Step-by-step explanation:
Answer:
The distance between the two given points is equal to √85.
Step-by-step explanation:
Let's recall what the distance formula is:
\displaystyle \huge\math\boxed{d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2} }\math
d= (x 1 −x2 ) 2 +(y 1 −y 2) 2
We are defined our two points as:
(x₁, y₁) → (1, -7)
(x₂, y₂) → (7, 0)
We can rewrite this into our different "variables":
x₁ = 1
y₁ = -7
x₂ = 7
y₂ = 0
Now given our distance formula and our variables, we can find the distance between the two points:
\begin{gathered}\displaystyle\huge\begin{aligned}d & = \sqrt{(1 - 7)^2 + (7 - 0)^2} \\& = \sqrt{(-6)^2 + (7)^2} \\& = \sqrt{36 + 49} \\& = \math\boxed{\sqrt{85}} \\\end{aligned}\end{gathered}
d= (1−7) 2+(7−0) 2= (−6) 2+(7) 2 = 36+49=\math 85
∴ since the radical is already in its simplest form, our distance between the two points is equal to √85.
Hope this helps!
Question
Gabriel and Raj were running a lemonade stand at the local park. They decided to pay their sister to operate the stand. The
following values represent the profit y after a hours of the stand being open.
Using a calculator or statistical software, find the linear regression line for the data.
Enter your answer in the form y = mx +b, with m and b both rounded to two decimal places.
Provide your answer below:
y=x+
[
X
1
2
3
4
5
6
7
y
3.58
5.18
6.24
7.97
7.09
8.31
11.33
The linear regression equation for the data is given by:
y = 1.08x + 2.76.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(1, 3.58), (2, 5.18), (3, 6.24), (4, 7.97), (5, 7.09), (6, 8.31), (7, 11.33).
Inserting these points into a calculator, the linear regression equation for the data is given by:
y = 1.08x + 2.76.
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Part of a multiplication table is shown.
15 20 25 30
18
30 36
21
35 42
24 32 40 48
What two numbers are needed to complete the pattern in
the multiplication table?
OA) 21 and 24
OB) 24 and 24
OC) 24 and 28
OD) 21 and 28
The correct option is C) 24 and 28 for the given multiplication table.
What is defined as the multiplication table?The multiplication table (already known as the time's table) provides multiples of numbers. Multiplying a number by a set of whole numbers yields the multiplication table.The given multiplication are-
15 20 25 30This is the table 5 starting with;
5×3 = 15 ....... 5×6 = 30
18 __ 30 36This is the table of 6 starting with;
6×3 = 18 ....... 6×6 = 36
Thus, the missing number is;
6×4 = 24
21 __ 35 42This is the table 7 starting with;
7×3 = 21 ....... 7×6 = 42
Thus, the missing number is;
7×4 = 28
24 32 40 48This is the table of 8 starting with;
8×3 = 28 ....... 8×6 = 48
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The correct question is-
Part of a multiplication table is shown.
15 20 25 30
18 __ 30 36
21 __ 35 42
24 32 40 48
What two numbers are needed to complete the pattern in
the multiplication table?
OA) 21 and 24
OB) 24 and 24
OC) 24 and 28
OD) 21 and 28
if 3 equal 8 what will equal 600
Answer:
if 3 equal 8 , then 600 will be 1600.
f(x) =2x | g(x)=-8x+2 | h(x)=x^2+x+3
Find f(g(6))
Find g(h(-4))
Find g((f)x)
With how you solved it please! (Will give first correct answer brainliest
Step-by-step explanation:
f(x) = 2x
g(x) = -8x + 2
h(x) = x² + x + 3
= f(g(6))
= 2x
= 2.(-8x + 2)
= 2.(-8.6 + 2)
= 2.(-48 + 2)
= 2.(-46)
= -92
= g(h(-4))
= -8x + 2
= -8.(x² + x + 3) + 2
= -8.((-4)² + (-4) + 3) + 2
= -8.(16 - 1) + 2
= -8.15 + 2
= -120 + 2
= -118
= g(f(x))
= -8x + 2
= -8.(2x) + 2
= -16x + 2
One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Are the two triangles similar?
