The linear function corresponding to the line in the graph will be y = 200x - 120000.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given data,
A linear function is given as,
y = mx + c
Here m is the slope and c is the y-intercept.
The slope m will be as follows,
Slope m = (600 - 400)/(1 - 0)
m = 200
Put m = 200 and (600,0)
0 = 200(600) + c
c = -120000
Thus, the linear equation will be as,
y = 200x - 120000
Hence "y = 200x - 120000 is the linear function that corresponds to the line in the graph.".
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find the scalar products i^⋅i^, j^⋅j^, and k^⋅k^.
The scalar product of two parallel unit vectors, is equals to one i.e., i.e., [tex]\hat{i}[/tex]⋅[tex]\hat{i}[/tex] = 1 ,[tex]\hat{j}[/tex] ⋅[tex]\hat{j}[/tex] = 1 and [tex]\hat{k}[/tex]⋅[tex]\hat{k}[/tex]= 1 . Scalar Product: The scalar product is also known as dot product. The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other vector and multiplying it by magnitude of other vector. That gives scalar as a result. Scalar don't have a direction associated with them. Mathematically, [tex]$\vec{A}$[/tex][tex]\vec{A}$.[/tex][tex]\vec{B}$[/tex] = |A| |B| cosθ
We have to determine the scalar product of [tex]\hat{i} . \hat{i}[/tex], [tex]\hat{j} .\hat{j}[/tex], and [tex]\hat{k} .\hat{k}[/tex] . Here [tex]\hat{i}[/tex] and [tex]\hat{i}[/tex] are the unit vectors in the direction along the x-axis. So, they are parallel to each other, that's why θ = 0° and |[tex]\hat{i}[/tex]| = 1 . Therefore, [tex]\hat{i} .\hat{i}[/tex] = ( 1) (1) cos 0° = 1. Similarly [tex]\hat{j} .\hat{j}[/tex] = 1 ( unit vectors in direction along the y-axis) and [tex]\hat{k} .\hat{k}[/tex]= 1 ( along z-axis). Hence, the dot product of the two unit vectors [tex]\hat{i} .\hat{i}[/tex], [tex]\hat{j}.\hat{j}[/tex], and [tex]\hat{k} .\hat{k}[/tex] is equal to one for each.
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A concert started at 6:46 pm the concert needed at 9:01 pm how long did it last?
Answer:
It lasted for 3 hours 15 minutes.
PLEASE HELPPPPP which is the correct one?
The work below shows a common mistake. Click the part of the problem where the error occurs.
Hypotenuse² = Perpendicular² + Base²
10² = 1²+x²
x²= 100 -1
x=√99
x≈9.94
Terry is trying to bisect acute angle abc. He begins by placing the point of the compass at point b. Select the three remaining steps for terry to bisect the angle. Terry is trying to bisect acute angle abc. He begins by placing the point of the compass at point b. Select the three remaining steps for terry to bisect the angle. Measure the angle size. Draw a circle around point c, so that all points are equidistant. Use a straightedge to connect the vertex to the intersection of the two overlapping circles. Draw congruent circles centered at each intersection point on the sides of the angle. Draw circle b with a radius so that it intersects each side of the angle
An angle bisector is a line that is drawn between the angle, which divides the angle into two equal parts. For example, if we bisect an angle that is 70°, then it will be two angles of 35°
We can draw an angle bisector either by measuring the angle using a protractor or marking the half. But the commonly used method is by using a compass.
Step 1
Draw the angle with vertex a, b, and c
Step 2
Draw a circle with b as the Centre, that intersects with each side of the angle.
Step 3
Draw congruent circles or arcs, centered at each intersection point on the sides of the angle.
Step 4
Use a straight line to connect point b with the intersection of two overlapping circles or arcs.
The properties of angle bisectors are
All points are of equal distance from both arms.Using this technique we can bisect any type of angle, acute, obtuse, or right.For further information regarding angle bisectors, kindly refer
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(2x + 5) + (3x - 7)?
Answer: 5x-2
Step-by-step explanation:
2x+5 + 3x-7
2x-2 + 3x
5x-2
can someone answer this question really quick
Simplify the expression by combining like terms.
