Kate is constructing an equilateral triangle. She has already used her straightedge to construct the line segment shown.
A line segment with endpoints labeled as A and B.
What should Kate do for her next step?
Use the straightedge to draw a line that passes through point A.
Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass.
Use the straightedge to draw another line segment that does not intersect AB¯¯¯¯¯.
Place the point of the compass on point A and draw an arc, using a width for the opening of the compass that is less than 12AB.
The next step that Kate should take in construction of an equilateral triangle after using a straight edge to construct the given line segment is;
Option B; Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass.
This is about steps involved in constructing an equilateral triangle which means 3 equal sides.
First step; This first step entails drawing a line with the given measurement of the side of the equilateral triangle and label it ABSecond step; This step entails placing the point of the compass at point A and opening the leg to touch point B which means length AB will be the width to be used to draw an arc.Step 3; The same process in step 2 is carried out but this time the point of the compass will be placed at point B and opening the second leg to touch point A which means length AB will be the width to be used to draw an arc to intersect the other one drawn.Step 4; The point of intersection is now joined by a straight line to points A & B respectively.Thus, option B is the correct next step.
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The table below shows the average yearly balance in a savings account where interest is compounded annually. no money is deposited or withdrawn after the initial amount is deposited. which type of function best models the given data?
a. linear function with a negative rate of change
b. linear function with a positive rate of change
c. exponential decay function
d. exponential growth function
The given data represents the average yearly balance in a savings account where interest is compounded annually. The function that best models the data is an exponential growth function.
Explanation:The given data represents the average yearly balance in a savings account where interest is compounded annually. Since the balance is increasing over time, the function that best models the data is an exponential growth function. Option d, exponential growth function, is the correct answer.
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write "all horses drink water" as a conditional statement
A rectangular garden measures 38m by 20m, to the nearest metre. Calculate the maximum possible area of the garden.
What is the measure of each interior angle of a regular 10 sided polygon?
help me solve this???
3p - 1 = 5(p - 1) - 2(7 - 2p)
Write the equation of the line perpendicular to the given line and passing through the given point: y=3x−2 through (3,4)
Answer:
all work is shown and pictured
Answer:
y= -1/3x+5
Step-by-step explanation:
PleAse help and show how you got it if you don’t mind
Find the value of x and y
x+4y=21, 4x-16=y
Can someone check this for me? Thanks.
(b) Suppose it is also known that AD ≅ CD. Which postulate or theorem can be used to prove that ΔABD ≅ ΔCBD?
I'm guessing it's the SAS congruence postulate but I'm not very good at this so I'm not sure.
Which shows the reflection of the figure over the line
Answer:
The answer appears to be A
Step-by-step explanation:If you redrew the answer backwards, the reflection would match the first one
Answer:
Step-by-step explanation:
Which ordered pairs in the form (x, y)(x, y) are solutions to the equation
7x−5y=287x−5y=28 ?
Select each correct answer.
(4, 10)(4, 10)
(−1, −7)(−1, −7)
(7, 9)(7, 9)
(−6, −14)
What does the triangle exterior angle theorem make sense based on the triangle sum theorem??
Find all real and imaginary zeros for a polynomial function
A polynomial function is an algebraic expression with one or more terms. The real zeros can be found by setting the function equal to zero and solving for x. The imaginary zeros can be found using the complex conjugate theorem.
Explanation:A polynomial function is an algebraic expression that consists of one or more terms. The real zeros of a polynomial function are the values of x that make the function equal to zero. To find the real zeros, set the polynomial function equal to zero and solve for x using methods such as factoring, synthetic division, or the quadratic formula.
The imaginary zeros of a polynomial function are the values of x that make the function equal to a complex number. These can be found by using the complex conjugate theorem. If a + bi is a zero, then a - bi is also a zero, where a and b are real numbers and i is the imaginary unit, sqrt(-1).
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From a normally distributed population, a simple random sample of size 30 is taken. The mean of the sample is 144 and the standard deviation of the sample is 12.
Which interval is the 90% confidence interval for the population mean?
(139.7, 148.3)
142.4, 145.6)
143.3, 144.7)
140.4, 147.6)
The 90% confidence interval for the population mean is (140.4, 147.6), derived from a sample with a mean of 144 and a standard deviation of 12.
Let's break down the steps used to calculate the 90% confidence interval for the population mean:
- Sample mean ([tex]\bar{x}[/tex]): 144
- Sample standard deviation (s): 12
- Sample size (n): 30
- Critical value at 90% confidence (z): 1.645
The formula for the confidence interval is:
[tex]\[ (\bar{x} - z \cdot \frac{s}{\sqrt{n}}, \ \bar{x} + z \cdot \frac{s}{\sqrt{n}}) \][/tex]
Calculate the standard error (SE):
SE = s / sqrt(n)
SE = 12 / sqrt(30)
SE ≈ 2.188
Calculate the margin of error (ME):
ME = z * SE
ME = 1.645 * 2.188
ME ≈ 3.594
Calculate the lower limit (L):
L = [tex]\bar{x}[/tex] - ME
L = 144 - 3.594
L ≈ 140.406
Calculate the upper limit (U):
U = [tex]\bar{x}[/tex] + ME
U = 144 + 3.594
U ≈ 147.594
So, the 90% confidence interval for the population mean is approximately (140.406, 147.594), which rounds to (140.4, 147.6) when considering the appropriate level of precision. Therefore, the correct answer is (D) (140.4, 147.6).
