Given the following system, what variable will eliminate?

Answer:

f(0) =4

f(6) =8

Step-by-step explanation:

f(0) = ?

We know 0 is less than 5 so we use  the first part of the step function

f(0) = 0+4

      = 4

f(6) = ?

 6 is between 5 and 7 so we use the second part of the step function

f(6) =8

Answer:

40 units²

Step-by-step explanation:

substitute the given values for s and h into the formula

SA = ( 2 × 2² ) + (4 × 2 × 4 ) = 8 + 32 = 40

Answer:

40 units²

Step-by-step explanation:

Given that the surface area for a rectangular prism with a square base is SA=2s2+4sh.

Where the values of the variables in the equation which are s and h are known, the area can be computed by the substitution of the known variables into the equation.

Hence where s = 2 and h = 4

SA = 2(2)² + 4(2)(4)

= 8 + 32

= 40 units²

The AAS corollary from geometry states that two triangles are congruent if two angles and the non-included side of one triangle are equal to the two angles and the non-included side of another triangle. Because of this, option C is the correct answer as it confirms that triangles VRT and STR have these equal parts.

The subject here is the Angle-Angle-Side (AAS) corollary in mathematics, specifically geometry. According to the AAS corollary, two triangles are congruent (identical in form) if two angles and the non-included side of one triangle are equal to the corresponding two angles and the non-included side of another triangle. Therefore, the set of relationships that confirm VRT and STR are congruent would be the one that shows that two angles and the non-included side in triangle VRT are equal to those in triangle STR.

Based on this, option C. SRT VTR and VT SR is the correct answer. It shows that angles SRT and VTR are equal (two angles) and sides VT and SR are equal (one side). Since the side (VT or SR) is not included between the two mentioned angles (SRT or VTR), this satisfies the conditions of the AAS corollary and can be used to show that triangles VRT and STR are congruent.

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-5 < 3 + m      subtract 3 from both sides

-5 - 3 < 3 - 3 + m

-8 < m → m > -8

Answer:

Step-by-step explanation:

-5 < 3 + m

-3   -3

- 8 < m --- m > -8

CHECKING:

-5 < 3 + 8

-5 < 11

This is a TRUE statement because -5 is less than 11.

Hope this helps you!!! :)

Answer:

A) buddy  = sadie + 14

B) buddy + sadie = 136

A) buddy -sadie = 14

Adding equations A & B

2 * buddy = 150

buddy = 75 pounds

sadie = 61 pounds

Step-by-step explanation:

If their total weight is 136 pounds, sadie weigh 61 pounds.

Let the weight of Sadie=x

Let the weight of Buddy=y

Hence:

y=x+14

Total weight= x +y=136 pounds

Formulate

14+2×x=136

x+x+14=136

2x=136-14

2x=122

Divide both side by 2x

x=122/2

x=61 pounds

Inconclusion If their total weight is 136 pounds, sadie weigh 61 pounds.

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Answer:

(III), (VI),(VII), (I), (IV)

Step-by-step explanation:

Solving the system of equations one by one by elimination method

(I) 2x+y=10

   x-3y= -2   ( multiply by 2)

we have unique solution

x=4, y=2

(II) 2x+y=10    (multiply by -3)

 -6x-3y= -2

No solution.

(III) x+2y=5   (multiply by 2)

    2x+y=4

Unique solution

x=1, y=2

(IV) 5x+ y= 33

     x=18-4y ---> x+4y=18    (multiply by 5)

Unique solution

x=6, y=3

(V) Y=13 -2x   ----> 2x+y=13     ( multiply by 4)

   8x + 4y =52

No solution

(VI) x+ 3y =5

    6x-y=11    (multiply by 3)

Unique solution

x=2, y=1

(VII) Y=10 + x    ----> -x+y=10   (multiply by 2)

      2x + 3y =45

Unique solution

x=3 , y=13

Values of x in increasing order= (III), (VI),(VII), (I), (IV)

Answer:

C) [tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{1}{x}  \ g(x) = x^2 + 2x -5[/tex]

To find (g-f)(x) , we need to calculate g(x) - f(x)

WE know f(x) = 1/x  and g(x) = x^2 + 2x -5

Plug in g(x) and f(x) and then subtract

[tex]g(x)-f(x)=x^2 + 2x -5- (\frac{1}{x})[/tex]

All are unlike terms so we cannot combine like terms

[tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]

In order to find (g - f)(x), you need to subtract f(x) from g(x). The correct subtraction results in the expression x^2+2x-5-1/x, corresponding with answer choice C.

The question asks you to calculate (g - f)(x) where f(x) = 1/x and g(x) = x^2 + 2x -5. This entails finding the difference between g(x) and f(x).

Firstly, write out g(x) and f(x):

Secondly, subtract f(x) from g(x):

g(x) - f(x) = (x^2 + 2x - 5) - (1/x)

This simplifies to: g(x) - f(x) = x^2 + 2x - 5 - 1/x

Therefore, the correct answer is C. x^2+2x-5-1/x

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Answer:

Write an inequality that represents the condition based on the number of liters of air and water.

