A triangular prism. The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet. The 2 triangular sides have a base of 2 feet and height of 1.5 feet.

Trenton is building a skateboarding ramp in the shape of a triangular prism. According to his plan, the ramp would have a base of 2 feet, a height of 1.5 feet, and a length of 3 feet. The riding surface would measure 2.5 feet.



If Trenton wants to cover all faces of the ramp with plywood, how much plywood will he need to buy?


Trenton will need
square feet of plywood.

Answer:

48 units²

Step-by-step explanation:

Lateral Surface Area :

Answer:

48 units²

Step-by-step explanation:

The lateral area of a square based pyramid comprises the four triangular sides.

Area of a triangle = 1/2 × base × height

                             = 1/2 × 8 × 3

                             = 1/2 × 24

                             = 12 units²

Lateral SA = 4 × area of triangle

                 = 4 × 12

                 = 48 units²

The average rate of change of the function over the interval [-1, 2] is: C. 2.5.

The average rate of change over an interval of a function is: f(b) - f(a) / b - a.

Given the interval  [-1, 2]:

a = -1; f(a) = -5

b = 2; f(b) = 2.5

Average rate of change = (2.5 - (-5)) / (2 - (-1)) = 7.5/3

Average rate of change = 2.5 (option C).

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Step-by-step explanation:

length = the original length

width = the original width

length = width + 10 or

width = length - 10

(length + 4) × (width + 8) = 135

A

now we are using the first equation in the second to solve then for length :

(length + 4) × (length - 10 + 8) = 135

(length + 4) × (length - 2) = 135

length² - 2×length + 4×length - 8 = 135

length² + 2×length = 143 or

length² + 2×length - 143 = 0

this is the equation to model the scenario.

solving in general such a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = length

a = 1

b = 2

c = -143

length = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =

= (-2 ± sqrt(4 + 572))/2 =

= (-2 ± sqrt(576))/2 =

= (-2 ± 24)/2 = (-1 ± 12)

length1 = -1 + 12 = 11

length2 = -1 - 12 = -13

a negative solution for a length is not applicable, so,

length = 11

width = length - 10 = 11 - 10 = 1

B

the expanded length = 11 + 4 = 15

the expanded width = 1 + 8 = 9

the expanded perimeter is then

2×15 + 2×9 = 30 + 18 = 48

Answer:

Quadrilateral:  shape with 4 sides

Perpendicular means at right angles.  Therefore, draw two sides at a right angles to each other.  Mark this with a right angle symbol.

Draw 2 sides that are parallel.  Mark these with arrows.

Please see attached diagrams.

Abby can make 5 complete groups with 9 extra bonus coupons.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Here, Abby has total number of coupons = 159

        Number of coupons in a group = 30

Total number of groups = Total Coupons / coupons in a group

                                         = 159 / 30

                                         = 5.3

Thus, Abby can make 5 complete groups with 9 extra bonus coupons.

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The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

From the question, we are to determine the number of seeds in 2 ounce package

From the given information,

An orchid seed weighs 3.2 × 10⁻⁸ ounces

If an orchid seed weighs 3.2 × 10⁻⁸ ounces

Then,

2 ounce package will contain [tex]\frac{2}{3\times 10^{-8} }[/tex] seeds

= 0.67 × 10⁸

= 6.7 × 10⁷ seeds

Hence, the number of seeds in 2 ounce package is 6.7 × 10⁷ seeds

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The trip would have taken 6 hours.

(300 mi) / (50 mi/h) = 6 h

cos²(x) = 3 sin²(x)

1 - sin²(x) = 3 sin²(x)

1 = 4 sin²(x)

1/4 = sin²(x)

± √(1/4) = sin(x)

± 1/2 = sin(x)

sin(x) = 1/2   or   sin(x) = -1/2

[x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ]

… … … or   [x = arcsin(-1/2) + 2nπ   or   x = π - arcsin(-1/2) + 2nπ]

(where n is any integer)

[x = π/6 + 2nπ   or   x = 5π/6 + 2nπ]

… … … or   [x = -π/6 + 2nπ   or   x = 7π/6 + 2nπ]

Answer:y=5x+1

Step-by-step explanation:the y intercept is the y value when x=0 which we can read off as run. Slope =rise/run=(change in y value)/(change in x value) for any two points.

