Answer:
Subtract 14 from both sides of the equation.
Step-by-step explanation:
The subtraction property of equality tells you the equal sign only remains valid if you subtract the same value from both sides of the equation.
Here, we want the 14 on the left side to be replaced by 0. Thus we must add its opposite. Since we must do the same thing to both sides of the equation, we must subtract 14 from both sides of the equation.
Answer:
Last option: Subtract 14 from both sides of the equation.
Step-by-step explanation:
To solve the equation [tex]x+14=21[/tex] you must solve for the variable "x".
To calculate the value of the variable "x" it is important to remember the Subtraction property of equality. This states that:
[tex]If\ a=b\ then\ a-c=b-c[/tex]
Therefore, applying this property, you should subtract 14 from both sides of the equation to find the value of the variable "x". Then:
[tex]x+14-(14)=21-(14)\\\\x=7[/tex]
The slope of a line will depend on which of the two points you choose to call (x1, y1) and which you choose to call (x2, y2) when calculating the slope.
Answer:
FALSE
Step-by-step explanation:
The slope can be calculated using any two points on the line in any order and the result will be the same.
Does a rhombus have opposite sides that are parallel
Answer:
Yes.
Step-by-step explanation:
Look at a Rhombus.
Answer:
Yes, rhombus have opposite sides that are parallel.
Step-by-step explanation:
A rhombus is a four-sided shape where all sides have equal length, let's say s.
Consider the picture given, here are some facts:
* All sides have equal length
* Opposite sides are parallel, and opposite angles are equal
* A rhombus is sometimes called a rhomb or a diamond.
Tags: Rhombus, opposite sides, parallel, rhomb, diamond
TW is a perpendicular bisector of chord QE. Identify the diameter. The answer with the red arrow is Incorrect!
Answer:
50m
Step-by-step explanation:
By using the information we have, we can create an equation using the Pythagorean theorem to solve for r. Once we have r double it to get diameter
Answer:
The answer is 50m
Need help with a math question
Hey there! Thanks for asking your question here on Brainly.
Let's split this question up into two parts: large and cold drink. Now that we have our two parts, we need to figure out which would be the numerator and which would be the denominator. Looking at the question, the size large would be the numerator because that is the part out of the whole we are finding. The whole would be cold drink because that is given, meaning that we are looking for the larges out of the entire cold drink section.
Now, we'll find the total amount of customers that ordered cold drinks for the whole part of our fraction. That is 25 customers. Next, we set the numerator of our fraction to the amount of customers that ordered large, cold drinks. Therefore, our fraction would be 5/25. The fraction in decimal form is 0.2, and in percent form is 20%.
Therefore, the probability that a customer ordered a large given that he or she ordered a cold drink is 20%.
Hope this helps! If there is anything else that I can help you with, please let me know! :)
Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on their axis of symmetry. A) g(x), h(x), f(x)
B) f(x), h(x), g(x)
C) g(x), f(x), h(x)
D) h(x), f(x), g(x)
Answer:
Option D) h(x), f(x), g(x)
Step-by-step explanation:
we know that
The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola
Part 1) we have
[tex]f(x)=4x^{2} -1[/tex]
This is a vertical parabola open upward
The vertex is a minimum The vertex is the point (0,-1)
The x-coordinate of the vertex is 0
so
The axis of symmetry is x=0
Part 2) we have
[tex]g(x)=x^{2}-8x+5[/tex]
This is a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
[tex]g(x)-5=x^{2}-8x[/tex]
[tex]g(x)-5+16=x^{2}-8x+16[/tex]
[tex]g(x)+11=x^{2}-8x+16[/tex]
[tex]g(x)+11=(x-4)^{2}[/tex]
[tex]g(x)=(x-4)^{2}-11[/tex]
The vertex is the point (4,-11)
The x-coordinate of the vertex is 4
so
The axis of symmetry is x=4
Part 3) we have
[tex]h(x)=-3x^{2}-12x+1[/tex]
This is a vertical parabola open downward
The vertex is a maximum
Convert the equation into vertex form
[tex]h(x)-1=-3x^{2}-12x[/tex]
[tex]h(x)-1=-3(x^{2}+4x)[/tex]
[tex]h(x)-1-12=-3(x^{2}+4x+4)[/tex]
[tex]h(x)-13=-3(x+2)^{2}[/tex]
[tex]h(x)=-3(x+2)^{2}+13[/tex]
The vertex is the point (-2,13)
The x-coordinate of the vertex is -2
so
The axis of symmetry is x=-2
Part 4) Rank their axis of symmetry from least to greatest
1) h(x) -----> axis of symmetry -2
2) f(x) -----> axis of symmetry 0
3) g(x) -----> axis of symmetry 4
so
h(x),f(x),g(x)
BRAINLIEST! write a verbal expression to represent the given equation.
