For two functions, a(x) and b(x), a statement is made that a(x) = b(x) at x = 2. What is definitely true about x = 2?
Both a(x) and (x) have a maximum or minimum value at x = 2.
Both a(x) and b(x) have the same output value at x = 2.
Both a(x) and b(x) cross the x-axis at 2.
Both a(x) and (x) cross the y-axis at 2.​

To work out the volume of a prism, you multiply the area of cross-section by the height (or length).

So for a cylinder, you work out the area of the circle and then multiply it by the height.

Area of circle (or cross-section) = π × radius²

                                                = π × 0.7²

                                                = 0.49π   m²

Now to get the volume of the cylinder, you times this area of the cross-section by the height of the cylinder:

Volume = 0.49π × 1.5

            = 2.3 m³  (accurate to 2 decimal places)

---------------------------------------------------------------

Answer:

The maximum volume of rainwater the cylinder can hold is:

2.3 m³

The maximum volume of rainwater will be "2.3 m³".

Given values are:

Height = 1.5 m

Diameter = 1.4 m

The Area of circle will be:

= [tex]\pi\times radius^2[/tex]

= [tex]\pi\times 0.7^2[/tex]

= [tex]0.49 \pi \ m^2[/tex]

hence,

The volume of cylinder be:

= [tex]0.49 \pi\times 1.5[/tex]

= [tex]2.3 \ m^3[/tex]

Thus the answer above is correct.  

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Answer: [tex]x=2[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

We know that the slope of this line is:

[tex]m=-\frac{3}{2}[/tex]

And the y-intercept is:

[tex]b=3[/tex]

Since the line intersects the x-axis when [tex]y=0[/tex],  we can substitute values into  [tex]y=mx+b[/tex]:

 [tex]0=-\frac{3}{2}x+3[/tex]

The final step is to solve for "x", then:

[tex]-3=-\frac{3}{2}x\\\\(-3)(-2)=3x\\\\6=3x\\\\x=\frac{6}{3}\\\\x=2[/tex]

The x-intercept of the line is 2.

We must figure out the value of x when the y-coordinate is 0, in order to identify the x-intercept of a line.

We can express the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept,

Given that the slope of the line is -3/2 and the y-intercept is 3.

Substituting the given values into the equation, we have y = (-3/2)x + 3.

To find the x-intercept, we set y = 0 and solve for x:

0 = (-3/2)x + 3

Subtracting 3 from both sides:

(-3/2)x = -3

To isolate x, we multiply both sides by -2/3:

x = (-3)(-2/3)

x = 2

Therefore, the x-intercept of the line is 2.

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Answer:

[tex]a=(9-10c)/b[/tex]

Step-by-step explanation:

we have

[tex]ab+10c=9[/tex]

Solve for the variable a

That means----> isolate the variable a

Subtract 10c both sides

[tex]ab+10c-10c=9-10c[/tex]

[tex]ab=9-10c[/tex]

Divide by b both sides

[tex]ab/b=(9-10c)/b[/tex]

[tex]a=(9-10c)/b[/tex]

Answer: y = -x + 9

Step-by-step explanation:

First, to find the slope of the line we will use: (y₂-y₁)/(x₂-x₁)

Using the two points, we get: (8-1)/(1-8)

Simplify it: 7/-7

Finally, the slope is -1

We can now write: y = -x + b

Next we will plug in a point into the equation we have:

(8,1)  -->   1 = -8 + b          Then solve algebraically

b = 9

Then finish the equation:

y = -x + 9

The equation in slope-intercept form for the line passing through the points (8,1) and (1,8) is y = -x + 9, calculated by first finding the slope and then using it to determine the y-intercept.

To write an equation in slope-intercept form of the line passing through the points (8,1) and (1,8), we first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points gives us m = (8 - 1) / (1 - 8) = 7 / -7 = -1. With the slope and one of the points, we can then find the y-intercept (b) by rearranging the slope-intercept equation y = mx + b to b = y - mx, using one of the given points, for example, (8,1), which gives us b = 1 - (-1)(8) = 1 + 8 = 9. Therefore, the equation of the line in slope-intercept form is y = -x + 9.

Hello There!

The answer would be "B"

We have to move the decimal place over for each one depending on what the power of the number is.

Answer:

your answer would be B. :)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

[tex]h = \frac{3V}{\pi r^2}[/tex]

Step-by-step explanation:

Divide left and right by 1/3 π r²...

