A rectangular prism has a volume of 5x2 + 45x-180.
Its base has a length of x-3 and a width of 5.
Which expression represents the height of the prism?

1) x-3
2) x² + 9x-36
3) X-9
4) x+12

Answer:

The percentage increase in volume of the prism is impossible to find. This is because the current dimension or the diagram from which the dimension of the prism could be determined is not given.

However I will explain the methods to follow in finding this percentage increase, assuming that the current dimension of the prism is given.

Step-by-step explanation:

Assuming the volume the of prism is x ft³. After adding 1 ft to each dimension, the volume becomes y ft³.

The percentage increase = (y/x) × 100

= z%

That is,

Percentage increase = [(New volume) ÷ (Old volume)] × 100

The resulting value, z% is the percentage increase.

Answer:

[tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.

Step-by-step explanation:

Please refer to the attached figure.

[tex]\triangle IJK[/tex] is shown with the following measurements:

[tex]\angle K = 90^\circ[/tex]

Side KI = 5.3 ft

Side JK = 2.1 ft

To find : [tex]\angle I[/tex] = ?

Using trigonometric identity for tangent of an angle:

[tex]tan\theta = \dfrac{\text{Perpendicular}}{\text{Base}}[/tex]

Here [tex]\theta = \angle I[/tex]

Perpendicular is side JK.

Base is side KI.

Putting the values in above formula:

[tex]tan\theta = \dfrac{\text{JK}}{\text{KI}}\\\Rightarrow tan\theta = \dfrac{2.1}{5.3}\\\Rightarrow tan\theta = 0.3962\\\Rightarrow \theta = 21.6^\circ[/tex]

Hence, [tex]\angle I = 21.6 ^\circ[/tex] is the correct answer.

Answer:

constant because it isn't going up or down, just moving straight

Step-by-step explanation:

Answer:

constant

Step-by-step explanation:

Since this is a horizontal line the slope is zero

This means the graph is constant

Answer:

Going from left to right:

1.) Yes

2.) No

3.) Yes

4.) No

5.) No

6.) Yes

7.) No

8.) No

9.) Yes

10.) No

11.) Yes

12.) Yes

13.) No

14.) Yes

15.) Yes

16.) No

Step-by-step explanation:

Functions cannot have any repeating x-coordinates.

1.) Yes

2.) No

3.) Yes

4.) No

5.) No

6.) Yes

7.) No

8.) No

9.) Yes

10.) No

11.) Yes

12.) Yes

13.) No

14.) Yes

15.) Yes

16.) No

Answer:

I think it's number one

Step-by-step explanation:

Answer:

[tex]\frac{18p-5}{30}[/tex]

Step-by-step explanation:

Answer:

18p-5 over 30.

Found in the LCM method

Answer:

1/9

Step-by-step explanation:

Where my coins at bruh and yo number jhit

The value of the expression {(-3)⁰}/{(-3)²} is 1/9.

Exponentiation is one of the mathematics operations.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

Start Fraction (negative 3) Superscript 0 Over (negative 3) squared End Fraction

In numerator form:

{(-3)⁰}/{(-3)²}

= 1/9

Therefore, 1/9 is the value.

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Answer:x=4 y =1

Step-by-step explanation:

your welcome

Answer:

x = 4, y = 1

Step-by-step explanation:

Substitute the y in the first equation for x-3

X + 2(x-3) = 6

3x -6 = 6

3x = 12

x = 4

Plugging 4 into the second equation

y = 4-3

y = 1

Answer: 88 cm

Step-by-step explanation:

The area of a circle is A=πr². Since we know the area, we can use find the radius, and use the radius to find the circumference,

616=πr²

196=r²

r=14

Now that we have the radius, we can use it to find the circumference. The formula for circumference is C=2πr.