Answer: I think

Step-by-step explanation:Let the coordinate of the point be (x,y,z). Since the point is located 3 units behind the YZ− plane, 4 units to the right of XZ− plane and 5 units above the XY−plane ,x=−3,y=4 and z=5 Hence, coordinates of the required points are (−3,4,5)

The correct answer is option D.The point 1.6 with bar will be lies between 1 and 2.

The image of the question is attached with the answer below:-

The number line is the line on which real numbers are marked with the same interval between them. Number lines are used to mark any point of the real number on the line.

We can see in the image that A, B, C and D points are marked on the number line. The line is marked with real numbers that are integers.1.6 bar number will lie between 1 and 2 numbers.

Therefore the correct answer is option D.The point 1.6 with a bar will be lies between 1 and 2.

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Answer:

D

Step-by-step explanation:

Answer:

10.5

Step-by-step explanation:

quick math

Answer:

yes they do

Step-by-step explanation:

they share a ray

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{4}{x}~~ = ~~\cfrac{x}{9}\implies 36=x^2\implies \sqrt{36}=x\implies 6=x[/tex]

Answer:

x=0

Step-by-step explanation:

Expand the equation 4 + [tex]\sqrt{x}[/tex]+1=5

[tex]\sqrt{x} +5=5[/tex]

        -5   -5

subtract 5 from both sides

[tex]\sqrt{x} = 0[/tex]

x=0

square both sides

True= x=0

Answer:

the answer is x=0

Step-by-step explanation:

[tex]4+\sqrt{x} +1=5[/tex]

add "4 +1" which equals 5

[tex]\sqrt{x} +5=5[/tex]

now -5 on both sides :)

[tex]\sqrt{x}[/tex]

now you're left with a square root

[tex]\sqrt{x}=0[/tex]

Answer:

76°

Step-by-step explanation:

The 2 base angles are equal so

52+52+vertex angle=180° (Angle Sum Property)

104+ vertex angle=180°

vertex angle= 180-104

vertex angle=76°

Answer:

The answer to the equation is B.

Step-by-step explanation:

Answer:

i took the test and its B

Step-by-step explanation:

Answer & explanation:

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer. For example, "How many minutes do 6th grade students typically spend on homework each week?" is a statistical question.

Pls, choose me as brainliest!

Answer:

Step-by-step explanation:

Method

Inversely in this sentence means

y = k/x    

So you first step is to find the value of k. You do that by setting up an inverse relationship with y = 2 , x = 5

2 = k/5                     Multiply both sides by 5

2*5 = 5*k/5

10 = k

Now you are able to answer the question.

y = 10/x

3= 10/x                      Multiply both sides by x

3*x = x * 10/x

3x = 10                      Divide both sides by 3

3x/3 = 10/3

x = 3.33 or x = 3 1/3

Answer

x = 3.33 or x = 3  1/3

Answer:

last option

Step-by-step explanation:

hope it helps

One way to determine the factors of x³ + 5x² - 6x - 30 by grouping is shown by option D. x² (x + 5) - 6(x + 5).

Polynomials are mathematical expressions which consist of one or more terms involving variables and coefficients connected with operations like multiplication, subtraction, addition and natural number powers of variables.

Given a cubic polynomial,

x³ + 5x² - 6x - 30

Taking the first two terms together and the other two terms together,

(x³ + 5x²) + (- 6x - 30)

Taking x² common from first and -6 common from second,

x² (x + 5) - 6(x + 5)

Hence the correct option is D.

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Answer:

D) x = 12

Step-by-step explanation:

Given:

[tex]\sf{\dfrac{5}{2}x-7=\dfrac{3}{4}x+14 \implies \dfrac{10}{4}x-7=\dfrac{3}{4}x+14}[/tex]

1. Multiply both sides by 4

[tex]\sf{4\left(\dfrac{10}{4}x-7\right)=4\left(\dfrac{3}{4}x+14\right)}\\\\\implies 10x-28=3x+56[/tex]

2. Subtract 3x from both sides

[tex]\sf{10x-3x-28=3x-3x+56}\\\\\implies 7x-28=56[/tex]

3. Add 28 to both sides

[tex]\sf{7x-28+28=56+28}\\\\\implies 7x=84[/tex]

4. Divide both sides by 7 to isolate the variable:

[tex]\sf{\dfrac{7x}{7}=\dfrac{84}{7}}\\\\\implies x=12[/tex]

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Answer:

D / 242

Step-by-step explanation:

hope this helps!

