5. What is the slope that runs through the points (-4, 10) and (-4, 3)?

(a). The domain of the function C(t) based on the context of the problem  is t≥0

(b). The greatest concentration of the medication  that a patient will have in their body is 7mg/L

Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.

(a). C(t) = (-8t² +50t)/(t² + 3t +2 )

The domain of the function :

Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.

t, cannot take negative values (i.e. it is not possible to have a negative time).

The least possible value of t is 0

So, the domain of the function based on the context is:  t≥0

(b).From the graph, the maximum y-value is 7.

Hence, the greatest concentration of the medication is 7mg/L

(a). The domain of the function C(t) based on the context of the problem  is t≥0

(b). The greatest concentration of the medication  that a patient will have in their body is 7mg/L

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The cosine function for a specific angle in a triangle is defined by the ratio of the triangle's adjacent side and hypotenuse.

This is further explained below.

Generally, trigonometric functions are a set of real functions that link the ratios of the lengths of two sides of a right-angled triangle to an angle in the triangle.

They find widespread use in all fields of study that are in some way connected to geometry, including geodesy, solid mechanics, celestial mechanics, navigation, and a great many more.

In conclusion, The ratio of a triangle's adjacent side to its hypotenuse is used to determine the cosine function for a certain angle in the triangle.

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +8}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(1~~,~~4)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +8}{2}=1\implies x+8=2\implies \boxed{x=-6} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=4\implies y+7=8\implies \boxed{y=1}[/tex]

Answer:

x = 3 ± 5[tex]\sqrt{2}[/tex]

Step-by-step explanation:

x² - 6x - 41 = 0 ( add 41 to both sides )

x² - 6x = 41

to complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 3)x + 9 = 41 + 9

(x - 3)² = 50 ( take square root of both sides )

x - 3 = ± [tex]\sqrt{50}[/tex] = ± 5[tex]\sqrt{2}[/tex] ( add 3 to both sides )

x = 3 ± 5[tex]\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

The three consecutive integers whose sum is -33 are -12, -11 and -10

Brainlist maybe :)?

Answer:

a. 4 x (5 + 3) = 32

b. 3 + 4 x (5 + 6) = 47

c. (2 + 7) x (5 + 3) =72

Step-by-step explanation:

Answer:

4/33

Hopes this helps!

Have a good day :)

Answer:

y = -5x + 4

Step-by-step explanation:

Slope-intercept form of the equation is:

y = mx + b

In the question, we are given m = -5 and b = 4.

Fill in the numbers for m and b.

The m tells you how steep the line is (the slope) And b tells you where the line crosses the y-axis (y-intercept).

Answer:

Step-by-step explanation:

Slope:

[tex]\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

y2=(-7)

y1=(-1)

x2=(-1)

x1=5

[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}}[/tex]

Solve.

[tex]\sf{\dfrac{-7-\left(-1\right)}{-1-5}=\dfrac{-6}{-6}=\boxed{\sf{1}}}[/tex]

Therefore, the slope is 1, which is our answer.

I hope this helps, let me know if you have any questions.

Answer:

B

Step-by-step explanation:

The Solution:

GIven:

We are asked to graph the given inequalities.

Below is the graph of the inequalities:

Thus, the correct answer is [option 1]

Answer:

0.25.2

Step-by-step explanation:

1.51/2

So,halves

0.25.2

ANSWER

The graph of y = sin θ shifted to the left by π/2 units

EXPLANATION

This is the graph of y = sin θ shifted to the left π units. In function notation, this shift is represented by adding π to the variable: y = sin (θ + π).

Also, we know that the graph of y = cos θ is like the graph of y = sin θ but shifted π/2 units to the left. So, if we shift the graph of y = cos θ π/2 units to the left, we get the given graph.

Therefore, the only description that does not match the graph is the graph of y = sin θ shifted to the left by π/2 units.

Based on the rate that the team is rescuing people per hour, the total number of people that the team can rescue in another two hours is 6 people.

First, find the rate at which people are being rescued by the search and rescue team per hour.

The rate of people rescued is:
= Number of people rescued / Number of hours

= 15  / 5

= 3 people per hour

The number of people rescued in 2 hours is:

= Number of hours x People rescued per hour

= 2 x 3

= 6 people

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18 inches space should he leave between pictures of the wall with length 74 inches

Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.

Mark wants to hang for rectangular pictures in a row on a wall so that the horizontal space between each picture is always the same

Length of each picture is =8 inches

Length of the wall=74 inches

The  horizontal wall space before the first picture and after the fourth picture = 12 inches

we are asked to find the space between pictures

12+12+8+8+8+8+x=74

x+56=74

x=18

the distance between the picture is 18 inches

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Answer: Do you know the answer to this yet??

Step-by-step explanation:

The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)

Given,

Kevin took $45 with him to spend on snack

and, The price for each bucket of popcorn was $4.

