Which graph represents the given equation? A. A parabola declines through (negative 1, 4), (negative 1, 3), (0, 2) and (1 point 5, negative 4 point 5) and rises through (2, negative 4), (3, 0) and (4, 6) on the x y coordinate plane. B. A parabola declines through (negative 4, 5), (negative 3 point 5, 2), (negative 3, 0) and (negative 1 point 5, negative 4 point 5) and rises through (0, negative 2), (1, 3) and (1, 4) on the x y coordinate plane. C. A parabola declines through (negative 2 point 3, 5), (negative 2, 2) and (negative 0 point 5, negative 3 point 1) and rises through (0, negative 2), (1, 4) and (1, 5) on the x y coordinate plane. D. A parabola declines through (negative 1, 5), (negative 0 point 5, 2), (0, negative 2) and (0 point 5, negative 3 point 1) and increases through (2, 2), (2 point 5, 5) on the x y coordinate plane.
Answers
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain the graph of a quadratic function?To obtain the graph of a quadratic function, these three features have to be obtained from the function's definition:
The x-intercepts, which are the roots of the function.The y-intercept, which is the value of y when the function crosses the y-axis.The vertex, which is the turning point of the function.The function for this problem is defined as follows:
y = 1.5x² + 4x - 2.
Hence the numeric values of the coefficients are listed as follows:
a = 1.5, b = 4, c = -2.
Inserting these coefficients into a calculator, the x-intercepts of the function are given as follows:
x = -3.09 -> hence the function passes through point (-3.09, 0).x = 0.43 -> hence the function passes through point (0.43, 0).The y-intercept of the function is given by coefficient c = -2, hence the function also passes through point (0, -2).
The x-coordinate of the vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate of the vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing InformationThe problem asks for the graph of the following function:
y = 1.5x² + 4x - 2.
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Related Questions
a tank is filing with petrol at rate of 35 litre per minute. the tank already had 10 liters in it before the filling began. write an equation in standard form for this situation.
Answers
The equation for the situation is written as y = 35x + 10
How to write an equation in standard form for this situationInformation gotten from the question include
a tank is filing with petrol at rate of 35 liter per minute
the tank already had 10 liters in it before the filling began
What is linear function ?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
Definition of variables to suit the problem to be solved
y = total petrol in the tank in liters
m = rate of filling liter per minute = 35
x = number of liters
c = quantity prior to filling = 10
The equation is written as
y = 35x + 10
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Multiple-Choice Exam A student takes a 20-question, multiple-choice exam with two choices for each question and guesses on
each question. Assume the variable is binomial.
Find the probability of guessing at least 10 out of 20 correctly. Round the answer to at least four decimal places.
P(guessing at least 10 out of 20 correctly)
27
0
E
Answers
The probability is 0.5881.
From the question, we have
n = 20
P(X[tex]\geq[/tex]10) = 1-P(X<10)
P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)
P(X[tex]\leq[/tex]9) = P(X=0)+P(X=1)+..................+P(X=9)
=0.4119
P(X[tex]\geq[/tex]10) = 1-P(X[tex]\leq[/tex]9)
=1-0.4119
=0.5881
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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these are the first five terms in a Fibonacci sequence.
1 5 6 11 17
Write down the next two terms in the sequence.
Answers
Answer: 28 and 45
Step-by-step explanation: you add 11 and 17 to get 28 and then add 28 and 17 to get 45
NO LINKS!! Use the diagram below to answer the following questions. Part 3
Answers
Answer:
a) Line r
b) Line q
c) Line s
d) Line q
e) Line p
Step-by-step explanation:
A transversal is a line that crosses two other lines in the same plane at two distinct points.
a) The transversal connecting ∠1 and ∠5 is line r.
Line r is the transversal of lines p and q. ∠1 and ∠5 are corresponding angles as they are in the same position relative to lines p and q crossed by the transversal r.b) The transversal connecting ∠7 and ∠14 is line q.
Line q is the transversal of lines r and s.∠7 and ∠14 are alternate interior angles as they are on the inner side of lines r and s, but on opposite sides of the transversal q.c) The transversal connecting ∠8 and ∠11 is line s.
