Find the y-intercept and slope of the line below. Then write the equation is slope intercept form (y=mx+b).

Given:

Given that a right triangles.

Required:

To find the value of variables in each triangle.

Explanation:

In right triangles,

(C)

Here,

To answer this question we will set and solve a system of equations.

Let k be the number of orders that Kala served on Monday, a be the number of orders that Abdul served, and j be the number of orders that Joe served.

Since they served a total of 71 orders, Kala served 5 fewer orders than Abdul, and Joe served 2 times as many orders as Abdul, then we can set the following system of equations:

Substituting the second and third equation in the first one we get:

Adding like terms we get:

Adding 5 to the above equation we get:

Dividing the above equation by 4 we get:

Finally, substituting a=19 in the second and third equation we get:

Answer:

Number of orders Kala served: 14.

Number of orders Abdul served: 38.

Number of orders Joe served: 19.

2.303

1) For the following expression:

We can simplify that and then round it off to the nearest thousandth:

2) Let's rewrite them simplifying using the logarithm property of multiplication:

Note that the base of the Natural Log is the Euler's number "e" so let's move on now using the calculator, finally:

Note that only at the last step we have rounded it off. And that's the

answer

Answer

The rate of change of both functions is 2.

Explanation

To know the statement that best compares the rate of change of the two functions, we need to first calculate the rate of change for each function.

Rate of change of function A

Using x₁ = 7, y₁ = 14, x₂ = 8 and y₂ = 16

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 16 - 14 = 2

Δx = (x₂ - x₁) = 8 - 7 = 1

⇒ Rate of change = 2/1 = 2

Rate of change of function B

From the graph

Using coordinate x₁ = 2, y₁ = 4, x₂ = 3 and y₂ = 6

Rate of change = Δy/Δx

Δy = (y₂ - y₁) = 6 - 4 = 2

Δx = (x₂ - x₁) = 3 - 2 = 1

⇒ Rate of change = 2/1 = 2

Since the rate of both functions are the same (2), then the statement that best compares the rate of change of the two functions in the options given is "The rate of change of both functions is 2"

Total driving time =24

Mom drove =75 mile per hours

Dad drove = 60 miles per hours

Total distance =1710

Let

Total time:

Formula:

For Ava's mom:

For Ava's dad:

Put the value of "x" then:

Solve the both eq then:

So Ava's mom drive 18 hours

Ava's dad driving 6 houras

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

We use z score formula to calculate :

z = (x-μ)/σ

where,

z = standard score

x = observed value

μ = mean of students height

σ = standard deviation of students height

x  = 63 inches

μ = 70 inches

σ = 3 inches

For x shorter than 63 inches we calculate

Z = (x - μ)/σ

then put the given values in above equation.

= (63 - 70)/3

= -2.33333

Probability value is :

P(x<63) = 0.0098153

Approximately to the nearest thousandth = 0.010

The probability that a randomly selected student will be taller than 71 inches tall is 0.010.

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(h,k) are the coordinates of the vertex.

Use the given point (x,y) and the vertex (h,k) in the equation above to find the value of a:

Point: (-3 ,1) x = -3 y=1

Vertex: (-4 , -2) h= -4 k=-2

Use the vertex and a to write the equation:

From the graph, the y - axis 10 uints while the x - axis is 5 units

The x - axis is labeled inches and its half of the feet

For every half inch on x - axis you have 1 feet

The graph that displays the scale is graph D

The answer is OPTION D

The expression N(s) models the number of students that got a score "s" on the quiz.

Then the expression N(8) represents the number of students that scored 8 on the quiz.

And N(5) represents the number of students that scored 5 on the quiz.

Can be read as: "The number of students whose score on the quiz was 8 is greater than the number of students whose score on the quiz was 5"

Therefore, you can conclude that there were more students who scored 8 than students who scored 5. (option 2)

Answer:

Explanation:

Here, we want to answer the questions given

a) To answer this, we have to write the equations in the slope-intercept form:

The slope-intercept form is:

m is the slope while b is the y-intercept

The equations would be:

We can see that the equations are same

Since the equations are same, the slope is same which is 7

b) The y-intercept value is same too

c) Since the equations are same, there are infinitely many solutions for the system of equations

The next step to constructing a tangent line from Q to circle P is to construct the perpendicular bisector of the segment PQ.

