 45954.
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A family took a road trip it takes 1/4 tank of gas to travel 1/5 of the total distance at this rate,What fraction of the total distance can the family travel using tmp tank of gas.
A movie theatre currently has 49 empty seats. 3
people enter every minute to fill those seats. The
scenario is modeled by the arithmetic sequence
= 46 − 3( − 1)
The number of empty seats based on the arithmetic sequence in 6 minutes is 28.
How to illustrate the information?It should be noted that an expression simply means the function that's given to show the relationship between the variables.
From the information, the movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence:
= 46 − 3m.
In this case m = number or minutes.
The empty seats in 6 minutes will be:
= 46 - 3m
= 46 - 3(6)
= 46 - 18
= 28
There are 28 empty seats.
The complete question is written below.
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A movie theatre currently has 49 empty seats. 3 people enter every minute to fill those seats. The scenario is modeled by the arithmetic sequence
= 46 − 3m. Find the numberof empty seats in 6 minutes.
The sides of ABC are a, b, and c. If the lengths of a = 7 and b = 10, what are the
possible lengths of c?
A) 3
B) 3
C) 3
D) 7
Answer all questions.
1. Slope of the line is: c. -3/2.
2. (4, 0) lies on the line.
3. The angle relationship is congruent angles.
4. x = 19
5. m<A = 39
6. The angle relationship is corresponding angles.
7. a. congruent angles.
8. x = 12
9. m<A = 72°
10. m<B = 43°
What is the Slope of a Line?The slope of a line = change in y/change in x
What are Angle Relationships?Angle relationships is used to determine the measures of angles depending on how the two angles relate, whether they are congruent or supplementary angles. For example, corresponding angles are congruent, linear pair angles are supplementary.
1. Slope of the line that passes through (-7, 3) and (-5, 0):
Slope (m) = (3 - 0)/(-7 -(-5)) = 3/-2
Slope (m) is: c. -3/2.
2. The graph of the equation y = 1/2x - 2 is shown in the attachment, which shows that the point that lies on the line is:
(4, 0)
3. The angle relationship is congruent angles.
4. 39 = 2x + 1
39 - 1 = 2x
38 = 2x
38/2 = x
x = 19
5. m<A = 2x + 1 = 2(19) + 1
m<A = 39
6. The angle relationship is corresponding angles.
7. They are: a. congruent angles.
8. 38 = 3x + 2
38 - 2 = 3x
36 = 3x
36/3 = x
x = 12
9. m<A = 180 - 108 [supplementary angles]
m<A = 72°
10. m<B = 180 - 65 - 72
m<B = 43°
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In a group of 40
people, 22 of them
have brown hair.
What percent of
them don't have
brown hair?
Answer:
Step-by-step explanation:
Hi:
First determine those without brown hair:
40-22=18 don't have brown hair.
18/40 don't have brown hair:
Divide by 2
9/20
Multiply by 5 to get percent
45/100= 45 percent don't have brown hair
If p = 10^m, q = 10^n and p^n*q^m = 100 then prove that mn=1
Answer:
Step-by-step explanation:
[tex]\displaystyle\\p=10^m;q=10^n;p^n*q^m=100\\\\p^n*q^m=(10^m)^n*(10^n)^m=10^{mn}*10^{nm}=10^{2mn}=100^{mn}=100\\\\\Rightarrow\ mn=1[/tex]
Two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. More than 36 employees stated their preference. Ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. His work is shown below.
Step
Ren’s work
Step 1
Two-thirds x less-than 36
Step 2
x less-than 54
Step 3
A number line going from 51 to 57. An open circle is at 54. Everything to the left of the circle is shaded.
Where, if any, did Ren first make a mistake in his work?
Step 1
Step 2
Step 3
No mistake found
Answer: Ren first make a mistake in his work at step 1
Step-by-step explanation:
Step 1 : 2x/3 < 36 Step 2 : x < 54Step 3 :
A number line going from 51 to 57. An open circle is at 54. Everything to the left of the circle is shadedMistake is in 1st step it self which is cascaded in further stepsCorrect would be 2x/3 > 36 as more than 36 employees stated their preference hence 2x/3 must be greater than 36
Answer: Its a correct me if i'm wrong
Step-by-step explanation:
27.405 x 18 using algorithm
The value of the expression using algorithm is 493.29 .
An algorithm is a finite sequence of exact instructions used to solve a class of particular problems or carry out a calculation in mathematics and computer science.
For performing calculations and processing data, algorithms are employed as specifications. Advanced algorithms can do automated deductions (also known as automated reasoning) and employ logical and mathematical checks to reroute the execution of the code along several paths (referred to as automated decision-making).A well-defined formal language and a finite amount of time and space are both capable of being used to represent an algorithm for computing a function. In accordance with the instructions, a calculation is to be performed that, once completed, goes through a finite number of precisely defined subsequent phases, producing "output", and finally concludes at a specific ending state. Starting with an initial state and starting input—which may be empty—the computation can be performed.The given expression is 27.405 x 18
This can be computed using algorithm of multiplication to get the result 493.29 .
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An architect's sketch of plans for the front of a garage in the shape of pentagon is shown below. What is the approximate perimeter of the front of the garage?
The graph shows a five-edged polygon. The five edges are on (minus 5.5, 0), (minus 5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).
