The expression of (√t)² is t.
What are square and square roots?A number can be squared, but it can also be divided into its square root. The value we get from multiplying a number by itself yields its square value, whereas the value we get from finding a number that, when squared, yields the original value of the number yields its square root value. In the event that 'a' is the square root of 'b,' then a a = b. Any number has two square roots, one with a positive value and the other with a negative value, because any number's square is always a positive number. As an illustration, the square root of 4 has the values 2 and -2. A number's power 1/2 value is represented by a number's square root. In other words.
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Find the derivatives of the following using increment method.1.y = 6x² +10x - 3
Given
[tex]y=6x²+10x-3[/tex]Find
derivatives using increment method.
Explanation
Given
[tex]y=6x²+10x-3[/tex]replace x and y by
[tex]\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}[/tex]so ,
[tex]\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}[/tex]now divide by
[tex]\Delta x[/tex]so ,
[tex]\begin{gathered} y^{\prime}=\frac{12\Delta x^2+10\Delta x+6\Delta^2x^2}{\Delta x} \\ \\ y^{\prime}=12x+10+6\Delta x \end{gathered}[/tex]now taking limit
[tex]\begin{gathered} \lim_{\Delta x\to0}y^{\prime}=\lim_{\Delta x\to0}(12x+10+6\Delta x) \\ \\ y^{\prime}=12x+10 \end{gathered}[/tex]Final Answer
Therefore , the derivative of the function using increment method is 12x + 10
Divide. Enter the correct answer.
17+2=
WILL MARK BRAINLIEST FOR THE BEST AND MOST ANSWERED OUT REPLY
1. A recent election poll claims that Candidate A is projected to win the election with 53% of the vote. If a sample of 2436 voters is polled, determine if Candidate A can be guaranteed a win with 95% confidence.
Select an answer
a. yes
b. no
c. Not enough information
Explain why or why not using two sentences.
Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).
So, candidate A has a projection of winning 53% votes.
A sample of 2436 voters is pulled, then:
2436/100 × 53 = 1,291 votesCan candidate A be guaranteed 95% votes which are:
2436/100 × 95 = 2,314 votesDifference: 2,314 - 1,291 = 1,023
Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).
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Need help solving this problemNote for part A I got 4/22 and it was incorrect
First, we need to find the total frequency. This is given by adding all the given frequencies. That is,
[tex]\begin{gathered} f_{\text{total}}=4+6+7+5 \\ f_{\text{total}}=22 \end{gathered}[/tex]and the relative frequency is the division of the frequency of the corresponding interval by the total frequency,
[tex]f_{\text{rel}}=\frac{f_{\text{ interval}}}{f_{total}}[/tex]Therefore, the answers are:
a) 4/22 but written in simple form:
[tex]\frac{2}{11}[/tex]b)
[tex]\frac{5}{22}[/tex]Find MN such that LN = 5.7.
Line LN is compounded by segments LM and MN. The lenght of segment LM is fixed (1.3), and we need to find how long should segment MN be so the whole segment LN has a length of 5.7.
The length of segment LN is the sum of lengths of segments LM and MN. Writing it as an equation:
[tex]LN=LM+MN[/tex]We an replace the values we know in the equation:
[tex]5.7=1.3+MN[/tex]Now, we just need to solve for MN:
[tex]\begin{gathered} MN=5.7-1.3 \\ \\ MN=4.4 \end{gathered}[/tex]Segment MN should have a length of 4.4 for the segment LN to be 5.7. Correct answer is option D.
fine the value of x. please help
Answer:
141 degrees
Step-by-step explanation:
The total angle interior of a triangle is 180 degrees. And the 2 angles opposite of x equal it so x=103+38
what is the equation of the line perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1)
The linear equation perpendicular to y = 1/2x+1 that contains the point ( - 2 ,1) is:
y = -2x - 3
How to get the equation of the perpendicular line?Let's say that:
y = m*x + b
Where m is the slope and b is the y-intercept.
Is the line we want to find.