35A+25W>1000

and the following inequality represents the condition based on the number of Joules of energy:

0.8A+1.3W<170

Step-by-step explanation:

Answer:

Step-by-step explanation:

I got it right on khan

Answer:

I think the answer is neither. Hope this helps.

Step-by-step explanation:

Answer:

The equation of this line is y - 3 = 4/7(x - 7)

Step-by-step explanation:

To find this, start with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the slope in for m and the two coordinates in for (x1, y1).

y - 3 = 4/7(x - 7)

Answer:

The machine uses 1575 meters of yarn per cardigan and uses 1500 meters per pullover.

Step-by-step explanation:

Let P be yarn needed by machine for each pullover and C be yarn needed by machine for each Cardigan.

We are told that the machine takes the same length of yarn to make 21 pullovers as to make 20 cardigans. We can represent this information as:

[tex]20C=21P...(1)[/tex]

The machine used a total of 457,500 meters of yarn to make 100 cardigans and 200 pullovers. We can represent this information as:

[tex]200P+100C=457,500...(2)[/tex]

Let us solve our system of equations using substitution method.

From equation (1) we will get,

[tex]C=\frac{21P}{20}[/tex]

Upon substituting this value in equation (2) we will get,

[tex]200P+100(\frac{21P}{20})=457,500[/tex]

[tex]200P+5*21P=457,500[/tex]

[tex]200P+105P=457,500[/tex]

[tex]305P=457,500[/tex]

[tex]P=\frac{457,500}{305}[/tex]

[tex]P=1500[/tex]

Therefore, the machine uses 1500 meters of yarn per pullover.

Upon substituting P=1500 in equation (1) we will get,

[tex]20C=21*1500[/tex]

[tex]20C=31,500[/tex]

[tex]C=\frac{31,500}{20}[/tex]

[tex]C=1575[/tex]

Therefore, machine uses 1575 meters of yarn per cardigan.

Answer:

1575 meters of yarn per cardigan

1500 meters per pullover

Step-by-step explanation:

Answer:

He earned 1800 reward points for 600 dollars

Step-by-step explanation:

Given the statement: Omar has a new credit card. He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points.

Unit rate are expressed as a quantity of 1, such as 3 feet per second or 4 miles per hour, they are called unit rates.

Earn  300 reward point for every 100 dollars.

⇒ unit rate per reward = [tex]\frac{100}{300}[/tex] dollars

we have to find how many dollars he earned for 1800 points.

[tex]Number of dollars = unit rate \times 1800[/tex]

                                 = [tex]\frac{100}{300} \times 1800 = 600[/tex]

Therefore, he earned 1800 reward points for 600 dollars

Answer:

$600 money Omar spends .

Step-by-step explanation:

As given

Omar has a new credit card.

He earns 300 reward points for every 100 dollars he spends.

i.e

300 reward points for every 100 dollars .

Let  us assume that the Omar earned 1800 reward points when he spends x money.

Than the equation becomes

[tex]x = \frac{1800\times 100}{300}[/tex]

[tex]x = \frac{1800}{3}[/tex]

x = $600

Therefore $600 money Omar spends .

Answer:

25 represents how much he makes per hour

Step-by-step explanation:

Answer:

[tex]\frac{7}{9}[/tex]

Step-by-step explanation:

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.  

The size of the sample space is the total number of possible outcomes  

The event space is the number of outcomes in the event you are interested in.  

so  

Let

x------> size of the event space

y-----> size of the sample space  

so

[tex]P=\frac{x}{y}[/tex]

step 1

Find the probability of selecting a literature book

we have

[tex]x=3[/tex]

[tex]y=3+4+2=9[/tex]

substitute

[tex]P=\frac{3}{9}[/tex]

step 2

Find the probability of selecting an algebra book

we have

[tex]x=4[/tex]

[tex]y=3+4+2=9[/tex]

substitute

[tex]P=\frac{4}{9}[/tex]

step 3

Find the probability of selecting a literature book or an algebra book

Adds the probability of selecting a literature book plus the probability of selecting an algebra book

[tex]P=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}[/tex]

Answer:

Step-by-step explanation:

Is it mutually exclusive?

Answer:

You only have 30 more minutes

Step-by-step explanation:

Answer:

75% voted

Step-by-step explanation:

you add the 75 to 19 to figure out the total amount of people in the club.

75+19=76

Then you divide the people who voted which is 57 by the total amount of people in the club which is 76

57/76=0.75

then you move the decimal two places to the left and you get 75%

Answer:

either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.

