Is Erik's statement correct? Why or why not?
Yes, the solids are both cones and appear to have
the same volumes.
Yes, the area of the bases and the heights of the
cones are the same, so the volumes are equal.
O No, the heights of the cones are not the same, so
Cavalieri's principle does not apply.

Answer:

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Step-by-step explanation:

Compare [tex]ax^2+bx+c[/tex] to [tex]3x^2+4x-2[/tex].

We have [tex]a=3,b=4,c=-2[/tex].

The quadratic formula is for solving equations of the form [tex]ax^2+bx+c=0[/tex] and is [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

So we are going to plug in our values in that formula to find our solutions,x.

If you want to notice it in parts you can.

Example I might break it into these parts and then put it in:

Part 1: Evaluate [tex]b^2-4ac[/tex]

Part 2: Evaluate [tex]-b[/tex]

Part 3: Evaluate [tex]2a[/tex]

------Let's do these parts.

Part 1: [tex]b^2-4ac=(4)^2-4(3)(-2)=16-12(-2)=16+24=40[/tex].

This part 1 is important in determining the kinds of solutions you have. It is called the discriminant.  If it is positive, you have two real solutions.  If it is negative, you have no real solutions (both of the solutions are complex).  If it is 0, you have one real solution.

Part 2: [tex]-b=-4[/tex] since [tex]b=4[/tex].

Part 3: [tex]2a=2(3)=6[/tex].

Let's plug this in:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

or in terms of our  parts:

[tex]x=\frac{\text{Part 2} \pm \sqrt{\text{Part 1}}}{\text{Part 3}}[/tex]

[tex]x=\frac{-4 \pm \sqrt{40}}{6}[/tex]

40 itself is not a perfect square but it does contain a factor that is.  That factor is 4.

So we are going to rewrite 40 as [tex]4 \cdot 10[/tex].

[tex]x=\frac{-4 \pm \sqrt{4 \cdot 10}}{6}[/tex]

[tex]x=\frac{-4 \pm \sqrt{4} \cdot \sqrt{10}}{6}[/tex]

[tex]x=\frac{-4 \pm 2\cdot \sqrt{10}}{6}[/tex]

I'm going to go ahead and separate the fraction like so:

[tex]x=\frac{-4}{6} \pm \frac{2 \cdot \sqrt{10}}{6}[/tex]

Now I'm going to reduce both fractions:

[tex]x=\frac{-2}{3} \pm \frac{1 \cdot \sqrt{10}}{3}[/tex]

[tex]x=\frac{-2}{3} \pm \frac{\sqrt{10}}{3}[/tex]

Final answer:

Using the quadratic formula with a=3, b=4, and c=-2, the solution set for the quadratic equation 3x^2 + 4x - 2 = 0 is x = (-4 + 2√(10)) / 6 and x = (-4 - 2√(10)) / 6.

Explanation:

To find the solution set of the quadratic equation 3x2 + 4x - 2 = 0, we can use the quadratic formula:

x = (-b ± √(b2 - 4ac)) / (2a)

Here, comparing with the standard form ax2 + bx + c = 0, we identify a = 3, b = 4, and c = -2. Substituting these values into the quadratic formula gives us:

x = (-(4) ± √((4)2 - 4(3)(-2))) / (2(3))

x = (-4 ± √(16 + 24)) / 6

x = (-4 ± √(40)) / 6

x = (-4 ± 2√(10)) / 6

Which simplifies to two solutions:

x = (-4 + 2√(10)) / 6

x = (-4 - 2√(10)) / 6

These are the two solutions to the given quadratic equation.

Answer:

Step-by-step explanation:

We have:

rectangle 4.8 m × 3.8 m

two triangles with base b = 4.8 m and height h = 2.6 m

two triangle with base b = 3.8 m and height h = 2.9 m.

