Graph the linear function.
g(x) = -1/2x +2

Answer:

It depends on the equation.

If the bases are equal and the variables are only in the exponents, set the exponents equal.

If there are variables in the exponents, but you cannot set the bases equal, then use logarithms.

Example 1:

[tex] 4^{2x + 5} = 4^9 [/tex]

Here you have the same base on both sides. The variables are in the exponents. Set the exponents equal and solve for x.

2x + 5 = 9

2x = 4

x = 2

Example 2:

[tex] 3^{2x} = 9^{6} [/tex]

The bases are different, but you can make the bases equal using laws of exponents. Remember that 9 = 3^2.

[tex] 3^{2x} = (3^2)^{6} [/tex]

[tex] 3^{2x} = 3^{12} [/tex]

Now you have equal bases, so the exponents must be equal.

2x = 12

x = 6

Example 3:

[tex] 10^{x + 2} = 9 [/tex]

Here you can't make the bases equal, so you take the log of both sides and use laws of logs.

[tex] \log(10^{x + 2}) = \log 3^2 [/tex]

[tex] (x + 2) \log 10 = 2 \log 3 [/tex]

Recall that: [tex] \log 10 = 1 [/tex]

[tex] x + 2 = 2 \log 3 [/tex]

[tex] x = 2 \log 3 - 2 [/tex]

Answer:

Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section

Step-by-step explanation:

Given:

Total number of sections filled = 3¹/₂ = 7 / 2 sections

Number of fraction parents watching play = 3/5

Find:

Fraction[Total number of sections filled filled with parents]

Computation:

Fraction[Total number of sections filled filled with parents] = Total number of sections filled x Number of fraction parents watching play

Fraction[Total number of sections filled filled with parents] = [7/2] x [3/5]

Fraction[Total number of sections filled filled with parents] = 21 / 10 sections

Fraction[Total number of sections filled filled with parents] = 2¹/₁₀ section

Answer:

Its the rectangle

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

1.35n is 4.05

4.05÷1.35 is 3

n is 3

Answer:

3 : 1

Step-by-step explanation:

4.05 : 1.35 can be written as [tex]\frac{4.05}{1.35}[/tex] in fraction.

To write 4.05 : 1.35 in "n : 1" ratio format , you need to make the denominator of the fraction as 1.

[tex]=> \frac{4.05 \div 1.35}{1.35 \div 1.35}[/tex]

[tex]=> \frac{3}{1}[/tex]

[tex]=> \boxed{3 : 1}[/tex]

Answer:

9.04

Step-by-step explanation:

tan 37 = x/12

0.7536 x 12= x

x = 9.04

Answer:

Remember that if we have a proposition P, ¬P is the negation of that proposition.

We have:

W = car is white

¬W = car is not white

N = car is new

¬N = car is not new

M = the car is mine

¬M = the car is not mine.

Now, whit that defined, let's analyze the statements:

a: " If the car is not white and new, then it is mine."

We can write this as:

"Not W and N, then M"

using only symbols this is:

(¬W ∧ N) ⇒ M

where the symbol ∧ means "and"

and the symbol ⇒ means "then"

b " The car being white or new is a sufficient condition for it being not mine."

We can rewrite this in a simpler way:

"if the car is white or new, then is not mine"

We can write this as:

W or N, then, not M

using the symbols, we get:

(W ∨ N) ⇒ ¬M

Where the symbol ∨ means "or"

c " The car is mine if and only if it is new and not white."

This can be rewritten as:

"M if and only if N and not W"

Using only symbols, we get:

M ⇔ (N ∧ ¬W)

Where "⇔" means "if and only if"

Answer:

Step-by-step explanation:

yes two triangles are congruent by SSS theorem (side Side Side)

Answer:

x³ - 1 = 12x

Step-by-step explanation:

A number cubed decreased by 1 is equal to the product of the number and 12

x³ - 1 = 12x

Answer:

26.

Step-by-step explanation:

As the vertex angles are equal:

24/54 = x / x+10

54x = 24x + 240

30x = 240

x = 8

So EG = x + x + 10

=  8 + 8 + 10

= 26..

Answer:

slope = 1/6

Step-by-step explanation:

(-3--4)/1--5)

rise/run

so slope = 1/6

Answer:

12.5 pi or 39.26990

Step-by-step explanation:

First we can find the radius, which is half the diameter, 5 feet. To find the area of a semi-circle we would find the area of the circle and then divide by 2:

[tex]\frac{\pi r^2}{2}[/tex]

We can substitute what we have:

[tex]\frac{25\pi }{2}[/tex]

This gives us:

12.5 pi or 39.26990(Not sure what format you need it in)

Answer:

14 questions correct

Step-by-step explanation:

x/20 *100 = 70

so x/ 20 = 70/100(0.7)

x/20 = 0.7

x = 0.7*20

x =14

Answer:

-6

Step-by-step explanation:

Substitute the value of the variable into the equation and simplify.

