is the first question true or false question 2 is asking are angles one and two adjacent angles forming a straight angle? The third question ask does the angle addition postulate say the m<1+m<2=180?the last question says if you agree with the last few statements then you can substitute the value of angle one into the equation above to find out the measure of angle 2. What does angle 2 equal ?
Answers
The line l and line m is parallel to each other and line q is transverse line. So angle 1 and angle 42 are corresponding angles. Thus,
[tex]\angle1=42[/tex]So the corresponding angle postuates is the reason why angle 1 = 42 is True.
The angle 1 and angle 2 has a common arm (or side) and commom vertex. So angle 1 and angle 2 are adjacent angles. The angle 1 angle 2 together form a straight line. So answer is True.
The angle 1 and angle 2 form a straight line. So sum of angles is equal to 180 degrees.
[tex]\angle1+\angle2=180[/tex]So answer is True.
Substitute 42 for angle 1 in equation to determine the measure of angle 2.
[tex]\begin{gathered} \angle2+42=180 \\ \angle2=180-42 \\ =138 \end{gathered}[/tex]The measure of angle 2 is 138 degrees.
Related Questions
What is the value of (n + 4)3 - 1 when n = -2? n + 4
Answers
Special right triangles Find the missing side lengths. Leave your answers as radicals in simplest form? The image is down below.
Answers
Given:
To Find:
Missing side lengths
Explanation:
[tex]\begin{gathered} \cos \theta=\frac{Opposite\text{ side}}{\text{hypotenuse side}} \\ \cos 30\degree=\frac{AB}{BC} \\ \frac{\sqrt[]{3}}{2}=\frac{2\sqrt[]{3}}{BC} \\ BC=2\sqrt[]{3}\times\frac{2}{\sqrt[]{3}} \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \sin \theta=\frac{Opposite\text{ side}}{\text{hypotenuse side}} \\ \sin 30\degree=\frac{AC}{BC} \\ \frac{1}{2}=\frac{AC}{4} \\ AC=\frac{4}{2} \\ y=2 \end{gathered}[/tex]Final Answer:
[tex]\begin{gathered} x=4 \\ y=2 \end{gathered}[/tex]
Here is an equation: 50 + 1 = 51.1. Perform each of the following operations and answer these questions: What doeseach resulting equation look like? Is it still a true equation?a. Add 12 to each side of the equation.b. Add 10+ 2 to the left side of the equation and 12 to the right side.C. Add the equation 4 + 3 = 7 to the equation 50 + 1 = 51.2. Write a new equation that, when added to 50+1 = 51, gives a sum that is also a trueequation.3. Write a new equation that, when added to 50 + 1 = 51. gives a sum that is a falseequation.
Answers
Equations
We are given the equation:
50 + 1 = 51
Which is obviously true.
a. Adding 12 to each side of the equation:
50 + 1 + 12 = 51 + 12
Operating:
63 = 63
Which is also true.
b. Adding 10 + 2 to the left side of the equation and 12 to the right side:
50 + 1 + 10 + 2 = 51 + 12
Operating:
63 = 63
The resulting equation is true.
c. Now we add the equation 4 + 3 = 7 to the first equation 50 + 1 = 51. Adding the left side and the right side independently:
50 + 1 + 4 + 3 = 51 + 7
Operating:
58 = 58
The resulting equation is true
2. We can add any equation to 50 + 1 = 51 in such a way that the resulting equation is true, as long as the new equation to add is also true.
For example, add 10 + 20 = 5 + 5 + 10 + 10 to 50 + 1 = 51
Since both equations are true, we expect to have a true equation as a result:
10 + 20 + 50 + 1 = 5 + 5 + 10 + 10 + 50 + 1
Operating:
81 = 81
The resulting equation is true.
3. If we add a false equation to our given equation, the result is also a false equation. For example, add 12 = 10 + 1 to 50 + 1 = 51:
50 + 1 + 12 = 51 + 10 + 1
Operating:
63 = 62
This equation is false because we added a false equation to a true equation
2 Here are two equations:Equation 1: 6x + 4y = 34Equation 2: 5x – 2y = 15ide whether each (x, y) pair is a solution to one equation, both equations, ora. Decide whether eacneither of the equations,i (3,4)ii. (4,2.5)ill. (5,5)iv. (3,2)b. Is it possible to have more than one (x, y) pair that is a solution to bothequations? Explain or show your reasoning,what is the Explanation to show my reasoning
Answers
To check if the pairs are solution to the system of equations we need to replace the values of "x" and "y" on each equation of the system and check if they're valid for hat pair. We have:
a) (3, 4).
