The midpoint and distance between (-3,10) and (15,-2) are ( 6,4 ) and 6√13 respectively.
What is the midpoint and distance between the given coordinates?The midpoint formula is expressed as;
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Given the data in the question;
Point 1(-3,10)
x₁ = -3y₁ = 10Point 2( 15,-2 )
x₂ = 15y₂ = -2Plug the given values into the midpoint formula and simplify.
[ (x₁ + x₂)/2, (y₁ + y₂)/2 ]
[ ( -3 + 15)/2, ( 10 + (-2) )/2 ]
[ ( 12)/2, ( 10 - 2 )/2 ]
[ ( 12)/2, ( 8 )/2 ]
( 12/2, 8/2 )
( 6,4 )
Therefore, the midpoint is (6,4).
Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √( ( 15 - (-3) )² + ( -2 - 10 )² )
D = √( ( 15 + 3 )² + ( -2 - 10 )² )
D = √( ( 18 )² + ( -12 )² )
D = √( 324 + 144 )
D = √( 468 )
D = 6√13
Therefore, the distance between the points is 6√13.
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13. Using the information in the table, write and solve an equation to find the number
of toppings when you would pay the same amount for Pizza A and Pizza B.
Pizza A
Pizza B
Cheese pizza Price per topping
$1.50
$1.00
$10
$12.50
On solving the question, 5 topping would pay the same amount for Pizza A and Pizza B, the value of equation 0.50x=2.50=> x=5
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
let x be the number of toppings,the total cost of a pizza is given by:
pizza cost+topping cost
for pizza a =10+1.50x
for pizza b=12.50+1.00x
we solve for when cost are same and for how many toppings
10+1.50x=12.50+1.00x
10+0.50x=12.50
0.50x=2.50
x=5
would pay the same amount for Pizza A and Pizza B. are 5 toppings,
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At a cell phone assembly plant, 82% of the cell phone keypads pass inspection. A random sample of 101 keypads is analyzed. Find the probability that the proportion of the sample keypads that pass inspection is between 0.75 and 0.87.
The z-score for the 0.75 proportion is -1.95.
What is z-score?The Z-score calculates the deviation of the measure from the mean in standard deviations. We seek for the p-value linked with this Z-score after locating the Z-score in the z-score database.
The likelihood that the value of the measure will be less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure is greater than X is obtained by deducting 1 from the p-value.
In a set with mean X and standard deviation μ, the z score of a measure X is given by:
Z=(X-μ)/σ
In this problem, we have that:
n=100,p=0.82
So,μ=E(X)=np=100×0.82=82
Therefore, √V(X)=√np×(1-p)=√100×0.82×0.18=3.841
For Finding the probability that less than 75 in the sample keypads pass inspection.
Using continuity correction, this is (P(75-0.5)<=P(74.5)), which is the p-value of Z when X = 74.5.
=>z= (74.5-82)/3.841
=>z= - 7.5/3.841
=>z= - 1.95 has a p-value to 0.
Hence, if a random sample of 100 keypads is analyzed and 75 pass inspection, then the z-score for 0.75 proportion is -1.95
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Find the common difference of the arithmetic sequence − 19 , − 11 , − 3
Answer:
+ 8
Step-by-step explanation:
This is an arithmetic progression (AP) as there is a common difference between successive terms.
For example, looking at the first two terms,
Difference = 2nd term - 1st term
= -11 -(-19)
= -11 + 19
= +8
To check,
Looking at the second and third terms,
Difference = 3rd term - 2nd term
= -3 -(-11)
= -3 + 11
= +8
Hence, there is a common difference of +8 between consecutive terms, making it an AP.
Which graph represents the solutions to this equation?
X²+8x=-20
Answer:
The one with the vertex of (-4,4)
Step-by-step explanation:
Cash $14,692
Owe Knapp College 10,981
Owe Ashley’s Boutique 1,682
Owe Buzz Electronics 787
Jewelry 2,575
Lauren Juliana has been saving and would now like to purchase a boat. She does not have enough to pay cash, so she has contacted a lending institution about purchasing on credit. The lending institution has asked her to begin the loan process by completing a net worth statement. Prepare a net worth statement for Lauren Juliana. Select Current Date in the appropriate field to indicate today’s date. In each section, enter items in descending order of amount
Barren's net worth statement exists shown to the right.
What is meant by net worth statement?Your total worth, including both financial and non-financial assets, equals your net worth less any outstanding obligations.
Using a net worth statement, you can view your financial situation at any given time. It is comparable to a "financial snapshot," showing the dollar amounts of your assets and liabilities (liabilities or debts).
Assets - Liabilities = Net Worth is the equation for calculating net worth.
The total of Lauren Juliana's debts will be subtracted from the total of her assets to determine her net worth (cash and jewelry).
= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)
simplifying the equation, we get
= $ 3,817
barren's net worth statement is shown to the right.
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The required total net worth of Lauren Juliana is $ 3,817.
What is implied by total assets articulation?Your all out worth, including both monetary and non-monetary resources, rises to your total assets less any remaining commitments.
Utilizing a total assets proclamation, you can see what is going on at some random time. It is equivalent to a "monetary preview," showing the dollar measures of your resources and liabilities (liabilities or obligations).
Resources - Liabilities = Total assets is the condition for working out total assets.
The complete of Lauren Juliana's obligations will be deducted from the absolute of her resources for decide her total assets (money and adornments).
= ($ 14,692 + $ 2,575) - ($ 10,981 + $ 1,682 + $ 787)
working on the situation, we get
= $ 3,817
desolate's total assets articulation is displayed to one side.
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if the length of the basketball court is (x+16) and the width is (x-2). what is the area
Answer:
[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]
Step-by-step explanation:
a basketball court is a rectangle, therefore its area is length x width.
the length given is (x+16)
the width given is (x-2)
substitute into the rectangular area equation:
length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32
specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].
therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].
i hope that helps :)
Answer:
therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].
Step-by-step explanation:
31 is what percent of 37?
Answer: The total answers count 37 - it's 100%, so we to get a 1% value, divide 37 by 100 to get 0.37. Next- calculate the percentage of 31: divide 31 by 1% value (0.37), and you get 83.78% - it's your percentage grade.
Which is a true statement regarding Springside?
Springside does not affect the correlation.
Springside weakens the correlation shown in the scatterplot.
Springside strengthens the correlation shown in the scatterplot.
Removing Springside would increase the value of the correlation coefficient.
The result of the interpretation of the graph:
Spring side weakens the correlation shown in the scatter plot.
The correct option is D.
What is a correlation coefficient?The precise metric used in a correlation analysis to quantify the strength of the linear relationship between two variables is the correlation coefficient. In a correlation report, the r stands for the coefficient.
Given:
The mean test score is represented in the scatter plot as a function of the average class size.
This demonstrates that there is a negative link between the mean class size and the mean test score,
with the mean score decreasing as the mean class size increases.
The correct response is:
Spring-side decreases the association displayed in the scatter plot.
However, for Spring side, the mean test score is higher than most other schools with lower class sizes, which is a different outcome than predicted.
Therefore, spring-side weakens the correlation shown in the scatter plot.
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The complete question:
A newspaper collected information on schools in its circulation area in order to compare their quality. Two measures the newspaper collected for each school, mean class size and mean score on a statewide reading exam, are shown in the scatter plot. One school in the report, Spring side Elementary, is labeled in the graph.
Which is a true statement regarding Spring side?
Spring side does not affect the correlation.
Spring side weakens the correlation shown in the scatter plot.
The spring side strengthens the correlation shown in the scatter plot.
Removing Spring side would increase the value of the correlation coefficient.
The scatter plot is attached in the image.
Laura and Shelby ordered pizzas and chips. Lara ordered 5 pizzas and 2 bags of chips and paid $55. Shelby ordered 10 pizzas and 4 bags of chips and paid $95. How much would 1 pizza and 1 bag of chips cost?
Cannot be determined.
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here 5 pizzas and 2 bags of chips cost $55 and 10 pizzas and 4 bags of chips cost $95
let the cost of one pizza be p and a bag of chips be c then we construct the following linear equations:
5p+2c=55
10p+4c=95
Clearly the equations are colinear but 10p+4c≠110=1(5p+2c0
and thus two lines don't have a unique solution.
Hence, the cost cannot be determined as the two equations have no solution in common.
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Answer the problem in the photo below! Please answer simply:)
Answer:
32
Step-by-step explanation:
Let's start with x to the third power. x=4 So that would be 4 to the third power. that would be 4x4=16. 16x4=64. So that would be 1/2*64. That equals 32
Complete table with the Y-values for the equation y=ײ+1
The complete table of values of the function is
x 0 1 2 3
y 0 2 5 10
How to complete the table of values of the function?From the question, we have the following parameters that can be used in our computation:
The equation of the function is given as
y = x² + 1
The above function is a quadratic function
This is so because it has the following representation
y = ax² + bx + c
When this function is compared to the equation y = x² + 1, we have the following notations
a = 1
b = 0
c = 1
From the incomplete table of values, we have the x values to be
x = 1, 2, 3
Substitute x = 1, 2, 3 in the equation y = x² + 1
So, we have
When x = 1, y = (1)² + 1 = 2
When x = 2, y = (2)² + 1 = 5
When x = 3, y = (3)² + 1 = 10
When these values are represented on a table, we have
x 0 1 2 3
y 0 2 5 10
The above represents the complete table
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Complete question
Complete table with the Y-values for the equation y=ײ+1
x 0 1 2 3
y 0
true or false 3 times the speed will have 9 times the force of impact
Answer: true
Step-by-step explanation:
how to work out the area of a parallelogram
the base timed by the height
A _____ is a flat surface that has no thickness.
any help? please make sure it's correct thank you
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
The slope will be perpendicular to equation through A and B because of the 90 degree angle at B.