Line s is the transversal of lines p and q. ∠8 and ∠11 are alternate exterior angles as they are on the outer side of lines p and q, but on opposite sides of the transversal s.d) The transversal connecting ∠6 and ∠15 is line q.
Line q is the transversal of lines r and s. ∠6 and ∠15 are alternate exterior angles as they are on the outer side of lines r and s, but on opposite sides of the transversal q.e) The transversal connecting ∠3 and ∠9 is line p.
Line p is the transversal of lines r and s. ∠3 and ∠9 are consecutive interior angles as they are on the inner side of lines r and s, and are on the same side of the transversal p.Solve the system of equations by graphing.
x=-y
x+y=7
Answers
The graph of the system of equations shows that there is no solution to the system.
How to Solve a System of Equations by Graphing?To solve a system of equations by graphing, plot each of the lines on a graph. Then, find the point where both lines intersect each other.
The x-coordinate and the y-coordinate of the point where both lines of the equations intersect is the solution to the system.
Given the system of equations, x = -y and x + y = 7, both lines have been plotted on a graph shown below. It shows that there are is no point of intersection which means the system of equations have no solution.
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If 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. Find the probability of more than 5 people use the emergency room.
Answers
The probability of more than 5 people is 0.4729
Find the probability of more than 5 people use the emergency room?Since 49% of the people in a community use the emergency room at a hospital in one year, a sample of 11 people use the emergency room. To find the probability of more than 5 people use the emergency room, we use binomial probability.
What is binomial probability?The binomial probability of x is given by P(X = x) = ⁿCₓpˣ(1 - p)ⁿ⁻ˣ
where
n = number of total trialsp = probability of event andx = number of required trialsSince
n = 11, p = 49% = 0.49 and x = 5,We determine the probability of x ≤ 5.
So, P(X ≤ 5) = ¹¹C₀p⁰(1 - p)¹¹⁻⁰ + ¹¹C₁p¹(1 - p)¹¹⁻¹ + ¹¹C₂p²(1 - p)¹¹⁻² + ¹¹C₃p³(1 - p)¹¹⁻³
+ + ¹¹C₄p²(1 - p)¹¹⁻⁴ + ¹¹C₅p⁵(1 - p)¹¹⁻⁵
= ¹¹C₀(0.49)⁰(1 - 0.49)¹¹ + ¹¹C₁(0.49)¹(1 - 0.49)¹⁰ + ¹¹C₂(0.49)²(1 - 0.49)⁹ + ¹¹C₃(0.49)³(1 - 0.49)⁸
+ ¹¹C₄(0.49)⁴(1 - p)⁷ + ¹¹C₅(0.49)⁵(1 - 0.49)⁶
= (1)(1)(0.51)¹¹ + (11)(0.49)(0.51)¹⁰ + (55)(0.49)²(0.51)⁹ + (165)(0.49)³(0.51)⁸
+ (330)(0.49)⁴(0.51)⁷ + (462)(0.49)⁵(0.51)⁶
= 0.0006071 + (11)(0.49)(0.0011904) + (55)(0.2401)(0.0023341) + (165)(0.117649)(0.0045768)
+ (330)(0.0576480)(0.0089741) + (462)(0.0282475)(0.0175963)
= 0.0006071 + 0.0064163 + 0.0308230 + 0.0888452
+ 0.1707218 + 0.2296378
= 0.5270512
≅ 0.5271
So, P(X ≤ 5) = 0.5271, the probability of more than 5 people is P(X ≥ 5) = 1 - P(X ≤ 5)
= 1 - 0.5271
= 0.4729
The probability is 0.4729
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2/8+ 1/2 Least multiple that is the same: Add using renamed fractions
Answers
The addition using Least multiple, [tex]\frac{2}{8}+\frac{1}{2}[/tex] is equal to [tex]\frac{3}{4}[/tex].
What is Least Common Denominator?When two or more fractions are there, the least common denominator is the lowest number among all the common multiples of the denominators.
To find the LCD of numbers, factorization method can be used and if the numbers are co-prime then the LCD is just the multiplication of those numbers.
The denominator of given fractions is 8 and 2.
