Answers
Surface area of a rectangular prism:
[tex]SA=2(wl+hl+hw)[/tex]Substitute 1.2 for all of the variables in the formula:
[tex]SA=2[(1.2)(1.2)+(1.2)(1.2)+(1.2)(1.2)][/tex]Using a calculator, you should get an answer of:
[tex]SA=8.64\text{ }yd[/tex]The answer is that the surface area of this shape is 8.64 yards.
Related Questions
Part A in. (a) For the following figure, the value of x is 45° 8 in. 459 B 45
Answers
Answer
The value of x = 8 in.
y = 8√2 = 11.31 in.
For the second question,
x = 8.3 units
Explanation
Isoscelles triangles have two of their sides being of the same lengths and those two sides are the ones whose base angles are the same.
From the image, we can see that two angles of the triangle have the same measures, hence, we can easily conclude that
x = 8 inches.
To find y, we will use pythagoras theorem.
The Pythagorean Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this triangle,
hyp = y
a = 8 in
b = x = 8 in
a² + b² = (hyp)²
8² + 8² = y²
64 + 64 = y²
y² = 128
Take the square roots of both sides
√(y²) = √128
y = 8√2 = 11.31 in
For the other question.
In a right angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For that triangle,
Hyp = 11 units
Opp = ?
Adj = x
θ = 41°
We can then use trignometrical identities to solve this
CAH allows us to say
Cos 41° = (Adj/Hyp)
Cos 41° = (x/11)
x = 11 Cos 41°
x = 11 (0.7547)
x = 8.3 units
Hope this Helps!!!
how do you do how do you point plot on a graph
Answers
To point plots on a graph, take the following steps:
1. Identify the x-coordinates and y-coordinates from the variable/data you have. It should be written in this form: (x, y)
2. Label both axes on the graph(x-axis and y-axis). The x-axis is usually on the horizontal line while the y axis is the horizontal line.
3. Start plotting your first 2 points on both axes (usually the numbers on first row). Plot the x value and also plot the y value at the appropriate points
4. Finally, Continue plotting the numbers by pointing each point on the graph (take them in rows)
First of all:
1. sketch the graph on paper/ or you can have the graph book.
2. Identify the x-coordinate and y coordinate from the question/data given, where your x coordinate will be on the vertical line and the y coordinate will be on the horizontal line.
3. Then after you start plotting your points on the axes.
4. Then plot/March each points together.
If Angle A is acute and Angle B is obtuse and Angle A is 2X+5 and Angle B is 6X+55, then how many degrees would Angle A be?
Answers
Angle A is 35° and Angle B is 145°
Supplementary angles are angles that give 180° when added together
Angle A and Angle B are supplementary angles such that
∠A + ∠B = 180°
Given that ∠A is acute angle and ∠B is obtuse angle
also , ∠A = 2x+5 and ∠B = 6x+55
using supplementary angle property ,
2x+5 + 6x+55 = 180
solving for x ,
8x + 60 = 180
x = 15
8x = 180 - 60
8x = 120
∠A = 2x+5
substituting value of x
∠A = 2(15)+ 5 = 30+5
∠A = 35°
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Which expression represents the area of the remainingpaper shape in square centimeters?O (x-7)(x-9)O (3x-2)(3x-8)O (3r-4)(3x +4)O (9x - 1)(x+16)
Answers
A square corner of 16 cm² is removed from a square paper with an area of 9X squared, square centimeters. which expression represents the area of the remaining paper shape in the square centimeters?
we have taht
Find out the difference
9x^2-16
apply difference of squares
9x^2-16=(3x-4)(3x+4)
answer is
(3x-4)(3x+4)
Find the slope and y intercept of the line shown below question number 4
Answers
The image of the line provided seems to go through the following points:
(0, 4) , (-4, 5), and (4, 3)
Knowing at least two points is essential to calculate the slope via the formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]so, for example if we use the points (0, 4) and (-4, 5) to calculate the slope, we get:
[tex]\text{slope}=\frac{5-4}{-4-0}=-\frac{1}{4}[/tex]Therefore, the slope is -1/4 (negative one fourth)
Notice as well that one of the points we chose is (0, 4) which in fact is the y-intercept of the line (the point at which the line crosses the y-axis ).
