To find the coordinates of the midpoint
We will use the formula;
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\text{ }\frac{y_1+y_2}{2})[/tex]x₁ = -4 y₁=7 x₂ = 0 y₂=-3
substituting into the formula
Xm = x₁+x₂ /2
=-4+0 /2
=-2
Ym= y₁+ y₂ /2
=7-3 /2
=4/2
=2
The coordinates of the midpoint m are (-2, 2)
Can you help me with question number 4 and double check all my other work. (I don’t really understand functions.)
SOLUTION
The relation is a function because each x-value has a unique y-value. That is each domain has only one image. Therefore, the relation is a function
A number times the sum of 12 and 32 (write as an algebraic expression)
ANSWER
x(12 + 32)
EXPLANATION
Let x be 'the number'.
A number times... means 'a number multiplied by...'
The sum of 12 and 32 is (12 + 32)
The complete algebraic expression is x(12 + 32)
What is the position of see on the number line belowWrite your answer as a fraction or mixed number
Answer:
1/3
Explanation:
We can see that from 0 to 1 the number line is divided into 6 parts and the point is right after the second part. Therefore, the fraction that represents point C is 2/6
This fraction is also equal to 1/3 because we can divide the line from 0 to 1 into 3 parts and take the first. The point will be at the exact same position of C.
Therefore, the answer is:
1/3
Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The equation will be
P = 8h
here, P = total pay
h= working hours.
a) Jayla says that the equation y=2*3 matches the graph Substitute the ordered pairs (from part() into the equation to prove that jayla is correct. Make sure to show ALL steps
From the graph let's take the points as the ordered pairs:
(3, 3), (4, 5), and (5, 7)
Given the equation:
y = 2x - 3
Let's verify for all points, if the equation matches the graph:
a) (x, y) ==> (3, 3)
Substitute 3 for x and 3 for y in the equation
y = 2x - 3
3 = 3(3) - 3
3 = 6 - 3
3 = 3
b) (x, y) ==> (4, 5)
Substitute 4 for x and 5 for y:
y = 2x - 3
5 = 2(4) - 3
5 = 8 - 3
5 = 5
c) (x, y) ==> (5, 7)
Substitute 5 for x and 7 for y:
y = 2x - 3
7 = 5(2) - 3
7 = 10 - 3
7 = 7
Since the left side equals the right side of the equation, the equation
y=2x-3 matches the graph.
Therefore, Jayla is correct.
which ordered pair is a solution of the equation 7x−5=4y−6?PLEASE HURRY THIS IS DUE NOW A. only (2,4)B. only (3,6)C. both A and BD. neither A or B
To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:
1. Case: Ordered pair (2, 4):
[tex]7\cdot(2)-5=4\cdot(4)-6\Rightarrow14-5=16-6\Rightarrow9\ne10[/tex]This ordered pair is NOT a solution.
2. Case: Ordered pair (3, 6):
[tex]7\cdot(3)-5=4\cdot(6)-6\Rightarrow21-5=24-6\Rightarrow16\ne18[/tex]This ordered pair is NOT a solution.
Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).
The safe load, L, of a wooden beam of width w, height h, and length l, supported at both ends, varies directly as the product of the width and the square of the height, and inversely as the length. A wooden beam 5 inches wide, 8 inches high, and 216 inches long can hold a load of 7670 pounds. What load would a beam 3 inches wide, 5 inches high, and 240 inches long of the same material, support? Round your answer to the nearest integer if necessary.
we know that
L=KW(h^2)/l
we have that
W=5 in
h=8 in
l=216 in
L=7670 pounds
step 1
Find the value of K (constant of proportionality)
substitute the given values in the equation
7670=K(5)(8^2)/216
7670=k(1.4815)
k=5,177.25
step 2
we have the equation
L=(5,177.25)W(h^2)/l
for
W=3 in
h=5 in
l=240 in
substitute in the equation and solve for L
L=(5,177.25)(3)(5^2)/240
L=1,617.89 pounds
Round your answer to the nearest integer
so
L=1,618 pounds
What is 4527 written in scientific notation?A.4.527B.4.527 x 10*2C.4.527 x 10*3D.4.527 x 10*4
Solution
- The question would like us to convert the number 4527 to scientific notation.
