Solve the equation. leave your answer in exact form. 4^(x-3)=13

Answer:

b

Step-by-step explanation:

Answer:

2x² - 4x

Step-by-step explanation:

Subtract the known binomial from the sum to obtain the other binomial

5x² - 6x - (3x² - 2x)

= 5x² - 6x - 3x² + 2x

= 2x² - 4x ← the other binomial

Answer:

C

Step-by-step explanation:

First, write 4 ½ in improper form.  2 × 4 + 1 = 9. So the fraction is 9/2.

Now divide:

9/2 ÷ 1/3

To divide by a fraction, multiply by the reciprocal:

9/2 × 3/1

27/2

13 1/2

Answer C.

Answer:

818.4 in²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of circle - ( area of white sector + area of triangle )

  = ( π × 27.8²) - (π × 27.8² × [tex]\frac{210}{360}[/tex] +(0.5 × 27.8 ×27.8 × sin150°)

  = 2427.95 - (1416.30 + 193.21 )

  = 2427.95 - 1609.51 ≈ 818.4 in²

Answer:

y - 3 = a(x + 1)^2

Step-by-step explanation:

The vertex equation of a vertical parabola is:

y - k = a(x - h)^2.

If the vertex is at (-1, 3), then the equation becomes:

y - 3 = a(x + 1)^2, where a is a constant.

Next time, would you please share the answer choices.  Thank you.

Answer:

Step-by-step explanation:

all parabola have equation : y = a(x +1)²+3   a in R

the answer is 11.

use BEDMAS, and calculate the equation inside the brackets (answer to that is 44/15)

then divide it by 4/15 and you get 11

let's firstly convert the mixed fractions to improper fractions and proceed.

[tex]\bf \stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}}~\hfill \stackrel{mixed}{1\frac{2}{5}}\implies \cfrac{1\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{7}{5}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \stackrel{\textit{recall that by PEMDAS, parenthesis first}~\hfill }{\left(\cfrac{13}{3}-\cfrac{7}{5} \right)\div \cfrac{4}{15}\implies \left(\stackrel{\textit{using an LCD of 15}}{\cfrac{(5)13-(3)7}{15}} \right)\div \cfrac{4}{15}\implies \left(\cfrac{65-21}{15} \right)\div \cfrac{4}{15}} \\\\\\ \left(\cfrac{44}{15}\right)\div \cfrac{4}{15}\implies \cfrac{44}{15}\times \cfrac{15}{4}\implies \cfrac{44}{4}\cdot \cfrac{15}{15}\implies 11\cdot 1\implies 11[/tex]

A. 272 1/4 ft

B. 68 5/8 ft

Hope this helps!

Shannon and Leslie need to carpet 272.25 square feet in a room with an entertainment system that takes up 12.25 square feet. Therefore, they need to buy 12.25 square feet of carpet.

Shannon and Leslie are planning to carpet a square room that measures 16.5 feet by 16.5 feet. However, they need to account for an entertainment system that juts out into the room, taking up 3.5 feet by 3.5 feet of space.

A. Area of the space with no carpet:

To determine the area of the space with no carpet, we first calculate the area of the entertainment system:

Area of entertainment system = 3.5 feet * 3.5 feet = 12.25 square feet

Next, we subtract the area of the entertainment system from the total area of the room:

Total area of room - area of entertainment system = area of space with no carpet

272.25 square feet - 12.25 square feet = 260 square feet

Therefore, the area of the space with no carpet is 260 square feet.

B. Carpet needed for the room:

To calculate the amount of carpet Shannon and Leslie need to buy, we simply subtract the area of the space with no carpet from the total area of the room:

Total area of room - area of space with no carpet = area of carpet needed

272.25 square feet - 260 square feet = 12.25 square feet

Shannon and Leslie need to buy 12.25 square feet of carpet.

Answer:

y-intercept = (0,2).

Step-by-step explanation:

We have been given a table of the function g(x) as shown below:

x g(x)

0 2

1 6

2 10

Using that table we need to find about what is the y-intercept of the given function g(x).

By definition of y-intercept, we know that, y-intercept is the y-value or function value of g(x) value when x=0.

From table we see that g(x)=2 when x=0.

So the y-intercept = 2.

In point form we can write y-intercept as (0,2).

