The straight road crosses the boundaries of the range of the ambulance service at two points
The length of the road that lies within the range of the ambulance service is approximately 37.95
Reason:
The function that represents the ambulance circular service area is x² + y² = 400
The equation that represents the straight road, y = 3·x + 20
Required:
Length of the road that lies within the range of he ambulance
Solution:
The length of the road is given by the distance between the intersection
points of the road and the ambulance service region as follows;
At the intercepts, we have;
The x, and y-values of the line and the circle are equal, therefore, we have;
At the intercept, y = 3·x + 20, which gives;
x² + y² = 400
x² + (3·x + 20)² = 400
x² + 9·x² + 120·x + 400 = 400
10·x² + 120·x + 400 - 400 = 0
10·x² + 120·x = 0
x² + 12·x = 0
x² + 12·x = x·(x + 12) = 0
x = 0, or -12When x = 0, y = 3×0 + 20 = 20
When x = -12, y = 3×(-12) + 20 = -16
The intersection points of the line and the circle are;
A(0, 20), and B(-12, -16)The length of the segment AB, d, is given as follows;
d = [tex]\sqrt{((-12) - 0)^2 + (-16 - 20)^2} = \sqrt{1440} =12 \cdot \sqrt{10}[/tex]The length of the road that lies within the range of the ambulance service, d, given to the nearest hundredth = 12·√(10) ≈ 37.95
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Which of the following is a trinomial with a constant term?
A. x + 2y + 10
a
B. X
c. Y6+ 8y3 + 64y
+
D. x2 + y
Answer:
The answer would be
A. x + 2y + 10
A constant term is considered any term that does not change or have a variable with it. 10 is the only displayed constant term.
Answer:
[tex]\\ \sf\longmapsto x^2+y[/tex]
Step-by-step explanation:
Trinomial means the expression has 3 roots.
In the last one
x has degree 2 so it has 2roots. And there is another variable namely y so another root.Total 3 roots
If j= 14, find the value of 1/2j.
Answer:7
Step-by-step explanation:
1/2 of j is the same as j ÷ 2
14 ÷ 2 = 7
Find all possible values of P in x^2-10x+P=(x-A)(x-B) if P, A and B are all whole numbers
The value of P in the expression [tex]x^2-10x+P=(x-A)(x-B)[/tex] is 25
Given the expression [tex]x^2-10x+P=(x-A)(x-B)[/tex]
To get the value of P, we will use the completing the square method;
Add the square of the half of the coefficient of x
The coefficient of x is -10Half of the coefficient of x is -10/2 = 5Square of half of the coefficient of x = 5^2 = 25Hence the complete quadratic expression will be [tex]x^2-10x + 25[/tex]
Hence the value of P in the expression [tex]x^2-10x+P=(x-A)(x-B)[/tex] is 25
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Find the original price of a pair of shoes if the sale price is $28 after a 50% discount.
Answer:
The original price was 56 dollars
Step-by-step explanation:
28 divided by 0.5 equals 56
7-12 plz help me identify each pair of angles
7. supplementary
8. same side interior angles
9. alternate exterior angles
10. vertical angles
11. complementary angles (I’m not entirely sure about this one)
12. alternate interior angles
question 3 please!!!!!!!!!
Answer:
RIS
Step-by-step explanation:
Answer:
Step-by-step explanation:
Calvin kicked a soccer ball laying on the ground. It was in the air for 5 seconds before it hit the ground. While the soccer ball was in the air it reached a height of approximately 25 feet. Assuming that the soccer ball’s height (in feet) is a function of time (in seconds), what are the domain and range in the context of this problem?
Refer to the attachment
Please someone help me with this im giving brainliest!!
Answer:
A) Second step
would be the answer
How? Can a i get a clear explanation. is the question wrong or am i wrong?
Answer:
U are wrong no need to be pushy to u
If y varies directly with X,
Y
and y= 4.5 when x= 2.5,
what is y when x= 12?
Y
Answer:
y=1.8x
Step-by-step explanation:
Dividing fractions word problems 1 1 A 16-kilometer stretch of road needs repairs. Workers can repair 2- kilometer of road per week. 4 How many weeks will it take to repair this stretch of road? Weeks Stuck? Reviews related articles/videos or use a hint.
Answer:
8 weeks
Step-by-step explanation:
16km is the total, 2km is what is completed in a single (1) week.
so our equation is 16÷2
Week 1: 2km
Week 2: 4km
Week 3: 6km
Week 4: 8km
Week 5: 10km
Week 6: 12km
Week 7: 14km
Week 8: 16km (final)
6 Ella is a salesperson for a cosmetics company. She is paid $500 per week and a commission of 3% on sales in excess of $800.
What does Ella earn in a week in which she makes sales of $600?
The total amount that Ella earned in a week in which she made sales of $600 is; $500
How to solve Algebra Word problems?The parameters given about Ella who is a salesperson are;
Amount paid per week = $500
Commission on sales exceeding $800 = 3%
Total sales for the week = $600
From the parameters above, we see that she didn't make sales exceeding the commission limit of $800 and as such she didn't earn any extra commission.
Therefore her weekly pay was still $500
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Which congruent angles can prove that
lines Land M are parallel?
A. 2 and 7
B. 5 and 8
C. 4 and 6
Answer:
C 4 and 6
Step-by-step explanation:
Because 4 and 6 are coointerior
Solve for the indicated variable. Include all of your work in your answer. Submit your solution.
Answer:
[tex]h = \frac{2a}{a + b} [/tex]
Given f(x) = -x + 5, solve for 2 when f(x) = -10.
