Question 1 Find the surface area of the prism. Write your answer as a mixed number in simplest form
Answers
The formula is given by;
S.A = 2lh + 2hw + 2lw
where l is the length
h is the height
w is the width
From the question diagram;
l = 1 3/10 = 13/10 when changed to improper fraction
w= 1 2/5 = 7/5 when changed to improper fraction
h = 1 1/5 = 6/5 when changed to improper fraction
Substituting the values into the formula;
S.A = 2(13/10)(6/5) + 2(6/5)(7/5) + 2(13/10)(7/5)
Then we go ahead and evaluate;
S.A = 156/50 + 84/25 + 182/50
=78/25 + 84/25 + 91/25
=253/25
= 10 3/25
[tex]=10\frac{3}{25}ft^2[/tex]Related Questions
A triangle has side lengths 10, 16, and 11. Is the triangle acute, obtuse, or right? Explain.thank you ! :)
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side lengths 10 16 and 11
10^2 + 11^2 = 16^2
100 + 121 = 256
221 = 256 not true so it isn't a right triangle
if the sum of the squares of the two shorter sides (221) is greater than the square of the third side (256) the triangle is acute, since 221 < 256, the triangle is obtuse
5^4 / 5^7 simplify the monomial
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Use the quotient rule of exponents to simplify the answer.
The quotient between two powers n and m of the same base a can be rewritten as:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]Then:
[tex]\frac{5^4}{5^7}=5^{4-7}=5^{-3}[/tex]Therefore, the monomial can be simplified to:
[tex]5^{-3}[/tex]what is the y value of the solution to the system of equations shown below y = 22 - 6 y = 50 – 21
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Given the equation system:
[tex]\begin{cases}y=2x-6 \\ y=5x-21\end{cases}[/tex]To determine the y-value of the solution of the equation system, first, you have to calculate the value of x.
To determine the value of x, equal both expressions:
[tex]2x-6=5x-21[/tex]-Pass the x-term to the left side of the equation and the constant to the right side of the equation by applying the opposite operation to both sides of it:
[tex]\begin{gathered} 2x-5x-6=5x-5x-21 \\ -3x-6=-21 \end{gathered}[/tex][tex]\begin{gathered} -3x-6+6=-21+6 \\ -3x=-15 \end{gathered}[/tex]-Divide both sides by -3 to reach the value of x:
[tex]\begin{gathered} -\frac{3x}{-3}=-\frac{15}{-3} \\ x=5 \end{gathered}[/tex]Now that you have determined the value of x, replace it in either one of the equations to calculate the corresponding y-value, for example, replace the first equation with x=5
[tex]\begin{gathered} y=2x-6 \\ y=2\cdot5-6 \\ y=10-6 \\ y=4 \end{gathered}[/tex]So the corresponding y value for the solution of this equation system is y= 4 (option D)
-4 = 2p + 10 need help find p
Answers
p is -7
Explanation:-4 = 2p + 10
we need the p to stand alone. So we make it the subject of formula
subtract 10 from both sides:
-4 -10 = 2p + 10 - 10
-14 = 2p + 0
-14 = 2p
divide both sides by 2:
-14/2 = 2p/2
-7 = p
The value of p is -7
Algebra 1 Write a system of inequalities to represent the shaded portion of the graph.
Answers
Given: A shaded portion of the graph
Required: System of inequalities to represnt the shaded portion.
Explanation:
Firstly consider the the non-dotted line.
It passes through two points. (0,3) and (-1.5,0)
So write the equation of line using two point form.
[tex]\begin{gathered} y-3=\frac{3-0}{0-(-1.5)}(x-0) \\ y-3=2x \end{gathered}[/tex]so the equation is
[tex]2x-y+3=0[/tex]Since (0,0) lies in shaded region, therefore the inequality is
[tex]2x-y+3\ge0[/tex]Now, consider the dotted line.
It passes through two points. (-3,0) and (0,-1).
Equation of dotted line is
[tex]\begin{gathered} y-0=\frac{0-(-1)}{-3-0}(x+3) \\ y=-\frac{1}{3}(x+3) \end{gathered}[/tex]So the equation is
[tex]\begin{gathered} 3y=-x-3 \\ x+3y+3=0 \end{gathered}[/tex]Now, since (0,0) lies in the shaded portion, therefore the inequality is
[tex]x+3y+3>0[/tex]Final Answer: The system of inequalities are
[tex]\begin{gathered} 2x-y+3\ge0 \\ x+3y+3>0 \end{gathered}[/tex]Tobias is making a 3-digit number by choosing three different numbers from the following list: 1, 2, 5, 6, 8 How many different 3-digit numbers could Tobias make?