- In order to write a number to its scientific notation, we need to follow these steps:
1. Move the decimal place to the right of the first digit of the number. Make sure you count each step as you move the decimal point from right to left or left to right.
2. The number of steps corresponds to the exponent of 10 that multiplies the decimal form of the original number.
- We can apply these steps to solve the question given as follows:
- Thus, we have that the scientific notation of the number 4527 is
[tex]4.527\times10^3[/tex]Final Answer
The scientific notation of the number 4527 is
[tex]4.527\times10^3\text{ (OPTION C)}[/tex]
The coordinates of point F are (8,4) and the coordinates of point G are (-4,9). What is the slope of the line that is perpendicular to line FG. Enter the answer as a simplified fraction.
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for finding slope is
m = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial values of y
x2 and x1 are the final and initial values of x
From the given points ,
x1 = 8, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12
Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5
Thus, the slope of the perpendicular to line FG is 12/5
Find the domain. Then use the drop down menu to select the correct symbols to indicate your answer in interval notation. If a number is not an integer then round it to the nearest hundredth. To indicate positive infinifty ( \infty ) type the three letters "inf". To indicate negative infinity(-\infty ) type "-inf" with no spaces between characters. \frac{ \sqrt[]{x-4} }{\sqrt[]{x-6}} AnswerAnswer,AnswerAnswer
The domain of a function is all values of x the function can have.
Since this function has radicals, and the value inside a radical needs to be positive or zero, and also the denominator of a fraction can't be zero, we have the following conditions:
[tex]\begin{gathered} x-4\ge0 \\ x\ge4 \\ \\ x-6>0 \\ x>6 \end{gathered}[/tex]Since the first condition contains the second, so the domain set is represented by the second condition:
[tex](6,\text{inf)}[/tex]help pleasesjjsnsbsbbbsbs
Student asking the same question for third time in less than ten minutes. Can't help him or her out with additional information to complete the exercise.
Closing the session!
Elijah is snorkeling above a shipwreck. The ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation. What is Elijah's elevation?
Elijah's elevation when Elijah is snorkeling above a shipwreck is -14.
What is elevation?Elevation simply has to do with the height above sea level.
In this case, Elijah is snorkeling above a shipwreck and the ship has an elevation of -105 feet. Elijah is snorkeling at 2/15 of the ship's elevation.
Elijah's elevation will be:
= Fraction of his snorkeling × Ship's elevation
= 2/15 × (-105)
= -14
This shows the elevation of Elijah.
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How can use theorem 7-4 to find missing segments? (7-4 is similarity) :)
Given
AD = 6.4
BD = 3.6
Find
AC,BC and DC
Explanation
Using Pythogoras theorem in triangle ADC
[tex]AC^2=DC^2+6.4^2------(1)[/tex]Using PT in triangle BDC
[tex]BC^2=DC^2+3.6^2-------(2)[/tex]Adding equation (1) and (2)
[tex]\begin{gathered} AC^2+BC^2=DC^2+3.6^2+DC^2+6.4^2 \\ AC^2+BC^2=2DC^2+53.92 \end{gathered}[/tex]Using PT in triangle ABC
[tex]10^2=AC^2+BC^2[/tex]Equating above 2 equations
[tex]\begin{gathered} 100=2DC^2+53.92 \\ DC^2=23.04 \\ DC=4.8 \end{gathered}[/tex]Putting this value of DC in equation (2)
[tex]\begin{gathered} BC^2=4.8^2+3.6^2 \\ BC^2=23.04+12.96 \\ BC=6 \end{gathered}[/tex][tex]\begin{gathered} 10^2=AC^2+BC^2 \\ 100=AC^2+36 \\ AC=8 \end{gathered}[/tex]Final Answer
AC = 8
BC = 6
DC = 4.8
IF log x = 1/₂, find log (10x²)
Answer:
2
Step-by-step explanation:
log ab = log a + log b
Similarly,
log 10x² = log 10 + log x²
log a^b = b log a
Similarly,
log 10x² = 2 log x
= 2 * 1/2
= 2/2
= 1
Note :-
The value of log 10 = 1
Hence,
log 10x²
= log 10 + log x²
= 1 + 1
= 2
In parallelogram ABCD… Justify your answer with the applicable property.
