The average rate of change of the function f(x) on the interval−6≤x≤2 is -0.5
This is further explained below.
What is the average rate?Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.
A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.
In conclusion, The average rate of change on x e(a, b)
[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]
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Simplify the expression: 4(5x-3)20x-128x17x8
Answer:
20x-12
Explanation:
Given the expression:
[tex]4\mleft(5x-3\mright)[/tex]To simplify, we first distribute.
[tex]=4(5x)-4(3)[/tex]Next, we open the bracket to obtain:
[tex]=20x-12[/tex]The correct choice is the first one.
Solve for x. (x-8a)/ 6 = 3a-2x
Given the equation:
[tex]\frac{x-8a}{6}=3a-2x[/tex]To solve for x, first we move the 6 to the other side of the equation:
[tex]\begin{gathered} \frac{x-8a}{6}=3a-2x \\ \Rightarrow x-8a=(3a-2x)\cdot6 \end{gathered}[/tex]Since the 6 was dividing, we pass it to the other side multiplying. Now we apply the distributive property and move the term -8a to the other side:
[tex]\begin{gathered} x-8a=(3a-2x)\cdot6 \\ \Rightarrow x-8a=18a-12x \\ \Rightarrow x=18a-12x+8a \\ \end{gathered}[/tex]Finally, we move the -12 to the other side with its sign changed:
[tex]\begin{gathered} x+12x=18a+8a=26a \\ \Rightarrow13x=26a \\ \Rightarrow x=\frac{26}{13}a=2a \\ x=2a \end{gathered}[/tex]therefore, x=2a
Find the Discriminant and describe the number and type of solutions of the equations. 1) 4x^2 + 8x + 4 =0
Given:
[tex]4x^2+8x+4=0[/tex]To find the discriminant, use the formula:
[tex]\Delta=b^2-4ac[/tex]Where a = 4, b = 8, c = 4
Thus, we have:
[tex]\begin{gathered} \Delta=8^2-4(4)(4) \\ \\ \Delta=64-64\text{ =0} \end{gathered}[/tex]The discriminant is = 0
To find the number of solutions, since the disriminant is zero, we have two real and identical roots.
ANSWER:
Discriminant = 0
Number of roots = 2 real and identical roots
thanks for the help!!!!!
The required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
We have been given that the trigonometric function
sin (A) = -60/61 and cos(B) = 9/41
So cos (A) = √1 - (-60/61)² = 11/61, and sin(B) = √1 - (9/41)² = 40/41
To compute the trigonometric functions sin(A + B) and sin(A - B)
⇒ sin(A + B) = sinA cosB + cos A sinB
⇒ sin(A + B) = (-60/61)(9/41) + (11/61)(40/41)
⇒ sin(A + B) = -540/2501 + 440/2501
⇒ sin(A + B) = -100/2501
⇒ sin(A - B) = sinA cosB - cos A sinB
⇒ sin(A - B) = (-60/61)(9/41) - (11/61)(40/41)
⇒ sin(A - B) = -540/2501 - 440/2501
⇒ sin(A - B) = -980/2501
Thus, the required values of given the trigonometric functions are sin(A + B) = -100/2501 and sin(A - B) = -980/2501.
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Write a recursive formula for an, the nthterm of the sequence 8, -2, -12, ....
We have the sequence: 8, -2, -12...
We can prove that this is an arithmetic sequence as there is a common difference d=-10 between consecutive terms.
Then, the recursive formula (the expression where the value of a term depends on the value of the previous term) can be written as:
[tex]a_n=a_{n-1}-10[/tex]Answer: the recursive formula is a1 = 8, a(n) = a(n-1) - 10
This table shows the amount of gas Sharla's car uses to travel different distances on a highway.Number of Gallons Number of Miles41446216324912432Based on the data in the table, how many miles per gallon does Sharla's car get on a highway?O A. 18 mpgO B. 28 mpgOC. 36 mpgO D. 72 mpg
We'll calculate the miles per gallon using the following formula and the data on the table:
[tex]\text{mpg}=\frac{miles\text{ traveled}}{\text{gallons used}}[/tex]From the first set of data:
[tex]\text{mpg}_1=\frac{144}{4}=36[/tex]From the second:
[tex]\text{mpg}_2=\text{ }\frac{216}{6}=36[/tex]From the third
[tex]\text{mpg}_3=\frac{324}{9}=36[/tex]and from the fourth
[tex]\text{mpg}_4=\frac{432}{12}=36[/tex]Since all the data on the table showed us that the car gets 36 miles per gallon, we can conclude that it indeed gets 36 miles per gallon.
