The slope of the line passing through the point (2,1) and (7,8) is 7/5
What is a slope?
Slope is the inclination of the line with x-axis. measure of how steep a curve or line is. There are various way to calculate the slope of a line. One of the basic way is from coordinates. It is the ratio of difference of y coordinate to the corresponding x- coordinate. it is also known as slope formula
We are given the coordinates as
(2, 1) and (7, 8).
We use the slope formula to find the slope
Slope = (8-1)/(7-2)
Slope = 7/5
Hence the slope of the passing through the given point is 7/5
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The scatterplot illustrates the relationship between distance and success rate of field-goal attempts for a sample of football kickers.
Which of the following is an accurate description of the scatterplot?
The kickers have unusually low success rates when the distance is large.
The kickers have unusually high success rates when the distance is small.
As the distance of the attempt increases, the kickers have a lower success rate for their field goals.
As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
The statement that best describes the relationship that is displayed by the scatter plot is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
What is a Scatter Plot?A scatter plot is used to show the relationship between two variables that are different, whereby the trendline formed by each data point determines whether the relationship between the two variables is negative or positive.
If the trendline slopes upwards, it is positive, if it slopes downwards, it is negative.
If it is negative, it means as one variable increases, the other one decreases. On the other hand, if it is positive, it implies that as one variable increases, the other variables decreases.
The scatter plot given shows that the relationship between the distance of the attempt and success rate is negative. This implies that, as the distance of the attempt increases, the success rate decreases.
Therefore, the accurate description is: D. As the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
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Answer:
D. as the distance of the attempt increases, the kickers tend to have a lower success rate for their field goals.
Step-by-step explanation:
Help quick, State if the two triangles are congruent. If they are state how you know.
The two triangles are congruent and they are congruent by ASA.
How to ascertain if triangles are congruent?Triangles are congruent when they have exactly the same three sides and exactly the same three angles. This simply implies the corresponding sides and angles of the triangles are congruent.
Let's check if the triangles are congruent.
One of the congruent angles in the triangles are vertically opposite angle.
Recall vertically opposite angles are congruent.
In these two triangles, we have a congruent angle pair and a congruent side pair.
Therefore, we can say the triangles are congruent by ASA.
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please help me asap
Answer:
z = 52°
Step-by-step explanation:
Formula we use,
→ A + B + C = 180°
Then the value of z will be,
→ 81° + 47 ° + z = 180°
→ 128° + z = 180°
→ z = 180° - 128°
→ [ z = 52° ]
Hence, the value of z is 52°.
how many Robin eggs, laid end to end, would be about equal in length to two raven eggs? justify your answer.
Answer:
Step-by-step explanation:
The average length of two raven eggs is about 0.1 m.
Since the average length of a robin egg is about 0.02 m, 5 eggs laid end to end would measure about 0.1 m.
A carpenter needs 8.5 feet of rope for a project. How much will the carpenter spend if the rope costs $4.57 per foot?
Answer: The carpenter will spend $38.84
Step-by-step explanation:
8.5 feet of rope and the rope costs 4.57 per foot
8.5x4.57=38.845
Since half a cent does not exist we can get rid of the 5 at the end
Therefore the carpenter will have to spend $38.84
Unless you want to round it up, then it will be $38.85
Complete the two column proof.
The two-column table to prove ∠ABC ≅ ∠DBE using the angle addition postulate is presented as follows;
Statements [tex]{}[/tex] Reasons
1. ∠ABD is a right angle [tex]{}[/tex] 1. Given
∠CBE is a right angle
2. ∠ABD are complementary [tex]{}[/tex] 2. Definition of complementary angles
3. ∠CBE are complementary [tex]{}[/tex] 3. Definition of complementary angles
4. ∠ABC ≅ ∠DBE [tex]{}[/tex] 4. Congruent complements theorem
What is the angle addition postulate?The angle addition postulate states that the when two angles are placed side by side such that they share a common ray, the measure of the angle formed by the two angles is the sum of the measure of the individual angles.