Answers
Tobias could generate 512, 216, or 125 different 3-digit numbers.
What is 3 digit number?Three-digit numbers begin at 100 and end at 999. As a result, the smallest three-digit number is 100, while the largest three-digit number is 999. In mathematics, the number is defined by the number of digits.Three-digit numbers range from 100 to 999. As a result, 100 is the smallest three-digit number and 999 is the largest.Budget figures in the triple digits range from 100 to 999 or are in the hundreds.As a result, the answer is 900. The sequence contains 900 three-digit numbers, making 999 the 900th word. A digit is one of the elements of a set that makes up a numeration system. Thus, in a specific context, a digit is a number. The digits in the decimal (base-10) Arabic numbering system are the elements of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.Therefore,
8 × 8 × 8 = 512
6× 6 × 6 = 216
5 × 5 × 5 = 125
Hence, Tobias could generate 512, 216, or 125 different 3-digit numbers.
To learn more about 3-digit number, refer to:
brainly.com/question/713808
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Which statements are true about the graph of this line? 1. The slope is increasing 2. y=x-23. The slope is decreasing 4. y=x+2
Answers
Answer:
1. The slope is increasing
2. y=x-2
Explanation:
First we need to get the slope of the line. Using the coordinate points;
(6,4) and (2, 0)
Slope m = y2-y1/x2-x1
m = 0-4/2-6
m = -4/-4
m = 1
Since the slope is a positive value, hence the slope is increasing
Get the intercept
Substitute m = 1 and (2, 0) into y = mx+c
0 = 2(1) + c
0 = 2+c
c = -2
Get the required equation
y - mx+c
y = 1x + (-2)
y = x - 2
Hence the correct option is slope is increasing and y = x-2
Question 7 of 10Use the function below to find F(1).F(t)=2..23tO A. 3-Im1O B. 2O C.O D.SUBMIT
Answers
Answer: C. 1/4
Explanation
Given
[tex]F(t)=2\cdot\frac{1}{2^{3t}}[/tex]As we are asked to find F(1), then we have to substitute 1 over t:
[tex]F(1)=2\cdot\frac{1}{2^{3(1)}}[/tex]By multiplying the expression in the exponent we get:
[tex]F(1)=2\cdot\frac{1}{2^3}[/tex]We can rewrite this expression as follows as we have 2 elevated to the third power:
[tex]F(1)=\frac{2}{2\cdot2\cdot2}[/tex]Simplifying;
[tex]F(1)=\frac{1}{2\cdot2}[/tex][tex]F(1)=\frac{1}{4}[/tex]you started at (3,1) you move let 2 units . where do u end
Answers
I don't understand how to do trigonometry
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For the unknown angle, perpendicular side is 10 and base side is 14.
Determine the measure of unknown angle by using the trigonometry in triangle.
[tex]\begin{gathered} \tan \theta=\frac{10}{14} \\ \theta=\tan ^{-1}(\frac{10}{14}) \\ =35.53 \\ \approx35.5 \end{gathered}[/tex]So measure of unknown angle is 35.5 degrees.
According to the property , which choice is equivalent to the quotient below?A.36B.6C.12D.-6
Answers
The given quotient is:
[tex]\sqrt{\frac{72}{2}}=\sqrt{36}=6[/tex]Hence, the given quotient is equivalent to 6.
Therefore, the correct answer is choice B:
6
If Jenna buys an item for 40 percent of the regular price, will she pay more or less than half price?
Answers
Consider that if x is the regular price, the 40% of the regular price can be written as 0.4x.
Now consider that the half price of the regular price can be written as 0.5x.
0.4x is less than 0.5x, then, you can conclude:
Jenna will pay less than half price.
Find the measure of angle CEF, angle D, arc AC, and angle EBD.
