If tan A= 28 /45 and cosB= 13 12 and angles A and B are in Quadrant I, find the value of tan(A+B).
The value of Tan A + B is 6.009.
How to solve for the tangent[tex]sin^2 A + cos^2 A = 1sin^2 A = 1 - cos^2 Asin A = sqrt(1 - cos^2 A)sin A = sqrt(1 - (28/45)^2)sin A = sqrt(1 - 784/2025)sin A = sqrt(1241/2025)cos A = 28/45\geq[/tex]
We have to solve for Tan B
[tex]sin^2 B + cos^2 B = 1sin^2 B = 1 - cos^2 Bsin B = sqrt(1 - cos^2 B)sin B = sqrt(1 - (13/12)^2)sin B = sqrt(55/144)Therefore, tanB = sinB / cosB = (sqrt(55/144)) / (13/12) = (12 sqrt(55)) / 143[/tex]
[tex]tan(A+B) = (3207 \sqrt{55}) + 1804 \sqrt{124})) / (3115 - 207 \sqrt{(341)}[/tex]
= 6.009.
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What are the features of the function f(x)=2log3 (x+7)graphed below?
The key features of the function f(x) = 2log₃(x+7) graphed below include the following:
The domain of this function is [-7, ∞]The range of this function [-∞, ∞] or all real numbers.x-intercept = (-6, 0).y-intercept = (0, 2log₃(7)).Vertical asymptote is at: x = -7No extreme points.What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this logarithmic function shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-7, ∞].
Range = [-∞, ∞].
In conclusion, we can logically deduce that this logarithmic function has a vertical asymptote is at x equal to negative seven.
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Julia volunteers at a zoo. She records the number of people in each group of visitors in one day.
Based on Julia's data, if a larger zoo has 600 groups of visitors in a day, how many of them would you expect to be groups of 5 or more?
People in Group 1 2 3 4 5 6 7 8
Frequency
9 52 27 38 16 6 5 7
about
groups
We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.
To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.
To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:
Group Size Frequency Relative Frequency
1 9 9/150 = 0.06
2 52 52/150 = 0.35
3 27 27/150 = 0.18
4 38 38/150 = 0.25
5 16 16/150 = 0.11
6 6 6/150 = 0.04
7 5 5/150 = 0.03
8 7 7/150 = 0.05
We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.
To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:
Number of groups with 5 or more people = 600 x 0.23 = 138
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Qd=50-4Px+0.5I+10Py-2Pz
Answer:
The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.
To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.
We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).
Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.
Step-by-step explanation:
6) The height h(t) of a projectile is given by
h(t) = −t² + 7t + 9.
Find the time (s) at which the rocket is
20 ft above the ground.
Answer:
2.38 s
4.62 s
Step-by-step explanation:
The height of a projectile is given by the function:
[tex]h(t) = -t^2 + 7t + 9[/tex]
where:
h(t) is the height of the rocket about the ground (in feet).t is the time (in seconds).To determine the time(s) at which the rocket is 20 ft above the ground, set h(t) = 20 and solve for t.
[tex]-t^2+7t+9=20[/tex]
To solve the equation for t, complete the square.
Subtract 9 from both sides:
[tex]-t^2+7t=11[/tex]
Divide both sides by -1:
[tex]t^2-7t=-11[/tex]
Add the square of half the coefficient of the term with the variable "t" to both sides of the equation:
[tex]t^2-7t+\left(\dfrac{-7}{2}\right)^2=-11+\left(\dfrac{-7}{2}\right)^2[/tex]
Simplify:
[tex]t^2-7t+\dfrac{49}{4}=\dfrac{5}{4}[/tex]
We have now created a perfect square trinomial on the left side of the equation. Factor the perfect square trinomial:
[tex]\left(t-\dfrac{7}{2}\right)^2=\dfrac{5}{4}[/tex]
To solve for t, square root both sides:
[tex]t-\dfrac{7}{2}=\pm \sqrt{\dfrac{5}{4}}[/tex]
[tex]t-\dfrac{7}{2}=\pm\dfrac{\sqrt{5}}{2}[/tex]
Add 7/2 to both sides of the equation:
[tex]t=\dfrac{7}{2}\pm\dfrac{\sqrt{5}}{2}[/tex]
[tex]t=\dfrac{7\pm\sqrt{5}}{2}[/tex]
Therefore, the times at which the rocket is 20 ft above the ground is:
[tex]t=\dfrac{7-\sqrt{5}}{2}=2.38\; \rm s[/tex]
[tex]t=\dfrac{7+\sqrt{5}}{2}=4.62\; \rm s[/tex]
Isosceles triangle LMN is graphed with vertices L(0, 1), M(3, 5), and N(6,1). What is the slope of side LN?
