Therefοre, the sοlutiοn οf the given prοblem οf trigοnοmetry cοmes οut tο be cοt²(135-b) = 3.
A Trigοnοmetry is what?Relatiοnships between cubic splines and maths variable astrοphysics is believed tο have been created when the variοus fields came tοgether. Many metric prοblems can be sοlved triangle οr the results οf their calculatiοn can indeed be determined with the help οf precise mathematical methοds. Trigοnοmetry is the study οf six basic trigοnοmetric calculatiοns. They gο by a variety οf titles and acrοnyms, including sine, deviatiοn, angle, and sο fοrth (csc).
Here,
First, we need tο find the value οf cοs(b) using the given infοrmatiοn that sin(2b) = -1/5:
=> sin(2b) = 2sin(b)cοs(b)
=> -1/5 = 2sin(b)cοs(b)
We knοw that sin^2(b) + cοs^2(b) = 1, sο we can rearrange this equatiοn tο sοlve fοr cοs(b):
=> cοs²(b) = (1 - sin²(b))
Substituting this intο the equatiοn we fοund abοve:
=> -1/5 = 2sin(b)cοs(b)
=> -1/5 = 2sin(b)√(1 - sin²(b))
Squaring bοth sides and simplifying:
=> 1/25 = 4sin²(b)(1 - sin²(b))
=> 1/25 = 4sin²(b) - 4sin²(b)
=> 4sin²(b) - 4sin²(b) + 1/25 = 0
We can sοlve fοr sin^2(b) using the quadratic fοrmula:
sin²(b) = [4 ± √(16 - 4(4)(1/25))] / (2(4))
sin²(b) = [4 ± 2/5] / 8
sin²(b) = 3/10 οr 1/20
Since sin(2b) is negative, we knοw that sin(b) is negative as well, sο sin²(b) = 3/10. Therefοre:
cοs²(b) = 1 - sin²(b) = 1 - 3/10 = 7/10
Nοw we can use the identity
=> cοt²(θ) = 1 / [tan²(θ)] tο find cοt²(135-b):
1 / [tan(135-b)] = cοt(135-b)
By applying the fοrmula tan(x) = sin(x) / cοs(x):
=> tan(135-b) Equals cοs(135-b) / sin(135-b) (135-b)
The identities sin( + 90) = cοs() and cοs( + 90) = -sin() are used tο illustrate:
=> Cοs(90-b) = sin(135-b) = sin(45 + (90-b)) = sin (b)
=> Sin(90-b) = cοs(135-b) = cοs(45 + (90-b)) = cοs (b)
Using these numbers in place οf:
=> 1/tan(135-b) = sin(b) / cοs(b) (3)
=> 1 / [tan(135-b)] = cοt(135-b) = 1 / [(-1/√(3))²] = 3
Cοnsequently, cοt2(135-b) = 3.
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Complete question:
Solve for b in cot²(135-b) if sin²b = -1/5
Evaluate. Write your answer as a fraction or whole number without exponents. 3^-1
Answer:
1/3
Step-by-step explanation:
The exponent -1 indicates that we need to take the reciprocal of the base 3.
So, 3^(-1) = 1/3
Therefore, the answer is 1/3.
Answer:
1/3
Step-by-step explanation:
Rewrite the expression using the negative exponent rule [tex]b^{-n}[/tex] = [tex]\frac{1}{b^{n} }[/tex]
The answer is 1/3
Find the value of x if ABCD is a square ( given in picture)
The diagonal of the square bisect the angles. Therefore, the angle x in the square is 60 degrees.
How to find the angle of a square?A square is a quadrilateral with each angles equal to 90 degrees. The sum of angles in a square is 360 degrees.
The diagonal of a square is perpendicular to each other. It divided the square into two congruent isosceles triangle.
The diagonal of a square bisects the angles of a square. Therefore, the angles are 45 degrees each after bisection.
