Answer:
slope of the tangent
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1)[/tex]
The slope of the tangent to the interval (-1 ,1)
m = 4.6 ,5, 5.4
Step-by-step explanation:
Step(i):-
Given function is f(x) = 0.2 x² + 5 x − 12
Slope of the tangent formula
[tex]m = \frac{d y}{d x}[/tex]
Let y = f(x) = 0.2 x² + 5 x − 12 ...(i)
Differentiating equation(i) with respective to 'x' , we get
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1) -0[/tex]
let x=-1
[tex]m = \frac{dy}{dx} = 0.2 (2 X -1) +5 = 4.6[/tex]
let x=0
m = 5
let x=1
[tex]m = \frac{dy}{dx} = 0.2 (2 X 1) +5 = 5.4[/tex]
conclusion:-
slope of the tangent
[tex]\frac{d y}{d x} = 0.2(2 x) + 5 (1)[/tex]
The slope of the tangent to the interval (-1 ,1)
m = 4.6 , 5, 5.4
The x-values at which the slope of the tangent line to the function f(x) belongs to the interval (-1, 1) are x ∈ (-15, -10).
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
To find the x-values at which the slope of the tangent line to the function f(x) = 0.2x² + 5x − 12 belongs to the interval (-1, 1), we need to find the x-values at which the derivative of the function f(x) has a value within that interval.
The derivative of f(x) is given by f'(x) = 0.4x + 5. Therefore, we can find the x-values at which f'(x) belongs to the interval (-1, 1) by solving the inequality 0.4x + 5 ∈ (-1, 1).
To solve this inequality, we can rewrite it as follows:
-1 < 0.4x + 5 < 1
-1 - 5 < 0.4x < 1 - 5
-6 < 0.4x < -4
Dividing both sides of the inequality by 0.4, we get:
-15 < x < -10
Therefore, the x-values for which the slope of the tangent line to the function f(x) lies x ∈ (-15, -10).
Learn more about the function here:
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Use the unit circle to find the value of sin 3π/2 and cos 3π/2
Answer:
sin=-1
cos=0
Step-by-step explanation:
The sin of an angle on the unit circle is y value of that point. You can see that the y value of it is at -1. The cosine of the angle is the x coordinate, which you can see is 0. Hope this helps!
methods to write an equation in standard form given two points on a line
Step-by-step explanation:
1. Read the sum
2. Think about what the sum is about.
3. What method could you use, for example, for division, you could use bus stop method. For multiplication The column metho.
Answer:
bus stop method, the column method.
Step-by-step explanation:
Which pattern below does not follow the same rule as the other three patterns?
A 2 , 4 ,8,16,32
B 5 , 10 , 20 , 40 , 80
C 15 , 25 , 35 , 45 , 55
D 25 , 50 , 100 , 200 ,
Answer:
C. 15, 25, 35, 45, 55
Step-by-step explanation:
In the other three, they multiply by two but on C., the just add ten
Answer:
C does not follow the same rules as the others
Step-by-step explanation:
As you can see pattern a, b, and d all follow a times2 rule. The only that does not is c. C follows a plus10 rule
Dalton has $40,000 in a savings account that earns 11% annually. How much money will he have in his savings account in 5 years?
Answer:
40,000+11%
40,000+ 4,400(5)
Step-by-step explanation:
62000 in 5 years
PLS HELP ASP HURRY BEST ANSWER GETS BRAINLESST AND FOLLOW
20. Is the is the combined mass of 2 red-footed macaws and three blue and gold macaws closer to 3 kilograms or 4 kilograms? explain
the graph helps!! pls answer asp
Answer:
Step-by-step explanation:
First find total the weight of all red footed macaws whic is 525(2)=1050
and then the blue and gold macaws 800(3)= 2400
So add them both together yu get 3450grams or 3.45kg
So it is closer to 3kg because the total weight is under 3.5kg so that means you round down to 3kg. If it was 3.5kg you would round up to 4kg but their combined weight is not more than 3.45kg
Choose the symbol that would make this problem correct a
Answer: I will answer your question, but first you need to show me the problem.
Step-by-step explanation:
a dosage is changed from 15 mg per day to 12 mh per day. what is a percentage decrease
Answer:
20%
Step-by-step explanation:
dosage change from 15 mg/d to 12 mg/d
change= 15-12= 3
change %= 3/15*100%= 20% decrease
HELP!!! WILL MARK BRAINLIEST!!!
The following graph describes function 1, and the equation below it describes function 2. Determine which function has
a greater maximum value, and provide the ordered pair.
Function 1
Function 2
f(x) = -x2 + 2x - 3
Function 1 has the larger maximum at (1,4).
Function 1 has the larger maximum at (4,1).
Function 2 has the larger maximum at (1, -2).