Now, finding the lowest common multiple of 8 and 2,
LCD is 8,
Now, renaming the fraction by multiplying 4 on numerator and denominator of [tex]\frac{1}{2}[/tex],
[tex]\frac{1 \times4}{2 \times4} =\frac{4}{8}[/tex]
Now, denominator is same, so adding the fractions,
[tex]\frac{2}{8}+\frac{4}{8} =\frac{2+4}{8} \\\\=\frac{6}{8}[/tex]
Dividing the numerator and denominator by 2,
[tex]\frac{6}{8} =\frac{6/2}{8/2}\\ =\frac{3}{4}[/tex]
Therefore, by adding the given fractions we get [tex]\frac{3}{4}[/tex].
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What is the simplified value of the exponential expression 27
1/3
Answers
Answer:
3
Step-by-step explanation:
[tex]27^{\frac{1}{3}}[/tex]
1 ) Factor the number [tex]27=3^{3}[/tex]
[tex]=\left(3^3\right)^{\frac{1}{3}}[/tex]
2 ) Simplify...
3
Hope this helps! :)
Solve the compound inequality 3x+1>2x-3>x-11 enter the exact answer in interval notation
Answers
The exact interval notation of given equation is x > - 8.
What is interval notation for compound inequalities?
The numbers that bound a continuous set of real numbers can be used to express the continuous set in interval notation. Intervals have many characteristics in common with ordered pairs when written.
We have,
3x+1 > 2x-3 > x-11
Apply the rule that if m > v > n, then m > v and v > n to the given compound inequality to find the solution.
∴ m = 3x + 1,
v = 2x - 3,
n = x - 11.
Hence, by applying the rule of compound inequality we get,
3x + 1 > 2x - 3 and 2x - 3 > x - 11
3x + 1 > 2x - 3
3x + 1 - 1 > 2x - 3 -1
3x > 2x - 4
3x - 2x > 2x - 4 - 2x
x > - 4
2x - 3 > x - 11
2x - 3 + 3 > x - 11 + 3
2x > x - 8
2x - x > x - 8 - x
x > - 8
The two computations above indicate that the acquired intervals, x > - 4 and x > - 8, will be combined to yield the answer to the given inequality.
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Find a polynomial of degree n that has only the given zero(s). (There are many correct answers.)
x = -8,0, 1; n = 3
Answers
Answer: f(x) = x³ + 7x² -8x
Step-by-step explanation:
Zeros means that at that x-value, the graph crosses the x-axis and y = 0. Hence, to meet those criteria, the function would be:
[tex]f(x)=x(x+8)(x-1)[/tex]
At those three x-values, the corresponding y-values would equal 0.
Multiply them out to find the polynomial function:
[tex]f(x)=x(x+8)(x-1)=x(x^{2} -x+8x-8)=x^{3} +7x^{2} -8x[/tex]
100 points 2 questions
Question 1
There are 140 people in a theater watching a movie. The number of children present is 3 times the number of adults. How many children are watching the movie?
12 children
35 children
3 children
105 children
question 2
A catering company pays cooks $85 per shift and waiters $45 per shift. Yesterday, 10 people worked for the company at a special event. If the total amount paid to the employees was $570, how many cooks worked at the event?
3 cooks
7 cooks
10 cooks
12 cooks
Answers
Answer:
105 Children and 3 cooks
Step-by-step explanation:
I took the test :)
a) The total number of children watching the movie is 105 children
b) The total number of cooks that worked at the event is 3 cooks
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
a)
Let the number of children be = a
Let the number of adults be = b
Let the total number of people in the theater be = 140
Now , the equation will be
a + b = 140 equation (1)
And , the number of children present is 3 times the number of adults
So ,
a = 3b
Divide by 3 on both sides of the equation , we get
b = a/3
Substituting the value of b in equation (1) , we get
a + b = 140
a + a/3 = 140
( 4a ) / 3 = 140
Multiply by 3 on both sides of the equation , we get
4a = 420
Divide by 4 on both sides of the equation , we get
a = 105
Therefore , the value of a is 105 and the number of children watching the movie is 105 children
b)
Let the number of cooks be = x
Let the number of waiters be = y
Let the amount for each cook be = $ 85
Let the amount for each waiter be = $ 45
The total number of workers = 10
Now , the equation will be
x + y = 10 be equation (1)
The total amount paid to the employees be = $ 570
Now , the equation will be
85x + 45y = 570 be equation (2)
On simplifying equation (1) and equation (2) , we get
Multiply equation (1) by 45 , we get
45x + 45y = 450 be equation (3)
Subtract equation (3) from equation (2) , we get
40x = 120
Divide by 3 on both sides of the equation , we get
x = 3
Therefore , the value of x is 3 and the number of cooks that worked in the event is 3 cooks
Hence ,
a) The total number of children watching the movie is 105 children
b) The total number of cooks that worked at the event is 3 cooks
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Some people took part in a game. The frequency shows information about their scores.
