A 12-foot ladder is resting against a wall and makes an angle of 52 degrees with the ground, the height to which the ladder will reach the wall is 9.456 foot.
What is height?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base and something above it. Height is a term used to describe everything that may be measured vertically, high or low.
From the lowest to the highest point to the lowest point, it calculates the vertical distance. In general, it refers to a coordinate geometry object's measurement along the y-axis.
let, h = height of ladder
Given that,
length of ladder = 12 ft
angle with the ground = 52°
As we know,
sinθ = h/12
or, sin (52°) = h/12
or, 0.7880 = h/12
or, h = 9.456 foot.
the height to which the ladder will reach the wall 9.456 foot.
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the perimeter of a square is 48 centimeters, what is the area in square centimeters
Answer:
144cm²
Step-by-step explanation:
If the square is perfectly even on all sides, the you first need to divide 48 by 4, as a square has 4 sides.
48/4 = 12cm
Then, to find the area, you need to multiply 12 by 12.
12 cm x 12 cm = 144cm²
Hope this helps :)
5(x+6) - 2x = 3(x+10)
Answer:
All Real Numbers
Step-by-step explanation:
I assume you are solving for x.
The Interval Notation would be: (-∞,∞)
help ???????????????
a. 4(x - 5)^2
= 4 * (x - 5)^2
= 4 * ((x - 5) * (x - 5))
= 4x^2 - 40x + 100
b. 3(x + 1) (2x - 9)
= (3(x + 1)) (2x + −9)
= (3(x + 1))(2x) + (3(x + 1))(−9)
= 6x^2 + 6x − 27x − 27
= 6x^2 − 21x − 27
c. -2(4x + 2)^2
= -2 * (4x + 2)^2
= −2 * ((4x + 2) * (4x + 2))
= 32x^2 − 32x − 8
or d. -2(4x + 2)^2 - 5 (with subtracting 5)
= −32x^2 + −32x + −8 + −5
= (−32x^2) + (−32x) + (−8 + −5)
= −32x^2 + −32x + −13
d. -3(5x - 2)^2 + 5 (with negative)
= 75x^2 + −60x + 12 + 5
= 75x^2 + −60x + 12 + 5
= (75x^2) + (−60x) + (12 + 5)
= 75x^2 + −60x + 17
or d. 3(5x - 2^2 + 5 (without negative)
= (3)(5x + −4 + 5)
= (3)(5x) + (3)(−4) + (3)(5)
= 15x − 12 + 15
= 15x + 3
Determine if the triangle pairs are similiar.
Yes , the triangles ΔSTU and ΔSRQ are similar triangles
What are similar triangles?
If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔSTU
Let the second triangle be ΔSRQ
Now , for the triangles to be similar , the corresponding sides of the triangles should be in the ratio
So , on simplifying , we get
The measure of side ST = 21
The measure of side SU = 35
The measure of side SQ = 6
The measure of side SR = 10
Now , for similar triangles ,
ST / SQ = SU / SR
Substituting the values in the equation , we get
21 / 6 = 35 / 10
3.5 = 3.5
Therefore , the corresponding sides of the triangles are equal
Hence , the pair of triangles are similar triangles
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Age is an example what kind of data categorical or quantitative?
Age, BMI, creatinine, and the amount of time between conception and death are a few examples of quantitative characteristics.
How do you know if data is categorical or quantitative?Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data reflect groupings is referred to be a categorical variable.A categorical variable's data will always be qualitative, while a numeric variable's data will always be quantitative. As a result, based on whether the variable is numeric or categorical, you may determine the kind of data before it is collected.Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data. Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.Learn more about quantitative data refer to :
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Vashti is designing the cover of the school yearbook. She wants to draw a flower on the cover that looks the same for each rotation of 45 degrees. How many petals should the flower have?
The number of petals that the flower should have is of:
8 petals.
When does a figure has rotational symmetry?A figure has rotational symmetry when it can be rotated by an angle measure which is greater than 0º and less than 360º and the rotated image is equals to the original figure, that is, the image is equals to the pre-image.
In this problem, we want the flower to have a rotation symmetry of 45 degrees.
The total angle measure of the flower is given as follows:
360º.
Then the number of petals needed for the flower to have a rotational symmetry of 45º is calculated as follows:
360/n = 45.
Applying cross multiplication, we have that:
45n = 360
n = 360/45
n = 8 petals.
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The video game club lost 8 members which was 28% of their group.
What was the original attendance of the video game club?
HELP!!!
The original attendance of the video game club was 28.57 members.
To determine the original attendance of the video game club, you can use the following formula:
Original attendance = (Number of members lost) / (Percent of group that left)
Plugging in the values from the problem, we get:
Original attendance = (8 members) / (28%)
To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:
Original attendance = (8 members) / (0.28)
Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:
Original attendance = 28.57 members
Therefore, the video gaming club had 28.57 members when it first started.