Function 2 has the larger maximum at (-2, 1).
Answer:
the answer is function 1 has the larger max. at (4,1)
Step-by-step explanation:
draw function 2 : the vertex is (1,-2)
the vertex of function 1 is (4,1)
The function 1 has a greater maximum value than function 2, and the ordered pair is (1,4).
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
f(x) = -x2 + 2x - 3
Now,
To find the maximum value of a function, we can use the vertex form of a quadratic equation, which is y=a(x−h)2+k
, where (h,k) is the vertex of the parabola. The maximum value of the function is the y-coordinate of the vertex.
For function 1, we can rewrite it as [tex]$$f(x) = -(x-1)^2 + 4$$[/tex]
by completing the square. This means that the vertex of function 1 is (1,4) and the maximum value is 4.
For function 2, we can rewrite it as
[tex]$$f(x) = -\frac{1}{4}(x+2)^2 - 2$$[/tex]
by completing the square. This means that the vertex of function 2 is (−2,−2) and the maximum value is -2.
Therefore, by the given function answer will be (1,4).
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If Maria is trying to find 42% of 350 which of the following calculations will give her the correct answer?
Answer:
42% * 320
Step-by-step explanation:
it's 147
Step-by-step explanation:
42/100 ×350/1=147
You want to make a picture frame for a photo. The photo is 8 inches by 10 inches. How many feet of wood do you need?
Answer:
80 inches
Step-by-step explanation:
Your pretty much finding the area so you would multiply 8 x 10
Answer:
80 inches
Step-by-step explanation:
8x10
The least common denominator of 1/3, 5/8, and 1/2 is:
Answer: 24
Step-by-step explanation:
You need to find the common denominator. In the case 24 is the least one because when you multiply 3 by 8, you finally have a common denominator for all three.
If you found this answer helpful, give it a five-star rating and a thanks! It would really mean a lot!
Melanie had two $10 bills one$5 bill,four dimes, and six pennies. Then she bought a fruit cup for $2.19
Answer:
$23.27
Step-by-step explanation:
yes
Writing expression in a+bi form. Picture included!
Answer:
[tex]-1 - \frac{\sqrt{3}}{2} i[/tex]
Step-by-step explanation:
[tex]\frac{-4 - \sqrt{-12}}{4}[/tex]
Distributing
[tex]\frac{-4}{4} - \frac{\sqrt{-12}}{4}[/tex]
[tex]-1 - \frac{\sqrt{12 \times -1}}{4}[/tex]
[tex]-1 - \frac{\sqrt{12} \times \sqrt{-1}}{4}[/tex]
[tex]-1 - \frac{\sqrt{12}}{4} i[/tex]
[tex]-1 - \frac{\sqrt{4 \times 3}}{4} i[/tex]
[tex]-1 - \frac{2 \sqrt{3}}{4} i[/tex]
[tex]-1 - \frac{\sqrt{3}}{2} i[/tex]
Hi pls can someone help me
Answer:
divide 10, - 10
+10, divide 10
Step-by-step explanation:
Answer:
350 → D → B → 25
350 → A → D → 36
Step-by-step explanation:
2nd question :
[tex]350 \div 10 = 35 \\ 35 - 10 = 25[/tex]
3rd question :
[tex]350 + 10 = 360 \\ 360 \div 10 = 36[/tex]
PLS HELP ASAP NEED FAST
Answer:
there is no mistake.
Step-by-step explanation:
the steps are all correct.
it cant be 'they should be divided' since that's not how it works.
it cant be 'tan 68 should be cos 68' since for cos we need [tex]\frac{adjacent}{hypotenuses}[/tex]
and since for tan it is [tex]\frac{opposite}{adjacent}[/tex] it cant be[tex]\frac{14}{x}[/tex]
Slove the equation y+3=-y+9 on edge
A)y=1
B)y=3
C)y=6
D)y=9
Answer:
y + 3 = -y + 9
-y -y
3 = -2y + 9
+2y +2y
2y + 3 = 9
-3 -3
2y = 6
y = 3
Alex is making a milkshake.She needs 1/3 cups of milk.She decided to add 1/4 more cups.How much milk is she putting into her milk shake?Be sure to show your equation
Answer:
7/12
Step-by-step explanation:
1/3 x4/4 = 4/12
1/4 x 3/3 = 3/12
4/12 + 3/12 = 7/12 = 5.83
If m∠1 ≅ 115°, find m∠8. answers : 205° 115° 65° 25°
Answer:
65°
Step-by-step explanation:
∠1=115°
∠2=65°
∠3=65°
∠4=115°
∠5=115°
∠6=65°
∠7=115°
∠8=65°
We get this because Line m and l are parallel. Also ∠1+∠2=180° so if ∠1 is 115°, then ∠2 is 180°-115° or 65°.