For this, Leo can construct arcs from point P and from point Q that are greater than half the length of segment PQ.

The next step is to construct arcs from point P that are greater than half the length of segment PQ.

To calculate the area for the upper (left) graph, we can use x = 1, 2, 3 and 4 to find the upper limit of each rectangle:

Since the x-interval of each rectangle is 1 unit, the area of each rectangle is given by its y-value, so we have:

Now, for the bottom (right) graph, the limits of the rectangles are x = 2, 3, 4 and 5.

So, let's find the value of f(5):

So the area is given by:

The price of the bookcase in the funiture store is:

$206.72

Given that the markup is 36% of $152

This is:

0.36 * 152 = $54.72

Therefore, the price of the bookcase in the funiture store is:

$152 + $54.72

= $206.72

When we are adding/subtracting polynomials, we add or subtract like terms.

For example,

x^2 added with x^2 terms

x^4 added with x^4 terms

numbers (constants) added with numbers etc.

Since we are "adding" the 2nd parenthesis polynomial, we can take out the parenthesis and put them in order and them simply add/subtract(!) The steps are shown below:

Note: there were like terms with "x's" and "constants". We added/subtracted them only.

The budget is 20000 times greater.

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

Company A = $2 × [tex]10^{4}[/tex]e

Company B = $ 5 × [tex]10^{8}[/tex]

The difference = $2 × [tex]10^{4}[/tex]

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There are two known angles in such a manner:

We know that the sum of internal angles of a triangle is equal to 180 degrees. This means that we can find the missing angle by adding all the internal angles and making it equal to 180

The missing angle is 45 degrees.

Given:

A line passes through the point,

The slope of the line is m = -1.

The objective is to find the equation of the line in point-slope and slope-intercept form.

Explanation:

To find equation in point-slope form:

The general formula of point-slope form is,

On plugging the given values in equation (1),

To find the equation in slope-intercept form,

The general formula of slope-intercept form is,

On further solving the equation (2),

Hence,

The equation of the line in point-slope form is y+6 = -x+5.

The equation of the line in slope-intercept form is y = -x-1.

GIVEN:

We are told that Jina had an opening balance of $240 in her toll road account.

Also, we are told that the amount left in the toll road account is given by the function;

Required;

(a) To find how much money she has left in her acount after 11 trips.

(b) To find out how many trips she can take until her account is empty.

Step-by-step solution;

We first take note of the variable t, which represent the number of trips taken. Also, the function shows how many trips multiplied by 16 would be subtracted from the opening balance. The result would be how much amount (variable A) would be left in her account.

Therefore;

(a) After 11 trips, Jina would have;

For the (A) part, the answer is $64.

(b) For her account to be empty, then the function given would be equal to zero. That is, after an unknown number of trips, the balance would be zero. We can now re-write the function as follows;

Add 16t to both sides of the equation;

This means after 15 trips she would have emptied her toll road account.

ANSWER:

Given

According to rules of transformation:

f(x)+c shift c units up and f(x)-c shift c units down.

For the given function g(x) = 5x-7, 7 is being subtracted from 5x.

Where 5x is represented by f function.

Therefore, we could apply the rules of transformation f(x)-c shift c units down.

Here the value of c is 7.

Answer: g(x) is translated 7 units down from f(x)

1 - reference point should consist of abstract coordinates.

2- it should be stationary

3- it should be related to all the variables in the frame.

The regression Quadratic equation y = 49 + 7.55x - 6.15x².

The technique of finding the equation of a parabola that most closely matches a collection of data is known as quadratic regression. The graph points that make up the parabola-shaped shape of this set of data are given. The parabola's equation is written as y = ax² + bx + c, where a never equals zero.

For data presented as ordered pairs, you can calculate the model's degree by identifying differences between dependent values. The model will be linear if the initial difference has the same value. The model will be quadratic if the second difference has the same value as the first.

As, we know the Quadratic model

Quadratic model, y = a + bx + cx²

Now, value of

a = 49

b = 7.55

c = -6.15

Then, the Regression Quadratic model is

y = 49 + 7.55x - 6.15x²

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Hi

a) = (8x2) x (10 ‐³ x10 ‐⁴)

= 8 x 2 you get 16 then 10‐³-⁴

16 x 10 ‐⁷

= 1.6 x 10¹ x 10 ‐⁷

= 1.6 x 10 ‐⁶

final answer

1.6 x 10 ‐⁶

Given the word problem, we can deduce the following information.