Hence, let's find the angle x in the square.
Therefore,
180 - 105 + x + 45 = 180
75 + x + 45 = 180
x + 120 = 180
subtract 120 from both sides of the equation
x + 120 - 120 = 180 - 120
x = 60 degrees
Therefore,
x = 60 degrees
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decrease 72 in the ratio 4:3
Answer:
4+3=7
4/7*72/1=288/7=41.1
3/7*72/1=216/7=30.9
41.1:30.9=4:3
PLEASE HELLP MY WITH THIS An experiment consists of randomly drawing a card and recording its suit, then rolling a die and recording whether it is even or odd. The following tree diagram represents some of the possible outcomes. A 2-column tree diagram: Card & Die. The card column shows Heart, Diamond, & Club, each of which branches to even & odd in the Die column.What needs to be done to complete the tree diagram?
Add "Spade" to the Card column, with branches to "Even" and "Odd" in the Die column. Thus, option 3 is correct.
What is the probability?Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.
Tο cοmplete the tree diagram, we need tο add the missing branch fοr the spades suit in the card cοlumn.
Here is the cοmpleted tree diagram:
We have added the missing branch fοr the spades suit, which alsο branches intο even and οdd fοr the die rοll. We have alsο filled in the οutcοmes fοr each branch οf the tree, which include the pοssible values fοr the card (2, 3, 4, 5, 6, οr 1 fοr Ace) and the die rοll (even οr οdd).
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A grounds committee of a housing community plans to build a basketball court in an empty rectangular field
The mathematical equation f(w) = w² - 6w provides a representation of the remaining surface area, measured in square meters, of the field following the construction of the basketball court.
The rectangular field has an area of length x width, which can be expressed as (2w)(w) = 2w² square meters.
The basketball court has an area of length x width, which can be expressed as (w)(w+6) = w² + 6w square meters.
To find the remaining area of the field after the basketball court is built, we need to subtract the area of the basketball court from the area of the rectangular field.
So the function f(w) representing the remaining area, in square meters, is:
f(w) = 2w² - (w² + 6w)
f(w) = 2w² - w² - 6w
f(w) = w² - 6w
Therefore, the function f(w) = w² - 6w represents the area, in square meters, remaining of the field once the basketball court is built.
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Complete question:
A grounds committee of a housing community plans to build a basketball court in an empty rectangular field.
1. The rectangular field-has a width of 2w meters and a length that is 13 meters longer than its width.
2. The basketball court has a width of w meters and a length that is 6 meters longer than its width.
Which function, f(w), represents the area, in square meters, remaining of the field once the basketball court is built?
I need help with this question
The value of cos C is 3/5
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
In a right angle triangle, the longest side is called the hypotenuse and the other two sides are called opposite and adjacent. The line facing the acute angle( tetha) is the opposite. The ratio of the sides with the acute angle are called trigonometric ratio.
sin(tetha) = opp/ hyp
cos( tetha) = adj/ hyp
tan(tetha) = opp/adj
In the triangle, using angle C,
opposite = 4
adjascent = 3 and hypotenuse = 5
cos (C) = 3/5
therefore the value of cos (C) = 3/5
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An item is regularly priced at $70. Shen bought it on sale for 20% off the regular price. How much did Shen pay?
An item is regularly priced at 70. Shen bought it on sale for 20% off the regular price. Shen paid 56 for the item on sale.
To determine how much Shen paid for the item on sale, follow these steps:
Find the discount amount
Subtract the discount amount from the regular price.
Calculate the discount amount.
Discount amount = Regular price × Discount percentage
Discount amount = 70 × 20%
Discount amount = 70 × 0.20
Discount amount = 14
Calculate the sale price.
Sale price = Regular price - Discount amount
Sale price = 70 - 14
Sale price = 56
Shen paid 56 for the item on sale.