Lines that are perpendicular have opposite reciprocal slopes.
The slope of the line we know is 2 (The slope is the number before the x). The opposite reciprocal is -[tex]\frac{1}{2}[/tex].
Now that we have the slope we need a point on the line. They give us that point at (0,6) We will use the y value of 6 and the x value of 0 from the point given to find the y-intercept.
slope (m) = - [tex]\frac{1}{2}[/tex]
y = 6
x = 0
We will substitute all of this information into y = mx + b to solve for b (y-intercept)
y = mx + b
6 = - [tex]\frac{1}{2}[/tex] (0) + b
6 = b
Now that we have the slope (- [tex]\frac{1}{2}[/tex]) and the y-intercept (6) we can write the equation
y = - [tex]\frac{1}{2}[/tex] x + 6
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c m is the slope and c the y- intercept )
y = 2x + 1 ← is in slope- intercept form
with slope m = 2
BC is perpendicular to AB
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{BC}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
the line BC has point C at (0, 6 ) ⇒ c = 6
y = - [tex]\frac{1}{2}[/tex] x + 6 ← equation of line BC
Ed is using the recipe shown to make fruit salad. He wants to use 30 diced strawberries in his fruit salad. How many bananas, apples, and pears should Ed use in his fruit salad?
Fruit Salad Recipe - 4 bananas, diced. 3 apples, diced. 6 pears, diced. 10 strawberries, diced.
Answer:
12 bananas
9 apples
18 pears
Step-by-step explanation:
You are tripling the recipe.
10 x 3 = 3
4 x 3 = 12
3 x 3 = 9
6 x 3 = 18
Idil owns a small business selling clothing. She knows that in the last week 3
customers paid cash, 25 customers used a debit card, and 53 customers used a credit
card.
with
Based on these results, express the probability that the next customer will pay
cash or a credit card as a percent to the nearest whole number.
The probability that the next customer will pay cash or a credit card is 56%, since 3 customers paid cash and 53 customers used a credit card out of a total of 81 customers.
What is customers?Customers are individuals or organizations who purchase goods and services from a business. They play an important role in a company's success as they provide the revenue needed to sustain and grow the business. Customers become loyal to a business when they are provided with quality products, excellent customer service, and competitive prices. Companies that focus on customer satisfaction often develop long-term relationships with their customers, as they understand the importance of customer loyalty. Companies must strive to continually meet the changing needs of their customers in order to remain successful in the long term.
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Please do 1. and 2.! 25 points, please need asap!
Step-by-step explanation:
1
We can see that RS divides ∆PQS into two equal parts
So,
PR = RQ
Therefore
RQ = 5.1
Now
PQ = PR + RQ
=> PQ = 5.1 + 5.1
=> PQ = 10.2
2
Here
KM is the angle bisector
So
JM = ML
JM = 46
Need help finding missing answers
Check the picture below.
so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean? well, it means that CG = GD, and since CD is 34, that means that GD = 17.
let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said
[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]
Natalie is driving on the freeway. She just passed mile marker 290. The markers have
been increasing as she drives by them. The fastest Cameron will drive is 80 miles per
hour. However, there is a bit of traffic that might slow her down, but she doesn't know
exactly how much it will slow her down.
a. Write an inequality to represent Natalie's position relative to the mile markers
three hours from now.
b. Rewrite this inequality to reveal Natalie's speed.
Need help with this ASAP
On solving the provided question we can say that - the inequality equation which will be formed is 290x [tex]\geq[/tex] -23 + y
What is inequality?A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.
here,
we have 290x
so the inequality equation which will be formed is
-y + 290x [tex]\geq[/tex] -23
290x [tex]\geq[/tex] -23 + y
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A biology class examined some flowers in a local meadow. They saw 36 flowers, of which 25% were perennials. How many perennial flowers did the students see?
Answer: nine
Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9
Answer:
9
Step-by-step explanation:
1 first split 36 by 4 because 25% is 1/4
2 once when divided you should get 9 because 9x4 is 36
Solve each equation for both variables help please 15 points
Answer:
x = 12 and y = 11
Step-by-step explanation:
4x+3y=-15 -----equation 1st
4x-y = -27 ____equation 2nd
then,
Multiple equation second by 3 and slove it with equation first
4X +3Y = -15
12X -3Y = -81 (Multiples it with 3)
-8x = -96 (subtracted)
x=-96/-8
therefore, x=12
again,
from equation first
4x+3y = -15
or 4 × 12 + 3y = -15
or 3y = -15+48
or 3y= 33
or y=33/3
therefore, y =11
I hope this helps. If you have any doubt feel free to ask!!
