find the missing side.​

Answer:

(a) [tex]T(x) = 101 + 0.029 x[/tex]

(b) [tex]T^{-1}(x) = \frac{1000(x - 101)}{29}[/tex]

(c) See explanation

Step-by-step explanation:

[tex]T(x) = 172 + \frac{29}{1000}x[/tex]

Given

[tex]Flat = 101[/tex]

[tex]Rate = 29\ per\ 1000[/tex]

Solving (a): The function for total amount

This is calculated as:

[tex]T(x) = Flat + Rate * x[/tex]

Where:

[tex]x \to[/tex] taxable value

So, we have:

[tex]T(x) = 101 + \frac{29}{1000} * x[/tex]

[tex]T(x) = 101 + 0.029 * x[/tex]

[tex]T(x) = 101 + 0.029 x[/tex]

Solving (b): The inverse function

[tex]T(x) = 101 + 0.029 x[/tex]

Rewrite as:

[tex]y = 101 + 0.029x[/tex]

Swap the variables

[tex]x = 101 + 0.029y[/tex]

Make y the subject

[tex]0.029y = x - 101[/tex]

Divide by 0.029

[tex]y = \frac{x - 101}{0.029}[/tex]

Multiply  by 1000/1000

[tex]y = \frac{1000(x - 101)}{29}[/tex]

Replace y with the inverse function

[tex]T^{-1}(x) = \frac{1000(x - 101)}{29}[/tex]

Solving (c): Interpret (b)

The inverse function, in this case; is the taxable value calculated from the amount of property tax

Answer:

x=2*sqrt(5)

Step-by-step explanation:

Since the triangle is isosceles, the other side (not x) is sqrt(10). Using Pythagoras, we have 10+10=x^2, x=2*sqrt(5)

Answer:

It is the first option: The sum of 4 tens and 9 tens is 13 tens, which is regrouped as 1 hundred and 3 tens.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

just logic

Answer:

6

Step-by-step explanation:

We can find the value x using Euclidian theorem

x^2 = 3*12

x^2 = 36

x = 6

Answer:

[tex]\displaystyle x = \frac{ln2}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra II

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle e^{3x} + 6 = 8[/tex]

Step 2: Solve for x

Answer:

x = 1/3 ln(2) or approximately 0.23104

Step-by-step explanation:

e^3x+6 =8

Subtract 6 from each side

e^3x+6-6 =8-6

e^3x =2

Take the natural log of each side

ln( e^3x) =ln(2)

3x = ln(2)

divide by 3

3x/3 = 1/3 ln(2)

x = 1/3 ln(2)

x is approximately 0.23104

Answer:

0.18

Step-by-step explanation:

The value of y is 3.

Answer:

Solution given;

: y + 3 = –y + 9

add +y on both term

y+y+3=-y+y+9

subtract both side by 3

2y+3-3=9-3

2y=6

divide both side by 2

2y/2=6/2

y=3

Answer:

y = 3

Step-by-step explanation:

y + 3 = –y + 9

Add y to each side

y+y + 3 = –y +y+ 9

2y +3 = 9

Subtract 3 from each side

2y+3-3 = 9-3

2y = 6

Divide by 2

2y/2 = 6/2

y = 3

Step-by-step explanation

They sold $480 of tshirts, the ratio is 480;20, simplified to 24:1.

One shirt is $20, but $4 is the amount taken from 20 for the equipment.

Multiply $24 by the $4 taken for the equipment. (Equals $96)

They make 4/20 (1/5) of the the sales as a profit for equipment.

Multiply 1/5 by 480 and you will get $96 as the club's profits.

I hope this helped ya

The chess club needs 20 T-shirts and 30 baseball caps.

Profit is a term that often refers to the financial gain that a company receives when revenue exceeds costs and expenses. A child at a lemonade stand, for example, spends one quarter to make one cup of lemonade. She then charges $2 for the drink. Her profit on a cup of lemonade is $1.75.