First equation:
[tex]\begin{gathered} 6x+4y=34 \\ 6\cdot3+4\cdot4=34 \\ 18+16=34 \\ 34=34 \end{gathered}[/tex]The equation is valid, so the pair is a solution to the first equation.
Second equation:
[tex]\begin{gathered} 5x-2y=15 \\ 5\cdot3-2\cdot4=15 \\ 15-8=15 \\ 7=15 \end{gathered}[/tex]The equation is invalid, so the pair is not a solution to the second equation.
b) (4, 2.5)
First equation:
[tex]\begin{gathered} 6\cdot(4)+4\cdot(2.5)=34 \\ 24+10=34 \\ 34=34 \end{gathered}[/tex]The equation is valid, so the pair is a solution to the first equation.
Second equation:
[tex]\begin{gathered} 5\cdot4-2\cdot2.5=15 \\ 20-5=15 \\ 15=15 \end{gathered}[/tex]The equation is valid, so the pair is a solution to the second equation.
The pair is a solution to both equations.
c) (5,5)
First equation:
[tex]\begin{gathered} 6\cdot5+4\cdot5=34 \\ 30+20=34 \\ 50=34 \end{gathered}[/tex]The equation is invalid, so the pair is not a solution to the first equation.
Second equation:
[tex]\begin{gathered} 5\cdot5-2\cdot5=15 \\ 25-10=15 \\ 15=15 \end{gathered}[/tex]The equation is valid, so the pair is a solution to the second equation.
d) (3,2)
First equation:
[tex]\begin{gathered} 6\cdot3+4\cdot2=34 \\ 18+8=34 \\ 26=34 \end{gathered}[/tex]The equation is invalid, so the pair is not a solution to the first equation.
Second equation:
[tex]\begin{gathered} 5\cdot3-2\cdot2=15 \\ 15-4=15 \\ 11=15 \end{gathered}[/tex]The equation is invalid, so the pair is not a solution to the second equation.
b) Is it possible to have more than one pair that is a solution to both equations?
To check the number of equations a system has we can divide the numbers that multiply x and y on each equation.
[tex]\begin{gathered} \frac{x_1}{x_2}=\frac{6}{5} \\ \\ \frac{y_1}{y_2}=\frac{4}{-2}=-2 \end{gathered}[/tex]When they are different the system only has one solution. This happens because the slope of each equation is different, therefore they only intersect once. In order for a system to have more than one solution the equations must have the same slope and pass through the same points.
Put the following equation of a line into slope-intercept form, simplifying allfractions.3x + y = 1
Answers
Slope - intercept form follows the following format:
[tex]y=mx+b[/tex]From the equation being asked, 3x + y = 1. What we are going to do to make it slope-intercept form, we have to get rid of 3x on the left side and move it to the right side. To do that, we must subtract 3x on the left side as well as on the left side so that the equation remains balanced. Let me show it to you.
[tex]\begin{gathered} 3x+y=1 \\ 3x+y-3x=1-3x \\ 3x-3x+y=-3x+1 \\ 0+y=-3x+1 \\ y=-3x+1 \end{gathered}[/tex]Therefore, the slope-intercept form of the equation 3x + y = 1 is y = -3x + 1.
Simplify 9xy -4x +3y-12xy +6x
Answers
The expression is given to be:
[tex]9xy-4x+3y-12xy+6x[/tex]Step 1: Group like terms together
[tex]-4x+6x+9xy-12xy+3y[/tex]Step 2: Simplify the expression by performing the required operations on like terms
[tex]2x-3xy+3y[/tex]ANSWER:
[tex]9xy-4x+3y-12xy+6x=2x-3xy+3y[/tex]Which value is a solution for the equation cot a = ? O O A. 3 O B. 37 O c 4 o DD. D.