Answer:
x = -6, y = 3
Step-by-step explanation:
1) 4x + 3y = -15
2) 4x - y = -27
0 + 4y = 12 subtract equation (2) from equation (1)
4y = 12
y = 12/4 = 3 substitute y = 3 into either equation 1 or 2 and solve for x
4x + 3(3) = -15
4x = -24
x = -6
Check your answers by plugging x = -6, y = 3 into the equations:
4(-6) + 3(3) = -15 correct!
4(-6) - 3 = -27 correct!
Find two Equivalent fractions of 4/2
Answer:
40/20 & 22/11
Step-by-step explanation:
To find an equivalent fraction to 4/2, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:By dividing the original fraction by 2, we get:4 ÷ 2 / 2 ÷ 2 = 21. By multiplying the original fraction by 2, we get:4 × 2 / 2 × 2 = 8/4. Here is the full list of equivalent fractions to 4/2. 2/1, 4/2, 6/3, 8/4, 10/5, 12/6, 14/7, 16/8, 18/9, 20/10, 22/11, 24/12, 26/13, 28/14, 30/15, 32/16, 34/17, 36/18, 38/19, 40/20...
PLEASE HELP ASAP DUE TODAY NOW!!!!!!!!!!!
Answer:
0.910
Step-by-step explanation:
since it'snot perfect it can't be one and since it a positive slope it is 0.9102.
A model of a railroad car has a Scale Ratio of 1:87.1. If the model railroad car is 1.4 in high, how
tall is the actual railroad car?
Please answer this for me quick it’s due on Monday for me!!!
Answer:
The scale ratio of 1:87.1 means that for every 1 unit of measurement on the model (in this case, inches), there are 87.1 units of measurement on the actual railroad car. This means that the actual railroad car is 87.1 times larger than the model in every dimension. If the model is 1.4 inches tall, the actual railroad car would be 1.4 x 87.1 = <<1.4*87.1=122.54>>122.54 inches tall.
If tan k times 90 = 0 then k is an even integer.
It is true that If tan k times 90 = 0 then k is an even integer.
What is meant by integer?An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples. All positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity are included in the category of integers.
Here,
Since they include negative numbers but otherwise follow the same rules, integers add to this collection of numbers. Due to the fact that all positive integers are whole numbers, not all integers will be whole numbers (because certain integers can be negative).
To Use the unit circle
tan(x) = 0 only when x is 0 or a multiple of 180 (in degrees)
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One pair of base angles of an isosceles trapezoid each have a measure of 2(x–10)°. The other pair of base angles of the trapezoid each have a measure of (4x+8)°. What is the value of x?
Answer:
x = 32
Step-by-step explanation:
• any lower base angle is supplementary to any upper base angle.
here base angle = 2(x - 10) and upper base angle = 4x + 8
supplementary angles sum to 180°
sum the base and upper base angles and equate to 180
2(x - 10) + 4x + 8 = 180
2x - 20 + 4x + 8 = 180
6x - 12 = 180 ( add 12 to both sides )
6x = 192 ( divide both sides by 6 )
x = 32
How much is the monthly amortization on an automobile loan of ₱ 900,000 to be amortized over a 5-year period at a rate 9.5% compounded monthly?
The monthly amortization on the automobile loan, given the loan amount, the period, and the compounding frequency, is ₱ 18, 901.68
How to find the amortization ?The monthly amortization is constant so it will be an annuity. Seeing as we have the loan amount, this means that the present value of an annuity formula can be used to find the monthly amortization.
First, find the period in months:
= 5 x 12 months a year
= 60 months
The interest in months :
= 9 . 5 % / 12 months per year
= 9.5 / 12 %
The monthly amortization is:
= Loan amount / ( Present value interest factor of annuity, 60 periods, 9.5 / 12 %)
= 900, 000 / 47.614827336156
= ₱ 18, 901.68
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Is the answer 650 or 277 ?
Answer:
Step-by-step explanation:
The product of all of the solutions of (4x + 2k)(2 -5x ) = 0 is (−15). Find k.
Answer:
k = 75------------------------------
Given equation:
(4x + 2k)(2 - 5x) = 0Its solutions are:
4x + 2k = 0 and 2 - 5x = 04x = - 2k and 2 = 5xx = - 0.5k and x = 0.4The product of the solutions is -15:
- 0.5k * 0.4 = - 15- 0.2k = - 15k = - 15/- 0.2k = 75