Which expressions are equivalent to the one below? Check all that apply.ln(e5)A.1B.5C.5 • ln eD.5e
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SOLUTION:
We want to find the equivalent expression to;
[tex]ln(e^5)[/tex]We can rewrite it as;
[tex]\begin{gathered} 5ln(e) \\ =5 \end{gathered}[/tex]Thus, the answers are;
[tex]5Ine\text{ }and\text{ }5[/tex]OPTION B and C
Related Questions
In the following exercise a formula is given, along with the values of all but one of the variables in the formula. Find the value of the variable that is not given S = 2LW+2WH + 2LH; S = 108, L= 3, W= 4
Answers
Answer:
H = 6
Explanation:
We are given the values of S, L, and W, and so we put them into the formula to get
[tex]108=2(3)(4)+2(4)H+2(3)H[/tex]We simplify the above to get
[tex]108=24+8H+6H[/tex]Subtracting 24 from both sides gives
[tex]108-24=24-24+8H+6H[/tex][tex]84=8H+6H[/tex]Adding the like terms on the right-hand sides gives
[tex]84=14H[/tex]Finally, dividing both sides by 14 gives
[tex]\frac{84}{14}=\frac{14H}{14}[/tex]which gives
[tex]H=6[/tex]which is our answer!
at one point during the summer, Marsha has read 500 pages of her summer reading assignment, and Jan has read read 460 pages. marsha reads reads 20 pages per week for the reminder of the summer, how many weeks,w,will it take before the girls have read the same number of pages?
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Answer:
500 + 20w = 460 + 30w
Explanation:
We will calculate an equation for the number of pages read by each girl.
Marsha has read 500 pages and she reads 20 pages per week. It means that after w weeks, she will read 20 times w plus the 500 initial pages, so:
M = 20w + 500
In the same way, Jan has read 460 pages and she reads 30 pages per week. So, the equation that model the number of pages that she reads after w weeks is:
J = 30w + 460
Now, we need to find w such that M and J would be equal, so, we will formulate the following equation:
M = J
20w + 500 = 30w + 460
500 + 20w = 460 + 30w
Therefore, the answer is:
500 + 20w = 460 + 30w
Eduardo has 45 yards of rupe light.Exactly how many more yards does he need to finish the car's ceiling?ItemLength of Rope Light (yds)Front spoilerRear spoilerCeilingDONENaimmisDashboardWhat is the fraction
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Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a stringthat is 18 feet long and makes a 30 degree angle with the ground. How high is the kite?
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ANSWER:
9 feet
STEP-BY-STEP EXPLANATION:
We can calculate the value of the height of the kite by means of the trigonometric function sine, which is the following:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \theta=30\text{\degree} \\ \text{hypotenuse = 18} \\ \text{opposite }=x \end{gathered}[/tex]Replacing and solving for x:
[tex]\begin{gathered} \sin 30=\frac{x}{18} \\ x=\sin 30\cdot18 \\ x=9 \end{gathered}[/tex]The height of the kite is 9 feet
MINI Statistics in 2021 900Carissa Brooks & 10Homework: 2.52016 (18 completeNW Score:Score: DaX 25.49Aceasta es am 38,000 miles and advisor 2, 250 mes. Assume the lens of the res have a belspetsin)the tears are my cheese 3700 ms 31.000 ms. meore that corresponds to amanten
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In order to find the z-score for the value 34000, we can use the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where μ is the mean and σ is the standard deviation.
So using x = 34000, μ = 38000 and σ = 2250, we have:
[tex]Z=\frac{34000-38000}{2250}=-\frac{4000}{2250}=1.78[/tex]So the z-score for the value 34000 is 1.78.
Solve each equation mentally. 2×=10. -3×=21
Answers
Explanation:
To solve this you have to divide the number on the right side by the coefficient of x:
2x=10 --> 10/2=5
-3x=21 --> 21/(-3)=-7
Answers:
2x=10 --> 5
21/(-3) --> -7
Given the venn diagram below, what is the correct notation!A. G∩(M∪F)′B. (M∩F)′C. none of theseD. (M∪F)′
Answers
Sets
The image shows a Venn diagram of two sets M and F inside of a containing set G.