Given :

Total no. of items to be sold = 50

Total profit to be made = $230

Profit on each T-shirt = $4

Profit on each Baseball cap = $5

Let no. of t-shirts be x

Let no. of t-shirts be y

Forming equations according to given problem :

Eq 1 : x + y = 50

Eq 2 : 4x + 5y = 230

Multiplying Eq 1 with 4 we get : 4x + 4y = 200

Subtracting Eq 1 from Eq 2

Solving Eq1 and Eq2 we get x = 20 and y = 30.

Therefore, The chess club needs 20 T- shirts and 30 baseball caps.

To learn more about profits, refer to :

https://brainly.com/question/1078746

#SPJ2

[tex]\bf \large \rightarrow \: \: 2x \: ( \: 3x \: - \: 2y \: + \: 4z \: )[/tex]

[tex]\bf \large \rightarrow \: \:6 {x}^{2} \: - \: 6y \: + \: 8x z[/tex]

Espero que te sea de ayuda.

Answer:

Step-by-step explanation:

C = 16 * 3 = 48

Answer:

36

Step-by-step explanation:

Answer:

36 feet

Step-by-step explanation:

I can confirm that 36 feet is the correct answer. as seen below, I was able to get 100%

Answer:

4.292

Step-by-step explanation:

(x+3)(x-1)=24

expand

x²+2x-3=24

x²+2x-27=0

Using the quadratic formula..

[tex]\frac{-2+\sqrt{2^2-4*1*-27}}{2}=\frac{-2+10.5830052443}{2}=4.292[/tex]

there is another answer, but it doesn't make sense in the context of this question

the un-rounded answer is 4.29150262215

Answer:

A

Step-by-step explanation:

Answer:

The answer is <ead

please mark me brainliest

Answer:

The p-value of the test is 0.0734 < 0.1, which means that there is significant evidence, at the 0.1 level of significance, to conclude that the proportion of odd numbers is significantly different from 50%.

Step-by-step explanation:

Test if the proportion of odd numbers is significantly different from 50%.

At the null hypothesis, we test if the proportion is of 0.5, that is:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if the proportion differs from 0.5, that is:

[tex]H_1: p \neq 0.5[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.5 is tested at the null hypothesis:

This means that [tex]\mu = 0.5, \sigma = \sqrt{0.5(1-0.5)} = 0.5[/tex]

Two thousand numbers are selected randomly; 960 were even numbers.

This means that [tex]n = 2000, X = \frac{960}{2000} = 0.48[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.48 - 0.5}{\frac{0.5}{\sqrt{2000}}}[/tex]

[tex]z = -1.79[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample proportion differs from 0.5 by at least |0.48-0.5| = 0.02, which is P(|z|<1.79), which is 2 multiplied by the p-value of z = -1.79.

Looking at the z-table, z = -1.79 has a p-value of 0.0367

2*0.0367 = 0.0734

The p-value of the test is 0.0734 < 0.1, which means that there is significant evidence, at the 0.1 level of significance, to conclude that the proportion of odd numbers is significantly different from 50%.

Answer:

[tex]5.06 x 10^{-3}[/tex]

Step-by-step explanation:

Move decimal 3 place to right.

Because the decimal was moved to right, the exponent is negative.

Answer:

answer is A

hope it helps please mark as brainliest answer and give me thanks

Answer:

D=8

Step-by-step explanation:

normal division rules

33 goes into 47 1 time

then it leaves 17D

if we divide 170 by 33, we get 5 and if we divide 179 by 33, we still get 5. So we have 17D-165. That leaves us with something that you multiply 33 with to have a 2 in the ones place so that you get a remainder of 2. (In order to get 2 in the remainder, we need a 2 in the ones place because 4-2=2. In order to get that we need to see which number multiplied with 33 would get us a number smaller than 179 but also has a 2 in the ones place. Theres only one number and thats 4. 33*4=132. So in order to get only 2 in the remainder, we need the rest to be subtracted. This means that 17D-165=134. This way we can see that D=8

Answer:

It's B, I tried using mathaway and that's the closest to the answer I got. Try it. I always use mathaway for any math problems, use that for now on if you're stuck

Step-by-step explanation:

Answer:

C=125°

Step-by-step explanation:

Hi there!

