I need help on this please

Answer:

Function C is the only one that matches both definitions for the domain and range.

Step-by-step explanation:

First let's understand what the domain and range definitions mean in plain English.

The following statement means x is defined such that x can be any real number except for 1.

[tex]\{x | x \ne 1, x \epsilon R \}[/tex]

The following statement means y is defined such that y can be any real number except for 3.

[tex]\{y | y \ne 3, y \epsilon R \}[/tex]

So let's see what functions match those definitions. Take a look at the denominator of the functions in question 7, if we plug in x = 1 for any of them, we would be dividing by zero, which we know we can't do since the function would not be defined at that value. Therefore the domain definition is correct for all functions, we cannot use x = 1 for any of them.

Let's move on to the range. Our goal is to find a function where plugging in y = 3 would give us an undefined result. Simply plugin y = 3 into all of the given equations and simplify.

Therefore the function C is the only one that matches both definitions for the domain and range.

Answer:

k(3) is 7 and f(h(15)) is 43

Step-by-step explanation:

(a).

[tex]{ \sf{k(x) = h(x) + g(x)}} \\ { \sf{k(x) = (3 \sqrt{x + 1}) + ( - {x}^{2} + 3x + 1) }} \\ { \sf{k(x) = (3 \sqrt{3 + 1} ) + ( - {3}^{2} + 3(3) + 1) }} \\ { \sf{k(x) = 6 + 1}} \\ { \sf{k(x) = 7}}[/tex]

b).

[tex]{ \sf{f(h(x)) = 4(3 \sqrt{x + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{15 + 1}) - 5 }} \\ { \sf{f(h(15)) = 4(3 \sqrt{16} ) - 5}} \\ { \sf{f(h(15)) = 48 - 5}} \\ { \sf{f(h(15)) = 43}}[/tex]

Step-by-step explanation:

We'll find the distance using the all-famous "Distance Formula." You'll probably come across it quite a bit, so it's best to have it written down somewhere.

The Distance Formula: [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

Our points are (8, -3) and (4, -7), so we'll plug in those numbers accordingly.

For reference:

x2 = 4

x1 = 8

y2 = -7

y1 = -3

The calculation:

(substitute)

[tex]\sqrt{(4-8)^2+((-7)-(-3))^2 }[/tex]

(simplify)

[tex]\sqrt{(-4)^2+(-4)^2 }[/tex]

(square things)

[tex]\sqrt{16+16 }[/tex]

(add)

[tex]\sqrt{32}[/tex]

Answer:

[tex]\sqrt{32}[/tex]

Answer:

[tex]\boxed {\boxed {\sf C. \sqrt{32}}}[/tex]

Step-by-step explanation:

The distance between 2 points can be determined with the following formula.

[tex]d= \sqrt{(x_2-x_1)^2+ (y_2-y_1)^2[/tex]

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. We want to find the distance between the points (8, -3) and (4, -7). If we match the value with its corresponding variable, then we see:

Substitute the values into the formula.

[tex]d= \sqrt{(4-8)^2+(-7--3)^2[/tex]

Solve inside the parentheses.

[tex]d= \sqrt {(-4)^2+(-4)^2[/tex]

Solve the exponents.

[tex]d= \sqrt {16+16[/tex]

Add.

[tex]d= \sqrt {32}[/tex]

This radical can be simplified, but since it is an answer choice, we can leave it as is.

The distance between the points (8, -3) and (4, -7) is √32 and choice C is correct.

Shortest distance = Displacement

And please provide the diagram

Must click thanks and mark brainliest

Answer:

Hello,

Step-by-step explanation:

we must first remember that:

[tex]\boxed{sin(5x)=5sin(x)-20*sin^3(x)+16*sin^5(x)}\\\\[/tex]

Let say t=sin(x)