Answer:

The answer to this question is the first option:

Line segment TU is parallel to line segment RS because 32/36=40/45

Answer:

The correct option is 1.

Step-by-step explanation:

From the given figure it is clear that QT=32, TR=36, QU=40 and US=45.

The converse of side splitter theorem states that if a line divides two sides proportionally, then that line is parallel to the third side.

The ratio in which TU divides the two sides is

[tex]\frac{QT}{TR}=\frac{32}{36}=\frac{8}{9}[/tex]

[tex]\frac{QU}{US}=\frac{40}{45}=\frac{8}{9}[/tex]

[tex]\frac{QT}{TR}=\frac{QU}{US}=\frac{8}{9}[/tex]

It means the line TU divides two sides proportionally.

Using converse of side splitter theorem, Line segment TU is parallel to line segment RS because

[tex]\frac{32}{36}=\frac{40}{45}[/tex]

Therefore the correct option is 1.

Answer:

Step-by-step explanation:

Uploaded a pic of the answer. It’s correct

Given: We have the expression [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-1: [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]

Step-2: [tex]\left ( 875\times x^{5} \times y^{}\right )^{1/3}[/tex]                              [break the cuberoot as power [tex]1/3[/tex]]

Step-3: [tex]\left ( 125.7 \right )^{1/3}\times x^{5/3}\times y^{9/3}[/tex]                    [break [tex]875=125\times 7[/tex]]

Step-4: [tex]\left ( 5^{3} \right )^{1/3}\times 7^{1/3}\times x^{\left ( 1+2/3 \right )}\times y^{9/3}[/tex]       [ [tex]125=5^{3} \\\frac{5}{3} =1+\frac{2}{3}[/tex]]

Step-5: [tex]5^{1}\times 7^{1/3}\times x^{1}\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]] 

Step-6: [tex]5\times x\times y^{3}\left ( 7^{1/3}\times x^{2/3} \right )[/tex]

Step-7: [tex]5xy^{3}\left ( 7x^{2} \right )^{1/3}[/tex]

Step-8: [tex]5xy^{3}\sqrt[3]{7x^{2}}[/tex]

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Answer:

C.

Step-by-step explanation:

The answer is C because when you add the absolute values (distance to zero) of the two numbers, you get the number 8. Divide this by 2, and you will get 4.  Then, you add four to the lower number, -6, and you get -2.

Answer: C. -2

Step-by-step explanation:

Hello There!

I attached an image below which explains everything and gives some examples.

Final answer:

The product rule for exponents allows you to add the exponents when multiplying two terms with the same base, simplifying the calculation. Examples include multiplying powers of the same number, or dealing with terms in scientific notation.

Explanation:

Understanding the Product Rule for Exponents

The product rule for exponents states that when you multiply two expressions with the same base, you can simply add the exponents. This rule simplifies the multiplication of exponentiated quantities.

Examples of Using the Product Rule

For instance, if you have 53 multiplied by 54, the product rule allows you to add the exponents: 53+4 = 57. Another example involves numbers in scientific notation. When you multiply 3.2 x 103 by 2 x 102, the result is 6.4 x 103+2 = 6.4 x 105.

If both terms have exponents, multiply the digit terms as usual and then add the exponents of the exponential terms. This concept also applies to logarithms, where the logarithm of a product of two numbers equals the sum of their individual logarithms.

Answer:

y = -1

Step-by-step explanation:

Details have been given in the question, we need to break them apart and create our equations accordingly.

"the sum of two times x and 3 times y is 5"

2x + 3y = 5

"the sum of two times x and 3 times y is 5"

x - y = 5

So, our two equations are:

2x + 3y = 5

x - y = 5

Solve using substitution method, by moving y to the other side.

x = y + 5

2(y + 5) + 3y = 5

2y + 10 + 3y = 5

Combine like terms

5y + 10 = 5

Subtract 10 from both sides

5y = -5

y = -1

Answer:

360 degrees

Step-by-step explanation:

we know that

The sum of the n exterior angles for any convex polygon with n sides is always 360 degrees

Example

An equilateral triangle has three equal interior angles measures 60 degrees

Each exterior angle measures 120 degrees

The sum of the exterior angles is equal to  120+120+120=360

Answer:

8.75 hours

Step-by-step explanation:

We can use ratios to solve.  Put the pages over the time and set them equal.