Tow "N" Go Towing Company charges a flat fee of $75 plus an additional $5 for every mile the car is towed. Which function models the cost, T(), of towing a car for miles?
Answer:
5N + 75 I believe
please help this is for my study guide thanks! (simplify)
One way of simplifying the given expression is by using the following definition:
[tex]k^{-1}=\frac{1}{k}[/tex]So, for the given expression, we have:
[tex]-3k^{-1}=-3\cdot\frac{1}{k}=-\frac{3}{k}[/tex]Therefore, a possible answer is:
[tex]-\frac{3}{k}[/tex]5. Four hamsters have a combined weight of 5.112 grams. If all the hamsters weigh the same, how many kilograms does one hamster weigh? kilograms
We were told that Four hamsters have a combined weight of 5.112 grams. We know that
1000 grams = 1 kilogram
Thus,
5.112 grams = 5.112/1000
= 0.005112 kilograms
Since all the hamsters weigh the same, then the weight of one hamster is
0.005112 /4
= 0.001278 kilogram
The weight of one hamster is 0.001278 kilogram
On a coordinate plane, a parabola with a solid boundary line opens up. It goes through (negative 1, 0), has a vertex at (4, negative 125), and goes through (9, 0). Which inequality in standard form represents the shaded region? y greater-than-or-equal-to x squared + 8 x + 9 y greater-than-or-equal-to x squared minus 8 x minus 9 y greater-than-or-equal-to 5 x squared minus 40 x minus 45 y greater-than-or-equal-to 5 x squared + 40 x + 45
The inequality represented by the parabola is given as follows:
y ≥ 5x² - 40x -45.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:
y = a(x - h)² + k
In which the parameters are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.In the context of this problem, the vertex is given by:
(4, -125).
Hence:
y = a(x - 4)² - 125
When x = -1, y = 0, hence the leading coefficient is found as follows:
0 = 25a - 125
25a = 125
a = 125/25
a = 5.
Hence the equation is given as follows:
y = 5(x - 4)² - 125
y = 5(x² - 8x + 16) - 125
y = 5x² - 40x -45.
The inequality has a solid boundary line, hence it contains the equal sign, and the values above the parabola are plotted, hence it is given by:
y ≥ 5x² - 40x -45.
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A rectangle has vertices at (-2, 11), (-2,4), (6, 11), and (6, 4). Pablo says the area of the rectangle is 49 square units and his work is shown below. Steps Step 1 Pablo's Work Base: 1- 21+61= 8 Step 2 Step 3 Height: 11-4-7 Area: 8x7=49 square units Where, if at all, did Pablo first make a mistake finding the area of the rectangle? Step 1 Step 2 Step 3
The result of the calculation of the base is good because the distance between -2 and 6 is 8. The result of the calculation of the height is good because the distance between 4 and 11 is 7. The mistake is seen in the part of the multiplication, because 8x7 is equal to 56 , not 49.
So, the mistake was made when doing the Step 3.
After entering the table values in his calculator, Cory used the LinReg button to get the results shown. Identify the correlation coefficient and the type of correlation.
The value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
What is correlation?It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.
[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]
From the data given in the table,
The value of the correlation coefficient can be found using the formula:
r = -0.2984713607
After rounding off:
r = -0.2985
As the value of r is not near the -1 so the relation between x and y is weak negative:
Thus, the value of the correlation coefficient is -0.2985, and the relation between x and y is a weak negative option (B), and (D) are correct.
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help me please
thank you
Answer:
(-7, 3)
Step-by-step explanation:
what Since the endpoints of the interval are not included, use parentheses.