The formula of an area of a rectangle l × w:

[tex]A = lw[/tex]

Substitute:

[tex]A_1 = (4.8)(3.8) = 18.24\ m^2[/tex]

The formula of an area of a triangle:

[tex]A=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_2=\dfrac{(4.8)(2.6)}{2}=6.24\ m^2\\\\A_3=\dfrac{(3.8)(2.9)}{2}=5.51\ m^2[/tex]

The Surface Area:

[tex]S.A.=A_1+2A_2+2A_3\\\\S.A.=18.24+2(6.24)+2(5.51)=41.74\ m^2[/tex]

Answer:

GIVE THE OTHER DUDE BRAINLISET

Step-by-step explanation:

The scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.

To obtain 180 ounces of a 30% salt mixture, the scientist should use 90 ounces of Solution A (20% salt) and 90 ounces of Solution B (80% salt) by solving a system of two equations.

To solve the problem, we need to create a system of equations based on the quantities of salt in each solution and the desired final mixture. We want to mix Solution A (20% salt) and Solution B (80% salt) to get 180 ounces of a mixture that is 30% salt. Let the amount of Solution A be x ounces and the amount of Solution B be y ounces.

The two equations representing the system are:

Now, we solve this system of equations. Multiplying the second equation by 100 for simplicity, we get:

20x + 80y = 54  * 100

Using the first equation to express y in terms of x, we get y = 180 - x. Substitute y into the second equation:

20x + 80(180 - x) = 5400

Opening parentheses and simplifying gives us:

20x + 14400 - 80x = 5400

Subtract 20x from each side:

-60x + 14400 = 5400

Solving for x, we find that:

x = (14400 - 5400) / 60 = 90

Substituting x into y = 180 - x, we get y = 180 - 90 = 90.

Therefore, the scientist should use 90 ounces of Solution A and 90 ounces of Solution B to get the desired mixture.

Answer:

[tex]x^{2} -1[/tex]

Step-by-step explanation:

we know that

Every difference of squares problem can be factored as follows:

[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]

If the polynomial represent a difference of squares every number must be a perfect square (Remember that a number is a perfect square if its square root is an integer.)

Verify each case

case 1) we have

[tex]x^{2} -1[/tex]

In this case both numbers are perfect square

so

[tex]x^{2} -1=(x+1)(x-1)[/tex]

therefore

The polynomial represent a difference of squares

case 2) we have

[tex]x^{2} -8[/tex]

In this case 8 is not a perfect square

therefore

The polynomial not represent a difference of squares

case 3) we have

[tex]4x^{2} +16[/tex]

[tex]4x^{2}+16=4(x^{2}+4)[/tex]

In this case both numbers are perfect square

but is a sum of squares

therefore

The polynomial not represent a difference of squares

case 4) we have

[tex]9x^{2}-18[/tex]

[tex]9x^{2}-18=9(x^{2}-2)[/tex]

In this case 2 is not a perfect square

therefore

The polynomial not represent a difference of squares

Answer:

Option C is correct.

Step-by-step explanation:

The equation given is y = 0.5x +5

where x is the number of miles and y is the total cost.

We need to find total cost y if the car has traveled 30 miles

so, x=30

Putting value of x in the given equation:

y = 0.5x +5

y = 0.5(30) + 5

y = 15 + 5

y = 20

So, the total cost is $20

Option C is correct.

Answer:

the answer is $20 i just did that one :))

Step-by-step explanation:

good luck!

Answer:

See below.

Step-by-step explanation:

An equation with infinite solutions is, strictly, an identity.

An example is 2(x + 3) = 4x + 6

Simplifying  we get 4x + 6 = 4x + 6. We can replace by any value of x  and the equation will hold true.

Answer:

the answer is 'because'

Answer:

Option D. Tre made an error when adding or subtracting

Step-by-step explanation:

we have the equation

[tex]3.57x + 1.61 = 4.71 - 2.63x[/tex]

Solve for x

Group terms that contain the same variable and move the constant to the other side

[tex]6.2x= 4.71 - 1.61[/tex]

Combine like terms

[tex]6.2x=3.1[/tex]

[tex]x=0.5[/tex]

Verify

Step 1: 3.57(0.5) + 1.61 = 4.71 - 2.63(0.5) ---> is correct

Step 2: 1.785 + 1.61 = 4.71 - 1.315  ----> is correct

Step 3: 3.395 = 6.025 ---> is not correct

because

4.71-1.315=3.395 instead of 6.025

therefore

Tre made an error when  subtracting

Answer: The answer is d

Step-by-step explanation:

Answer:

See explanation.