so we have al the elements to built the equation of this line:
slope = -1/4
y intercept = 4 for the (0, 4) on the plane
Then the equation could be built using:
y = (-1/4) x + 4
Which shows another way to write 6*3? A.3 + 3 + 3 + 3 + 3 + 3 B.3 × 3 × 3 × 3 × 3 × 3 C.6 × 6 × 6 D.6 + 6 + 6
Answers
Another way to write the given expression 6×3 is by use of addition operator 6+6+6 .
We know that multiplying a number by another number is another way of adding the number that many times.
If we multiply a with n it can be written as
a × n = a + a + a + a +.... n terms
Similarly we can use the same formula for 6×3.
6×3 = 6+6+6
Addition can be defined and carried out using abstractions known as numbers, such as integers, real numbers, and complex numbers, in addition to counting things.
Addition is a part of the arithmetic branch of mathematics. In algebra, a different area of mathematics, addition can also be performed on abstract objects like vectors, matrices, subspaces, and subgroups.
The words, addends, or summands collectively refer to the quantities or components that must be combined to make a whole number; this terminology also includes the summing of multiple terms. This needs to be differentiated from multiple factors.
Hence the given expression can be written as 6+6+6 .
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the figure below has a point marked with a large dot.first rotate the figure 90 degrees counterclockwise about the origin.then give the coordinates of the Mark point in the original figure in the final figure.
Answers
When we do a 90 degree counterclockwise rotation about the origin, a point moves from ( x,y) to ( -y,x)
Using the point with the blue dot
It is originally at (2,-3)
It will move to (3,2)
factor each trinomial. if the trinomial cannot be factored write prime. show ALL work1.) 5x^2+17x+62.) 2x^2+5x-12
Answers
In order to determine the factors of the given trinomials, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^{2}-4ac}}{2a}[/tex]where a, b and c are the coefficients of the polynomial:
ax² + bx + c
Replace the values of the coefficients of the given trinomials into the quadratic formula.
1) 5x² + 17x + 6
a = 5, b = 17, c = 6
[tex]\begin{gathered} x=\frac{-17\pm\sqrt[]{17^{2}-4(5)(6)}}{2(5)} \\ x=\frac{-17\pm13}{10} \end{gathered}[/tex]the two solutions for x are:
x1 = (-17-13)/10 = -30/10 = -3
x2 = (-17+13)/10 = -4/10 = -2/5
The factors are given by the following expression:
(x - x1)(x - x2)
Then, you have:
5x² + 17x + 6 = (x - (-3))(x - (-2/5)) = (x + 3)(x + 2/5)
Mobile Cookies delivers packs of cookies which cost $2.60 per package to deliver. The fixed cost to run the delivery truck is $252 per day. If the company charges $5.60 per pack, how many packages must be delivered daily to make a profit of $33?
Answers
95 packages must be delivered daily to make a profit of $33.
What is the meaning of profit?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Given that the delivers cost per packets is $2.60 and the cost to run a truck is $252.
Assume that they need deliver x packs of cookies to make a profit of $33.
The total cost to deliver x packs of cookies is $(2.60x + 252).
Given that company charges $5.60 per pack.
The revenue is $5.60x.
The total profit is $(5.60x - (2.60x + 252)) = $(5.60x - 2.60x - 252) = $(3x - 252).
Given that the profit is $33.
Thus 3x - 252 = 33
Add 252 on both sides:
3x = 285
Divide both sides by 3:
x = 95.
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On a certain day the probability of rain is 80% probability of thunder is 3/5 and the probability of both is 2/5. What is the probability that it will rain or thunder?