4 pages       7 pages

------------- = ---------------

5 hours        x hours

Using cross products

4 * x = 5 *7

4x =35

Divide by 4 on each side

4x/4 = 35/4

x =8.75 hours

Answer:

[tex]\large\boxed{x^4+\dfrac{8}{7}x^3+6x+1}[/tex]

Step-by-step explanation:

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest.

We have:

[tex]\dfrac{8}{7}x^3+x^4+6x+1[/tex]

Look at the degrees for each term in the expression:

[tex]\dfrac{8}{7}x^3[/tex] has a degree of 3

[tex]x^4[/tex] has a degree of 4

[tex]6x[/tex] has a degree of 1

[tex]1[/tex] has a degree of 0

Write this trinomial in order by degree, highest to lowest

[tex]x^4+\dfrac{8}{7}x^3+6x+1[/tex]

The standard form of given equation is 8/7x^3 + x^4 + 6x + 1 is 7x^4 + 8 x^3 + 4 x + 7 = 0.

To write the equation 8/7x^3 + x^4 + 6x + 1 in standard form, you need to rearrange the terms in descending order of exponents.

Standard form for a polynomial is where the terms are written from the highest power to the lowest power of the variable.

So,  8/7x^3 + x^4 + 6x + 1 = 0

7x^4 + 8 x^3 + 4 x + 7 = 0.

Answer:

17x(1 - 2y)

Step-by-step explanation:

Given

17x - 34xy ← factor out 17x from each term

= 17x(1 - 2y) ← in factored form

Answer:

17x(1 - 2y)

Step-by-step explanation:

Answer:

Where is the point?

Step-by-step explanation:

Answer:

B at 4.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false as it now stands.

If we combine -3x^2 and 3x^2, we get 0, so:

"The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is equivalent to

"The sum of (expression) and 7x^2 is 10x^2".

Subtracting 7x^2 from both sides yields (expression) = 3x^2.

So:  Although "The sum of -3x^2 or 3x^2 and 7x^2 is 10x^2" is false,

"The sum of 3x^2 and 7x^2 is 10x^2" is true, and the formerly missing term is 3x^2.

Answer:62

Step-by-step explanation:

The differance between 2 consecutive even number is 2...so if the first consecutive even number is x, then the next 4 consecutive even number will(x+2),(x+4),(x+6),(x+8)

So

X+(x+2)+(x+4)+(x+6)+(x+8)=310

5x+20=310

So,x=58

As the third number is (x+4)

Putting the value of x the final result comes(58+4)=62.

2,2n+2,2n+4,2n+6,2n+8 - 5 consecutive even integers

2n+4 - 3rd number

[tex]2n+2n+2+2n+4+2n+6+2n+8=310\\10n+20=310\\10n=290\\n=29\\\\2n+4=2\cdot29+4=62[/tex]

Answer:2

Step-by-step explanation:

If you devide 58 by 7,you will get 8 as quotient..so 7×8=56..

So you will find (58-56)=2 as remainder..

Answer:

The Remainder of 58÷7 is 2

Step-by-step explanation:

The Remainder of a Division Operation is calculated by finding how many times the denominator goes into the numerator without going over and then subtracting that from the numerator.

For Example : [tex]58/7 = 8.28[/tex] ......which means 7 goes into 58 , 8 times.

Next we multiply 7*8 to give us 56.

Lastly, we subtract 58-56 to give us a remainder of 2.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Check the picture below.

let's notice the "white" ∡1 is an inscribed angle with an intercepted arc of (x-32), and the "green" ∡5 is also an inscribed angle with an intercepted arc of (2x).

the ∡6 and ∡2 are both external angles, however they intercepted two arcs, a "far arc" and a "near arc", thus we'll use the far arc - near arc formula, as you see in the picture, and we'll use the inscribed angle theorem for the other two.

[tex]\bf \measuredangle 1=\cfrac{x-32}{2}\implies \measuredangle 1 =\cfrac{32}{2}\implies \measuredangle 1 = 16 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 5 =\cfrac{2x}{2}\implies \measuredangle 5 = x\implies \measuredangle 5 = 64 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \measuredangle 2 = \cfrac{(2x+8)~~-~~(x-32)}{2}\implies \measuredangle 2=\cfrac{2x+8-x+32}{2} \\\\\\ \measuredangle 2=\cfrac{x+40}{2}\implies \measuredangle 2=\cfrac{104}{2}\implies \measuredangle 2=52 \\\\[-0.35em] ~\dotfill\\\\ \measuredangle 6=\cfrac{[(2x+8)+(x)]~~-~~(2x)}{2}\implies \measuredangle 6=\cfrac{3x+8-2x}{2}\implies \measuredangle 6=\cfrac{x+8}{2} \\\\\\ \measuredangle 6=\cfrac{72}{2}\implies \measuredangle 6=36[/tex]

Answer:

B. ¾π

Step-by-step explanation:

This radian measure is in the top negative side of the unit circle --> [-x, y].

