Answers
Angles h and the one whose measure equals 97° are supplementary angles, this means that their measures sum up to 180°, then we can formulate the following expression:
h + 97° = 180°
From this equation, we can solve for h to get:
h + 97° - 97° = 180° - 97°
h + 0 = 180° - 97°
h = 83°
Angles g and the one whose measure equals 97° are vertical angles since they're located at opposite sides of intersecting lines, this kind of angles are congruent, then their measures are the same, then:
g = 97°
Similarly, m and the angle whose measure equals 66° are supplementary angles, then:
m + 66° = 180°
m + 66° - 66° = 180° - 66°
m = 180° - 66°
m = 114°
Angles k and the one whose measure equals 66° are vertical angles, then:
k = 66°
Related Questions
3. Sara is making a quilt. One of the fabric pieces she is using is 1 1/2inches x 3inches. She will need 20 of these pieces. How many feet of fabric will she needof this pattern?
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Now the quilt measures 1.5 inches by 3inches. This means that the length of the quilt is 3 inches and the breadth is 1.5 inches, considering the quilt to be a rectangle. They are asking us the length of the quilt she will need measured in "feet" and not in inches.
Since she needs 20 pieces, the length required is 3 inches x 20 = 60 inches.
converting 60 inches to feet becomes 60/12 = 5 feet. Because 12 inches make 1 feet. Therefore, the answer is 60/12 = 5 feet.
The radius of a circle is 2 miles. What is the circumference?Give the exact answer in simplest form. ____ miles (pi/fraction)
Answers
The formula for the circumference of a circle is :
[tex]C=2\pi r[/tex]Where r is the radius of the circle which is equal to 2 miles
The circumference will be :
[tex]C=2\pi(2)[/tex][tex]C=4\pi[/tex]The answer is 4π miles or 12.56 miles in decimal
I need help with something
Answers
First note that the y-intercept of the function A i in 4and for the function B is in 12
so the
What is the explicit formula for this arithmetic sequence? 9.15. - 27 27.
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Solution
For this case we have the following sequence:
-9, -15, -21, -27
Then we can find the common difference on this:
d= -15-(-9)= -15+9= -6
d= -21-(-15)= -21+15= -6
Then the general formula would be given by:
d. an = -9 +(n-1)*(-6)
then the correct solution for this case is:
d.
This is the top part which has the information and part A (or the first question)I wasn’t able to fit Part B
Answers
The function f(a) represents the cost of a pizza.
The function g(b) represents the delivery charge on the cost.
PART A.Having said that, a represents the cost of a pizza, b represents the cost of a pizza and sales tax, f(a) represents the cost of a pizza and sales tax, g(b) represents the delivery fee. At last, g(f(a)) represents the cost of the pizza, sales tax, and delivery fee.
PART B.Let's find the composition of functions
[tex]g(f(a))=1.06a+5[/tex]Hence, the answer to part B is the last option.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Match each equation to the line of best fit that it models.
Answers
Consider the individual graph.
1)
Given:
We get the points (0,2) and (7,3) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]Substitute x =7 and y =3 in the equation to find the value of m.
[tex]3=m(7)+2[/tex]Solve for m.
[tex]3-2=7m[/tex][tex]m=\frac{1}{7}[/tex]Substitute m=1/7 and b =2 in the line equation.
[tex]y=\frac{1}{7}x+2[/tex]Answer:
[tex]y=\frac{1}{7}x+2[/tex]2)
Given:
We get the points (0,2) and (7,6) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]Substitute x =7 and y =6 in the equation to find the value of m.
[tex]6=m(7)+2[/tex]Solve for m.
[tex]6-2=7m[/tex][tex]m=\frac{4}{7}[/tex]Substitute m=4/7and b =2 in the line equation.
[tex]y=\frac{4}{7}x+2[/tex]Answer:
[tex]y=\frac{4}{7}x+2[/tex]3)
Given:
We get the points (0,2) and (7,1) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]Substitute x =7 and y =1 in the equation to find the value of m.
