Given this is a one of the endpoints of the segment:
[tex](1,-3)[/tex]You know that the midpoint is:
[tex](2,9)[/tex]By definition, the formula for finding the midpoint of a segment is:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where:
- The coordinates of the midpoint are:
[tex](x_m,y_m)[/tex]- And the coordinates of the endpoints are:
[tex]\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}[/tex]In this case, you can set up that:
[tex]\begin{gathered} x_m=2 \\ y_m=9 \\ \\ x_1=1 \\ y_1=-3 \end{gathered}[/tex]Then, you can set up this equation to find the x-coordinate of the other endpoint:
[tex]2=\frac{1+x_2}{2}[/tex]Solving for:
[tex]x_2[/tex]You get:
[tex](2)(2)=1+x_2[/tex][tex]\begin{gathered} 4-1=x_2 \\ x_2=3 \end{gathered}[/tex]Set up the following equation to find the y-coordinate of the other endpoint:
[tex]9=\frac{-3+y_2}{2}[/tex][tex](9)(2)=-3+y_2[/tex][tex]\begin{gathered} 18+3=y_2 \\ y_2=21 \end{gathered}[/tex]Hence, the answer is:
[tex](3,21)[/tex]B. When are the y-values the same? When are theydifferent?
B. When are the y-values the same? When are they
different?
Since there are absolute values, and the y =|x| and y =x will be the same when the values of x are positive and they're going to be different when the values for x are negative ones.
Like this:
y =x | y = |x|
3 y =3
-3 3
(Worth 50 points) Jell E. Bean owns the local frozen yogurt shop. At her store, customers serve themselves a bowl of frozen yogurt and top it with chocolate chips, frozen raspberries, and any of the different treats available. Customers must then weigh their creations and are charged by the weight of their bowls.
Jell E. Bean charges for five pounds of dessert, but not many people buy that much frozen yogurt. She needs you to help her figure out how much to charge her customers. She has customers that are young children who buy only a small amount of yogurt as well as large groups that come in and pay for everyone’s yogurt together.
A. Is it reasonable to assume that the weight of the yogurt is proportional to its cost? How can you tell?
B. Assuming it is proportional, make a table that lists the price for at least ten different weights of yogurt. Be sure to include at least three weights that are not whole numbers.
C. What is the unit rate of the yogurt? (Stores often call this the unit price.) Use the unit rate to write an equation that Jell E. Bean can use to calculate the amount any customer will pay.
D. If Jell E. Bean decided to start charging for each cup before her customers started filling it with yogurt and toppings, could you use the same equation to find the new prices? Why or why not?
Answer:
D.
Step-by-step explanation:
I need some help please out
Question:
Solution:
Let the following equation:
[tex]\sqrt[]{12-x}=\text{ x}[/tex]this is equivalent to:
[tex](\sqrt[]{12-x})^2=x^2[/tex]this is equivalent to:
[tex]12-x=x^2[/tex]this is equivalent to:
[tex]x^2+x-12=\text{ 0}[/tex]thus, we can conclude that
x= 3.
A kid is selling cupcakes, each cupcake sold for $1.25 and cookies for $1.75, Jason sold 92.50 worth of cake and cookies if he sold both combined how many cakes were sold and how many cookies
Set x and y to be the number of cupcakes and cookies, respectively.
Therefore, according to the question,
[tex]Cost=1.25x+1.75y[/tex][tex]\Rightarrow1.25x+1.75y=92.50[/tex]There is only one provided equation; therefore, we cannot determine x and y but just x in terms of y or vice versa. To determine x and y, more information is needed.Solving for x,
[tex]x=\frac{92.50-1.75y}{1.25}[/tex]caluculate the length of AC to 1 decimal place in the trapezium below.
Check the picture below.
usign the pythagorean theorem let's find the side CD, then let's get the side AC using the same pythagorean threorem.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=\stackrel{hypotenuse}{16}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{7}\\ \end{cases} \\\\\\ \sqrt{16^2 - 7^2}=CD\implies \sqrt{207}=CD \\\\[-0.35em] ~\dotfill[/tex]
[tex]c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{CD}\\ b=\stackrel{opposite}{11}\\ \end{cases} \\\\\\ AC=\sqrt{(\sqrt{207})^2~~ + ~~11^2}\implies AC=\sqrt{207 + 121}\implies \boxed{AC\approx 18.1}[/tex]
Use trigonometric ratios to determine the length of x in the right triangle below.71°5 cmRound your answer to the nearest tenth, and do not include "x ="or the units in your answer. Just enter the numericalvalue
For the given right triangle, one angle is 71 degree, and perpendicular side for angle 71 degree is x and base side is 5 cm.