Answer:

32 1/2

    2

or

160.25

Step-by-step explanation:

the equivalent to 641/4

is 160.25 in decimal

32 1/2

    2

32 whole number 1/2 over or divided by 2

For this case we must indicate an expression equivalent to the following:

[tex]\frac {641} {4}[/tex]

It is observed that the fraction can not be simplified, so, its decimal form is given by:

[tex]\frac {641} {4} = 160.25[/tex]

We can convert to a mixed number, for this, We convert the decimal number to a fraction by placing it on a power of ten. Since there are 2 numbers to the right of the decimal point, we place the decimal on [tex]10 ^ 2 = 100[/tex]. So:

[tex]160 \frac {25} {100}[/tex]

We simplify:

[tex]160 \frac {1} {4}[/tex]

Answer:

[tex]160.25\\160 \frac {1} {4}[/tex]

Answer: Cubic Inches

Step-by-step explanation: Because its measured in inches, that would eliminate the choice of centimeters. Its a cube so you use inches cubed. Square inches are for a 2-dimensional object. Such as square feet of a house, as the floor is technically 2-dimensional.

Answer:

Ello mate !

The answer would be cubic inches !

The algebraic expression that represents the phrase 'the difference of the number of roses and 18 lilies' is 'r - 18'. The term 'difference' in math denotes subtraction operation.

In algebra, the phrase 'the difference of the number of roses and 18 lilies' is represented as a subtraction operation between two variables or a variable and a number. In this case, the expression can be represented as r - 18, where 'r' represents the number of roses and '18' represents the number of lilies. However, in this scenario, the type of the flower doesn't really matter, it's just about the quantity which is represented by the term '18'. The key term difference denotes subtraction in mathematical terms.

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Answer:

The mass of each cereal box is 500 grams

Step-by-step explanation:

Remember that

1 K=1,000 g

we know that

The total mass of 8 cereal boxes is 4 kilograms

4 k=4*1,000=4,000 g

therefore

The total mass of 8 cereal boxes is 4,000 grams

To find the mass of each box, divide the total mass by eight

so

[tex]\frac{4,000}{8}=500\ g[/tex]

Answer:

B because u will have to first open the bracket according to BODMAS: bracket of division multiplication addition and subtract trust me before solving something like this use this BODMAS

Answer:

Step-by-step explanation:

Please use " ^ " to indicate exponentation:   y= x^2 + 11x + 24.  Thanks.

Because x^2 is positive, the graph of this parabola opens up.

We can find the vertex and roots (zeros) as follows, using the quadratic formula:

With a = 1, b = 11 and c = 24,

       -11  ± √ [ (11^2-4(1)(24) ]       -11 ± √25

x = ------------------------------------ = --------------- = -3    and   x = -8

              2(1)                                     2

This tells us that the x-intercepts are at (-3, 0) and (-8, 0).  The minimum value is at x = -b / (2a), which here is x = -11 / [2] = -5 1/2 (which is halfway between the zeros).

The vertex (and thus, the minimum) is at (-5 1/2, f(-5 1/2) ).

Answer: a on edge 2021

Step-by-step explanation:

Answer:

[tex]y = 5x - 11[/tex]

Step-by-step explanation:

1) Find slope

2) Substitute 1 point back into formula to find y-intercept, aka c

ANSWER

[tex]y = 5x - 11[/tex]

EXPLANATION

The given line passes through:

(3,4) and (2,-1).

The slope is given by:

[tex]m = \frac{ - 1 - 4}{2 - 3} [/tex]

[tex]m = \frac{ - 5}{ - 1} = 5[/tex]

The equation can be found using

[tex]y-y_1=m(x-x_1)[/tex]

We plug in the point and slope to get:

[tex]y - 4 = 5(x - 3)[/tex]

[tex]y - 4 = 5x - 15[/tex]

[tex]y = 5x - 15 + 4[/tex]

[tex]y = 5x - 11[/tex]

This is the slope-intercept form