[tex]1=m(7)+2[/tex]Solve for m.
[tex]1-2=7m[/tex][tex]m=\frac{-1}{7}[/tex]Substitute m= -1/7and b =2 in the line equation.
[tex]y=\frac{-1}{7}x+2[/tex]Answer:
[tex]y=\frac{-1}{7}x+2[/tex]4)
Given:
We get the points (0,2) and (6.7) that lie on the best fit from the graph.
Required:
We need to find the equation of the line.
Explanation:
Recall that the y-intercept is the point where the line crosses the y-axis.
At (0,2), the line crosses the y-axis.
The y-intercept, b= 2.
Consider the line equation.
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Substitute b =2 in the equation.
[tex]y=mx+2[/tex]Substitute x =6 and y =7 in the equation to find the value of m.
[tex]7=m(6)+2[/tex]Solve for m.
[tex]7-2=6m[/tex][tex]m=\frac{5}{6}[/tex]Substitute m= 5/6 and b =2 in the line equation.
[tex]y=\frac{5}{6}x+2[/tex]Answer:
[tex]y=\frac{5}{6}x+2[/tex][tex]y=\frac{5}{6}x+2[/tex]Condense the following expression using exponent properties.p5 k.p10 k:12HTML EdiBI U AA - IITT: 12ptPar
Answers
If two terms have the same base (the letter or number below the exponent), then their multiplication is equal to the number with the same base but with the exponent given by the sum of both exponents. So, in this case we have
[tex]\begin{gathered} r^5k\cdot r^{10^{}}k^{12}=r^{5+10}k^{1+12}=r^{15}k^{13} \\ (\text{if procedure is needed)} \end{gathered}[/tex]So, the condensed expression is
[tex]\begin{gathered} r^{15}k^{13} \\ (\text{ correct answer)} \end{gathered}[/tex]in one year, the Perseid meteor shower had a meteor appear every o appear every 15 minutes on average. That same year, the Leonid meteor shower had a meteor appear ry 4 minutes on average
Answers
In one year, there are 365 days. In one day, there are 24 hours.
The number of minutes in an year is,
[tex]\begin{gathered} N=365\times24\times60 \\ N=525600 \end{gathered}[/tex]The Perseid meteor appear every 1 1/5 minutes.
The number of Perseid meteors in one year is,
[tex]\begin{gathered} P=\frac{N}{1\frac{1}{5}} \\ =\frac{525600}{\frac{5\times1+1}{5}} \\ =438000 \end{gathered}[/tex]The Leonid meteor appear every 4 2/3 minutes.
The number of Leonid meteors showered in one year is,
[tex]\begin{gathered} L=\frac{N}{4\frac{2}{3}} \\ L=\frac{525600}{\frac{4\times3+2}{3}} \\ =\frac{525600\times3}{14} \end{gathered}[/tex]The number of Persoid meteors more than the Leonid meteors is,
[tex]\begin{gathered} n=N-L \\ =438000-\frac{525600\times3}{14} \\ =\frac{4555200}{14} \\ =\frac{2277600}{7} \end{gathered}[/tex]Let m be the number of times Persoid meteors is more than the Leonid meteors in each minute. Then,
[tex]\begin{gathered} m=\frac{\frac{N}{1\frac{1}{5}}}{\frac{N}{4\frac{2}{3}}} \\ =\frac{4\frac{2}{3}}{1\frac{1}{5}} \\ =\frac{\frac{4\times3+2}{3}}{\frac{5\times1+1}{5}} \\ =\frac{\frac{14}{3}}{\frac{6}{5}} \\ =\frac{70}{18} \\ =\frac{35}{9}=3\frac{8}{9} \end{gathered}[/tex]Therefore, Persoid meteors is 3 8/9 times more than the Leonid meteors showered in each minute
the roof of a tennis stadium opens 421 inches in 50 seconds
Answers
if the roof opens 421 inches in 50 second, to know the rate that the roof opens per second we need to divide the data we have, so
[tex]\frac{421}{50}=8.42\text{ in/s}[/tex]Use the standard normal table to find the z-score that corresponds to the cumulative area 0.0401. If the area is not in the table, use the entry closest to the area. If thearea is halfway between two entries, use the z-Score halfway between the corresponding Z-scores.