Answers
The probability it will rain or thunder = 100%
Explanation:Probability it will rain = 80%
P(rain) = 4/5 (simplest term in fraction)
Probability of thunder = 3/5
P(thunder) = 3/5
Probability of both rain and thunder = 2/5
P(rain and thunder) = 2/5
We need to find the probability of rain or thinder = P(rain or thunder)
To find the probability of P(rain or thunder), we will apply the formula for the addition rule on any two events:
[tex]P(A\text{ or B\rparen = P\lparen A\rparen +}P(B)\text{ - P\lparen A and B\rparen}[/tex]Applying the formula in our question:
[tex]P(rain\text{ or thunder\rparen = P\lparen rain\rparen + P\lparen thunder\rparen - P\lparen rain and thunder\rparen}[/tex]substitute the values in order to find the probability:
[tex]\begin{gathered} P(rain\text{ or thunder\rparen = }\frac{4}{5}\text{ + }\frac{3}{5}-\text{ }\frac{2}{5} \\ \\ P(rain\text{ or thunder\rparen = }\frac{4\text{ + 3 - 2}}{5} \\ P(rain\text{ or thunder\rparen = }\frac{5}{5} \\ \\ P(rain\text{ or thunder\rparen = 1} \end{gathered}[/tex]In percentage, the probability it will rain or thunder = 100%
Write the given fraction in simplest form 25/27
Answers
Notice that:
[tex]\begin{gathered} 25=5\cdot5, \\ 27=3\cdot3\cdot3. \end{gathered}[/tex]Then 25 and 27 have no common factors.
Since the denominator and the numerator have no common factors, then the given fraction is in its simplest form.
Answer: 25/27.
[tex]\frac{25}{27}\text{.}[/tex]Which of the following is an equation of a line parallel to the equaticy = 4x+12O A. y=-x-2y4O B. y = -4x – 2O c. y = 4x-2O O D. y=-x-2
Answers
Given
The equation of the line is,
[tex]y=4x+1[/tex]To find the equation of the line parallel to y=4x+1.
Explanation:
It is given that,
The equation of the line is,
[tex]y=4x+1[/tex]Since two parallel lines have same slope.
Then,
The slope of the line parallel to y=4x+1 is, 4.
Therefore, the equation of the line parallel to y=4x+1 is of the form,
[tex]y=4x+k[/tex]Hence, the equation of the line parallel to y=4x+1 is c) y=4x-2.
find the standard deviation of 3, 7, 4, 6, 5 if necessary, round your answer to the nearest tenth
Answers
3, 7, 4, 6, 5
First, find the mean.
Mean = Sum of the values / number of values
Mean = (3+7+4+6+5) /5 = 25/5 = 5
Then, find the variance:
Calculate each value difference from the mean
5-3 = 2
7-5 = 2
5-4= 1
6-5=1
5-5= 0
Square each difference, add them, and divide by the number of values.
Variance : (2^2+2^2+1^2+1^2+0^2 )/ 5 = (4+4+1+1) /5 = 10 /5 = 2
Standard deviation= square root of the variance:
√2 = 1.4
A cell phones was purchased for $400 and depreciates at a rate of 17% per year. How much is the cell phone worth after 4 years? Round to the nearest cent .
Answers
1) Gathering the data
Cell phone
$400
Depreciates at -17% yearly
Period: 4 yrs
2) Let's write an exponential function to calculate that depreciation:
y = The brand new price x (depreciation rate)^time
17%= 0.17
[tex]\begin{gathered} y=400(1-0.17)^4 \\ y=400(0.83)^4 \\ y=189.83 \end{gathered}[/tex]3) So 4 years from the data of the purchase, the cell phone worths $189.83
Construct an obtuse angle called ABC. Bisect ABC and call the new angles ABP and PBC. Now bisect the ABP so that there are 3 angles. The measure of angle PBC is 66 degrees. Fe measures of the two smaller angles are equal to 11y and 3x respectively. What are the values of x and y in degrees?
Answers
Now,
3x + 11y + 66 = 66x2
3x + 11y + 66 = 132
3x + 11y = 132 - 66
3x + 11y = 66 ...............................(equ 1)
tell whether the red line segment is the height or Stan height.