Tyler wants to crate a scale drawing of his bedroom. His bedroom is a rectangle with length 5m and width 4m. He decides on a scale of 1 to 80
The dimension of the rectangle after the scale will be 5 cm wide and 6.25 cm long.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
Tyler wants to sketch out his bedroom to scale. His bedroom is a rectangle that is 5 meters long and 4 meters wide. He chooses based on a scale of 1 to 80.
Then the dimension of the rectangle after the scale.
Width = (1/80) x 4
Width = 5 cm
Length = (1/80) x 5
Length = 6.25 cm
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Determine the smallest possible co-terminal
angle for a) 410. b)-45
The smallest possible co-terminal are:
a)50
b) -495
Define co terminal angles.Angles that share the terminal side with an angle occupying the standard position are said to be co terminal angles. In the conventional position, the vertex is at the origin and one side of the angle is fixed along the positive x-axis.
In other words, two angles are co terminal when their vertices and sides are the same but their angles themselves differ.
Additionally, you can recall the concept of co terminal angles as angles that differ by an exact number of full circles.
Given Data
The smallest co terminal angle for:
a) 410
Divide the first number by the second, rounding down (towards the floor).
[tex]\frac{360}{410}[/tex]
= 1
after that, multiply the divisor by the result (called the quotient),
360(1)
= 360
Take this amount out of your starting amount.
410-360
= 50
b) -45
- 45 [tex]\frac{pie}{4}[/tex]
= -495
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what is the answer to 8/8^12
Tim likes to play video games. If he cancomplete a level in of an hour, howmany levels can he complete in 4hours?
Given:
Number of levels he can complete in 1 hour = 1 level
To find the number of levels he can complete in 4 hours, we have:
4 * 1 = 4
What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
The diameter d is 35 ft.
Therefore, the radius r is given by:
[tex]r=\frac{35}{2}=17.5\text{ ft}[/tex]Therefore, the area of the slice is given by:
[tex]\frac{37^{\circ}}{360^{\circ}}\times\pi\times17.5^2\approx98.88[/tex]Therefore, the required area is approximately 98.88 ft².
Therefore, the closest correct answer is choice 98.83 ft².
help me please
thank you
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: A, [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
hi Ms or Mr i need help with this problem would mind helping me out step by step? because i don't understand this
Looking at the given diagram,
HI + JI = JH
Given the HI = 3x - 5
JI = x - 1
HJ = 7x - 27
Therefore,
3x - 5 + x - 1 = 7x - 27
3x + x - 7x = - 27 + 5 + 1
- 3x = - 21
Diving bith sides - 3, it becomes
- 3x/3 = - 21/- 3
The negative signs nullify each other
x = 7
What is the graph of the equation y = 2x + 4?
The y-intercept is which means the line crosses the y-axis at the
). Plot this point.
point
The slope of the line is positive, so it goes
Start at the y-intercept. Move up
0
0 and then move right
). Plot this point.
You are now at the point (
0
Draw a line to connect the two points.
from left to right.
Answer: 8
Step-by-step explanation: x2 + 4 is 4 x 2
:D
2. Write an equation of the ellipse with foci at (0, +2) and co-vertices at （+1, 0）.དུ དུའི - 1།14︽ 》སོ – །
Given,
The foci of the ellipse is (0, +2)(0.-2)
The co vertices of the ellipse is (1, 0)(-1, 0)
The genral equation of ellipse is,
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]The equation of the foci is,
[tex]\begin{gathered} (0,\text{ }\pm c)=(0,\text{ }\pm2) \\ \text{The value of c is 2.} \end{gathered}[/tex]The equation of co vertices is,
[tex]\begin{gathered} (\pm a,\text{ 0)=(}\pm1,\text{ 0)} \\ \text{The value of a is 1.} \end{gathered}[/tex]we know that,
[tex]\begin{gathered} b^2=a^2+c^2 \\ b=\sqrt[]{5} \end{gathered}[/tex]Substituting the value then,
[tex]\begin{gathered} \frac{x^2}{1^2}+\frac{y^2}{\sqrt[]{5}^2}=1 \\ x^2+\frac{y^2}{5}=1 \end{gathered}[/tex]Hence, option d is correct.