Score Frequency
1 - 7 19
8 - 10 16
11 - 15 6
16 - 20 14
21 - 35 15
36 - 50 4
Estimate the mean.
Give your answer rounded to 2 decimal places.
points
Answers
The mean of the given scores is 15.43
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Score Mid-values Frequency Total score
1 - 7 4 19 19 x 4 = 76
8 - 10 9 16 16 x 9 = 144
11 - 15 13 6 13 x 6 = 78
16 - 20 18 14 18 x 14 = 252
21 - 35 28 15 28 x 15 = 420
36 - 50 43 4 43 x 4 = 172
Total 74 1142
Mean = 1142 / 74 = 15.43
Thus,
The mean of the given scores is 15.43
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The temperature in Quebec City was 5°C at 4 pm. By midnight, the temperature dropped 15 degrees.
-20
A B
0 5
Point A
O Point B
Point C
Point D
Which point is a representation of the colder midnight temperature in degrees Celsius?
D
Mark this and return
Save and Exit
Next
Submit
4
Answers
A is the Point of representation of the colder midnight temperature in degrees Celsius.
The temperature in Quebec City was 5°C at 4 pm. By midnight, the temperature dropped 15 degrees.
To find out which point is a representation of the colder midnight temperature in degrees Celsius:
We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).
We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.
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It takes Rayleigh 34 minutes complete 4 problems.
At this rate, how long will she take to complete 10
problems?
Answers
Answer:1 hour and 15 minutes
Step-by-step explanation:
so it takes her 34 minutes for 4 problems so for 2 problems its 17 minutes
and then you do the 34 times 2 because its 4 problems so you add that and that = 68 minutes and then you add 17 for the 2 problems and thats 85 minutes or 1 hour and 15 minutes
Answer:
1 hour & 25 minutes (85 minutes)
Step-by-step explanation:
Time taken for 1 problem,
→ 34 ÷ 4
→ 8.5 minutes
Now time taken for 10 problems,
→ 8.5 × 10
→ 85 minutes
Hence, answer is 85 minutes.
suppose that $36,000 is deposited in an account and the balance increases to $39,786.15 after 2.5 years. how long will it take for the account to grow to $51,806.67? Assume continous compounding
It will take about _ years for $36,000 to grow to $51,806.67
Answers
Answer:
About 9 years===================================
Continuous compounding equation:
[tex]P(t) = P_0e^{rt}[/tex]Given[tex]P_0=36000[/tex][tex]P(t)=39.876.15[/tex][tex]t=2.5[/tex]Find the value of r[tex]39786.15= 36000*e^{r*2.5}[/tex][tex]e^{2.5r}=39786.15/36000[/tex][tex]ln \ e^{2.5r}= ln \ 1.10517[/tex][tex]2.5r=0.099[/tex][tex]r=0.099/2.5[/tex][tex]r=0.04[/tex]Now find the time t for the balance to grow to $51806.67:
[tex]51806.67= 36000*e^{0.04t}[/tex][tex]51806.67/36000=e^{0.04t}[/tex][tex]e^{0.04t}= 1.439[/tex][tex]ln \ e^{0.04t}= ln \ 1.439[/tex][tex]0.04t=0.3639[/tex][tex]t=0.3639/0.04[/tex][tex]t=9.0975[/tex]The time required is about 9 years.
