If f(x)= 15x+7x and g(x)= x^2-5x, find (f+g)(x)

b=-7

Please look at the attached picture to see what I did

The value of b=-7.

y=3x+b

point(2,-1)

x=2, y=-1

subtract into equation

-1 = 3(2) +b

-1 = 6+b

-1-6 = b

b= -7

Coordinates are a couple of numbers that describe the precise function of a factor on a cartesian aircraft through the use of the horizontal and vertical lines known as the coordinates. commonly represented by (x, y) the x cost and y price of the point on a graph. Each factor or an ordered pair consists of two coordinates.

A factor-to-factor graph also referred to as a line graph, is a pictorial rendition of records wherein specific values of a feature are plotted as dots on a coordinate aircraft.

Learn more about graphs through the point  here: https://brainly.com/question/14323743

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Answer:

  6 is in the "hundreds" place

Step-by-step explanation:

The value of the 6 can be found by setting the other digits to zero:

  00,600.00 = 600

The 6 represents six hundred, hence is in the hundreds place.

Answer:

see below

Step-by-step explanation:

Choose a couple of values for x. Figure out the corresponding values for y. Plot those points and draw a line through them.

Let's choose x=0 and x=4. Then the corresponding y-values are ...

y = 2·0 = 0 . . . . . point (x, y) = (0, 0)

y = 2·4 = 8 . . . . . point (x, y) = (4, 8)

These are graphed below.

Answer:

A

Step-by-step explanation:

The bottles are cylindrical.  The volume of a cylinder is:

V = πr²h

where r is the radius (half the diameter) and h is the height.

The bottles are similar, so we can write a proportion to find the height of the smaller bottle:

3/10 = 1.5/h

h = 5

The volume of the big bottle is:

V = π(3/2)²(10)

V ≈ 70.7

The volume of the small bottle is:

V = π(1.5/2)²(5)

V ≈ 8.8

So the difference in volume is:

V = 70.7 - 8.8

V = 61.9

Answer:

A

Step-by-step explanation:

got it right

Answer:

  24%

Step-by-step explanation:

2610 of the 10730 students are graduates. The probability of choosing a graduate at random from all students is ...

  2610/10730 × 100% ≈ 24.324% ≈ 24%

[tex]5\frac{3}{7}[/tex] Kilometers of thread.

The key to solve this problem is using the rule of three.

We have to change mixed number to improper fraction in order to solve the problem.

A mixed number is a number formed by an integer and a proper fraction (one whose quotient is less than 1).

An improper fraction  is one whose denominator is less than its numerator.

To change a mixed number to an improper fraction:

1. Multiply the whole number by the denominator and add to the numerator.

2. The denominator of the mixed number is unchanged.

It takes [tex]2\frac{1}{4}[/tex] kilometers of thread to make [tex]3\frac{1}{2}[/tex] boxes of shirts. How many kilometers of thread would it take to make 8 boxes?

We need to change [tex]2\frac{1}{4}[/tex] and [tex]3\frac{1}{2}[/tex] to an improper franctions:

[tex]2\frac{1}{4}=\frac{(2)(4)+1}{4}=\frac{9}{4}[/tex]

[tex]3\frac{1}{2}=\frac{(3)(2)+1}{2}=\frac{7}{2}[/tex]

To calculate how many kilometers of thread would it take to make 8 boxes, we use the rule of three:

9/4 Km of thread -------------> 7/2 boxes of shirts

                    x     <-------------  8 boxes of shirts

[tex]x = \frac{(\frac{9}{4})(8)}{\frac{7}{2}}= \frac{19}{\frac{7}{2}}\\x=\frac{38}{7}[/tex]

Convert the improper fraction 38/7 to a mixed number:

1. Divide the numerator by the denominator.

38÷7 = 5 and a remainder of 3

2.  5 become the whole number, the remainder is the numerator, and the denominator is unchanged.

38/7 = 5 3/7

It would take 5 3/7 kilometers of thread make 8 boxes of shirts.