[tex]sin(x)+cos(x)=1.4\\\\t+\sqrt{1-t^2}=1.4\\\sqrt{1-t^2}=1.4-t\ we\ square\\1-t^2=1.4^2+t^2-2.8*t\\2t^2-2.8*t+0.96=0\\\Delta=2.8^2-4*2*0.96=0.16=0.4^2\\\\t=\dfrac{2.8-0.4}{4} =0.6\ or\ t=\dfrac{2.8+0.4}{4}=0.8\\\\t^3=0,216\ or\ t^3=0,512\\\\t^5=0,07776\ or\ t^5=0,32768\\\\\boxed{sin(5x)=5*0.6-20*0.216+16*0.07776=-0,07584}\\\\or\\\\\boxed{sin(5x)=5*0.8-20*0.512+16*0.32768=-0,99712}[/tex]

f is a function defined by

{(-3, 1), (-2, 2), (-1, -3), (0, -1), (1, 3), (2, -2), (3, 0)}

so f (1) = 3. Then

h (g (i (j (f (1))))) = h (g (i (j (3))))

j is defined by

{(-3, 0), (-2, 1), (-1, 2), (0, -1), (1, -2), (2, 3), (3, -3)}

so j (3) = -3, and

h (g (i (j (f (1))))) = h (g (i (-3)))

And so on. Next you have i (-3) = 2, then g (2) = 0, and finally, h (0) = 0, so your answer is correct.

Answer:

Our three numbers are 8, 48, and 16.

Step-by-step explanation:

Let the first, second, and third numbers be x, y, and z, respectively.

The sum of them is 72. In other words:

[tex]x + y + z = 72[/tex]

The second number y is three times the third number z. So:

[tex]y = 3z[/tex]

And the third number z is eight more than the first number x. So:

[tex]z = x + 8[/tex]

To find the numbers, solve for the system. We can substitute the last two equations into the first:

[tex]x + (3z) + ( x + 8) = 72[/tex]

Substitute again:

[tex]\displaystyle x + 3(x+8) + x+8 = 72[/tex]

Solve for x. Distribute:

[tex]x+3x+24+x+8=72[/tex]

Combine like term:

[tex]5x + 32 = 72[/tex]

Subtract:

[tex]5x = 40[/tex]

And divide:

[tex]x=8[/tex]

Thus, the first number is eight.

And since the third number is eight more than the first, the third number z is 16.

The second number is three times the third. Thus, the second number y is 3(16) or 48.

Our three numbers are 8, 48, and 16.

9514 1404 393

Answer:

  (a) Yes , the base is 1/e

Step-by-step explanation:

The variable is in the exponent, so this is an exponential function.

The base is the number that has the exponent. The base is (1/e).

Answer:

Step-by-step explanation:

bvxbvxbvxbvcvbbb cv

Answer:

The choose D. 15/16

Step-by-step explanation:

[tex] 1\frac{1}{4} \times \frac{3}{4} = \frac{15}{16} [/tex]

I hope I helped you^_^

Answer:

Step-by-step explanation:

slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4

eq. of line is y-0=3/4(x-0)

y=3/4 x

put x=4

y=2

2=3/4×4

2=3

which is true if 2<3

2<3

so y<3/4 x

Answer:

8 of the 11

Step-by-step explanation:

4+4=8 of the 11

Part of oranges usef from the orange packet used on 1st day = 4/11

Part of oranges used from the orange packet used on 2nd day = 4/11

Total part of oranges used from the orange packet

= (4/11) + (4/11)

= 8/11

So, Sipho's dad used 8 elevenths of the oranges.

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

[tex]x= \frac{-b +- \sqrt{b^2-4ac} }{2a}[/tex]

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² =  x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1[/tex]

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

[tex]x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\[/tex]

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

[tex]x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2[/tex]

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

Answer:

5x^2-12x+7

Step-by-step explanation:

7x^2-5x+3-(2x^2 + 7X - 4)

Distribute the minus sign

7x^2-5x+3 - 2x^2 - 7X + 4

Combine like terms

5x^2-12x+7

Answer:

-12x + 17

Step-by-step explanation:

hope this helps!

Answer:

y = 5

Step-by-step explanation:

[tex]7y-10=25\\7y=35\\y=5[/tex]

Answer:

$343

step by step explanation: interest=PRT/100

:I=700×7×7/100

:I=$343.

