3) A particular motorcycle is 9 ft long. A
model of it was built with a scale of 1 in :3
ft. How long is the model?

Answer:

71, 72, 73

Step-by-step explanation:

So we want to find three consecutive integers that equal 216.

Let the first integer be n.

Then the second integer is n+1, and the third integer is n+2.

Thus:

[tex]n+(n+1)+(n+2)=216[/tex]

Combine like terms:

[tex]3n+3=216[/tex]

Subtract 3 from both sides:

[tex]3n=213\\[/tex]

Divide 3 from both sides:

[tex]n=71[/tex]

So, the first term is 71.

And the other two is 72 and 73.

And we are done :)

Answer:

1) 1

2) (2,3)

3) x⁴

Step-by-step explanation:

1)

We have the expression:

[tex]7x+1[/tex]

The degree of an equation is the largest exponent of the equation.

We can rewrite our expression as:

[tex]=7x^1+1x^0[/tex]

1 is the largest exponent.

Thus, our degree is 1.

2)

We have the system of equations:

[tex]x+y=5\\3x-y=3[/tex]

To solve, we can use substitution.

From the first equation, subtract x from both sides:

[tex]y=5-x[/tex]

Substitute this into the second equation:

[tex]3x-(5-x)=3[/tex]

Simplify:

[tex]3x-5+x=3[/tex]

Add 5 to both sides:

[tex]3x+x=8[/tex]

Combine like terms:

[tex]4x=8[/tex]

Divide both sides by 4:

[tex]x=2[/tex]

So, x is 2.

Substitute this back into the first equation:

[tex]x+y=5[/tex]

Substitute x for 2:

[tex]2+y=5[/tex]

Subtract 2 from both sides:

[tex]y=3[/tex]

Our solution is (2,3)

3)

We have the expression:

[tex]\frac{x^4}{x^0}[/tex]

Anything to the zeroth power (except for 0) is 1. Assuming x is not 0:

[tex]=x^4/1\\=x^4[/tex]

And that's the simplest it can get.

Answer:

[tex]\Huge \boxed{\mathrm{1. \ 1}} \\ \\ \\ \Huge \boxed{\mathrm{2. \ (2,3)}} \\\\\\ \Huge \boxed{{3. \ x^4 }}[/tex]

Step-by-step explanation:

The degree is the largest exponent on the variable.

[tex]7x^1 + 1x^0[/tex]

The largest exponent on the variable is 1.

The degree is 1.

System of equations:

[tex]x+y=5 \\ \\ 3x-y=3[/tex]

Solving y for the first equation.

Subtracting x from both sides.

[tex]y=5-x[/tex]

Substitution method.

[tex]3x-(5-x)=3[/tex]

Distribute negative sign.

[tex]3x-5+x=3[/tex]

Combining like terms.

[tex]4x-5=3[/tex]

Adding 5 to both sides.

[tex]4x=8[/tex]

Dividing both sides by 4.

[tex]x=2[/tex]

Substitution method.

[tex]y=5-2 \\ \\ \\ y=3[/tex]

[tex]\displaystyle \frac{x^4 }{x^0 }[/tex]

Subtract exponents with same bases when dividing.

[tex]x^{4-0}[/tex]

[tex]x^4[/tex]

Answer:

15 + 2.05 x = 2.35 x

Step-by-step explanation:

Let x be the number of gallons you would have to buy for the two places to be the same.

At the club, there is a monthly fee of $15 that is charged once in a month. They also charge $2.05 per gallon, which is charged every gallon of gas you buy.

We can write an expression: 15 + 2.05 x

At the gas station, they charge $2.35 per gallon with no other fees.

We can also write an expression: 2.35 x

For the prices to be the same, we have 15 + 2.05 x = 2.35 x

If we were to solve, then we have:

(2.35 - 2.05) x = 15

x = 15 / 0.3 = 50 gallons

Answer:

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Step-by-step explanation:

Let be [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex], the first and second derivatives of the function are, respectively:

[tex]f'=54-6\cdot x^{2}[/tex]

[tex]f''=-12\cdot x[/tex]

Now, let equalize the first derivative to zero and solve the resulting expression:

[tex]54-6\cdot x^{2} = 0[/tex]

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

[tex]x =\pm 3[/tex]

According to the given interval, only [tex]x=3[/tex] is a valid outcome. Lastly, this is evaluated in the second derivative expression:

[tex]f''=-12\cdot(3)[/tex]

[tex]f'' = -36[/tex]

[tex]x = 3[/tex] leads to an absolute maximum.

