Algebra nation section 2

Answer:

x=-2

Step-by-step explanation:

Carry over the 5 to the other side of the equal sign and do its reverse. So 3-5=-2 which means x is equal to -2.

Answer:

x=-2,x=-8

Step-by-step explanation:

Answer: 11

Steps

1. 100-15=85

2. 85/8=10.625

3. 10.625 rounds up to 11

Final answer:

Terry needs to buy at least 11 boxes of candles to meet her requirement of having at least 100 candles, as she must purchase whole boxes and not a fraction of a box.

Explanation:

Terry has 15 candles and needs a total of at least 100 candles. To find the least number of boxes she needs to buy, we should first find out how many more candles are required to reach a minimum of 100 candles:

100 - 15 = 85 candles needed.

Next, we calculate how many boxes of 8 candles this equates to by dividing the number needed by the number of candles per box:

85 ÷ 8 = 10.625.

Since Terry cannot buy a fraction of a box, we round up to the nearest whole number, which gives us 11 boxes.

Therefore, the least number of boxes Terry needs to buy is 11 to acquire at least 100 candles.

Answer:

The answer in one common tangent only ⇒ answer (B)

Step-by-step explanation:

∵ The two circles touch internally in a common point

* At this point we can draw only one tangent

∵ This point is common in the two circles

∴ The tangent will be common for the two circles

∴ There is only one common tangent can be draw passing

   through the common point which the two circles

   touch each other on it

∴ The answer is (B)

Answer:

[tex]f(x)=x^3+x^2-4x-4[/tex]

Step-by-step explanation:

From the graph, the x-intercepts are;

[tex]x=-2[/tex]

[tex]x=-1[/tex]

[tex]x=2[/tex]

These are root of the polynomial function represented by the given graph.

By the remainder theorem;

[tex]f(-2)=0,f(-1)=0,f(2)=0[/tex]

According to the factor theorem, if [tex](x-a)[/tex] is a factor of [tex]f(x)[/tex], then [tex]f(a)=0[/tex]

This implies that;

[tex](x+2),(x+1),(x-2)[/tex] are factors of the required function.

Hence; [tex]f(x)=(x+1)(x-2)(x+2)[/tex]

We expand using difference of two squares to obtain;

[tex]f(x)=(x+1)(x^2-4)[/tex]

We expand using the distributive property to get;

[tex]f(x)=x^3-4x+x^2-4[/tex]

Rewrite in standard form to obtain;

[tex]f(x)=x^3+x^2-4x-4[/tex]

Answer:

Choice A: f(x) = x^3 + x^2 − 4x − 4

Step-by-step explanation:

Here's a great and simple answer.

Ok first we need to take the x intercepts to solve.

If we look at the graph we see the x ints are -2,+1 and +2.

To solve we need to put them into factor form

= (x-2) (x+2) and (x+1)

Simplify: (x-2) (x+2) = (x^2-4) and (x+1)

Now we take (x^2-4) and (x+1) and multiply them to find our answer

(x^2-4) (x+1)

= x^2(x) and x^2(1) = x^3 and x^2.

now the other: -4(x) and -4(+1) = -4x and -4

We have nothing common here so we just join them

= x^3 + x^2 - 4x - 4, and that is the same as choice A.

Answer:

Multiply the length times width:

30 1/2 x 9 1/3= 284.6

Hence, the area of the rectangular space is:

                          284.6667 square yards.

It is given that the length(l) of the rectangular space is: [tex]30\frac{1}{2}\ yard[/tex] .

which in improper fraction is: [tex]\dfrac{61}{2}\ yard[/tex]

Similarly, the width(b) of the rectangular space is: [tex]9\frac{1}{3}\ yard[/tex]

which in improper fraction is: [tex]\dfrac{28}{3}\ yard[/tex]

As we know that the area of the rectangular space is calculated as:

[tex]Area=l\times b\\\\\\Area=\dfrac{61}{2}\times \dfrac{28}{3}\ \text{square\ yards}\\\\\\Area=284.6667\ \text{square\ yards}[/tex]

 Hence, Area is: 284.6667 square yards.

Answer:

(-6,3)

Step-by-step explanation:

Answer:

the image point is(-6,3)

Step-by-step explanation:

HOPE THIS HELPS

add the 32+0.05 to find the n

Answer: 32 liters

Step-by-step explanation:

W(0)= 32 so the glass tanks volume is 32

Answer:

8

Step-by-step explanation: i got it wrong and it tole me the answer.

Answer: D: 8

Step-by-step explanation:

Happy cheating

I think the first part is 466

The correct answer is 4.66 ×10^8, consider what I said on the last question

Answer:

4*4*4 = 4³

Step-by-step explanation:

Claire has 4 stamps.

Julia has 4 times as many as Claire or 4*4 = 4².

