To find the slope of a line using two points on the line, you can use the slope formula. Which formula will find the slope of a line
y = rise/run
y = run/rise
Final answer:
The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The formula represents the rise over run between these points.
Explanation:
We can use a specific formula to calculate the slope of a line using two points on that line. The slope is found by taking the difference in the y-value (also known as the rise) and dividing it by the difference in x-value (also known as the run). In mathematical terms, if we have two points (x1,y1) and (x2,y2), the formula for slope (m) is as follows:
m = (y2 - y1) / (x2 - x1)
Therefore, between two given points, you subtract the y-value of the starting point from the y-value of the end point to find the rise, and then remove the x-value of the starting point from the x-value of the end point to determine the run. The slope is then the quotient of these two differences.
Match each problem (term) with its sum or difference (definition).
Term Definition
4.23 + 16.21 A) 26.09
42.3 + 1.621 B) 2.609
4.23 − 1.621 C) 20.44
42.3 − 16.21 D) 43.921
GET THIS RIGHT ILL GIVE U BRAINLIEST!!!!!!!
Each mathematical term has been calculated and the correct sum or difference matched with its definition: 4.23 + 16.21 matches with C) 20.44, 42.3 + 1.621 with D) 43.921, 4.23 - 1.621 with B) 2.609, and 42.3 - 16.21 with A) 26.09.
To match each mathematical term with its correct sum or difference, we simply perform the addition or subtraction:
4.23 − 1.621 = 2.609, so this term matches with definition B)
Each problem has been matched with its corresponding definition based on the results of the arithmetic operations.
which expression is equivalent to 6a+12
Answer:
2(3a + 6) would be correct.
Hope this was helpful !
Step-by-step explanation:
Construct two tangents to circle O, at A and at B, where AB is a diameter. What relationship exists between the two tangents
When two tangents are drawn to a circle at endpoints A and B of a diameter, the tangents are perpendicular to the radii at their points of tangency and are parallel to each other, forming two congruent right triangles.
Explanation:The question involves constructing two tangents to a circle from two points, A and B, where AB is the diameter of the circle. By the properties of circles and tangents, we know that a tangent to a circle is perpendicular to the radius at the point of tangency. Since AB is the diameter, points A and B are on opposite ends of the circle, and when we draw tangents at these points, each tangent will be perpendicular to the radii OA and OB respectively. Additionally, since AB is a diameter, it creates a linear pair with the two tangents, meaning that the two tangents are parallel to each other. This setup creates two congruent right triangles, namely triangle OAT and triangle OBT, where T represents the points of tangency on each tangent.
Two tangents to a circle from points A and B, where AB is a diameter, are congruent and parallel to each other, forming right angles with the diameter.
Explanation:When constructing two tangents to a circle at points A and B, where AB is a diameter, an interesting relationship exists between those tangents. By the properties of tangents to a circle from an external point, we know that two tangents drawn to a circle from the same external point are equal in length. Therefore, the two tangents you would draw from points A and B to any point on the circumference of the circle would be congruent to each other.
Additionally, since each tangent is perpendicular to the radius of the circle at the point of tangency, the tangents are parallel to each other because they are both perpendicular to the same diameter. In the context of circle O with AB as a diameter, we can also conclude that the angles formed between the tangents and the diameter AB are right angles due to the geometric properties of tangents.
HELP PLEASE!!! Which figure shows a reflection of pre-image DEFG over the x-axis ? ( there’s only an A B and C )
how much would 500 invested at 4 interest compounded continuously be worth after 7 years round your answer to the nearest cent?
Which is a zero od the quadratic function f(x)=16x²+32x-9?
Which number system BEST describes this set? {-10, 0, 28 7 , 102.9} A) integers B) natural numbers C) rational numbers D) irrational numbers
Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at
90
miles per hour. The eastbound train travels at
80
miles per hour. How long will it take for the two trains to be
272
miles apart?
Do not do any rounding.
A triangle with vertices at A(20, –30), B(10, –15), and C(5, –20) has been dilated with a center of dilation at the origin. The image of B, point B', has the coordinates (2, –3). What is the scale factor of the dilation?
110110
1515
5
10
Answer:
5
Step-by-step explanation:
A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What are the coordinates of A’?
A. (1,-4)
B. (-5,2)
C. (1,10)
D. (11,2)
Solution:
The Point in the coordinate plane is A(-5,-4).
Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is
[tex]=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7[/tex]
When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).
Now, the Point B is translated by the rule , (x,y)—->(x+6,y),
So,the point B is translated to, (-5+6,10)=(1,10)
Option C: (1,10) is the glide reflection of point A(-5,-4).
The coordinates of A' after the glide reflection (translation and reflection over y = 3) from A(-5, -4) are (1, -4), so the answer is A.
In a glide reflection, first apply a translation and then a reflection. Let's follow the given transformations step by step:
Translation: (x, y) → (x + 6, y)
This means you move the point A(-5, -4) six units to the right and keep the same y-coordinate. Applying the translation:
A' = (-5 + 6, -4)
= (1, -4)
Reflection over the line y = 3:
In this reflection, points above the line will move below it and vice versa, while points on the line will remain unchanged.
Since the original point A(-5, -4) is below the line y = 3, its reflection A' will be above the line.
Therefore, the coordinates of A' are (1, -4) ,the correct option is A. (1, -4).
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Which expression gives the area of the triangle shown below?
The expression gives the area of the triangle shown below 1/2cx is the answer.
The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.
What is the formula of the triangle?
The formula of a triangle
A=1/2bh.