We must recall the following notations:
U = Union of sets. Everything inside of any of the sets.
∩ = Intersection between two sets. The common part of both sets.
' = Negation. Everything outside of a set or a set operation.
It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.
As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.
But we want the outside of that white part, so we use (M U F)'.
That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:
A. G∩(M∪F)′
Answer:
Step-by-step explanation:
The image shows a Venn diagram of two sets M and F inside of a containing set G.
We must recall the following notations:
U = Union of sets. Everything inside of any of the sets.
∩ = Intersection between two sets. The common part of both sets.
' = Negation. Everything outside of a set or a set operation.
It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.
As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.
But we want the outside of that white part, so we use (M U F)'.
That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:
A. G∩(M∪F)′
which of the following is the correct way to simplify
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We need to apply the law of exponents. In this case we need to
Keep the base and add the exponents,
that is the third option.
Can I find a tutor to help me bro ?
Answers
Solution
Given the quadratic equation:
x² + 2x + 7 = 21
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
a = 1, b = 2, c = - 14
(1) The number of solutions of a given quadratic equation is determine by the discriminant.
From the given values;
(2)² - 4(1 x -14) = 4 + 56 = 60
60 > 0 ( 2 solutions)
1 positive solution and 1 negative solution
Thus, number of positive solutions to this equation is one
(2) The greatest solution or positive solution to the equation is calculated as;
A bouncy ball is dropped such that the height of its first bounce is 6.25 feet and each successive bounce is 74% of the previous bounces height. What would be the height of the sixth bounce the ball
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EXPLANATION
The heigth of the first bounce is 6.25 feet
Each successive bounce is 74% of the previous bounces height
For the first bounce, the ball hit a height of 6.25 feet
The first successive bounce = 74% of the previous bounce
The previous bounce = 6.25 feets
Hence, 74% x 6.25 = Next successive bounce
The next successive bounce = 74/100 x 6.25
The next succesive bounce = 0.74 x 6.25
= 4.625 feets
For the next successive bounce
The previous successive bounce = 4.625 feets
The next successive bounce = 74% x 4.625
The next successive bounce = 0.74 x 4.625
The second successive bounce = 3.4225 feets
For third successive
Isabelle is making a scrapbook. Each page of the scrapbook is a square with a length of 11in. If each page holds three pictures that each have an area of 15in2, what is the remaining area on each page in square inches that can be used for decoration?
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Given:
A page of the scrapbook is a square with a length of 11 in
Each page holds three pictures that each have an area of 15in²
To find the remaining area, we will find the area of the page and the total area of the pictures, then subtract the area of the pictures from the area of the page
The area of the page = 11 x 11 = 121 in²
Total area of the pictures = 3 x 15 = 45 in²
So, the remaining area = 121 - 45 = 76 in²
please help me the blue line is what I have to find
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Weare given to complete a blank in the equation:
2 m - 3 - _____ + 17 = 14
So, we start by combining all the terms we can combine (the pure numerical terms that don't have the variable "m")
2 m - 3 + 17 - ______ = 14
2 m + 14 - _______ = 14
Now we subtract 14 from both sides of the equal sign:
2 m - ____ = 0
which means that the blank should be exactly "2m" such that subtracted from 2m gives a perfect zero.
Answer: complete the blank with "2 m"
Amanda likes to launch model rockets. For one of Amanda's rockets, the function S(t)= −16t^2+41t+112 gives the height of the rocket above the ground in feet, in terms of the number of seconds t since the rocket's engine stops firing.Please use 4 or more decimals.How far above the ground is the rocket when it stops firing?After how many seconds does the rocket reach its maximum height?What is the maximum height reached by the rocket?After how many seconds will the rocket hit the ground?
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Answer:
• (a)112 feet
,• (b)1.28125 seconds.
,• (c)138.265625 feet.
,• (d)4.22091 seconds
Explanation:
The height of the rocket in terms of the number of seconds t since the rocket's engine stops firing is given below.
[tex]S\mleft(t\mright)=-16t^2+41t+112[/tex]Part A
At the time the rocket stopped firing, t=0.