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An investor buys stock in a company and in the 12 months after she invests the value of the stock decreases by 30%. By what amount will the value of the stock need to go up from there in order that the price of the stock will be equal to what investor first paid for it?
The value of the stock needs to go up by 42.86% to be equal to what the investor first paid for it.
Let's say the investor initially paid $100 for the stock. A 30% decrease in the value of the stock would mean it is now worth $70. To bring the value of the stock back up to $100, it needs to increase by $30, which is 42.86% of the current value ($30/$70).
Therefore, the value of the stock needs to go up by 42.86% from its current value for the investor to break even.
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Grant was making banners from cardboard as a picture to celebrate Parker‘s high school graduation. How many square inches of cardboard will Grant need for each banner that he makes?
5in
4in
8in
10in
For the standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
Define the term area?The amount of cardboard needed to make a banner depends on the size of the banner. If we know the dimensions of the banner, we can calculate the area of cardboard needed.
Assuming that the banner is a rectangle, let's say its width is w inches and its height is h inches.
Then, the area of the banner can be calculated as:
Area = width x height
Area = w x h
To find out how many square inches of cardboard are needed, we need to add a margin to the dimensions of the banner to account for the thickness of the cardboard. Let's say the margin is m inches.
Then, the width of the cardboard needed is (w + 2m) inches, and the height of the cardboard needed is (h + 2m) inches.
The area of the cardboard needed can be calculated as:
Area of cardboard = (width of cardboard) x (height of cardboard)
Area of cardboard = (w + 2m) x (h + 2m)
So, the total area of cardboard needed for one banner is:
Total area of cardboard = Area of cardboard + Area of margin
Total area of cardboard = (w + 2m) x (h + 2m) + 4m(w + h + 2m)
if we assume that the banner is 2 feet wide (24 inches) and 4 feet long (48 inches), and we add a margin of 1 inch on each side, then we can calculate the total area of cardboard needed as follows:
Total area of cardboard = (24 + 2) x (48 + 2) + 4(1)(24 + 48 + 2)
Total area of cardboard = 26 x 50 + 4(74)
Total area of cardboard = 1300 + 296
Total area of cardboard = 1596 square inches
So, for this standard size banner with a 1-inch margin, Grant would need approximately 1596 square inches of cardboard to make one banner.
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PLEASE HELP ME WITH GEOMETRY 4 QUESTIONS FOR 20 POINTS
Please help i dont understand your help helps me alot
Thank you so so much <3
Answer:
14
Step-by-step explanation:
6/9 = x+2/24
Cross multiply to expand
9( x + 2) = 24x 6
9x + 18 = 144
Subract 18 from both sides
9x = 126 Divide both sides by 9
X = 14
10/ 2x-9 = 20/9
Cross multiply
20( 2x - 9) = 10 x 9
40x - 180 = 90
Add 180 to both sides
40x = 270
Divide both sides by 40
X = 6.75
Scale question
Convert 240miles to inches
240 x 63, 660 = 15,206,400
Ratio is 3:15,206,400
Reduce to lowest term by divide both sides by 3
Scale is 1: 5068800
Find the length of MN. Round to the nearest tenth of a foot.
The length of MN is equal to: 32.2 ft.
What is Pythagorean theorem?In Mathematics, Pythagorean's theorem is modeled by the following mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the length of sides of a right-angled triangle.
In order to determine the length of MN in right-angled triangle LNM, we would have to apply Pythagorean's theorem.
LN² + MN² = LM²
16² + MN² = 36²
256 + MN² = 1,296
MN² = 1,296 - 256
MN² = 1,040
MN = √1,040
MN = 32.2 ft.
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Find sin(cos^-1(1/2)) and tan (sec^-1(x/3))
√3/2 and √3x / x.