The height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
The length of Manny's shadow, which is 414 feet long, is 512 feet.
The tree's shadow extends 17 feet.
Here, we'll assume that the height is x.
According to the data given, the calculation is as follows:
414 : 512 = 17 : x
⇒ 414 / 512 = 17 / x
⇒ (414)x = (512)(17)
⇒ x = (512)(17)/(414)
⇒ x =21.02
⇒ x = 21 feet
Therefore, the height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.
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Your question is incomplete, probably the complete question is:
One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Manny is 512 feet tall, and his shadow is 414 feet long. The shadow of the tree is 17 feet long. How can you determine the height of the tree?
Green Sun has net working capital of $400, current assets of $2,315, and inventory of $1,100. �What is the Quick ratio?
Answer:
3:5.7
Step-by-step explanation:
please Mark me as
Answer:
its not a accurate questions
cant be answered
Step-by-step explanation:
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 300 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 82 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 568 mg of cholesterol. How much cholesterol is in each item?
Answer: 300
Step-by-step explanation:
A ball is thrown up on the surface of a moon. It’s height above the lunar surface (in feet) after ‘t’ seconds is given by the formula
h =592t - 16/7t^2
Find the time that the ball reaches its maximum height.
Step-by-step explanation:
we get the points with extreme values as the 0 points of the first derivative of the function.
h'(t) = 592 - 32/7 t = 0
592 = 32/7 t
4144 = 32t
t = 129.5 seconds
so, it will reach its max. height after 129.5 seconds.
The time that the ball reaches its maximum height is 129.5 seconds.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The height above the lunar surface (in feet) after ‘t’ seconds is given by the formula;
⇒ h =592t - 16/7t²
Now,
We have to find the derivative of above formula and equate to zero for the maximum time as;
⇒ h =592t - 16/7t²
⇒ h' =592 - 16/7 × 2t = 0
⇒ 592 - 32/7 t = 0
⇒ 32/7 t = 592
⇒ 32t = 592 × 7
⇒ 32t = 4,144
⇒ t = 4,144/32
⇒ t = 129.5 seconds.
Thus, The time that the ball reaches its maximum height is 129.5 seconds.
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If f(x) = x−6x^2 find (f(x + h) − f(x))/h
The value of (f(x + h) − f(x))/h is 1 - 6h - 12x.
For any function, say f(x) = x + a, the value of f(x+b) = (x + b) + a or (x + b + a)
Here, we are given that
f(x) = x−6x^2
and we need to find the value of (f(x + h) − f(x))/h
Firstly,
f(x + h) = (x+h) - 6(x+h)^2
Now, f(x + h) − f(x) = (x+h) - 6(x+h)^2 - (x−6x^2)
= (x+h) - 6(x+h)^2 - x + 6x^2
= x - x + h - 6(x^2 + h^2 + 2xh) + 6x^2
= h - 6x^2 - 6h^2 - 12xh + 6x^2
= h - 6x^2 + 6x^2 - 6h^2 - 12xh
= h - 6h^2 - 12xh
= h( 1- 6h - 12x)
Thus, (f(x + h) − f(x))/h = [h( 1- 6h - 12x)] / h
= 1 - 6h - 12x
Therefore, the value of (f(x + h) − f(x))/h is 1 - 6h - 12x.
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Whats 1,250 - 250 x 2?
Answer:750
Step-by-step explanation:
multiply the numbers
1250-250x2
1250-500
subract the two numbers and you will get
750
HELP PLS, I NEED AN ANSWER ASAP, 25 POINTS AVALIABLE
The gradient of the line y = x/3 - 4 is; 1/3
What is the gradient of the given line?