Answer:
9 years
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $36,000A = $39,786.15t = 2.5 yearsSubstitute the given values into the formula and solve for r to find the annual interest rate:
[tex]\implies \sf 39786.15=36000 \cdot e^{2.5r}[/tex]
[tex]\implies \sf \dfrac{39786.15}{36000}= e^{2.5r}[/tex]
[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=\ln e^{2.5r}[/tex]
[tex]\implies \sf \ln \left(\dfrac{39786.15}{36000}\right)=2.5r[/tex]
[tex]\implies \sf \dfrac{1}{2.5}\ln \left(\dfrac{39786.15}{36000}\right)=r[/tex]
[tex]\implies \sf r=\dfrac{2}{5}\ln \left(\dfrac{39786.15}{36000}\right)[/tex]
[tex]\implies \sf r=0.03999996933...[/tex]
[tex]\implies \sf r=0.04\;(2\;d.p.)[/tex]
Therefore, the annual interest rate is 0.04 = 4%.
To calculate how many years it will take for $36,000 to grow to $51,806.67, substitute the values into the formula and solve for t:
[tex]\implies \sf 51806.67=36000 \cdot e^{0.04t}[/tex]
[tex]\implies \sf \dfrac{51806.67}{36000}= e^{0.04t}[/tex]
[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= \ln e^{0.04t}[/tex]
[tex]\implies \sf \ln\left(\dfrac{51806.67}{36000}\right)= 0.04t[/tex]
[tex]\implies \sf \dfrac{\ln\left(\dfrac{51806.67}{36000}\right)}{0.04}=t[/tex]
[tex]\implies \sf t=9.10 \; (2\;d.p.)[/tex]
Therefore, it will take about 9 years for $36,000 to grow to $51,806,67.
Draw out this scenario using
precise measurements and
answer the question.
You are fighting aliens and
need to shoot down a UFO. The
UFO is hovering 50 ft (10 cm) in
front and 100 ft (20 cm) in the
air above you. What angle do
you need to set your Anti
Aircraft gun to hit the UFO?
Answers
In order to hit the UFO, the Anti Aircraft gun should be set an an angle of elevation of approximately 63.435° above the horizontal in the direction of the UFO
What is an angle of elevation?An angle of elevation is an angle that the line of sight makes with the horizontal.
The location of the UFO are;
The distance of the UFO from the front of the observer (horizontal distance) = 50 feetThe distance of the UFO from above the observer (the vertical distance of the UFO) = 100 feetThe angle, θ, to which the anti aircraft gun needs to be set is found from the trigonometric ratio for tangent as follows.
[tex]tan(\theta) = \dfrac{Length \, of \, the \, side \, opposite \, to \, angle \, \theta}{Length \, of \, the \, side \, adjacent \, to \, \theta}[/tex]
The length of the side opposite to the angle θ to which the gun should be directed is the length of the height of the UFO from the observer, therefore;
Length of the side opposite to θ = 100 feet
Length of the side adjacent to θ is the length of the horizontal distance from the observer;
Length of the adjacent side to θ = 50 feet
Therefore;
[tex]tan(\theta) = \dfrac{100\, feet}{50\, feet} = 2[/tex]
tan(θ) = 2
θ is found using the inverse tangent function (arctangent) as follows;
θ = arctan(2) ≈ 63.435°
The direction the anti aircraft un should be set is at angle of elevation of approximately 63.435° above the horizontal
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Melanie recorded a tape of her guitar playing. It cost her $2,700 to record the master tape, and it costs $2.50 to make each copy. If she sells the tapes for $10 each, how many tapes must she sell to break even?
Answers
The number of tapes Melanie must sell to break even is 360 tapes.
How to find the number of tapes Melanie must sell to break even?To find the number of tapes Melanie must sell to break even, we must follow these steps.
We must identify how much she earns for each tape that she sells, for this we must subtract the sale price of each tape, by the value that she pays to make each tape.
10 - 2.5 = 7.5Now we must divide the total cost of the mother tape by the profit she makes on each tape she sells.
2,700 / 7.5 = 360Based on the above, we can infer that she must sell 360 tapes to cover the value of the mother tape and each of the tapes that she needs to sell. Next it is checked:
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The 3rd term of a GP is 18 and the 7th term is 3⅝, find the GP
Answers
The geometric sequence in which the 3rd term is of 18 and the 7th term is of 29/8 is defined as follows:
[tex]a_n = 40(0.67)^{n - 1}[/tex]
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms yields always the same result, called common ratio q.