Answers
The slant height is the height that can be found using the height of the pyramid and the half length from the center of one of the sides to the center of the pyramid, this would be the hypotenuse.
The red line in this case represents the height of the pyramid.
Number 11. Find a quadratic equation with (-2,3) and y intercept of 11
Answers
Answer:
[tex]y=2x^2+8x+11[/tex]Explanation:
A quadratic equation in vertex form is generally given as;
[tex]y=a(x-h)^2+k[/tex]where (h, k) is the coordinate of the vertex.
Given the coordinate (-2, 3), we'll have that;
h = -2
k = 3
Given a y-intercept of 11 and we know that at the y-intercept x = 0.
Substituting the above values into the vertex form equation and solving for a, we'll have;
[tex]\begin{gathered} 11=a\lbrack0-(-2)\rbrack^2+3 \\ 11=4a+3 \\ 4a=8 \\ a=\frac{8}{4} \\ a=2 \end{gathered}[/tex]Substituting a = 2, h = -2 and k = 3 into the vertex form equation and taking it to standard form, we'll have;
[tex]\begin{gathered} y=2(x+2)^2+3 \\ y=2(x^2+4x+4)+3 \\ y=2x^2+8x+8+3 \\ y=2x^2+8x+11 \end{gathered}[/tex]27,9,3,1,1/3,1/9....Write the sigma notation for the infinite series. ________________
Answers
Given
Series,
[tex]27,9,3,1,\frac{1}{3},\frac{1}{9},...[/tex]Find
Write the sigma notation for the infinite series.
Explanation
as we see the given series is a geometric series .
here , a = 27
common ratio , r = 9/27 = 1/3
so ,
[tex]\begin{gathered} \sum_{n\mathop{=}1}^{\infty}ar^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(27)(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{-3}(\frac{1}{3})^{n-1} \\ \\ \sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4} \end{gathered}[/tex]Final Answer
Hence , the sigma notation for the infinite series is
[tex]\sum_{n\mathop{=}1}^{\infty}(\frac{1}{3})^{n-4}[/tex]7th grade math I'm stuckhelp me fill in the blanks!
Answers
ok
item price before tax sales tax price including tax
pillow 8 8 x 0.0725 = 0.58 8 + 0.58 = $8.58
blanket 22 22 x0.0725 = 1.595 22 + 1.595 = $23.595
trash can 14.5 14.5 x 0.0725 = 1.051 14.5 + 0.0725 =$15.55
Fill in the missing number to complete the pattern.18, 12, ,0
Answers
using Ap formula,
[tex]\begin{gathered} a+(n-1)d \\ a=18 \\ d=12-18=-6 \\ 18+(3-1)-6 \\ 18-12=6 \end{gathered}[/tex]The missing term = 6
Elisa designed a flower garden in the shape of a square with a side length of 10 feet. She plans to build a walkway along the diagonal. What is the closest measure of the length of the walkway?
Answers
A square has all equal sides, then each side has a measure of feet
The diagonal can be found using the following formula:
[tex]d=\sqrt[]{2a}[/tex]Where a represents a side.
Replacing:
[tex]\begin{gathered} d=\sqrt[]{2(10)} \\ d=\sqrt[]{20} \\ d=14.1421 \end{gathered}[/tex]Hence, the closest measure of the walkway length is 14.1421 feet.
a debt company wants to build a uniquely shaped decks how many square feet of wood will the company need to cover the deck designer below shaped like a regular pentagon a trapezoid the height of the trapezoid is 4.5 ft round your answer to one decimal place to find the area of the Pentagon divided into 5 similar triangles you see if I could the radius at the Pentagon the distance from each vertex Center is 4.25 ft
Answers
72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
To find the total wood required we need to add the area of pentagon and area of trapezoid.
Firstly we will draw the 5 similar triangle in the pentagon as shown below:
Lets name one triangle as ABC.