Answers
First, we compute the arccot of both sides of the equation:
[tex]\cot ^{-1}(\cot \frac{x}{2})=\cot ^{-1}0=\frac{1}{2}(\pi+2\pi n)\text{.}[/tex]Therefore:
[tex]\begin{gathered} \frac{x}{2}=\frac{1}{2}(\pi+2n\pi), \\ x=\pi+2n\pi\text{.} \end{gathered}[/tex]For n=1:
[tex]x=\pi+2\pi=3\pi\text{.}[/tex]Answer: Option B.
Does this graph represent a function? Why or why not? A. No, because it is not a straight lineB. No, because it fails the vertical line test C. Yes, because it passes the vertical line test D. Yes, because it is a curve
Answers
It is important to know that a function has to pass the vertical line test, which is about drawing a vertical line across the function. If this vertical line inercepts more than one point of the function, then the graph doesn't represent a function.
Hence, it's not a function because it fails the vertical line test.The answer is B.Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.34<3x+7 and 43>3x+7
Answers
So,
Here we have the following inequalities:
[tex]34<3x+7\text{ and }43>3x+7[/tex]We're going to solve each inequality and then notice which could be the solution set.
Let's begin with:
[tex]\begin{gathered} 34<3x+7 \\ 34-7<3x \\ 27<3x \\ \frac{27}{3}And now, let's solve the other one:[tex]\begin{gathered} 43>3x+7 \\ 43-7>3x \\ 36>3x \\ \frac{36}{3}>x \\ 12>x \end{gathered}[/tex]Now, what we have to do is to graph both solution sets and find the intersection between them:
As you can notice, both solution sets intersect at the interval (9,12).
So, the solution set is (9,12), which is: 9
If you have to graph it, put:
Which is 9
6, 6, 59, 19, 6, 46, 7, 3,54, -1, 22, 49 what is the median?what is the mode?what is the mean?Are these averages parameters or statistics?
Answers
the given data set is
6, 6 59, 19, 6, 46, 7, 3, 54, -1, 22, 49
now let's rearrange this data
-1, 3, 6, 6, 6, 7, 19, 22, 49, 54
the median: this is the middle number in an ungrouped data
Melany grew 4 plants with 2 seeds packets. With 10 seed packets, how many total plants can Melanie have in her backyard
Answers
Ratio:
Plants / seeds
4 /2
For 10 seeds:
x / 10
Equal both
4/2 =x /10
Solve for x:
2 (10) = x
20 = x
20 plants
A rectangular sheet of paper measures 8.5 inches by 11 inches. Ava is calculating its area in squareFEET. The first step of Ava's work is shown below.1 ft1 ft1. Area = 8.5 in x12 inx 11 in x12 in2. ?Which equation follows directly from step 1 to find Ava's solution in the correct units?AArea = 8.5 in x 11 inBArea =in xinсArea = 8.5 ft x 11 ftDArea =8.512ft x12ft
Answers
A rectangular sheet of paper measures 8.5 inches by 11 inches. Ava is calculating its area in square
ft. The first step of Ava's work is shown below.
__________________
From inches to feet
12 in = 1 ft
x in * 1ft/ 12 = y ft
__________________________________
A= 8.5 in * 11 in
A= 93.5 sq in * (1ft/ 12 in)^2 = 93.5 sq in * (1ft/ 144 in)
or
Area = (8.5 in* 1ft/ 12 in) x 11 in*( 1ft/ 12 in)
Area = (0.71 1ft) x ( 0.92 ft)
____________
2. Which equation follows directly from step 1 to find Ava's solution in the correct units?
A Area = 8.5 in x 11 in ( FALSE inches)
B Area = in x in
с Area = 8.5 ft x 11 ft ( FALSE the given units are in )
D Area = 8.5/ 12 ft x 11 / 12 ft (This is the answer)
_________________
Can you see the updates?
Could you send me a picture of the options?
If you do not need further explanation on this question, we can end the session.
I want to remind you this answer will always be saved in your profile. I’d really appreciate you letting me know how I did by rating our session after you exit. Thanks, and have a great day!
A drawing class was assigned a final project where students had to choose one art medium and one subject. The teacher kept track of the types of projects submitted. A plant An insect Acrylic paint 21 5 Chalk 5 7 Charcoal 7 11 What is the probability that a randomly selected student chose to draw a plant or did not use acrylic paint? Simplify any fractions.