I'll send a better pic I just need help doing the work and understanding what it's about
The formula to calculate the rate of change is given to be:
[tex]r=\frac{y_2-y_1}{x_2-x_1}[/tex]In the question, time will be the x-variable while distance will be the y-variable.
QUESTION A: Between 0 and 1.
Between 0 and 1, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=0 \\ x_2=1 \\ y_1=6 \\ y_2=4 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{4-6}{1-0}=\frac{-2}{1} \\ r=-2 \end{gathered}[/tex]The rate is -2.
QUESTION B: Between 1 and 3.
Between 1 and 3, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=1 \\ x_2=3 \\ y_1=4 \\ y_2=2 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{2-4}{3-1}=\frac{-2}{2} \\ r=-1 \end{gathered}[/tex]The rate is -1.
QUESTION C: Between 3 and 6.
Between 3 and 6, we will use the following parameters to calculate the rate:
[tex]\begin{gathered} x_1=3 \\ x_2=6 \\ y_1=2 \\ y_2=3 \end{gathered}[/tex]Therefore, the rate is:
[tex]\begin{gathered} r=\frac{3-2}{6-3} \\ r=\frac{1}{3} \end{gathered}[/tex]The rate is 1/3.
A rectangle's base is 2 in shorter than five times its height. The rectangle's area is 115 in². Find this rectangle's dimensions.
The rectangle's height is
The rectangle's base is
Answer:
The rectangle's height is 5 in,The rectangle's base is 23 in.Step-by-step explanation:
Let the dimensions are b and h.
The area of rectangle is the product of two dimensions.
We have:
b = 5h - 2,bh = 115 in².Solve the equation by substitution:
h(5h - 2) = 1155h² - 2h = 1155h² - 2h - 115 = 05h² - 25h + 23h - 115 = 05h(h - 5) + 23(h - 5) = 0(h - 5)(5h + 23) = 0h - 5 = 0 and 5h + 23 = 0h = 5 and h = - 23/5The second root is discarded as negative.
The height is 5 in,The base is: 5*5 - 2 = 23 inAnswer:
Height = 5 in
Base = 23 in
Step-by-step explanation:
[tex]\boxed{\textsf{Area of a rectangle} = \sf Base \times Height}[/tex]
Let x be the height of the rectangle.
Given values:
Height = x inBase = (5x - 2) inArea = 115 in²Substitute the values into the formula for area and solve for x:
[tex]\begin{aligned}\sf Area & = \sf Base \times Height\\\\115&=x(5x-2)\\115&=5x^2-2x\\5x^2-2x-115&=0\\5x^2-25x+23x-115&=0\\5x(x-5)+23(x-5)&=0\\(5x+23)(x-5)&=0\\\\\implies 5x+23&=0 \implies x=-\dfrac{23}{5}\\\implies x-5&=0 \implies x=5\end{aligned}[/tex]
As length is positive, x = 5.
To find the rectangle's dimensions, substitute the found value of x into the expressions for the height and base:
[tex]\implies \sf Height=5\;in[/tex]
[tex]\begin{aligned}\implies \sf Base&=\sf 5(5)-2\\&=\sf 25-2\\&=\sf 23\;in\end{aligned}[/tex]
Solve the triangle: a = 12,c = 2-2, B = 33". If it is not possible, say so.A= 25.1",b = 1.8, C = 121.9"This triangle is not solvable.A = 45*,b= V2.C = 102VEA= 30', b = -, C = 117"
ANSWER:
A=25.1 degrees
b = 1.8
C = 121.9 degrees
SOLUTION:
We can solve this problem using the cosine law, since we are given the length of 2 sides of triangle and the angle they formed.