The answer would be....:B.90 ML

The volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

The weight of the cat is 8 lbs. Therefore, the weight of the cat in kg will be,

Weight of cat = 8 lbs = (8×0.454) kgs = 3.632 kgs

Since for one kg, the recommended dose is 5 mg, therefore, the recommended dose for the cat will be,

Recommended dose for cat = 3.632kg × 5 = 18.16 mg

Now, as given that one ml of solution contains 2mg of drugs, therefore,

1 ml = 2mg

1 mg = 1/2 ml

18.16 mg = 18.16 × 1/2 = 9.08ml ≈ 9 ml

Hence, the volume of the solution should be given to a cat that weighs 8 lbs. is 9 ml. Thus, the correct option is D.

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Answer: [tex]-x^2-x+9[/tex]

Step-by-step explanation:

To simplify the given polynomial [tex]2x^2+6x-7x+8-3x^2+1[/tex] we need to add the like terms. Then we get:

[tex]2x^2+6x-7x+8-3x^2+1=(2x^2-3x^2)+(6x-7x)+(8+1)=-x^2-x+9[/tex]

Therefore, we get that the polynomial simplified is:

[tex]-x^2-x+9[/tex]

Which is a trinomial ( A polynomial that has three terms) of degree 2 (Because the highest exponent is 2).

Answer:

Final answer is [tex]-x^2-x+9[/tex].

Step-by-step explanation:

Given polynomial is [tex]2x^2+6x-7x+8-3x^2+1[/tex].

Now we need to simplify the given polynomial so we can begin with combining like terms.

[tex]2x^2+6x-7x+8-3x^2+1[/tex]

[tex]=2x^2-3x^2+6x-7x+8+1[/tex]

[tex]=(2-3)x^2+(6-7)x+(8+1)[/tex]

[tex]=(-1)x^2+(-1)x+(9)[/tex]

[tex]=-x^2-x+9[/tex]

Hence final answer is [tex]-x^2-x+9[/tex].

Answer:

C

Step-by-step explanation:

A geometric series will only converge if - 1 < r < 1

sum to infinity = [tex]\frac{a}{1-r}[/tex]

The nth term formula for a geometric series is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

The only summation with - 1 < r < 1 is C where r = - 0.2

Answer:  The correct option is

(C) [tex]\sum_{n=1}^{\infty}4(-0.2)^{n-1}.[/tex]

Step-by-step explanation:  We are give to select the geometric series that converges.

We know that

the general (n-th) term of a common geometric series is given by

[tex]a_n=ar^{n-1}.[/tex]

And the series converges if the modulus of the common ratio is less than 1, .e., |r| < 1.

Now, for the first infinite geometric series, we have

[tex]a_n=\dfrac{2}{3}(-3)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-3~~~\Rightarrow |r|=3>1.[/tex]

That is, the series will not converge. Option (A) is incorrect.

For the second geometric series, we have

[tex]a_n=5(-1)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-1~~~\Rightarrow |r|=1.[/tex]

That is, the series will not converge. Option (B) is incorrect.

For the third geometric series, we have

[tex]a_n=4(-0.2)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-0.2~~~\Rightarrow |r|=0.2<1.[/tex]

That is, the series will CONVERGE. Option (C) is correct.

For the fourth geometric series, we have

[tex]a_n=0.6(-2)^{n-1}.[/tex]

So, the common ratio will be

[tex]r=-2~~~\Rightarrow |r|=2>1.[/tex]

That is, the series will not converge. Option (D) is incorrect.

Thus, (C) is the correct option.

Answer: Hm i'm pretty sure that is hunderdths...

Step-by-step explanation:

The place value of 5 in 6.857 is (1/100)th

A digit's numerical value as a result of its position in a number.

1st decimal place - (1/10)th

2nd decimal place - (1/100)th

3rd decimal place - (1/1000)th

In 6.857, 5 is lying at the second decimal position, hence has the place value of (1/100)th .