Answers
Answer:
The probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;
[tex]P(A\cup B^{\prime})=\frac{51}{56}[/tex]Explanation:
Given the table in the attached image;
Let A represent the event that a randomly selected student chose to draw a plant, and B' represent the event that a randomly selected student did not use acrylic paint;
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(T)}=\frac{33}{56} \\ P(B^{\prime})=\frac{n(B^{\prime})}{n(T)}=\frac{30}{56} \end{gathered}[/tex]Recall that the probability that a randomly selected student chose to draw a plant or did not use acrylic paint will be;
[tex]P(A\cup B^{\prime})=P(A)+P(B^{\prime})-P(A\cap B^{\prime})[/tex]The probability of A and B' is;
[tex]P(A\cap B^{\prime})=\frac{n(A\cap B^{\prime})}{n(T)}=\frac{12}{56}[/tex]Substituting the values;
[tex]\begin{gathered} P(A\cup B^{\prime})=P(A)+P(B^{\prime})-P(A\cap B^{\prime}) \\ P(A\cup B^{\prime})=\frac{33}{56}+\frac{30}{56}-\frac{12}{56}=\frac{63-12}{56} \\ P(A\cup B^{\prime})=\frac{51}{56} \end{gathered}[/tex]Therefore, the probability that a randomly selected student chose to draw a plant or did not use acrylic paint is;
[tex]P(A\cup B^{\prime})=\frac{51}{56}[/tex]What is the volume of this rectangular prism?2/5 cm, 2/5 cm, 2/5 cm
Answers
To calculate the volume of a rectangular prism you have to multiply the length by the width by the height, the formula is
[tex]V=l\cdot w\cdot h[/tex]The given prism has the following measures:
[tex]\begin{gathered} l=\frac{2}{5}cm \\ w=\frac{2}{5}cm \\ h=\frac{2}{5}cm \end{gathered}[/tex]Replace the formula of the volume with the measures of the prism
[tex]V=\frac{2}{5}\cdot\frac{2}{5}\cdot\frac{2}{5}[/tex]Note that the sides have the same length, so if you multiply 2/5 by 2/5 by 2/5 is the same as calculating (2/5)³
Then
[tex]\begin{gathered} V=(\frac{2}{5})^3 \\ V=\frac{2^3}{5^3} \\ V=\frac{8}{125}cm^3 \end{gathered}[/tex]The volume of the prism is 8/125 cm³, you can express it as a decimal value as 0.064 cm³
Question 1 (1 point)Transform into slope-intercept form.x + y = 8Yes
Answers
Given the standard form of the equation:
[tex]\text{ x + y = 8}[/tex]Writing in slope-intercept form, the equation must be similar to y = mx + b, solving the equation of y in terms of x.
We get,
[tex]\text{ x + y = 8}[/tex][tex]\text{ x + y - x = 8 - x}[/tex][tex]\text{ y = -x + 8}[/tex]Therefore, the slope-intercept form of the equation x + y = 8 is y = -x + 8.
Hello, I need some help with Part 2 question 4! Please show work as the instructions asked!
Answers
Answer:
• Potential Roots are: 1, -1, 1/2, -1/2, 2,-2,4, and -4.
,• Actual roots: -1 and -2.
,• Code piece: H.
Explanation:
Given the polynomial:
[tex]2x^3+8x^2+10x+4[/tex]Applying the rational Toot theorem:
The constant = 4
• The factors of the constant, p = ±1,±2, and ±4
The leading coefficient = 2
• The factors of the leading coefficient, q = ±1 and ±2.
The potential roots are obtained below:
[tex]\begin{gathered} \frac{p}{q}=\pm\frac{1}{1},\pm\frac{1}{2},\pm\frac{2}{1},\pm\frac{2}{2},\pm\frac{4}{1},\pm\frac{4}{2} \\ \frac{p}{q}=\pm1,\pm\frac{1}{2},\pm2,\pm4 \end{gathered}[/tex]Potential Roots are: 1, -1, 1/2, -1/2, 2,-2,4, and -4.