Given:

Principal, P = $700

Rate of interest, R = 7% = 0.07

Time period, T = 7 months (it is considered as a monthly investment)

∴ Simple Interest, SI = PRT

SI = 700 × 0.07 × 7

SI = $343

Straightforward Simple Interest is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes credit of Rs. 5000, at a pace of 10 p.a. for a very long time, the individual's advantage for quite some time will be S.I. on the acquired cash.

Straightforward recipes generally start with an equivalent sign (=), trailed by constants that are numeric qualities and computation administrators like in addition to (+), short (- ), asterisk(*), or forward cut (/) signs.

Learn more about Simple Interest here

https://brainly.com/question/2294792

#SPJ2

Answer:

3.75 hours

Step-by-step explanation:

d = rt

where d is the distance, r is the rate and t is the time

45 = 12 t

Divide each side by 12

45/12 = t

3.75 hours = t

Answer:

AB

Step-by-step explanation:

For the multiplication of two matrices to be defined then the number of columns of the first matrix must be equal to the number of rows of the second matrix. For example, 2*3 and 3*2 matrices can be multiplied since the number of columns of the first matrix must be equal to the number of rows of the second matrix.

Matrix A = 2*2

Matrix B = 2*3

Matrix C = 3*3

Matrix D = 1 * 3

From the matrices given, we can see that the matrices that can be multiplied together are AB and BC since the number of columns of the first matrix must be equal to the number of rows of the second matrix. Hence the correct option is AB

Answer:

Both are true

Step-by-step explanation:

Both are true

9514 1404 393

Answer:

  [165, 175) meters

Step-by-step explanation:

The rule with respect to questions like this is that the bounds are ±1/2 of the place value of the least-significant digit. Here, the integer portion of the number has trailing zeros, and there is no decimal point or fractional part. Ordinarily, this combination of characteristics would signal that the trailing zeros are not significant, so the only significant digits are 1 and 7. The place value of the least significant digit is 10, so the bounds on the measurement are this number ±1/2(10) = ±5.

Of course, 175 rounds up to 180, so the upper bound is a limit, rather than an actual value. The height should be interpreted in this context as ...

  165 m ≤ height < 175 m

The lower and upper bounds are 165 m and 175 m, respectively.

_____

Additional comment

The best way to avoid any ambiguity as to whether trailing zeros are significant is to use scientific notation. If a zero in the ones place is significant, that is conventionally indicated by a decimal point: "170.". If scientific notation is used, the number would be reported as 1.70×10² to indicate the trailing zero is significant.

For reference, Earth's tallest tree is a redwood just under 116 meters high.

Answer: 101

Step-by-step explanation:

.

Answer:

m= 0, -0.2

Step-by-step explanation:

that's what I got when I did it

Answer:

Step-by-step explanation:

200m^4 + 80m^3 + 8m^2 = 0

~Factor

8m²(5m + 1)(5m + 1) = 0

~Set everything to equal 0 and solve

8m² = 0 → m² = 0 → m = 0

5m + 1 = 0 → 5m = -1 → m = -1/5

5m + 1 = 0 → 5m = -1 → m = -1/5

Best of Luck!

Answer:

A

Step-by-step explanation:

based on line p and q

Answer: p || q

Or A

Step-by-step explanation:

good luck

Answer:

5

Step-by-step explanation:

Subtract  

5

from  

10

.

|

5

|

The absolute value is the distance between a number and zero. The distance between  

0

and  

5

is  

5

.

5

Answer:

56.25

Step-by-step explanation:

(9x12.5)÷2

just use a c calculator

Answer:

2 minutes and 5 seconds

Step-by-step explanation:

60+20+15+15+15= 125 Seconds ( 2 minutes and 5 seconds )

I added three fifteens as I don't know the number of chambelanes.

Hope it helps!

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Each point moves to 3 times its original distance from P.

  A is 2 up and 1 left of P, so A' will be 6 up and 3 left of P.

  B is 1 down and 2 left of P, so B' will be 3 down and 6 left of P.

  C is 2 right of P, so C' will be 6 right of P.

Answer:

y=-1/3x+7

Step-by-step explanation:

y=mx+c

m=-1/3, c=7

y=-1/3x+7

Answer:

y=2x+1

Step-by-step explanation:

y is directly proportional to x if it increases as x increases