4n-3=21
Answer:
four base n minus 3 is equal to 21
Step-by-step explanation:
this is verbal
The label on the car's antifreeze container claims to protect the car between −40°C and 140°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C equals five ninths times the quantity F minus thirty two.. Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
Negative forty is less than five ninths times the quantity F minus thirty two.
Five ninths times the quantity F minus thirty two is less than one hundred forty.
Negative forty is greater than five ninths times the quantity F minus thirty two is greater than one hundred forty.
Negative forty is less than five ninths times the quantity F minus thirty two is less than one hundred forty.
Answer:
Option D is the answer.
Step-by-step explanation:
The label on the car's antifreeze container claims to protect the car between -40°C and 140°C.
So inequality which models this situation will be -40°C < T < 140°C
Now we have to show this inequality in Fahrenheit temperature with the help of [tex]C=\frac{5}{9}(F-32)[/tex]
So the compound inequality in Fahrenheit temperature will be
[tex]-40<\frac{5}{9}(F-32)<140[/tex]
Answer: FLVS ALGEBRA 1
The answer would be D
Step-by-step explanation:
The label says that the cars antifreeze is -40°C and 140°C.
so the inequality which models this situation will be -40°C < T < 140°C
Now you got to show this inequality in Fahrenheit temperature.
So the compound inequality in Fahrenheit temperature will be Option D
Cell phone company A charges $10/month plus $0.75 per text message and $1 per minute of talk. Data is unlimited. Company B charges $100/month plus $0.10 per text message and $1 per minute of talk. Data is unlimited. Emily’s monthly average is 400 texts messages, 90 minutes of talk, and 2.1 gigs of data. Which company should she choose? (4.1)
a. Company A because they offer a lower monthly flat fee.
b. Company A because the total bill will be lower.
c. Company B because the total bill will be lower.
d. Company B because they offer a lower monthly flat fee.
After calculating the monthly costs for Emily's usage, Company A would cost $400 while Company B would cost $230. Therefore, Company B is the better choice for Emily as it offers a lower total bill.
To determine which cell phone company, A or B, offers a better monthly plan for Emily who uses 400 texts, 90 minutes of talk, and 2.1 gigs of data per month, we need to calculate the total monthly costs for both companies.
Company A:
Monthly fee: $10Text messages: 400 * $0.75 = $300Talk: 90 * $1 = $90Total Cost for Company A: $10 + $300 + $90 = $400Company B:
Monthly fee: $100Text messages: 400 * $0.10 = $40Talk: 90 * $1 = $90Total Cost for Company B: $100 + $40 + $90 = $230After calculating the costs, it is clear that Company B offers a lower total bill despite the higher monthly flat fee. Hence, Emily should choose Company B because the total bill will be lower.
Solve the system of equations Please If you could solve this it would honestly mean so much! Thank you!
y=3x+2
-3x+2y=10
Answer:
(2, 8)
Step-by-step explanation:
There are a couple of different ways to do this, but I am going to use substitution since we already have one of those equations solved for y. If y=3x+2, then we can sub 3x+2 in for y in the other equation:
-3x + 2(3x + 2) = 10 and
-3x + 6x + 4 = 10 and
3x + 4 = 10 and
3x = 6 so
x = 2. Now that we know x = 2, we can sub a 2 in for x in either equation to solve for y:
y = 3x + 2 gives us, with the substitution, y = 3(2) + 2 so y = 8. The solution set is (2, 8)
Need help with a math question
Answer:
24°
Step-by-step explanation:
see attached
Answer: [tex]z=24\°[/tex]
Step-by-step explanation:
We need to find the measure of "x":
Based on the figure, we know that:
[tex]48\°+x+x=180\°[/tex]
Then, we need to solve for "x". Therefore, its measure in degrees is:
[tex]48\°+2x=180\°\\\\2x=180\°-48\°\\\\2x=132\°\\\\x=\frac{132\°}{2}\\\\x=66\°[/tex]
By definition, the sum of the interior angles of a triangle is 180 degrees. Since we know the measure of "x" and we know that one of the interior angles is a the right angle (an angle that measures 90 degrees), we can conclude that:
[tex]z+90\°+x=180\°[/tex]
Substituting the value of "x" into the equation and solving for "z", we get:
[tex]z+90\°+66\°=180\°\\\\z=24\°[/tex]
Solve x − 5y = 6 for x.