[tex]S(0)=-16(0)^2+41(0)+112=112[/tex]The rocket was 112 feet above the ground when it stopped firing.
Part B
The value of t at which the rocket reaches its maximum height is the equation of the line of symmetry.
To find this equation, we use the formula below.
[tex]t=-\frac{b}{2a}=-\frac{41}{-2\times16}=1.28125\text{ seconds}[/tex]The rocket reaches its maximum height after 1.28125 seconds.
Part C
To find the maximum height, substitute t=1.28125 into S(t).
[tex]\begin{gathered} S\mleft(t\mright)=-16t^2+41t+112 \\ \implies S(1.28125)=-16(1.28125)^2+41(1.28125)+112 \\ =138.265625\text{ ft} \end{gathered}[/tex]The maximum height of the rocket is 138.265625 feet.
Part D
When the rocket hits the ground, the height is 0.
Set S(t)=0 and solve for t as follows.
[tex]S(t)=-16t^2+41t+112=0[/tex]Using the quadratic formula:
[tex]\begin{gathered} t=\dfrac{-41\pm\sqrt[]{41^2-4(-16)(112)}}{2\times-16}=\dfrac{-41\pm\sqrt[]{1681-(-7168)}}{-32} \\ =\dfrac{-41\pm\sqrt[]{1681+7168}}{-32} \\ =\dfrac{-41\pm\sqrt[]{8849}}{-32} \\ t=\dfrac{-41+\sqrt[]{8849}}{-32}\text{ or }t=\dfrac{-41-\sqrt[]{8849}}{-32} \\ t=-1.658\; \text{or }t=4.22091 \end{gathered}[/tex]Since t cannot be negative, the rocket will hit the ground after 4.22091 seconds.
-Quadratic Equations- Determine the number and the nature of the solutions to (3a + 24)² = -36 and then solve
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ANSWER
There are two solutions and they are both complex solutions. The solutions are:
[tex]a=2i-8;a=-2i-8[/tex]EXPLANATION
We want to determine the number and nature of solutions to the equation:
[tex](3a+24)^2=-36[/tex]To do this, solve the equation by first, finding the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{(3a+24)^2}=\pm\sqrt[]{-36}=\pm\sqrt[]{-1\cdot36} \\ \Rightarrow3a+24=\pm\mleft\lbrace\sqrt[]{36}\cdot\sqrt[]{-1}\mright\rbrace \\ 3a+24=\pm6i \end{gathered}[/tex]Now, solve the equation for a:
[tex]\begin{gathered} 3a=\pm6i-24 \\ \Rightarrow a=\pm\frac{6i}{3}-\frac{24}{3} \\ \Rightarrow a=2i-8;a=-2i-8 \end{gathered}[/tex]Hence, there are two solutions and they are complex solutions.
Which best explains the transformation of TUV to form T'U'V
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the figure T'U'V' is reflected on the x-axis, therefore is transformed by (x, - y)
answer: the first one
(Combining Equations)-2x + 7y = -5 -2x - 4y = 6
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-2x + 7y = -5 --------------------------(1)
-2x - 4y = 6 ------------------------------(2)
subtract equation (2) from equation (1)
11y = -11
Divide both-side of the equation by 11
y = -1
substitute y=-1 into equation(1) and then solve for x
-2x + 7(-1) = -5
-2x - 7 = -5
add 7 to both-side of the equation
-2x = -5+7
-2x = 2
Divide both-side of the equation by -2
x= -1
which is rational?3 2/3 + 3
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shelton earns an hourly wage at a grocery store. the following expression represents Sheltons take home pay after taxes, social security, and his health care plan deducted. let x represent the number of hours shelton worked. 10.25x-0.21(10.25x) part A: which term represents sheltons total pay before deduction. part B:which term represents sheltons deductions. part C:how much is sheltons hourly wage. part D:what percentage is decuted from sheltons pay for taxes , social security , and health care plan. part E: shelton wants to save 1675 for a new laptop. if shelton saves 25% of his take hime pay,how many hours will be need to work to meet his savings goal
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The expression that represents Shelton's take-home pay after all deductions is:
[tex]10.25x-0.21\mleft(10.25x\mright)[/tex](a)Shelton's total pay before deduction = $10.25x
(b) Shelton's deductions = $0.21(10.25x)
(c)Since x represents the number of hours Shelton worked, his hourly wage will be: $10.25
(d)Since 0.21 of his total pay is deducted, the percentage that is deducted from Shelton's pay is 21%.