1. Two planes, which are 2320 miles apart, fly toward each other.

2. Their speeds differ by 80 mph.

3. They pass each other in 4 hours.

To find the speed of each plane, we use the formula:

distance = (rate)(time)

Since they are flying towards each other, the sum of both speeds is 2x+80. So,

distance = (rate)(time)

2320 miles = (2x+80 mph)(4 hrs)

Thus, the equation to solve this is:

2320 = (2x+80)(4)

Segment C prime D prime has endpoints located at C′(0, 0) and D′(4, 0). It was dilated at a scale factor of one half from centre (4, 0). the pre-image

B- segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

According to the question,

Segment C prime D prime has endpoints located at C' (0, 0) and D' (2, 0).

The coordinates are given as:

C' (0, 0) and D' (4, 0).

Since,

Centre of dilation = D = (4,0)

Here, CD seems to be the dilated image of CD by something like a factor of two. It follows that M must have been at (0,0).

It's one-half units left from the centre of dilated.

Then, C` = 1/2 x 4  = 2

Since the dilation is (4, 0),

C = (2+4, 0) = (6,0)

Hence,

segment CD is located at C(2, 0) and D(6, 0) and is twice the length of segment C prime D prime period

Segment simplifies  data collection and integrates new tools, allowing you to spend more time using data and less time collecting it. A segment allows you to track events that occur when a user interacts with user interfaces. "Interfaces" is the segment's umbrella term for all the digital real estate you own: your website, mobile apps and processes running on a server or OTT device.

When you capture interaction data in a segment, you can send it (often in real time) to your marketing, product and analytics tools and data warehouses. In most cases, you don't even need to touch the tracking code to connect to the new tools.

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step 1

Find out the slope of the given line

we have

-(4/3)x+2y=4/3

isolate the variable y

2y=(4/3)x+(4/3)

Divide both sides by 2

y=(4/6)x+(4/6)

simplify

y=(2/3)x+(2/3)

the slope is m=2/3

Remember that

If two lines are perpendicular, then their slopes are negative reciprocal

that means

the slope of the perpendicular line to the given line is

m=-3/2

step 2

Find out the equation in slope-intercept form of the perpendicular line

y=mx+b

we have

m=-3/2

point ( 1,0)

substitute and solve for b

0=-(3/2)(1)+b

0=-(3/2)+b

b=3/2

therefore

the equation is

Let's begin by listing out the information given to us:

Line AB is parallel to Line CD; this implies that the angle formed by the two lines are right angles (90 degrees)

E is the intersecting point of both lines AB & CD (figure attached)

Let us put this into its mathematical form:

ok

I'll use the law of gases to solve this problem

V1 = 42 cm^3

T1 = 84 °K

P = 8 Kg/cm^2

T2 = x

V2 = 74 cm^3

P2 = 10 kg/cm^2

Equation

P1V1/T1 = P2V2/T2

Solve for T2

T2 = P2V2T1 / P1V1

Substitution

T2 = (10*74*84) / (8*42)

Simplification

T2 = 62160 / 336

Result

T2 = 185°K

The domain of the function which is the entire x values during the strike is

Given the table showing the number of days since wound began to heal and area of wound in square millimeters

To determine the statement that are correct from the option provided

From the table shown it can be seen that as the day increases by 1, the area of wound in square millimeters decreases by a common ratio of

Suppose that an expression to represent the area of wound is

The modelled expression from the table is

Let us use the modelled expression to verify each of the given conditions

The modelled expression can be simplified as shown below:

Then, we have the modelled expression becomes

From the two modelled expression we can see that

Then we can conclude that the two conditions that are true from the options are

If the value of c = n, the value of a is 31.25, and

If the value of c = n, the value of b is 0.8

The solution of the factor with power 2 in the function f(x) can be found as:

(x-2)=0

x=2.

So, the root is x=2.

The multiplicity is the power of the factor (x-2) with its root given as x=2.

So, the multiplicity of the root x=2 is 2.