∠ABD = ∠ABC + ∠CBD (angle addition postulate)
∠ABD = 90° (definition of right angle)
∠ABC + ∠CBD = 90° (substitution property of equality)
∠ABC and ∠CBD are complementary (definition of complementary)
Similarly
∠CBE = ∠CBD + ∠DBE (angle addition postulate)
∠CBE = 90° (definition of right angle)
∠CBD + ∠DBE = 90° (substitution property of equality)
∠CBD and ∠DBE are complementary (definition of complementary)
∠ABC is a complementary angle to ∠CBD and ∠DBE is a complementary angle to ∠CBD
Therefore;
∠ABC is congruent to ∠DBE (congruent complements theorem)
∠ABC ≅ ∠DBEThe congruent complement theorem states if an angle ∠A is a complement to an angle ∠C and if an angle ∠B is also a complement of angle ∠C then ∠A is congruent to ∠B.
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g) In the figure alongside, AB is an electric pole. When an
electric wire falls, its one end touches the ground at P,
5 m away from the base of the pole. If the length of the wire
from the top of the pole to the ground is 13 m, complete
the following problems.
(i) Find the height of the pole.
(ii)If the other end of the wire touches the grand at Q, 9 m away from the
base to the opposite side of the pole, find the length of the falling wire.
Step by step solution
The height of the electric pole is 12 m
When an electric wire falls, its one end touches the ground at P, 5 m away from the base of the pole,
base = 5
length of the wire from the top of the pole to the ground is 13 m
Height of the plant can be calculated by pythagoras theorem
h² = p² + b²
13² = p² + 5²
p² = 169 - 25
p = √144
p = 12m
Therefore, the height of the electric pole is 12 m
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Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Answer:
The answer is –3 < 1
Step-by-step explanation:
-3 is below zero. 1 is above zero. therefore, -3 less than 1
Irma and Cindy went to an arcade where the machines took tokens. Irma played 9 games of
skee ball and 10 games of pinball, using a total of 58 tokens. At the same time, Cindy played
5 games of skee ball and 4 games of pinball, using up 26 tokens. How many tokens does
each game require?
Every game of skee ball requires how many tokens?
and every game of pinball requires how many tokens?
Every game of skee ball game requires 2 tokens and every game of pin ball game require 4 tokens.
Given that,
Cindy and Irma visited an arcade where the games accepted tokens. Irma used 58 tokens in total while playing 9 games of skee ball and 10 games of pinball. Cindy used up 26 tokens playing 5 games of skee ball and 4 games of pinball concurrently.
We have to find how many tokens are needed for each game. How many tokens are required for each skee ball game.
Let us take the skee balls as x and the pin ball as y.
We get,
9x+10y=58---> equation (1)
5x+4y=26---> equation (2)
Multiply equation (1) with 5 and equation (2) with 9.
5(9x+10y=58)⇒45x+50y=290
9(5x+4y=26)⇒45x+36y=234
------------------------ (subtracting those equation)
0+14y=56
14y=56
y=56/14
y=4
Substitute y=4 in equation(2)
5x+4y=26
5x+4(4)=26
5x+16=26
5x=26-16
5x=10
x=10/5
x=2
Therefore, Every game of skee ball game requires 2 tokens and every game of pin ball game require 4 tokens.
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an experimenter flips a coin 100 times and gets 56 heads. find the 96.5% confidence interval for the probability of flipping a head with this coin. a) [0.355, 0.615] b) [0.375, 0.665] c) [0.455, 0.665] d) [0.505, 0.510] e) [0.455, 0.465] f) none of the above
The probability of the experiment is = 0.375, 0.665.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-
probability that first spin is grey = 6/8probability that second spin is blue = 2/8probability of both = 6/8 * 2/8 = 12/64 which reduces to 3/16learn more about probability click here:
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What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = [tex]\frac{1}{6}[/tex] x + 9
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 9) and (x₂, y₂ ) = (6, 10) ← 2 points on the line
m = [tex]\frac{10-9}{6-0}[/tex] = [tex]\frac{1}{6}[/tex]
the line crosses the y- axis at (0, 9 ) ⇒ c = 9
y = [tex]\frac{1}{6}[/tex] x + 9 ← equation of line
In a certain chemical, the ratio of zinc to copper is 4 to 13. A jar of chemical contains 325 grams of copper. How many grams of zinc does it contain
Given -
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Prove -
How many grams of zinc does it chemical contain.
Answer
suppose that scalar multiple of the zinc and copper be y .