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

In ΔAHD, the side opposite angle DAH is DH, and the hypotenuse is AD, so we have ...

  sin(∠DAH) = DH/AD = 4/8

  ∠DAH = arcsin(4/8) = 30°

That makes ΔAHD a 30°-60°-90° triangle, so the side lengths have the ratios 1 : √3 : 2.

∠CAB = 2·30° = 60°, so ΔABC is also a 30°-60°-90° triangle having the same ratios of side lengths.

In short, ...

  AH = √3·DH = 4√3

  AC = 2·AH = 8√3

  AB = 2·AC = 16√3

  BC = √3·AC = 8·(√3)² = 24

Answer:

Part 1) The statement is false

Part 2) The statement is false

Part 3) The statement is true

Step-by-step explanation:

Let

h(t)-----> the height of an object launched to the air

t ----> the time in seconds after the object is launched

we have

[tex]h(t)=-16t^{2} +72t[/tex]

Verify each statement

case 1) The factored form of the equation is h(t)=-16(t-4.5)

The statement is false

Because

The factored form is equal to

[tex]h(t)=-16t(t-4.5)[/tex]  

case 2) The object will hit the ground at t=72 seconds

The statement is false

Because

we know that

The object will hit the ground when h(t)=0

substitute in the equation and solve for t

[tex]0=-16t(t-4.5)[/tex]  

so

[tex](t-4.5)=0[/tex]  

[tex]t=4.5\ sec[/tex]  

case 3) The t-value for the maximum of the function is 2.25

The statement is true

Because

Convert the quadratic equation in vertex form

[tex]h(t)=-16t^{2} +72t[/tex]

[tex]h(t)=-16(t^{2} -4.5t)[/tex]

[tex]h(t)-81=-16(t^{2} -4.5t+2.25^{2})[/tex]

[tex]h(t)-81=-16(t-2.25)^{2}[/tex]

[tex]h(t)=-16(t-2.25)^{2}+81[/tex] ---> quadratic equation in vertex form

The vertex is a maximum

The vertex is the point (2.25,81)

Answer:

[tex]A = 144\ ft[/tex]

Step-by-step explanation:

The area of a triangle is:

[tex]A = 0.5b*h[/tex]

Where b is the base of the triangle and h is the height

In this case we know the hypotenuse of the triangle and the angle B.

Then we can use the sine of the angle to find the side opposite the angle

By definition we know that

[tex]sin (\theta) = \frac{opposite}{hypotenuse}[/tex]

In this case hypotenuse = 24

opposite = b

Then:

[tex]sin (45) = \frac{b}{24}[/tex]

[tex]b= 24*sin(45)[/tex]

[tex]b=12\sqrt{2}[/tex]

Now

[tex]cos(\theta) = \frac{adjacent}{hypotenuse}[/tex]

adjacent = a = h

[tex]cos(45) = \frac{h}{24}[/tex]

[tex]h = 24*cos(45)\\\\h=12\sqrt{2}[/tex]

Then the area is:

[tex]A = 0.5*12\sqrt{2}(12\sqrt{2})\\\\A=144\ ft[/tex]

ANSWER

[tex]Area = 144 {ft}^{2} [/tex]

EXPLANATION

We use the sine ratio to find the missing side.

[tex] \sin(45 \degree) = \frac{AC}{24} [/tex]

[tex]24\sin(45 \degree) = AC[/tex]

[tex]AC = 24 \times \frac{ \sqrt{2} }{2} [/tex]

[tex]AC = 12 \sqrt{2} ft[/tex]

The triangle is a right isosceles triangle.

This implies that,

AC=BC=12√2 ft.