(e)If Shelton saves 25% of his take-home pay, this will be:
[tex]0.25(10.25x-0.21\mleft(10.25x\mright))[/tex]If he wants to save $1,675, we then have:
[tex]0.25(10.25x-0.21\mleft(10.25x\mright))=1675[/tex]We are required to solve for x.
[tex]\begin{gathered} 0.25(10.25x-2.1525x)=1675 \\ 0.25(10.25x-2.1525x)=1675 \\ 0.25\times8.0975x=1675 \\ 2.024375x=1675 \\ x=\frac{1675}{2.024375} \\ x=827.4\approx827\text{ hours} \end{gathered}[/tex]Shelton will work for 827 hours to meet his goal.
Can you please help me
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length of arc PQ = 3.14 meters (option B)
Explanation:[tex]\begin{gathered} \text{Length of an arc in radians = r}\theta \\ \end{gathered}[/tex]The angle given is in degrees:
[tex]\text{length of an arc using angle in degr}ees\text{ = }\theta/360\times2\pi r[/tex][tex]\begin{gathered} \theta\text{ = 60}\degree \\ PR\text{ = radius =3m } \\ \text{let }\pi\text{ = 3.14} \\ \text{length of arc PQ = }\frac{60}{360}\times2\times3.14\times3 \end{gathered}[/tex][tex]\begin{gathered} \text{length of arc PQ = }\frac{1}{6}\times3.14\times6\text{ = 3.14} \\ \text{length of arc PQ = 3.14 meters ( option B)} \end{gathered}[/tex]please explain What is the simplified form of the expression?
2x 2 + 4y + 3x 2 – 2y + 3y
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The simplified form of the expression is found to be 5(x² + y) by adding or subtracting all the similar terms
What is the difference between a mathematical expression and an equation?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
What does "simplification of an algebraic expression" mean?The technique of expressing an algebraic expression in the most effective and compact form without altering the original expression's value is known as simplification. The procedure involves gathering related terms, which calls for adding or removing terms from an expression.
The given expression is 2x² + 4y + 3x² -2y +3y
We need to simplify this expression.
2x² + 4y + 3x² -2y +3y
= 2x² + 3x² + 4y - 2y + 3y
= 5x² + 5y
= 5(x² + y)
Therefore, the simplified form of the expression is found to be 5(x² + y) by adding or subtracting all the similar terms.
Learn more about simplified expressions here:
https://brainly.com/question/723406
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7. A large cooler contains the following drinks: 5 lemonades, 9 Sprites, 7 Cokes, and 10 root beers. You randomly pick two cans, one at a time (without replacement). Compute the following probabilities.(a) What is the probability that you get two cans of Sprite? (b) What is the probability that you do not get two cans of Coke? (c) What is the probability that you get either two root beers or two lemonades? (d) What is the probability that you get one can of Coke and one can of Sprite? (e) What is the probability that you get two drinks of the same type?