The value of sin (cos-1 (1/2)) and tan (sec-1 (x/3)) are:Sin (cos-1 (1/2)):In the trigonometry section, the cosine inverse (or arccosine) is used to find the angle whose cosine value is equal to a given number.The cosine inverse (or arccosine) of a number is the angle whose cosine is equal to that number (cos-1). Therefore, cos-1 (1/2) represents the angle that has a cosine of 1/2.The sine is the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle.Sin (cos-1 (1/2)) = sqrt (1 - cos2 (cos-1 (1/2)))Since cos (cos-1 (1/2)) = 1/2, we can substitute it.Sin (cos-1 (1/2)) = sqrt (1 - (1/2)2) = sqrt (3/4) = √3/2Tan (sec-1 (x/3)):The secant inverse (or arcsecant) is used to find the angle whose secant value is equal to a given number.The secant inverse (or arcsecant) of a number is the angle whose secant is equal to that number (sec-1). Therefore, sec-1 (x/3) represents the angle that has a secant of x/3.The tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.Tan (sec-1 (x/3)) = sqrt (sec2 (sec-1 (x/3)))Since sec (sec-1 (x/3)) = 3/x, we can substitute it.Tan (sec-1 (x/3)) = sqrt (3/x) = √3 /√x = (√3 /√x) × (√x /√x) = √3x / xTherefore, sin (cos-1 (1/2)) = √3/2 and tan (sec-1 (x/3)) = √3x / x.
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make a mathematical expression of the dimension
The expression of the dimensions are 3w - 2 by w
How to determine the expression of the dimensionsFrom the question, we have the following parameters that can be used in our computation:
The length of a rectangle is 2 less than 3 times as long as the width
Using the following variable definitions, we have
l = the length of the rectanglew = the width of the rectangleBased on the given information, we can express the length (l) in terms of the width (w):
l = 3w - 2
Hence, the dimensions are 3w - 2 by w
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For circle B, if BG=BE, what conclusion can be made
If BG=BE, we can conclude that triangle BGE is an isosceles triangle.
In a circle, the radius is a line segment that connects the center of the circle to any point on the circle. Therefore, BG and BE are both radii of the circle. In an isosceles triangle, two sides have the same length, and the third side is a different length. In this case, the two sides with the same length are BG and BE, and the third side is GE. Since BG and BE are radii of the circle and therefore have the same length, we can conclude that triangle BGE is isosceles, and the angles opposite BG and BE are congruent.
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What is the volume of a cylinder with a height of 2 feet and a radius of 6 feet?
Use 3.14 for pi.
please help me use this for a study guide i have a test tomorrow!!
The volume of a cylinder is πr²h.
Given, that H = 2 ft and R = 6 Feet.
So V = πr²h = 3.14 x 6 x 6 x 2
= 3.14 * 72
= 226.08 ft³
Answer:
The volume of the cylinder is 226.08 feet^3
Step-by-step explanation:
The volume of a 3-d shape with sides straight up is
BaseArea × height.
For a cylinder the base is a circle. Area of a circle is pi•r^2
So the Volume of your cylinder is:
V = pi•r^2 • h
Fill in the info given.
V = 3.14 • 6^2 • 2
= 226.08
The units for volume are cubed, that is, 3rd power.
So 226.08 cubed ft
or 226.08 ft^3
Hope this helps!
Which of these could be the area of Circle B? b. About 300 in2
c. About 900 in2
d. About 2,700 in2
The area of Circle B could be about 300 in², about 900 in², or about 2,700 in² depending on its radius.
To determine which one is correct, you would need to know the radius or diameter of the circle.
Use the formula for the area of a circle, which is
A = πr²,
where A is the area and
r is the radius.
If you have the radius, plug it into the formula and calculate the area.
Compare the calculated area to the options provided (300 in², 900 in², or 2,700 in²)
to determine which one is closest to the area of Circle B.
Without more information about Circle B's radius or diameter, it is impossible to determine the exact area from the
options given.
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I don’t understand can you help me please
Properties of trapezoids UC^(9) Quadrilateral HIJK is an isosceles trapezoid, HJ=7z-94, and IK=2z+76. What is the value of z ?
