Answer:
[tex]y=-11x-16[/tex]
Step-by-step explanation:
We want to find the equation of the tangent line to the function:
[tex]f(x)=4x^2+5x[/tex]
At the point (-2, 6).
First, we will need the slope of the tangent line. So, differentiate* the function:
[tex]f'(x)=8x+5[/tex]
Find the slope when x = -2:
[tex]f'(-2)=8(-2)+5=-11[/tex]
Now, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Our point is (-2, 6) and our slope is -11. Substitute:
[tex]y-(6)=-11(x-(-2))[/tex]
Simplify:
[tex]y-6=-11(x+2)[/tex]
Distribute:
[tex]y-6=-11x-22[/tex]
And add six to both sides. Therefore, our equation is:
[tex]y=-11x-16[/tex]
If you have not yet learned differentiation, here's the method using the difference quotient! The difference quotient is given by:
[tex]\displaystyle f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}[/tex]
Here, x = -2. Substitute:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{f(-2+h)-f(-2)}{h}[/tex]
Substitute (we are given the point (-2, 6). So, f(-2) = 6).
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{(4(-2+h)^2+5(-2+h))-(6)}{h}[/tex]
Expand and simplify:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{(4(4-4h+h^2)+(-10+5h))-(6)}{h}[/tex]
Distribute:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{16-16h+4h^2-10+5h-6}{h}[/tex]
Simplify:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{4h^2-11h}{h}[/tex]
Evaluate the limit (using direct substitution):
[tex]\displaystyle f'(-2) = \lim_{h\to 0}4h-11=4(0)-11=-11[/tex]
Which side lengths form a right triangle?
Answer:
[tex]\text{B. }1.5, 2, 2.5,\\\text{C. }4, 4, \sqrt{32}[/tex]
Step-by-step explanation:
All right triangles must follow the Pythagorean Theorem [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the hypotenuse of the triangle.
Verify:
[tex]1.5^2+2^2=2.5^2\checkmark,\\4^2+4^2=\sqrt{32}^2\checkmark[/tex]
I'm really lost . can somebody plz help
Answer:
7.5
Step-by-step explanation:
Median = middle number in terms of value
To make it easier to identify the middle number lets list the number from least to greatest
1, 4, 4, 7, 8, 8, 10, 15
Now we can simply find the middle number
We notice that there are two middle numbers as there is an even amount of numbers
Those two numbers being 7 and 8
When finding the median, if there are two middle numbers, you simply add the two numbers together and divide the sum by two to get the median.
So median = 8 + 7 = 15 / 2 = 7.5
Answer:
7.5
Step-by-step explanation:
The median of a set of numbers is the middle number, so we have to order them first from least to greatest. The order would be 1, 4, 4, 7, 8, 8, 10, 15. You can see that there are an even number of numbers, so if we take the two numbers in the middle of the order (7 and 8) and add them to get 15 and divide 15 by two, we get an answer of 7.5.
I hope this helped you!
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
the formula is C=2√πA
so simplifying that would give us c=2(4π)
simplify again and we get c=8π
i will mark brainest if you can tell me what x+l cubed it
Answer: XLCubed (XLCubed Ltd) is a business intelligence software and consulting services company. ... XLCubed software is used by business end users to create dynamic reports, dashboards, and planning solutions which are then deployed either via Microsoft Excel or the Web.
Step-by-step explanation:
For each part below use the figure to fill in the blank if necessary you may learn what the markings on a figure indicate PLZ HELP I WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
A toy factory can produce 135 toys in 5 hours. At this rate, how many hours will it take to produce 243 toys?
Answer:
9 hours
Step-by-step explanation:
you can find the unit rate by dividing 135 by 5 to get 27 toys per hour
243 ÷ 27 = 9
Which equation represents an inverse variation?
O y = 2x
Oy-
O yo
X
O y = -5x
Examine the diagram of circle O, where JW⎯⎯⎯⎯⎯⎯⎯⎯ and JV⎯⎯⎯⎯⎯⎯⎯ are tangent to circle O at points W and V, respectively. The diagram as described in the problem. © 2016 StrongMind. Created using GeoGebra. If JW=x8+4 and JV=x4+2, what is the length of JW?
a. 2
b. 6
c. 16
d. 10
Answer:
6
Step-by-step explanation:
Just got it right.