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A large cooler contains the following drinks,
5 Lemonades, let L reprersent Lemonade
9 Sprites, let S reprersent Sprite
7 Cokes, let C represent Coke and
10 Root beers, let R represent Root beer
Total drinks in the cooler is
[tex]=5+9+7+10=31[/tex]Total outcome = 31 drinks
The formula of probability is
[tex]\text{Probability}=\frac{required\text{ outcome}}{total\text{ outcome}}[/tex]a) The probability that you get two cans of Sprite is
[tex]\begin{gathered} Prob\text{ of picking the first Sprite without replacement is} \\ P(S_1)=\frac{9}{31} \\ Prob\text{ of picking the second Sprite is} \\ P(S_2)=\frac{8}{30} \\ \text{Probability of getting two cans of Sprite}=(PS_1S_2)=\frac{9}{31}\times\frac{8}{30}=\frac{12}{155} \\ (PS_1S_2)=\frac{12}{155} \end{gathered}[/tex]Hence, the the probability that you get two cans of Sprite is 12/155
b)
The probability that you get two cans of Coke
[tex]\begin{gathered} Prob\text{ of picking the first Coke without replacement is} \\ P(C_1)=\frac{7}{31} \\ Prob\text{ of picking the second Coke is} \\ P(C_2)=\frac{6}{30} \\ \text{Probability of getting two cans of Coke is} \\ P(C_1C_2)=\frac{7}{31}\times\frac{6}{30}=\frac{7}{155} \\ P(C_1C_2)=\frac{7}{155} \end{gathered}[/tex]The probability that you do not get two cans of Coke will be
[tex]\begin{gathered} \text{Prob that you do not get two cans of Coke is} \\ 1-P(C_1C_2)=1-\frac{7}{155}=\frac{155-7}{155}=\frac{148}{155} \\ \text{Prob that you do not get two cans of Coke }=\frac{148}{155} \end{gathered}[/tex]Hence, the probability that you do not get two cans of Coke is 148/155
c)
The probability that you get two cans of Root beers is
[tex]\begin{gathered} Prob\text{ of picking the first Root b}eer\text{ without replacement is} \\ P(R_1)=\frac{10}{31} \\ Prob\text{ of picking the second Root b}eer\text{ is} \\ P(R_2)=\frac{9}{30} \\ \text{Probability of getting two cans of Root b}eer\text{ is} \\ P(R_1R_2)=\frac{10}{31}\times\frac{9}{30}=\frac{3}{31} \\ P(R_1R_2)=\frac{3}{31} \end{gathered}[/tex]The probability that you get two cans Lemonades is
[tex]\begin{gathered} Prob\text{ of picking the first Lemonade without replacement is} \\ P(L_1)=\frac{5}{31} \\ Prob\text{ of picking the second Root b}eer\text{ is} \\ P(L_2)=\frac{4}{30} \\ \text{Probability of getting two cans of Lemonade is} \\ P(L_1L_2)=\frac{5}{31}\times\frac{4}{30}=\frac{2}{93} \end{gathered}[/tex]The probability that you get either two root beers or two lemonades is
[tex]P(R_1R_2)+P(L_1L_2)=\frac{3}{31}+\frac{2}{93}=\frac{11}{93}[/tex]Hence, the probability that you get either two root beers or two lemonades is 11/93
d)
[tex]\begin{gathered} Prob\text{ of picking the first Coke without replacement is} \\ P(C)=\frac{7}{31} \\ \text{Prob of picking a can of Sprite is} \\ P(S)=\frac{9}{30} \end{gathered}[/tex]After getting both Sprite and Coke you will multiply the probabilities and then multiply them with 2 because you may choose Coke in first try and Sprite in second or the other way around
The probability that you get one can of Coke and one can of Sprite is
[tex]P(CandS)=2\times(\frac{7}{31}\times\frac{9}{30})=2(\frac{21}{310})=\frac{21}{155}[/tex]Hence, the probability that you get one can of Coke and one can of Sprite is 21/155
e)
Prob of two of each of the cans of drinks (without replacement) are as follow
[tex]\begin{gathered} P(L_1L_2)=\frac{2}{93} \\ (PS_1S_2)=\frac{12}{155} \\ P(C_1C_2)=\frac{7}{155} \\ P(R_1R_2)=\frac{3}{31} \end{gathered}[/tex]The probability that you get two drinks of the same type is
[tex]\begin{gathered} \text{Prob of two drinks of the same type is} \\ =P(L_1L_2)+(PS_1S_2)_{}+P(C_1C_2)+P(R_1R_2) \\ =\frac{2}{93}+\frac{12}{155}+\frac{7}{155}+\frac{3}{31}=\frac{112}{465} \\ \text{Prob of two drinks of the same type}=\frac{112}{465} \end{gathered}[/tex]Hence, the probability that you get two drinks of the same type is 112/465
7)Find the equation of the line that goes throughthe points (-1, 4) and (0, 5).Find m:Which point is the y-intercept?x43bEquation in the form y = mx + b:Graph the line:Y
Answers
Given the following question:
Point A = (-1, 4) = (x1, y1)
Point B = (0, 5) = (x2, y2)
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{5-4}{0--1}=\frac{1}{1}=1 \\ m=1 \end{gathered}[/tex]Now write in slope intercept form where...
