Answer: I believe that, at that specific rate, it will take Suzanne 100 hours to drive 4,000 miles.
The graph shows the solution to which system of inequalities?
21 ≤ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≤ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≤ (x + 8)2 + y2
21 ≥ x2 + (y + 6)2 and 84 ≥ (x + 8)2 + y2
Answer:
D
Step-by-step explanation:
The shaded area is the intersection of the two inner areas of the two circles.
Because the area is inside both circles, the two inequalities must be less than or equal to the equation of the circles.
(If the inequalities are greater than or equal to the equation of the circles, the shaded areas will lie outside the circle.)
Hence, choice D is the correct choice.
It may assist to rewrite the inequalities such that it becomes apparent the equations are indeed less than or equal to the constant:
[tex]\displaystyle x^2 + (y+6)^2 \leq 21 \text{ and } (x+8)^2 + y^2 \leq 84[/tex]
Answer:
D
Step-by-step explanation:
Each side of a square is increased 6 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?
Please explain the answer, words confuse me :
Answer:
x = 3 inches
Step-by-step explanation:
Let x = the side of the original square, so the area is x²
After increasing, the side becomes x + 6. so the area becomes (x + 6)²
The area is multiplied by 9 means
(x + 6)² = 9 * x²
Take a square root, get
x + 6 = 3 * x
2x = 6
x = 3 inches
Let L represent the side length of the original square.
Note that:
L² = A(L + 6)² = 9A1. Square root both sides:
(L + 6)² = 9 x L²=> √(L + 6)² = √9 x L²2. Simplify the RHS:
=> L + 6 = 3 x L=> L + 6 = 3L3. Subtract L from each side.
=> 6 = 2L4. Divide 2 both sides.
=> L = 3 inchesDouble check:Area of square with 3 inches as side length: 3² = 9 in²Area of square with 9 inches as side length: 9² = 81 in²=> 81 ÷ 9 = 9 (True)
This shows that the area of the original square is 9 times smaller than the increased square.
Which of the ratios below is equivalent to 1:3? Select all that apply
Let f(x) be the function 4x2 - 6x + 11. Then the quotient
f(10 + h) – f(10)
can be simplified to ah + b for:
h
a
and
b
[tex]f(x) = 4 {x}^{2} - 6x + 11[/tex]
[tex]f(10 + h) = 4 ({10 + h})^{2} - 6(10 + h) + 11 \\ [/tex]
[tex]f(10 + h) = 4(100 + 20h + {h}^{2}) - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 400 + 80h + 4 {h}^{2} - 60 - 6h + 11 \\ [/tex]
[tex]f(10 + h) = 4{h}^{2} + 74h + 351[/tex]
_____________________________________________
[tex]f(10) = 4 ({10})^{2} - 6(10) + 11[/tex]
[tex]f(10) = 400 - 60 + 11[/tex]
[tex]f(10) = 351[/tex]
_____________________________________________
Thus :[tex] \frac{f(10 + h) - f(10)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h + 351 - (351)}{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} + 74h }{h} = \\ [/tex]
[tex] \frac{4 {h}^{2} }{h} + \frac{74h}{h} = \\ [/tex]
[tex]4h + 74[/tex]
_____________________________________________
[tex]ah + b[/tex]
[tex]4h + 74[/tex]
So :
[tex]a = 4[/tex]
[tex]b = 74[/tex]
If it doesn't give me the perimeter, how do i find x from this? thank you!
The way the angles are labeled tell you that they are all congruent. The two triangles you see here also share the side that joins them. Then by the angle-side-angle postulate, the two triangles are congruent, so x + 23 = 13, or x = -10.
