The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula
m = (y2 - y1)/(x2 - x1)
m = (1 - (-3))/(3 - 1)
m = 4/2
m = 2
Therefore the slope, or the average rate of change, between these points is 2.
nesecito ayuda para hacer el ejercico es para hoy!!!!! Un número se multiplica por 37 y al sumar los productos parciales resulta 7890. ¿Cuál es la suma de cifras del número
10
Sara was thinking of a number. Sara adds 19 to it, then doubles it and gets an answer of 39.2. What was the original number?
Answer:
0.6
Step-by-step explanation:
2(x+19)=39.2
x+19=19.6
x=0.6
At the beginning of spring, Elijah planted a small sunflower in his backyard. When it was first planted, the sunflower was 25 inches tall. The sunflower then began to grow at a rate of 1 inch per week. How tall would the sunflower be after 7 weeks? How tall would the sunflower be after w weeks?
Answer:32
Step-by-step explanation:25+ 1(7)
Which ones are correct?
Answer:
120 x 10^3
7 x 10^5
9 x 10^4
Step-by-step explanation:
A small rectangular tray measures 16 cm by 18 cm. How long is the diagonal?
Answer:
24.1cm
Step-by-step explanation:
Which of the following is the product of (3x − 5) and (3x + 5)?
Answer:
[tex] {9x}^{2} - 30x + 25[/tex]
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
(3x + 5)(3x - 5)
By using identity
(a + b)(a - b) = a² - b²
3x² - 5²
9x² - 25
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. Illustrate by graphing both the curve and the tangent line on a common screen. x=t, y=e^-t, z=2t-t^2; (0, 1, 0)
Answer:
[tex]x = t[/tex]
[tex]y = 1 - t[/tex]
[tex]z = 2t[/tex]
Step-by-step explanation:
Given
[tex]x=t[/tex]
[tex]y=e^{-t}[/tex]
[tex]z=2t-t^2[/tex]
(0, 1, 0)
The vector equation is given as:
[tex]r(t) = (x,y,z)[/tex]
Substitute values for x, y and z
[tex]r(t) = (t,\ e^{-t},\ 2t - t^2)[/tex]
Differentiate:
[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]
The parametric value that corresponds to (0, 1, 0) is:
[tex]t = 0[/tex]
Substitute 0 for t in r'(t)
[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]
[tex]r'(0) = (1,\ -e^{-0},\ 2 - 2*0)[/tex]
[tex]r'(0) = (1,\ -1,\ 2 - 0)[/tex]
[tex]r'(0) = (1,\ -1,\ 2)[/tex]
The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)
It should be noted that:
The equation of a line through position vector a and parallel to vector v is given as:
[tex]r(t) = a + tv[/tex]
Such that:
[tex]a = (0,1,0)[/tex] and [tex]v = r'(0) = (1,-1,2)[/tex]
The equation becomes:
[tex]r(t) = (0,1,0) + t(1,-1,2)[/tex]
[tex]r(t) = (0,1,0) + (t,-t,2t)[/tex]
[tex]r(t) = (0+t,1-t,0+2t)[/tex]
[tex]r(t) = (t,1-t,2t)[/tex]
By comparison:
[tex]r(t) = (x,y,z)[/tex] and [tex]r(t) = (t,1-t,2t)[/tex]
The parametric equations for the tangent line are:
[tex]x = t[/tex]
[tex]y = 1 - t[/tex]
[tex]z = 2t[/tex]
Find the height of a flagpole to the nearest tenth if the angle of elevation of tbe sun is 28 degrees & the shadow of the flagpole is 50 feet
Answer:
Step-by-step explanation:
tan28=h/50
h=50tan28
h=26.6ft
What side lengths should be used to model a rectangle with an area of x2 + 3x – 10 square units?
x – 5 and x + 2
x – 2 and x + 5
x and x + 3
x + 3 and x – 10
Answer:
x - 2 and x + 5
Step-by-step explanation:
Given Area Of rectangle
= x² + 3x - 10
= x² + ( 5 - 2)x - 10
=x² + 5x - 2x - 10
= x ( x + 5 ) - 2 ( x + 5 )
= ( x + 5 ) ( x - 2 )
Hope it will help :)❤
Answer:
B. x-2 and x+5
Step-by-step explanation:
Find the equation of a line that passes through the point (-2,4) and has a gradient of -3.
Leave your answer in the form
y
=
m
x
+
c
Equation of a line is y = mx +c
m is the gradient, which is given as -3 so now you have:
y = -3x + c
Replace y and x with the given point and solve for c:
4 = -3(-2) + c
Simplify:
4 = 6 + c
Subtract 6 from both sides:
c = -2
The equation becomes:
y = -3x-2
Pls help, thank you :)
Answer:
(3)
Step-by-step explanation:
For f (x) = 2x+1 and g(x) = x2 - 7, find (fºg)(2).
Answer:
Step-by-step explanation:
Your first step will be to set up the problem:
f(x) - g(x)
Next you will substitute in your values:
(2x + 1) - (x2 - 7)
The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:
2x + 1 - x2 + 7
Then combine your like terms:
2x - x2 + 8
Lastly put your expression in standard form (highest exponent to lowest)
-x2 + 2x + 8
Hope this helped!