Answers
Answer:
Given that,
To find the z-score that corresponds to the cumulative area 0.0401.
we have that,
The standard normal distribution is a type of normal distribution. It mostly appears when a normal random variable has a mean value equal to 0 and value of standard deviation is equal to 1. The random variable of a standard normal distribution is considered as a standard score or z-score.
The total area under the curve should be equal to 1. The normally distributed curve should be symmetric at the centre. There should be exactly half of the values are to the right of the centre and exactly half of the values are to the left of the centre.
Let z be the required z score, we get,
[tex]P(ZFrom the z table, we get,[tex]z=-2.65[/tex]Answer is:
[tex]z=-2.65[/tex]solve the system for equations using the elimination method. show your work. write your solution as an ordered pair
Answers
Answer
(x, y) = (3, -6)
x = 3
y = -6
Explanation
We are asked to use elimination method to solve the system of equations.
x + 5y = -27
-2x - 5y = 24
To do this, we just need to add the two equations
x + 5y = -27
-2x - 5y = 24
___________
x - 2x + 5y - 5y = -27 + 24
-x + 0 = -3
-x = -3
x = 3
We can then solve for y
x + 5y = -27
x = 3
x + 5y = -27
3 + 5y = -27
5y = -27 - 3
5y = -30
Divide both sides by 5
(5y/5) = (-30/5)
y = -6
Hope this Helps!!!
Select the correct answer.Sarah owns a flower shop and can model the profits from selling springtime bouquets using this equation, where b is the number of springtimebouquets.P=-582 + 4506 - 1,000Which statement is true if Sarah needs to make a profit of at least $9,000?
Answers
SOLUTION
[tex]9000\ge-5b^2+450b-1000[/tex]SOLVING THE INEQUALITY
[tex]\begin{gathered} -5b^2+450b-1000\le \:9000 \\ -b^2+90b-2000\le \:0 \end{gathered}[/tex][tex]-\left(b-40\right)\left(b-50\right)\le \:0[/tex][tex]\left(-\left(b-40\right)\left(b-50\right)\right)\left(-1\right)\ge \:0\cdot \left(-1\right)[/tex][tex]\left(b-40\right)\left(b-50\right)\ge \:0[/tex][tex]b\le \:40\quad \mathrm{or}\quad \:b\ge \:50[/tex]give the value of each trigonometric ratio cos M = cos N = sin M = sin N = tan M = tan N =
Answers
Solve for the cosine of angle M as,
[tex]\cos M=\frac{MP}{MN}=\frac{60}{68}=\frac{15}{17}[/tex]Solve for the cosine of angle N as,
[tex]\cos N=\frac{NP}{MN}=\frac{32}{68}=\frac{8}{17}[/tex]Solve for the sine of angle M as,
[tex]\sin M=\frac{NP}{MN}=\frac{32}{68}=\frac{8}{17}[/tex]Solve for the sine of angle N as,
[tex]\sin N=\frac{MP}{MN}=\frac{60}{68}=\frac{15}{17}[/tex]Solve for the tangent of angle M as,
[tex]\tan M=\frac{NP}{MP}=\frac{32}{60}=\frac{8}{15}[/tex]Solve for the cosine of angle M as,
[tex]\cos M=\frac{NP}{MN}=\frac{32}{68}=\frac{8}{17}[/tex]Which of the following describes how the dotted line represents the solid line (f(x))?