Next, find the actual roots by substituting each of the potential roots for x:
[tex]\begin{gathered} f(1)=2(1)^3+8(1)^2+10(1)+4=24 \\ f(-1)=2(-1)^3+8(-1)^2+10(-1)+4=0 \\ f(0.5)=2(0.5)^3+8(0.5)^2+1(0.5)+4=11.25 \\ f(-0.5)=2(-0.5)^3+8(-0.5)^2+1(-0.5)+4=0.75 \\ f(2)=2(2)^3+8(2)^2+10(2)+4=72 \\ f(-2)=2(-2)^3+8(-2)^2+10(-2)+4=0 \\ f(4)=2(4)^3+8(4)^2+10(4)+4=300 \\ f(-4)=2(-4)^3+8(-4)^2+10(-4)+4=-36 \end{gathered}[/tex]From the calculations above, the actual roots are -1 and -2.
Thus, the actual roots are:
[tex]x=-2;x=-1[/tex]The code piece is H.
Find the inverse of the function. y = x + 8 Write your answer in the form ax + b.
Answers
y = x + 8
Therefore, the inverse can be found below
[tex]\begin{gathered} y=x+8 \\ x=y+8 \\ y=x-8 \\ f^{-1}(y)=x-8 \end{gathered}[/tex]Logan is putting hardwood floor in his kitchen and his bedroom. The kitchenmeasures 25 ft. by 25 ft. and the bedroom is 25 ft. by 20 ft. If Logan wishes topurchase a 20% excess of the hardwood, how many sq. ft. of hardwood does he need?
Answers
He needs 1 350 sq ft of hardwood
Explanation:
Data:
Kitchen's measurements: 25 ft by 25 ft
Bedroom's measurements: 25 ft by 20 ft
Excess wanting to purchase: 20% => 1.20
Formula:
Area of the kitchen: A(k) = side * side
Area of the bedroom: A(b) = side * side
Total Area: A = A(k) + A(b)
Amount of sq. ft of hardwood neede: T(h) = A + (A * 20%) = A + (A * 20 / 100) = A * 1.20
Solution:
A(k) = 25 * 25 = 625 sq. ft
A(b) = 25 * 20 = 500 sq. ft
A = 625 + 500 = 1 125 sq. ft
T(h) = 1 125 * 1.20 = 1 125 + ( 1 125 * 20 / 100 ) = 1 350 sq. ft
Erin opened a savings account and deposited $300,00. The account earns 10% Interest,compounded monthly. If she wants to use the money to buy a new bicycle in 3 years, howmuch will she be able to spend on the bike?
Answers
Since the money is deposited on an account that gets compounded monthly, we need to use the following expression:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Where A is the final amount, P is the invested principal, r is the interest rate, n is the number of times it get compounded in a year, and t is the number of elapsed years.
[tex]\begin{gathered} A=300\cdot(1+\frac{0.1}{12})^{12\cdot3} \\ A=300\cdot(1+0.00833)^{36}_{} \\ A=300\cdot(1.00833)^{36} \\ A=300\cdot1.34802 \\ A=404.41 \end{gathered}[/tex]Erin will be able to spend $404.41 on the bike.
how do i solve number 2The drawings are already drawn.
Answers
If Cos(θ)=12/13 it means that we can form a triangle with hypotenuse 13 and adjacent length 12. Using them to find the opposite length with the pythagorean theorem, we have:
[tex]\begin{gathered} a^2+b^2=c^2 \\ (12)^2+b^2=13^2\text{ (Replacing the values)} \\ 144+b^2=169\text{ (Raising the numbers to the power of 2)} \\ b^2=25\text{ }(\text{Subtracting 144 from both sides of the equation)} \\ b=5\text{ (Taking the square root of both sides)} \\ \text{The opposite length is 5} \end{gathered}[/tex]If the opposite length is 5 and the angle is in the fourth quadrant then sin(θ)=-5/13.
Given that sin(2θ)=2sin(θ)cos(θ), then sin(2θ)=2(-5/13)(12/13)= -120/169.
Given that cos(2θ)=cos^2(θ)-sin^2(θ), then cos(2θ)=(12/13)^2 - (-5/13)^2 =119/169
Answers:
cos(θ)=12/13
sin(θ)=-5/13
sin(2θ)=-120/169
cos(2θ)=119/169
X^2+y^2=y is written in polar form as r = ?