Solution
For this case we have the following measures:
m <1= x+12
m < 2= 6x -18
We can set up both angles equal:
x +12 = 6x -18
Solving for x we have:
12+18 = 5x
5x = 30
x= 30/5= 6
Then the value of m< 2 is:
m< 2= 6*6 -18= 36-18= 18
the best second answer is:
If a quadrilateral is ||gram the opposite angles are congruent
Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, close to -0.5?A. Graph AB. Graph BC. Graph CD. Graph D
A negative linear relationship occurs when for increasing x values, the values of y are decreasing.
Observing the graphs, we can see a positive linear relationship for graphs A and C (x - increases, y - increases).
For Graph D, we can observe no correlation.
For graph B, we can observe a negative linear relationship (x - increases, y - decreases).
Answer: Graph B
6. Oliver is playing a game in which he has to choose one of two numbers (2 or 7) and then one of five vowels (a, e, i, o, or u). How many possible outcomes are there? 2 7 There are possible outcomes.
Answer
Number of possible outcomes for everything = 240 ways
Explanation
The number of possible outcomes can be calculated by taking each of these two groups.
First group contains 2 elements
Number of possible ways to pick the elements = 2! = 2 × 1 = 2 ways
Second group contains 5 elements
Number of possible ways to pick the elements = 5! = 5 × 4 × 3 × 2 × 1 = 120 ways
Number of possible outcomes for everything = 2! × 5! = 2 × 120 = 240 ways
Hope this Helps!!!
use the formula Sn to find the sum of the first five terms of the geometric sequence.
First, find the common ratio r:
-4/9 : 4/3 = -1/3
4/3 : -4 = -1/3
-4:12 = -1/3
r= -1/3
[tex]Sn=\frac{a(r^n-1)}{r-1}[/tex]Where:
a= first term = 12
n= number of terms = 5
Replacing:
[tex]Sn=\frac{12(-\frac{1^{}}{3}^5-1)}{-\frac{1}{3}-1}[/tex]Sn= 244/27 = 9 1/27
What Is the inverse of.. (ignore pencil writing) -matrices- (there may be more than one answer
To find the inverse of the matrix, first let's find the determinant:
[tex]\begin{gathered} |A|\text{ = 3(2) - 5(1)} \\ |A|\text{ = 6 - 5} \\ |A|\text{ = 1} \end{gathered}[/tex]Then, we'll find the Adjunct of the matrix:
[tex]\begin{gathered} \begin{bmatrix}{3} & {5} & {} \\ {1} & {2} & {} \\ {} & {} & {}\end{bmatrix}\text{ : interchange }3\text{ and 2. negate 1 and 5} \\ \text{Adjunct = }\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} In\text{verse of the matrix = }\frac{1}{|A|}\times\text{ adjunct} \\ A^{-1}\text{ = }\frac{1}{1}(\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}) \\ A^{-1}\text{ =}\begin{bmatrix}{2} & {-5} & {} \\ {-1} & {3} & {} \\ {} & {} & {}\end{bmatrix}\text{ (option B)} \\ \end{gathered}[/tex]A Parks and Recreation department in a small city conducts a survey to determine what recreational activities for children it should offer. Of the 1200 respondents,400 parents wanted soccer offered625 parents wanted baseball/softball offered370 parents wanted tennis offered150 parents wanted soccer and tennis offered315 parents wanted soccer and baseball/softball offered230 parents wanted baseball/softball and tennis offered75 parents wanted all three sports offeredHow many parents didn’t want any of these sports offered?a) 155b) 75c) 0d) 425
There were 1200 respondents:
400 parents wanted soccer offered
370 parents wanted tennis offered
625 parents wanted baseball/softball offered
150 parents wanted soccer and tennis offered
315 parents wanted soccer and baseball/softball offered
230 parents wanted baseball/softball and tennis offered
75 parents wanted all three sports offered
Therefore:
We have to add all the options that were mixed with different sports:
150 + 315 + 230 = 695 - 75= 620 (We subtract 75 because it's already included in the other values as we can see in the diagram)
We have to add all the parents that chose only one sport:
400 + 370 + 625= 1395
We have to subtract 620 from 1395:
1395 - 620= 775 parents who chose any sport
Now:
1200 - 775 = 425 respondents who didn't want any.