-8x+4=-26x+1
please help me out
Answer:
0
Step-by-step explanation:
I did it in standard form but this is the equation 18x + 3 = 0
Answer:
x = -1/6
Step-by-step explanation:
-8x+4=-26x+1
4-1 = -26x+8x
3 = -18x
3/-18 = x
x = -1/6
The area of cross section of the large piston in a hydraulic machine is 1m² and that of small piston is 0.5m².calculate the force that must be applied on the small piston to lift a load of 1000N on the large piston
Answer:
The force that must be applied on the small piston has a magnitude of 500 newtons.
Step-by-step explanation:
By Pascal's Principle, we know that pressure within any point of a closed hydraulic system is the same. Hence, the hydraulic machine can be described by the following model:
[tex]\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}[/tex] (1)
Where:
[tex]F_{1}, F_{2}[/tex] - Forces applied on the small and large pistons, in newtons.
[tex]A_{1}, A_{2}[/tex] - Areas of the small and large pistons, in square meters.
If we know that [tex]A_{1} = 0.5\,m^{2}[/tex], [tex]A_{2} = 1\,m^{2}[/tex] and [tex]F_{2} = 1000\,N[/tex], then the force to be applied on the small piston is:
[tex]F_{1} = \left(\frac{A_{1}}{A_{2}} \right)\cdot F_{2}[/tex]
[tex]F_{1} = \left(\frac{0.5\,m^{2}}{1\,m^{2}} \right)\cdot (1000\,N)[/tex]
[tex]F_{1} = 500\,N[/tex]
The force that must be applied on the small piston has a magnitude of 500 newtons.
A regular octagon has a perimeter of 30 centimeters. Find the length of each side.
Step-by-step explanation:
Perimeter=8l
30cm=8l
l=30/8=3.75cm
Answer and Step-by-step explanation:
An octagon has 8 sides in total. The perimeter of a shape is the sum of all sides added together.
To find the length of each side, we divide the perimeter by the amount of sides.
30 ÷ 8 = 3.75
The answer is 3.75 centimeters.
#teamtrees #PAW (Plant And Water)
a+b=2ab
b+c=3bc
cta=7ca
Answer:
a+b=2ab
b+c=2bc
c+a=2ca
j=the money used in south Africa is is called the rand . the estrange rate 7 rand for $1. Find how many dollars you would receive if you estrange 21 rand.
Answer:
$3
Step-by-step explanation:
21 rand /7
I. Write the answer with the proper label. ( 2 pts each)
Calculate the distance .
30 minutes at 120 km/h
2 ½ hours at 70 miles/h
B. Calculate the speed.
A car travels 500 km in 6 hours, find the average speed.
A man ran for 10 km in 1.25 hours, what was his average speed?
C. Calculate the time.
210 kilometers at 120 km/h
90 miles at 60 miles/h
II. Identify what is missing then solve. Do not forget to label your answer. (4 pts)
Every Friday after work, Mark travels from Bulacan to Santa Rosa to visit his family. The trip takes 4.2 hours at an average speed of 65 km/h. How many kilometers does he travel from Bulacan to Santa Rosa?
Katrina drove 325km in 5 hours while Martha drove a total of 210 km in 3 hours. Who drove faster? By how much?
with a solution
What is the area of this figure? Enter enter in the box ___units2
Answer:
Step-by-step explanation:
U still in school
Answer:
42 square units
Step-by-step explanation:
We can divide the figure in two triangles and one rectangle
the two triangles are congruent
base = |-5-2| = 7
height = 2
Total area of the two triangles = (7 *2)/2 * 2 = 14 square units
the rectangle have the length that is equal to the base of the triangles
height = |-2-2| = 4
Area = 7 *4 = 28 square units
Final area = 14+ 28 = 42 square units
15. What is the average low temperature forecasted
for the five days?