Answers
The Solution:
The Correct answer is [option B]
Explanation:
Water flows through a pipe at a rate of 6 fluid ounces per day. Express this rate offlow in cubic meters per year. Round your answer to the nearest hundredth.*Note: you must use these exact conversion factors to get this question right.VolumeTime1 cup (cup) = 8 fluid ounces (fl oz)1 minute (min) = 60 seconds (sec)1 pint (pt) = 2 cups (cups)1 hour (hr) = 60 minutes (min)i quart (t) = 2 pints (pt)1 day (day) = 24 hours (hr)1 gallon (gal) = 4 quarts (9)1 week (week) = 7 days (days)1 cubic foot (ft") = 7.481 gallons (gal)1 month (month) = 30 days (days)1 liter (L.) = 1000 milliliters (mL)1 year (year) = 365 days (days)1 cubic meter (m) = 1000 liters (L)1 gallon (gal) = 3.785 liters (L.)1 fluid Ounce (fl oz) = 29.574 milliliters (L.)
Answers
Step 1
Given: A flow rate of 6 fluid ounces per day
Required: To convert 6 fluid ounces per day to cubic meters per year to the nearest hundredth
Step 2
To solve this problem we use the method of dimensional analysis for consistency
Convert 6 fluid ounces to cubic meter
[tex]\begin{gathered} \frac{6\text{ }\times3.785\times1\text{cubic meter}}{8\times2\times2\times4\times1000} \\ =\frac{22.71}{128000} \\ =0.000177421875\text{ cubic meter} \end{gathered}[/tex]Step 3
Convert 1 day to year
[tex]\begin{gathered} \frac{1year}{365\text{ days}}=\frac{\text{xyear}}{1\text{ day}} \\ xyear=\frac{1\text{ year}\times1\text{ day}}{365\text{ days}} \\ 1day\text{=0.002739726027 years} \end{gathered}[/tex]Step 4
Get the final answer
[tex]\begin{gathered} =\frac{0.000177421875\text{ cubic meter}}{\text{0.002739726027 years}} \\ =\text{ 0.064758984 cubic meters/ year} \\ =0.06\text{cubic meters/ years}\approx\text{ to the nearest hundredth} \end{gathered}[/tex]Answer = 0.06 cubic meters per year
What is the mode of the data set? Heart Rate 5/06/0007/008/009/05/0 = 50 beats per minute 6070none0
Answers
As you have the next data set:
[tex]\lbrace50,60,60,60,70,70,80,80,90\rbrace[/tex]And the mode is the number that appears the most.
The mode of the given data is 60 (it repeats 3 times)
d. Among those surveyed, 1776 were called by landline and 1363 were called by cell phone. What percentage of the survey subjects were called by cell phonecell phone?
Answers
ANSWER
[tex]42.9[/tex]EXPLANATION
Given;
The number of people called by landline is; 1776
The number of people called by cell phone is; 1463
Hence, the total number surveyed is;
[tex]1776+1337=3116[/tex]The percentage of those surveyed through cell phone is;
[tex]\begin{gathered} \frac{n(cellphone)}{Total}\times100 \\ =\frac{1337}{3116}\times100 \\ =0.4290\times100 \\ =42.91 \end{gathered}[/tex]Consider the system of inequalities, 4x + 5y is greater and equal to 11 - 6x + 3y < 15
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Solution
For this case
Factor the given polynomial completely. If the polynomial cannot be factored, say that it is prime.
Answers
Given a quadratic polynomial
[tex]x^2-5x-24[/tex]Using factorization method
[tex]\begin{gathered} x^2-8x+3x-24 \\ (x^2-8x)+(3x-24) \\ \end{gathered}[/tex]factor out the common factor
[tex]\begin{gathered} x(x-8)+3(x-8) \\ we\text{ have} \\ (x-8)(x+3) \end{gathered}[/tex]The final answer
[tex]x^2-5x-24=(x-8)(x+3)[/tex]Answer:
(x-8)(x+3)
Step-by-step explanation:
you could use the formula:
(a-b)(a+b)=a^2+b^2
Double checking our work:
(x-8)(x+3)
x^2+3x-8x-24
x^2-5x-24
can someone please help me??????
Answers
Answer: Not enough information.
Step-by-step explanation:
We will look at the answer options and the triangles shown to decide on our answer.
We can tell we have one congruent side, as indicated by the hash line, and one congruent angle, as shown by the vertical angles.