C=2π(14)

C=28π

C=88 cm

Answer: 87.96 cm

Step-by-step explanation:

Radius = √a/π

=√616 / π = 14 cm

Circumference = 2πr

= 2 x π x 14

= 87.96 cm

Answer: 17.9

Step-by-step explanation:

Using Heron's formula:

Area of a triangle is given by:

√s(s-a)(s-b)(s-c)

Where a, b and c ara sides of the triangle and

S = (a+b+c) / 2

In the question above sides are :

XY=XZ= 20 and YZ=18

S = (20 + 20 + 18) / 2 = 58/2 = 29

Area = √29(29-20)(29-20)(29-18)

Area = √29(9)(9)(11)

Area = √25839

Area = 160.74513

Altitude = height(h)

Area = 0.5 × base × height

Base = yz = 18

160.74513 = 0.5 × 18 × h

160.74513 = 9 × h

h = 160.74513 / 9

h = 17.9 (3 s.f)

Answer:

the answer is 10

Step-by-step explanation:

the other shape is half of all the degreed of the first one

Answer: 10

Step-by-step explanation:

AB:  3.0/2 = 1.5 = EF

BC:  5.0/2 = 2.5 = FG

CD:  4.0/2 = 2.0 = GH

DA:  8.0/2 = 4.0 = EH

1.5+2.5+2.0+4.0 = 10

Answer:

The domain is {0.5, 1, 1.5, 2}

The range is {1.9, 3.8, 5.7, 7.6}

Step-by-step explanation:

The cost, y is in dollars, and x in pounds of almonds is shown in the  table.

x (pounds)                 y ($)

0.5                               1.9

1                                   3.80

1.5                                5.70

2                                  7.60

The grocery store sells almond at $3.80 per pound, the relation between y and x is given by the function:

y = 3.8x

The x values are the independent variables and they serve as the input of the function while the y values are the dependent variables (dependent on x) and the serve as the output of the function.

The domain consist of input values which is the x values. The domain is {0.5, 1, 1.5, 2}

The range consists of all output values i.e the y values. The range is {1.9, 3.8, 5.7, 7.6}

Any number of pounds of almonds can be purchased, including partial amounts, so the relation described in the table is continuous.

Because x can be any positive number of pounds, the domain of the relation is x ≥ 0, or x-values greater than or equal to 0.

Because y can be any positive dollar amount, the range of the relation is y ≥ 0, or y-values greater than or equal to 0.

Let's organize what the problem gives us:

We can already tell that the initial amount of kids Mr. Smith has before we factor in the brother count is equal to 4, for the 4 daughters that were stated as a given in the problem.

Now, the tricky part comes in the form of "each daughter had 4 brothers." Remember that within a family, everyone has the same siblings. It doesn't matter which family member's perspective you are looking from, but your siblings will always stay the same. We can show this with an example:

Suppose I had a family of 4 kids total. I had 2 daughters and 2 sons. Their names were Rose, Sakura, David, and Andrew. Rose would then have 3 siblings: Sakura, David, and Andrew. Sakura would also have 3 siblings: Rose, David, and Andrew, so on and so forth.

Applying this example and knowledge to our current problem, if Mr. Smith's daughters each had 4 brothers, then the total number of kids Mr. Smith has is 8 total kids (4 daughters + 4 sons) since each daughter's brother would be the same sibling.

This would be called double-counting if you counted that each daughter would have 4 different siblings, resulting in a false answer of 16 kids (4 daughters multiplied by 4 brothers for each daughter).

∴ Mr. Smith has 8 kids.

___

Topic: Math

Unit: ?

Answer:

44 cm

Please see the attached picture for full solution

Hope it helps....

Good luck on your assignment

Answer:

[tex]x=8[/tex]

Step-by-step explanation:

[tex]\log _{10}\left(10x-1\right)=\log _{10}\left(9x+7\right)\\\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)\\10x-1=9x+7\\\mathrm{Add\:}1\mathrm{\:to\:both\:sides}\\10x-1+1=9x+7+1\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\10x-9x=9x+8-9x\\\mathrm{Simplify}\\x=8\\[/tex]

The solution of the equation ㏒₅(10x - 1) = ㏒₅(9x + 7) is x = 8.

A logarithm is simply the opposite function of the exponentiation.