Step-by-step explanation:

The 'base' of a rectangular prism refers to only one side of the rectangular prism, which is a rectangle.

The formula for the area of a rectangle is as follows:

[tex]A=lw[/tex]

Where A = area, l = length, and w = width.

The 'base' of a cylinder refers to only one side of the cylinder, which is a circle.

The formula for the area of a circle is as follows:

[tex]A=\pi r^2[/tex]

Where A = area and r = radius.

Just in case you typed your question incorrectly and were asking for surface area, here is the formula for surface area for both as well:

Rectangular prism: [tex]A=2(wl+hl+hw)\\[/tex]

Cylinder: [tex]A=2\pi rh+2\pi r^{2}[/tex]

The other degree amount is 90 in a clockwise rotation.

Answer:

x=-2  y=3

Step-by-step explanation:

7x-2y=-20

9x+4y=-6

Multiply the first equation by 2

2(7x-2y) = 2 * -20

14x - 4y = -20

Add this to the second equation

14x - 4y = -40

9x+4y=-6

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

23x = -46

Divide by 23

23x/23 = -46/23

x = -2

Now we solve for y

9x+4y=-6

9(-2) +4y = -6

-18 + 4y = -6

Add 18 to each side

-18+18 +4y = -6+18

4y = 12

Divide by 4

4y/4 = 12/4

y=3

Answer:

w=5

Step-by-step explanation:

14-9=5

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{ w + 9 = 14}[/tex]

[tex]\huge\text{SUBTRACT by the \#9 on your sides! }[/tex]

[tex]\huge\text{Like: w + 9 - 9 = 14 - 9}[/tex]

[tex]\huge\text{Cancel out: 9 - 9 because it equals 0}[/tex]

[tex]\huge\text{Keep: 14 - 9 because it helps us solve for w}[/tex]

[tex]\huge\text{w = 14 - 9}[/tex]

[tex]\huge\text{14 - 9 = w}[/tex]

[tex]\huge\text{14 - 9 = 5}[/tex]

[tex]\huge\text{w = 5}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: w = 5}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Step-by-step explanation:

Given function is:

f(x) = x/1 + x

In order to find f(x+h) we have to put x+h in place of x

[tex]f(x)=\frac{x}{1+x} \\f(x+h)=\frac{x+h}{1+x+h}[/tex]

Therefore,

[tex]f(x+h)=\frac{x+h}{1+x+h}[/tex]

Answer: B

Got it right lol

Answer:

Decreasing

Step-by-step explanation:

y=mx+b is called slope-intercept from because it tells you the slope,m, and the y-intercept,b.

If the slope is positive then the line is increasing.

If the slope is negative then the line is decreasing.

If the slope is zero then the line is horizontal or constant.

So let's solve our equation for y:

y+x=3

Subtract x on both sides:

y=-x+3

The slope is -1.

Therefore the line is decreasing.

just a quick addition to @Freckledspots' great reply above.

y + x = 3

y = 3 - x

if we pick any random "x" value, and then pick another value larger than the one before for "x", to get a "y" value, if "y" is decreasing, the the first value of "y" will be larger, else it's increasing, let's do so, say using hmmm x = 2 and x = 7.

x = 2

y = 3 - 2

y = 1

x = 7

y = 3 - 7

y = -4

as "x" moves to the right, from 2 to 7, "y" moved down, from 1 to -4, thus is decreasing.

Answer:

B. 7,596,288 ft³

Step-by-step explanation:

volume of cylinder = π * r^2 * h

volume = 3.14 * (240 ft)^2 * 42 ft

volume = 7,596,288 ft³

Answer: B . [tex]7,596,288 ft^3[/tex]

Step-by-step explanation:

The volume of a cylinder is given by :_

[tex]\text{Volume}=\pi r^2 h[/tex], where r is radius and h is height of the cylinder.