➜ ASA needs two congruent angles and one side, we only have one angle.
➜ HL needs a congruent hypotenuse and a congruent leg, this is for right triangles only.
➜ SAS needs two congruent sides and one congruent angle, we only have one side.
Since we only have one side, one angle, and no right angles, we do not have enough information to be sure if these triangles are congruent or not.
Flynn bought 3 cheeseburgers and 4 sodas for $24.50. Catherine bought one cheeseburger and two sodas for $9.00. Set up you what the cost of one cheeseburgers is? *Do not include $ signs in your answer Type your answer... Previous
Answers
Flynn bought 3 cheeseburgers and 4 sodas for $24.50.
3 b + 4 s = 24.50
Where:
b= price of a cheeseburger
s= price of a soda
Catherine bought one cheeseburger and two sodas for $9.00
b + 2s = 9
We have the system of equations:
3 b + 4 s = 24.50
b + 2s = 9
Solve the second equation for s:
b+2s=9
2s= 9 -b
s= (9-b)/2
s= 4.5-0.5b
Replace s on the first equation and solve for b
3b+ 4 (4.5-0.5b) = 24.50
3b + 18 - 2b = 24.50
3b -2b = 24.50-18
b= 6.5
Cost of one cheeseburger 6.5
27 A basketball has a diameter of 9.5 cm Which of the expressions shows how to determine the volume of air the basketball can hold? has A. (4.753 B. 1957 C. **44.757 D. 420.59
Answers
Answer:
Option C
Because the radius is 9.5/2 = 4.75
What is the quotient (4-x)/(x^2+5x-6) divided (x^2 - 11x + 28) / (x^2 + 7x +6) in simplified form? State any restrictions on the variable.See image
Answers
Explanation:
To solve the question, we will have to get the factor of the terms given
Let us follow the steps below
Step 1: Write out the given expression
[tex]\frac{4-x}{x^2+5x-6}\div\frac{x^2-11x+28}{x^2+7x+6}[/tex]Step 2: simplify each term by writing them in factor form
[tex]\frac{4-x}{(x-1)(x+6)}\div\frac{(x-4)(x-7)}{(x+1)(x+6)}[/tex]Step 3: Re-write the expression
[tex]\frac{4-x}{(x-1)(x+6)}\times\frac{(x+1)(x+6)}{(x-4)(x-7)}[/tex]Step 4: Simplify further and cancel out like terms
[tex]\frac{4-x}{x-1}\times\frac{x+1}{(x-4)(x-7)}[/tex]Step 5: simplify by factoring out the negative sign
[tex]\frac{-(x-4)}{x-1}\times\frac{x+1}{(x-4)(x-7)}[/tex]Step 6: Resolve the expression
[tex]\frac{-1(x+1)}{(x-1)(x-7)}[/tex]Thus, we have the simplified form to be
[tex]\frac{-x-1}{(x-1)(x-7)}[/tex]Then for the restrictions, these will be values of x which makes it undefined
These values are
[tex]x=1\text{ and x=7}[/tex]In order to save money for prom, Tom is going to walk his neighbor's dog for $6an hour and wash cars for $7.50 an hour. His mother told him he is not allowedto work more than 15 hours in order to keep up with his homework. If Tomwould like to make at least $75 to cover prom expenses, help him determinecombination of hours he can work between the 2 jobs.A. Write and graph a system of linear inequalities.B. What are 2 possible solutions?
Answers
Let's use the variable x to represent the number of hours walking the dog and the variable y to represent the number of hours washing cars.
If he can work a maximum of 15 hours, we have the inequality:
[tex]x+y\le15[/tex]Also, if he wants to make at least $75, we have the inequality:
[tex]6x+7.5y\ge75[/tex]In order to graph these inequalities, let's find two points that are on the line of the corresponding equation:
[tex]\begin{gathered} x+y=15 \\ (7,8)\text{ and }(8,7) \\ 6x+7.5y=75 \\ (0,10)\text{ and }(5,6) \end{gathered}[/tex]Now, graphing each inequation with the corresponding solution area (first one in blue, second one in green, common region in orange), we have:
Analysing the options, two of them that are inside the solution area are 4 hrs dog walking and 8 hrs car washing (A) and 10 hrs dog walking and 3 hrs car washing (C).