Given, radius of pentagon = 4.25 ft. (Let x)
Now, in triangle ABC,
BD=DC=2.5 ft. (half of the BC)
By applying Pythagoras theorem,
[tex]AB^{2} =AD^{2} +BD^{2} \\AD=\sqrt{AB^{2} -BD^{2} } \\AD=\sqrt{11.81} \\AD=3.44 ft.[/tex]
We know that AD is the height of triangle ABC.
So, Height = AD = 3.44 ft.
Area of triangle ABC = [tex]\frac{1}{2}[/tex] * base * height
=[tex]\frac{1}{2}[/tex] * 5 ft. 3.44 ft. = 8.59 square feet.
Area of pentagon = area of 5 similar triangle
= 5 * area of triangle ABC
= 5 * 8.59 = 42.96 square feet
Area of trapezoid = [tex]\frac{1}{2}[/tex] * (sum of the parallel side) * height
= [tex]\frac{1}{2}[/tex] * (5+8) * 4.5
= [tex]\frac{1}{2}[/tex] * 13 * 4.5 = 29.25 square feet.
Total square feet of wood required = area of pentagon + area of trapezoid
= 42.96 + 29.25 = 72.21 square feet
Rounding to one decimal place 72.21 square feet ≈ 72.2 square feet.
Thus, 72.2 square feet of wood will the company need to cover the deck designer shaped like a regular pentagon and a trapezoid.
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suppose the odds against winning the lottery are 59,000,000 to 1. What is the probability of the event of winning the lottery given those odds? P(E) = __________
Answers
The odds against winning the lottery is 59,000,000 : 1
Thus,
Not winning bets = 59,000,000
Winning bets = 1
Total bets = 59,000,000 + 1 = 59,000,001
Thus,
The probability of winning = 1/59,000,001
Answer[tex]P(E)=\frac{1}{59,000,001}[/tex]Let f(x)=8x+5 and g(x)=6x^2+2x after simplifying (f+g)(x)=
Answers
We have to find (f+g)(x), where:
[tex]\begin{gathered} f(x)=8x+5 \\ g(x)=6x^2+2x \end{gathered}[/tex]We can write:
[tex](f+g)(x)=f(x)+g(x)=(8x+5)+(6x^2+2x)=6x^2+10x+5[/tex]Answer: (f+g)(x) = 6x^2+10x+5
If the radius of the circle is 6cm, what is the length of arc BC? Round to the neare:thousandth (3 decimal places) and use the pi button on the calculator.
Answers
Given that:
Radius of the circle = 6 cm
Central angle of the arc = 120 degrees
The formula to find the arc length of a circle of radius is
[tex]Arc\text{ length=}\frac{\theta}{360^{\circ}}\cdot2\pi r[/tex]Substitute the given values into the formula.
[tex]\begin{gathered} Arc\text{ length=}\frac{120^{\circ}}{360^{\circ}}\cdot2\pi\cdot6 \\ =12.566\text{ cm} \end{gathered}[/tex]To make 6 cups of ramen, 2/3 cups of noodles is needed. How many cups of ramen can you make with 1 3/4 cups of noodles?
Answers
Explanation
The question calls for using the direct proportion concept. This can be seen below.
Let the number of cups of ramen you can make with 1 3/4 cups of noodles be x. Therefore;
[tex]\frac{6}{x}=\frac{\frac{2}{3}}{1\frac{3}{4}}[/tex]We can them crossmultiply
[tex]\begin{gathered} \frac{2}{3}x=\frac{7}{4}\times6 \\ \frac{2}{3}x=21 \\ 2x=63 \\ x=\frac{63}{2} \\ x=31\frac{1}{2} \end{gathered}[/tex]Answer:
[tex]31\frac{1}{2}\text{cups}[/tex]Answer:
31.5
Step-by-step explanation:
i need help with math
Answers
The following basic properties and characteristics can be used to easily identify parallel lines:
They always are straight lines with equal spacing between them.They are parallel lines.They never cross, no matter how much farther you stretch them in just about any given direction.A transversal line intersecting two parallel lines at two separate positions will form four angles at each point.The statement are given as;
The measurement for the angles for the transversal are-
∠2 = 91° and ∠5 = 89°
Thus,
∠2 = ∠3 = 91° (vertically opposite angles)
The sum ∠3 + ∠5 = 180 (for the parallel lines)
91° + 89° = 180° (supplementary angles).