The area of the triangle is:

[tex]Area = \frac{1}{2} bh[/tex]

We substitute the values to get,

[tex]Area = \frac{1}{2} \times 12 \sqrt{2} \times 12 \sqrt{2} [/tex]

[tex]Area = 144 {ft}^{2} [/tex]

Answer:

theoretical is 15 each

experimental is Red: 13 Blue: 14 Yellow:18 Green:15

Step-by-step explanation:

the theoretical probability is what should statisticly happen when you do it so if there are for outcomes with an equal chance of occurring then 1 out of every 4 or 1/4 of the time each one should happen so divide 60 by 4 and you get 15

the experimental probability is what happens when someone actually spins it 60 times and in your scenario

RESULTS HERE

Red: 13 Blue: 14 Yellow:18 Green:15

is what happened so that is the experimental probability

Answer:

35 years

Step-by-step explanation:

We have been given an exponential decay function that models the weight of the bones of an extinct dinosaur;

[tex]f(x)=10e^{-0.02x}[/tex]

The initial weight of the bones is;

substitute x with 0 in the function, f(0) = 10 grams

We are required to determine the number of years it will take for the bones to be less than 5 grams. The solution can be achieved either analytically or graphically. I obtained the graph of the function from desmos graphing tool as shown in the attachment below.

From the graph, the bones will weigh 5 grams after approximately 34.65 years. This implies that it will take 35 years for the bones to be less than 5 grams.

Note that [tex]+\vee-[/tex] stands for plus or minus.

For the quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are [tex]x_{1,2}=\dfrac{-b+\vee-\sqrt{b^2-4ac}}{2a}[/tex] that means that for [tex]a=4, b=-10, c=5\Longrightarrow x_{1,2}=\dfrac{-(-10)+\vee-\sqrt{(-10)^2-4\cdot4\cdot5}}{2\cdot4}[/tex] this simplifies to [tex]\boxed{x_1=\dfrac{5+\sqrt{5}}{4}}, \boxed{x_2=\dfrac{5-\sqrt{5}}{4}}[/tex]

Hope this helps.

Answer:

[tex]\large\boxed{x=\dfrac{5-\sqrt5}{4},\ x=\dfrac{5+\sqrt5}{4}}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula for}\ ax^2+bx+c=0\\\\\text{if}\ b^2-4ac<0,\ \text{then the equation has no real solution}\\\\\text{if}\ b^2-4ac=0,\ \text{then the equation has one solution:}\ x=\dfrac{-b}{2a}\\\\\text{if}\ b^2-4ac,\ ,\ \text{then the equation has two solutions:}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\text{We have the equation:}\ 4x^2-10x+5=0\\\\a=4,\ b=-10,\ c=5\\\\b^2-4ac=(-10)^2-4(4)(5)=100-80=20>0\\\\x=\dfrac{-(-10)\pm\sqrt{20}}{2(4)}=\dfrac{10\pm\sqrt{4\cdot5}}{8}=\dfrac{10\pm\sqrt4\cdot\sqrt5}{8}=\dfrac{10\pm2\sqrt5}{8}\\\\=\dfrac{2(5\pm\sqrt5)}{8}=\dfrac{5\pm\sqrt5}{4}[/tex]

Answer:

12

Step-by-step explanation:

SOH CAH TOA reminds you that ...

Sin = Opposite/Hypotenuse

so ...

sin(45°) = (6√2)/x

Your memory of trig functions tells you sin(45°) = 1/√2, so we have ...

1/√2 = (6√2)/x

Multiplying by (√2)x gives ...

x = 6(√2)^2 = 6·2

x = 12

_____

You can simply recognize that this is an isosceles right triangle, so the hypotenuse (x) is √2 times the leg length:

x = (6√2)·√2 = 6·2 = 12

she went down the slope 10.2 meters, -10.2

then she jumped down to the lake 1.5 meters, -1.5

-10.2 - 1.5 = -11.7 meters.

so she pretty much went 11.7 meters down from her original location.

Answer: 28x + 8y + 2

Answer:

28x +8y +2

Step-by-step explanation:

It can work well to simplify the contents of the parentheses, then apply the overall multiplier.