The first step that we must take before solving a problem is to understand what the problem statement is asking us to do and what is given to us to do so.  Looking at the problem they are asking what the slope of the line is. What is provided to us is an equation which was captured as [tex]y=-2x + 3[/tex].

The next step that we must take is to determine what the slope of the line is. Let us first define what slope is.

Slope-Intercept form is a form in which an equation can be expressed in and it follows the y = mx + b format.  M is equal to the slope while b displays the y-intercept of the expression.

The easiest way to determine the slope using slope-intercept form us by looking at the coefficient of the variable x (in this case) which is also known as m.  Looking at our equation, we can see that the coefficient in front of the variable x is -2.

Therefore, the option that would best match the details that we provided would be option B, -2.

Answer:

B. -2

General Formulas and Concepts:
Algebra I

Slope-Intercept Form:
[tex]\displaystyle y = mx + b[/tex]

Step-by-step explanation:

Step 1: Define

Identify given equation.

[tex]\displaystyle y = -2x + 3[/tex]

Step 2: Find Slope m

Let's compare our given equation to the general equation Slope-Intercept Form to identify our values for slope m and y-intercept b:

We can see that our y-intercept b is equal to 3 and that our slope m is equal to -2.

∴ the slope of the given line is equal to -2 and the answer choice that correlates with this is answer choice B.

___

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Topic: Algebra I

Answer:

a) v>4.5

b) w<6.5

a) 0.3 recurring

b) 5/11

Answer:

[tex]y=\dfrac{1}{2}(x+5)^2-3[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]

[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]

Parent function

[tex]y=-x^2[/tex]

Reflected in the x-axis

[tex]-f(x) \implies y=-(-x^2)\implies y=x^2[/tex]

Compressed vertically by a factor of 1/2

Multiply the whole function by the given scale factor:

[tex]\dfrac{1}{2}f(x)\implies y=\dfrac{1}{2}x^2[/tex]

Translated 3 units down

Subtract 3 from the whole function:

[tex]f(x)-3 \implies y=\dfrac{1}{2}x^2-3[/tex]

Translated 5 units left

Add 5 to the variable of the function:

[tex]f(x+5) \implies y=\dfrac{1}{2}(x+5)^2-3[/tex]

To sketch the parabola

Vertex = [tex](-5, -3)[/tex]

Axis of symmetry:  [tex]x = -5[/tex]

Plot points:

[tex]x=-9 \implies \dfrac{1}{2}(-9+5)^2-3=5 \implies (-9,5)[/tex]

[tex]x=-7 \implies \dfrac{1}{2}(-7+5)^2-3=-1 \implies (-7,-1)[/tex]

[tex]x=-3 \implies \dfrac{1}{2}(-3+5)^2-3=-1 \implies (-3,-1)[/tex]

[tex]x=-1 \implies \dfrac{1}{2}(-1+5)^2-3=5 \implies (-1,5)[/tex]

[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]

[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]

[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]

The results for the matching between function and its period are:

If a given function presents repetitions, you can define the period as the smallest part of this repetition. As an example of periodic functions, you have: sin(x) and cos(x).

[tex]\mathrm{Period\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}[/tex]

The period of sin(x) and cos(x) is 2π.

For solving this question, you should analyze each option to find its period.

1) Option 1

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi }{\frac{1}{2} }=4\pi[/tex]

Thus, the option 1 matches with the letter D.

2) Option 2

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{4} =\frac{\pi }{2}[/tex]

Thus, the option 2 matches with the letter A.

3) Option 3

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}\\ \\ \mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{2} =\pi[/tex]

Thus, the option 3 matches with the letter C.

4) Option 4

[tex]\mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{\mathrm{periodicity\:of}\:\sin \left(x\right)}{|b|}\\ \\ \mathrm{Period\:of\:}a\cdot \sin \left(bx\:+\:c\right)\:+\:d=\frac{2\pi}{8} =\frac{\pi }{4}[/tex]

Thus, the option 4 matches with the letter B.

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