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14. Harold borrowed $9,000 for 5 years at an APR of 3.6%.
a. What is Harold's monthly payment? Round to the nearest cent. (Round your answer to the nearest cent and use the rounded answer for further calculations)
b. What is the total amount that Harold paid in monthly payments for the loan?
c. What is the amount Harold will pay in finance charges?
a. Harold's monthly payment is given as follows: $164.13.
b. The total amount paid is given as follows: $9,847.8.
c. The finance charge is of: $847.8.
What is the monthly payment formula?The monthly payment formula is defined as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.The values of these parameters for this problem are given as follows:
P = 9000, r = 0.036, n = 5 \times 12 = 60.
Then:
r/12 = 0.036/12 = 0.003.
Then the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]
A = $164.13.
Then the total amount paid is of:
Total = 60 x 164.13 = $9,847.8.
Meaning that the finance charge is given as follows:
9847.8 - 9000 = $847.8.
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A worker in a silver mine descends 26 feet use an integer to represent the change in the workers position
Answer: -26 feet
Step-by-step explanation:
alyssa has $75 less than three times eric together they have $905 how much money do they each have
Alyssa has the money of worth $660
Eric has the money of worth $245
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let x be the amount Alyssa has.
Let y be the amount Eric has.
alyssa has $75 less than three times eric
=> x= 3y - 75
Together they have $905
=> x + y =905
Substitute x
=> 3y - 75 +y = 905
4y = 905 +75 = 980
y = 980 /4 = 245
x= 3y - 75 = 3(245) - 75 = 660
Alyssa has $660
Eric has $245
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8 (a) The formula for the area of a trapezium is A = = h(c + d)
(* Find an expression for c in terms of A, hand d.
The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
What is the area of the trapezium?
The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.
To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:
A = h(c + d)/2
2A = h(c + d)
2A/h = c + d
c + d = 2A/h
Then, we can subtract d from both sides of the equation to solve for c:
c = (2A/h) - d
Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.
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the owners of a supermarket chain are looking into the effectiveness of the supermarket's loyalty card program. specifically, they would like to know if the percentage of shoppers in their stores who use the loyalty card has changed from 63% in 2014. chloe works in the marketing department of the chain and is assigned to answer the owners' inquiry. she randomly selects 196 customers from various stores in the chain and finds that 114 use the loyalty card. what are the null and alternative hypotheses for this hypothesis test?
The null and different hypotheses for hypothesis test are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
Null hypotheses
Null hypothesis is usually what researchers or scientists try and confute, and if the null hypothesis is accepted, we have a tendency should modification our opinion, i.e., we have a tendency should modification our original opinion or statement so as to match the null hypothesis. H0 denotes the null hypothesis.Given that:
sample size (η)= 196
sample proposition (p^) = 114/196
Let p denote the population proportion of people who use a loyalty card.
The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]
Hence, the null and alternative hypothesis are
[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63
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A line passes through the points (−4, 7) and (5, −8). What is the slope of the line?
Answer:
-5/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1) ==> (x1, y1), (x2, y2) are the coordinates and
m is the slope
(x1, y1), (x2, y2) ==> (x1=-4, y1=7), (x2=5, y2=-8)
m=(-8-7)/(5-(-4)) ==> plug in known values
m=(-15)/(5+4) ==> simplify
m=-15/9
m=-5/3
The teacher grades 16 of the 48 quizzes before school.
If the teacher grades 15 of the remaining quizzes after school, how many quizzes still need to be graded?
Responses
8 quizzes
8 quizzes
23 quizzes
23 quizzes
25 quizzes
25 quizzes
40 quizzes
The number of quizzes still need to be graded is 17quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.
For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.
Algebraic equations in mathematics frequently have one or more variables.
It is given that,
grades of the teacher out of 48 quizzes before school = 16
grades of the teacher of the remaining quizzes after school = 15
Let us assume 'X' as the number of quizzes still need to be graded.
then X= 48-16+15
=48-31
=17
Hence, The number of quizzes still need to be graded is 17quizzes.
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The number of quizzes still need to be graded is 17 quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.Algebraic equations in mathematics frequently have one or more variables.It is given that,grades of the teacher out of 48 quizzes before school = 16, grades of the teacher of the remaining quizzes after school = 15.Let us assume 'X' as the number of quizzes still need to be graded.then X= 48-=48-31
=17
Hence, The number of quizzes still need to be graded is 17 quizzes.
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Help please asap!!!!
Answer:
y = 1/3x + 8/3
Step-by-step explanation:
The slope of a line that is perpendicular to the line y = -1/3x + 7 is the negative reciprocal of the slope of the given line, which is -3. So, the slope of the perpendicular line is 1/3.
The point where the perpendicular line intersects the given line is also the point where the two lines intersect, which is (4,2) in this case. So, we can use this point to find the equation of the perpendicular line using the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope of the line and (x1,y1) is a point on the line.
In our case, the equation of the perpendicular line is:
y - 2 = 1/3(x - 4)
We can simplify this equation to obtain:
y = 1/3x + 8/3
Therefore, the equation of the perpendicular line is y = 1/3x + 8/3.
Which of the following best describes the second law passed under the Morrill Act?
Eastern schools had to research which crops were suitable for farms in Midwestern America.