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Find the value of x and the value of y.
if 120 marks is 60% what is full marks
What is the value of f(−1) when f(x)=2x+2 ?
Enter your answer in the box.
f(−1)=
It takes to sell A three hours to produce two cells.If you start with cell A,how many cells will you have in 24 hours
In 24 hours, you will have 48 cells if you start with cell A and keep making cells at the same rate.
If it takes three hours to produce two cells, we can calculate the production rate as follows:
Production rate of A = 2 cells / 3 hours
Now, we want to find out how many cells will be produced in 24 hours:
Number of cells produced in 24 hours = Production rate of A × Number of hours
Number of cells produced in 24 hours = (2 cells / 3 hours) × 24 hours
Number of cells produced in 24 hours = 2 cells/hour × 24 hours
Number of cells produced in 24 hours = 48 cells
Therefore, if you start with cell A and continue producing at the same rate, you will have 48 cells in 24 hours.
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Which answer is the solution set to the given inequality |x+7| < 17
A theorem is a statement that can be easily prove using a corollary
⇒A theorem is a statement that can be easily prove using a corollary
False Statement
Corollary Means , a Theorem written in another way , when it has been proved.
For Example:The Sum of Angles of Triangle is 180°.-----Theorem
Corollary→If three distinct rays intersect at three points , and sum of interior Angles formed at their point of Intersection is 180°, then it is a Triangle.
Correct Statement will be:
A theorem is a statement that can be easily proved using an Axiom or Postulate.
An isometry preserves distance.
True
False
If only one number in a fraction is negative,does that mean the whole fraction is negative
In six years, Clem Kadiddlehopper will be five times as old as he was 26 years ago. How old is he now?
which set of ordered pairs in the form of x y does NOT represent a function of x?
A. {(1, 1.5), (2, 1.5), (3, 1.5), (4, 1.5)}
B. {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
C. {(1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5)}
D. {(1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)}
A function is a relationship that maps elements from one set (the inputs) into elements of another set (the outputs). Such that each input can be mapped into only one output.
The correct option is B: {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
Using the general definition, to find which set of ordered pairs does not represent a function, we need to see in which set we have the same input (the first element of the ordered pair) assigned to two different outputs (the second element of the ordered pair).
Here the one that does not represent a function is option B:
{(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
Because we have the input x = 1 assigned to two different outputs, y = 3.3 and y = 4.5
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A line passes through (−1,−6) and (7,2) .Find the slope-intercept form of the equation of the line. Then fill in the value of the slope, m, and the value of the y-intercept, b, below.
The equation of the line passing through the points (- 1, -6) and (7, 2) will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.
What is the slope intercept form of a straight line?The slope intercept of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a straight line passing through the points (- 1, -6) and (7, 2)
We have a straight line that passes through the coordinates as follows -
(- 1, -6)
(7, 2)
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 + 6)/(8)
m = 8/8
m = 1
The line is passing through the point (7, 2). We can write -
y = mx + c
y = x + c [m = 1]
2 = 7 + c
c = 2 - 7
c = -5
The equation of the straight line will be -
y = x - 5
Now, the slope of the line will be [m] = 1 and the y - intercept will be -5.
Therefore, the equation of the line passing through the points (- 1, -6) and (7, 2) will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.
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HELP!
Solve −2(2x + 5) − 3 = −3(x − 1). (1 point)
−10
−16
16
−13
Solve 4(x + 1) = 4x + 4. (1 point)
1
All real numbers
0
No solution
Answer:
all numbers are real
Step-by-step explanation:
A local theater has floor seating, balcony seating, and box seating. if the theater contains 2,500 seats with 425 seats in the balcony and 215 box seats, how many seats are on the floor?
A die is rolled twice. what is the probability of showing a 3 on both rolls?
Which of the following is a solution to the inequality y > –2x + 6? a.(4, 4) b.(0, 0) c.(1, 1) d.(2, 2)
The correct answer is a.(4, 4) because when you substitute x = 4 and y = 4 into the inequality y > -2x + 6, the inequality holds true, indicating that (4, 4) is a solution.
To determine which of the given points is a solution to the inequality y >
-2x + 6, we substitute the x and y values of each point into the inequality and check if the inequality holds true.
Therefore, the correct answer is a.(4, 4), since it is the only point that satisfies the inequality y > -2x + 6.