To find angle C, we can use the cosine law:

[tex]cosC=\frac{a^2+b^2-c^2}{2ab}[/tex]

Plug in the given information

[tex]cosC=\frac{9^2+3^2-11^2}{2(9)(3)}[/tex]

[tex]cosC=\frac{-31}{54}[/tex]

[tex]C=cos^-^1(\frac{-31}{54})[/tex]

[tex]C=cos^-^1(\frac{-31}{54})\\C=125[/tex]

Therefore, angle C is approximately 125 degrees.

I hope this helps!

Answer:  D) reflection across y = -x

Explanation:

When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).

When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is [tex](x,y) \to (-y,-x)[/tex]

So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).

Similarly, B(1,5) moves to B ' (-5, -1)

Finally, C(6,9) becomes C ' (-9, -6)

Answer:

y = -3x+4

Step-by-step explanation:

The slope intercept form of an equation is

y = mx+b where m is the slope and b is the y intercept

y = -3x+4

Answer:

4.2 cents

Step-by-step explanation:

Take the total cost and divide by the number of ounces

1.01 /24

0.04208

Round to the nearest tenth of a cent ( 3 decimal places)

0.042

4.2 cents

Answer:

(g ∘ f)(2) =5

Step-by-step explanation:

f(x) = 3x − 2

g(x) = x + 1

(g ∘ f)(2).

Find f(2) = 3(2) -2 = 6-2 = 4

Then find g(4) = 4+1 = 5

This is equivalent to the fraction 1085/2

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

Explanation:

AP stands for "arithmetic progression", which is another name for "arithmetic sequence"

a1 = -10 is the first term

the 15th term happens when n = 15, so

an = a1 + d*(n-1)

a15 = -10 + d(15-1)

a15 = 14d-10

Set this equal to 11 (the stated 15th term) and solve for d

a15 = 11

14d-10 = 11

14d = 11+10

14d = 21

d = 21/14

d = 3/2

d = 1.5 is the common difference

Let's find the nth term

an = a1 + d(n-1)

an = -10 + 1.5(n-1)

an = -10 + 1.5n - 1.5

an = 1.5n - 11.5

-------------------------------

The last term is 41, so we'll replace the 'an' with that and solve for n

an = 1.5n - 11.5

41 = 1.5n - 11.5

41+11.5 = 1.5n

52.5 = 1.5n

1.5n = 52.5

n = (52.5)/(1.5)

n = 35

So the 35th term is 41.

-------------------------------

We're summing n = 35 terms from a1 = -10 to an = 41

S = sum of the first n terms of arithmetic progression

S = (n/2)*(a1 + an)

S = (35/2)*(-10+41)

S = 542.5

The 35 terms add up to 542.5 which is the final answer

As an improper fraction, this converts to 1085/2

Answer:

1. x = -2 , 3

2. x = - 1, 5

3. -1, 6/5

4. - 0/3, 1.3

Step-by-step explanation:

1.

[tex]ln(x+5)=ln(x-1)+ln(x+1)\\\\x+ 5 = (x-1)(x+1)\\\\x + 5 = x^2 - 1\\\\x^2 - x - 6 = 0 \\\\x^2 - 3 x + 2 x - 6 =0 \\\\x(x-3)+2(x-3)=0\\\\x = -2 and 3[/tex]

2.

[tex]e^{x^{2}}=e^{4x +5}\\\\x^2 - 4x - 5 = 0 \\\\x^2 - 5x + x - 5 = 0 \\\\x (x-5)+1 (x-5)=0\\\\x = -1 and 5[/tex]

3.

[tex]log_{4}(5x^2 +2)=log_{4}(x +8)\\\\5x^2 - x - 6 = 0 \\\\5 x^2 - 6 x + 5x- 6 = 0 \\\\5 x (x + 1)-6(x+1)=0\\\\x = -1 and \frac{6}{5}[/tex]

4.