What is an equation of the line that passes through the point (3,-1)(3,−1) and is parallel to the line 5x+3y=65x+3y=6?
Answer:
6yx hope this helped dude!
Step-by-step explanation:
Answer:
6yx
Step-by-step explanation:
PLEASE HELP!!! I WILL GIVE BRAINLIEST
Answer:x=2y=3
Step-by-step explanation: I did this before
Answer the following for the given figure.
HELPPPPPPPPP PLEASEEEEEE
I WILLL MARK YOU BRILL
please help me with this
13x² -7x -8 how to solve this
Answer:
132x-8
Step-by-step explanation:
I think I might be wrong, but hopefully this is helpful, and yet I still find this confusing.
It's a simplification I don't know if you needed that.
what is the area of the shaded region in the figure below
Answer:
4 cm^2
Step-by-step explanation:
2 x 2 x 0.5 x 2 = 4 cm^2
Hi there!
[tex]\huge\boxed{4 \text{ cm}^{2}}[/tex]
Find the area of the shaded area using the given dimensions:
The shaded area is divided up into two triangles, each with a base of 2 cm and a height of 2 cm. Use the following equation to solve for area:
A = 1/2(bh)
A = 1/2(2 · 2)
A = 1/2(4) = 2 cm²
There are two triangles, therefore:
2 × 2 = 4 cm²
A colony of 500 bacteria doubles in size every 200 hours. What will the population be 400 hours from now?
Answer:
1000
Step-by-step explanation
200+200=400
so
500+500=1000
what is the density of the oak board? it is 5.5 inches wide, 1.5 inches thick and 3 feet long
multiply 5.5 the width with 1.5 by 3 which gives you 24.75 inches feet long.
5.5 x 1.5 x 3=24.75 that's your answer.
Answer:297 cubic inches, other person is incorrect.
Step-by-step explanation:5.5 inches* 1.5inches * 3 feet
Convert 3 feet to inches and you have 36 inches. So now it becomes 5.5inches*1.5inches*36inches = 297 cubic inches
Hi i need help with this please?!??!!
Answer:
May be your answer is option 3
1. A car travels at an average rate of speed of 60 miles per hour for 7.5 hours. How many miles does this car travel?
Answer:
450
Step-by-step explanation:
60 x 7.5=450
ASAP!! WILL MARK BRAINLIEST!!!!!!!!
Complete the table below to solve the equation 2.5x - 10.5 = 64(0.5^x)
x f(x)= 2.5x - 10.5 g(x) = 64(0.5^x)
2
3
4
5
6
Answer in table format, picture below
Answer:
x = -0.35
Step-by-step explanation:
tep 1 - Multiply 64 and 0.5x. The answer ends up being 32x
Step 2 - You need to get all of the variables on one side and the regular numbers on the other side. To do that, you need to subtract 2.5x from each side so you are left with the equation -10.5 = 29.5x
Step 3 - The final step is to isolate the variable. To do this, you divide each side by 29.5 meaning that x = -0.35
You put $500 in a savings account. The account earns $20 simple interest in 6 months. What is the annual interest rate? Write your answer as a percent
Answer:
8%
Step-by-step explanation:
For simple interest, we use the equation I = PRT, where I is the interest earned, P is the principal/amount invested, R is the rate as a decimal, not percentage, and T is the time in years.
For this problem, we have to use 0.5 for T, because 6 months is 1/2 a year.
20 = (500)(r)(0.5)
20 = 250r
r = 0.08 = 8%
Which equation is correct?
75 × 4 = 70 + 5 × 4
75 × 4 = 70 × 4 + 5 × 4
75 × 4 = 700 × 4 + 5 × 4
75 × 4 = 70 × 4 + 5
What is the area of the triangle below? 00 17 O A. 136 sq. units O B. 68 sq. units O C. 25 sq. units O D. 50 sq. units
Answer:
B) 68 units^2
Step-by-step explanation:
8 x 17 x 0.5 = 68 units^2
In the last year, U.S. car sales of all makes and models have dropped by 16%. Let's say that a car dealer sells 325 cars. If this number drops by 16%, how many cars will the dealer sell then? Round to the nearest whole number.
A 203 cars
B 309 cars
C 273 cars
D 256 cars
Answer:
c. 273 cars
Step-by-step explanation:
First you need to find what 16% of 325 is
325x.16=52
because the number sold dropped by 16% you will subtract 52 from 325
325-52=273
you can also calculate the answer by subtracting 100% by 16%
100%-16%=84%
now you can calculate 84% of 325
325x.84=273
8) If 15 balls cost Rs 225 then the cost of 8 balls is
Answer:
The cost of 8 balls is Rs $ 120.
Step-by-step explanation:
Given that 15 balls cost Rs $ 225, to determine the cost of 8 balls it is necessary to perform the following mathematical calculation:
(225/15) x 8 = X
15 x 8 = X
120 = X
Thus, the cost of 8 balls is Rs $ 120.
-1. A coffee shop spends $400 for an order of 20 cases of paper cups. How much is
one case of paper cups? Write and solve an equation.
Answer:
$20
Step-by-step explanation:
400/20=20