Answers
For the all questions we use the theorem of chords and arcs and get that for the first question:
[tex]\measuredangle CEF=\text{ }\frac{1}{2}(30^{\circ}+58^{\circ})=44^{\circ}[/tex]Now, to find angle D:
[tex]\measuredangle D=\frac{1}{2}(arcAB\text{ -arcGF)=}\frac{1}{2}(58^{\circ}-20^{\circ})=19^{\circ}[/tex]Next for arcAC we use that WC and WA are tangent to the circle
O is the center of the circle ( O is not E). Now we recall that the inner angles of a quadrilateral is 360 so
[tex]\measuredangle\alpha=360-80-90-90=100[/tex]By the definition of arcAC
[tex]arc\text{AC}=\measuredangle\alpha=100[/tex]Finally we use the fact that the value of inscribed angles is half of the value of the central angle, using this we get :
[tex]\measuredangle EBD=\measuredangle CBG=\frac{1}{2}\measuredangle COG\text{ = }\frac{1}{2}(\text{arcFC}+\text{arcGF)}=\frac{1}{2}50^{\circ}=25^{\circ}[/tex]I need help on a problem
Answers
Consider the given expression,
[tex]\sqrt[]{32}[/tex]Consider the formulae,
[tex]\begin{gathered} x^{m+n}=x^mx^n \\ \sqrt[]{xy}=\sqrt[]{x}\times\sqrt[]{y} \end{gathered}[/tex]Then the expression can be solved as,
[tex]\sqrt[]{32}=\sqrt[]{16\times2}=\sqrt[]{16}\times\sqrt[]{2}[/tex]Thus, the expression can be further simplified as,
[tex]\begin{gathered} \sqrt[]{32} \\ =\sqrt[]{16}\times\sqrt[]{2} \\ =\sqrt[]{4^2}\times\sqrt[]{2} \\ =4\times\sqrt[]{2} \\ =4\sqrt[]{2} \end{gathered}[/tex]2.) What is the total number of different seven-letter arrangements that can be formed using the letters in the word "MILLION"? * O 1) 30 O 2) 210 3) 1,260 4) 2,520
Answers
ANSWER
3) 1260
EXPLANATION
We want to find the total number of different seven letter arrangements that can be made out of MILLION.
First, we know that MILLION has 7 letters.
We don't want a case of repeated letters, because we want 7 different letter arrangements.
There are 2 repeated letters there, I and L, therefore, our answer will be:
[tex]\frac{7!}{2!\text{ 2!}}\text{ = }\frac{5040}{2\cdot\text{ 2}}\text{ = 1260}[/tex]There are 1260 ways to arrange it.
Find the equation of the line passing the poin (-7,2) that is perpendicular to line 4x-3y=10
Answers
Explanation
Step 1
find the slope of the given equation:
two lines are perpendicular it the product of the slopes equals -1, so
[tex]\begin{gathered} \text{ line 1 is perpendicular to line 2} \\ L1\parallel L2 \\ \text{if} \\ m_1\cdot m_2=-1 \end{gathered}[/tex]then , let
[tex]\begin{gathered} \text{ Line 1} \\ 4x-3y=10 \end{gathered}[/tex]to know the slope, we need to convert the equation into the form:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]to do that, let's isolate y
so
[tex]\begin{gathered} 4x-3y=10 \\ \text{subtract 4x in both sides} \\ 4x-3y-4x=10-4x \\ -3y=10-4x \\ \text{divide both sides by -3} \\ \frac{-3y}{-3}=\frac{10-4x}{-3} \\ y=-\frac{10}{3}+\frac{4}{3}x \\ y=\frac{4}{3}x-\frac{10}{3} \\ y=\frac{4}{3}x-\frac{10}{3}\rightarrow y=\text{ mx+b} \end{gathered}[/tex]hence,
[tex]\text{slope 1=m}_1=\frac{4}{3}[/tex]Step 2
now, let's find the slope of the line 2
[tex]\begin{gathered} \text{let} \\ m_1=\frac{4}{3} \\ \end{gathered}[/tex]replacing
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ \frac{4}{3}\cdot m_2=-1 \\ \text{ to isolate, multiply both sides by 3/4} \\ \frac{4}{3}\cdot m_2\cdot\frac{3}{4}=-1\cdot\frac{3}{4} \\ m_2=-\frac{3}{4} \end{gathered}[/tex]so, the slope 2 is -3/4
Step 3
finally, let's find the equation of the line
use the expression
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where} \\ \text{ m is the slope} \\ \text{and (x}_0,y_0)\text{ are the coordinates of a known point} \end{gathered}[/tex]let
[tex]\begin{gathered} m=m_2=-\frac{3}{4} \\ (x_0,y_0)=(-7,2) \end{gathered}[/tex]replace and isolate y
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=-\frac{3}{4}(x-(-7)) \\ y-2=-\frac{3}{4}(x+7) \\ y-2=-\frac{3}{4}x-\frac{21}{4} \\ \text{add 2 in both sides} \\ y-2+2=-\frac{3}{4}x-\frac{21}{4}+2 \\ y=-\frac{3}{4}+\frac{-21+8}{4} \\ y=-\frac{3}{4}x-\frac{13}{4} \\ y=-\frac{3}{4}x-\frac{13}{4} \end{gathered}[/tex]therefore, the answer is
[tex]y=-\frac{3}{4}x-\frac{13}{4}[/tex]I hope this helps you
what is a solution in algebra?