Negative StartFraction 4 over 3 EndFraction.
0
StartFraction 4 Over 3 EndFraction.
3
\
helphelphelphelphelphelphelphelphelphelphelphelphelp
The volume of the flower vase, can be found to be 2, 199 cm ³.
How to find the volume ?The volume of the flower vase can be found by subtracting the volume of the cone from the volume of the rectangular prism.
Volume of rectangular prism :
= Length x Width x Height
= 20 x 12 x 10
= 2, 400 cm ³
The volume of the cone is:
= π x radius ² x height / 3
= π x 4 ² x 12 / 3
= 201. 06 cm ³
Volume of vase:
= 2, 400 - 201. 06
= 2198.94
= 2, 199 cm ³
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Harold ran 3 miles in 24 minutes. How long would it take him to run 4 miles?
Answer:32 minutes
Step-by-step explanation:
He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes
The football players had to sell DEVIL FOOTBALL t-shirts to raise money for their next uniforms.They charged $14 for short sleeve shirts and $17 for long sleeve shirts. At the end of the fundraiser, they had sold 24 shirts and had made $378. How many of each type of shirt did they sell?
Use
S as the number of short sleeve shirts and
L as the number of long sleeve shirts.
PLS HELP
Answer:
Let's set up a system of equations to solve for S and L:
S + L = 24 (they sold a total of 24 shirts)
14S + 17L = 378 (the total amount made from selling the shirts was $378)
We can solve for one variable in the first equation and substitute it into the second equation:
S = 24 - L
14(24 - L) + 17L = 378
336 - 14L + 17L = 378
3L = 42
L = 14
So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:
S + 14 = 24
S = 10
Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.
Ben wants to compare the scores of this year's basketball games to the scores of last year's games. He made the following double stem-and-leaf plot to make
his comparison.
Comparison of
Basketball Scores
Between the Last
Two Years
Last
Year
995
97753
6654
9
Stem
OB. 20
OC 16.
0
1
2
3
4
5
What is the difference between the median score this year and the median score last year?
OA 18
OD. 17
This
Year
999
7889
456778
233
2
Accounting question.help
The computations of the net profit or loss using the following cost valuation methods are as follows:
FIFO, net profit = $20,000
Weighted Average, net profit = $17,555.54.
What are the inventory cost valuation methods?The inventory cost valuation methods include FIFO (First In, First Out), LIFO (Last In, First Out), WAC (Weighted Average Cost), and Specific Identification.
Under the FIFO basis, the cost of inventory is evaluated based on the assumption that inventory that are first brought in are the first to be sold.
Under the Weighted Average Cost method, the average cost is computed by dividing the total cost of goods available for sale by the number of units.
Other inventory cost valuation methods include LIFO and Specific Identification.
FIFO Basis:Cost of Goods Sold = $80,000 ($10,000 x 3 + $12,000 x 2 + $13,000 x 2)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $20,000 ($106,000 - $80,000 - $6,000)
Weighted Average Cost Basis:Weighted Average Cost per tractor = $11,777.78 ($106,000 ÷ 9)
Cost of Goods Sold = $82,444.46 ($11,777.78 x 7)
Sales Revenue = $106,000 ($15,000 x 7)
Overhead = $6,000
Net Profit = $17,555.54 ($106,000 - $82,444.46 - $6,000)
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Bacteria was put in a petri dish with antibacterial soap. Determine the logarithmic regression of the bacteria. Use either a
calculator or spreadsheet program.
Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.
Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel
Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."
In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.
The resulting equation is
Bacteria = 447.91 * ln(Time) - 1733.1
This equation represents a logarithmic regression of the bacteria population over time.
To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation
Bacteria = 447.91 * ln(12) - 1733.1
Bacteria ≈ 44.1
So we would predict a bacteria population of about 44.1 at 12 hours.
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Please help! I will mark brainiest! I do not understand the parenthesis being added.
Answer:
<4√97,-9√97>
Step-by-step explanation:
First, we need to find the values of A-C and B-D:
A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >
B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >
Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:
|A-C| = √((-4)^2 + 9^2) =√(97)
Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:
|A-C|(B-D) = √(97) * < 4, -9 >
= < 4√(97), -9√(97) >
So the final answer is < 4√(97), -9√(97) >.