3.6x+5.9−2.2−1.7x
Enter your answer as an expression, like this: 42x+53
Answer:
[tex]1.9x+3.7[/tex]
Step-by-step explanation:
[tex]3.6x-1.7x+5.9-2.2=1.9x+3.7[/tex]
Can please name line d
Answer:
a) tangent
b) radius
c) diameter
d) chord
Step-by-step explanation:
You want the vocabulary words associated with various segments in and around a circle.
TangentA tangent is a line or segment that is external to the circle and intersects it at one point. A tangent is always perpendicular to a radius. (Segment a is a tangent.)
RadiusA radius of a circle is a line segment between the center and a point on the circle. (Segment b is a radius.)
ChordA chord is a line segment internal to the circle that joins two points on the circle. (Segment d is a chord.)
DiameterA diameter of a circle is a chord that contains the center of the circle. (Segment c is a diameter, and also a chord. The more specific descriptor is "diameter.")
which is equivalent to 7 superscript startfraction 3 over 5 endfraction baseline times 7 superscript startfraction 1 over 5 endfraction baseline?
7^(3/5) * 7^(1/5) is equivalent to (7^3)^(1/5) * (7^1)^(1/5), which is equivalent to 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7.
When you see an expression like 7^(3/5) * 7^(1/5), it is helpful to think about the properties of exponents. One property is that when you have the same base raised to different exponents, you can multiply the exponents. So, for example, 7^3 * 7^1 = 7^(3+1) = 7^4.
Another property is that when you have a base raised to a power, and then that result is raised to another power, you can multiply the exponents. So, for example, (7^3)^2 = 7^(3*2) = 7^6.
Using these properties, we can simplify the original expression as follows:
7^(3/5) * 7^(1/5) = (7^3)^(1/5) * (7^1)^(1/5) = 343^(1/5) * 7^(1/5) = 343^(1/5) * (7^(1/5))^1 = 343^(1/5) * 7
So, 7^(3/5) * 7^(1/5) is equivalent to 343^(1/5) * 7
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Find the value of X given that the triangles are similar
Answer:kaka
Step-by-step explanation:
your mom
Answer:
x = 66
Step-by-step explanation:
[tex]\frac{60}{70} =\frac{x}{11+x}[/tex]
[tex]60(11+x)=70(x)[/tex]
[tex]660+60x=70x[/tex]
[tex]10x=660[/tex]
[tex]x=\frac{660}{10}[/tex]
[tex]x=66[/tex]
Hope this helps
Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $1000 worth of shoes. How much was his commission?
Tyler’s brother made $25 as commission.
What is commission?Commission, also known as sales commission, is a payment given to employees based on the sales they make. Commission is often calculated as a percentage of the value of a sale.
Given that, Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $1000 worth of shoes.
Since, his commission is 2.5% of the sale.
And, he sold $1000 worth of shoes.
Therefore, commission = 2.5% of 1000
= 2.5 / 100 x 1000
= 25
Hence, the commission is made is $25
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Mayerlin was out at a restaurant for dinner when the bill came. Her dinner came to $13. She wanted to leave a 30% tip. How much was her meal plus the tip, before tax, in dollars and cents?
Answer:
$16.90
If this help please set brainliest.
Step-by-step explanation:
To calculate the tip, you first need to multiply the cost of the meal by the tip percentage: $13 * 30% = $3.90.
Then, you can add the cost of the tip to the cost of the meal to find the total cost before tax: $13 + $3.90 = $16.90.
That means the total cost of Mayerlin's meal plus the tip, before tax, was $16.90.
Answer:
$16.90
Step-by-step explanation:
First, we would need to figure out what 30% of $13 is.
0.30 (or 0.3) × 13 = 3.9
This means her tip was $3.90
Now we need to add that to the total price of her bill.
3.9 + 13 = 16.90
Therefore, Mayerlin spent sixteen dollars and ninety cents on her meal.