= -2(x(3-17) +y(12-16) +(-5+4)) . . . . collect terms

= -2(-14x -4y -1)

= 28x +8y +2 . . . . use the distributive property

Answer:

D, y = cos(x -π/2)

Step-by-step explanation:

When the cosine function is shifted right by π/2 units, it looks like the sine function. That is what we have here. To shift f(x) to the right, replace x by x-(amount of shift). Here, this means the graph is described by ...

y = 2cos(x -π/2)

_____

The vertical scale factor is 2 on the graph and in all answer choices.

____________________________________________________

Answer:

Your answer would be x + y = 1

____________________________________________________

Step-by-step explanation:

In this scenario, we know that the line of CD passes through the coordinates (0,1), and would also be parallel to the equation x + y = 3.

When two lines are parallel, that means that their slopes are equal.

The slope of the line must be:

[tex]x + y = 3[/tex]

Move the x to the other side by subtracting

[tex]y= -x + 3[/tex]

The slope for the equation would be -1, since there is a invisible one after the equal sign. When there's no other number there, it would be 1.

The slope of the line CD would be -1.

Now, we would need to plug in -1 into the equation, to find the standard form.

[tex](y - 1) = m(x - 0)\\\\(y-1)=-1(x)\\\\x+y=1[/tex]

[tex]x + y = 1[/tex] should be your FINAL answer.

____________________________________________________

Answer:

16/29

Step-by-step explanation:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(basketball or baseball) = P(basketball) + P(baseball) - P(both)

= (13/29) + (7/29) - (4/29)

= 16/29

The probability that a randomly chosen student plays either sport is 16/29.

Answer:

reflective and slide the y is -1

Step-by-step explanation:

refect over the -1 x axis and the translate x-1 and y-1

Answer:

A) 525,500

B) decreasing by 0.995% per year

C) 430,243

D) After 20 years, the population can be expected to be about 20% smaller.

E) 2009

Step-by-step explanation:

A) t=0 represents the year 2000, so put 0 where t is in the expression and evaluate it. Of course, e^0 = 1, so the y-value is 525.5 thousand, or 525,500.

__

B) Each year, the population is multiplied by e^-0.01 ≈ 0.99004983, or about 1 - 0.995%. That is, the population is decreasing by 0.995% per year.

__

C) t represents the number of years since 2000, so the year 2020 is represented by t=20. Put that value in the equation and do the arithmetic.

y = 525.5·e^(-0.01·20) = 525.5·e^-0.2 ≈ 430.243 . . . . thousands

The population in 2020 is predicted to be 430,243.

__

D) The decrease is about 1% per year, so a rough estimate of the decrease over 20 years is 20%. The population of about 500,000 will decrease by about 100,000 in that time period, so will be about 400,000. The value we calculated is in that ballpark. (The actual decrease is about 18.13%; or about 95.2 thousand.)

__

E) Your working shows the general idea, but you need to remember the numbers in the equation are thousands:

480 = 525.5·e^(-0.01t)

0.913416 = e^(-0.01t) . . . . divide by 525.5

ln(0.913416) = -0.01·t . . . . take the natural log

-100ln(0.913416) = t ≈ 9.06

The population will be 480 thousand after 9 .06 years, in the year 2009.

2,8,8,8

8,2,8,8

8,8,2,8

8,8,8,2

4 combinations.

Hope this helps!

Answer:

D

Step-by-step explanation:

(cos t) (sec t − cos t)

1 − cos² t

sin² t

The expression cos t(sec t - cos t) simplifies to sin² t, which matches option D.

The student has asked to simplify the expression cos t(sec t − cos t).

To simplify this expression, we start by distributing cos t across the parentheses:

cos t × sec t − cos t ×cos t

1 − cos² t (since cos t × sec t = 1)

1 − (1 − sin² t) (using the Pythagorean identity cos² t + sin² t = 1)

sin² t

Thus, the expression simplifies to sin² t, which corresponds to option D.

Answer:

  (a) max P(A∩B) = 1/3; min P(A∩B) = 1/12

  (b) max P(A∪B) = 1; min P(A∪B) = 3/4

Step-by-step explanation:

Let the universal set be the numbers 1–12, U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, each with probability 1/12.