Answer:
37.26 units
Step-by-step explanation:
You want to know the perimeter of the pentagon defined by the points (-5.5, 0), (-5.5, 7), (0, 9.7), (5.5, 7), and (5.5, 0).
GraphThe attached graph shows the points and the distances between them. The perimeter is the sum of those distances.
7 +6.13 +6.13 +7 + 11 = 37.26
The perimeter of the polygon is about 37.26 units.
__
Additional comment
The length of the slant edges can be found using the distance formula.
d = √((x2 -x1)² +(y2 -y1)²) = √((0 -5.5)² +(9.7 -7)²) = √(30.25 +7.29)
= √37.54 ≈ 6.12699
The lengths of the horizontal and vertical edges can be found by differencing the x- and y-coordinates of the points, respectively. (The distance formula can be used, as well.)
Simplify the linear expression by combining like terms. 2x + 8y - 7x - y
Please hurry!!!
Answer:
-5x + 7y
Step-by-step explanation:
2x - 7x = -5x
8y - y = 7y
4.
This figure is made from a part of a square and a part of a circle
8
4
unit?
a
What is the perimeter of this figure, to the nearest sind?
What is the area of this figure, to the nearest square
A portion of a square and a portion of a circle were used to create this figure. The perimeter of the figure is 36.28 units.
Given that,
A portion of a square and a portion of a circle were used to create this figure.
We have to find the perimeter of the figure.
Three linear sides are measured in units of 4, 8, 8, 4.
Radius of the circular part = 4 units
Measure of a polygon's circumference equals the polygon's perimeter.
From the figure we can see,
Figure perimeter equals the sum of the lengths of the three straight lines and the circumference of the quarter circle.
Measure of linear sides = 4 + 8 + 8 + 4 = 24 units
Circumference of the quarter circle = 1/4(2πr)
=1/2×π×4
=2×π
=2×3.14
=6.28 units.
Perimeter of the figure is 30+6.28
=36.28 units.
Therefore, the perimeter of the figure is 36.28 units.
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in a certain english class, one fourth of the number of girls is equal to one sixth of the total number of students. what is the ratio of the number of boys to the number of girls in the class?
Answer:
1
Step-by-step explanation:
Comment
This is a very interesting question.
The first statement says
1/3 girls = 1/6 of the total Multiply both sides by 3
3(1/3) girls = 3(1/6) total
girls = 1/2 of the total
The boys must be 1/2 as well because all the students who are not girls must be boys.
Ratio (boys / girls) = 1/2 // 1/2 = 1
The ratio is 1
Robert pays for his family to go to the arcade he pays an interest fee for his food and additional amount per game that his family plays as shown in the graph use the graph to answer 5-7
Answer:
5) ¾, The slope is ¾ since the cost increases by 3 dollars for every 4 games Robert and his family play.
6) 12, The y-intercept is 12 since Robert had to pay an entrance fee of 12 dollars in order to enter the arcade.
7) y=¾x+12
What is the slope of the line created by this equation?
Round your answer out to two decimal places.
9x+4y = 4
[tex]9x+4y=4\implies 4y=-9x+4\implies y=\cfrac{-9x+4}{4} \\\\\\ y=\cfrac{-9x}{4}+\cfrac{4}{4}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{9}{4}}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Write the sentence as an absolute value inequality, then solve the inequality.
Twice a number n is no less than 10 units from −1.
An inequality | 2n -(- 1) | ≥ 10
| 2n + 1 | ≥ 10
after solving the inequality we get the value of n, n ≥ 4.5 and n ≤ - 5.5
According to the question, given that
An inequality which has twice a number n is no less than 10 units from −1.
then inequality : | 2n -(- 1) | ≥ 10
| 2n + 1 | ≥ 10
So, 2n + 1 ≥ 10 or 2n + 1 ≤ - 10
2n ≥ 10 - 1 2n ≤ - 10 - 1
2n ≥ 9 2n ≤ - 11
n ≥ 4.5 n ≤ - 5.5
Therefore, we get the value n, n ≥ 4.5 and n = ≤ - 5.5 after solving inequality.
Algebraic expressions are contrasted in a mathematical statement known as an inequality using the greater-than (>), less-than (), and other inequality symbols. A pair of inequalities connected by and or or form a compound inequality. In this lesson, linear and compound inequalities in one variable will be resolved using the properties of inequalities. After this, the study of absolute-value equations and inequalities continues.
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ƒ(x) = x²+x+6
g(x) = 3x +5
Find: f(g(x)) c
The value of f(g(x)) is f(g(x)) = 9x² + 33x + 36.
What are composite functions and how are they defined?
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Mathematically, Let g: A→B and h: B→C denote two functions, then the composition of g and h denoted by hog: A→C given by hog(x) = h(g(x)) for all x ∈ A.
Given, f(x) = x² + x + 6 and g(x) = 3x + 5
Thus, following the above literature,
f(g(x)) = fog(x) = (3x + 5)² + (3x + 5) + 6 = 9x² + 33x + 36
Therefore, the required value of f(g(x)) is f(g(x)) = 9x² + 33x + 36.
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Given ƒ(x) = −x − 1, find ƒ(0).
The value of f(0) is '-1'.
Let's see the step-by-step solution:
Step 1:
For f = -x -1
substitute the x with 0
So, f(0) = -0-1
Step 2:
Simplifying it: -0-1: -1
Thus, the value of f(0)= -1