Determine the measure of side x by using trigonometric ratio.
[tex]\begin{gathered} \tan 71=\frac{x}{5} \\ x=5\cdot\tan 71 \\ =14.5210 \\ \approx14.5 \end{gathered}[/tex]So value of x is 14.5 cm
Answer: 14.5
a diver stands on a platform 15ft above a lake. he doesn't dive off the platform and lands in the water below. his height (H) above the lake after X seconds is shown on the graph below. what is the reasonable domain for the scenario?
The reasonable domain is when the time starts at 0 seconds and when the height is equal to 0 meters. Then, the domain is
[tex]0\le x\le3[/tex]which corresponds to the first option
Does the following equation have a unique solution, no solution or infinitely manysolutions:3x + 9 = 3x - 9A. Unique SolutionB. No SolutionC. Infinitely Many Solutions
The given equation is:
[tex]3x+9=3x-9[/tex]Solve the equation:
[tex]\begin{gathered} \text{ Subtract }3x\text{ from both sides:} \\ 3x+9-3x=3x-9-3x \\ \Rightarrow9=-9 \end{gathered}[/tex]Notice that the equation results in a contradiction. Hence, the equation has no solution.
The answer is B.
find the order pairs by following the tablegiven:y=x^2 -12x+36table of x : ?,5,9,4y : 0,?,1,?,?
x = ? , 5 , 9 , 4
y= 0, ? , 1 , ?
To find the missing x value, replace the matching value of y (0) in the equation and solve for x:
0 = x^2-12x +36
Apply the quadratic formula
[tex]\frac{-b\pm\sqrt[]{b^2-4\cdot A\cdot c}}{2\cdot a}=\frac{12\pm\sqrt[]{(-12)^2-4\cdot1\cdot36}}{2\cdot1}[/tex][tex]\frac{12\pm\sqrt[]{144-144}}{2}=\frac{12}{2}=6[/tex]For x = 5:
y= (5)^2-12 (5) +36 = 25-60+36 = 1
For y=1
1 =x^2-12x+36
0 = x^2-12x+36-1
0= x^2-12x+35
[tex]\frac{12\pm\sqrt[]{(12)^2-4\cdot1\cdot35}}{2\cdot1}=\frac{12\pm\sqrt[]{144-140}}{2}=\frac{12\pm2}{2}=\frac{14}{2}=7\text{ }[/tex]x =7
For x=9
y= (9)^2-12 (9)+36 = 81-108+36=9
For x=4
y= (4)^2-12(4)+35 = 16-48+36=4
BD bisects ZABC such that mZABD =(4x – 5) and mZDBC =(3x + 2)Find the value of ..17
Solution
For this case we know that
m m < DBC = 3x+2
So then we can do the following:
4x -5 = 3x+2
4x-3x = 5+2= 7
x = 7
Directions - Graph the following slope intercept equation:y=-1/3x+4
Answer:
See below for graph
Explanation:
Given the slope-intercept equation:
[tex]y=-\frac{1}{3}x+4[/tex]To graph it, first, we find the x and y-intercepts.
When x=0
[tex]\begin{gathered} y=-\frac{1}{3}(0)+4 \\ y=4 \end{gathered}[/tex]We have the point (0,4).
When y=0
[tex]\begin{gathered} 0=-\frac{1}{3}x+4 \\ \frac{1}{3}x=4 \\ x=12 \end{gathered}[/tex]We have the point (12,0).
We then draw a line joining points (0,4) and (12,0).
For the function f(x)= 8/9+4xfind f-1(x)
The inverse of the function is f⁻¹(x) = x/4 - 2/9
The given function is :
f(x)= 8/9+4x
This can be written in the form of an equation such as
y = 8/9+4x
Now we have to find the value of x in terms of y
4x = y - 8 / 9
or, x = y/4 - 2/9
When a code is formed, the domain and its codomain are sometimes not clearly given, and without doing a calculation, one may just be aware that such a domain is a part of a bigger set.
A function from X to Y" often refers to an action that may accept a sufficient subset of X as its domain in mathematical analysis. A "function as from reals here to reals" might be used to explain the function of a valid real variable, for example.
Instead of the entire set of real numbers, a "function out from reals to the reals" refers to a group of real numbers with a non-empty open interval. This kind of job is
Hence the inverse of the function is given by f⁻¹(x) = x/4 - 2/9
To learn more about functions visit:
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It takes Anastasia 50 minutes to walk 3 1/2 miles to the park. At this rate, about how many minutes should it take her to walk 5 miles?