Answers
To understand what is a solution we need to state first what is an equation:
Equation is a mathematical statement that is formed by
What is the slope intercept equation of this line?101(0.4)-10(2-2) 16-10A. y = 4x-3B. y=-3x + 4O c. y = 3x + 4O D. --****
Answers
Given:
Graph is given.
Two given points are:
[tex](0,4)\text{ and (}2,-2)[/tex]To find: Slope intercept equation
Formula :
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}[/tex]Explanation:
The equation of the line is
[tex]\begin{gathered} \frac{y-4}{-2-4}=\frac{x-0}{2-0} \\ \frac{y-4}{-6}=\frac{x}{2} \\ \frac{y-4}{-3}=x \\ y-4=-3x \\ y=-3x+4 \end{gathered}[/tex]Option B is the final answer.
Factor 35r + 40s - 30t. Write your answer as a product with a whole number greater than 1.
Answers
Answer:
5(7r+8s-6t)
Explanation:
Given the expression:
[tex]35r+40s-30t[/tex]The greatest common factor of 35, 40 and 30 = 5
Therefore:
[tex]\begin{gathered} 35r+40s-30t=5\mleft(\frac{35r}{5}+\frac{40s}{5}-\frac{30t}{5}\mright) \\ =5(7r+8s-6t) \end{gathered}[/tex]Combine like terms Зу +3y +5+ 7x^3 - у - 6- 7x^3
Answers
Like terms have the same variables and exponents. Constants are also like terms.
The given expression is
Зу + 3y + 5+ 7x^3 - у - 6 - 7x^3
By combining like terms, it becomes
7x^3 - 7x^3 + 3y + 3y - y + 5 - 6
= 5y - 1
1. What value of 6 makes the equation48 = b= 12 true?
Answers
SOLUTION
From the equation
48 divided
[tex]\begin{gathered} \frac{48}{b}=12 \\ \\ \frac{48}{b}=\frac{12}{1} \\ \\ \text{Cross multiplying } \\ 12b=48 \\ \text{dividing both sides by 12,} \\ \frac{12b}{12}=\frac{48}{12} \\ \\ b=\text{ 4} \end{gathered}[/tex]So, b = 4 makes the equation to be true
I need help on this please
Answers
Given data:
The given expression is 3xy^0 3x^2.
The given value of x is 5.
The given value of y is 3.
Substitute 5 for x, and 3 for y in the given expression.
[tex]\begin{gathered} 3(5)(4)^03(5)^2=15\times75 \\ =1125 \end{gathered}[/tex]Thus, the value of the given expression is 1,125, so third option is corrrect.
Convert: 160 centimeters =inches (Round your answer to the nearest tenth)
Answers
We will have the following:
[tex]160cm\ast\frac{1in}{2.54cm}\approx63.0in[/tex]It will be approximately 63.0 in.
Solve for a: а/4 > 2
Answers
To solve the inequality:
[tex]\frac{a}{4}>2[/tex]we multiply both sides by 4, then:
[tex]\begin{gathered} 4\cdot\frac{a}{4}>4\cdot2 \\ a>8 \end{gathered}[/tex]Therefore the solution is:
[tex]a>8[/tex]and in interval form is:
[tex](8,\infty)[/tex]What is the measure of Zx?Angles are not necessarily drawn to scale.х41°- Zo2=0
Answers
Notice that angle of measure x degrees PLUS the angle of measure 41 degrees add up to give a RIGHT angle (90 degrees) as marked with the identifiable little square by the vertex.
Then we can write the equation:
x + 41 = 90
and solve for x by subtracting 41 from both sides
x = 90 - 41 = 49 degrees.
In the case of the second problem, we are seeing two "supplementary angles" whose addition should give 180 degrees (a straight line)
So we write the equation:
x + 133 = 180
and solve for x by subtracting 133 from both sides:
x = 180 - 133 = 47 degrees.