Two lines are perpendicular if the product between the slopes is -1, so this line is perpendicular to:
y = (1/2)*x + 1
Only if:
m*(1/2) = -1
m = -1*2 = -2
So the linear equation is of the form:
y = -2*x + b
If this line passes through (-2, 1), then:
1 = -2*(-2) + b
1 = 4 + b
1 - 4 = b
-3 =b
The linear equation is y = -2x - 3
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suppose that you need to build as many chairs as possible. each chair requires one seat, one back, and four legs. if you have 12 seats, 15 backs, and 44 legs, which of the chair components limits the number of chairs you can make? legs seats backs how many chairs can you make with the 12 seats, 15 backs, and 44 legs? what chair components will be leftover after making as many chairs as possible? seats and backs legs and backs seats and legs
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
What is meant by probability?The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.
The maximum number of chairs that can be made will be the minimum of the number of parts divided by the number of parts required for each chair, as calculated across the various types of parts required.
seats: 12 available, used 1 per chair: 12/1 = 12 chairs possible
backs: 15 available, used 1 per chair: 15/1 = 15 chairs possible
legs: 44 available, used 4 per chair: 44/4 = 11 chairs possible
The maximum number of chairs that can be made will be the minimum of 12, 15, and 11. That exists, 11 chairs can be made, limited by the number of available legs.
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PLEASE HELP ME. SERIOUSLY. I HAVE 30 MINUTES LEFT.
Let D be the dilation with center O and scale factor r>0 so that Dilation (P) = P' and
Dilation (Q) = Q'.
233.8
If |OQ|= 10 units, 10Q'] = 15 units, and IP'Q'] = 11.2 units, determine |PQ|. Round your
answer to the tenths place, if necessary.
incase you cant see, he right side is P, and below it is P1
Dilation factor is 3/2.
Define dilation factor.Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.
Given,
OQ = 10
OQ' = 15
Let dilation factor be r
OQ ×r = OQ'
10× r = 15
r = 3/2
Dilation factor is 3/2.
Coordinates of P = (-4, -3)
Coordinates of P' = (-6, -4.5)
b) ΔOPQ ≅ ΔOP'Q'
Congruent,
[tex]\frac{OQ}{OQ'}[/tex] = [tex]\frac{PQ}{P'Q'}[/tex]
[tex]\frac{10}{15}[/tex] = [tex]\frac{PQ}{11.2}[/tex]
PQ = 7.46
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Rectangles DEFG with vertices D(1,0) E(7,2) F(8, -1) and G (2, -3)
A. Translations along the the rule (x, y) —> (x -8 y -3)
Part A
[tex]D(1,0) \longrightarrow D'(1-8, 0-3)=D'(-7, -3)\\\\E(7,2) \longrightarrow E'(7-8, 2-3)=E'(-1, -1)\\\\F(8,-1) \longrightarrow F'(8-8, -1-3)=F'(0, -4)\\\\G(2,-3) \longrightarrow G'(2-8, -3-3)=G'(-6, -6)[/tex]
Part B
Reflecting over the x axis means [tex](x, y) \longrightarrow (x, -y)[/tex].
[tex]D'(-7, -3) \longrightarrow D''(-7, 3)\\\\E'(-1, -1) \longrightarrow E''(-1, 1)\\\\F'(0, -4) \longrightarrow F''(0, 4)\\\\G'(-6, -6) \longrightarrow G''(-6, 6)[/tex]
find the value of x in each case
Answer:
x=23
Step-by-step explanation:
The amount of degrees in a triangle is 180 degrees.
line AC and line DF are straight angles meaning that the opposite angles are equal to each other. That means that angle FBC is also equal to x. Because line AC and EF are parallel we know that FBC and BFE are equal. Therefore, BFE is equal to x. The sum of the values of each angle of the triangle should add up to 180. 5x+65=180
5x=115
x=23
Using the drawing tools to form the correct answer on the provided graph
Horizontal line with the given function: y = 4
Explanation:
Since the midline of a sine function is the horizontal centerline about which the functions oscilliart above and below, the corresponding line here is y = 4 with x = 0.
NB:
The midline is parrallel to y = 0 ~ the x-axis.
what are the coordinates of a’?
A tennis racket sells for $54.At the spring clearanceevent, the price is 30% lessthan the original. What isthe sale price?