In this picture, the base is the length of the bottom part of the triangle (c).
It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).
X is the height of the triangle.
Therefore, 1/2cx is the answer.
So option D is correct.
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can some one plz help me...Banks cannot provide amortization schedules to borrowers.
A) true
B) false,
The correct answer is:
False.
Explanation:
When you take out a loan, banks provide all of the relevant information for the loan. This includes the interest rate, payment amount, and an amortization schedule, which shows the amount paid and the amount of principal this takes off of the loan every month for the life of the loan.
Carl puts 1.10 in his penny bank every day in the month of July. His total savings was 55at the end of June. What’s the best estimate for Carl’s savings at the end of July
Answer:
About 85 is the answer
The coordinates of the vertices of / are G(–2, 3), H(–1, 2), and I(–3, 1). If / is reflected across the x-axis to create /, find the coordinates of the vertex located at point W.
Answer:
A. (–2, –3)
that is the answer
Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
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You roll a number cube twice. Find the probability of the events.
1.Rolling a 3 twice
2.Rolling an even number and a 5
3.Rolling an odd number and a 2 or 4
4.Rolling a number less than 6 and a 3 or a 1
Answer:
In a number cube, a dice, you have six sides with the numbers 1, 2, 3, 4, 5 and 6. And when you roll it, each number has the same probability of showing.
a) rolling a 3 twice.
In the first roll you get a 3, with a probability of 1/6, and with the second roll you also get a 3, also with a probability of 1/6. The probability of bot evets to happen is equal to the product of the individual probabilities.
P = 1/6*1/6 = 1/36
b) An even number and a 5.
In the first roll you can get 2, 4 or 6, so you have 3 out of 6 options, the probability is 3/6 = 1/2, in the second roll you need you get a 5, the probability is 1/6.
P = 1/2*1/6 = 1/12.
But we also have the probability where the first dice is a 5 and the second a pair number, so the real probability is 2*P = 1/6
c) an odd number and 2 or 4.
for an odd number the probability is 3/6 = 1/2, for getting 2 or 4 the probability is 2/6 = 1/3
then we have that P = 2*(1/3)*(1/2) = 1/3
d) a number less than 6, you have 5 options, then the probability is:
p = 5/6, and for 3 or 1 the probability is 2/6 = 1/3
then P = 2*(5/6)*(1/3) = 5/9
Help!! Would the answer be c??
The steps below show the incomplete solution to find the value of x for the equation 7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step? (4 points)
Select one:
a. 4x = 24
b. 4x = 16
c. 4x = 5
d. 4x = 80
Answer: is a
Step-by-step explanation:
Find the equation of the axis of symmetry for the parabola y = x2 + 4x – 5 .
Bianca has 3:5 The ratio of the number of books Bianca has to the number books Chrissy has 10:11 If amy has 36 books how many books does Bianca have
If x is 6, then 7x = _____. 13 42 42x 76
Answer: 42
Step-by-step explanation:
x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x
=42
please help asap! 14 points
Which graph shows a line that is perpendicular to line QR?
A watch manufacturer has two factories (FA, FB) and 60% of their watches are made at FA. It is known that 10% of them are made at FA and 15% made at FB are defective. What is the probability that a selected defective watch was manufactured at FB?
BRAINLIESTTTTT ASAP!!!
Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)^2 = 3
(x − 3)^2 = 2
(x − 2)^2 = 1
(x − 1)^2 = 4
ALGEBRA 1 PLEASE HELP
5x+y=6
5x+3y=-5
The y-coordinate of the solution to the system shown as______
A) -5
B) -1
C) 1/2
D) 1
Name the property of real numbers illustrated by the equation 16(3t + 4v) = 48t + 64v.
The top of a rectangular table has an area of 100 square feet and width of 5 feet. What is the length in feet of the surface
The length of the surface of the rectangular table that has an area of 100 sq. ft is: 20 ft.
What is the Area of a Rectangle?Area of rectangle = (length)(width).
The table given has a rectangular surface.
Area of the rectangular table = 100 square feetWidth of the rectangular table = 5 feet(length)(5) = 100
Length = 100/5
Length of the rectangular table = 20 feet.
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800% of what number is 4,240?
Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
The t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
To model the population of cells, we can use an exponential growth equation. Since the population doubles every day, the equation would be:
[tex]P(t)=P_{0} *2^{t}[/tex]
Where:
[tex]P(t)[/tex] is the population size at time t.
[tex]P_{0}[/tex] is the initial population size ([tex]10[/tex] cells in this case).
[tex]t[/tex] is the time in days.
So, for this scenario, the equation becomes:
[tex]P(t)=10*2^{t}[/tex]
Now, we want to find out how many days it will take for the population to reach [tex]1,000,000[/tex] cells. We can set up the equation:
[tex]1,000,000=10*2^{t}[/tex]
To solve for t, we need to isolate it. First, divide both sides by [tex]10[/tex] :
[tex]100,000=2 t[/tex]
Now, take the logarithm base 2 of both sides to solve for t:
[tex]log_{2} (100,000)=t[/tex]
Using a calculator, we find:
[tex]t=16.61[/tex]
Since t represents days, and we can't have a fraction of a day for the population to reach [tex]1,000,000[/tex] cells, we need to round up to the nearest whole number. Therefore, it will take approximately [tex]17[/tex] days for the population to reach [tex]1,000,000[/tex] cells.
COMPLETE QUESTION:
Create an equation to model a population of cells which starts with [tex]10[/tex]cells and doubles in size every day. How many days will it take to reach [tex]1,000,000[/tex] cells?