Solve the equation for x.
(x=21)= 103
X =

Answer:

to the right of x = 2 the function is increasing

{ x | x > 2}

Step-by-step explanation:

Recall that this is a quadratic function, and therefore responds to the shape of a parabola. In this case is also a parabola with branches opening up since the coefficient of the square term is positive. So, we just need to find where the vertex is located, and we know that to the left of the x-value of the vertex the function is decreasing, and to the right of it the function is increasing.

The formula for the x of the vertex of a parabola of the form:

[tex]y=ax^2+bx+c[/tex]

is  [tex]x_{vertex}=\frac{-b}{2\,a}[/tex]

which in our case gives:

[tex]x_{vertex}=\frac{-b}{2\,a} =\frac{4}{2} =2[/tex]

Therefore, to the left of x = 2 the function decreases , and to the right of x = 2 the function is increasing.

Answer:

12

Step-by-step explanation:

Round 4.038 down to 4

Round 5.5 up to 6

Round 2.17 to 2

4+6+2 = 12

Answer:

a. is false

Step-by-step explanation:

4 liters= 1.057 gal

1.057 is greater than 1

Hope this helps :)

Answer:

204.4m

Step-by-step explanation:

formula for SA of a rectangle is 2lw+2lh+2hw

so it would be 2(6x5) +2(6x3)+2(5x3)=126m

formula for SA of a triangle is bh+2ls+lb

so it would be 5x2+2(6x3.2)+6x5=78.4m

then add 78.4+126=204.4m

Answer:

X Z Y

Step-by-step explanation:

The first Question is X

The second Question is Z

The third question is Y

Answer:

Q1: X

Q2: Z

Q3: Y

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: 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

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:

Point N

Step-by-step explanation:

According to Euclidean geometry, two points are coplanar when they are in the same line segment. By this approach, it is clear that points K and N are part of the same line segment and, consequently, point N is coplanar to point K.

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:

B

Step-by-step explanation:

So we have:

[tex]g(x)=x^2+3x-1[/tex]

To find g(5), substitute 5 for x:

[tex]g(5)=(5)^2+3(5)-1[/tex]

Square and multiply:

[tex]g(5)=25+15-1[/tex]

Add:

[tex]g(5)=40-1[/tex]

Subtract:

[tex]g(5)=39[/tex]

So, our answer is B :)

Answer: OPTION 2. 39

Step-by-step explanation:

g(x)=x²+3x-1 ⇔ Given

g(5)=(5)²+3(5)-1 ⇔ Plug the value of x in (5)

g(5)=25+15-1 ⇔ do all the operation (square, multiplication, etc.)

g(5)=40-1 ⇔ combine like term (first do the first two)

g(5)=39 ⇔ combine like term

Hope this helps!! :)

Please let me know if you have any question

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:

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:

Around 372,527 (rounding down)

Step-by-step explanation:

To solve this, divide the amount of the books sold in the month it was released (33,900) by the percentage of total copies this number represents (9.1% or .091):

33,900/.091 = 372,527.473 or 372,527 (if you round down) or 372,528 (if you round up)

I hope this helps!

-TheBusinessMan

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:

Step-by-step explanation:

first you would get it into y=mx+b and you would get -4y=-x+4 and simplify

y=[tex]\frac{1}{4}[/tex]x+1 and if you graph it it would look like this

Answer:

The number to be subtracted = -11/2

Step-by-step explanation:

(3*rational number)-x=1/2

The rational number given = -5/3

Then thrice the rational number

= 3*rational number

= 3*(-5/3)

= -5

(3*rational number)-x=1/2

-5-x= 1/2

-5- 1/2= x

-11/2= x

The number to be subtracted = -11/2

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:

1819

Step-by-step explanation:

Answer:

The radius is [tex] 2\sqrt{15} [/tex]

The center is (3, 3)

Step-by-step explanation:

Equation of circle in standard form with center at (h, k) and radius r:

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

We need to complete the square in x and y.