A) x = −5y + 6
B)x = −5y − 6
C) x = 5y + 6
D) x = 5y −6
Answer:
x = 5y + 6
Step-by-step explanation:
Add 5y to both sides
x - 5y + 5y = 5y + 6 (variable always goes first)
-5y + 5y = 0
x = 5y + 6
Answer:
The correct option is C) x = 5y + 6.
Step-by-step explanation:
Consider the provided equation.
[tex]x - 5y = 6[/tex]
We need to solve the equation for x.
Add 5y to both sides of the equation.
[tex]x - 5y+5y = 6+5y[/tex]
Simplify the equation.
x=6+5y
Hence, the value of the equation for x is x=6+5y.
Therefore, the correct option is C) x = 5y + 6.
PLZ HELP MARKIN BRAINEST!!!
There are 25 total Seniors.
12 of the Seniors want to see more candid pictures.
The percent would be 12/25 = 0.48 x 100 = 48%
Please help, I'm so close to finishing all these.
Answer:
d. 43°
Step-by-step explanation:
KM is a bisector of ∠LKN, so ...
∠LKN = 2(∠4)
7q +2 = 2(4q -5)
12 = q . . . . . . . . . . . add 10-7q, simplify
Now, we can put 12 where q is in the expression for ∠4:
∠3 = ∠4 = 4·12 -5 = 43
Find the value of tan( π + θ) if θ terminates in Quadrant III and sinθ = -5/13
ANSWER
[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]
EXPLANATION
We first obtain
[tex] \cos( \theta) [/tex]
using the Pythagorean Identity.
[tex]\cos ^{2} ( \theta) + \sin ^{2} ( \theta) = 1[/tex]
[tex] \implies \: \cos ^{2} ( \theta) + ( - \frac{5}{13} )^{2} = 1[/tex]
[tex]\implies \: \cos ^{2} ( \theta) + \frac{25}{169}= 1[/tex]
[tex]\implies \: \cos ^{2} ( \theta) = 1 - \frac{25}{169}[/tex]
[tex]\implies \: \cos ^{2} ( \theta) = \frac{144}{169}[/tex]
[tex]\implies \: \cos ( \theta) = \pm \: \sqrt{\frac{144}{169} } [/tex]
[tex]\implies \: \cos ( \theta) = \pm \: \frac{12}{13} [/tex]
In the third quadrant, the cosine ratio is negative.
[tex]\implies \: \cos ( \theta) = - \: \frac{12}{13} [/tex]
The tangent function has a period of π and [tex]\pi + \theta[/tex] is in the third quadrant.
This implies that:
[tex] \tan(\pi + \theta)= \tan( \theta) [/tex]
[tex]\tan(\pi + \theta)= \frac{ \sin( \theta) }{ \cos( \theta) } [/tex]
[tex]\tan(\pi + \theta)= \frac{ - \frac{ 5}{13} }{ - \frac{12}{13} } [/tex]
This gives us:
[tex]\tan(\pi + \theta)= \frac{5}{12} [/tex]
Which expression is equivalent to 6x3 + 3y2 – 5x3 + 2y2?
A. x6 + 3y4
B. 6x3y2
C. x3 + 5y2
D. 6x6y4
Answer:
x3 + 5y2
Step-by-step explanation:
The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y² so option (C) will be correct.
What is an expression?
A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
Given,
6x³ + 3y²– 5x³ + 2y²
Combine all likely terms
(6x³ - 5x³) + (3y² + 2y²)
⇒ x³ + 5y²
Hence,The expression 6x³ + 3y²– 5x³ + 2y² is equivalent to x³ + 5y².
To learn more about expression,
https://brainly.com/question/14083225
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At a supermarket salad bar, the price of a salad depends on its weight. Salad costs $.19 per ounce. Write a rule to describe the function. How much would an 8-ounce salad cost?
Answer:
For an 8-ounce salad would cost $1.52
Step-by-step explanation:
Every ounce would cost $0.19.
So you would multiply the cost with how much you would buy.