[tex]log(x-1)+log 5x = 2\\\\5 x (x-1) =2 \\\\5x^2 - 5x -2 = 0 \\\\x = \frac{5\pm\sqrt{25+40}}{10}\\\\x = \frac{5\pm 8}{10}\\\\x = 1.3, - 0.3[/tex]

Answer:

Step-by-step explanation:

[tex]\displaystyle\ \large \boldsymbol{} +\left \{ {{-x+y=3} \atop { \ \ x-2y=5}} \right. => \\\\\\x \!\!\!\!\diagup-x\!\!\!\!\diagup-2y+y=5+3\\\\-y=8\\\\ y=-8\ ; \ x=-11[/tex]

Answer:

[tex]{ \tt{ = \frac{ {p}^{2} + 8p + 16 }{ {p}^{2} - 16 } }} \\ \\ = { \tt{ \frac{ {(x + 4)}^{2} }{(x - 4)(x + 4)} }} \\ \\ = { \tt{ \frac{(x + 4)}{(x - 4)} }}[/tex]

Answer:

(y + 5)² = -16(x + 5)

Step-by-step explanation:

We are told the focus is at (-3, -5)

Directrix is at x = -7

This is a horizontal parabola and thus the general equation is;

(y - k)² = -4p(x - h)

Where;

(h, x) is the coordinate of the vertex.

The axis where the point where the axis of symmetry meets the directrix is at; (-7, -5) since directrix is at x = -7

Thus, coordinates of vertex is;

(-7 + (-3))/2, (-5 + (-5))/2

> (-5, -5)

Thus, equation is;

(y - (-5))² = -4p(x - (-5))

(y + 5)² = -4p(x + 5)

Where p is the distance from vertex to directrix. Thus;

p = -(-7 - (-3))

p = -(-7 + 3)

p = 4

Thus;

(y + 5)² = -4(4)(x + 5)

(y + 5)² = -16(x + 5)

Answer:

(y + 5)² = -16(x + 5)

Step-by-step explanation:

[tex]\sf Your \: question \: is \: incomplete. \: [/tex]

______________________

[tex]\sf \: I \: believe \: this \: is \: the \: answer \: you \: wanted[/tex] ⟹

[tex]\sf If \: the \: discriminant \: of \: an \: equation \: is \: zero, \: then \\ \sf \: the \: equation \: will \: have \:\underline{ 1 \: real \: solution \: with \: real \: and \: equal \: roots}.[/tex]

[tex]\boxed{ \sf{Explanation}} [/tex]

[tex]\sf If \: discriminant \: of \: quadratic \: equation \: ax^{2} + bx + c \: \\ \sf is \: b^{2} - 4ac = 0 \: then \: it \: will \: have \\ \sf↦\underline{1 \: real \: solution \: with \: real \: and \: equal \: roots.} [/tex]

Answer:

see explanation

Step-by-step explanation:

If b² - 4ac = 0

Then the roots are real and equal

Answer:

(a), (c) and (d)

Step-by-step explanation:

Required

Which is linear

A linear function is represented as any of:

[tex]y = mx + b[/tex]

[tex]y - y_1= m(x - x_1)[/tex]

[tex](a)\ 8x - 3y = 2[/tex]

Rewrite as:

[tex]- 3y = -8x+2[/tex]

Divide by -3

[tex]y = \frac{8}{3}x - \frac{2}{3}[/tex] -- by comparison to [tex]y = mx + b[/tex], this is linear

[tex](b)\ y = |x - 4|-7[/tex]

This is an absolute function. It is not linear

[tex](c)\ y + 8=5(x - 4)[/tex]

By comparison to [tex]y - y_1= m(x - x_1)[/tex], this is linear

[tex](d)\ y = -7[/tex]

by comparison to [tex]y = mx + b[/tex], this is linear because [tex]m= 0[/tex]

Others are not linear