I know the answer, but I don't understand how. The answer is 90 degrees
In the circle the measure of arc YP as per the given measurements is equal to option D. 166°
In the circle,
Measure of arc ST = 70°
Measure of arc RS = 96°
Measure of angle YZP = 128°
Arc formed by vertically opposite angles are equal
This implies,
Measure of arc YT = Measure of arc PR
Measure of arc ST + Measure of arc RS + Measure of arc YT = 180°
⇒70° + 96° + Measure of arc YT = 180°
⇒Measure of arc YT = 180° - 166°
⇒Measure of arc YT = 14°
⇒ Measure of arc PR = 14°
Measure of arc YP = 360° - ( Measure of arc (PR + RS + ST + TY ))
⇒ Measure of arc YP = 360° - ( 14° + 96° + 70° + 14° )
⇒Measure of arc YP = 360° -194°
⇒ Measure of arc YP = 166°
Therefore, the measure of arc YP is equal to option D. 166°
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Find the 13th term of the geometric sequence 4, −8, 16, ...
Answer:
Step-by-step explanation:
Parallelogram EFGH, E(-1,5), F(2,8), G(4,4), and H(1,1). Find the perimeter and area of the parallelogram. Round to the tenths place
The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.
To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:
EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)
FG =√(20)
GH = √(18)
HE = √(20)
Therefore, the perimeter is:
Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4
Similarly,
The area of the parallelogram is given as,
= 18 square centimeters
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You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground. How steep was the ramp? We are missing a side or and angle? Regular or Inverse Trig?
The steepness of the ramp is approximately 56 feet.
How to find the steepness of the ramp?You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.
Therefore, let's find how steeped the ramp is.
Hence, using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
55² + 10² = c²
c² = 3025 + 100
c² = 3125
square root both sides of the equation
c = √3125
c = 55.9016994375
c = 56 feet
Therefore,
steepness of the ramp = 56 feet
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peaceful travel agency offers vacation packages each vacation packages includes a city, and a airline.The agency has 6 cities, and 2 airlines to choose from.how many different vacation packages do they offer
Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.
How to Solve the Problem?To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:
Add up to number of get-away bundles = number of cities x number of airlines
Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:
Add up to number of get-away bundles = 6 x 2 = 12
In this manner, Serene Travel Organization offers 12 diverse get-away bundles.
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On the first day of school, the eighth graders get to select one of two dances to attend for no cost. They can attend either the Fall Fling or the Spring Social for free.
Of the 144 boys in eighth grade, 82 choose to attend the Fall Fling for free. Of the 156 girls in eighth grade, 75 choose to attend the Spring Social for free.
The president of the eighth grade class constructed the following two-way table to show the numbers of boys and girls that choose each dance. Some of the values and totals are incorrect.
If the following two-way table was constructed from the data, select all the values the president of the eighth grade class has in
the correct spots.
The two-way table constructed from the data showing the numbers of boys and girls that choose each dance category should look like this:
Boys Girls Total
Fall Fling 82 81 163
Spring Social 62 75 137
Total 144 156 300
What is a two-way table?A two-way table is a data display tool that displays the frequencies for two different categories collected from a single group.
A two-way table use rows to represent one category variable and the columns to represent a second category variable, while the cells display the proportions or frequencies of each row and column combination.
The total number of boys in eighth grade = 144
The number of boys who choose to attend the Fall Fling = 82
Therefore, the number of boys who attend the Spring Social = 62 (144 - 82)
The total number of girls in eighth grade = 156
The number of girls who choose to attend the Spring Social = 75
Therefore, the number of girls who attend the Fall Fling = 81 (156 - 75)
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Answer:
62, 82, 163, 300
Step-by-step explanation:
I got this on study island
Trigonometry question. Please help me
The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
What is a rectangular base pyramidIn a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.
The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.
The apex angles bec and aed formed by the opposite width of the rectangle base are equal.
In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
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The ratio of alcohol and water in a mixture of 72 units is 2 ratio 1 what is the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2
The amount of water needed is 72 liters.
Given that, the ratio of the alcohol and water in a mixture of 72 units is 2 ratio 1, we need to find the amount of water that must be added to the mixture in order to make this ratio 1 ratio 2,
So,
The quantity of water in it = 72 / 3 × 1 = 24
New ratio =
48 / 24+x = 1/2
96 = 24+x
x =72
Hence, the amount of water needed is 72 liters.
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There are 140 in the seventh grade, and 10% are in the Environmental Club. How many students are in the Environmental Club?
Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations to solve the length of the room is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
c) ( y + 25 ) ( y - 30 ) = 0
Given data ,
Let the area of a rectangular room is 750 square feet.