Therefore, 425 parents didn't want any of the sports offered.
The answer is D) 425.
3. Solve the system using elimination (not substitution or matrices). negative 2 x plus y minus 2 z equals negative 8A N D7 x plus y plus z equals negative 1A N D5 x plus 2 y minus z equals negative 91. If the system has a single solution, write the solution as an ordered triple, (x, y, z).2. If the system has infinite solutions, write the solutions IN TERMS OF z.The solution should look something like left parenthesis 3 minus 3 z comma space minus 1 plus 7 z comma space z right parenthesis but not like left parenthesis negative 6 plus 3 y comma space y comma space 2 minus 5 y right parenthesis or not like left parenthesis x comma space 3 plus 5 x comma space minus 1 plus 4 x right parenthesis. None of these are the solution, they are just examples of what the answer could look like and not look like.3. Be sure to show all appropriate work. Extraneous work may be counted against you. Your handwritten work should include the steps used to find the solution. You should label your steps with how you combined your equations, like 2E1+E3. Solutions with no work will receive no credit.
Given the system of equation
[tex]\begin{gathered} -2x+y-2z=-8\ldots\ldots\ldots\text{.}(1) \\ 7x+y+z=-1\ldots\ldots\ldots\text{..}(2) \\ 5x+2y-z=-9\ldots\ldots\ldots\text{.}(3) \end{gathered}[/tex]step 1: Make z the subject of the formula in equations (2)
[tex]z=-1-7x-y\ldots\ldots\ldots(2)[/tex]step 2: Substitute the value of z obtained into equation (1)
10
step 3: Substitute the value of z obtained in step 1 into equation (3)
[tex]\begin{gathered} 5x+2y-(-1-7x-y)=-9 \\ 5x+2y+1+7x+y=-9 \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \end{gathered}[/tex]step 4: Solve equations (4) and (5) simultaneously,
[tex]\begin{gathered} 12x+3y=-10\ldots\ldots\ldots\text{.}(4) \\ 12x+3y=-10\ldots\ldots\ldots\text{.}(5) \\ \text{subtract equation (5) from (4)} \\ (12x-12x)+(3y-3y)=-10-(-8) \\ 0\text{ + 0 = }-10+10 \\ 0=0 \end{gathered}[/tex]Therefore, the system has infinite solutions
The solution in terms of z is
[tex]\begin{gathered} x=-\frac{1}{3}z+\frac{7}{9} \\ y=\frac{4}{3}z-\frac{58}{9} \\ z=z \end{gathered}[/tex]If 1 is added to a number and the sum is tripled, the result is 5 more than the number. Find the number
Answer;
[tex]n=1[/tex]Explanation;
Here, we want to get a number
Since the number is not known at the moment, we can start by identifying the number with an a;phabet
Let us call this n
If 1 is added to the number
mathematical representation;
[tex]1+n[/tex]And the sum is tripled;
[tex]3(1+n)[/tex]The result is 5 more than the number
5 more than the number is simply;
[tex]5+n[/tex]So, we equate this to what we had initially as follows;
[tex]5+n=3(1+n)[/tex]We can now solve this equation for n
[tex]\begin{gathered} 5+n=3+3n \\ 5-3=3n-n \\ 2n=2 \\ n=\frac{2}{2} \\ n=1 \end{gathered}[/tex]The dose of a drug is critical. Too small a dose may be treat a patient effectively, A nurse must give a patient 40mg of a drug for each kilogram of the patient’s mass. If the patient weighs 165lbs how many milligrams of the drug should be given?