Slope is defined as the gradient of a graph at any point
We are given the equation of the line as;
y = x/3 - 4
Now, the formula for equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Thus, from the given equation, we can tell that the gradient which is the slope is 1/3.
Thus, we conclude that the gradient of the line y = x/3 - 4 is; 1/3
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A rectangular garden is 6 ft longer than it is wide. Its area is 667 ft2. What are its dimensions?
The dimensions of the rectangular garden are 29 feet by 23 feet .
A rectangle is a quadrilateral with parallel opposite sides and equal angles. There are a lot of rectangular objects all around us. Any rectangular form's two defining characteristics are its length and width. A rectangle's longer and shorter sides are its width and length, respectively.
The area of a rectangle is given by length × width
Now the given area of the rectangle is 667 ft² .
Let the width of the rectangle is x ft. Therefore length = x + 6
Now area of the rectangle is x (x+6) = x² + 6 x
Therefore x² + 6 x = 667
or, x² + 6 x - 667 = 0
or, (x-23)(x+29) = 0
Either x = 23 or x = -29(not possible)
Hence the width is 23 feet.
Length = 23 + 6 = 29 feet
Therefore the dimensions of the rectangle are 29 feet by 23 feet .
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Which characteristics are appropriate for the Brand of camcorder? Choose all that apply
Question options:
O Nominal
O Scale
O String
O Numeric
Answer:
numeric
Step-by-step explanation:
-2 ( 3x + 2 ) ≥ 6x – 4
Answer: x ≤ 0. Interval Notation: (-∞, 0]
Is this or is this not a function?
Answer:
This is not a function
Step-by-step explanation:
Assuming that the line in question is parallel with the y axis, by using the line test we can see that the line is not a function. The line test is where you draw straight lines going vertically over the graph and if the lines touch the figure in question more than once that means it's not a function.
This can also be proved by imagining there are 2 different points on the line in question. Since the line is straight vertically that means that the points will share the same x value for different y values, which makes it not a function
Answer:
This is not a function.
Step-by-step explanation:
The questioned parallel line within the y-axis does not meet the requirements to be a function. The line test, as the other person stated, is a test where lines are drawn over the points to determine if the graph / model is, or is not a function. Doing so in this process, if the lines touch the same point more than once, that means the graph is not a function.
(2 x 10⁴) + (3 x 10³) =
Answer:
23000
Step-by-step explanation:
(2 x 10⁴) + (3 x 10³)
= (2 x 10000) + (3 x 1000)
= 20000 + 3000
= 23000
Determine the sum of (8x1 – x + 4) and (3x + 5)
Answer:
x = 1/9
Step-by-step explanation:
8x¹ - x +4 can be also written as 7x + 4 or 7x = -4
And 3x + 5 can be written as 3x = -5
So,
7x = -4
-(3x = -5)
4x = 1
x = 1/9
Carlos and Shawn are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Carlos sold 13 small boxes of oranges and 5 large boxes of oranges for a total of $133. Shawn sold 10 small boxes of oranges and 8 large boxes of oranges for a total of $148. Find the cost of each of one small box of oranges and one large box of oranges.
Answer: The cost of one small box of oranges is $6, while the cost of one large box of oranges is $11.
Step-by-step explanation:
First, set x for the cost of one small box of oranges in dollars, and y for the cost of one large box of oranges in dollars.
Hence, the equations will be:
[tex]13x+5y=133[/tex]
[tex]10x+8y=148[/tex]
Then solve for the equations using the method of elimination. In order to eliminate one of the variables, you need to make the coefficients the same. So, we can multiply the first equation by 8 and the second equation by 5. That would make the equations:
[tex]104x+40y=1064[/tex]
[tex]50x+40y=740[/tex]
Then you can eliminate the y by subtracting.
[tex]54x = 324[/tex]
Then divide by 54 on both sides.
[tex]x=6[/tex]
Now that x is solved, solve for y by substituting for x.