0.19(cost per ounce)×8(how much ounce)=1.52(total pay)
Answer: B. F(x) = 0.19x ; $1.52
Step-by-step explanation:
To find the cost of 8 ounce sale , substitute 8 for x .
F(x)= 0.19x
F(8)= 0.19(8)
F(8)=1.52
There was a party with 50 students. They had a cylinder root beer keg that was 17 inches in height and 13 inches in diameter. They also had cylinder cups to drink the root beer out of, they were 3 inches in diameter and 4 3/4 inches tall. Would there be enough root beer for everyone to have at least one cup?
Answer:
Yes, there will be enough root beer for everyone to have at least one cup
Step-by-step explanation:
step 1
Find the volume of the cylinder root beer keg
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=13/2=6.5\ in[/tex] -----> the radius is half the diameter
[tex]h=17\ in[/tex]
substitute
[tex]V=\pi (6.5)^{2} (17)[/tex]
[tex]V=718.25\pi\ in^{3}[/tex]
step 2
Find the volume of the cylinder cups
The volume is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=3/2=1.5\ in[/tex] -----> the radius is half the diameter
[tex]h=4\frac{3}{4}\ in=4.75\ in[/tex]
substitute
[tex]V=\pi (1.5)^{2} (4.75)[/tex]
[tex]V=10.6875\pi\ in^{3}[/tex]
step 3
Multiply the volume of one cup by 50 (the total number of students) and then compare the result with the volume of the cylinder root beer keg
so
[tex]10.6875\pi*(50)=534.375\pi\ in^{3}[/tex]
[tex]534.375\pi\ in^{3}< 718.25\pi\ in^{3} [/tex]
therefore
There will be enough root beer for everyone to have at least one cup
Answer:
Yes. There is enough for everyone.
Step 1: Find the volume of the keg
Diameter : 13
Radius : 6.5
Height : 17
Formula for the area of a circle (base) is πr^2
Solve that using the above formula.
Base area = 132.73
Multiply that by the height.
Keg volume : 2,256.45 inches cubed
Step 2: Find the volume of the cups
Diameter : 3
Radius : 1.5
Height : 4 3/4
Formula for area of a circle (base) is πr^2
Solve that using the above formula.
Base area = 7.07
Multiply that by the height.
Cup volume : 33.58 inches cubed
Step 3: Multiply cup volume by 50
33.58 x 50 = 1,678.79
Step 4: Check how much root beer you have for everyone.
Root beer needed : 2,256.45
Root beer available : 1,678.79
Is there enough root beer?
Yes
uppose a jumbo ice cream cone is filled with vanilla and strawberry ice cream at a ratio of 2:1. If the diameter of the cone is 3 inches and the height is 8 inches, what is the volume of strawberry ice cream in the cone? (to nearest tenth in3) A) 6.3 in3 B) 9.4 in3 C) 12.6 in3 D) 18.8 in3
Answer:
A) 6.3 in³
Step-by-step explanation:
The formula for the volume of a cone is ...
V = (1/3)πr²h . . . . . where r is the radius and h is the height
Only 1/(2+1) = 1/3 of the volume of your cone is strawberry ice cream, so the volume of ice cream (in terms of cone diameter) is ...
V = (1/3)(1/3)π(d/2)²h
V = π(d/3)²(h/4) . . . . rearranged slightly
For our diameter of 3 inches and height of 8 inches, this is ...
V = π(3 in/3)²(8 in/4) = 2π in³ ≈ 6.3 in³
The volume of strawberry ice cream is about 6.3 in³.
Mike and Jamal are 9 miles apart, and are planning to meet up. Mike is walking at an average speed of 3 miles per hour to meet Jamal. Jamal is driving at an average speed of 25 miles per hour to meet Mike.
Which equation can be used to find t, the time it takes for Mike and Jamal to meet?
25t – 3t = 0
25t – 3t = 9
25t + 3t = 1
25t + 3t = 9
Answer:
25t + 3t = 9
Step-by-step explanation:
Since they are going to each other, their speeds need to be combined, since they both contribute to reduce the distance between them.
So, 25t + 3t = 9 is the answer, because
25t is the distance Jamal will drive in an hour,
3t is the distance Mike will walk in an hour,
9 is the distance to be covered so they can meet.
Answer:
25t + 3t = 9
Step-by-step explanation:
determine whether the function f(x) = 3(x − 1)4 is even or odd.
Answer:
the function is odd
Step-by-step explanation:
A function f(x) is said to be even if f(-x) = f(x)
On the other hand, f(x) is said to be odd if f(-x)≠ f(x).