EXPLANATION
We need to multiply the number of needed milligrams by the weight of the patient, but first turning the weight in lbs into kilograms,
[tex]?Kilograms=165lbs*\frac{0.453}{1lb}=74.745Kg[/tex]Now, multiplying the obtained weight by the number of miligrams, give us the dose:
[tex]Dose=40\frac{mg}{Kg}*74.745Kg=2989.8mg[/tex]In conclusion, the nurse should give 2989 mg of the drug.
For which value(s) of x will the rational expression below equal zero? Che all that apply. (x - 5)(x+2) x + 1 A.-5 B. 2 c. 1 1 D. -1 E. 5 F. -2
The rational expression we have is:
[tex]\frac{(x-5)(x+2)}{x+1}[/tex]For a rational expression to be equal to 0, the numerator of the expression has to be equal to 0.
The numerator is: (x-5)(x+2)
That has to be equal to 0:
[tex](x-5)(x+2)=0[/tex]Here, we apply the zero product property, which tells us that if a product is equal to 0, one of the two elements, or the two elements, are equal to 0:
[tex]\begin{gathered} x-5=0 \\ x+2=0 \end{gathered}[/tex]We solve the two equations, and get the two values that will make the rational equation equal to 0:
[tex]\begin{gathered} x=5 \\ x=-2 \end{gathered}[/tex]Answer:
E. 5
F. -2
Which equation is equivalent to: 3r=78+14 ?A. −3r=−78+14B. 3r−14=78C. 3r=78−14D. −3r=78−14
A third friend wants to offer Rebecca andSteve some of the animal models she hasalready made. The model she has of thegiant squid is 5 inches tall. Using thesame scale (2 in:5ft), how tall would thegiant squid be in real life?
From the present question, it is said that the scale of a model is equal to:
[tex]e=\frac{2in}{5ft}[/tex]It means that the ratio of the size of the model and the real size of the giant squid must be always this same value. It was given that the size of the model is 5 in. Because we don't know the size of the real-life giant squid, we will use it as x. From this, we can write the following relation:
[tex]\frac{5in}{x}=\frac{2in}{5ft}[/tex]Now, we just need to isolate x in the present relation to find how tall would be a giant squid in real life.
[tex]\begin{gathered} \to2in\times x=5in\times5ft \\ x=\frac{5in\times5ft}{2in}=\frac{25}{2}ft=12.5ft \end{gathered}[/tex]From the solution developed above, we conclude that the real-life giant squid would be 12.5 ft tall.
Suppose it is believed that the probability a patient will recover from a disease following medication is 0.8. In a group of twenty such patients, the number who recover would have mean and variance respectively given by (to one decimal place):
Based on the number of patients and the probability that a patient will recover from the disease, the mean 16 patients would be and the variance would be 1.79
How to find out mean and the variance?The mean can be found by the formula:
= Number of patients in group x Probability that patient will recover
= 20 x 0.8
= 16 patients
The Variance is:
= Number of people x probability of recovery x (1 - probability of recover)
= 20 x 0.8 x (1 - 0.8)
= 3.2
So the standard deviation is:
= √3.2
= 1.79
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Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
Solve T=C(8+AB) for A
Which equation is the best approximation of the trend line
approximatesThe equation of a line is given by
[tex]\begin{gathered} y=mx+c \\ m=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \end{gathered}[/tex]Taking two points from the line of best fit
Point A(14,200) and Point B (18,400)
[tex]\begin{gathered} x_1=14;y_1=200;x_2=18;y_2=400 \\ \frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1} \\ \frac{400-200}{18-14}=\frac{y-200}{x-14} \\ \frac{200}{4}=\frac{y-200}{x-14} \\ \frac{50}{1}=\frac{y-200}{x-14} \\ y-200=50(x-14) \\ y-200=50x-700 \\ y=50x-700+200 \\ y=50x-500 \end{gathered}[/tex]Hence, the equation that best approximate the trend line is y=50x-500