[tex]13(6) + 5y = 133[/tex]
[tex]5y+78=133[/tex]
[tex]5y=55[/tex]
[tex]y=11[/tex]
So, x=6 and y=11.
3x – y = -1 x – 2y = -12
The solution to the system of equation is (2, 7)
System of equationGiven the system of equation expressed as:
3x – y = -1 * 2
x – 2y = -12 * 1
________________
6x – 2y = -2
x – 2y = -12
Subtract to have;
6x-x = -2-(-12)
5x = 10
x = 2
Substitute x = 2 into 2 to have:
2 - 2y = -12
-2y = -14
y = 7
Hence the solution to the system of equation is (2, 7)
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A house is purchased for $145,000 and each year increases in value by 6% of its value the previous year. (6 marks) Let be the value of the house in year . Write a difference equation which gives the value of the house after years. Solve the difference equation. Find the projected value of the house in 15 years.
The projected value of the house after 15 years is $347500.
A house is purchased for $145,000.
The value of the house increases each year by 6% of its value the previous year.
Let y(n) denote the value of the house after n years.
Initial value is $145,000.
⇒ y(0) = 145,000
The value of the house increases each year by 6% of its value the previous year.
Therefore the growth is exponential, and we have
y(n) = y(0)(1+0.06)ⁿ
When n = 1
⇒y(1) = 145000 × (1.06)
⇒y(1) = 153700
When n = 2,
⇒y(2) = 145000 × (1.06)²
⇒y(2) = 162922
Therefore, when n = 15,
⇒y(15) = 145000 × (1.06)¹⁵
⇒y(15) = 3,47,500
Therefore, the projected value of the house after 15 years is $347500.
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C. describe how you could compare the corresponding sides and angles of figure STUV and its image, figure WXUY
Both the diagrams; figure STUV and its image, figure WXUY are congruent to each other.
What exactly is congruence?If two images are precisely the same in terms of length, width, and height, they are congruent.If one geometric figure can be superimposed on another so that their total area coincides, a certain geometric figure is considered to be congruent or to be situated in the reference of congruence.For the given two diagrams;
WXUY image to mirror STUV
If we rotate the STUV anticlockwise so that side UV coincides with side UY, then side ST≅ WX side TU ≅ side XU, side UY≅ side UV, side YW≅ side VS will be equal, as will angle S≅W, TUV≅XUV, X≅T, and Y≅V will be equal.
Therefore, the side corresponds to the area side ST≅ WX side of TU ≅ side XU, side UY≅ side UV, side YW≅ side VS, and the angle S≅W, TUV≅XUV, X≅T, and Y≅V".
Thus, the given two diagram figure STUV and image, figure WXUY are congruent to each other.
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Solve the equation P = b + a + c for b.
b= ?
Answer:
b= p-(a+c)
Step-by-step explanation:
negative 19 plus the quantity negative 4 and five tenths plus 6 and 87 hundredths end quantity divided by 3 all times 5 squared minus 7 and 3 tenths
19.6
−18.4
31.45
−6.55
Answer: 19.6
Step-by-step explanation:
As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 130 milligrams of Medication A with 182 milligrams of Medication B. However this week, the doctor said to only use 140 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
Proportionately, the number of milligrams of Medication A that should be mixed this week with 140 milligrams of Medication B is 100 milligrams.
What are proportions?Proportions are the ratios of variables to others.
Proportions show the number or value relationships of two variables.
Decimals, percentages, and fractions can represent proportions.
Data and Calculations:The mixture of Medication A and B last week:
Medication A = 130 milligrams
Medication B = 182 milligrams
The proportion of Medication A to Medication B = 0.714287
The mixture of Medication A and B this week:
Medication B = 140 milligrams
Medication A = x
x = 140 x 0.714287
x = 100 milligrams
Thus, using equivalent proportions, 140 milligrams of Medication B should be mixed with 100 milligrams of Medication A.
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What do you hypothesize about rational numbers with denominators that are prime
numbers?