To plot the graph

Now, According to the question:

Sketch the graph that represents the situation and label the intercepts

Let,

x ------> the number of bags of popcorn

y -----> the number of drinks.

we know that

The price for each bag of popcorn was $4

The price of each drink was half the price of a bag of popcorn

So, The price of each drink was (1/2)$4 = $2

The total bags of popcorn multiplied by $4 plus the number of drinks multiplied by $2 must be equal $45

The equation that represent this situation is :

4x + 2y = 45 -----(1)

Now, Find the y - intercept form:

The y-intercept is the value of y when the value of x is equal to zero

For, x = 0 put the value of x in equation(1)

4(0) + 2y = 45

2y = 45

y = 22.5

The y-intercept is the point (0,22.5)

That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero

For, y = 0 put the value of x in equation(1)

4x + 2(0) = 45

4x = 45

x = 11.25

The x-intercept is the point (11.25, 0)

That means -----> The number of drinks that Kevin can buy when the number of bags of popcorn is equal to zero

Hence, The equation is 4x + 2y = 45 and The y-intercept is the point (0,22.5) and The x-intercept is the point (11.25, 0)

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There are 11 red counters left so the difference is −11.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Add some zero pairs because need to remove 7 yellow counters}$.

Since you need to remove 7 yellow counters, add 7 zero pairs.

When you remove yellow counters, there are 11 red counters left so the difference is:

−4−7=−11

​There are 4 red counters so you should add 7 zero pairs in order to eliminate 7 yellow counters. There are 11 red counters left so the difference is −11.

Therefore, there are 11 red counters left so the difference is −11.

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If f(x) = x^5 + 4x - 5,  is divided by x - 3  the remainder is 220.

What is a remainder ?

In mathematics, the term "remnant" refers to the amount that is "left over" after performing a calculation. In mathematics, the integer that is left over after dividing two integers to produce an integer quotient is known as the residual (integer division). In algebra of polynomials, the "remainder" is the polynomial that is left over after dividing one polynomial by another. The operation that yields such a remainder when a dividend and a divisor are both present is the modulo operation.

How are functions divided?

Simply multiply or divide the numbers at each point where it makes sense to multiply or divide a function. If the functions are specified by formulas, you can simply multiply or divide the formulas (inserting numbers before or after is irrelevant).

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Probability of a randomly chosen male applicant that has a graduate degree is 28/175.

Total number of applicants for a job= 350

Number of male applicants having a graduate degree = 56

We have to calculate the probability of a randomly chosen applicant that has a graduate degree, given that they are male.

We know ,

Probability = ( Total Number of favorable outcomes) / (Total Outcomes)

probability of a randomly chosen applicant that has a graduate degree, given that they are male = (Number of male applicants having a graduate degree)/ (Total number of applicants for a job) = 56/350 = 28/175

So, the probability of a randomly chosen applicant that has a graduate degree, that has a graduate degree, given that they are male is 28/175.

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P(k + 1) follows, and it is likewise true.

As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+

To demonstrate that the mathematical proposition P(n) holds for all natural integers n = 1, 2, 3, 4,..., one uses the mathematical induction technique. It is frequently referred to as the induction principle in mathematics. We establish that P(1) holds in order to demonstrate a result P(n) using the mathematical induction technique. If P(1) is valid, we can assume that P(k) holds for some natural number k and use this assumption to demonstrate that P(k+1) is valid. The assertion P(n) applies to all natural numbers if and only if P(k+1) holds true.

Let

P(n): 1×2 + 2×3+3×4+........+n(n+1)=[tex]\frac{n(n+1)(n+2)}{3}[/tex]

Putting n =1 we get

P(1):1×2 =2

and

[tex]\frac{1(1+1)(1+2)}{3}=\frac{1(2)(3)}{3} =2[/tex]

Therefore P(1) is true.

Let P(K) is true

So,

P(k): 1×2 + 2×3+3×4+........+k(k+1)=[tex]\frac{k(k+1)(k+2)}{3}[/tex]

Now we have to show that P(k +1 )is also true.

P(k+1): 1×2 + 2×3+3×4+........+k(k+1)+(k+1)(k+2)=[tex]\frac{k(k+1)(k+2)}{3}+ (k+1)(k+2)[/tex]

= (k+1)(k+2)[[tex]\frac{k}{3}+1[/tex]]

=[tex]\frac{(k+1)(k+2)(k+3)}{3}[/tex]

P(k + 1) follows, and it is likewise true.

As a result, after demonstrating that P(k) is true for any chosen value of k, we also demonstrated that P(k + 1) is true. According to the induction hypothesis, P(n) is true for all n ∈ Z+.

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The ellipse has 2 axis, the minor and the major axis,

The major axis is denoted in blue color and the minor axis in purple color. By comparing our equation with the general equation of the ellipse:

where the lenght of the major axis is given by

Fron the given equation, we can note that

Therefore, the lenght of the major axis is 36 feet. Therefore, the maximum distance between any two persons is 36 feet corresponding to the major axis, which is option 3 from top to bottom

Answer:

Tom is correct.

Step-by-step explanation:

Squaring is equivalent to multiplying a number by itself, ie:

2 squared = 2x2 = 4

6 squared = 6x6 = 36

48.50 U.S. dollars = 281 Egyptian pounds

What is a dollar?