[tex]\begin{gathered} y=mx+b \\ m=1 \\ y=4 \\ x=-1 \end{gathered}[/tex]Substitute to find b:
[tex]\begin{gathered} 4=1(-1)+b \\ 1\times-1=-1 \\ \text{ +1 on both sides} \\ 4+1=5 \\ 5=b \\ b=5 \\ y=1x+5 \end{gathered}[/tex]b = 5
y intercept is (0, 5)
Now graph the following equation:
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for < or ">" for >(4,2)(-4,0)
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EXPLANATION
We can write an inequality in slope-intercept form by using the two given points, (x_1,y_1)= (-4,0) and (x_2,y_2)=(4,2), as shown as follows:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing terms:
[tex]\text{Slope}=\frac{(2-0)}{(4-(-4))}[/tex]Subtracting terms:
[tex]\text{Slope}=\frac{2}{8}=\frac{1}{4}[/tex]Now, we need to find the y-intercept.
As we can see in the dashed line, the y-intercept is at point (x,y)=(0,1).
Hence, the equation of the dashed line is as follows:
y = (1/4)x + 1
But as the solution represents all the points that are below this line, the inequality should be as following:
y < (1/4)x + 1
What is the hcf of 13 and 31?
Answers
Answer: 1
Step-by-step explanation:
The factors of 13 are: 1, 13
The factors of 31 are: 1, 31
So the hcf is 1
Convert 185 pounds into kilograms
Answers
We want to convert 185 pounds to kilograms
1 pound = 0.4536 kilograms
Therefore,
185 pounds = 185 * 0.4536
185 pounds = 83.916 kilograms
185 pounds is 83.916 kilograms
Triangle Ris a right triangle. Can we use two copies of TriangleR to compose a parallelogram that is not a square? Explain yourreasoningR.R
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If we have a right triangle R as:
We have a right angle.
The only way we can make a parallelogram that is not a square is placing the triangle so the parallelogram does not have any right angle. That would be;
This way, the right angles are added to one of the other angles, in order to have none right angles, as it is the condition to have a four-side figure that is not a square or rectangle.
(If the triangle R can compose a square, it should have two equal sides, not like our figure).
Sorry if it's a little blurryAlso this worksheet is about simplify
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Write four different equation with -3 as solution.
5x + 20 = 5 subtract 20 both sides
5x = 5 - 20
5x = -15 divide by 5 both sides
x = -15/5
x = -3
3x - 6 = -3x - 24 add 3x both sides
3x + 3x - 6 = - 24
6x - 6 = -24 add 6 both sides
6x = -24 + 6
6x = -18 divide by 6 both sides
x = -18/6
x = -3
1/3 x + 10 = 9 subtract 10 both sides
1/3 x = 9 -10
1/3 x = - 1 multiply by 3 both sides
x = -1(3)
x = -3
x + 23 = 20 subtract 23 both sides
x = 20 - 23
x = -3
In all previous procedures you constructed the equation by taking into account that x=-3, that is the key to determine the expressions left side and right side. For example in the last procedure for x + 23 = 20, you know that -3 plus 20 is equal to 20.
Based on the triangles shown below, which statements are true? Select All that apply.
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Answer:
All the options except the third choice are correct.
Explanation:
In the given figure:
[tex]\angle\text{GER}\cong\angle\text{TEA (Vertical Angles)}[/tex]Since angles G and T are congruent:
• Triangles GER and TEA are similar triangles.