As given
In a certain chemical, the ratio of zinc to copper is 4 to 13.
The chemical contains 546 grams of copper.
Than equation is
13y = 546
13y = 546
y = 42
Zinc contain in the certain chemical = 4y
= 4 42
= 168 grams
Therefore 168 grams of zinc contain in a certain chemical .
a random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces. in this problem, what is the 0.7?
In this problem 0.7 is the standard deviation of the contents.
Define standard deviation.It is a statistic that gauges a dataset's dispersion from its mean, and it is calculated as the variance's square root. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance. The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean. A dataset's dispersion from its mean is measured by standard deviation. It is determined as the variance's square root. In the financial industry, standard deviation is frequently employed as a gauge of an asset's relative riskiness.
Given,
A random sample of 196 bottles of cologne showed an average content of 4 ounces. it is known that the standard deviation of the contents (i.e., of the population) is 0.7 ounces.
In this problem 0.7 is the standard deviation of the contents.
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graph the following inequality:
Please help thx
The equations y=3+2 and y=2x+1 both will meet at x=3
What is inequality?A difference between two values indicates whether one is smaller, larger, or simply not equal to the other.a b asserts that a and b are not equal.If a b, then a must be less than b.When a > b, an is greater than b. (those two are known as strict inequality)If a and b are divided, a must be smaller than or equal to b.When a and b are together, an is greater than or equal to b.Acc to our question-
Given, 3x−2<2x+1⇒3x−2x<1+2⇒x<3orx∈(−∞,3)The lines y=3x−2 and y=2x+1 both will intersect at x=3 Clearly, the dark line shows the solution of 3x−2<2x+1.Hence,The lines y=3x−2 and y=2x+1 both will intersect at x=3
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on saturday leon biked an average speed of 14.5 miles per hour for 1.5 hours. then on sunday he biked an average speed of 15 miles per hour for 2.75. what was the total distance leon biked in miles that weekend
The total distance leon biked in miles that weekend is 19.5 miles.
The answer provided below has been developed in a clear step by step manner.
On Saturday, Leon biked 1.5 hours at a speed of 14.5 miles per hour that means distance = 14.5 * 1.5 = 21.75 miles
On Sunday, he biked 2.75 hours at a speed of 15 miles per hour that means distance =15 * 2.75 =41.25 miles
Distance = speed*time use this formula
He farther did in sunday = 41.25 - 21.75 miles = 19.5 miles
Therefore, that weekend Leon rode his bike a total of 19.5 miles.
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Hamad lends $5,500 at a rate of 5 ½%. Find how long it will take for his investment to earn $205 in interest? Round to the nearest day
The time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
Define the term simple interest?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest does not really compound, therefore a borrower will only charge interest mostly on principal sum, and a borrower will never be required to pay further interest on the interest that has already incurred.The formula for calculating the simple interest is-
SI = PRT/100
In which,
SI = simple interest (= $205)P = principal amount ($5,500)R = rate of interest (5 ½%) = 11/2 %T= time in years.Put in formula.
205 = 5,500×11×T/200
T = 205×200 / 5,500×11
T = 0.67 years
T = 8.13 months = 253 days.
Thus, the time taken to earn the interest of $205 on the investment by Hamad is 2563 days.
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Write 2^40 as a pwer with the following base (2^8)
By algebra properties, the resulting expression of the power 2⁴⁰ is (2⁸)⁵.
How to rewrite a power expression according algebra properties
In this problem we must rewrite a power expression in terms of the power 2⁸, which is the base of the resulting expression. This can be done by applying algebra properties:
Step 1 - Write the original expression presented in the statement.
2⁴⁰
Step 2 - By definition of multiplication between real numbers.
2⁽⁸⁾⁽⁵⁾
Step 3 - By the definition of the power of a power.
(2⁸)⁵
The resulting expression is (2⁸)⁵.
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Lora's phone records data for screen time each week. Last week, she used 840 minutes. This week, Lora used 504 screen time minutes on the phone. Calculate the percent decrease in screen time this week.