Answer:
15
Step-by-step explanation:
replace x with -10
Consider the following data set:
2 , − 3 , − 3 , 1 , 8 , 12 , 14 , 2
Find the lower quartile.
Answer:
-3, -3, 1, 2, | 2, 8, 12, 14
Lower quartile is negative 1
Because the middle number is the median because there is an odd set of numbers.
To find the quartile you have to arrange the numbers from lowest to highest.
When you find middle number you have to find the half of the lower half of the middle, which you will solve the lower quartile. Since there are even numbers you add the two middle numbers and divide it by 2. And you'll get the answer hope that helped
Please help! If you do so you will get 50 points and brainiest!
Answer:
1
Step-by-step explanation:
Find the equation (in terms of x) of the line through the points (-2,4) and (2,0)
y =
Answer:
y = - x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 4 ) and (x₂, y₂ ) = (2, 0 )
m = [tex]\frac{0-4}{2-(-2)}[/tex] = [tex]\frac{-4}{2+2}[/tex] = [tex]\frac{-4}{4}[/tex] = - 1 , then
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (2, 0 )
0 = - 2 + c ⇒ c = 0 + 2 = 2
y = - x + 2 ← equation of line
-1.5x – 2x - 12(x + 10)
Answer:
-15.5x-120
Step-by-step explanation:
-1.5x-2x-12(x+10)=-1.5x-2x-12x-120
=-15.5x-120
Answer:
-3.5x - 12(x + 10)
-3.5x - 12x - 120
-15.5x - 120
Step-by-step explanation:
brainliest plz
The sum of three consecutive even integers is 642. What are the integers? (Show your work too please)
Answer:
212,214,216
Step-by-step explanation:
n+n+2+n+4=642
add the n's and 2 and 4
3n+6=642
subtract 6 from both sides
636 divided by 3
you get 212 then add 2 twice.
Answer:
212, 214, 216
Step-by-step explanation:
Basically you can divide 642 by 3 to find the average number of the 3. get You get 214, so that means 214 + 214 + 214 = 642
We need consecutive EVEN integers though, so you can take the one even BEFORE and then one even AFTER 214
This means 212 and 216 are used as they are 2 before and 2 after, so when added they still total 642.
Write the prime factorization of 128. Use exponents when appropriate and order the factors from least to greatest
128 = 2^7
There are just seven 2's being multiplied to get to 128,
We know that the factors of 128 are : 1, 2, 4, 8, 16, 32, 64, and 128 itself.
But we need a prime factorization, and so [tex]2^{7}[/tex] is the prime factorization of that number
Ted has 18 feet of lumber. How many 2 1/2 foot shelves can he make? Explain your answer.
Answer:
The answer is 7.2, and if you round it, it would be 7.
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice, where the rice-to-spice ratio is 15:1. He currently has 40 grams of the spice blend, and he can go buy more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David spends 4.50 dollars on rice.
What is the price of rice per gram?
Answer:
The price of rice per gram is 0.006$
Step-by-step explanation:
I. David wants to make 10 servings,
each require 75 g of rice and 5 spice. When ratio is 15:1
If rice : spice = 75 : x
15x = 75
x = 5
=> 5 * 15 : 1 * 5
= 75 : 5
So rice : spice is 75 : 5
II. When 1 serving require 75 : 5
So 10 servings is 10 * 75 : 5 * 10
= 750 : 50
So he must has 750 grams rice and 50 grams spice.
III. He must buy spice and rice which..
a) He has 40 grams spice, he'll buy for 10 grams spice.
b) He has no rice, he'll buy for 750 grams rice.
But the question only ask for price of rice which he spend 4.5$
= [tex]\frac{4.5}{750}[/tex]
= 0.006$
In 1 gram of rice he spend 0.006$
If 750 grams of rice, he'll spend 750 * 0.006$ = 4.5$ => true
That makes 0.006$ is the right answer.
Hope that help :)
What is the x-intercept of the line 2x -3y = -6?
Answer:
The x-int is 3/2y - 3 (x=3/2y-3)
Step-by-step explanation:
2x-3y=-6
2x=3y-6
x=3/2y-3
Will give brainiest to correct answer
Answer:
8 x 4 = 5 fours + 3 fours
= 20 + 12
= 32
Hope This Helps! •v•
there were 8 gallons of juice for the third grade picnic.How many gallons of juice were there for each of the third grade classes???? please help with my hw!!!
There are 26 red cards and 26 black cards in a standard deck of playing cards, for a total of 52 cards. There are 4 kings to a deck, two of which are red kings and two of which are black kings. A card will be randomly selected from a standard deck of playing cards. Let A represent selecting a king and let B represent selecting a red card. Calculate the following probabilities:
P (A) =
P (A ׀ B) =
Based on these probabilities, are A and B independent events? Explain your reasoning.
Simplify these epressions.
Name three fractions between 1/3 and 1/4
Answer:
[tex] \frac{2}{7} \\ \\ \frac{5}{16} \\ \\ \frac{7}{24} [/tex]
(a) The area of a rectangular parking lot is 7802 m².
If the width of the parking lot is 83 m, what is its length?
Length of the parking lot: Im
(b) The perimeter of a rectangular pool is 352 m.
If the length of the pool is 97 m, what is its width?
width of the pool: Im
Answer:
A) Length = 94 m
B) Width = 79 m
Step-by-step explanation:
A)
The area of a parking lot is 7802 m²
Area = length x width
7802 = length x 83
length = 7802 ÷ 83
length = 94 m
b)
The perimeter of a pool is 353 m
Perimeter = 2(length + width)
352 = 2(97 + width)
352 = 194 + 2width
2width = 352 - 194
2width = 158
width = 158/2
width = 79 m
-Chetan K