The lifetime in miles for a certain brand of tire is normally distributed with a mean of 22,000 miles and a standard deviation of 3,100 miles The tire manufacturer wants to offer a money-back guarantee so that no more than 3% of tires will qualify for a refund. What is the minimum number of miles the manufacturer should guarantee that the tires will last?
a. 15,800 miles
b. 16,170 miles
c. 25,007 miles
d. 27,828 miles
Step-by-step explanation:
3% = 0.03
we are looking for the 3rd percentile of Z.
checking the Z-table we find as the entry closest to 0.03 to be 0.0301 at z = -1.8 and 0.8.
so, the 3rd percentile of Z is -1.88
the cutoff number (the number of miles, where max. 3% of the tires will qualify for a refund) is
mean value + Z× standard deviation
22000 + -1.88 × 3100 = 16,172 ≈ 16,170
so, b. is correct
You borrow $20,000 to purchase a car. The interest rate is 7.5%. The loan is for 10 years. What is the total amount payed? How much would the payment be each month?
Answer:
$35,000
$291.67
Step-by-step explanation:
Assuming that this loan uses simple interest, the equation for this problem will be A=P(1+rt). In this formula: A is the total amount paid, P is the initial amount, r is the rate in decimal form, and t is the time in years.
First, set up the equation by plugging the known values into the formula.
A = 20,000(1+0.075*10)Next, uses this information to find A
A = 35000This means that the total amount paid was $35,000.
Next, find the monthly payments. Using the time in years, we can figure out that this loan was paid over 120 months. Additionally, the monthly payment was equal for each month. This means that to find the monthly payment, simply divide the total amount by the number of months.
35000/120 ≅ $291.67Each month, approximately $291.67 was paid.
Answer:
$28,488 repaid$237.40 monthlyStep-by-step explanation:
The monthly payment on a loan is given by the amortization formula. The total amount repaid is the product of the monthly payment and the number of payments made.
The amortization formula is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . principal P, interest rate r, t years
For the loan values given here, this is ...
A = 20,000(0.075/12)/(1 -(1 +0.075/12)^(-12·10)) ≈ 237.40
The total repaid over 120 payments is ...
$237.40 × 120 = $28,488
The total amount paid is $28,488. The monthly payment is $237.40.
__
Additional comment
The payment and total paid can be computed using a suitable calculator, spreadsheet, or app. The attached picture is from an Android version of a TI-84 calculator. It comes with a built-in set of financial functions, similar to those found in a spreadsheet.
If the least value the variable k can be is 12, which of the following inequalities best shows all the possible values of k?
k < 12
k > 12
k ≤ 12
k ≥ 12
Answer:
k≥12
Step-by-step explanation:
if k's smallest amount is 12, k has to be bigger (greater than) or equal to 12
therefore:
k≥12
Now that Elizabeth arranged the door prizes, she needs to set up table centerpieces. Elizabeth wants to make sure that every table at the party is set perfectly. She needs to put the exact same amount of balloons and flowers at each table. Elizabeth got a special price from party city and purchased 84 balloons and 96 flowers. What is the greatest number of tables she can have at the party? Show your work
Answer:
i am not really sure but
Step-by-step explanation:
The quadrant in which (5, -12) is located.
(5,-12) is located in the fourth quadrant.
Because 5 being positive and 12 being negative it lies in the 4th quadrant.
Step-by-step explanation:
Hope it helps you!!Cara loves coffee. She has a Coffee Club card that has $80 on it. She buys a large cup each day that costs $2.50. Which of the following inequalities and solution set determine how many days, d, her Coffee Club card will last.
2.5d ≤ 80
d ≤ 160 / 5
d ≤ 32
card will last 32 days
Find the maximum and minimum values of f(x,y) = 2+2x+4y-x^2-y^2 on the triangular region in the first quadrant bounded by the lines x=0, y0, y=9x.