We plug in -x in place of x in the given function and simplify;
f(-x) = 3(-x-1)^4
f(-x) = 3[-1(x+1)]^4
f(-x) = 3 *(-1)^4 * (x+1)^4
f(-x) = 3(x+1)^4 ≠ f(x)
Therefore, the function given is odd
Answer:
The given function is odd
Step-by-step explanation:
we need to determine the function [tex]f(x)=3(x-1)^{4}[/tex] is odd or even
Since, A function f(x) is said to be even if [tex]f(-x) = f(x)[/tex]
and f(x) is said to be odd if [tex]f(-x)= - f(x)[/tex] and [tex]f(-x) \neq f(x)[/tex]
We Replace x with -x in the given function and solve;
[tex]f(x)=3(x-1)^{4}[/tex]
[tex]f(-x)=3(-x-1)^{4}[/tex]
take out the negative common,
[tex]f(-x)=3[-(x+1)]^{4}[/tex]
Since [tex](-1)^{4}=1[/tex]
[tex]f(-x)=3(x+1)^{4}[/tex]
[tex]f(-x) \neq f(x)[/tex]
Hence, the given function is odd
A crew will arrive in one week and begin filming a city for a movie. The mayor is desperate to clean the city streets before filming begins. Two teams are available, one that requires 200 hours and one that requires "400" hours. If the teams work together, how long will it take to clean all of the streets? Is this enough time before the cameras begin rolling?
Final answer:
Two teams working together will take approximately 133.33 hours or about 5.56 days to clean the city streets. This is less than the one week (7 days) available before filming begins, so the streets will be clean in time.
Explanation:
To calculate how long it will take for two teams working together to clean the city streets, we use the concept of combined work rates.
The first team requires 200 hours to clean the streets, while the second team requires 400 hours.
When working together, we can add their rates of work, which means the first team cleans 1/200 of the city per hour, and the second team cleans 1/400 of the city per hour.
The combined rate of work will be:
1/200 (team A's rate) + 1/400 (team B's rate)
= 2/400 + 1/400
= 3/400
So, together they clean 3/400 of the city per hour. To find out how many total hours it will take to clean the entire city, we take the reciprocal of their combined rate
1 / (3/400)
= 400/3
≈ 133.33 hours
Since there are 24 hours in a day, we divide the total hours by 24 to find out how many days it will take:
133.33 hours / 24 hours/day
≈ 5.56 days
Given that the crew will arrive in one week, which is 7 days, this is within the time frame required before filming begins. The teams have enough time to clean the streets before the cameras start rolling.
There are 6 red marbles, 4 blue marbles, and 6 yellow marbles in a bag. A total of 2 marbles are chosen without replacing them. What is the probability of first choosing a yellow marble and then choosing a blue marble?
In total, there are 16 marbles.
So the probability of first choosing a yellow marble is:
[tex]\frac{6}{16}[/tex] (That's because in our bag if 16 marbles, 6 of them are yellow)
However, as stated in the question, we do not replace the marble.
That means we will now only have bag of 15 marbles in total (since we have already taken out the first marble)
So the probability of then choosing a blue marble is:
[tex]\frac{4}{15}[/tex] (that's because in our bag of 15 marbles, 4 of them are blue)
----------------------------------------------
Finally to get the answer we multiply the two probabilities that we worked out. That's because in probability, and = multiply
So P(choosing a yellow marble) and P(choosing a blue marble)
= P(choosing a yellow marble) times P(choosing a blue marble)
So the final probability is:
[tex]\frac{6}{16}[/tex] × [tex]\frac{4}{15}[/tex] = [tex]\frac{24}{240}[/tex]
This simplifies down to [tex]\frac{1}{10}[/tex]
------------------------------------------------------
Answer:
The probability of first choosing a yellow marble and then a blue marble is:
[tex]\frac{1}{10}[/tex]
What's the probability of rolling a number less than 5 and a head when rolling a die and then tossing a coin?
[tex]|\Omega|=6\cdot2=12\\|A|=4\cdot1=4\\\\P(A)=\dfrac{4}{12}=\dfrac{1}{3}[/tex]
Answer:
D. 1/3.
Step-by-step explanation:
Probability(Rolling a number < 5) = 2/3 and
probability( Getting a head) = 1/2
The required probability , since the 2 events are independent is the product of the above = 2/3 * 1/2 = 1/3.