Answer:

-6 (not 100% sure)

Step-by-step explanation:

4x = 28

4 × 7 = 28

so

29 - 5x

if x is 7, 5 × 7 = 35

29 - 35 = -6

Answer:B) x = 7 sin 65°

Step-by-step explanation:

Sine = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{7}[/tex]

So 7 × [tex]\frac{x}{7}[/tex] = x

Answer:

y = -4x + 3

Step-by-step explanation:

You just have to solve for y.

So you get only the y value on one side, so the equation would then be

4y = -16x + 12, then you have to solve for y, so you divide both sides of the equation by 4 and you are left with y = -4x + 3

Answer:

a. Use the regression equation

Step-by-step explanation:

Given

See attachment for missing part of question

Required

What can be used to predict diameter, given family income

We can see (by observation) that the data on the table can only be represented on a scattered plot, and scattered plot uses regression equation for data prediction.

i.e. [tex]y = mx + b[/tex] --- equation of line of best fit

In this case;

[tex]x \to income[/tex]

[tex]y \to diameter[/tex]

When the x value (income) is known, we can simply plug in the value in the above equation to get the y value (diameter)

Answer:

11x -8y = -9

Step-by-step explanation:

8x-4y=-4

-3x+4y=5

Subtract the second equation from the first

8x-4y=-4

-(-3x+4y=5)

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

Distribute the minus sign

  8x-4y=-4

+(3x-4y=-5)

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

11x -8y = -9

Answer:

the answer is B & F

Answer:

New price =$6.60

Step-by-step explanation:

[tex]deduction \ percent = 45\% \\\\dedecution \ price = \frac{45}{100} \times12 = \$5.40\\\\\ Therefore , cost \ of \ toy \after \ deduction = 12 - 5 .40= \$ 6.60[/tex]

Hello there I hope you are having an great day :) A toy has an original price of $12. Find the new price after 45% decrease,

Find the original price - $12

Get the the discount percentage - 45%

Calculate the savings: 45% of $12 = 3.73

Subtract the savings from the original price to get the sale price: $12 - $3.73 = £8.27

Original Price = Sale Price / ( 1 - Percent Off / 100 ) = 21.8182 that would b the answer :)

Answer: im sorry but there is nothing here to help? may you add a picture? or something file maybe?

Step-by-step explanation:

Answer:

-53

Step-by-step explanation:

You start off with the g of x equation

then you substitute -5 for the x value

after you solve that, you should get g of  x = 23

then you take the f of x equation and plug 23 in for x

then you simplify that and you should end up with an answer of -53

Step-by-step explanation:

i just need points so i can ask my questions

Answer:

#1 I believe the answer is 4 and for 2 I believe the answers are 3&4

Answer:

C

Step-by-step explanation:

S(6)= -2(1-(-3)^6)/1-(-3)

Answer: 0.1595

Step-by-step explanation:

Poisson Distribution Formula

[tex]$$P(\mathrm{X}=x)=\dfrac{\lambda^{x} e^{-\lambda}}{x !}$$\\\text{ where }$x=0,1,2,3, \ldots$\\\\$\lambda=$ mean number of occurrences in the interval\\\\$e=$ Euler's constant $\approx 2.71828$[/tex]

Here, [tex]\lambda= 6.3[/tex]

x= 6

[tex]P(X=6)=\frac{6.3^6e^{-6.3}}{6!}[/tex]

[tex]\approx0.1595[/tex]

Hence, the probability of having exactly six (6) errors on a page = 0.1595

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

Work Shown:

Here are the variables we're working with

In this case, we know that

We can use this formula to help find the answer

S = (n/2)*(a+b)

This formula only works for arithmetic sequences

So,

S = (n/2)*(a+b)

42 = (14/2)*(a+(-12))

42 = 7(a-12)

42/7 = a-12

6 = a-12

6+12 = a

18 = a

a = 18 is the first term of this arithmetic sequence

That's why the answer is choice D.

-----------

Side note: your book or your teacher may use the notation [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex] but I figured it would be easier to use 'a' and b in place of [tex]a_1[/tex] and [tex]a_n[/tex] respectively.

Answer:

No solution exists

Step-by-step explanation:

x - 1 < 2x + 2 < 2x + 1

examine the center and right terms

2x + 2 < 2x + 1

Subtract 2x from both sides

2 < 1      

This is False. Therefor

No solution exists

Answer:

6x + 27y = -6

Step-by-step explanation:

i looked it up sooo sorry if its wrong lol

Answer:

g(x)= ((x+4)^2) -2

Step-by-step explanation:

...............

Answer:

Step-by-step explanation:

Answer:  -157,464

Step-by-step explanation:

an=a^1*r^n-1

a10=8*-3^10-1

a10=8*-3^9

a10=8*-19683

a10=-157464

Answer:

a10 = -157,464

Step-by-step explanation:

a1 = 8

a2 = -24

r = a2/a1 = -3

an = a1 × r^(n - 1)

a10 = a1 × (-3)^(10 - 1)

a10 = 8 × (-3)^(9)

a10 = -157,464

Answer:

n = 20

Step-by-step explanation:

[tex]\frac{16}{40} = \frac{8}{n}[/tex]

Cross multiplication would result in:

16 * n = 8 * 40

16n = 320

n = 320 / 16

n = 20

Therefore the value of "n" in this proportion is 20.

Hope this helps!