Solve the equation: √(y−1)^2 =15 Please help ASAP!! Thank you!!!
Answer:
Remove the radical by raising each side to the index of the radical.
y = 226
Step-by-step explanation:
please help ill mark you as brainlesit if correct!
Answer:
[tex]\frac{1}{8}[/tex]
Step-by-step explanation:
Think, how many different variations are there? The answer is 16: 4 times 4=16
how many of these variations could be the same? lets check:
7 and 7 1
2 and 2 2
2 options out of 16, so the answer is 2/16 which can be simplified to:
[tex]\frac{1}{8}[/tex]
I hope this helps u!
Please give brainliests(i had 40 now for no reason down to 2 :.( ) and a thx ;)
The maximum weight allowed per car on The Twister carnival ride is 263 pounds. Your friend weighs 86 pounds. To be able to ride in a car together, how much can you weigh? Write and solve the inequality.
Answer:
to find your weight limit you take 263 and subtract 86 from that and get 177
meaning youu can weigh only up to 177lbs.
Step-by-step explanation:
Which graph represents this inequality? Y ≥ 4x-3
Answer:
It is the second graph B
Step-by-step explanation:
the first graph has the line graphed correctly except that it has a dashed line instead of a solid line because the equation is greater than and equal to the line should be solid not dashed
The inequality of the graph is the shaded area left side of the line. Then the correct option is B.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given as,
y ≥ 4x – 3
The inequality of the graph is the shaded area left side of the line.
Then the correct option is B.
The diagram is given below.
More about the inequality link is given below.
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Which statement is true about the value of StartAbsoluteValue negative 14 EndAbsoluteValue? StartAbsoluteValue negative 14 EndAbsoluteValue = negative 14 StartAbsoluteValue negative 14 EndAbsoluteValue less-than 14 It is the distance between –14 and 0 on the number line. It is the distance between –14 and 14 on the number line.
Answer:
(C)It is the distance between –14 and 0 on the number line.
Step-by-step explanation:
The absolute value of a number returns a positive value no matter te number inside the absolute sign.
Therefore, the absolute value of -14 is 14.
That is: [tex]|-14|=14[/tex]
It is the distance between -14 and 0 on the number line.
The correct option is C.
Answer:
C
Step-by-step explanation:
Use the method of combining like terms to find the equivalent expression to 6u+2v+3u−7v−2.
Step-by-step explanation:
The like terms are 6u and 7u and also 2v and -7v so the answer is 9u - 5v - 2.
The length of a spring varies directly with the mass of an object that is aftached to it. When a 30-gram object is attached, the
spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
vx
3
S =
10
3
3
M =
S
10
m =
1
30
S
Answer:
s = [tex]\frac{3}{10}[/tex] m
Step-by-step explanation:
Given s varies directly with m then the equation relating them is
s = km ← k is the constant of variation
To find k use the condition s = 9 when m = 30 , thus
9 = 30k ( divide both sides by 30 )
k = [tex]\frac{9}{30}[/tex] = [tex]\frac{3}{10}[/tex]
s = [tex]\frac{3}{10}[/tex] m ← equation of variation
Please help in simplify these expressions
Which of the following trigonometric expressions represents an inverse function?
Answer:
the second one:
tan-1(xdegree)
Step-by-step explanation:
Simplifying fractions (picture provided)
Answer:
2 1/4
Step-by-step explanation:
- 5 1/4 - ( - 7 1/2)
Subtracting a negative is like adding
- 5 1/4 + 7 1/2
Get a common denominator of 4
-5 1/4 + 7 2/4
Subtract
7 2/4 - 5 1/4
2 1/4
The right answer is 2 1/4
Please see the attached picture for full solution
Hope it helps
\frac{(2+4)^{4} }{2}
Plz Answer
Answer:
648
Step-by-step explanation:
[tex]\frac{(2+4)^{4} }{2}[/tex]=
[tex]\frac{6^{4} }{2}[/tex]=
[tex]\frac{1296}{2}[/tex]=
648
The volume of a cuboid of length 8m and breadth 5m is 200 cubic meter. Find its height
Hey!!
Given,
Length(l)=8m
Breadth(b)=5m
Volume of a cuboid(V)=200 m^3
Height(h)=?
Now,
Volume of a cuboid=l*b*h
or,200=8*5*h
or,200=40h
or,h=200/40
h=5 meter
The height is 5 meter.
Hope it helps
Good luck on your assignment
Answer:
[tex]height = 5m[/tex]
Step-by-step explanation:
[tex]volume = l \times b \times h \\ 200 = 8 \times 5 \times h \\ 200 = 40h \\ \frac{200}{40} = \frac{40h}{40} \\ h = 5m[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