The value of z can be determined by solving the equation 7z-94 = 2z+76, which yields z=35.
To determine the value of z in the given equation, it is necessary to solve the equation 7z-94 = 2z+76. Begin by subtracting 2z from both sides of the equation, which yields 7z-2z-94 = 76. Simplifying this yields 5z-94 = 76. To solve for z, add 94 to both sides of the equation, which yields 5z = 170. Dividing both sides by 5 yields z = 34. Since the equation is not asking for an exact value, it can be rounded to the nearest whole number, which is 35. Therefore, the value of z is 35.
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Pls answerrrrr
with simple working
Answer:
-137
Step-by-step explanation:
23, 15, 7, -1, -9,-17...........
-8 -8 -8 -8.....
∴ -8n+23
if n = 20
-8(20)+23=-137
Answer:
-137
Step-by-step explanation:
The pattern is -8 every term so
15 + (-8(20-1)) = -137
its pretty much multiplying the rate by what term you want. you subtract the 1 because you started with the first term.
What is the domain of H(t)?
The domain of the given function H (t) is 0 ≤ t ≤ 40.
What is the domain of a function?
The collection of all the values for which a function is defined is known as the domain of that function.
We are given that the height of a model rocket, H (t) is a function of time since it was launched, t.
From the graph, we can see that the value of t is represented on the x- axis is ranging from 0 to 40.
Hence, the domain of the given function H (t) is 0 ≤ t ≤ 40.
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You run a trail at 7 mph and walk back at 3 mph. If your total time is 2 hours, your round-trip distance is how many miles?
Point P divides the directed line segment from point A(-4,-1) to point B(6,4) in the ratio 2:3. The coordinates of point P are
The coordinates of point P are(0,1)
Line segment:A part of line which has 2 end points and it is also can be measured
example:
the objects which has starting and the ending point can be taken for consideration
pencil: which is straight and has a fixed length of about 16-22 cm
coordinates:The intersection of points in a grid system
example the points(25,10) is 25 units long and 10 units up
A(-4,-1) B(6,4) in the ratio 2:3
x1=-4, x2=6,y1=-1,y2=4,m=2,n=3
x=(mx2+nx1)/m+n
=2*6+3*(-4)/2+3
=12-12/5
=0/5
=0
y=my2=ny1/m+n
=2*4+3(-1)/2+3
=8-3/5
=5/5
=1
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Which equation represents exponential growth?
Answer:
Option C) is the correct answer.
Olivia ate at the same restaurant three times. Each visit, she ordered a sandwich and left a $2. 25 tip. She spent a total of $39. What is an equation that represents this situation, if c represents the cost of a salad?
Each visit, Olivia ordered a sandwich and left a $2. 25 tip. She spent a total of $39. Therefore, an equation that represents this situation, if c represents the cost of a salad is 4(x+2.25) = 39.
Equation:
An equation is a formula that expresses that two expressions are equal by joining them with the equal sign =.The word comparison and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined to contain one or more variables, and in English any well-formed formula composed of two expressions linked by equal signs is an equation.
According to the Question:
Let the cost of each salad = c
Therefore we can write
4(x+2.25) = 39
or, x+ 2.5 = 39
or, x = 39 − 2.5
or, x = 39 − 2.5
or, x = 26.5
Therefore, The equation that represents this situation, if c represents the cost of a salad is 4(x+2.25) = 39.
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What is 5 to the fourth power?
The correct response, based on the facts provided, is 625.
What does a math power mean?
When a base number is raised to an exponent in mathematics, the exponent represents how many times the base number has been multiplied, and the base amount is the factor that is multiplied by itself.
What do you call 5 to the power of?
In mathematics and mathematics, the fifth power, or subsolid, of a number, n, is obtained by multiplying five occurrences of n around each other:[tex]n⁵ = n × n × n × n × n.[/tex]The fourth power of a number or the squares of a number of times its cube can also be used to create fifth powers.