[tex]b\text{ =}\sqrt[]{c^2+a^2-2ac\cos B}[/tex]We substitute the given
[tex]\begin{gathered} b\text{ =}\sqrt[]{(2\sqrt[]{2})^2+(\sqrt[]{2})^2-2(\sqrt[]{2})(2\sqrt[]{2})\cos 33} \\ b\text{ = 1.8} \end{gathered}[/tex]Using Sine Law, we can get the angles
[tex]\begin{gathered} \frac{1.8}{\sin 33}=\frac{\sqrt[]{2}}{\sin A} \\ A=25.1 \end{gathered}[/tex]Since the total angle inside a triangle is 180, the angle at C is
[tex]C-33-25.1=121.9[/tex]Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this weight in grams?
Ok, so
First of all, we got that the wound was measured to be 0.8cm.
This measurement equals to:
[tex]0.8\operatorname{cm}\cdot\frac{10\operatorname{mm}}{1\operatorname{cm}}[/tex]0.8cm is equal to 8 millimeters.
Now, the greatest possible error in a measurement is one half of the precision (smallest measured unit).
8 mm was measured to the nearest 1 mm, so the measuring unit is 1 mm.
So, one half of the precision (1mm) is 0.5
Therefore, the greatest possible error is 0.5 mm
Judy has 15 books in her library. She bought several books at a thrift storeon Saturday. She now has 84 books in her library. How many books did shebuy at the thrift store? Write an equation to solve the problem use b forthe variable.
Let b the number of books Judy has bought.
The given data can be expressed as,
[tex]15+b=84[/tex]Answer:
69 books
15+ b= 84
Step-by-step explanation:
In the answer section, give the question letter and the word TRUE or FALSE for each of the following:
a) We rewrite the right side of the expression as:
[tex](-2)^4=((-1)\cdot2)^4=(-1)^4\cdot2^4=1\cdot2^4=2^4\ne-2^4.[/tex]So we see that the expression of point a is FALSE.
b) We consider the expression:
[tex]b^x.[/tex]We take the logarithm in base b, we get:
[tex]\log_b(b^x)=x\cdot\log_b(b)=x\cdot1=x.[/tex]We see that the logarithm of a number x to a base b is just the exponent you put onto b to make the result equal x. We conclude that this expression is TRUE.
c) We know that in any base a, we have:
[tex]\log_a(0)\rightarrow-\infty.[/tex]We conclude that the expression of this item is FALSE.
d) Logarithms are defined only for numbers greater than 0. So we conclude that this expression is FALSE.
e) We consider the expression:
[tex]\log_b(b^{10})-\log_b(1)=10.[/tex]Applying the properties of logarithms, we get:
[tex]\begin{gathered} 10\cdot\log_bb-0=10, \\ 10\cdot1=10, \\ 10=10\text{ \checkmark} \end{gathered}[/tex]We see that this expression is TRUE.
Answera) FALSE
b) TRUE
c) FALSE
d) FALSE
e) TRUE
May I please get help with this place. I have tried multiple times but still could not get the correct
(a) Which figures are parallelograms.
A parallelogram is a quadrilateral whose opposite sides are parallel, and therefore opposite angles are equal.
Figure B, and C are parallelogram since all of the opposite angles are equal.
Figure A is also a parallelogram since the all of the opposite sides are congruent.
FIGURE A,B, and C are parallelograms.
(b) Which figures are rectangles.
A rectangle is a parallelogram where all of the angles are 90°. A square is also a type of rectangle where all the sides are congruent.
FIGURE B and C are rectangles.
(c) Which figures are squares.
As mentioned earlier, as square is a rectangle where all the interior angles is 90°, and has all of the sides congruent.
FIGURE C is a square.
Find if -3w - 6(u + 2v) if u = -3j, v = i + 2], and w =combination of unit vectors.-;. Express your answer as a linear
we have the expressiob
-3w - 6(u + 2v)
where
u=-3j
v=i+2j
w=-(1/3)i-(7/3)j
substitute the given values in the expression
so
-3(-(1/3)i-(7/3)j)-6(-3j+2(i+2j))
(i+7j)-6(-3j+2i+4j)
(i+7j)-6(2i+j)
(i+7j)-12i-6j
answer is
-11i+j