I think your question seems like :-
Find the maximum and minimum values of f(x,y) = 2+2x+4y-x²-y² on the triangular region in the first quadrant bounded by the lines x = 0, y = 0, y = 9-x. The reason is below :
If you see carefully, the given lines were x = 0, y = 0, y = 9x , also these lines forms a Triangle in first quadrant (Given) , but these all lines doesn't form a triangle in 1st quadrant , we can't change the other two lines (As those two lines will work as permanent sides and support for the triangle) but third one can be , also neither 9 + x nor (9/x) can't form triangle in 1st quadrant with the given other two lines .Only with y = 9 - x the given situation can be achieved
But before starting the question let's recall some of the concepts :-
For a given function let it be f(x,y) ,
f(x,y) can have maximum or minimum if AC - B² > 0 , as per A < 0 and A > 0 , if A < 0 then maxima at critical points and if A > 0 , then minima at critical points f(x,y) have saddle points if AC - B² < 0 From AC - B² = 0 , nothing can be concludedWhere ,
[tex]{\boxed{\bf{A=\dfrac{\partial^{2}f}{\partial x^{2}}}}}[/tex] [tex]{\boxed{\bf{B=\dfrac{\partial^{2}f}{\partial x\partial y}}}}[/tex] [tex]{\boxed{\bf{C=\dfrac{\partial^{2}f}{\partial y^{2}}}}}[/tex]Now , consider the function ;
[tex]{:\implies \quad \sf f(x,y)=2+2x+4y-x^{2}-y^{2}}[/tex]
Partial Differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=2-2x}[/tex]
Now , partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial x\partial y}=0}[/tex]
Now , consider ;
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial x}=2-2x}[/tex]
Partial differentiating both sides w.r.t.x
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial x^{2}}=-2}[/tex]
Now , consider ;
[tex]{:\implies \quad \sf f(x,y)=2+2x+4y-x^{2}-y^{2}}[/tex]
Partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial f}{\partial y}=4-2y}[/tex]
Now , partial differentiating both sides w.r.t.y
[tex]{:\implies \quad \sf \dfrac{\partial^{2}f}{\partial y^{2}}=-2}[/tex]
Now to find the critical points , first order partial derivative of f(x,y) both w.r.t.x and w.r.t.y must be 0. So , if you equate them to 0 , you will get x = 1 and y = 2. So critical point is only one i.e (1,2)
Now , from the above conditions , let calculate AC - B² first , from which we will get maxima or minima
[tex]{:\implies \quad \sf (-2)(-2)-(0)^{2}}[/tex]
[tex]{:\implies \quad \sf 4\> 0}[/tex]
So , AC - B² > 0 and also A < 0 , so maxima at (1,2) , to find maxima we need to put x = 1 , y = 2 in f(x,y) i.e f(1,2) = 2 + 2(1) + 4(2) - 1² - 2² = 7 . Now , for minima , draw the triangle see attachment 1 . Now , in the attachment critical points are (0,9) , (0,0) and (9,0) . Now , we need to find f(x,y) at these all points too . If you calculate then you will get f(0,9) = -43 , f(0,0) = 2 and f(9,0) = -61 , out of which -61 is minimum
So , the required maxima and minima are 7 and -61
Note :- Also , refer to the attachments no. 2,3,4 as well for why I choosed the third line to be 9 - x rather than others.
The quantity of a number minus four, divided by three is five
Answer:
19
Step-by-step explanation:
because you inverse the operation
5 ×3 = 15
15 + 4 = 19
Utilize graphing to find the solution to
the following system of equations.
y = 5x - 10 AND – 5x + y = 40
A
All Real Numbers
B
No Solution
Answer:
Step-by-step explanation:
No solutions, the two lines are parallel.
An easy way to spot it is to put the second in slope-intercept form ([tex]y=5x+40[/tex]) and notice they have the same slope
18
82 ÷ 42-369
Can you
Hey there!