Given : A new dolphin tank is being built outside of Houston. The tank will be a cylinder with a depth of 42 feet and a radius of 240 feet.

i.e. r=240 and h = 42

Now, the volume of tank will be :_

[tex]\text{Volume}=(3.14) (240)^2 (42)=7,596,288[/tex]

Hence, the tank will hold [tex]7,596,288 ft^3[/tex] water.

Answer:

B. 130

Step-by-step explanation:

Since both sides of the triangle are 10, given that angle D is 25. We can conclude that angle F is also 25.

Total angle of triangle is equal to 180.

angle D + angle F + angle E = 180

25 + 25 + E = 180

50 + E = 180

E = 180 - 50

angle E = 130

Answer:

Step-by-step explanation:

(40*0.9)+(40*-x)

36-40X

Answer: 36-40X

   Answer:

[tex]\displaystyle =36-40x[/tex]

 Step-by-step explanation:

  Distributive property:

          ↓

[tex]\displaystyle A(B+C)=AB+AC[/tex]

A= 40, B=0.9, and C=x

[tex]\displaystyle 40*0.9-40x[/tex]

Then multiply numbers from left to right.

[tex]40*0.9=36[/tex]

[tex]\displaystyle 36-40x[/tex], which is our answer.

Answer:

Step-by-step explanation:

The formula of a volume of a rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have l = 5cm, w = 7cm and h = 12cm.

Substitute:

[tex]V=(5)(7)(12)=420\ cm^3[/tex]

Doubled the dimensions:

l' = (2)(5cm) = 10cm, w' = (2)(7cm) = 14cm, h = (2)(12cm) = 24cm.

Calculate the new volume:

[tex]V'=(10)(14)(24)=3360cm^3[/tex]

Calculate the quotient [tex]\dfrac{V'}{V}[/tex]

[tex]\dfrac{3360}{420}=8[/tex]

Generalization:

V = lwh - the volume of a prism l × w × h

2l × 2w × 2h - new dimensions

V' = (2l)(2w)(2h) = 8lwh = 8V - new volume

Answer: Option C

A data set with less variation will have a smaller __ interquartile range__.

Step-by-step explanation:

The datasets that have less variation are those that have smaller dispersion or variation measures.

Some of these measures of variance are variance, standard deviation, mean absolute deviation, range and interquartile range. Among the options shown, the only one that is used as a measure of variation is the interquartile range. The interquartile range is the difference between the third quartile and the first quartile of a data distribution. In other words, the interquartile range measures the range between the central 50% of the data.

Then the answer is the option C

Answer:

Step-by-step explanation:

[tex]\text{Put}\ g=2\ \text{to the expression}\ g(g+1)^2:\\\\2(2+1)^2=2(3)^2=2(9)=18[/tex]

Answer:

To simplify the following expression: 6 / (7+3i), we're going to multiply and divide the entire expression by (7+3i), as follows:

[tex]\frac{6 (7-3i)}{ (7+3i)(7-3i)} = \frac{42-18i}{58} = 0.72 - 0.31i[/tex]

Now, the denominator has NO imaginary numbers.

Answer:

21/29 - 9/29i

Answer:

-6/-5 is the slope

Step-by-step explanation:

Y2 - Y1 / X2 - X1 so

-1 - 11 / -5 - 5 = -12 / -10 simply it and get -6 / -5

Slope equals rise over run

Answer:

6/5

Step-by-step explanation:

Step-by-step explanation:

Just pick a bunch of values of x, and use the formula to find the corresponding value of y.

For example

When x = 0, y = 0+5 = 5 ----> Plot the point (0,5) on graph paper

When x = 1, y = 1+5 = 6 ----> Plot the point (1,6) on graph paper

When x = 2, y = 2+5 = 7 ----> Plot the point (2,7) on graph paper

Then connect the dots to get a linear graph. You should get a graph that looks  like the one attached.

You first make a table with x and y

like this: x      |        y

then you think of possible values for x then solve for y

it needs to be positive , 0, and a negative like:

under x, you do:

2

0

-3

then you take the equation and solve for y.

after, with the y values, create a Cartesian plane and plot the points

so the points would be (2,7), (0,5), and (-3,2)

then you connect the points and draw arrows on both ends.

then label the line w/ the equation

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

hey btw, i learned this just yesterday. lol

great timing

Answer:

Step-by-step explanation:

Given the function f(x), the  function g(x) = f(x) + k represents the function f(x) shifted k units downwards.