Damon has 4 times as many as Julia or 4*4*4 = 4³

Answer:

22/45

Step-by-step explanation:

Let A be the event of drawing a multiple of 2,  

So,  

p(A)=  23/45

Now, let A' be the opposite(complementary) event which means not drawing a multiple of 2

From the properties of probability, the sum of an event’s probability and its opposite(complementary) event’s probability is equal to 1.

p(A)+p(A')=1

We have to find the probability of not drawing a multiple of two i.e. p(A')

p(A')=1-p(A)

=1 - 23/45

=  (45-23)/45

=22/45

So the probability of not drawing a multiple of 2 from the hat is 22/45.

Final answer:

The probability of not drawing a multiple of two from the numbers 30 to 74, given the probability of drawing a multiple of two is 23/45, is computed by subtracting 23/45 from 1, resulting in a probability of 22/45.

Explanation:

The probability of not drawing a multiple of two is simply calculated by subtracting the probability of drawing a multiple of two from 1, as these probabilities are complementary.

Given that the probability of drawing a multiple of 2 is 23/45, we can find the probability of not drawing a multiple of two by doing the following:

1 - (probability of drawing a multiple of 2) = 1 - (23/45) = 22/45.

Therefore, the probability of not drawing a multiple of two is 22/45.

Answer:

The answer is D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The given circle has diameter  [tex]8\frac{3}{5}[/tex].

We can write as a decimal to obtain;

[tex]8\frac{3}{5}=8.6[/tex]

On the number line 8.6 is between 8 and 9 but closer to 9.

From the graph the correct answer is D

The 7th term in the geometric sequence with a first term of 5 and a common ratio of 2 is found using the formula for the nth term of a geometric sequence. The 7th term is calculated to be 320.

The student has asked to determine the 7th term in a geometric sequence whose first term is 5 and whose common ratio is 2. To find this, we can use the formula for the nth term of a geometric sequence, which is an = a1  times rⁿ⁻¹, where a1 is the first term, r is the common ratio, and n is the term number.

To find the 7th term:

Identify that the first term (a1) is 5

The common ratio (r) is 2

Insert these values into the formula to get a7 = 5  times 2⁷⁻¹

Calculate the exponent: 2⁶ = 64

Multiply by the first term: 5  times 64 = 320

Therefore, the 7th term in the geometric sequence is 320.

Answer:

Step-by-step explanation:

11x+11

or you could do

11(x+1)

Answer:

8/15

Step-by-step explanation:

there are 8 pints of lemonade totally. These 8 pints are divided into 15 glasses in equal amounts.

So each glass contains 8/15 pints of lemonade.

Hope i helped you:)

Answer:

0.53 repeated 3

Step-by-step explanation:

Just do 8 divided by 15 and you get 0.53333333333, which is just 0.53 with a little slash over the top. Hope this helps :)

Answer:

use the formula A = 1/2ab(sin C)

Step-by-step explanation:

Answer:

D - 56.6 MPH is the faster

Step-by-step explanation:

Find the unit rate by dividing the miles by hours

A. 589/11 = 53.55 MPH

B. 360/7 = 51.43 MPH

C. 111/2 = 55.5 MPH

D. 283/5 = 56.6 MPH

After calculating the speed for each option by dividing the distance by time, option D is found to be the fastest with a speed of 56.6 mph.

To find out which rate is the fastest, we need to calculate the speed for each option by dividing the distance by the time.

The speed is the distance traveled per unit of time, typically expressed in miles per hour (mph).

Comparing the calculated speeds, option D is the fastest with a speed of 56.6 mph.

Step-by-step explanation:

h=8m

b=2m

we know,

A=b×h

=2m×8m

=16m²

Answer:

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

Step-by-step explanation:

[tex]y = a (x - h)^{2} + k[/tex]

Standard form: [tex]y = ax^{2} + bx = c[/tex]

Our vertex is: [tex]xvertex = - \frac{b}{2a} \\y = x^{2} - 6x + 7 ( STANDARD -  FORM)\\[/tex]

Finally we get [tex]y = (x - 3^{2}) - 2[/tex] as our answer.

Have an amazing day!

Answer: D. The Median and they should predict 58.5 inches.

Step-by-step explanation: Before we start, we want to use median. This is because there is an outlier, 72, and that would mess up the mean by a small yet noticeable margin.

Since the median picks both numbers 58.5 and 58.5, that means that the answer will be D. The Median and they should predict 58.5 inches.

Answer:

D The median and they should predict 58.5

Step-by-step explanation:

If you count from the outsides and go to the inside with a pencil or you're fingers then you get 58.5 :D

Find the GCF (Greatest Common Factor) of both numbers. It is 3.

Divide both numbers by the GCF.  

The simplest form is 1/3.