Find the inverse of f(x)=x/4
Answer: x-4 i think
Step-by-step explanation:
Answer: f^(-1)(x) = 4x (inverse function desired)
Explanation: For if one let f(f^(-1)(x)) = x, (f^(-1)(x))/4 = x, and hence f^(-1)(x) = 4x.
if x2 + y2 = 225 and dy/dt = 4, find dx/dt when y = 9.
In the given algebraic expression if [tex]x^2+y^2[/tex] = 225 and dy/dt = 4, then dx/dt when y = 9 is ±3.
What are algebraic expression?An algebraic expression is a mathematical expression that can contain numbers, variables, and operators. Examples of algebraic expressions are: [tex]2x + 3, (x^2 - y^2) / (x-y)[/tex], and [tex]4y + 2x^2[/tex]. These expressions can be evaluated by replacing variables with specific values and simplifying the expressions in order of operations.
Given, [tex]x^2+y^2[/tex] = 225
dy/dt = 4
We have to find dx/dt.
When y = 9,
⇒ [tex]x^2+9(2)[/tex] = 225
⇒ [tex]x^2+81[/tex] = 225
⇒ [tex]x^2[/tex] = 225 - 81
⇒ [tex]x^2[/tex] = 144
Taking square root,
⇒ x = ±12
Differentiating with respect to t,
2x ([tex]\frac{dx}{dt}[/tex]) + 2y ([tex]\frac{dy}{dt}[/tex]) = 0
x ([tex]\frac{dx}{dt}[/tex]) + y ([tex]\frac{dy}{dt}[/tex])=0
Put dy/dt = 4 in the above expression,
(±12) ([tex]\frac{dx}{dt}[/tex]) + (9)(4)=0
(±12)([tex]\frac{dx}{dt}[/tex]) + 36 = 0
(±12) ([tex]\frac{dx}{dt}[/tex]) = −36
[tex]\frac{dx}{dt}[/tex] = ( -36/ ± 12)
dx/dt = ±3
Therefore, dx/dt = ±3
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What percentage of the shape is pink?
Write your answer using a percent sign (%).
Answer:
72%
Step-by-step explanation:
18/25 are pink.
18*4 = 72.
72 percent.
[tex]x+5=-3x+4[/tex]
Please help me answer these questions
Answer:
3.) B
How to solve:
Just get the cubed root of all the numbers inside the fraction
What is an extraneous solution and where do they come from?
An extraneous solution is A root of a converted equation that is not a root of the original equation because it was left out of the original equation's domain. It comes from correct solution steps and is not a valid solution of the equation.
What is an extraneous solution?We are aware that when we solve an equation, the values that result from the answer are always accurate. When we address the problem, there are various solutions that we may be able to get. The non-extraneous solutions are those that, if plugged back in, would produce the original equation, whereas the extraneous solutions are those that do not.
Therefore, the only way we can tell if something is unnecessary or not is if we re-enter the data we have and check to see if the equation still produces the same answer.
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A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. transversal t cuts parallel lines r and s. which angles must be congruent to ∠2? a. ∠3, ∠6, and ∠7 b. ∠7 only c. ∠7 and ∠6 d. ∠3, ∠5, and ∠6
In this situation, the angles that must be congruent to ∠2 are ∠3, ∠6, and ∠7. Thus, the answer is (a) ∠3, ∠6, and ∠7.
When a transversal intersects two parallel lines, corresponding angles are congruent. In other words, angles that are in the same position relative to the parallel lines and the transversal are congruent. Therefore, in this case, ∠2 and ∠5 are corresponding angles and are congruent, as are ∠3 and ∠6, and ∠4 and ∠7.
Thus, the answer is (a) ∠3, ∠6, and ∠7.
Congruent is a term used to describe two shapes or figures that have the same shape and size. It means that the lengths of the sides and the angles of the shapes are exactly the same. Congruence is an important concept in geometry and is used to prove theorems and solve problems.
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Which value of x satisfies the inequality ?
A.
6
B.
9
C.
12
D.
27
Answer:
Step-by-step explanation:
include the inequality.
a fromal state of theory usualyl a mathematical state of presumed relationship between two or more variables is called a
A mathematical state of the presumed relationship between two or more variables is called a model.