In this case, given that k=-3 (k<0). The graph is shifted 3 units down. Therefore,  we can conclude that the correct option is Option C.

The option "KM" does not represent a direct line segment in the drawing as there is no straight path connecting points K and M without passing through another point.

The figure contains various labeled points connected by lines representing different segments except for NK; hence option NK does not name an existing line segment in the drawing.

1) In this case, all options refer to line segments except for "KM." The points K and M are not connected by a straight line; instead, point N lies between them. Therefore, KM is not a direct line segment in this drawing.

It's essential to understand that a line segment is named after its end points and consists of these points and all the points on the line between them. Since there is no direct path from point K to M without passing through another point (N), KM cannot be considered as a single, uninterrupted line segment.

2)The image you provided contains a geometrical diagram with five labeled points: J, K, L, M, and N. Line segments are drawn connecting these points forming an X shape. The options given are JL, MN, JK, and NK.

Upon careful examination of the image, it is evident that line segments JL (from point J to L), MN (from point M to N), and JK (from point J to K) are present in the drawing. However, NK (from point N to K) is not a line segment depicted in this drawing.

Step-by-step explanation:

cosec²x = 1/sin²x = (sin²x+cos²x)/sin²x =1 + cos²x/sin²x = 1 + cot²x.

Therefore:

1+cot²x = 3cot x - 1

cot²x - 3 cot x + 2 = 0

let cot x = t

t²-3t+2=0

t²-2t-t+2=0

t(t-2)-(t-2)=0

(t-1)(t-2)=0

t1=1

t2=2

so:

cot x = 1 then x1 = π/4 + πk

cot x = 2 then x2 = arccot(2) + πk

k is an integral.

Answer:

m SQ = 95°

Step-by-step explanation:

The measure of the inscribed angle RSQ is one half the measure of its intercepted arc, that is

m RQ = 2 × 95° = 190°

To find the measure of SQ subtract the sum of the measures of SR and RQ from 360

m SQ = 360° - (75 + 190)° = 360° - 265° = 95°

[tex]\bf \cfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\implies \cfrac{a^{10}a^{-7}c^2c^2}{3^{12}\cdot 3^{-8}b^{-3}b^5}\implies \cfrac{a^{10-7}c^{2+2}}{3^{12-8}b^{-3+5}}\implies \cfrac{a^3c^4}{3^4b^2}~\hfill \begin{cases} a=4\\ b=8\\ c=3 \end{cases}[/tex]

[tex]\bf \cfrac{4^3\cdot ~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 3^4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 8^2}\implies \cfrac{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 64 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 1[/tex]

Answer:

Step-by-step explanation:

[tex]\dfrac{3^8a^{10}b^{-5}c^2}{3^{12}a^7b^{-3}c^{-2}}\qquad\text{use}\ \dfrac{x^n}{x^m}=x^{n-m}\\\\=3^{8-12}a^{10-7}b^{-5-(-3)}c^{2-(-2)}=3^{-4}a^3b^{-2}c^{4}\\\\\text{substitute:}\ a=4,\ b=8,\ c=3:\\\\(3^{-4})(4^3)(8^{-2})(3^4)=(3^{-4}\cdot3^4)\bigg(2^2\bigg)^3\bigg(2^3\bigg)^{-2}\\\\\text{use}\ (x^n)(x^m)=x^{n+m}\ \text{and}\ \bigg(x^n\bigg)^m=x^{nm}\\\\=(3^{-4+4})\bigg(2^{(2)(3)}\bigg)\bigg(2^{(3)(-2)}\bigg)=(3^{0})(2^6)(2^{-6})\\\\\text{use}\ x^{-n}=\dfrac{1}{x^n}\ \text{and}\ (x^n)(x^m)=x^{n+m}[/tex]

[tex]=(1)\left(2^{6+(-6)}\right)=2^0=1\\\\\text{Used}\ a^0=1\ \text{for any real value of}\ a,\ \text{except 0}.[/tex]