17%
34%
40%
67%
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
Given that, last week, Lora used 840 minutes. This week, Lora used 504 screen time minutes on the phone.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now,
Difference=840-504
= 336
Percentage decrease = Difference in value/Original value ×100
= 336/840 ×100
= 0.4 ×100
= 40%
The percent decrease in screen time this week is 40%. Therefore, option C is the correct answer.
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find the area of the trapezium
Step-by-step explanation:
To find the Area of a Trapezium, we use 1/2(a+b)*h
where a=2.8 and b=4.4, Height=3.5
1/2(2.8+4.4) *3.5
1/2(7.2)*3.5
3.6*3.5
12.6cm2
Answer:
Step-by-step explanation:
Area of a trapezium = 1/2(a + b) x h
1/2 (2.8 + 4.4) x 3.5
1/2 x 7.2 x 3.5
12.6
HOPE IT HELPS YOUPLS RATE AS BRAINLIEST ANSWERWhat is the image of the point (-7,5)(−7,5) after a rotation of 180^{\circ}180
∘
counterclockwise about the origin?
The coordinates of the image of the point (-7, 5) are (7, -5).
We are given point P. The coordinates of the point P are (-7, 5). We perform a transformation on the given point. We rotate the given point about the origin counter-clockwise. The angle of rotation is 180°. We need to find the coordinates of the image of the point after rotation.
Let the new coordinates of the image of the point after rotation be denoted by (X, Y). If the coordinates of the original point are (x, y), then the relations between the coordinates of the point and the image are given below.
X = x*cosθ - y*sinθ
X = (-7)*cos(180°) - (5)*sin(180°)
X = (-7)*(-1) - (5)*(0)
X = 7
Y = x*sinθ + y*cosθ
Y = (-7)*sin(180°) + (5)*cos(180°)
Y = (-7)*(0) + (5)*(-1)
Y = -5
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Which equation correctly applies the Associative Property of Addition?
8.9+(6.4 +7.2) (8.9 + 6.4) +7.2
1/6 + 4/6 = 5/6
=
1/3(1/2+3/4)= (1/3 x 1/2) + (1/3 X 3/4)
6-18 = 6 + (-18)
Answer:The equation 8.9+(6.4 +7.2) is correctly applying the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the order in which the numbers are added does not affect the sum.
Select all ordered pairs that are a solution to -5x + 3y > 12
options:
(3, 9)
(-5, 5)
(3, -6)
(-2, -5)
(2, 8)
(-6, 0)
The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:
(-5, 5)(2, 8)(-6, 0)How to determine the solution?In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (3, 9), we have:
-5x + 3y > 12
-5(3) + 3(9) > 12
-15 + 27 > 12
12 > 12 (False).
For ordered pair (-5, 5), we have:
-5x + 3y > 12
-5(-5) + 3(5) > 12
25 + 15 > 12
40 > 12 (True).
For ordered pair (3, -6), we have:
-5x + 3y > 12
-5(3) + 3(-6) > 12
-15 - 18 > 12
-33 > 12 (False).
For ordered pair (-2, -5), we have:
-5x + 3y > 12
-5(-2) + 3(-5) > 12
10 - 15 > 12
-5 > 12 (False).
For ordered pair (2, 8), we have:
-5x + 3y > 12
-5(2) + 3(8) > 12
-10 + 24 > 12
14 > 12 (True).
For ordered pair (-6, 0), we have:
-5x + 3y > 12
-5(-6) + 3(0) > 12
30 + 0 > 12
30-5 > 12 (True).
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3X + 2Y) (6X + 6Y) what is the answer
Answer:
18X^2 + 18XY + 12YX + 12Y^2
Step-by-step explanation:
you have to moltiplicate the first term with the other two and the same thing for the second term of the first moltiplication
Step-by-step explanation:
what is the question you need an answer for ?
I assume you only need the result of the multiplication of both terms.
remember, when multiplying summary terms, we need to multiply every part of one term with every part of the other term.
(3x + 2y)(6x + 6y) = 18x² + 18xy + 12xy + 12y² =
= 18x² + 30xy + 12y²
PLEASE HELP will mark brainliest
The slope of the given line in the graph is 0.
What is slope?
The steepness and direction of a line are measured by its slope. Any two points along the line can be used to calculate it. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The Slope, also known as the Gradient, of a straight line displays how steep the line is. The change in y coordinate relative to the change in x coordinate is known as the slope of an object.
Here the given graph points are,
[tex](x_1-y_1)=(1,1)\\(x_2,y_2)=(4,1)[/tex]
Using slope formula ,
=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
=> slope m = [tex]\frac{1-1}{4-1}[/tex]
=> slope m = 0/3
=> slope m=0.
Therefore slope of the line is 0.
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s 3)
3) Find the measure of 4A:
5x
130⁰
5x
Please help
Evaluate y² ÷ 8 if y = 4
I wasn't here when they learned this old show work
Answer:
2
Step-by-step explanation:
y² = 4²= 16 (in substitution way)
16÷8= 2
mark me on brainliest please follow me to
Answer:
2
Step-by-step explanation:
y^2/8
4^2/8
16/8
2
Hopes this helps please mark brainliest
write an equation of the line perpendicular to -4x+3y=12 and containing the point (6,8)
The equation of the line perpendicular to - 4x + 3y = 12 and containing the point (6,8) is 3x + 4y = 50.
What is a perpendicular line?
Perpendicular lines: A perpendicular line is a straight line that has been put up so that it forms a right angle with another line. The two lines are parallel to one another.
Here,
The slope of ax + by = c is given by m = -a/b
m = -(-4)/3 = 4/3
m = 4/3 for this line.
A perpendicular line will have a slope -1/m = -3/4
The line through (6, 8) with slope -3/4
y = (-3/4)x + b
8 = (-3/4)(6) + b
b = 8 + 9/2 = 25/2
y = (-3/4)x + 25/2
4y = -3x + 50
3x + 4y = 50
Hence, the equation of the line perpendicular to -4x+3y=12 and containing the point (6,8) is 3x+4y = 50.
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Sasha is studying a type of coral that grows at a constant rate. Every month, she visits two pieces of the coral and measures their heights. She made this table:
Month 1 2 3
Piece A's height (cm) 24 26 28
Piece B's height (cm) 27 29 31
When Piece A's height is 49cm, what will Piece B's height be?
Answer:
Step-by-step explanation: The constant growth for Plant A is two cm a month and the growth of Plant B is also two cm a month.
In relation, Plant B will also be 3cm taller than Plant A on any month so when Plant A is 49cm, Plant B is 52.
When Piece A's height is 49 cm then the Piece B's height will be 52 cm.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can see that Piece A's height increases by 2 cm each month and Piece B's height increases by 2 cm each month as well.
To find out what Piece B's height will be when Piece A's height is 49 cm, we need to find how many months it will take for Piece A to reach 49 cm.
From Month 1 to Month 2, Piece A's height increased by 2 cm, and from Month 2 to Month 3, Piece A's height increased by another 2 cm. Therefore, Piece A's height increases by 2 cm per month.
To go from 28 cm (Piece A's height in Month 3) to 49 cm, it takes 21 cm ÷ 2 cm/month = 10.5 months.
So 10.5 months after Month 3 is Month 13.5.
In Month 13.5, Piece A's height will be 49 cm and Piece B's height will be:
Piece B's height in Month 3 + 2 cm/month × (13.5 - 3 months)
= 31 cm + 2 cm/month × 10.5 months
= 52 cm
Therefore, when Piece A's height is 49 cm, Piece B's height will be 52 cm.
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In ΔTUV, m∠T = 58° and m∠U = 97°. Which list has the sides of ΔTUV in order from longest to shortest?
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
In ΔTUV, m∠T = 58° and m∠U = 97°.
Then the third angle of the triangle will be given as,
∠T + ∠U + ∠V = 180°
58° + 97° + ∠V = 180°
155° + ∠V = 180°
∠V = 180° - 155°
∠V = 25°
In a triangle, the opposite angle of the largest side will be the largest one.
The angle ∠U is the largest in triangle ΔTUV. Then the largest side will be TV.
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Please help me (see attachment)
A graph of the given equation (x - y = 6) is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
Next, we would rewrite the given equation in standard form as follows:
x - y = 6
Adding y to both sides of the equation, we have the following:
x - y + y = 6 + y
x = 6 + y
Rearranging the equation, we have the following:
y = x - 6
By critically observing the graph (see attachment), the y-intercept is equal to -6 and the x-intercept is equal to 6.
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