Answer:

[tex]\boxed{\bold{\frac{1}{3}}}[/tex]

Step-by-step explanation:

Simplify [tex]\bold{\frac{3}{9} }[/tex]

Find a number that goes into 3 and 9 evenly

Number: 3

Divide to simplify

3 ÷ 3 = 1

9 ÷ 3 = 3

Rewrite fraction

[tex]\bold{\frac{1}{3}}[/tex]

Regards,

             Mordancy

Answer:

-6x +10

Step-by-step explanation:

(-3+5) - (6x-8)

We cannot solve since there is no equals sign, we can only simplify

Combine the -3 and the 5 in the parentheses

(2) - (6x-8)

2  - (6x-8)

Distribute the minus sign

2 -6x +8

-6x +10

Answer:

  8

4 --

  11

Step-by-step explanation:

The gear ratio for the original gear system was 4/22. To get the 22 inch wheel to 26 inches, you have to multiply it by 26/22, so to keep the same ratio, you will also need to multiply 4 by 26/22. You get 104/22, which simplifies to 52/11 which simplified further to 4+8/11. You can check your answer by comparing the original ratio to the new ratio.

Using the principle of constant proportion, the new gear size for a bike with a 26-inch wheel while maintaining the original gear-to-wheel diameter ratio is approximately 4.73 inches.

The student asked about the gear size for a bike with a 26-inch wheel if the existing bike uses a 4-inch gear with a 22-inch wheel diameter, and the ratio of the gear size to the wheel diameter is constant.

To find the new gear size, we set up a proportion using the given gear and wheel sizes:

Cross-multiplying to solve for x gives us:

4 inches * 26 inches = 22 inches * x inches

104 = 22x

x = 104 / 22

x = 4.727272... inches

So, the new gear size would be approximately 4.73 inches if we maintain the same ratio for a bike with a 26-inch wheel.

In order to match each of the pairs you need to divide the numerator by the denominator to make it into a decimal.

Below are the pairs:

21/25 = 84%

13/20 = 65%

2/5 = 40%

3/4 = 75%

3/5 = 60%

21/25 = 84%

13/20 = 65%

2/5 = 40%

3/4 = 75%

3/5 = 60%

[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{xy}{2}=28\implies \stackrel{\textit{cross-multiplying}}{xy=56}\implies y=\cfrac{\stackrel{\stackrel{k}{\downarrow }}{56}}{x}[/tex]

The equation that represents an inverse variation with a constant of 56 is:

             Option: D

         D.   [tex]\dfrac{xy}{2}=28[/tex]                  

Inverse Variation--

It is a relationship between two variables such that it is given in the form that:

If x and y are two variables then they are said to be in inverse variation if there exist  a constant k such that:

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

i.e.

[tex]xy=k[/tex]

Here the constant of variation is 56

i.e. k=56

Hence, we have:

[tex]xy=56\\\\i.e.\\\\xy=28\times 2\\\\i.e.\\\\\dfrac{xy}{2}=28[/tex]

              Hence, option: D is the correct answer.

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ The formula for area of a trapezoid is a+b/2*h

a=3

b=8

h=4

3+8=11

11/2=5.5

5.5*4=22

Final answer:

The area of the trapezoid is 22 square inches

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

TROLLER

♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫

➷ The formula for area of a trapezoid

The area of the trapezoid is 22 square inches is a+b/2*h

a=3, b=8, h=4

3+8=11

11/2=5.5

5.5*4=22

✽

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

DOGE

Verify the identity:

[tex]csc^3x-csc^2x-cscx+1\qquad =cot^2x(cscx-1)\\\\csc^2x(cscx-1)-1(cscx-1) =\quad \downarrow\\\\(csc^2x-1)(cscx-1)\quad \qquad \ =\quad \downarrow\\\\\bigg(\dfrac{1}{sin^2x}-\dfrac{sin^2x}{sin^2x}\bigg)(cscx-1)\ =\quad \downarrow\\\\\\\bigg(\dfrac{1-sin^2x}{sin^2x}\bigg)(cscx-1)\qquad \ =\quad \downarrow\\\\\\\bigg(\dfrac{cos^2x}{sin^2x}\bigg)(cscx-1)\qquad \qquad =\quad \downarrow\\\\\\cot^2x(cscx-1)\qquad \qquad \qquad =cot^2x(cscx-1)\qquad \checkmark[/tex]

Sorry, I messed up. So I changed it.

Answer: is there a picture or something like that?

Step-by-step explanation:  

Answer:

The correct answer is 5

Step-by-step explanation:

To find this, start by multiplying them in any order. For ease, we'll multiply the first and last.

-2/3 * -3 = 2

Now we take that and multiply it by the remaining term.

2 * 2 1/2 = 5

The equation of the graph is y= -(x+3)^2 +1

Choice A is the correct answer

The equation of the given graph is:

            [tex]y=-(x-3)^2+1[/tex]

We know that the general equation of a downward parabola with vertex at (h,k) is given by the formula:

      [tex]y=a(x-h)^2+k[/tex]

where a<0

Here in each of the options we have a= 1 or -1

but as a has to be less than 1 this means that a= -1

Also, we have: (h,k)= (3,1)

i.e. h=3 and k=1

Hence, putting the values of h,k and a in the general equation we get:

      Hence, the equation of parabola is:

       [tex]y=-(x-3)^2+1[/tex]