The nth term of a geometric sequence is given by the rule presented as follows:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The rule for the nth term is also called the general rule.
The general takes the first term as the reference term, however, the 7th term can be written as a function of the 3rd term, as follows:
[tex]a_7 = a_3q^{4}[/tex]
The fraction that represents the mixed number 3 and 5/8 is:
(3 x 8 + 5)/8 = 29/8.
Then the common ratio of the sequence is calculated as follows:
[tex]\frac{29}{8} = 18q^{4}[/tex]
[tex]q^4 = \frac{29}{144}[/tex]
[tex]q = \sqrt[4]{\frac{29}{144}}[/tex]
[tex]q = \left(\frac{29}{144}\right)^{\frac{1}{4}}[/tex]
q = 0.67.
Then the first term of the sequence is obtained as follows:
[tex]a_3 = a_1q^2[/tex]
[tex]a_1 = \frac{a_3}{q^2}[/tex]
[tex]a_1 = \frac{18}{(0.67)^2}[/tex]
[tex]a_1 = 40[/tex]
Then the definition of the geometric sequence is:
[tex]a_n = 40(0.67)^{n - 1}[/tex]
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Tim has 53 boxcars. His grandfather gave him his entire collection from when he was a child. Use the following equation to find out how many cars Tim’s grandfather gave him: 1.6 x 102. How many cars does Tim have in all?
Answers
The number of cars that Tim has in all is 215.
How many cars does Tim have?The boxcars that Tim has is written in standard form. While the boxcars that Tim's grandfather gave him is written in scientific form. The first step is to convert the scientific form to standard form.
Number of boxcars that Tim's grandfather gave him: 1.62 x 10²
= 1.62 x 100
= 162
The next step is to add the boxcars that Tim's grandfather gave him to the number of boxcars that Tim has.
Total boxcars that Tim has = 162 + 53 = 215 box cars
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Find the distance from point A to XZ . Round your answer to the nearest tenth.
The distance is about (Blank)
units.
Answers
Using the distance formula, the distance between A to point Z to the nearest tenth is 4.1 .
How to find the distance using the coordinates?The 2D distance formula gives the shortest distance between two points in a two-dimensional plane.
Using the distance formula,
d = √(y₂ - y₁) + (x₂ - x₁)²
let's use the distance formula, to find the distance between point A and XZ.
Using the coordinates,
A(3, 3) and XZ(4, -1)
Therefore,
x₁ = 3
x₂ = 4
y₁ = 3
y₂ = -1
d = √(4 - 3)² + (-1 - 3)²
d = √1² + (-4)²
d = √1 + 16
d = √17
Therefore,
d = 4.12310562562
d = 4.1
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pls help ill give brainliest
Answers
Answer:
(-12, 10)
Step-by-step explanation:
You want to solve by elimination the system of equations ...
2x +4y = 16-2x -3y = -6EliminationThe point of elimination is to make one of the variables disappear from the equation.
Here, we observe that the x-coefficients are opposites in the two equations. When we add them, the result is 0: the x-term disappears. Adding the two equations, we have ...
(2x +4y) +(-2x -3y) = (16) +(-6)
y = 10 . . . . . . . . simplified
Finding the other variableUsing this value for y, we can find x. Substituting into the first equation gives ...
2x +4(10) = 16
2x = 16 -40 = -24 . . . . . subtract 40 and simplify
x = -12 . . . . divide by 2
The ordered pair that is the solution is (x, y) = (-12, 10).
hii! could someone help with this?
Answers
The projected cash receipts for April and the projected cash receipts for May can be found to be:
April - $187, 500May - $206, 250How to find the projected cash receipts?The projected cash receipts in April would be:
= ( 25% x Projected sales for April ) + ( 75% x Projected sales for March)
= (25% x 210, 000) + ( 75% x 180, 000)
= 52, 500 + 135, 000
= $187, 500
The projected cash receipts for May is then:
= ( 25% x Projected sales for May ) + ( 75% x Projected sales for April )
= ( 25% x 195, 000) + ( 75% x 210, 000)
= $ 48, 750 + 157, 500
= $206, 250
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How many tons are in 12,000 pound
Answers
Answer: 12,000pd=6 tons
Step-by-step explanation:
Dan builds identical model cars and sells them online. He records the number of models he completes every couple of hours. The graph shows Dan’s data. Choose two pairs of points on the line and calculate the slopes between them. Is Dan’s productivity constant? Explain
Answers
Yes, Dan productivity is constant and slope is given as 3/2.