Let event A be any of the numbers 1–9, {1, 2, 3, 4, 5, 6, 7, 8, 9}. If a number is chosen at random from U, the probability of event A is 9/12 = 3/4.

a1) Let event B be any of the numbers 1–4, {1, 2, 3, 4}. If a number is chosen at random from U, the probability of event B is 4/12 = 1/3.

The set A∩B is the numbers 1–4, {1, 2, 3, 4}, so the probability of that event is also 4/12 = 1/3.

In general the maximum value of P(A∩B) will be min(P(A), P(B)). Here, that is min(3/4, 1/3) = 1/3.

__

a2) Let event B be any of the numbers 9–12, {9, 10, 11, 12}. If a number is chosen at random from U, the probability of event B is 4/12 = 1/3. The set A∩B is the number {9}, so the probability of that event is 1/12.

In general, the minimum value of P(A∩B) is max(0, P(A) +P(B) -1). Here, that is max(0, 3/4 +1/3 -1) = 1/12.

__

b1) Let event B be defined as in (a2), the numbers 9–12. Then A∪B is the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, which is equal to the universal set, U. That is, the probability of event A∪B when drawing a number from U is 1.

In general, the maximum value of P(A∪B) is min(1, P(A)+P(B)). Here, that is min(1, 3/4+1/3) = 1.

__

b2) Let event B be defined as in (a1), the numbers 1–4. Then A∪B is the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. If a number is chosen at random from U, the probability of event A∪B is 9/12 = 3/4.

In general, the minimum value of P(A∪B) is max(P(A), P(B)). Here, that is max(3/4, 1/3) = 3/4.

Answer:

supplementary angle = 60 , complementary angle : none

Final answer:

A supplementary angle of 120 degrees is 60 degrees, and there is no complementary angle for 120 degrees because complementary angles must be less than or equal to 90 degrees.

Explanation:

Finding Supplementary and Complementary Angles

The task is to find the measure of a supplementary angle and a complementary angle for a given angle measure of 120 degrees. To find a supplementary angle, you subtract the given angle from 180 degrees. Thus, the supplementary angle of 120 degrees is 180 - 120 = 60 degrees. On the other hand, a complementary angle adds up to 90 degrees. Since 120 degrees is greater than 90, it is not possible to have a complementary angle to 120 degrees, therefore, we write 'none'. It's important to remember that complementary angles are always less than or equal to 90 degrees and hence, cannot be obtained for angles larger than 90 degrees.

In summary, the supplementary angle to 120 degrees is 60 degrees, and there is no complementary angle for 120 degrees.

The volume of 1 cube is s^3 where S is the side length.

Volume of one cube = 18^3 = 5832 cubic inches.

Now multiply the volume of one cube by the total number of cubes:

5832 x 10 = 58,320 cubic inches.

To find the volume of the stack of cubes, we need to find the volume of one cube and then multiply it by the number of cubes in the stack.

To find the volume of the stack of cubes, we need to find the volume of one cube and then multiply it by the number of cubes in the stack. The side length of each cube is given as 18 inches. The formula to find the volume of a cube is side length cubed, so the volume of one cube is 18³ cubic inches.

To find the volume of the stack, we multiply the volume of one cube by the number of cubes, which is 10. So the volume of the stack of cubes is 18³ * 10 cubic inches.

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Answer:

20. OPTION D.

12. OPTION B.

Step-by-step explanation:

20. An inverse variaton equation has this form:

[tex]y=\frac{k}{x}[/tex]

Where "k" is the constant of variation.