We have
tennis racket price $54
Firs we need to obtain the 30 %
54*.30=16.2
then in order to know the sale price we need to substract the 30% of the original price
54-16.2=37.8
the sale price is $37.8
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)
we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is
[tex]\begin{gathered} m=\frac{-3-0}{0-(-3)} \\ m=\frac{-3}{3} \\ m=-1 \end{gathered}[/tex]where we used the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, our searched line has the form:
[tex]y=-x+b[/tex]where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:
[tex]\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}[/tex]then, the searched line in slope-intercept form is
[tex]y=-x-3[/tex]Therfore, the given area can be modeled as
[tex]y>-x-3[/tex]because when a line is dashed it doesn't belong to the given area.
If f(x) = 12x and g(x) = -4x-12, find (f ·g)(x).
A.) -48x^2 - 12x
B.) -48x^2 - 144x
C.) -4x^2 - 144x
D.) -192x^2
Answer:
[tex]-48x^2 - 144x[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =12x(-4x-12) \\ \\ =-48x^2-144x[/tex]
2x + y = 2
Step 2 of 2: Determine the missing coordinate in the ordered pair (?, -3) so that it will satisfy the given equation.
Answer:
2.5
Step-by-step explanation:
Plug is -3 for y and solve for x
2x -3 = 2 Add 3 to both sides
2x = 5 Divide both sides by 2
x = [tex]\frac{5}{2}[/tex] o r 2[tex]\frac{1}2}[/tex] or 2.5
100 brainly!! Which of the following values are in the range of the function graphed below? Check all that apply.
Answer:
B
Step-by-step explanation:
In the community of Greendale, a local restaurant donates 15% of the total sales to student-based clubs on certain funding nights.
A- Write an equation to represent the relationship between the dinner sales (d) and the amount (a) the organization will receive.
B- What is the constant of proportionality? Interpret the constant proportionally for the problem situation.
C- How much will the organization receive if dinner sales are $3600?
NEED BY 2:35 CENTRAL TIME!!! OFFERING 35 POINTS! MIDDLE SCHOOL MATH!
The equation that represents the relationship between dinner sales and the amount the organisation would receive is a = 0.15d
The constant of proportionality is 0.15.
Th amount the organisation will receive if dinner sales is $3600 is $540
What is the relationship between dinner sales and the amount the organisation would receive?The equation that would be used to represent the relationship between dinner sales and the amount the organisation would receive is a linear equation.
A linear equation is an equation that has one variable that is raised to the power of one. A linear equation can either be either be a positive function or a negative equation. When a linear equation is drawn on a graph, the graph is a straight line.
The form of the linear equation would be:
total amount received by the organisation = percentage x amount the restaurant receives.
a = 0.15d
0.15 is the constant of proportionality. It is the value that relates the amount the organisation would receive and the amount the restaurant would receive.
a = 0.15 x 3600
a = $540
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Determine the rate at which the sloth travels.
Justify your answer.
Distance (ft)
987654MN-
6.
3-
2
1
0
Speed of a Sloth
1 2
3 4
Time (min)
The rate at which the sloth travels as required in the task content is; -22ft/min.
Speed as a rate of distance with respect to time.It follows from the task content that the rate at which the sloth travels is to be determined.
Since the correct representation of the data is such that the distance and corresponding time pairs are as follows;
(98, 1) , (76, 2) , (54, 3), (32, 4).
Hence, the rate of distance change per time is the speed of the sloth and hence, the rate of distance change is;
Rate = ∆Distance/∆time.
Rate, R = (98 - 76)/(1 - 2)
Rate, R = 22/-1
R = -22 ft/min.
Ultimately, the rate at which the sloth travels is therefore; -22 ft/min.
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Orlando is getting balloons for his grandmother's birthday party. he wants each balloon string to be 6 feet long. at the party store, string is sold by the yard. if orlando wants to get 72 balloons, how many yards of string will he need?
144 yards of string will need to use balloons for the party.
Given,
The length of balloon string Orlando wanted = 6 feet
Number of balloons = 72
We have to find the total length of strings wanted for 72 balloons in yards.
1 yard = 3 feet
Now,
Total length of strings Orlando needs = length of one string x number of balloons = 6 x 72 = 432 feet
Now convert 432 feet into yard
That is,
432 / 3 = 144 yards
So,
144 yards of string will need to use balloons for the party.