Thus, two lines are parallel.
The two lines are parallel; True.The measure of ∠7 = 89°; False,Correct; ∠7 = ∠3 = 91°(corresponding angles)
∠3 = ∠6 are same side of interior angles; FalseCorrect; They are opposite side of interior angles.
∠1 is congruent to angle ∠4 because they are vertical angles; True,Thus, the results for the given transversal lines are found.
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The number of McDonald's restaurants worldwide in 2014 was 36.258. In 2009, there were 32,737 McDonald's restau- rants worldwide. Let y be the number of McDonald's res- taurants in the year, where r = O represents the year 2009 (Source: McDonald's Corporation) a. Write a linear equation that models the growth in the number of McDonald's restaurants worldwide in terms of the year x. [Hinr. The line must pass through the points (0.32.737) and (5.30,258).]b. use this equation to predict the number of McDonald's restaurants worldwide in 2016.
Answers
a) y = 704.2x + 32737
b) There are 37,666 McDonald's restaurants in 2016
Explanations:The equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where m is the slope, and is given by the formula: } \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]For the line passing through the points (0, 32737) and (5, 36258)
x₁ = 0, y₁ = 32737, x₂ = 5, y₂ = 36258
Substituting the values into the equations above:
[tex]\begin{gathered} \text{m = }\frac{36258-32737}{5-0} \\ \text{m = }\frac{3521}{5} \\ m\text{ = }704.2 \\ y\text{ - 32737 = 704.2}(x\text{ - 0)} \\ y\text{ - 32737 = 7}04.2x \\ y\text{ = 7}04.2x\text{ + 32737} \\ \end{gathered}[/tex]b) In 2016, x = 7
substitute x = 7 into the equation
[tex]\begin{gathered} y\text{ = 704.2(7) + 32737} \\ y\text{ = }4929.4+32737 \\ y\text{ = }37666.4 \end{gathered}[/tex]There are 37,666 McDonald's restaurants in 2016
A rare manuscript increased in value 400% over the past 4 years. This was an increase of $1,000. What was the value of the manuscript 4 years ago? What is the value of the manuscript now?The value of the manuscript 4 years ago was $.The manuscript is now worth $
Answers
Given
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
To find:
a) What was the value of the manuscript 4 years ago?
b) What is the value of the manuscript now?
Explanation:
It is given that,
A rare manuscript increased in value 400% over the past 4 years.
This was an increase of $1,000.
Then, let x be the value of manuscript 4 years ago.
That implies,
[tex]\begin{gathered} 400\%\times4x=1000+x \\ \frac{400}{100}\times4x=1000+x \\ 16x=1000+x \\ 16x-x=1000 \\ 15x=1000 \\ x=\frac{1000}{15} \\ x=\text{ \$}66.67 \end{gathered}[/tex]And, the value of the manuscript now is,
[tex]\begin{gathered} 4x=4(66.67) \\ =\text{ \$}266.67 \end{gathered}[/tex]Hence, the value of the manuscript is $66.67, and the value off the manuscript now is $266.67.
(08.01 LC)Find the area of a circle with a diameter of 20 inches. Use 3.14 for pi.(1 point)
Answers
The area of a circle can be calculated using the following formula:
[tex]A=\pi r^2[/tex]Where
A represents the area
r represents the radius of the circle
π is the number pi, you have to use 3.14 for the calculatins
You have to calculate the area of a circle that has a diameter of 20 inches. The radius of a circle is half the diameter:
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{20}{2} \\ r=10in \end{gathered}[/tex]The area of the circle can be determined as follows:
[tex]\begin{gathered} A=3.14\cdot10^2 \\ A=314in^2 \end{gathered}[/tex]The area of the circle is 314in²