Monday: (Low F) 42 (High F) 55
Tuesday (Low F) 44 (High F) 57
Wednesday (Low F) 45 (High F) 60
Thursday (Low F) 34 (High F) 45
Friday (Low F) 40 (High F) 50
What is the length of Line segment A C?
3 ft
4 ft
18 ft
12 ft
On edge unity pls help
Answer:
4
Step-by-step explanation:
because its 4
The length of Line segment AC is 12ft.
Similar trianglesThe given triangle ABC is similar to triangle BMN
The length of AM = BM = 4ft
The length AB = BM + AM = 4 ft + 4ft = 8ft
The length of Line segment AC is calculated by using similar triangle proportions as follows;
[tex]\frac{AB}{BM} = \frac{AC}{MN} \\\\\frac{8}{4} = \frac{AC}{6} \\\\2 = \frac{AC}{6}\\\\AC = 2(6)\\\\AC = 12 \ ft[/tex]
Learn more about similar triangles here: https://brainly.com/question/11899908
A gas pump filled a 27 gallon tank in 6 minutes.How many minutes will it take to fill an 18 gallon tank?
Answer:
4 minutes
Step-by-step explanation:
27 gallon -> 6 min
1 min -> 27 ÷ 6
= 4.5 gallon
18 ÷ 4.5 = 4 min
please help me solve
please show how you got the answer
Answer:
Based on the linear relation shown above, when the y coordinate is 3, the x coordinate is 8.
Step-by-step explanation:
This is because every time you add an input of 2, you subtract an output of 4.
Basically in the x value you add 2 while in the why value you subtract 4.
(2, 13) (4, 9) (6, 5) (8, 1)
Answer:
8
Step-by-step explanation:
Can someone please explain to me how to find a scale factor ?
Answer:
XYUV=123=4
Step-by-step explanation:
The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure. Here, XYUV=123=4 . So, the scale factor is 4
Answer: albert ein is correct
Step-by-step explanation:
Suppose $p$ and $q$ are inversely proportional. If $p=28$ when $q=7$, find the value of $p$ when $q=49$.
Answer:$p$ =$4 when $q=49$.
Step-by-step explanation:
If $p$ and $q$ are inversely proportional, then mathematically, they are represented as
$p$ ∝ 1/$q$
So that introducing the constant of proportionality,k becomes
$p$ =k 1/$q$
$p$ =k /$q$
When $p=28$ when $q=7$,K becomes
$p$ =k /$q$
$28=K/ $7
k=$28 x $7 =$196
Now when $q=49$., $p$ becomes?
$p$ =k /$q$
$p$ =$196/49$
$p$ =$4
What is the sign of -x/-y when x > 0 and y > 0?
Answer:
pretty sure its positive
Step-by-step explanation:
hope this helps, have a great day!
Answer:
A is correct
Step-by-step explanation:
if we know that both x and y are positive, they are both going to be negative
and since we know that, -x divided by -y is the same as saying something negative divided by something negative which is ALWAYS positive because negatives cancel out leaving the answer positive something, something
Hi I need help can someone please help
Answer:
Angles 1 and 2 are 115 degrees. Angles 3 and 4 are 65 degrees.
Step-by-step explanation:
7x - 4 + 3x + 14 = 180 (angles 1 and 3 form a straight line so they add to 180 degrees)
10x + 10 = 180
10x = 170
x = 17
m<1 = 7(17) - 4 = 115
m<3 = 3(17) + 14 = 65
Opposite angles are equivalent so m<2 = 115 and m<4 = 65.
5(2x + 1) = 35 solve
Answer:
3
Step-by-step explanation:
5(2x + 1) = 35
10x + 5 = 35
10x = 30
x = 3
Help me with area, please.
Answer:
Num. 2: A = 25, Num. 3 = 63, Num. 4 = 80
Step-by-step explanation:
I'll help with as many as I can, so a few of them I won't be able too answer. You should re-post those later. Good luck, hope this helps.
For number 2:
First, turn the triangle into a rectangle by cutting it in half and attaching it to the other half so it forms a rectangle.
Since you cut the triangle in half, you also have to split 5 in half, so the bottom length is now 2.5.
