The amount of plywood needed by Trenton = total surface area of the triangular prism-shaped ramp = 21 ft².
What is the Surface Area of a Triangular Prism?Total surface area of a triangular prism = (perimeter of triangular base × length of prism) + 2(area of triangular base) = (s1 + s2 + s3 × L) + 2(1/2 × b ×h).
The amount of plywood needed to cover the ramp = total surface area of the triangular prism-shaped ramp.
We are given the parameters:
s1 = 2 fts2 = 1.5 fts3 = 2.5L = 3 ftb = 2 fth = 1.5 ftTotal surface area of the triangular prism-shaped ramp = (s1 + s2 + s3)L + 2(1/2 × b ×h) = (2 + 1.5 + 2.5)3 + 2(1/2 × 2 ×1.5)
= (18) + (3)
Total surface area = 21 ft²
Trenton will need 21 square feet of plywood.
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25 Select the correct answer. What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]? A. -2.5 B. -2 C. 2.5 D. 3 E. 6
The average rate of change of the function over the interval [-1, 2] is: C. 2.5.
How to Find the Average Rate of Change?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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Solve the system of equations:
y=2x
y=x²-8
The Answer please!!!!!!!!!!
The number of seeds in 2 ounce package is 6.7 × 10⁷ seeds
Calculating quantityFrom 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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If y varies inversely with x and y=2 when x=5, what is the value of x when y=3?
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.
k = 10y = 3x = ?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
Guys, can you please help me with The Question #47 of The Quadratic Relations for me, please? :)
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]
Which expression is equivalent to 12b + 3a? choices: a (a + b) x 12 b 3 (4b + a) c ab x 12 x 3 d (12 x 3) + (b x a)
Answer:
The answer to the equation is B.
Step-by-step explanation:
Answer:
i took the test and its B
Step-by-step explanation:
Match the function in the left column with its period in the right column.
The results for the matching between function and its period are:
Option 1 - Letter DOption 2 - Letter AOption 3 - Letter COption 4 - Letter BWhat is a Period of a Function?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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4 Solve these inequalities. Show the solutions on the number lines.
a 4v-2 > 16
b 6 ≥ 2(w-7)
0
5 a Write as a recurring decimal.
b Convert 0.45 to a fraction.
(5 marks)
Answer:
a) v>4.5
b) w<6.5
a) 0.3 recurring
b) 5/11
Please help asap!! drag each tile to the correct box.
arrange the steps in the correct order to solve this trigonometric equation.
cos^2x = 3sin^2x
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]
What is the value of a in the equation? 22 = startfraction a over 11 endfraction 2 33 222 242
Answer:
D / 242
Step-by-step explanation:
hope this helps!
Cindy wants to put new carpet in her entryway. The entryway is 15ft. long and 7ft. wide. She wants to buy 10% extra carpet in case it is needed. How much carpet will she need to order?
Answer:
10.5
Step-by-step explanation:
quick math
75 points! what is the lateral area?
Answer:
48 units²
Step-by-step explanation:
Lateral Surface Area :
Area of the side faces (exclude the base)4 x 1/2 x 8 x 32 x 2448 units²Answer:
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
A rectangle has a length 10 more than its width. If the width is increased by 8
and the length by 4, the resulting rectangle has an area of 135 square units.
Part A
Write an equation to model the above scenario. Use the model to find the length
of the original rectangle?
powered by
esmos
Part B
What is the perimeter of the expanded rectangle?
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
11. Find the coordinates of the point located six units behind the yz- plane, seven units to the right of the xz - plane, and eight units above the xy-plane. O x = -6, y = 7, z =-6 O x = -6, y = 7, z = 8 Ox=7, y = 7, z = 8 O x = 6, y= 7, z = 8
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)
y'all pls help im really confused on how to do this
A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of 50mph
70mph
Xmph
x=10MPH
x-5mph
The trip would have taken 6 hours.
(300 mi) / (50 mi/h) = 6 h
Could you help me find X,
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]
Which shows one way to determine the factors of x³ + 5x² - 6x - 30 by grouping?
O x(x²-5) + 6(x²-5)
O x(x² + 5)-6(x² + 5)
O x²(x - 5) + 6(x - 5)
O x²(x + 5)-6(x + 5)
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).
What are Polynomials?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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How are statistical questions different from other questions?
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.
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Abby has 159 bonus coupons. She wants to staple them in groups of 30. How many complete groups of 30 can Abby make?
5 complete groups
6 complete groups
14 complete groups
59 complete groups
Abby can make 5 complete groups with 9 extra bonus coupons.
What is Division?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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4+√x+1=5
I need the answer to this question
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]
What is the solution of 5/2-7= 3/4x+14,
O A.
x=-6
O B.
x=6
OC.
X=8
O D. x=12
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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[tex]\sqrt{8+2\sqrt{15}[/tex] Simplify this equation! Please help ASAP
[tex] \sqrt{8 \: + \: 2 \sqrt{15} } [/tex]
Factor the indicated expression:[tex] \sqrt{( \sqrt{3 } \: + \: \sqrt{5} ) ^{2} } [/tex]
Simplified the index, the root and also the exponent using the number 2.[tex] \boxed{ \bold{\sqrt{3} \: + \: \sqrt{5} }}[/tex]
MissSpanishWhat is the slope of the line y=-2x+3?
A. 3
B. -2
C. -3
D. 2
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 ⇒ Slope is the rate of change which can be expressed in an equation. For example, if a student buys 4 books per semester, the rate of change would be 4 as for every semester the student would add another 4 books.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:
Compare: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
Do ∠ABE and ∠DBC share a ray
Answer:
yes they do
Step-by-step explanation:
they share a ray
Which point on the number line most closley represents 1.ModifyingAbove 6 with bar?
A number line going from negative 6 to positive 6. Point A is between negative 2 and negative 1, point B is between 0 and 1, point C is 1, point D is between 1 and 2.
A
B
C
D
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:-
What is a number line?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:
what is the the value of m in the equation 1/2m-3/4n=16, when n=8
for the function f(x) = x^2, what effect will be multiplying f(x) by 1/2 have on the graph?
what is the slope-intercept equation of the line that includes the points in the table?
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.
The measure of the base angle of an isosceles triangle is 52.
What is the measure of the vertex angle?
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°
Can y’all help with this?
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.