Answer:
There is no special hypothesis that you can come up with. You could, of course, hypothesize that they are special numbers
Step-by-step explanation:
DJI manufactures the Mavic Air 2 quadcopter and offered a 6/4/3 chain discount to primary customers. Drone Nerds is a primary customer and ordered 15 Mavic Air 2's for a total $26,500 list price.
Drone nerds will get 15 Mavic air 2's for $23196.192 after offering a chain discount of 6/4/3.
Chain discount is the series of discounts that are offered from the list price of an object when bought from a store.
A general example of a 10/5 chain discount denotes that there will be a series of discounts on the list price. First a discount of 10% is awarded on the list price then a further 5% on the reduced price.
The List price of the drones is $26500.
Chain discount=6/4/3
So the first discount received is 6% on the $26500.
Price after the first discount=26500- 6%of 26500
Simplifying we get
[tex]=26500-.06\times26500\\=24910[/tex]
The price after the first discount is $24910
Now we will apply the 4% discount on $24910
Price after second discount=24910-4% of 24910
=$23913.60
Now we apply the third discount
Price after third discount is=23913.60-3%of 23913.60
=$23196.192
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The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each
The salaries of each will be 127975 and 182875.
How to compute the value?Lat the salaries of B = b
Let the salary of A = b + 54900
Therefore, we will add them together to get the value:
b + b + 54900 = 310850
2b + 54900 = 310850
2b = 310850 - 54900
2b = 255950
b = 255950/2
b = 127975
a = b + 54900 = 127975 + 54900 = 182875
Therefore, the salaries of each will be 127975 and 182875.
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If 7cakes cost $6.30 what is the cost of 12 such cakes
Answer:
$10.8
Step-by-step explanation:
First, to determine the price of one cake divide 6.30/7
You will determine one cake costs 90 cents.
So, multiply 0.90 by 12, and you get $10.8
PLEASE HELP
5|12-r|>15
Step-by-step explanation:
5.|12 - r| > 15
|12 - r| > 15/5
|12 - r| > 3
12 - r < -3 or 12 - r > 3
-r < -3 - 12 or -r > 3 - 12
-r < -15 or -r > -9
r > 15 or r < 9
√₂
You invested $7000 between two accounts paying 5% and 8% annual interest, respectively. If the total interest
earned for the year was $500, how much was invested at each rate?
was invested at 5% and $ was invested at 8%.
Save
>
Answer:
$2000 was invested at 5% and $5000 was invested at 8%.
Step-by-step explanation:
Assuming the interest is simple interest.
Simple Interest Formula
I = Prt
where:
I = interest earned.P = principal invested.r = interest rate (in decimal form).t = time (in years).Given:
Total P = $7000P₁ = principal invested at 5%P₂ = principal invested at 8%Total interest = $500r₁ = 5% = 0.05r₂ = 8% = 0.08t = 1 yearCreate two equations from the given information:
[tex]\textsf{Equation 1}: \quad \sf P_1+P_2=7000[/tex]
[tex]\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500[/tex]
Rewrite Equation 1 to make P₁ the subject:
[tex]\implies \sf P_1=7000-P_2[/tex]
Substitute this into Equation 2 and solve for P₂:
[tex]\implies \sf 0.05(7000-P_2)+0.08P_2=500[/tex]
[tex]\implies \sf 350-0.05P_2+0.08P_2=500[/tex]
[tex]\implies \sf 0.03P_2=150[/tex]
[tex]\implies \sf P_2=\dfrac{150}{0.03}[/tex]
[tex]\implies \sf P_2=5000[/tex]
Substitute the found value of P₂ into Equation 1 and solve for P₁:
[tex]\implies \sf P_1+5000=7000[/tex]
[tex]\implies \sf P_1=7000-5000[/tex]
[tex]\implies \sf P_1 = 2000[/tex]
$2000 was invested at 5% and $5000 was invested at 8%.
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