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Graph, on a separate piece of paper, the equation of a line with a slope of −3 and a y-intercept of 2.
Select the points that appear on the graph.
Multiple select question.
cross out
A)
(0, 0)
cross out
B)
(0, 2)
cross out
C)
(1, 1)
cross out
D)
(1, −1)
cross out
E)
(2, 0)
Based on the slope of the line and the y-intercept, when graphed, the points that will appear on the graph will be:
B. (0, 2) D. (1, -1)How to graph the line?The equation of a line takes the form:
y = mx + b
m = slope
b = y - intercept
This line would therefore take the equation form:
y = - 3x + 2
When graphed, the graph would be as attached.
As shown by the graph, the points that will appear include:
(0 , 2) (1 , - 1)
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What are the coordinates of the midpoint of segment whose endpoints are A(-2,7) and B(4,-2)?
PLEASE HELP!!!!!
Which of the following equations represents the line that passes through the point (4, 3) and has a slope of 1/2?
A) 2x-3y=-18
B)2x-3y=17
C)3x-2y=-17
D)3x-2y-18
The equation of a line that passes through the point (4, 3) and has a slope of 1 / 2 is y = 1 / 2 x + 1.
How to find the equation of a line?The equation of a line that passes through a point can be describe as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line passes through (4, 3) and the slope is 1 / 2.
Hence, let's find the y-intercept using (4, 3)
y = 1 / 2 x + b
3 = 1 / 2 (4) + b
3 = 2 + b
b = 3 - 2
b = 1
Therefore, the equation of the line is y = 1 / 2 x + 1.
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Paula measured the auditorium and made a scale drawing. The stage, which is 56 feet long in real life, is 84 inches long in the drawing. What scale did Paula use?
3 inches= ? feet
There are 2 feet in real life be 3 inches long in the scale drawing.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The stage, which is 56 feet long in real life, is 84 inches long in the scale drawing.
Let the x feet in real life be 3 inches long in the drawing.
According to the given question, we can write a ratio as
56 feet : 84 inches = x feet : 3 inches
⇒ 56 / 84 = x / 3
Apply the cross-multiplication operation,
⇒ 56 × 3 = x × 84
⇒ 168 = 84x
⇒ 84x = 168
⇒ x = 168 / 84
⇒ x = 2
Therefore, there are 2 feet in real life be 3 inches long in the scale drawing.
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can you help show me the steps to solve this?
Answer:69
Step-by-step explanation8966966969996^996969969969699696996996969699696969699696699696966969669669669669669669669669
PLS HELP ASAP
!!!!!!
the d score is a standardized measure of the degree to which the independent variable caused a change in the dependent variable. this is also known as the
The standardized measure of the degree to which the independent variable caused a change in the dependent variable is a standard change.
What is a dependent variable?A dependent variable is what is determined in an experiment or test and is the one that is influenced throughout the experiment. The dependent variable is affected by the independent variable.
In mathematical modeling, statistical modeling, and experimental sciences, dependent and independent variables are variables. Dependent variables are so named because their values are explored in an experiment under the assumption or requirement that they are dependent, by some law or rule, on the values of other variables.
In conclusion, the standard change illustrates the change.
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Here is a sketch of the unique triangles that can be
made with angle measures 80° and 20° and side
length 5.
PLEASE HELPPPP
ASAAAAPPPPP DUE AT END OF TODAY
Option (B) describes the correct unique possibilities of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same. Triangles can be divided into three types based on the lengths of their sides, and these are Scalene, Isosceles, and Equilateral.So, according to the given image:
We can easily observe that the triangle is an isosceles triangle with base angles being equal and the third angle being the smallest.Then, the correct option about the triangle will be an option (B).Therefore, option (B) describes the correct unique possibilities of the given triangle.
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Simplify 6 + 2(5 – 8)2 + 7
The answer is very simple. .
6 + 2 (5 - 8 ) ² + 7
Firstly we solve what is inside the parenthesis
[tex]6\text{ + 2}\cdot(-3)^2\text{ + 7}[/tex][tex]6\text{ + 2 (9) +7}[/tex]Then we solve the multiplications
[tex]6\text{ + 18 + 7 }[/tex]Finally we solve the sums.
[tex]\text{ 6 +18 + 7 = }31[/tex]That is the solution.