Answers
r = 3sinA is written in rectangular form as x²+y²=3y.The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.
What is polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.
The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.
Any complex number z = a + ib can be written in polar form as:
[tex]z=r([/tex]cos(0))+i sin(0))
Complex numbers are those numbers that contain the imaginary and the real part.
Raising this to nth power (n being an integer), we get:
[tex]zn=rn[/tex](cos(n0)+i sin(n0))
We need to find r = 3sinA is written in rectangular form as x²+y²
We know that
x = r cos A
y = r sin A
We have been given ;
r = 3sinA
Multiply by r on both sides;
r²=3r sin A
r²=3y
therefore,
x²+y²=3y
Hence, r = 3sinA is written in rectangular form as x²+y²=3y
To learn more about polar form refer to:
https://brainly.com/question/21538521
#SPJ1
- 5x + 3 > - 3x - 5Step 1 of 2: Solve the linear inequality for the given variable. Simplify and express your answer in algebraic notationAnswer 4 PointsKeypadKeyboard ShortcutsIf all real numbers satisfy the inequality, select All Real Numbers. If no real number satisfies the inequality, select No SolutionSelecting one of the alternative options will replace the entered value(s) with the selected value. Otherwise, the entered answer is used.ovO No SolutionNextO All Real Numbers
Answers
To solve the value of x in the given inequality, here are the steps:
1. Use the distributive property to match the expression with equivalentstandard form.(Draw an area diagram if you need to)(x + 3)(x + 4)x2 + x - 12(x - 3)(x + 4)x2 - 7x + 12(x - 4)(x-3)x2 + 7x + 12(x - 4)(x + 3)x? - X-12
Answers
The first expression is (x + 3)(x + 4)
To apply the distributive property, we would multiply each term in the first bracket by each term in the second bracket. Thus, we have
x * x + x * 4 + 3 * x + 3 * 4
x^2 + 4x + 3x + 12
= x^2 + 7x + 12
For the second expression,
(x - 3)(x + 4)
x * x + x * 4 + - 3 * x + - 3 * 4
x^2 + 4x - 3x - 12
= x^2 + x - 12
For the third expression,
(x - 4)(x - 3)
x * x + x * - 3 + - 4 * x + - 4 * - 3
x^2 - 3x - 4x + 12
x^2 - 7x + 12
For the fourth expression,
(x - 4)(x + 3)
x * x + x * 3 + - 4 * x + - 4 * 3
x^2 + 3x - 4x - 12
x^2 - x - 12
Joe borrowed $8000 at a rate of 10.5%, compounded monthly. Assuming he makes no payments, how much will he owe after 9 years?Do not round any intermediate computations, and round your answer to the nearest cent.
Answers
Given:
a.) Joe borrowed $8000 at a rate of 10.5%, compounded monthly.
For us to be able to determine how much will he owe after 9 years, we will be using the compounded interest formula:
[tex]\text{ A = P\lparen1 + }\frac{\text{ r}}{\text{ n}})^{nt}^[/tex]Where,
A=final amount
P=initial principal balance = $8,000
r =interest rate (in decimal form) = 10.5/100 = 0.105
n=number of times interest applied per time period = compounded monthly = 12
t=number of time periods elapsed (in years) = 9
We get,
[tex]\text{ A = P\lparen1 + }\frac{\text{ r}}{\text{ n}})^{nt}[/tex][tex]\text{ = \lparen8,000\rparen\lparen1 + }\frac{0.105}{12})^{12\text{ x 9}}\text{ = \lparen8,000\rparen\lparen1 + }0.00875)^{108}[/tex][tex]\text{ = \lparen8,000\rparen\lparen1.00875\rparen}^{108}[/tex][tex]\text{ = \lparen8,000\rparen\lparen2.49616052967\rparen}[/tex][tex]\text{ A = 19,969.28423739091}[/tex][tex]\text{ A }\approx\text{ \$19,969.28}[/tex]Therefore, the answer is $19,969.28
David races his bicycle for 280 ft. A wheel of his bicycle turns 35 times as the bicycle travels the distance. What is the diameter of the wheel? Use the value 3.14 for pie. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answers
Given that:
David races his bicycle for 280 ft
And the wheel of his bicycle turns 35 times.