8^2 ÷ 4^2 - 36 ÷ 9
= 8 × 8 ÷ 4 × 4 - 36 ÷ 9
= 64 ÷ 16 - 36 ÷ 9
= 4 - 36 ÷ 9
= 4 - 4
= 0
Therefore, your answer is: 0
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
HELPP 15 POINTS PLEASE PLEASE PLEASE
Answer:
a+(n-1)14
Step-by-step explanation:
ok so
a=the first number which is 16.50
n=the term.eg since 30.50 is the second number it's the second term
14 is the common difference d
I found 14 like this
30.50=16.50+(2-1)d
Therefore d=14
hence the formula is a+(n-1)14
A
+
55
60
55
70
75
80
85
90
B
Н
55
60
65
70
75
80
85
90
с
H
H
-
55
60
65
70
75
80
85
90
D
H
1
+
60
55
65
70
75
80
85
90
2) Four sets of data are shown in box-and-whisker plots. Which set has the largest MEDIAN?
Α)Α
B) B
OC
D) D
A bakery is collecting data to investigate how changing the price charged for a loaf of bread affects the bakery’s daily profit. The graph shows the data the bakery has collected. Which quadratic function is the best model for the data? y = − 8 ( x + 4 ) 2 + 800 y = − 8 ( x + 4 ) 2 + 800 y = − 8 ( x − 4 ) 2 + 800 y = − 8 ( x − 4 ) 2 + 800 y = − 200 ( x + 4 ) 2 + 800 y = − 200 ( x + 4 ) 2 + 800 y = − 200 ( x − 4 ) 2 + 800
Considering the vertex of the graph, it is found that the quadratic function that is the best model for the data is given by:
[tex]y = -200(x - 4)^2 + 800[/tex]
What is the equation of a quadratic function given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
[tex]y = a(x - h)^2 + k[/tex]
In which a is the leading coefficient.
Researching the problem on the internet, it is found that the vertex is at point (4,800), hence h = 4 and k = 800.
[tex]y = a(x - 4)^2 + 800[/tex]
It has a value of y = 0 at x = 6, hence:
[tex]0 = a(6 - 4)^2 + 800[/tex]
[tex]a = -200[/tex]
Thus, the model is:
[tex]y = -200(x - 4)^2 + 800[/tex]
More can be learned about quadratic functions at https://brainly.com/question/24737967
The system of equations has 2x-y=2(x+1) y=-2
A. no solution
B. one solution
C. infinitely many solutions
Answer:
A.
Step-by-step explanation:
This equation has no solution.
You invested $1,810 into an account which pays 3% interest per year. How much interest will you earn after a year?
Step-by-step explanation:
interest =
[tex] \frac{3}{100} \times 1810[/tex]
therefore
interest = $54.3 after a year
pls give brainliest
Answer:
54.3
Step-by-step explanation:
Interest earned = Prt
where P is the initial investment and r is the interest rate and t is time
Interest earned = 1810*0.03*1=54.3
andrea cycles 9 km on her bike in 2 hours. calculate her average speed in kilometers per hour.
Answer:
4.5km/h
Step-by-step explanation:
Here we know that she does 9 km per 2 hours. If we know how much she can travel in 2 hours it's very easy to find out how much she travels in 1. Because half of 2 hours is one hour. So we can simply half 9 km to find how much she travels in 1 hour:
9/2 = 4.5
4.5km/h
I hope this makes sense :)
Answer:
4.5 km per hour
.........
.....
if x=2 in the equation y=3x-5, what is the value of y?
Answer:1
Step-by-step explanation:
just plug them in
we know x =2
so in where ever it says x, we put in 2
y=3(2) -5
Answer:
y= 1
Step-by-step explanation:
y= 3x -5
To find the value of y when x= 2, replace x with 2 in the equation.
When x= 2,
y= 3(2) -5
y= 6 -5
y= 1
Jill bought 3 pints of strawberries for $3.98 each. What is the best estimate of how much Jill spent?
Answer:
i dont know but its $3.00 or $9,00
Step-by-step explanation:
Answer: 12.00 $
Step-by-step explanation: First things first, you need to estimate $3.98 to $4.00.