5 to the fourth power (also written as 5⁴) is:
[tex]5 × 5 × 5 × 5 = 625[/tex]
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Find the area of the figure. Round to the nearest tenth.
A 23.4 ft^2
B 28.3 ft^2
C 29.7 ft^2
D 36.0 ft^2
Answer:
C
Step-by-step explanation:
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
What is diameter?Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.
To solve for the area of a rectangle we use the expression:
A = length × widthInserting the dimensions of the rectangle:
4 × 4 = 36So, the area of the rectangle is 36 square feet.
Because the rectangle has a gap on the left side in the shape of a semicircle, we can first solve for the area of that semicircle.
How do we solve for the area of a semicircle?if you know the radius of a semicircle, you can use the formula:
[tex]A = \frac{\pi r^{2} }{2}[/tex]
But first, we need to solve for the radius.
Because the diameter is twice the size of the radius, we can use this expression:
4 ÷ 2 = 2So, the radius of the semicircle is 2ft.
Inserting 2 into the formula for r:
[tex]A = \frac{\pi 2^{2} }{2}[/tex]First, we need to evaluate the exponent:
[tex]A = \frac{\pi 2^{2} }{2} = \frac{\pi4}{2}[/tex]Dividing 4 by 2 gives:
[tex]\pi2[/tex]This simplifies to:
6.28319Subtracting that from the area of the rectangle:
36 - 6.28319 = 29.71681 = [tex]29.7ft^{2}[/tex] (Rounded to the nearest tenth)
Therefore, the answer is C.
6x + 5 = 5x + 8 + 2x
Is x = 3 a solution? Explain.
the alvin secretarial service procures temporary office personnel for major corporations. they have found that 50% of their invoices are paid within ten working days. a random sample of 12 invoices is checked. what is the probability that exactly 5 of the invoices will be paid within ten working days? round your answer to four decimal places.
The probability that exactly 5 of the invoices will be paid within ten working days is 19.34% or 0.1934.
This is a binomial distribution problem, with n = 12 (the sample size) and p = 0.5 (the probability of success, which is an invoice being paid within ten working days). We want to find the probability that exactly 5 of the invoices will be paid within ten working days.
Using the binomial probability formula, the probability of exactly 5 invoices being paid within ten working days is:
P(X = 5) = (12 choose 5) * (0.5)^5 * (1-0.5)^(12-5) = 0.1934
Where (12 choose 5) is the binomial coefficient, which represents the number of ways to choose 5 invoices from a sample of 12.
Therefore, the correct answer is 0.1934 rounded to four decimal places.
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8) Decide whether \( X \) and \( Y \) are good candidates for linear regression in the scatterplot given.
It is not possible to determine the relationship between the two variables based on this scatterplot.
The scatterplot below does not show a good candidate for linear regression because the points do not follow a clear pattern. There is no consistent trend that shows a correlation between the X and Y variables. Therefore, it is not possible to determine the relationship between the two variables based on this scatterplot.The linear regression is a statistical technique that enables the analysis of relationships between two or more continuous variables. The method attempts to find the line of best fit, which represents the overall relationship between the two variables. A scatterplot, which is a graphical display of a dataset, can be used to determine whether two variables are good candidates for linear regression.In order for two variables to be a good candidate for linear regression, they must have a strong positive or negative correlation. In other words, the points on the scatterplot must follow a clear pattern that shows a linear relationship between the X and Y variables. If there is no clear pattern or the points are randomly scattered, then it is not possible to determine the relationship between the two variables based on a linear regression model.
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7. Find the x-intercept of the line having
the equation 2x - 5y = 8.
A. -5/2
B. 4
C. -4
D. -2/5
E. 2/5
Answer:
E
Step-by-step explanation:
My answer
[tex] \frac{2}{5} [/tex]