A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system. A model is a simplified representation of a real-world system that allows us to better understand and predict the behavior of the system.
In order to create a model, we need to understand the relationships between the variables in the system. These relationships can be represented mathematically.
Once we have a mathematical representation of the relationships between the variables, we can use this model to make predictions about the behavior of the system.
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There are 42 female performers in a dance retail. The ratio of men to woman is 3:7. How many men are in the dance recital
Answer:
18 men
Step-by-step explanation:
3:7 ==> there are 3 men for every 7 women.
42 / 7 = 6 ==> divide the total number of women by the supposed ratio.
6 * 3 = 18 men
Hakeem is going to invest in an account paying an interest rate of 3.5% compounded
continuously. How much would Hakeem need to invest, to the nearest hundred
dollars, for the value of the account to reach $3,700 in 15 years?
The principal investment required to get a total amount of $3,700.00 from compound interest at a rate of 3.5% per year compounded 365 times per year over 15 years is $2,287.26.
What is Compound interest?Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Given Data
Rate = 3.5%
Final Amount = $3,700
Time = 15 Years
First, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 per year,
Then, solve the equation for P
P = A / (1 + r/n)^nt
P = 3,700.00 / (1 + 0.035/365)(365)^(15)
P = 3,700.00 / (1 + 0.00010137)^(4745)
P = $2,287.26
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2x³-x²-4x+2. X=-3
Find the Answer
Answer:
1 is the answer.After you minus and plus it,you will definitely get 1 as the answer.Trust me guys.
Find measures for 4-6
The measures of the angles of the triangles are
m∠1 = 55°
m∠2 = 125°
m∠3 = 35°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔCDE
And ∠BAC = m∠1
And , ∠CDE = m∠3
Now , from the triangle ΔABC
∠ABC = 180° - 110° ( Angle of a straight line is 180° )
So , the measure of angle ∠ABC = 70°
The sides of the triangle AC and BC are similar
So , The angles of the triangle are = 70° + x + x = 180°
On simplifying the equation , we get
70° + m∠1 + m∠1 = 180°
Subtracting 70° on both sides of the equation , we get
2m∠1 = 110°
Divide by 2 on both sides of the equation , we get
m∠1 = 55° = ∠ACB
And , ∠ACB and m∠2 are on a straight line
So , m∠2 = 180° - 55°
On simplifying the equation , we get
m∠2 = 125°
The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )
So , the angles of the triangle are = 90° + 55° + m∠3 = 180°
On simplifying the equation , we get
145° + m∠3 = 180°
Subtracting 145° on both sides of the equation , we get
m∠3 = 35°
Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°
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What’s the answer for
(-4, 7), (-6, -4
The slope of the line that passes through the points (-4, 7) and (-6, -4) is 5.5
How to calculate the slope of the line?From the question, we have the following parameters that can be used in our computation:
(-4, 7), (-6, -4
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (-4, 7) and (-6, -4)
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-4, 7) and (-6, -4)
Substitute the known values in the above equation
So, we have the following equation
Slope = (-4 - 7)/(-6 + 4)
Evaluate
Slope = 5.5
Hence, the slope of the line is 5.5
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What’s the answer for the slope of (-4, 7), (-6, -4)?
Evaluate the function for (a) x = -2, (b) x = 0, and (c) x = 2.
g(x)= 10x² - 8x
The function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is g(x)= 10x² - 8x
we need to find the value when x is -2
Replace x with -2
g(-2)=10(-2)²-8(-2)
=10×4+16
=40+16=56
Now when x =0
g(0)= 10(0)² - 8(0)=0
Now when x =2
Replace x with 2
g(2)=10(2)²-8(2)
=40-16
=24
Hence, the function for x = -2 is 56, x = 0 is 0 and x=2 is 24 for function g(x)= 10x² - 8x
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I NEED HELP!!!!!!!!
C(f)=5/9(f-32) if faith calculated C(68), what would her result be?
The numeric value of the function C(68) at f = 68 is given as follows:
C(68) = 20.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
C(f) = 5/9 x (f - 32).
The input at which we want to find the numeric value for the function is then given as follows:
f = 68.