Answer:
about 71minutes
Explanation:
If it takes Anastasia 50 minutes to walk 3 1/2 miles to the park, then;
50 minutes = 3.5 miles
To get the time taken for her to walk 5miles;
x = 5miles
Divide both expressions
50/x = 3.5/5
Cross multiply
3.5x = 50*5
3.5x = 250
x = 250/3.5
x = 71.42miles
Hence it will take her about 71minutes to walk 5miles
write the slope intercept form:through: (-2, 3), perp. to x=0
write the slope intercept form:
through: (-2, 3), perp. to x=0
we know that
If the line is perpendicular to x=0 (y-axis), then we have a horizontal line
and the equation of a horizontal line (slope is equal to zero) is
y=3x^2 - 9x - 36 = 0Use zero product property. Solve for x
Given the Quadratic Equation:
[tex]x^2-9x-36=0[/tex]You need to remember that the Zero Product Property states that if:
[tex]ab=0[/tex]Then:
[tex]a=0\text{ }or\text{ }b=0[/tex]In this case, you can factor the given equation by finding two numbers whose sum is -9 and whose product is -36. These numbers are 3 and -12. Then:
[tex](x+3)(x-12)=0[/tex]Based on the Zero Product Property, you know that:
[tex](x+3)=0\text{ }or\text{ }(x-12)=0[/tex]Then, by solving each part by "x", you get:
[tex]x=-3\text{ }or\text{ }x=12[/tex]Hence, the answer is:
[tex]x=-3\text{ }or\text{ }x=12[/tex]My test is tomorrow and I need help with my review please!
It is important to know that the sample would be the starters and the population is all members.
So, let's use the mean formula to find the mean sample
[tex]\bar{x}=\frac{\Sigma(x)}{n}[/tex]Where n = 21.
Now, we have to add all the heights of the starter players.
[tex]\begin{gathered} \Sigma(x)=75+81+72+84+79+68+77+84+79+78+83+76+83+71+80+75+77+84+77+80+75 \\ \Sigma(x)=1638 \end{gathered}[/tex]Then, we divide
[tex]\bar{x}=\frac{1638}{21}=78[/tex]Therefore, the mean sample is 78 inches.Now, let's find the population mean using all team data instead
[tex]\mu=\frac{\Sigma(x)}{N}[/tex]Where N = 35. Let's do the same process.
[tex]\begin{gathered} \mu=\frac{75+80+69+77+70+77+68+81+80+77+80+84+72+69+79+84+75+78+84+76+79+83+72+77+75+76+79+84+78+76+71+83+75+69+77}{75} \\ \mu=\frac{2689}{35}=76.83 \end{gathered}[/tex]Therefore, the mean population is 76.83 inches.describe the formations between f(x) = x-5 to g(x)=-6x+2
The given function is,
f(x) = x- 5
The transferred equation is,
g(x) = -6x + 2
So the transformation is,
[tex]g(x)=-6(f(x))-28[/tex]represents holly records
The holly records a temperature at 15 below zero
This implies that the temperature i
A spinner with 5 equally sized slices has 2 red slices, 2 yellow slices, and 1 blue slice. Keiko spun the dial 1000 times and got the following results. From Keiko's results, compute the experimental probability of landing on yellow
Probability is expressed as
number of favorable outcomes/number of total outcomes
But probability can also be classified as theoretical probability and experimental probability. The theoretical probability is the normal probability of each outcome while the expreimental probability is the probability of an outcome given that trials have been made.
In this scenario,
total number of trials = 400 + 195 + 405 = 1000
favorable outcomes = number of times that we landed on yellow = 405
the experimental probability of landing on yellow is
405/1000 = 0.405
8 increased by 3 times a number t in expression
A company produces standard size American flags with a measurement of 3’ x 5’. Another company produces mega American flags that are similar to this size. If the shorter side of the mega flag is 48',. What is the length of the longer side?
Solution:
Given:
[tex]\text{Standard size American flag of 3' x 5'}[/tex]Let L be the longer side of the mega flag.
Another company produces a similar flag of 48' x L
Since both flags are similar, then the ratio of the corresponding sides is equal.