It is the exponent to which a number or value is raised to get some other number.

That is, if c = aˣ, then we can write it as x =logₐ c.

Given that,

㏒₅(10x - 1) = ㏒₅(9x + 7)

Let the value of both be n.

So, ㏒₅(10x - 1) = n and  ㏒₅(9x + 7) = n

By the definition of logarithms,

10x - 1 = 5ⁿ and 9x + 7 = 5ⁿ

So,

10x - 1 = 9x + 7

10x - 9x = 7 + 1

x = 8

Hence the value of x is 8.

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Answer:

5

Step-by-step explanation:

the measure DF is 7

DE = 2

to get EF, you have to subtract 2 from 7

7 - 2 = 5

Answer:

I would love to  help but i dont know pounds so i will try to help in dollars then convert into pounds

lol :) just wait

Step-by-step explanation:

Answer:

A polygon is a plane figure with at least three straight sides and angles, and typically five or more.

Step-by-step explanation:

Answer:

x = 20°

Step-by-step explanation:

4x + 10 = 90

4x = 80

x = 20

Answer:

[tex] \boxed{x\degree = 20\degree} [/tex]

Step-by-step explanation:

Two Angles are Complementary when they add up to 90° (a Right Angle).

[tex] = > x\degree + (3x + 10)\degree = 90\degree \\ \\ = > x\degree + 3x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree + 10\degree = 90\degree \\ \\ = > 4x\degree = 90\degree - 10\degree \\ \\ = > 4x\degree = 80\degree \\ \\ = > x\degree = \frac{80}{4} \degree \\ \\ = > x\degree = 20\degree [/tex]

Volume of a Sphere Formula:
[tex]\displaystyle V = \frac{4}{3} \pi r^3[/tex]

Diameter/Radius Relationship:
[tex]\displaystyle r = \frac{d}{2}[/tex]

Let us clearly sort out what information this specific problem gives us:

We can consolidate this into mathematical symbols:

Given what we know, we now need to find the volume of the sphere. With knowledge implied, found under the General Formulas and Concepts section above, we can first solve for the radius [tex]\displaystyle r[/tex]:

[tex]\displaystyle\begin{aligned}r & = \frac{d}{2} \\& = \frac{10 \ \text{in}}{2} \\& = \boxed{5 \ \text{in}} \\\end{aligned}[/tex]

∴ the radius of the sphere is equal to 5 inches.

Now that we have our radius, we can substitute this value into our volume of a sphere formula and evaluate:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \boxed{ \frac{500}{3} \pi \ \text{in}^3 } \\\end{aligned}[/tex]

∴ the volume of the sphere is equal to [tex]\boxed{ \frac{500}{3} \pi \ \text{in}^3 }[/tex].

To estimate our answer, we can simply substitute the value of [tex]\displaystyle \pi[/tex] for 3.14, as defined by the problem, and evaluate once more:

[tex]\displaystyle\begin{aligned}V & = \frac{4}{3} \pi r^3 \\& = \frac{4}{3} \pi (5 \ \text{in})^3 \\& = \frac{4}{3} \pi (125 \ \text{in}^3) \\& = \frac{500}{3} \pi \ \text{in}^3 \\& = \frac{500}{3} (3.14) \ \text{in}^3 \\& \approx \boxed{ 523.333 \ \text{in}^3 }\end{aligned}[/tex]

∴ the volume of the sphere is approximately equal to [tex]\displaystyle \boxed{ 523.333 \ \text{in}^3 }[/tex].

∴ the best answer choice that corresponds to our gathered result is answer choice b. 523.333 cu. in.

___

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___

Topic: Geometry

Unit: Volume

Answer:

the answer for this question is increase 24.89%

Step-by-step explanation:

100%= 233 million

? = 291 million

100%/(233×10^6) : x/(291×10^6)

x=[100%×(291×10^6)]/(233×10^6)

x=124.8927039

x=124.89

124.89%-100%=24.89%

Answer:

x =42

q = 135°

p + q + r = 225°

Step-by-step explanation:

a)

Since, AB and BC are perpendicular lines.