[tex] x^2 + y^2 - 6x - 6y = 42 [/tex]

Separate x-terms and y-terms:

[tex] x^2 - 6x + ~~~~~y^2 - 6y + ~~~~~ = 42 + ~~~~~ + ~~~~~ [/tex]

To complete the square, you square half of the linear term's coefficient.

Linear term in x: -6x

Coefficient: -6

Half of the coefficient: -3

Square half of the coefficient: 9

We need to add 9 to both sides to complete the square in x.

The linear term in y is -6y, so we do the same and we also need to add 9 to both sides to complete the square in y.

[tex] x^2 - 6x + 9 + y^2 - 6y + 9 = 42 + 9 + 9 [/tex]

[tex] (x - 3)^2 + (y - 3)^2 = 60 [/tex]

Now that we have the equation in standard form, we can get the radius and center of the circle.

[tex] r^2 = 60 [/tex]

[tex] r = \sqrt{60} [/tex]

[tex] r = \sqrt{4 \times 15} [/tex]

[tex] r = 2\sqrt{15} [/tex]

The radius is [tex] 2\sqrt{15} [/tex]

The center is (3, 3)

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:

there are 63360 inches in 1 mile. if you divide 2 into 63360 and add that with it, that should give you the accurate answer

Answer:

first question answer: [tex]\frac{1}{12}[/tex]

second question answer: commutative property of multiplication

Answer:

[tex] \boxed{ \bold{ \boxed{ \sf{ \: 1. \: \: \: \: \: \frac{1}{12} }}}}[/tex]

[tex] \boxed{ \bold{ \boxed{ \sf{2. \: \: \: \: associative \: property \: of \: multiplication}}}}[/tex]

Step-by-step explanation:

1. [tex] \sf{ \sqrt{ \frac{1}{144} } }[/tex]

⇒[tex] \sf{ \sqrt{ \frac{ {1}^{2} }{ {12}^{2} } } }[/tex]

⇒[tex] \sf{ \sqrt{ { (\frac{1}{12}) }^{2} } }[/tex]

⇒[tex] \sf{ \frac{1}{12} }[/tex]

2. Associative property of multiplication

It states that the product of three or more integers remains unchanged even if they are grouped in different orders.

Hope i helped !

Best regards! :D

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:

D

Step-by-step explanation:

So we know that:

[tex]\cos(A)=1/3[/tex]

To co-function identities state that:

[tex]\cos(\theta)=\sin(90\textdegree-\theta)[/tex]

Therefore, this is the same as:

[tex]\cos(A)=\sin(90\textdegree-A)[/tex]

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

[tex]A+B=90[/tex]

Subtract A from both sides:

[tex]B=90-A[/tex]

So we can make the substitution:

[tex]\sin(90-A)=\sin(B)[/tex]

Thus, A is also correct.

The correct answer is D .

Answer:D

Step-by-step explanation:

So we know that:

To co-function identities state that:

Therefore, this is the same as:

B is correct.

Additionally, recall that in a right triangle, the two other angles must add up to 90. In other words:

Subtract A from both sides:

So we can make the substitution:

Thus, A is also correct.

The correct answer is D .

Answer:

Explanation:

Given;

Mass of a box (m) = 300kg

Area of box (a) = 15m²

Pressure exerted by the box (P) = ?

Acceleration due to gravity (g) = 9.8m/s²

Here,

Pressure = Force / Area

= mass × acceleration due to gravity / Area [Since, force=mass×acceleration due to gravity]

= 300 × 9.8 / 15

= 2940 / 15

= 196 N/m²

Answer:

No it is not satisfied

Step-by-step explanation:

The one-way ANOVA is used to measure whether the difference between the means of two independent groups are statistically significant.

For it to be satisfied, there has to be one independent variable which is categorical and one dependent variable. The dependent variable on its own has to be a continuous variable

The assumptions are:

1. Equal variance between population

2. Independence between observations

3. The random samples have to be gotten from a normal population.

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:

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

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