Is this a polynomial function? And if so ? What kind?
Answers
Given the graph:
Let's determine if the graph represents a polynomial function.
A polynomial function can be said to be a function which has non negative exponents and has only positive integers as the exponents.
It can be categorized as a quadratic function, cubic function, quartic function, etc.
Yes, the given graph represents a polynomial function and it is a quartic function.
The graph has 3 turning points.
A quartic graph has 3 turning points
The type of polynomial function shown in the graph is a quartic function.
ANSWER:
Yes, it is a quartic polynomial function.
a function f maps 3 5 7 9 onto 0 2 4 could f be represented by 3,0 5,2 7,4 9,2 exaplain your answer
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A function f maps ( 3,5,7,9) onto ( 0,2,4 ). Could f be represented by (3,0),(5,2). (7,4), (9,2)?
Yes, it is an onto mapping because 5 and 9 can be mapped to 2.
In mathematics, a function f from a set X to a set Y is surjective, if for every element y in the codomain Y of f, there is at least one element x in the domain X of f such that f(x) = y. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y.
What is the volume of a cylinder that has a radius of 3 and a height of 10? Use 3.14 for pi.
Answers
The volume of a cylinder is calculated as follows:
[tex]V=\pi\cdot r^2\cdot h[/tex]where r is the radius, and h is the height of the cylinder
Substituting with r = 3 and h = 10, we get:
[tex]\begin{gathered} V=\pi\cdot3^2\cdot10 \\ V=282.6 \end{gathered}[/tex]Solve for x. 4 - 5 25 Answer:
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In the equation, 25 is dividing on the right, then it will multiply on the left.
[tex]\begin{gathered} \frac{4}{5}=\frac{x}{25} \\ \frac{4}{5}\cdot25=x \\ 20=x \end{gathered}[/tex]Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.The vertices of AABC are A(2, 8), B(16, 2), and C6, 2). The perimeter of AABC is blankunits, and its area is blanksquare units.
Answers
Explanation
Part A
Given the vertices of triangle ABC as A(2, 8), B(16, 2), and C6, 2). We can form the triangle
Therefore, the side can be found using the distance between two points.
[tex]\begin{gathered} AC=\sqrt{(6-2)^2+(2-8)^2}=\sqrt{16+36}=\sqrt{52} \\ CB=\sqrt{(2-6)^2+(16-2)^2}=\sqrt{100}=10 \\ AB=\sqrt{(16-2)^2+(2-8)^2}=\sqrt{232}= \end{gathered}[/tex]Therefore, the perimeter of the triangle is
[tex]P=AC+CB+AB=\sqrt{52}+10+\sqrt{232}=32.44[/tex]Answer: Perimeter=32.44 units
Part B
From the image below,
The perpendicular height of the triangle is 6 units. While the base is 10 units.
The area of the triangle becomes
[tex]Area=\frac{1}{2}\times perpendicular\text{ height}\times base=\frac{1}{2}\times6\times10=30\text{ square units}[/tex]Area=30 square units
It took Mr. Sullivan 7 hours to drive a distance of 385 miles on a business trip. The followingweek he drove 165 miles in 3 hours. Is the relationship between the number of miles drivenand the amount of time for the two trips a proportional relationship?
Answers
Ratio 1: 385 miles in 7 hours.
• Ratio 2: 165 miles in 3 hours.
Now, a proportion is defined as the equality between two ratios, that means we need to put these two given ratios in an equation and see if they are equivalent.
[tex]\frac{385}{7}=\frac{165}{3}[/tex]Then, we divide each fraction
[tex]55=55[/tex]As you can observe both of them are equal to 55. That means they are in the same proportion.
Therefore, these two ratios have a proportional relationship.