Solve for x. Enter solutions least to greatest.x^2+3x-4=0
Answers
Given the equation:
[tex]\text{ x}^2\text{ + 3x - 4 = 0}[/tex]To find x, since the equation is in the standard form of Quadratic Equation, we will be using the Quadratic formula:
[tex]\text{ x =}\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex]At,
[tex]ax^2\text{ + bx + c = 0}[/tex]Where,
a = coefficient at x² = 1
b = coefficient at x = 3
c = constant = -4
Let's plug in the values to find for x:
[tex]\text{ x =}\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2-4ac}}{2a}[/tex][tex]undefined[/tex]
day to the nearest quarter hour. What are the total hours for the week? What cotal pay for the week? 1. DATE IN OUT OUT HOURS TEMPORARY EMPLOYEE TIME CARD NAME: Amanda Tacket 9/13 7:00 11:00 11:30 9/14 11:35 12.30 DEPT: Accounting 8:10 12:00 9/16 Note: No overtime rate. 7:05 11:09 11:50 EMPLOYEE SIGNATURE RATE per hour: $8.50 TOTAL HOURS:
Answers
For Amanda Tacket, date 9/13, from 7 to 11, there are 4 hours; from 11:30 to 4.45, there are 5 hours 15 minutes
For date 9/14, from 8:10 to 11.35 there are 3 hours 25 minutes and for the rest of the day 4 hour 5 minutes
for 9/15 is 3 hours 50 minutes first and then 3 hours 30 minutes
for 9/16 is 3 hours 30 minutes first and then 4 hours
for 9/17 4 hours 4 minutes first and then 3 hours 40 minutes
So the total for 9/13 is 9 hours 15 minutes
Total for 9/14 is 7 hours 30 minutes
Total for 9/15 is 7 hours 20 minutes
Total for 9/16 is 7 hours 30 minutes
Total for 9/17 is 7 hours 44 minutes
Total for the week is 39 hours and 19 minutes
Since it only takes up quarters of hours, it rounds to 39 hours 15 minutes, in fraction it would be 39.25 hours
Since the rate is $8.50 per hour, the pay would be 39.25 times $8.50 = $333.625
In parallelogram DEFG if m_DEF=120 find mZEFG. E 120° .70 D G Answer:
Answers
For a parallelogram, the sum consecutive angles are equal to 180 degrees.
Given: mTherefore,
[tex]\begin{gathered} m<\text{DEF}+m<\text{EFG}=180^{\circ} \\ 120^{\circ}+m<\text{EFG}=180^{\circ} \\ m<\text{EFG}=180^{\circ}-120^{\circ} \\ m<\text{EFG}=60^{\circ} \\ x^{\circ}=60^{\circ} \end{gathered}[/tex]Hence, m.
Using complete sentence, describe how the variable h and the variable k of the general formula for a cube root function effects the graph. And than here is the general formula,
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The variable k translates the graph of the function vertically, if k is positive then the translation is up; is k is negative the translation is up. Similarly the variable h translates the graph of the function horizontally, if h is positive the translation is to the right whereas if h is negative the translation is to the left.
Luna invested $8000 for 36 months at an interest rate of 4.8% per month. How much money will Luna have at the end of her investment?
Answers
Answer : $ 9, 152
Luna invested $8000 for 36 months at an interest rate of 4.8%
Let P = principal
T = time
r = rate
Using the simple interest,
[tex]\begin{gathered} I\text{ =}\frac{P\text{ x R x T}}{100} \\ P\text{ = \$8000} \\ r\text{ = 4.8\%} \\ t\text{ = 36 months} \\ 12\text{ months = 1 year} \\ 36\text{ months = x year} \\ \text{Cross multiply} \\ 12\cdot\text{ x = 1 x 36} \\ 12x\text{ = 36} \\ \text{Divide both sides by 12} \\ x\text{ = 36/12} \\ x\text{ = 3 years} \\ \text{Hence, t = 36 months = 3 years} \\ I\text{ = }\frac{8000\text{ x 3 x 4.8}}{100} \\ I\text{ = }\frac{115,\text{ 200}}{100} \\ I\text{ = \$1, 152} \end{gathered}[/tex]The total balance = Interest + principal
Balance = 1, 152 + 8000
Balance =$9, 152
The total money she will have at the end of the investment is $9, 152