If  Q varies inversely as the square of p, then the equation is:

[tex]Q=\frac{k}{p^2}[/tex]

Knowing that [tex]Q = 36[/tex] when [tex]p = 7[/tex], you can solve for "k" and caculate its value:

[tex]k=Qp^2\\k=(36)(7^2)\\k=1,764[/tex]

Then, to find the value of "Q" when [tex]p = 6[/tex], substitute the known  values into  [tex]Q=\frac{k}{p^2}[/tex]:

[tex]Q=\frac{1,764}{6^2}\\\\Q=49[/tex]

12. Given [tex](ab)^n[/tex], you get:

[tex](ab)^n=(a^1b^1)^n=a^{(1*n)}b^{(1*n)}=a^nb^n[/tex]

Then:

 [tex](ab)^n=a^nb^n[/tex]

This matches with the option B.

[tex]\displaystyle\\\text{If }~~180^o<\theta<270^o~~\text{then }~~\theta\in~\text{quadrant 3}\\\\\text{In the 3rd cotangent dial is positive.}\\\\\text{We use the formula: } ~~~\boxed{1+\cot^2\theta=\csc^2\theta}[/tex]

[tex]\displaystyle\\1+\cot^2\theta=\csc^2\theta\\\\\cot^2\theta=\csc^2\theta-1\\\\\cot^2\theta=\left(-\frac{3}{2}\right)^2-1\\\\\\\cot^2\theta=\left(\frac{3}{2}\right)^2-1\\\\\\\cot^2\theta=\frac{9}{4}-\frac{4}{4}\\\\\\\cot^2\theta=\frac{5}{4}\\\\\\\cot\theta=\pm\sqrt{\frac{5}{4}}\\\\\\\text{We will eliminate the negative solution.}\\\\\\\cot\theta=+\sqrt{\frac{5}{4}}\\\\\\\boxed{\bf\cot\theta=\frac{\sqrt{5}}{2}}}[/tex]

Answer:

[tex]10.4\ years[/tex]

Step-by-step explanation:

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y is the population of a town

x is the number of years since 2010

a is the initial value

b is the base

[tex]a=72,000\ people[/tex]

[tex]b=1+0.08=1.08[/tex]

substitute

[tex]y=72,000(1.08)^{x}[/tex]

For [tex]y=160,000\ people[/tex]

substitute in the equation and solve for x

[tex]160,000=72,000(1.08)^{x}[/tex]

[tex](160/72)=(1.08)^{x}[/tex]

Apply log both sides

[tex]log(160/72)=(x)log(1.08)[/tex]

[tex]x=log(160/72)/log(1.08)[/tex]

[tex]x=10.4\ years[/tex]

Given equation is [tex]f\left(x\right)=x^2-b^2[/tex].

Now we need to find about what are the key aspects of the graph of [tex]f\left(x\right)=x^2-b^2[/tex], where b is a real number.

We know that square of any number is always positive.

then [tex]b^2[/tex] must be a positive number.

So that means for any real number b, as the value of b increases then graph of f(x) shifts downward by [tex]b^2[/tex] units as compared to the graph of parent function [tex]f\left(x\right)=x^2[/tex]

Answer with explanation:

The graph of the function is:

   f(x)=x² -b²

Here, b is any Real Number.

f(x)=x² - k, where, k=b².

→y+k=x²

The given curve represents a Parabola having vertex at ,(0, -k) which can be Obtained by , putting, x=0 and, y+k=0→y= -k.

→The curve will open vertically Upwards having y axis as Line of Axis.

→It will cut, x axis at two points, if , k<0 and does not cuts the x axis , if k>0.

→Line, x=0, divides the Parabola into two equal Parts.

For this case we have the following system of equations:

[tex]8x-9y = -122\\-8x-6y = -28[/tex]

To solve, we add both equations:

[tex]8x-8x-9y-6y = -122-28\\-15y = -150\\y = \frac {-150} {- 15}\\y = 10[/tex]

We find the value of "x":

[tex]8x = -122 + 9y\\x = \frac {-122 + 9y} {8}\\x = \frac {-122 + 9 (10)} {8}\\x = \frac {-122 + 90} {8}\\x = \frac {-32} {8}\\x = -4[/tex]

The solution is (-4,10)

ANswer:

Option C