What is slope?
The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x.
Let we take one pair of point (4,6) and (2,3) and other pair of point is (6,9) and (0,0)
The slope between (4,6) and (2,3) is
m = y2-y1/x2-x1
m = 3-6/2-4
=3/2
The slope between (6,9) and (0,0)
m = 0-9/0-6
=3/2
Hence, both the slopes are equal, therefore his work is constant.
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Show how to add the following by adding the opposite: 8-(-3)
Answers
EXPLANATION:
Subtracting by a negative turns the number into a positive, so when you see 2 negative symbols next to each other, just add the second number to the first
Question 7(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = -2x² + 3x + 10, find f(1) and f(3). Choose the statement that is true concerning these two values.
Answers
The value of the function f(1) and f(3) is 11 and 1 when the function is f(x)= -2x² + 3x + 10
Given that,
The function is f(x)= -2x² + 3x + 10
We have to find f(1) and f(3).
What is function?The core concept of mathematics' calculus is functions. The functions are special types of relations. In mathematics, a function is represented as a rule that produces a distinct result for each input x.
Take the function
f(x)= -2x² + 3x + 10
Take x as 1
f(1)= -2(1)² + 3(1) +10
f(1)= -2+3+10
f(1) = 11
Now, Take x as 3
f(3)= -2(3)² + 3(3) +10
f(3)= -18+9+10
f(3) = 1
Therefore, The value of the function f(1) and f(3) is 11 and 1 when the function is f(x)= -2x² + 3x + 10
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Helps me please.
I’m so confused
Answers
Because y=mx+b
B is y when x is at zero in this case 3
M is the amount it’s increasing or decreasing in this case it’s -2
F(x) represents y so when you plug a number in for x it will give you the y value once you solve equation
We know this because 1-2=-1 and -1-2=-3 and -3-2=-5 they all decrease by 2 which is your m
What is the domain of the function shown in the graph below?
{x|x>-4}
{x|x ≥-4}
{yly ≥ 2}
Answers
The domain of the given function { x | x ≥ -4 } & { y l y ≥ 2 } is
[ -4 , ∞ ).
Given, a graph of the function,
{ x | x ≥ -4 }
{ y l y ≥ 2 }
Now, we have to find the domain of the function
As, we know that the domain of a function is the set of real values on which the given function is defined.
so, it is clear that the function is defined for all the real values greater than or equal to -4.
Hence, the domain of the given function { x | x ≥ -4 } & { y l y ≥ 2 } is
[ -4 , ∞ ).
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Find the unit rate.
16 = 12
Answers
The equation has a unit rate of 3/4
How to determine the unit rate?From the question, we have the following parameters
16y = 12x
The above equation is a linear equation
In fact, it is a linear equation that shows a proportional relationship
Note that all linear equations have a constant rate of change
So, the proportional relationship is given as
16y = 12x
Make y the subject
y = 12/16x
This gives
y = 3/4x
As a general rule
A proportional relationship is represented as y = kx
Where k represents the unit rate
So, we have the following representation
y = 3/4x and y = kx
By comparing the equations
k = 3/4
Hence, the unit rate of the equation is 3/4
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Possible question
Find the unit rate.
16y = 12x
UpEx delivers packages which cost $1.50 per package to deliver. The fixed cost to run the delivery truck is $198 per day. If the company charges $3.50 per package, how many packages must be delivered daily to make a profit of $32?
Answers
The number of packages that need to be delivered daily by UpEx to make a profit of $32 is 115 packages
How to find the number of packages?First, find the contribution margin of each package:
= Charge to deliver package - Cost to deliver package
= 3.50 - 1.50
= $2.00
To find the number of packages needed to make a profit of $32, the formula is:
= (Fixed cost + projected profit) / Contribution margin
= ( 198 + 32) / 2
= 230 / 2
= 115 packages
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