One turn equals the circumference of the wheel.
So, 35 turns will equal to 35 times the circumference of the wheel;
[tex]35C=280[/tex]Recall that the formula for calculating the circumference of a circle is;
[tex]C=\pi d[/tex]Where d is the diameter.
Substituting the above formula and solving for diameter d, we have;
[tex]\begin{gathered} 35C=280 \\ 35(\pi d)=280 \\ d=\frac{280}{35\pi} \\ d=2.54777 \\ d=2.5ft \end{gathered}[/tex]Therefore, the diameter of the wheel is 2
60° 16 inches 60 An equilateral triangle is folded in half. What is x, the height of the equilateral triangle? 8V3 in 16 in 16V 3 in 8 in
Answers
This is the line through the middle. The perpendicular bisector from the vertex.
This way, the triangle becomes [rough drawing]:
Rachel must choose a number between 49 and 95 that is a multiple of 5.6, and 10. Write all the numbers that she could choose. If there is more than onenumber, separate them with commas
Answers
To get the numbers that Rachel can choose, we will need to list out the multiples of 5, 6, and 10 that fall between 49 and 95 and then pick the common numbers from them.
Multiples of 5:
[tex]50,55,60,65,70,75,80,85,90[/tex]Multiples of 6:
[tex]54,60,66,72,78,84,90[/tex]Multiples of 10:
[tex]50,60,70,80,90[/tex]Looking at the numbers above, the common multiples are:
[tex]60,90[/tex]The sum of two numbers is -8 the differences is 44 final numbers
Answers
As per given by the question,
There are given that the sum of two number is -8 and their dufferences is 44.
Now,
Let the two number is, x and y
Then,
The sum of two number is -8.
So,
[tex]x+y=-8\ldots..(1)[/tex]And,
Their differences is 44.
So,
[tex]x-y=44\ldots(2)[/tex]Now,
For find the value of two number, x and y
From equation (2)
[tex]\begin{gathered} x-y=44 \\ x=44+y\ldots(3) \end{gathered}[/tex]Put the above value of x into the equation (1).
So,
[tex]\begin{gathered} x+y=-8 \\ 44+y=-8 \\ 44+y-44=-8-44 \\ y=-52 \end{gathered}[/tex]Now,
Put the value of y into the equation (2)
So,
[tex]\begin{gathered} x-y=44 \\ x-(-52)=44 \\ x+52=44 \\ x=44-52 \\ x=-8 \end{gathered}[/tex]Hence, the number is shown below:
[tex]x=-8\text{ and y=-52}[/tex]Rashad leans a 16-foot ladder against a wall so that it forms an angle of 73° with theground. How high up the wall does the ladder reach? Round your answer to thenearest hundredth of a foot if necessary,
Answers
Given:
16-ft ladder
Angle of 73 with the ground
First, let us sketch the problem for us to underdtand what do we need to do in order to solve this problem.
Now, we can rewrite the given as:
hypotenuse = 16
angle = 73
Find for the opposite side h.
For us to solve this, we will use the following equation
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]Plugging in the given data,
[tex]\sin 73=\frac{h}{16}[/tex]*Multiply both sides by 16
[tex]16\sin 73=h[/tex][tex]h=15.30[/tex]Therefore, the final answer would be 15.30 ft.
wutCL TeD VIaeoA shipping container is in the shape of a right rectangular prism with a length of 5.5feet, a width of 12 feet, and a height of 7.5 feet. The container is completely filled withcontents that weigh, on average, o.75 pound per cubic foot. What is the weight of thecontents in the container, to the nearest pound?Answer:Ibs Submit Answer
Answers
We start by calculating the volume of the right rectangular prism which is;
[tex]\begin{gathered} v=l\times h\times w \\ v=5.5\times7.5\times12 \\ v=495ft^3 \\ \text{The container is completely filled with contents that weigh 0.75 pounds } \\ \text{per cubic foot. This means;} \\ \text{Each cubic foot would contain;} \\ \text{Weight of contents=}495\times0.75 \\ \text{Weight}=371.25 \\ \text{Weight}\approx371 \end{gathered}[/tex]The weight of the contents in the container therefore is 371 pounds (to the nearest pound).