Hence,
[tex]\begin{gathered} \frac{3}{5}=\frac{48}{L} \\ \\ \text{Cross multiplying the equation,} \\ 3\times L=5\times48 \\ 3L=240 \\ \\ \text{Dividing both sides by 3,} \\ L=\frac{240}{3} \\ L=80^{\prime} \end{gathered}[/tex]Therefore, the length of the longer side of the mega flag is 80'
Which type of association does the scatter plot show? ту 00:00 Weak positive 00:00 Strong negative Strong positive Nonlinear
SOLUTION
From the diagram, we can see that Scatter Plot is NON- LINEAR.
Here’s math questions see below:Find and simplify the difference quotient f(x+h)-f(x) ___ hfor the given function: f(x)=2x-5
The given function is:
[tex]\begin{gathered} f(x)=2x-5 \\ f(x+h)=2(x+h)-5=2x+2h-5 \end{gathered}[/tex]So the expression is evaluated as follows:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{2x+2h-5-(2x-5)}{h} \\ =\frac{2x+2h-5-2x+5}{h} \\ =\frac{2h}{h} \\ =2 \end{gathered}[/tex]So the value of the expression is 2.
Use the information in the table to complete the remaining information. Note: The section to the right of the table states "Rewrite the information from the table as a list of ordered pairs in the form of (height, shoe size).
Given:
A table represents the height and the shoe size of seven students
We will rewrite the information from the table as a list of ordered pairs in the form of (height, shoes size).
So, the order pairs will be as follows:
[tex]\lbrace(5^{\prime}6^{\prime}^{\prime},8),(5^{\prime}7^{\prime}^{\prime},9),(5^{\prime}8^{\prime}^{\prime},9),(5^{\prime}10^{\prime}^{\prime},10),(6^{\prime}6^{\prime}^{\prime},13),(5^{\prime}10^{\prime}^{\prime},12),(5^{\prime}8^{\prime}^{\prime},11)\rbrace[/tex]A mapping diagram:
The table could be represented by the relationship as shown in the following figure:
(1,-4) (-2,5) in slope intercept form
We want the equation of the line through the points (1, -4) and (-2, 5)
So we start by finding the slope of the segment that joins those two points using the formula for slope:
slope = (y2 - y1) / (x2 - x1)
slope = (5 - -4) / (-2 - 1) = 9 / (-3) = -3
Then the slope is -3
Now we use the general slope-intercept form of a line:
y = m x + b
with m = -3
y = -3 x + b
and request one of the points to be on the line in order to determine "b"
-4 = -3 (1) + b
- 4 = -3 + b
add 3 to both sides to isolate b on the right
- 4 + 3 = b
then b = -1
Then the equation of the line is:
y = -3 x - 1
solve using the an=a1+(n-1)d formulaa1= -20, d=-4
Answer:
[tex]a_n=-20-4(n-1)[/tex]
Explanation:
We have the formula:
[tex]a_n=a_1+(n-1)d[/tex]And we are given:
a_1 = -20
d = -4
Thus:
[tex]a_n=-20+(n-1)(-4)=-20-4(n-1)[/tex]hi Mr or Ms i need help with this problem please guide me step by step because I don't understand this. the part with the Hj=7x-27 do i bring that down and make an equation? or do i leave that there and make an equation with 3x-5 and x-1?
Let's begin by listing out the information given to us:
HJ = 7x - 27
HI = 3x - 5
IJ = x - 1
The key to solving this is to bear in mind that HJJ = HI + IJ
7x - 27 = 3x - 5 + x - 1
7x - 27 = 3x + x - 5 - 1
7x - 27 = 4x - 6
Subtract 4x from each side, we have:
7x - 4x - 27 = 4x - 4x - 6
3x - 27 = - 6
Add 27 to each side, we have:
3x - 27 + 27 = 27 - 6
3x = 21
Divide each side by 3, we have:
x = 7
Find the y-intercept of a line that passes through (-2,6) and has a slope of -5
First find the equation of the line whose slope is -5 and passes through (-2, 6).
[tex]\begin{gathered} y-6=-5(x-(-2)) \\ y-6=-5(x+2) \\ y-6=-5x-10 \\ y=-5x-4 \end{gathered}[/tex]For y-intercept, substitute x = 0.
[tex]\begin{gathered} y=-5(0)-4 \\ y=-4 \end{gathered}[/tex]Thus, the y-intercept is -4.
if the area of a rectangle is 6 m, then the dimension would be 2 meters by 3 meters?True or False
To be able to verify the statement, let's first recall the formula in getting the area of a rectangle:
Question 21 and 22 list all 6 zeros, write in factored form
the zeros are
x=-1.5 -----> multiplicity 1
x=0
x=2 ----> multiplicity 2
possible function
y=-x(x+1.5)(x+2)^2 -----> leading coefficient must be negative