Therefore, the following holds:
[tex]\begin{gathered} \triangle\text{GRE}\sim\triangle\text{TAE} \\ \triangle E\text{GR}\sim\triangle E\text{TA} \\ \frac{GR}{TA}=\frac{RE}{AE} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \frac{EG}{ET}=\frac{GR}{TA} \\ ET=10,EG=5,TA=12,RG=\text{?} \\ \frac{5}{10}=\frac{RG}{12} \\ \frac{1}{2}=\frac{RG}{12} \\ 2RG=12 \\ RG=\frac{12}{2} \\ RG=6 \\ \text{Therefore if }ET=10,EG=5,and\; TA=12,then\; RG=6 \end{gathered}[/tex]Finally, angles R and A are congruent.
[tex]\begin{gathered} m\angle R=m\angle A \\ 80\degree=(x+20)\degree \\ x=80\degree-20\degree \\ x=60\degree \end{gathered}[/tex]The correct choices are:
[tex]\begin{gathered} \triangle\text{GRE}\sim\triangle\text{TAE} \\ \triangle E\text{GR}\sim\triangle E\text{TA} \\ \frac{GR}{TA}=\frac{RE}{AE} \\ I\text{f }ET=10,EG=5,and\; TA=12,then\; RG=6 \\ \text{If }m\angle R=80\degree\text{ and }m\angle A=(x+20)\degree,then\; x=60\text{ } \end{gathered}[/tex]Only the third choice is Incorrect.
Use the distance formula to determine if angle ABC is congruent to angle DEF.Select Yes or No for each statement.
Answers
Dorsain, this is the solution for option A:
Option A:
Step 1: Let's calculate the distance from A to B, as follows:
d = √0² - -5² + 0² - -7²
d = √5² + 7²
d = √25 + 49
d = √74
d = 8.6 units
Step 2: Let's calculate the distance from B to C, this way:
d = √4² - 0² + -7² - 0²
d = √4² - 7²
d = √16 + 49
d = √65
d = 8.06 units
Step 3: Let's calculate the distance from A to C, as follows:
d = √(4 - -5)² + (-7 - -7)²
d = √9² + 0²
d = √81
d = 9 units
Step 4: Let's calculate the distance from D to E, this way:
d = √(-1 - -6)² + (1 - -6)²
d = √5² + 7²
d = √25 + 49
d = √ 74
d = 8.6 units
Step 5: Let's calculate the distance from E to F, as follows:
d = √(5 - -1)² + (-8 -1) ²
d = √6² + -9²
d = √36 + 81
d = √117
d = 10.81 units
Step 6: Let's calculate the distance from D to F, this way:
d = √(5 - -6)² + (-8 - -6)²
d = √11² + -2²
d = √121 + 4
d = √125
d = 11.18 units
Step 7: We can conclude that only sides AB and DE are congruent, (8.6 units) but the other two sides of triangles ABC and DEF aren't congruent. Therefore, these two triangles are not congruent.
Now you can continue, following steps 1 to 7 to evaluate options B and C.
Find the greatest possible percent error in calculating the volume of the prism.
Answers
Answer:
23%
Step-by-step explanation:
Volume of a rectangular prism:
A rectangular prism has three dimensions, which are the base b, the height h and the width w.
The volume is:
V = b*w*h
In this question:
The base is 12 inches, so b = 12.
The width is 5 inches, so w = 5.
The height is 7 inches, so h = 7.
The volume is:
V = 12*5*7 = 420 cubic inches.
With error:
They are rounded to the nearest inch, so:
The base can go from 12 - 0.5 = 11.5 to 12 + 0.5 = 12.5 inches.
The width can go from 5 - 0.5 = 4.5 to 5 + 0.5 = 5.5 inches
The height can go from 7 - 0.5 = 6.5 to 7 + 0.5 = 7.5 inches.
Volume with the smallest values:
We have that b = 11.5, w = 4.5, h = 6.5. So
V = 11.5*4.5*6.5 = 336.375
Error of 420 - 336.375 = 83.625
As a percent, the error is of (83.625/420)*100 = 19.9%
Volume with the higher values:
We have that b = 12.5, w = 5.5, h = 7.5. So
V = 12.5*5.5*7.5 = 515.625
515.625 - 420 = 95.625
As a percent, the error is of (95.625/420)*100 = 22.7% = 23%