Let the width of the room is 5 feet less than the length of the room
So , on simplifying , we get
w = l - 5
Area of rectangle = length x width
And , A = l x w
A = l ( l - 5 )
750 = y ( y - 5 )
Therefore , the equation is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
On simplifying the quadratic equation , we get
c) ( y + 25 ) ( y - 30 ) = 0
Hence , the length of the rectangular room is solved
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The complete question is attached below :
Which equations can be used to solve for y, the length of the room? Select three options.
a) y(y + 5) = 750
b) y² – 5y = 750
c) 750 – y(y – 5) = 0
d) y(y – 5) + 750 = 0
e) (y + 25)(y – 30) = 0
Suppose it is known that the proportion of students at a local high school that take public transit to school is p = 0.15
The distribution of the sample is approximately normal with a mean of 0. 15 and a standard deviation of 0. 03852.
How to describe the distribution ?One can utilize the Central Limit Theorem (CLT) for proportions to detail the dispersion of the sample proportion. Explained by the CLT, if the size of the sample is sufficiently significant enough, then the distribution with respect to the sample proportion will be mostly indistinguishable from a typical distribution.
np ≥ 10
n(1-p) ≥ 10
Given that both conditions are fulfilled, we can essentially posit that the said sample proportion distribution is almost normal. In light of this knowledge, it would be pertinent to ascertain the mean (μ) and standard deviation (σ) of the sample proportion distribution.
Mean = p = 0.15
Standard deviation:
= √ ( ( 0.15 x ( 1 - 0. 15 ) ) / 86 )
= 0.03852
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PLEASE HELP FAST I’M HAVING A LITTE TROUBLE PLEASE GIVE THE RIGHT ANSWER
Answer:
C) 1/2 and 8
Step-by-step explanation:
-2x + y = 7 Eq. 1
6x + y = 11 Eq. 2
From Eq. 1:
y = 7 + 2x Eq. 3
From Eq. 2:
y = 11 - 6x Eq. 4
Equalyzing Eq. 3 and Eq. 4:
7 + 2x = 11 - 6x
2x + 6x = 11 - 7
8x = 4
x = 4/8
x = 1/2
From Eq. 3:
y = 7 +2* 1/2
y = 7 + 1
y = 8
Check:
From Eq. 2
6x + y = 11
6*1/2 + 8 = 11
3 + 8 = 11
I'm very confused on this question.
The value of angle x is determined as 107⁰.
What is the x?
The value of angle x is calculated by applying principle of intersecting chord theorem.
The intersecting chord theorem states that half of the difference between the arc of two intersecting chords is equal to the tangent angle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠MNP = ¹/₂( arc MLP - arc MP )
x = ¹/₂ [(360 -73) - (73)]
x = ¹/₂ (287 - 73 )
x = ¹/₂ (214)
x = 107⁰
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50 points. Out of 120 seventh and eighth grade CAVA students there were 30 students that chose Music as their elechive course and the rest chose World Language. There were a total of 60 eighth grade students and 40 of them chose
World Language as their elective.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table (6 pts)
Answer:
Based on the informtaion provided, the two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.
Total number of students = 120
This means that the number of students in 7th grade : 120- 60 = 60
Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.
This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.
Here, 40 eighth grade students chose World Language as their elective.
This means that out of total 90 students 90 - 40 = 50 students of 7th Grade chose World Language as their elective.
Now consider the 8th grade students,
Out of 60 students 40 chose World Language.
So, 60 - 40 = 20 must chose Music as their elective.
Now consider the 7th grade students,
Out of 60 students 50 chose World Language.
So, 60 - 50 = 10 students must chose Music as their elective.
Hence the required two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
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In the first group of 5, average was 6.5. In the second group of 15, the average was 4.5. What was the overall average of the two groups?
Step-by-step explanation:
First group of five total score = 5 * 6.5 = 32.5
Group of fifteen total score = 15 * 4.5 = 67.5
total score of 20 is 67.5 + 32.5 = 100
Average = 100 /20 = 5.0
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.
Given two points.
We have to find the slope of the line.
Slope of a line passing through (x, y) and (x', y') is,
Slope = (y' - y) / Ix' - x)
Here two points are,
(-3, -1) and (3, -10)
Slope = (-10 - -1) / (3 - -3)
= -9 / 6
= -3/2
Hence the slope of the line is -3/2.
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Find the x intercept of the line 1x -2y =23
Answer: x=23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When you have a value on the x-axis, your y=0
plug in y=0 to find your x-intercept
1x-2(0)=23
1x=23
x=23