PLEASE HELP AND SHOW ALL YOUR WORKING BRAINLIEST
Step-by-step explanation:
those little lines on each side show that each side is equal length. the line in the middle divided the rhombus in half to make two triangles, therefore making them equal.
A customer annual homeowner premium is $1000. By combining home and auto the customer could save 10% a year on her home insurance. The auto premium is $1500 per year. What would be her total combined premium?
Final answer:
To find the total combined premium, a 10% discount is applied to the $1,000 homeowner premium, totaling $100 in savings. The new homeowner premium is $900, which is then added to the $1,500 auto premium, resulting in a total combined premium of $2,400.
Explanation:
The student has asked a question about calculating combined insurance premiums when a discount is applied for bundling home and auto insurance. To determine the total combined premium, we'll first calculate the savings on the homeowner premium and then add the reduced home premium to the auto premium.
First, we find 10% of the homeowner premium:
10% of $1,000 = 0.10 * $1,000 = $100 savings.
Next, we subtract the savings from the original homeowner premium to determine the new premium for home insurance:
$1,000 - $100 = $900.
Now, we add the discounted home premium to the auto premium:
$900 + $1,500 = $2,400.
The total combined premium for home and auto insurance would be $2,400 after the 10% discount is applied to the home insurance.
Events A and B are disjointed.
P(A) = 8/15 ; P(B) = 4/15
Find P(A or B).
Answer:
[tex]P(A\hspace{3}or\hspace{3}B)=\frac{4}{5}=0.8 =80\%[/tex]
Step-by-step explanation:
If Events A and B are disjointed, this means that they are mutually exclusive events. Mutually exclusive events are those that if one event happens means that the other cannot occur. For this type of event the following properties are true:
[tex]A\cap B = \emptyset,\\\\P(A\cup B)=P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)[/tex]
Therefore:
[tex]P(A\hspace{3}or\hspace{3}B)=P(A)+P(B)\\\\P(A\hspace{3}or\hspace{3}B)=\frac{8}{15} +\frac{4}{15} =\frac{12}{15} =\frac{4}{5} =0.8[/tex]
You can also write the result as a percentage just multiplying by 100:
[tex]P(A\hspace{3}or\hspace{3}B)=0.8*100=80\%[/tex]
Which type of arc measures exactly 180 degrees
Answer:
semi circle
Step-by-step explanation:
Answer:
Semicircle
Step-by-step explanation:
The value of x is _____
Answer:
We only need one simple theorem for this.
Theorem 7 - The Exterior Angle Theorem: An exterior angle of a triangle is equal to the sum of the two remote interior angles.
So in this case, the measurement of the exterior angle is (45x)°, and the interior angles are (25x)° and (57 + x)°.
=> Therefore, we have:
25x + (57 + x) = 45x
25x + x - 45x = - 57
-19x = -57
x = -57/(-19) = 3
So x = 3
Outside angle = addition of the two inner angles.
45x = 25x + 57 + x
45x = 26x + 57
45x - 26x = 57
19x = 57
x = 57/19
x = 3
Did you follow the logic?
2. Using the DMS method to describe an angle, one degree of angle measurement can be divided into how many minutes?
A. 360′
B. 60′
C. 90′
D. 100′
Answer:
B
Step-by-step explanation:
1° = 60 minutes = 3600 seconds
It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Adam should cover to get to the park? Answer:
Answer:
120 miles
Step-by-step explanation:
We have to "interpret" the problem statement, because its literal meaning is that it takes Adam a negative amount of time to drive the distance when driving faster. 2.5 times 4 hours is 10 hours. 10 hours less than 4 hours is -6 hours, meaning that driving faster gets Adam to the park 6 hours before he started driving.
So, we assume the intent of the problem is that driving faster multiplies Adam's travel time by a factor of 1/2.5, 2/5 of what it was at the lower speed. Since travel time is inversely proportional to speed, Adam's speed is effectively multiplied by 2.5 by driving faster. We can use the relation ...
speed = distance/time
to relate the speeds (in mph) and times (in hours) given in the problem. For some distance d, we have ...
45 + d/4 = 2.5(d/4) . . . . . adding 45 mph to his speed multiplies it by 2.5
Multiplying by 4 gives ...
180 + d = 2.5d
180 = 1.5d . . . . . . . . subtract d
180/1.5 = d = 120 . . . divide by 1.5
Adam covers a distance of 120 miles to get to the park.