The United States dollar (symbol: $; code: USD; often abbreviated US$ or U.S. Dollar to differentiate it from other dollar-denominated currencies; known colloquially as the dollar, U.S. dollar, American dollar, or buck) is the official currency of the United States and numerous other nations. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, split it into 100 cents, and permitted the minting of coins denominated in dollars and cents. Federal Reserve Notes, generally known as greenbacks owing to their predominately green hue, are the currency of the United States.

Given, 1 U.S. dollar = 5.8 Egyptian pounds

so, 48.50 U.S. dollars = 5.8 x 48.50 = 281.30 Egyptian pounds

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Answer:

[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]

Step-by-step explanation:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Given:

Substitute the given values into the formula and solve for x:

[tex]\implies x=\dfrac{-4 \pm \sqrt{4^2-4(2)(-3)}}{2(2)}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{16-8(-3)}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{16+24}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{40}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{4\cdot 10}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm \sqrt{4}\sqrt{10}}{4}[/tex]

[tex]\implies x=\dfrac{-4 \pm 2\sqrt{10}}{4}[/tex]

[tex]\implies x=\dfrac{-2 \pm \sqrt{10}}{2}[/tex]

Therefore, the solutions are:

[tex]x=\dfrac{-2 + \sqrt{10}}{2}, \quad x=\dfrac{-2 -\sqrt{10}}{2}[/tex]

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Elsa used her money to make two purchases last year. The Total interest earned by the end of the year is 1200.

Given that,

Elsa used her money to make two purchases last year. She spent $7,000 on a certificate of deposit paying 3% interest annually and $9,000 on corporate bonds paying 11% interest annually.

We have to find the Total interest earned by the end of the year.

We know,

Total interest=adding the interest annually payment

Total interest=0.03×7000+0.11×9000

Total interest=1200

Therefore, The Total interest earned by the end of the year is 1200.

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Answers:

x = 108

y = 111/5 = 22.2

========================================================

Explanation:

The angles 72 and x form a 180 degree straight line.

72+x = 180

x = 180-72

x = 108

Angles x and 5y-3 are congruent corresponding angles assuming the lines pointing to the northwest are parallel

5y - 3 = x

5y - 3 = 108

5y = 108+3

5y = 111

y = 111/5

y = 22.2

Answer:

x = 108°

y = 22.2°

Step-by-step explanation:

Angles on a straight line sum to 180°.

[tex]\implies 72^{\circ} + x = 180^{\circ}[/tex]

[tex]\implies 72^{\circ} + x - 72^{\circ} = 180^{\circ} - 72^{\circ}[/tex]

[tex]\implies x = 108^{\circ}[/tex]

Corresponding Angles Theorem

When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.

Assuming the two lines that appear parallel in the given diagram are parallel:

[tex]\implies (5y - 3)^{\circ} = x^{\circ}[/tex]

[tex]\implies 5y - 3 = 108[/tex]

[tex]\implies 5y - 3 + 3 = 108 + 3[/tex]

[tex]\implies 5y = 111[/tex]

[tex]\implies 5y \div 5 = 111 \div 5[/tex]

[tex]\implies y = 22.2^{\circ}[/tex]

ATTACHED IS THE SOLUTION

SOLUTION:

Step 1:

In the question, we are considering the equation:

Step 2:

The details of the solution are as follows:

OCONCLUSION:

The final answer is:

Expressing the final answer in decimal, we have that:

According to the given function,

Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]

Vertical Asymptote = 4

Horizontal Asymptote = 0

X - intercept = No x - intercepts

Y - intercept = 1/4

Domain:

The  the domain of a function referred as the set of inputs accepted by the function

Given,

The function is,

[tex]f(x)=\frac{x-2}{x^2+2x-8}[/tex]

Here we need to find the domain, vertical asymptote, horizontal asymptote,  x - intercept, and y-intercept.

To find the domain and intercepts, we have to plot the graph for the given function.

So, the graph of the function is attached below. It can be drawn using the graphing calculator.

As per the graph,

Domain = [tex]\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)[/tex]

And the values of

x - intercept = No x-intercepts

y - intercept = 1/4

Now, the vertical asymptote is calculated as,

The line x=L is a vertical asymptote of the function f(x), if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x = -4

Then,

[tex]\lim_{x \to -4^+} \frac{1}{x + 4}=\infty[/tex]

Since the limit is infinite, then x=−4 is a vertical asymptote.

And the horizontal asymptote is,

Line y=L is a horizontal asymptote of the function y=f(x), if either '

[tex]\lim_{x \to \infty} f{\left(x \right)}=L[/tex] or [tex]\lim_{x \to -\infty} f{\left(x \right)}=L[/tex]  and L is finite.

When we calculate the limits:

[tex]\lim_{x \to \infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0\\\\\lim_{x \to -\infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0[/tex]

Thus, the horizontal asymptote is y=0.

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Answer:

You can follow these steps to multiply a fraction by a whole number:

Write the whole number as a fraction with a denominator of 1.

Multiply the numerators.

Multiply the denominators.

Simplify. , if needed. If your answer is greater than 1, you may want to write your answer as a mixed number.