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Answer:

not arithmetic

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Given

[tex]T_{n}[/tex] = 2n² - 1

Substitute in n = 1, 2, 3, 4 to generate the first 4 terms of the sequence

[tex]T_{1}[/tex] = 2(1)² - 1 = 2 - 1 = 1

[tex]T_{2}[/tex] = 2(2)² - 1 = 8 - 1 = 7

[tex]T_{3}[/tex] = 2(3)² - 1 = 18 - 1 = 17

[tex]T_{4}[/tex] = 2(4)² - 1 = 32 - 1 = 31

check the difference between consecutive terms

7 - 1 = 6

17 - 7 = 10

31 - 17 = 14

The differences are not common hence not an arithmetic sequence

Answer:

Step-by-step explanation:

The volume of a cone is

V = (1/3) * pi * r^2 * h

pi = 3.14

r = 3

h = 8

V = 1/3 * 3.14 * 3^2 * 8

V = 1/3 * 3.14 * 9 * 8

V = 75.36

V = 75.4

Answer:

y = 4 cosx

Step-by-step explanation:

The standard form of cosine is

y = acos(bx)

where amplitude = | a |

with maximum value a and minimum value - a

The only expression in this form is

y = 4cosx

Answer:

y = 4 cosx

Step-by-step explanation:

Answer: 26

Step-by-step explanation:

Add all together and the subtract by 12434.7 and you get 26 hope this helps!

The probability that Craig will get a green gumdrop and a piece of butterscotch candy is 4/25.

To find the probability that Craig will get a green gumdrop and a piece of butterscotch candy, we need to calculate the probability of each event happening separately and then multiply those probabilities together.

There are 5 gumdrops in the first jar with 4 being green, so the probability of choosing a green gumdrop is 4/5. In the other jar, there are 5 pieces of candy with 1 being butterscotch, so the probability of choosing a butterscotch candy is 1/5. Multiplying these probabilities together gives us 4/5 × 1/5 = 4/25.

Answer:0.139 moles

Step-by-step explanation:

moles =[tex]\frac{mass}{Mr}[/tex]

NOTE: molecular mass of silver is 107.8682

n= [tex]\frac{15}{107.8682}[/tex]

this will give you the final answer of

n= 0.139 moles OR 0.14 moles

Final answer:

To find the number of moles in 15 grams of silver, divide the mass by the molar mass of silver (107.87 g/mol). The result is approximately 0.139 moles of silver.

Explanation:

To find the number of moles in 15 grams of silver, we can use the molar mass of silver. First, the molar mass of silver (Ag) is 107.87 grams per mole, which is the mass of one mole of silver.

We can calculate the number of moles of silver using the formula:

Number of moles = Mass of the substance (in grams) / Molar mass of the substance (in grams per mole)

So, for silver:

Number of moles = 15 grams / 107.87 grams/mole

When we perform this calculation:

Number of moles = 0.139 moles (rounded to three decimal places)

Therefore, there are approximately 0.139 moles of silver in 15 grams of the metal.

Answer:

C. or D. I would say D though.

Step-by-step explanation:

All you have to do is look at the total with both children and adults, then you can take that and divide it by the total of either children or adults and then you would get the answer D.

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A_\triangle=\dfrac{1}{2}ab\sin\theta[/tex]

a, b - adjacent sides

θ - included angle

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

7.

a = 9in, b = 14in, θ = 85°

sin85° ≈ 0.9962

Substitute:

[tex]A_\triangle=\dfrac{1}{2}(9)(14)\sin85^o=\dfrac{1}{2}(126)(0.9962)\approx62.8 in^2[/tex]

8.

a = 12 in, b = 5 in, θ = 135°

sin135° = sin(180° - 45°) = sin45° ≈ 0.7071   used sin(180° - x) = sin(x)

Substitute:

[tex]A_\triangle=\dfrac{1}{2}(12)(5)\sin135^o=\dfrac{1}{2}(60)(0.7071)\approx21.2\ in^2[/tex]

Answer:

[tex]\frac{27}{4}[/tex]

Step-by-step explanation:

To do this, we must find a common denominator for each of these. This means we must do this

[tex]6*\frac{4}{4} =\frac{24}{4}[/tex]

Next we can add them

[tex]\frac{24}{4} +\frac{3}{4} =\frac{27}{4}[/tex]

Answer:

Step-by-step explanation:

Starting with 6  3/4, we could write 5 + 1 + 3/4, or 5  7/4.

This 5  7/4 is identical to 6  3/4, but the fractional part 7/4 is larger than the fractional part 3/4.

Answer:

38.