[tex]f(3) = 5 + 54\cdot (3) -2\cdot (3)^{3}[/tex]

[tex]f(3) = 113[/tex]

The absolute minimum is determined by evaluating at each extreme of the interval:

[tex]x = 0[/tex]

[tex]f(0) = 5 + 54\cdot (0) -2\cdot (0)^{3}[/tex]

[tex]f(0) = 5[/tex]

[tex]x = 4[/tex]

[tex]f(4) = 5 + 54\cdot (4) -2\cdot (4)^{3}[/tex]

[tex]f(4) = 93[/tex]

The absolute maximum and minimum of [tex]f(x) = 5 + 54\cdot x -2\cdot x^{3}[/tex] on [tex][0,4][/tex] are 113 and 5.

Answer:

x² + xy - 6y²

Step-by-step explanation:

FOIL

(x+3y)(x-2y)

F= x²

O= -2xy

I= 3xy

L= -6y²

Add these together = x² + xy - 6y²

Step-by-step explanation:

Hey, there!

Let me simply clear you.

While multiplying algebraic expression, you must be very careful about sign and brackets.

Here,

[tex](x + 3y)(x - 2y)[/tex]

Let's multiply (x-2y) by (x+3y)

[tex] = x(x - 2y) + 3y(x - 2y)[/tex]

[tex] = ({x}^{2} - 2xy) + (3xy - 6 {y}^{2}) [/tex]

Open brackets.

[tex] = {x}^{2} - 2xy + 3xy - 6 {y}^{2} [/tex]

Simplify the like terms.

[tex] = {x}^{2} + xy - 6 {y}^{2} [/tex]

Therefore, the answer is x^2 + xy- 6y^2.

Hope it helps.....

Answer:

square root of 1.9321 = 1.39

Step-by-step explanation:

Answer:

100 2/3

Step-by-step explanation:

50+50=100

1/3+1/3=2/3

100+2/3= 100 2/3

Answer:

Hey there! :)

Step-by-step explanation:

~Answer would be 100 2/3

(There is 3 steps for solving this question, the steps are provided below!)

Here is two ways you can solve this problem!:

Steps in order to solve this problem:

~ 1.Make both of the mixed number into a improper fraction.

151/3 + 151/3

~ 2.Now, when you add ‘151/3 + 151/3’ you will get 302/3.

~ 3.Finally you divide 302 and 3 which will give you 100 2/3

……………………………………………………………………………………………………

Another way to solve the question:

~1.Break up the mixed number:

50 1/3 = 50 + 1/3

50 1/3 = 50 + 1/3

~2.So this is the question you asked 50 1/3 + 50 1/3

Add 50+50 which gives you 100.

We solved for the whole number and now we have to solve for the fractions part.

1/3 + 1/3 = 2/3

~3.We got 100 as the whole and 2/3 as the fraction.

So now you just combine them both.

100 + 2/3 = 100 2/3

Therefore the answer is 100 2/3

Hope this helps!! I would be glad to help you with anything you don’t understand about this question! :D

Good luck!

Answer:

16 degrees

Step-by-step explanation:

Add 20 to -4

-4 + 20

= 16

So, the temperature at noon was 16 degrees

Answer:

16 degrees

Step-by-step explanation:

The question states that it increased +20 degrees by noon from 6:00 am. So,

-4 + 20 = 16

The temp would be 16 degrees at noon.

Answer:

Yes -15.5 is a rational number

Step-by-step explanation:

A rational number is a number that can be in the form p/q

where p and q are integers and q is not equal to zero.

-15.5 can easily be converted to fraction form which is = [tex]\frac{31}{2}[/tex]

Hope this helps you! :)

Answer:

Yes

Step-by-step explanation:

-15.5 can be rewritten as -155/10, which is a rational number.  Yes.

Furthermore, -155/10 can be reduced to the equivalent

-31/2

Answer: Option 1. irrational number, nonrepeating decimal

Step-by-step explanation:

the simplified version of √32 is 4√2

√2 is not a rational number since it can't be written in the form of fraction, so √32 is also irrational.

√2 is equal to 1.414213562... this is nonrepeating, which means, √32 is nonrepeating.

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Step-by-step explanation:

Remember:

X = 2.5

Y = 1.5

Z = 1

The chart:

         X             Y           Z

I      10000    7000    8000

II     6000     10000   5000

X

The first column represents X. Since X's value is 2.5, we multiply both those numbers by 2.5.

[tex]10,000*2.5=25,000[/tex]

[tex]6000*2.5=15,000[/tex]

These are the values of X.

Y

The second column represents Y. Since Y's value is 1.5, we multiply both of the values by 1.5.

[tex]7,000*1.5=10,500[/tex]

[tex]10,000*1.5 = 15,000[/tex]

These are the values of Y.

Z

The last column represents Z. Since Z's value is 1, we do not need to multiply the numbers, since they are already multiplied by 1.