Answer:
Step-by-step explanation:
Someone please help me with this!! I’ll give u a brainless or whatever it’s called!
Answer:
New price = 0.06 x Original price
New price $1,968
please help, this is my finals & i don’t know it
Answer:
i think that answer is correct
Step-by-step explanation:
one number is 4 less than 3 times a second number. Two times the first number decreased by two times the second is 8. what is the value of the larger number?
A.4
B.12
C.8
D.2
E.14
Answer:
Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.
Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:
x &= 3y - 4
2x - 2y &= 8
Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12
Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses what is the coordinate location of the Hill
The coordinate location of the hill halfway between them is (1, -1).
How to find the distance between two points?Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses.
The coordinate location of the hill can be calculated as follows:
using mid point formula,
(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
using the end points (-2, 3) and (4, -5)
(x, y) = (-2 + 4 / 2, 3 - 5 / 2)
(x, y) = (2 / 2. -2 / 2)
(x, y) = (1, -1)
Therefore, the coordinate location of the hill is (1, -1).
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It costs $270 for 3 people to go on a fishing trip. How many people can go for $1,080?
Answer:12
Step-by-step explanation:
270/3=90, this is the amount it costs for 1 person to go
1080/90=12
12 people can go for $1080
Explain Harvey's error in the following scenario.
Harvey's sow has just delivered five piglets. The veterinarian has examined the mother and babies, the
piglets have nursed, and it is time for everyone to get some rest. Harvey has filled the pen with clean, dry
straw, and he puts all the pigs in the pen to spend their first night together.
Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.
How should we treat a newborn pig?When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.
Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.
Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.
According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.
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PLEASE HELP ASAP!!!
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Which equation can Sharon use to find c, the average amount the cable company charges per channel?
0.20(c - 300)
0.20c - 300
300(c - 0.20)
300c - 0.20
How much on average does the cable company charge per channel?
The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.
The cable company charges an average of $0.80 per channel.
What is an Equation?An equation involves two expressions or statement on two sides connected with an equal sign.
Total number of channels = 300
Let c be the cable company charges per channel.
Then the charge satellite company charges per channel = c - 0.20
Monthly charge of satellite company = 300(c - 0.20)
Monthly satellite bill = $180
So, 300(c - 0.20) = $180
⇒ c - 0.20 = 180/300
⇒ c - 0.20 = 0.60
⇒ c = 0.60 + 0.20
⇒ c = 0.80
Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.
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Find the amount with the same value as:
70 x 7-2
A
0
B
14
C
149
D
17
The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numerical expression is given below.
⇒ 70 / (7 - 2)
Simplify the expression, then we have
⇒ 70 / (7 - 2)
⇒ 70 / 5
⇒ 14
The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.
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The correct expression is given below.
70 / (7 - 2)
The length of a side of a cube is 4x units. In cubic units, what is the volume of the cube?
Answer:
volume of cube= l^ 3
=(4x)^3
=64x^3 cubic units
at the city museum, child admission is $5.30 and adult admission is $9.80. on thursday, 143 tickets were sold for a total sales of $1149.40. how many adult tickets were sold that day?
The number of adult tickets which were sold that day as calculated from the given data is 29.
First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.
To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.
This is represented by the following equation,
$8.90A + $5.30C = $928
Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:
3 * C = A
Now we can answer our first problem by substituting 3 * C for A.
8.9 (3C) + 5.3C = 928
26.7C + 5.3C = 928
32C = 928
C = 29
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Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
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Describe fully the single transformation that the maps triangle a onto triangle b
The transformations that took for mapping ΔA onto ΔB are:
a) Translated the triangle A 2 units to the right,
b) Reflected the ΔA' (translated A) over the y-axis,
c) Reflected the ΔA'' (reflected A) over the x-axis, resulting in ΔB.
What are transformation rules applied to triangle A to form triangle B?The transformation rules are:
a) Translation: (x, y) ⇒ (x + 2, y) (In the right side direction)
b) Reflection over the y-axis: (x, y) ⇒ (-x, y)
c) Reflection over the x-axis: (x, y) ⇒ (x, -y)
Calculation:The given vertices of triangle A are: (-2, 3), (-5, 3), and (-5, 5).
a) Applying translation by 2 units to the right to triangle A:
(-2, 3) → (-2 + 2, 3) → (0, 3)
(-5, 3) → (-5 + 2, 3) → (-3, 3)
(-5, 5) → (-5 + 2, 5) → (-3, 5)
So, triangle A is translated to triangle A'.
b) Applying reflection over the y-axis to the triangle A':
(0, 3) → (0, 3)
(-3, 3) → (3, 3)
(-3, 5) → (3, 5)
So, triangle A' is reflected as triangle A''.
c) Applying reflection over the x-axis to triangle A'':
(0, 3) → (0, -3)
(3, 3) → (3, -3)
(3, 5) → (3, -5)
Thus, the formed triangle is B at the vertices (0, -3), (3, -3), and (3, -5).
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find the inverse of f(x)=√x+4-2
A function p(x) is shown on the graph below.
O True
O False
Answer:
True
Step-by-step explanation:
The point [tex](0,3)[/tex] lies on the graph.