Then mutiply the $4.00 with 3 because it says 1 pint for $4.00, and you will get $12.00.
Hopfuly this will help ヾ(＠^∇^＠)ノ.
please help I will give brainiest
Answer:
7
Step-by-step explanation:
The letter for sausage or red sauce is S at the end and R in the middle.
Counting, there is 7 outcomes that have either S at the end or R in the middle.
Beth and her father have a large model railroad in their basement. Beth figured out that the equation y = 260/3x relates the length of an item on her model railroad to the length of the real thing, where x is the size on the model and y is the real object’s size. Beth’s uncle has a different model railroad in his home. It has a different scale. He put together the following table for Beth.
I DONT GET IT
The scale factor used to represent the model from the real object size is y = (260/3)x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the real object size and x represent the size of the model.
Given that:
y = (260/3)x
The scale factor used to represent the model from the real object size is y = (260/3)x
Find out more on equation at: https://brainly.com/question/2972832
Which quadratic function is represented by the graph?
y = 0.5(x + 2)2 + 4
y = 0.5(x + 3)2 – 0.5
y = 0.5(x – 3)2 – 0.5
y = 0.5(x – 2)2 + 4
Answer: C
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (3, - 0.5), thus
y = a(x - 3)² - 0.5
To find a substitute either of the x- intercepts into the equation.
Using (4, 0), then
0 = a(4 - 3)² - 0.5 = a - 0.5 ( add 0.5 to both sides )
a = 0.5
y = 0.5(x - 3)² - 0.5 ← equation of quadratic function
Type the correct answer in each box. If necessary, use / for the fraction bar(s).
John recorded the number of cars passing a traffic signal at intervals of 2 minutes. He plotted his data on this graph.
The slope of the line is
, and the y-intercept is
.
Answer:
Slope: 20/7
Y-intercept: 0
Step-by-step explanation:
Hello!
This is a regular graph, and we can find out several things from it, including slope and y-intercept.
The slope is basically how steep or flat the line is. The more flat it is, the bigger the slope. The more steep it is, the more smaller the slope. We can find the slope by using rise over run, seeing how many values it rises over how many values it runs over the x-axis.
The y-intercept is basically where the line starts from in the y-axis. The y-axis is a vertical line usually at the left most area.
To find out the slope, we can see the best fit blue line, and we have to find the most accurate slope. In this problem, the line doesn't go through perfectly with the grid at until around (14, 40). Don't get mistaken for (2,5)! It's not an accurate slope. Since it goes UP and rises 40 and 'runs' 14 units, the slope is that but simplified.
\frac{40}{14} =\frac{20}{7}
The y-intercept is where the line starts from the y-axis, where it labels 'cars'. As you can see, the blue line starts at zero, so there is no y-intercept.
To take it further, the equation of the line is y=mx+b, where m is the slope and b is the y-intercept. In this problem, the equation would be
y=[tex]\frac{20}{7}[/tex]x.
Hope this helped!
Answer:
this guy is half right
Step-by-step explanation:
0 is right but not 20/7
8 is what percent of 16?
Answer:
8 is 50% of 16
Step-by-step explanation:
since 8 is half of 16
Raul added 1.72x10^4 to 8x10^4 and got the sum 9.72x10^10. do you agree with his answer? explain why you agree or disagree
the answer is : 9.72×10^4 or 972×10^2
Step-by-step explanation:
l didn't agree with the answer because
(1.72×10^4 + 8×10^4)
form above take common i.e., 10^4 so we get,
10^4 (1.72+8.00)
10^4(9.72)
so we get the answer is : 9.72×10^4 or
(972÷100)10^4
972 × 10^-2 ×10^4
972× 10^(-2+4)
972× 10^2
is 3.564 greater than 2.07636?
Answer:
Of course yes
Step-by-step explanation:
We first look at the ones place. So is 3>2? Yes, so the answer is yes.