[tex]8,000[/tex]

[tex]5,000[/tex]

These are the values of Z.

ADDING

Now that we have are 6 numbers solved, all we have to do is add them all together.

[tex](25+15+10.5+15+8+5)\\25,000+15,000+10,500+15,000+8,000+5,000=78,500[/tex]

Our final answer: $78,500 is the total. (first option)

Answer:

x=0

Step-by-step explanation:

4(x-5) = 4(4+x)

4x-20 = 16+4x

4x-4x = 16+20

0x=36

x = 36/0

x = 0

hope it might help

Please mark me as brainlist

Answer:

[tex]y = 5\cdot e^{2.3\cdot x}[/tex]

Step-by-step explanation:

A semilog plot consist in a logarithmic axis and a linear axis. In this case, the only equation that fulfill the statement conditions of a semilog plot is [tex]y = 5\cdot e^{2.3\cdot x}[/tex], as it is proved below:

1) [tex]y = 5\cdot e^{2.3\cdot x}[/tex] Given

2) [tex]y = \ln (5\cdot e^{2.3\cdot x})[/tex] Semilog plot

3) [tex]y = \ln 5 + \ln e^{2.3\cdot x}[/tex] [tex]\ln (a\cdot b) = \ln a + \ln b[/tex]

4) [tex]y = \ln 5 + 2.3\cdot x \cdot \ln e[/tex] [tex]\ln a^{b} = b\cdot \ln a[/tex]

5) [tex]y = \ln 5 + 2.3\cdot x[/tex] [tex]\ln e = 1[/tex]/Modulative property/Result

Answer:

Interest for the month = $12.25

Step-by-step explanation:

Given:

Amount in bank = $700

Rate of interest per month = 21% / 12 = 0.0175

Find:

Interest for the month

Computation:

Interest for the month = Amount in bank × Rate of interest per month

Interest for the month = $700 × 0.0175

Interest for the month = $12.25

Answer:

(0,3)

Step-by-step explanation:

You need to pick a point, P, that will give you a distance from A to P that is twice as long as from P to B, or ration 2:1

Point A is (-2,-7), point B is (1,8), and I picked (0.3) because it looked like it could be, but now we need to test it.

Distance formula is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2} + {(y_{2}-y_{1})^{2} } \\[/tex]

So AP would be

[tex]AP=\sqrt{(0--2)^{2} + {(3--7)^{2} } \\[/tex]

[tex]AP=\sqrt{(2)^{2} + {(10)^{2} } \\[/tex]

Do the same with PB, and you will find it's 5.1, giving an approximate ratio of 2:1.

Answer:

749.95+ 44.997 *or 45.00 giving 794.95

Answer:

in picture

Step-by-step explanation:

Answer:

-6w + 11wy + 6 - 4y

Step-by-step explanation:

Step 1: Write out expression

-6w + 9wy + 6 + 2wy - 4y

Step 2: Combine like terms

-6w + 11wy + 6 - 4y

Answer:

11wy-6w-4y+6

Step-by-step explanation:

−6w + 9wy + 6 + 2wy − 4y

Combine like terms

−6w  + 6 + 2wy+ 9wy − 4y

11wy-6w-4y+6

Answer:

The answer is A) the speed at which the car has traveled

Step-by-step explanation:

Answer:

a) E

b) line segment AB

Step-by-step explanation:

a) E

b) line segment AB (It's AB with the line over it - no arrowheads)

Answer:

Find a number that can be divided by both 6 and 9, which is 18. That means they will do laundry on the same day every 18 days.

Answer: 18 Days

Step-by-step explanation:

Let's look at their indivigual schedules for hte nex little While

<-0------6------12---->

t=Tim does laundry every 9 days

<-0---------9---------->

They haven't done laundry on the same day again yet, so let's keep going!

When we keep goin, we see thar the multiple first meet at 18

Ronal

<-0----6----18----27---->

Tim

<-0----9----18----27--->

Mathematically, we say that 18 is the least common multiple of 6 and 9. in math notation this looks like:

lcm (6, 9) = 18

Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Step-by-step explanation:

There are two kew parameters for a sphere: Center ([tex]h[/tex], [tex]k[/tex], [tex]s[/tex]) and Radius ([tex]r[/tex]). The radius is the midpoint of the line segment between endpoints. That is:

[tex]C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)[/tex]

[tex]C(x,y,z) = (1,-2,4)[/tex]

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

[tex]r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}[/tex]

[tex]r = 10\sqrt{3}[/tex]

The general formula of a sphere centered at (h, k, s) and with a radius r is:

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

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is [tex](x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30[/tex].

Answer:

In bold below.

Step-by-step explanation:

(a) The largest angle is opposite the largest side.