Which means that the lone instance of f in the definition of the function is replaced by 68, and then the numeric value is calculated as follows:
C(68) = 5/9 x (68 - 32) = 5/9 x 36 = 5 x 4 = 20.
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Reagan created a model of a rectangular flag. Her model is 13 inches long. It is a model of a flag that is 39 inches long. How many times wider is the actual flag than reagan's model?.
The number of times that the actual flag is wider than Reagan's model would be = 3 times.
Rectangle: What is it?
A rectangle is a particular kind of quadrilateral with opposite sides that are parallel and equal to one another and four right angles, according to the definition.
The rectangular flag measures 39 inches in length in actuality.
Reagan's model measured 13 inches in length.
The formula: = Length of actual flag / Length of model = 39/13 = 3 will tell you how many times broader the model is than the real flag.
The real flag is three times wider than Ronald Reagan's model, for a total of four times.
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What is the slope of line pq? what is the slope of line mn? how are the two lines related?
The slope of line pq is 0 and the slope of line mn is undefined. Both lines mn and pq are parallel to each other.
In the given question, we have to find the slope of line pq and the slope of line mn.
We also have to find how the two lines are related.
The graph of the line pg and mn is given below:
As we know that the slope of the line is
m = {y(2)-y(1)}/{x(2)-x(1)}
From the graph we can see that the line pq passes through the points p(-8,2) and q(4,2).
So x(1) = -8, y(1) = 2, x(2) = 4 and y(2) = 2
So, the slope of the line pq is:
m(pq) = (2-2)/(4-(-8))
m(pq) = 0/(4+8)
m(pq) = 0
From the graph we can see that the line mn passes through the points m(8,6) and n(8,-8).
So x(1) = 8, y(1) = 6, x(2) = 8 and y(2) = -8
So, the slope of the line mn is:
m(mn) = (-8-6)/(8-8)
m(mn) = (-8-6)/0
m(mn) = ∞
Lines PQ and MN are horizontal and vertical, respectively. The lines are therefore parallel to one another.
As a result, PQ's slope is 0 while MN's slope is unknown. The lines are parallel.
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The two lines are related in that the slope of both lines can be determined by the same formula. Depending on the coordinates of the two points, the two lines may have the same or different slopes.
The slope of line pq is given by the formula m = (y2-y1)/(x2-x1). Let's say that line pq has points (p1,q1) and (p2,q2). The slope of this line is then given by m = (q2-q1)/(p2-p1).
Now, the slope of line mn is given by the formula m = (y2-y1)/(x2-x1). Let's say that line mn has points (m1,n1) and (m2,n2). The slope of this line is then given by m = (n2-n1)/(m2-m1).
The two lines are related in that the slope of both lines can be determined by the same formula. The two lines may or may not have different slopes, depending on the coordinates of the two points. For example, if the two lines have points (1,2) and (3,4) for line pq, and points (3,4) and (5,6) for line mn, then the slope of line pq is m = (4-2)/(3-1) = 2/2 = 1. The slope of line mn is m = (6-4)/(5-3) = 2/2 = 1. Therefore, the two lines have the same slope of 1.
On the other hand, if the two lines have points (1,2) and (3,4) for line pq and points (1,3) and (3,5) for line mn, then the slope of line pq is m = (4-2)/(3-1) = 2/2 = 1. The slope of line mn is m = (5-3)/(3-1) = 2/2 = 1. Therefore, the two lines have different slopes of 1 and 2 respectively.
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Your school is donating items to the local food pantry. Your homeroom is having a competition to see who will donate the most items. You have already donated 14 items and plan to donate 3 more each week. Your friend has already collected 8 items and plans to collect 5 more items each week. Write and solve a system of equations for the number of weeks (x) when you both donate the same number of items (y).
It will take 3 weeks for both of us to have collected the same amount. Each of us will have collected 23 items at that time.
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Let x = weeks
Me: y = 14+3x
Friend: y = 8+5x
Equating the two equations
14+3x=8+5x
14=8+2x
6=2x
dividing both sides by 2
3=x
y=14+3(3)=23
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