[tex] m\angle ABC = 90\degree \\

\therefore 24\degree + x\degree + 24\degree = 90\degree \\

\therefore x\degree + 48\degree = 90\degree \\

\therefore x\degree = 90\degree - 48\degree \\

\huge \red {\boxed {\therefore x = 42}} \\[/tex]

b) (i)

Since, CD and EF are parallel lines and AB is a straight line.

[tex] \therefore q = 135\degree... (vertical \: \angle 's) \\\\

p + 135\degree = 180°..(straight\: line \: \angle' s) \\

p = 180\degree - 135\degree \\

\huge \purple {\boxed {p = 45\degree}} \\

\because r = p ... (vertical \: \angle 's) \\

\huge \purple {\boxed {r = 45\degree}} \\

p + q + r = 45\degree + 135\degree + 45\degree \\

\huge \purple {\boxed {p + q + r = 225\degree }}\\[/tex]

Answer:

Step-by-step explanation:

The discriminant is what's under the square root sign in the quadratic equation.  The equation for the discriminant is [tex]b^{2}-4ac[/tex], where b is the coefficient of x, a is the coefficient of [tex]x^{2}[/tex], and c is the number with no variable attatched to it.  If we plug in the numbers ([tex]17^{2} -4*4*3[/tex]) it gives you 241, which is the discriminant.  Since 241 is more than zero, it has 2 zeros.  If the discriminant was 0, there'd be 1 zero, and less then zero there would be zero zeros.

Answer:

a. length and width

Step-by-step explanation:

option a is correct answer

Answer:

OX = 5.4772 cm

Step-by-step explanation:

Please check image attached for the drawing of the circle with the chords and points.

From the theorem of intersecting chords, we have:

AE * EB = EF * EG

With AE = AX - EX, EB = BX + EX, EF = 6 - EO and EG = 6 + EO, we have:

(AX - EX) * (BX + EX) = (6 - EO) * (6 + EO)

(3 - EX) * (2 + EX) = 36 - EO^2

6 + EX - EX^2 = 36 - EO^2

EO^2 - EX^2 + EX = 30 (eq1)

From the triangle AEO, we have:

AE^2 + EO^2 = OA^2

(AX - EX)^2 + EO^2 = 6^2

(3 - EX)^2 + EO^2 = 36

9 - 6*EX + EX^2 + EO^2 = 36

EX^2 - 6*EX + EO^2 = 27 (eq2)

If we do (eq1) - (eq2), we have:

-2*EX^2 + 7*EX = 3

2*EX^2 - 7*EX + 3 = 0

Solving this quadratic equation, we have EX = 3 cm or EX = 0.5 cm

EX cannot be 3 cm, because AE would be 0 cm, so EX = 0.5 cm

Calculating EO, we have:

EO^2 - 0.5^2 + 0.5 = 30

EO^2 = 29.75

EO = 5.4544 cm

Now, using Pythagoras in the triangle EOX, we have:

EO^2 + EX^2 = OX^2

29.75 + 0.25 = OX^2

OX^2 = 30

OX = 5.4772 cm

Answer:

13

Step-by-step explanation:

To solve this, lets first find the number of footballs he still needs:

75-24 = 51

Now to find the number of packages, divide by 4, since there are 4 balls per package:

51/4 = 12 Remainder 3

Since there is a remainder, and the Coach MUST have at least 75, then we need to add a package to include the remainder:

12 + 1 = 13 Packages

Hey there! :)

Answer:

(2, 3) and (-2, 11).

Step-by-step explanation:

To solve this system of equations, we can set both equations equal to each other:

x² -2x + 3 = -2x + 7

Combine like terms:

x² -4 = 0

Factor using difference of squares:

(x - 2)(x + 2) = 0

Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:

f(x) = -2(2) + 7

f(x) = -4 + 7

f(x) = 3

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

f(x) = -2(-2) + 7

f(x) = 4 + 7

f(x) = 11

Therefore, the two ordered pairs are (2, 3) and (-2, 11).