So by the Cosine Rule:

8^2 = 4^2 + 6^2 - 2*4*6 cos x

cos x =  (8^2 - 4^2 - 6^2) / (-2*4* 6)

= -0.25.

x = 104.48 degrees.

(b) Area of the triangle = 1/2 * 4 * 6 sin 104.48

= 11.62

= 3 √15.

(c)  The shortest altitude will have the longest sides as the base.

Area = 1/2 * altitude * base

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

The cosine of the largest angle is 104.48 degrees

The area of the triangle is 3√15cm² is 3 √15

The length of the shortest altitude of the triangle​ is 0.75√15 cm.

A triangle can be defined as a figure that has three lines. It can be of various dimensions it can a scale as Pythagoras or an isosceles triangle. They all have different properties.

(a)

With the help of the Cosine Rule:

[tex]8^2[/tex] = [tex]4^2 + 6^2 - 2 \times 4\times6 cos x[/tex]

cos x = [tex](8^2 - 4^2 - 6^2) / (-2 \times 4 \times 6)[/tex])

= -0.25.

x = 104.48 degrees.

(b)

Area of the triangle

=[tex]1/2 \times 4 \times 6 sin 104.48[/tex]

= 11.62

= 3 √15.

(c)  

Area =[tex]1/2 \times altitude \times base[/tex]

3√15 = 1/2 * 8 * a

a = 3√15 / 4 cm

= 0.75√15 cm.

Learn more about triangle, here:

https://brainly.com/question/25813512

#SPJ2

Answer:

gay

Step-by-step explanation:

i mean it starts with a g doesnt it?

Answer:

google?

Step-by-step explanation:

There are can be can be many things found on the pages starting with the letter g.

Answer: 49

Step-by-step explanation:

We know, x = -2

Substituting value of x in [tex]8x^{2} -7x+3[/tex],

[tex]8(-2)^{2} - 7(-2) + 3\\=8(4) -7(-2) + 3\\=32+14+3\\=49[/tex]

Answer:

f(-2)=8*(-2)^2-7*(-2)+3=8*4+14+3=32+17=49

Step-by-step explanation:

Answer:

a. is false

Step-by-step explanation:

4 liters= 1.057 gal

1.057 is greater than 1

Hope this helps :)

Answer: 60

Step-by-step explanation:

[tex]A = s^2\\\\frac{dA}{dt}=2s \frac{ds}{dt}\\36=s^2 \\ s=6\\\frac{dA}{dt} = 2(6)(5)=60 \frac{cm^2}{s}[/tex]

Answer:

The area of the square is increasing at a rate of 60 cm²/s

Step-by-step explanation:

Let [tex]l[/tex] be the length of the side of the square

Hence, The area of the square is given by

[tex]A = l^{2}[/tex]

Where [tex]A[/tex] is the area of the square

From the question, each side of a square is increasing at a rate of 5 cm/s, that is,

[tex]\frac{dl}{dt} = 5 cm/s[/tex]

Now, to determine the rate at which the area of the square is increasing, That is [tex]\frac{dA}{dt}[/tex]

To find [tex]\frac{dA}{dt}[/tex], differentiate [tex]A = l^{2}[/tex] with respect to [tex]t[/tex]

From, [tex]A = l^{2}[/tex]

[tex]\frac{dA}{dt} = \frac{d(l^{2}) }{dl}[/tex] ×[tex]\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2l[/tex] ×[tex]\frac{dl}{dt}[/tex]

Now, to determine the rate at which the area of the square is increasing when the area of the square is 36 cm²

First, we will determine the length at this instance,

From, [tex]A = l^{2}[/tex]

[tex]36 = l^{2}\\ \sqrt{36} = l\\6 = l\\l = 6cm[/tex]

The length at this instance is 6cm

To determine the rate at which the area of the square is increasing at this instance

[tex]l = 6cm\\[/tex]

From the question,  [tex]\frac{dl}{dt} = 5 cm/s[/tex]

Hence,

[tex]\frac{dA}{dt} = 2l[/tex] ×[tex]\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 2(6)[/tex] × [tex]5[/tex]

[tex]\frac{dA}{dt} = 60 cm^{2}/s[/tex]

Hence. the area of the square is increasing at a rate of 60 cm²/s

Answer:

B C D

Step-by-step explanation:

i did the assignment

Answer:

rectangle, triangle,trapezoid

Step-by-step explanation:

Answer:

B. (13-6) n - 55

Step-by-step explanation:

The number of shirts to be sold is n

The cost to purchase one shirt is $13

The cost of making each shirt is $6

Let's assume the shirt is one

Profit for a Shirt = (13-6)

But then there are no number of shirts

Profit= (13-6)n

But then also, an advert was run for the total shirts combined

Profit= (13-6)n -55

Answer:

b. (13-6)n-55

ap3x