Now, simply multiply 2.5 by 10, and you have the area for number 2.
The area for number 2 is 25.
For number 3:
This one is much easier. Just think of the shape as a normal square that has been tipped to the side. That means that you would solve for area the same way: 9 x 7, which means that the area for number 3 is 63.
For number 4:
This one is also easy. Simply cut, and paste. Now the right side is 10, and the top side is 8. Multiply, and the area will be 80 m.
Please re-post 1 and 5, as I am not able to solve them. Sorry this answer took so long!
The distance around a circular park is 176 yards. What is the area of the park? Use 22/7 for π.
Answer:
2464 yd²
Step-by-step explanation:
Use the circle circumference formula: 2πr
2·[tex]\frac{22}{7}[/tex]·r=176
[tex]\frac{44}{7}[/tex]r=176
r=176·[tex]\frac{7}{44}[/tex]
r=28
Area of circle formula: πr²
[tex]\frac{22}{7}[/tex]·r²
[tex]\frac{22}{7}[/tex]·28²
[tex]\frac{22}{7}[/tex]·784
=2464 yd²
Multiply -2x^5(4x^2)
Answer:
-8x^7
Step-by-step explanation:
Hint :
Formula :
[tex] a^ma^n=a^{m+n}[/tex]
Answer :
[tex] - 8 {x}^{7} [/tex]
Explanation :
[tex] - 2x^5(4x^2)[/tex]
[tex]−2 \times 4x^5x^2[/tex]
[tex]−2 \times 4( {x}^{2} x^5)[/tex]
[tex]−2 \times 4 {x}^{2 + 5} [/tex]
[tex]−2 \times 4x^7[/tex]
[tex] - 8 {x}^{7} [/tex]
Hope it is helpful...Jenna sells apples and pears. If 20 apples and 60 pears re sold every hour, there will be 80 pears when all the apples are sold. If 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold. How many pears are there at the stall?
Answer:
There are 1,360 pears.
Step-by-step explanation:
Suppose that there are P pears and A apples.
We know that:
"If 20 apples and 60 pears are sold every hour, there will be 80 pears when all the apples are sold."
Suppose that all of these are sold after N hours, then:
20*N = A
80*N = P - 80
We also know that:
"if 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold."
60*N = A
20*N = P - 400
Then we have four equations:
20*N = A
80*N = P - 80
60*N = A
20*N = P - 400
From the first one and the second one, we get:
20*N = A = 20*N = P - 400
A = P - 400
Now we have 3 equations:
80*N = P - 80
60*N = A
A = P - 400
Now we can just replace the third equation into the second one, then we get:
60*N = A = P - 400
Now we have two equations:
80*N = P - 80
60*N = P - 400
Now, remember that we want to find the number of pears, so we want to find the value of P.
To do it, we can take the quotient of the two equations, so we get:
(80*N)/(60*N) = (P - 80)/(P - 400)
8/6 = (P - 80)/(P - 400)
Now we can solve this for P
(8/6)*(P - 400) = P - 80
(8/6)*P - (8/6)*400 = P - 80
(8/6)*P - P = (8/6)*400 - 80
(2/6)*P = (8/6)*400 - 80
P = (6/2)*( (8/6)*400 - 80 )
P = 3*( (8/6)*400 - 80 ) = 1,360
There are 1,360 pears.
What is the answer to the expression -5x + 1 = 31
Answer:
x = -6
Step-by-step explanation:
-5x + 1 = 31
Subtract 1 from each side
-5x + 1-1 = 31-1
-5x = 30
Divide by -5
-5x/-5 = 20/-5
x = -6
Answer:
x = - 6
Step-by-step explanation:
- 5 x + 1 = 31
subtract 1 from 31
- 5 x = 31 - 1
- 5 x = 30
Divide 30 by - 5
x = 30 / - 5
x = - 6
what is the Quotient of 16.29÷100
Answer:
~0.16
Step-by-step explanation:
quotient, i believe, is just the answer to a division problem. divide normally and u get 0.1629
Answer:
Maybe the answer is 0.1629