Step-by-step explanation:

Answer: [tex]\frac{4}{15}[/tex]

Step-by-step explanation:

Given: Number of blue marbles = 8

Number of red marbles = 7

Total number of  marbles = 8+7=15

Now, the probability that she first pulls a blue marble is given by :-

[tex]P(B)=\frac{\text{blue marbles}}{\text{Total marbles}}\\\\=\frac{8}{15}[/tex]

Now, total marbles left in bag = 15-1=14

Now, the probability that she second pulls a red marble is given by :-

[tex]P(B)=\frac{\text{red marbles}}{\text{Total marbles left}}\\\\=\frac{7}{14}=\frac{1}{2}[/tex]

Thus, the probability that she first pulls a blue marble and then a red marble is given by :-

[tex]P(B)\timesP(R)=\frac{8}{15}\times\frac{1}{2}=\frac{4}{15}[/tex]

Answer:

7.8 hours.

Step-by-step explanation:

We have been given that Willis drove 239.82 miles in 4.2 hours at a constant speed.

First of all let us find out speed at which Willis traveled 239.82 miles using speed formula.

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Speed}=\frac{239.82\text{ miles}}{4.2\text{ hours}}[/tex]

[tex]\text{Speed}=57.1\frac{\text{ miles}}{\text{ hour}}[/tex]

Now let us find time taken by Willis to cover a distance of 445.38 miles.

[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]

[tex]\text{Time}=\frac{445.38\text{ miles}}{57.1\frac{\text{ miles}}{\text{ hour}}}[/tex]

[tex]\text{Time}=\frac{445.38\text{ miles}}{57.1}\times\frac{\text{hour}}{\text{ miles}}}[/tex]

[tex]\text{Time}=\frac{445.38}{57.1}\times\text{hour}[/tex]

[tex]\text{Time}=7.8\text{ hour}[/tex]

Therefore, it will take Willis 7.8 hours to drive 445.38 miles at the same speed.

Answer:

B.) 28%

Step-by-step explanation:

There are 50 total spins so far and 28% of them have been 4's. So that is the probability.

Answer:

43680 different arrangements are possible.

Step-by-step explanation:

The total number of horses are :16

We have to find different arrangement of four horses

Since, we have to find arrangements means we will use permutation

So, the required arrangement will be:

[tex]^{16}P_4[/tex]

Now, using: [tex]^{n}P_r=\frac{n!}{(n-r)!}[/tex]

Here, n= 16 and r=4 on substituting the values we get:

[tex]^{16}P_4=\frac{16!}{(16-4)!}[/tex]

[tex]\Rightarrow \frac{16!}{12!}[/tex]

[tex]\Rightarrow \frac{16\cdot 15\cdot 14\cdot 13\cdot 12!}{12!}[/tex]

Cancel out the common term that is 12! we get:

[tex]16\cdot 15\cdot 14\cdot 13[/tex]

After simplification we get: 43680

Hence, 43680 different arrangements are possible.

Answer:

heptagon

Step-by-step explanation:

This polygon has 7 sides

heptagon is a seven sided polygon

decagon is a ten sided polygon

dodecagon is a 12 sided polygon

hexagon is a six sided polygon

Answer:

Yes they can be

Answer:

4b^3 + 10b^2 - 32b + 15

___________________

             2(2b - 3)

Step-by-step explanation:

Take out the greatest common factor of (4b - 6) which is 2 and 3.

Answer:

-30

Step-by-step explanation:

-18x1 - 4x3 = -18-12= -30

Answer:

c) Length = 12, width = 8 and height = 23.

Step-by-step explanation:

Let the length be x, then the width = x - 4 and the height = 2x - 1.

a) The polynomial is x(x - 4)(2x - 1)

b) x(x - 4)(2x - 1) = 2208

c) x(x - 4)(2x - 1) - 2280 = 0

2x^3 - 9x^2 + 4x - 2280 = 0

I'll use graphical software to find a solution for this. Its easily obtained online.

There is one real root and its x = 12.

So the dimensions of the box are L = 12, W = 8 and H = 23 inches.

Answer:

a) V(l)=2l³-9l²+4l

b) 2208=2l³-9l²+4l

c) 12in × 8in × 23in

Step-by-step explanation:

Got a 100% on edge 2020

In reference to the image below, the trigonometric ratio cos  [tex]\alpha[/tex]° is calculated by dividing the base by the hypotenuse, thus making part c) 15 ÷ 17 the correct option.

The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.

In the given question, the trigonometric ratio cos is given by dividing the base of the triangle to the hypotenuse.

In any question,

hypotenuse = side opposite of the right angle = 17

base  = side adjacent to the acute angled marked =  15

Thus giving the value of cos [tex]\alpha[/tex]° as 15 ÷ 17.

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The complete question is given below:

A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as  [tex]\alpha[/tex] degrees.

What is the value of cos [tex]\alpha[/tex]°?

a. 8 ÷ 17

b. 17 ÷ 8

c. 15 ÷ 17

d. 8 ÷ 15

The figure of triangle is given below:

Answer:

y=6

Step-by-step explanation:

I took the test and got 100%