Step-by-step explanation:

range is taking the highest number subtracting it by the smallest

Answer:

the answer is 38

Step-by-step explanation:

you subtract the biggest number with smallest number

Answer:

Option D. [tex]cos(54\°)=\frac{0.5s}{7}[/tex]

Step-by-step explanation:

we know that

A regular pentagon can be divided into 5 isosceles triangles

The length side of the legs of one isosceles triangle is equal to the radius

The vertex angle of one isosceles triangle is equal to 360/5=72 degrees

The base angle of one isosceles triangle is equal to 54 degrees

Let

s------> the length side of the regular pentagon

so

[tex]cos(54\°)=\frac{(s/2)}{r}[/tex]

substitute the given value

[tex]cos(54\°)=\frac{(s/2)}{7}[/tex]

[tex]cos(54\°)=\frac{0.5s}{7}[/tex]

Answer:

Line x is represented by the function f(x)=3x + 5

Step-by-step explanation:

f(x)=3x+5;   y -intercept = 5

When x = 0, y = 3(0) + 5 = 5

When x = - 2, y = 3(-2) + 5 = -1

So the coordinate points (0,5) and (-2, 1)

Look at the second line (x), it has the y-intercept at 5 and matching those 2 coordinate points above.

So answer is the second line (x)

Hello there! It is the second line, line X.

The equation asks which line is represented by the given equation, f(x)=3x+5. Well, since the equation is in y-intercept form, y = mx + b, we know m is the slope, so the slope is 3, and b is the y intercept, so they intercept is 5.

If any of the lines on the graph intersect at (0,5), or through the y axis at 5, they have a y intercept of 5 and could potentially be the correct answer. There is only one lune that does this, line x, making this the answer.

I hope this was helpful and have a great rest of your day!  

Answer:

1/4 , B

Step-by-step explanation:

This is because it is being kept on multiplying by 1/4 for each pattern.

Answer:

B) 1/4

Step-by-step explanation:

right on edu.

Answer:

-7

Step-by-step explanation:

When you divide a polynomial f(x) by (x-c), the remainder r will be f(c).  

hence you will get the remainder by putting the 2 as value of x:  

f(x) = -3x² + 7x - 9

f(2) = -3(2)² +7(2) - 9

      = -3(4) + 14 - 9

      = -12 + 5

remainder = -7

Final answer:

When substituting x with 2 in the polynomial -3x² + 7x - 9, you simply evaluate it directly. The calculation gives -3(2²) + 7(2) - 9, resulting in a remainder of -7.

Explanation:

To find the remainder when a polynomial is divided by a monomial like x - 2, you can use synthetic division. However, you have asked about the division of -3x² + 7x - 9 by 2, which is actually a simple polynomial evaluation, not a division problem. We will substitute x with 2 in the polynomial and find the remainder.

The polynomial is -3x² + 7x - 9. To find the remainder when we substitute x = 2, we evaluate the polynomial:

-3(2)2 + 7(2) - 9 = -3(4) + 14 - 9 = -12 + 14 - 9 = 2 - 9 = -7.

Therefore, the remainder when 2 is substituted into the polynomial -3x² + 7x - 9 is -7.

Answer:

Number: 4153

Step-by-step explanation:

4153 - 738 = 3415

as we know the resulting number starts with 3 and is a 4 digit number so we fix 4 in the thousands position of original number. Subsequently we fix 4 in the hundredth position of the number after subtraction from  738

4_ _ 3 - 738 = 34_ _

now we have a 2 empty spaces and 9 number to choose from, start from the lowest .

4 1 0 3 - 738 = 3365 , 4 has to be in the hundredth position

we increment the middle numbers by four and then by 1 until we get our answer

4 1 4 3 - 738 = 3 4 0 5

4 1 5 3 - 738 = 3 4 1 5  --------- Answer

The value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5) with an oblique asymptote at y = 3x + k is k = 41.

To find the value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5), where f(x) has an oblique asymptote at y = 3x + k, we need to determine the relationship between the numerator and denominator as x approaches infinity.

To do this, we can perform polynomial division. Divide the numerator (9x^2 + 37x + 41) by the denominator (3x + 5). The result should give us the oblique asymptote equation y = 3x + k.

Performing polynomial division:

3x + 5 ) 9x^2 + 37x + 41
- (9x^2 + 15x)
----------------------
22x + 41

The result of the division is 22x + 41.

Therefore, the oblique asymptote equation y = 3x + k becomes y = 22x + 41.

Comparing this equation to y = 3x + k, we can see that the value of k is 41.

So, the value of k in the equation f(x) = (9x^2 + 37x + 41) / (3x + 5) with an oblique asymptote at y = 3x + k is k = 41.

Answer:

The value of x is x

Step-by-step explanation:

Answer: x = 5

Step-by-step explanation: