Answer: $505,000
Step-by-step explanation:
The salary difference between a teacher and a cashier is:
$42,630 - $17,380 = $25,250
This means that a teacher earns $25,250 more per year than a cashier.
To find out how much more a teacher would earn over a 20-year career, we need to multiply the salary difference by the number of years:
$25,250 x 20 = $505,000
Therefore, a teacher would earn $505,000 more than a cashier over a 20-year career.
50 POINTS!!!!
A composite figure is represented in the image. A six-sided composite figure. A vertical line on the left is labeled 4 meters. The base is labeled 9 meters. There is a small portion from the vertical line that is parallel to the base that is labeled 3 meters. This portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled. What is the total area of the figure?
Answer:
4.6 inches
Step-by-step explanation:
i believe. IM SORRY IF IM WRONG!!
If this portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled. The total area is 45 square meters.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
Here, we have,
Since the rectangle has a length of 4 meters and a width of 9 meters we need to find the area of rectangle
Area of rectangle = length × width
Area of rectangle = 4 m × 9 m
Area of rectangle = 36 m^2
Since the triangle has a base of 6 meters (9 meters - 3 meters o) and a height of 3 meters we need to find the Area of triangle
Area of triangle = (1/2) × base × height
Area of triangle = (1/2) × 6 m × 3 m
Area of triangle = 9 m^2
Now let find the total area of the composite figure
Total area = Area of rectangle + Area of triangle
Total area = 36 m^2 + 9 m^2
Total area = 45 m^2
Therefore the total area of the figure is 45 square meters.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
Step-by-step explanation:
slope of a=3
slope of b=(4-2)/(1-0)=2/1=2
slope of c is negative
1. a has the steepest slope.
2. a has the largest y-intercept.
3. c is decreasing.
4.b after 3 weeks,you have 8 as a solution.
The figure below shows a satellite orbiting Earth. The satellite passes directly over two tracking stations A and B, which are 68 miles apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be 83.9 degrees and 86.2 degrees respectively. How far is the satellite from station
A and how high is the satellite above the ground? Round answers to the nearest whole mile.
Step-by-step explanation:
let the third vertex=C
180-86.2=93.8°
angle near the satellite=180-(83.9+93.8)=180-177.7°=2.3°
angles of triangle are 83.9°,93.8°,2.3°
by sine formula
[tex]\frac{AC}{Sin~93.8} =\frac{AB}{Sin 2.3} \\\frac{AC}{Sin(180-93.8)} =\frac{68}{Sin~2.3} \\\frac{AC}{Sin~86.2} =\frac{68}{Sin~2.3} \\AC=\frac{Sin~86.2}{Sin~2.3} \times~68\\AC \approx 1690.69\\AC\approx1691~mile[/tex]
What value of x will make this proportion true/ 14/x=1/2 7, or 18, or 24, or 28, show the problem worked.
Answer:
378
Step-by-step explanation:
[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{27}[/tex] Cross multiply and solve for x
x = (14)(27)
x = 378
Helping in the name of Jesus.
7. polynomial has zeros
x = -1 mul. 2
x = 3 mul. 1
x = 1 mul. 1
and goes through the
point (2,-18). Write the function in factored form. Remember to find the leading coefficient "a".
“mul” is multiplicity
Answer:
the final factored form of the function is:
f(x) = 6(x+1)^2(x-3)(x-1)
Step-by-step explanation:
To write the function in factored form, we need to use the zeros and their multiplicities.
From the given zeros, we can write:
x = -1 (multiplicity 2) means (x+1)(x+1) = (x+1)^2 = 0
x = 3 (multiplicity 1) means (x-3) = 0
x = 1 (multiplicity 1) means (x-1) = 0
So the factored form of the function is:
f(x) = a(x+1)^2(x-3)(x-1)
To find the value of "a" and satisfy the condition that the function goes through the point (2,-18), we can substitute the given point into the function:
-18 = a(2+1)^2(2-3)(2-1)
-18 = a(-3)
Solving for "a", we get:
a = 6
So the final factored form of the function is:
f(x) = 6(x+1)^2(x-3)(x-1)
WILL GIVE TRUE 100 POINTS AND BRAINLYEST FOR THE CORRECT ANSWER
Step-by-step explanation:
See image.....as these are definitions, it is self-explanatory:
A letter of the alphabet is chosen, then a digit from 1-9 is chosen. Find the probability of getting X, then a prime number.
Answer:
There are 26 letters in the alphabet, and 9 digits from 1 to 9.
The probability of choosing X as the letter is 1/26, since there is only one X in the alphabet.
The probability of choosing a prime number digit is 4/9, since there are 4 prime numbers among the digits 1-9 (2, 3, 5, and 7) and 9 total digits.
Therefore, the probability of choosing X followed by a prime number digit is:
P(X and prime) = P(X) × P(prime) = (1/26) × (4/9) = 4/234
So the probability of getting X followed by a prime number is 4/234, or approximately 0.017 or 1.7%.
Need help for this question.
The measure of the angle x is 41.41° in the given triangle.
What is a triangle?Triangle is a clοsed twο-dimensiοnal shape. It is a three-sided pοlygοn. All sides are made οf straight lines. The pοint where twο straight lines jοin is the vertex. Hence, the triangle has three vertices. Each vertex fοrms an angle.
Given that cos θ = side adjacent to angle x/hypotensive
Here, side adjacent to angle x = 6
hypotensive = 8
cos x = 6/8
x = arccos 6/8
x = 41.41°
Thus, the measure of the angle x is 41.41° in the given triangle.
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find the intersection (2,2) (2,4) (8,4) (8,2)
The intersection (2,2) (2,4) (8,4) (8,2) is (5,3).
On the coordinate plane, the four points that are given together form a rectangle. We must first locate the midway of both diagonals in order to determine where the diagonals will connect.
The midpoint of the diagonal that passes through the points (2,2) and (8,4) is ((2+8)/2, (2+4)/2). (5,3).
The midpoint of the diagonal that passes through the points (2,4) and (8,2) is ((2+8)/2, (4+2)/2). (5,3).
Consequently, the diagonals' point of intersection is (5,3).
Due to the fact that a rectangle's two diagonals meet here in the middle, this location also serves as the rectangle's centre.
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Find the probability of exactly three
successes in eight trials of a binomial
experiment in which the probability of
success is 45%.
P(3) = 8C3 (0.45)³ (0.55)8-3
Solve part of the answer.
8C3 = [?]
Answer: 8c3 = 56
the rest of the equation;
P(3) = 56 * (0.45)^3 * (0.55)^5
P(3) = 56 * 0.091125 * 0.05031737
P(3) = 0.257
To express this probability as a percentage, we multiply by 100:
P(3) = 25.7%
25.7% is the final answer (not 8c3)
helpp!!!!11!1!1 !!!:(
The number of books that each kid in Mr. Johnson's sixth-grade class read during the summer was recorded. 5 books have been read on average by Mr. Johnson's students.
There are six students in Mr. Johnson's sixth-grade class, and their number of books read is 0, 2, 4, 6, 8, and 10.
To find the median, we need to find the middle value in the list of numbers. If there is an odd number of values, then the median is the middle number. If there is an even number of values, then the median is the average of the two middle numbers.
In this case, there are six numbers, which is an even number, so we need to find the average of the two middle numbers, which are 4 and 6.
The average of 4 and 6 is (4 + 6)/2 = 5.
Therefore, the median number of books read by Mr. Johnson's students is 5.
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Emily is selling t-shirts for $7 each. If she earns a total of $126, how many t-shirts did she sell? Write and solve an equation to solve this problem. (Hint. You need to identify a variable AND embed it in the equation.)
Answer:
7x = 126 is the equation
She sold 18 t-shirts.
Step-by-step explanation:
Since she sold t-shirts for 7 each, we need to find how many T-shirts she sold. 126 dollars is how much she made, so we need to divide.
126/7 = 18.
The equation would be:
7x = 126.
The measures of the angles of abc are given by the expression in the table
Answer:
∠A=125° and ∠B=35°
Step-by-step explanation:
We know that, by angle sum property of triangles,
∠A +∠B+∠C=180°
⇒ (6x−1)° +20° +(x + 14)°=180°
⇒ 6x−1 +20 +x + 14=180 [Open parenthesis]
⇒7x+33=180
⇒7x=180-33 [Subtracting 33 from both sides]
⇒7x=147
⇒x=21 [Divide 7 from both sides]
Now substitute value of x in the expressions of ∠A and ∠B.
Therefore, ∠A=(6(21)-1)°=(126-1)°=125°
∠B=(21+14)°=35°
Find the circumference of the object 6mm. Use 3.14 or {22}{7}
The circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.
What is circumference οf a circle?The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line.
Units like cm οr unit m are typically used tο measure it. The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.
The fοrmula fοr the circumference οf a circle is:
C = 2πr
where C is the circumference, π is pi (apprοximately equal tο 3.14 οr {22}/{7}), and r is the radius οf the circle.
In this case, the radius οf the οbject is 6mm. Therefοre, we can plug this value intο the fοrmula and use either 3.14 οr {22}/{7} fοr π:
C = 2 × 3.14 × 6mm
C = 37.68mm (rοunded tο twο decimal places)
C = 2 × ({22}/{7}) × 6mm
C = 37.71mm (rοunded tο twο decimal places)
Therefοre, the circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.
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The circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.
What is circumference οf a circle?The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line.
Units like cm οr unit m are typically used tο measure it. The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.
The fοrmula fοr the circumference οf a circle is:
C = 2πr
where C is the circumference, π is pi (apprοximately equal tο 3.14 οr {22}/{7}), and r is the radius οf the circle.
In this case, the radius οf the οbject is 6mm. Therefοre, we can plug this value intο the fοrmula and use either 3.14 οr {22}/{7} fοr π:
C = 2 × 3.14 × 6mm
C = 37.68mm (rοunded tο twο decimal places)
C = 2 × ({22}/{7}) × 6mm
C = 37.71mm (rοunded tο twο decimal places)
Therefοre, the circumference οf the οbject is apprοximately 37.68mm οr 37.71mm, depending οn whether we use 3.14 οr {22}/{7} fοr π.
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Complete question:
Find the circumference of the object which has a radius 6mm. Use 3.14 or {22}{7}.
please help this assignment is due tonight and i am very bad at math
the length of AC is 5. we can get the answer with the help of Pythagorean theorem in triangle ABC.
what is Pythagorean theorem ?
The Pythagorean theorem is a fundamental concept in geometry that relates to the relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
In the given question,
In triangle ABC, we have:
angle ABC = 90 degrees (given)
AB = 4 (given)
AD = 3 (given)
Let's call the length of AC "x". We want to find the value of x.
From the given information, we know that BD is the altitude of triangle ABC from vertex B to the side AC. Therefore, the length of BD is equal to the length of AD, which is 3.
Using the Pythagorean theorem in triangle ABD, we can find the length of the hypotenuse AB:
AB² = AD² + BD²
AB² = 3² + 4²
AB² = 9 + 16
AB² = 25
AB = 5
Now, we can use the Pythagorean theorem in triangle ABC to find the length of AC:
AC² = AB² + BC²
AC² = 5² + BC²
But we don't know the length of BC. However, we can use the fact that triangle ABD and triangle ABC are similar. This is because angle ABD is a right angle (from the definition of altitude BD), and angle ABC is a right angle (given), so angle ABD and angle ABC are both right angles. Therefore, the two triangles share angle A and are similar by the AA (angle-angle) similarity criterion.
Since triangles ABD and ABC are similar, we have:
AB/AD = AC/BD
Substituting the known values, we get:
5/3 = x/3
Solving for x, we get:
x = 5
Therefore, the length of AC is 5.
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Solving Problems Using Trigonometric Ratios Solve the trigonometry problems below
If a ramp is 3m high and 10m long. what is the measure of angle formed by the ramp and ground
Answer:
16.7 degrees
Step-by-step explanation:
We can use the tangent ratio of a right triangle to solve this problem.
The tangent of an angle is the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the ramp (3m) and the adjacent side is the length of the ramp (10m).
So we have:
tan(theta) = opposite / adjacent
tan(theta) = 3 / 10
To find the angle, we need to take the inverse tangent (or arctangent) of both sides:
theta = arctan(3 / 10)
Using a calculator, we get:
theta ≈ 16.7 degrees
Therefore, the angle formed by the ramp and ground is approximately 16.7 degrees.
You plan to borrow $3825 at 15% annual interest for 4 years. What will your monthly
payment be? Use the formula . Make sure to label each variable. must show work
We can use the formula for the monthly payment of a loan to calculate the amount we need to pay each month:
M = (P * r * (1+r)^n) / ((1+r)^n - 1)
Where:
M = the monthly payment
P = the principal (the amount borrowed)
r = the monthly interest rate (which is the annual interest rate divided by 12)
n = the total number of months in the loan term (which is the number of years multiplied by 12)
Plugging in the given values, we get:
P = $3825
r = 15% / 12 = 0.0125
n = 4 years * 12 = 48 months
M = ($3825 * 0.0125 * (1+0.0125)^48) / ((1+0.0125)^48 - 1)
M ≈ $94.87
Therefore, the monthly payment will be approximately $94.87.
an 800 deposit for 2 years months earned 200$ in interest
The marked price of a DVD player is $320. if a 15% discount is offered, find the actual selling price of the DVD player
The selling price of the DVD player after a 15% discount is applied can be found as follows:
Discount = 15% of the marked price = (15/100)*$320 = $48
Selling price = Marked price - Discount = $320 - $48 = $272
Therefore, the actual selling price of the DVD player after a 15% discount is $272.
Answer:
$272
Step-by-step explanation:
Formula:
Selling price = Marked price - Discount
We first find the discount by taking 15% off of $320 which is $48
We then insert the Maked price and the Discount into the formula which is:
Selling price = $320 - $48
Selling price = $272
A pizza parlor in Tallahassee sells a pizza with a 16-inch diameter. A pizza parlor in Jaco, Costa Rica, sells a pizza with a 27.8-centimeter diameter.
Part A: How many square inches of pizza is the pizza from Tallahassee? Show every step of your work. (1 point)
Part B: How many square centimeters of pizza is the pizza from Jaco, Costa Rica? Show every step of your work. (1 point)
Part C: If 1 in. = 2.54 cm, which pizza has the larger area? Show every step of your work. (1 point)
Part D: Using the diameter of each pizza, determine the scale factor relationship between the pizzas. (1 point)
A) 64π inches² B) 94.15π inches² C) the pizza from Tallahassee is larger. D) The scale factor relationship between the pizzas is: 1.462
Part A: The diameter of the pizza from Tallahassee is 16 inches, so the radius is 8 inches. The area of the pizza is:
A = πr²
= π(8)²
= 64π inches²
Part B: The diameter of the pizza from Jaco, Costa Rica is 27.8 centimeters. Converting this to inches, we get:
27.8 cm ÷ 2.54 cm/inch = 10.94 inches
The radius is 5.47 inches, so the area of the pizza is:
A = πr²
= π(5.47)²
= 94.15π inches²
Part C: Converting the area of the pizza from Tallahassee to square centimeters, we get:
64π inches² × (2.54 cm/inch)² = 1648.89 centimeters²
The area of the pizza from Jaco, Costa Rica is 94.15π inches² × (2.54 cm/inch)² = 594.85π centimeters². Therefore, the pizza from Tallahassee is larger.
Part D: The scale factor relationship between the pizzas is:
16 inches ÷ 27.8 cm × 2.54 cm/inch = 1.462
This means that the diameter of the pizza from Tallahassee is 1.462 times larger than the diameter of the pizza from Jaco, Costa Rica. Since area is proportional to the square of the diameter (or radius), the area of the pizza from Tallahassee is (1.462)² = 2.14 times larger than the area of the pizza from Jaco, Costa Rica.
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Help with math problems
The value of the surds are;
11. 12√3 - 16
13. -15√5 + 30
What are surds?Surds are defined as the values in square root that can no longer be further simplified into whole numbers or integers.
From the information given, we have that;
(-2√3 + 2)(√3 - 5)
expand the bracket, we have;
-2√3×√3 + 10√3 + 2√3 -10
-2(3) + 10√3 + 2√3 - 10
expand the bracket
-6 + 10√3 + 2√3 - 10
collect like terms
12√3 - 16
(-2- 3√5)(5 - √5)
expand the bracket
-2(5) + 25 - 15√5 + 3(5)
expand further
-10 + 25 - 15√5 + 15
collect the like terms
-15√5 + 30
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Pythagorean theorem find the length of the leg in the triangle 45, 51
Answer:
68.01
Step-by-step explanation:
let the unknown be y
opposite is 45
adjacent is 51
hypotenuse is ?
=y^2=45^2+51^2
y^2=2025+2601
y^2=4626
y=68.01
pls help lol it’s due tomorrow
The measure of angle D is 100°
What is sum of angle in a Triangle?A triangle is a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°.
Since the the sum of angle in a triangle is 180°, then to get the value of angle D will subtract the sum of the known angles from 180.
Therefore,
angle D = 180-( 40+40)
= 180-80
= 100°
therefore the measure of angle D Is 180°
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500. Mark this and return
The answer is failed to estimate number of rock songs on his MP3 player.
What is a MP3 player and how does it work?
It's a compressed digital audio file. A player stores these files on a memory chip so that you can play it back at your leisure. Contains a miniature hard disk drive, which can store huge quantities of data. MP3s usually contain music, but the format is also used for general audio files such as audiobooks and podcasts.
The statements that are true about Josiah's solution are:
He set up a proportion correctly using the information given.
He correctly solved for x, the number of rock songs on his MP3 player.
Therefore, he did not find the average of the number of rock songs in the sample to estimate the number of rock songs on his MP3 player.
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A cylinder has a height of 8 yards and a radius of 2 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answer:
the volume of the cylinder is approximately 100.48 yards.
[tex] \: \: [/tex]
Volume of a cylinder is:
V = πr²h
where r is the radius of the base, h is the height, and π is approximately 3.14.
Substituting the given values, we get:
V = π(2 yards)²(8 yards)
V = π(4 yards²)(8 yards)
V = 32π yards³
Using the approximation π ≈ 3.14, we get:
V ≈ 100.53 yards³
Therefore, the volume of the cylinder is approximately 100.53 cubic yards rounded to the nearest hundredth.
A pole that is 3.2 m tall casts a shadow that is 1.59 m long. At the same time, a nearby building casts a shadow that is 44.25 m long. How tall is the building? Round your answer to the nearest meter.
The building is 89 m tall.
What is proportional?
A comparison of two numbers is called a proportion. Two sets of supplied numbers are said to be directly proportional to one another in terms of proportion if they increase or decrease in the same ratio between them.
height of pole : 3.2 m
shadow of pole : 1.59 m
shadow of building : 44.25 m
let the height of building : x m
Now, according to the question:
height of pole/shadow of pole = height of building/shadow of building
Putting values into the equation.
we get, 3.2 / 1.59 = x / 44.25
3.2 × 44.25 = 1.59x
141.6 = 1.59x
∴ x = 141.6/1.59
= 89 m
hence, height of the building is 89 m.
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9.47,10.21,10.57,?,12.15 what pattern is it? What will
Be in the blank space
Answer: 10.95
Step-by-step explanation:
To identify the pattern, we need to look at the differences between the given numbers.
The difference between 10.21 and 9.47 is 0.74.
The difference between 10.57 and 10.21 is 0.36.
The difference between 12.15 and 10.57 is 1.58.
We can see that the differences between the numbers are not constant. However, the differences themselves follow a pattern: they are increasing by 0.38 each time.
So, to find the missing number, we can add 0.38 to 10.57:
10.57 + 0.38 = 10.95
Therefore, the missing number is 10.95.
Find
1-The mid point
2-The slop
3-The length
4 - The equation
Answer:
1, the mid point
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:
midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Substituting the given endpoints (4, -4) and (0, 9), we get:
midpoint = ((4 + 0) / 2, (-4 + 9) / 2) = (2, 2.5)
Therefore, the midpoint of the line segment with endpoints (4, -4) and (0, 9) is (2, 2.5).
2, the slope
The slope of the line passing through the points (4, -4) and (0, 9) can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Substituting the given coordinates, we get:
slope = (9 - (-4)) / (0 - 4) = 13 / (-4) = -3.25
Therefore, the slope of the line is -3.25.
3, the length
The length of the line passing through the points (4, -4) and (0, 9) can be found using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given coordinates, we get:
distance = sqrt((0 - 4)^2 + (9 - (-4))^2) = sqrt(16 + 169) = sqrt(185)
Therefore, the length of the line is sqrt(185).
4, the equation
The equation of the line passing through the points (4, -4) and (0, 9) can be found using the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is one of the points.
Substituting the given slope and one of the points, we get:
y - (-4) = -3.25(x - 4)
Simplifying, we get:
y + 4 = -3.25x + 13
y = -3.25x + 9
Therefore, the equation of the line passing through the points (4, -4) and (0, 9) is y = -3.25x + 9.
need help on this question :p
Answer:
d= 90 Degrees
e= 97 Degrees
f = 83
Answer:
see belowStep-by-step explanation:
To find:-
The values of e , f and d .Answer:-
We can see that angles e and 97° are vertically opposite angles. So they will be equal as vertically opposite angles are equal .
Hence here ,
→ e = 97°
Secondly e and f form linear pair , and the sum of linear pair is 180° . Hence here ,
→ e + f = 180°
→ 97° + f = 180°
→ f = (180-97)°
→ f = 83°
Same goes with d and 90° . They both form linear pair. So that ,
→ 90° + d = 180°
→ d = 180°-90°
→ d = 90°
These are the required values of the unknown angles.
Question 5(Multiple Choice Worth 2 points)
(Rotations MC)
Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of P′ if the preimage is rotated 90° counterclockwise.
P′(1, 5)
P′(−1, −5)
P′(5, −1)
P′(−5, 1)
The image vertices of P' if the preimage is rotated 90° counter clockwise is P'(-5,1)
What is image vertices?An image vertex refers to a point in the plane that results from applying a transformation to a given vertex. A transformation is a mathematical operation that changes the position, size, or shape of a figure.
According to question:The image vertices of P' when the preimage polygon PSRT is rotated 90° counter clockwise can be found by applying a transformation to each vertex of the polygon. This transformation involves switching the x- and y-coordinates of each vertex and negating the new y-coordinate.
(x, y) -> (-y, x)
For the vertex P(1, 5), we can apply this transformation to get the image vertex P':
P' = (-5, 1)
Similarly, we can apply the transformation to the other vertices of the polygon:
S(1, 0) -> S'(0, 1)
R(−2, −3) -> R'(3, -2)
T(−4, 2) -> T'(2, 4)
Therefore, the image vertices of P' are P'(-5, 1), S'(0, 1), R'(3, -2), and T'(2, 4).
This means that the rotated polygon has the vertices P', S', R', and T', which form a new polygon that is 90° counter clockwise rotated from the original polygon PSRT.
To know more about image vertices visit:
https://brainly.com/question/10722084
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