equation in slope-intercept form of the line that pae through the point (4, 7) and is parallel to the line represented by y = 2x - 5 is ( y - y1 ) = m( x - x1 ) => y - 7 = 2 (x-8) => 2x - y - 1 = 0
What is slope?A number that specifies a line's direction and slope is known as the slope or slope of a line in mathematics. A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x).
equation is -
y = 2x - 5
since these are parallel to each other,
slope, m= 2
now the equation is -
( y - y1 ) = m( x - x1 )
y - 7 = 2 (x-8)
2x - y - 1 = 0
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Kana tried to solve the system of equations below. She says there are no solutions. Is Kana correct? Explain your reasoning.
The solution for the given system of equations:
x = 6 and y = 6.
Kana is incorrect about the solutions of the given equations.
What are algebraic properties?Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.
Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Identity: a + 0 = a , a ⋅ 1 = a
Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1
Distributive: a ( b + c ) = a b + a c
Given equations,
4x-2y=12 -----(a)
2x+2y=24 -----(b)
Multiplying -2 to the equation (b) like kana solution
-2 (2x+2y=24 )
By Distributive property
-2(2x+2y) = -2(24)
- 4x - 4y = - 48 ---------(c)
Now adding equation (a) and equation(c)
4x - 2y = 12
- 4x - 4y = - 48
__+___+____+__
- 6y = -36
⇒ y = 36/6 = 6.
Putting value of y in equation (b).
2(x) + 2(6) = 24
2x + 12 = 24
2x = 24 - 12
2x = 12
x =12/2 = 6
By the above calculation,
Value of x = 6 and
value of y = 6.
Hence, for the system of equations given
the solutions are:
x = 6 and y = 6
which proves that Kana is incorrect that there are no solutions.
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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...
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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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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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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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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Is the answer 650 or 277 ?
Answer:
Step-by-step explanation:
hello i neeed help with my math question 5
Answer:
Add a file to it.
Step-by-step explanation:
We can't see anything.
2. Two sidewalks in a park are represented by lines on a coordinate grid.
Sidewalk 1: 3x + 3y = 6
Sidewalk 2: y = x + 6
(a) Find the solution to the system of equations by using the substitution method.
(b) Show ALL of your steps.
Answer: x is -2 and y is 4 if needed (-2,4) is the origin form
Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of y=-x+2 to y=-(-2)+2 mult -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4
cesar is making a solution for his chenistry class. he puts 3/4 gram sodium chloride and 1/3 gram potassium chloride on the scale. what is the combined mass of the compounds?
The combined mass of the compounds is 13/12 grams
How to determine the combined mass of the compounds?From the question, we have the following parameters that can be used in our computation:
3/4 gram sodium chloride and 1/3 gram potassium chloride
The combined mass of the compounds is then calculated as
Combined mass = sodium chloride + potassium chloride
Substitute the known values in the above equation, so, we have the following representation
Combined mass = 3/4 + 1/3
Evaluate the sum
Combined mass = 13/12
Hence, the combines mass is 13/12 grams
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WILL GIVE POINTS
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
a. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x
b. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x
c. On Day 3, Ben's post will have 2(3)^3 = 227 = 54 shares, Carter's post will have 10(2)^3 = 108 = 80 shares. On Day 10, Ben's post will have 2(3)^10 = 259049 = 118098 shares, Carter's post will have 10(2)^10 = 101024 = 10240 shares.
d. Adding 45 to the function representing Amber's photo shares changes the function to f(x) = 3(4)x + 45. The new function will shift the graph upward by 45 units.
e. Based on the functions, Ben's post travels the fastest because the base of the exponent, 3, is greater than the base of the exponent, 2, for Carter's post.
f. It depends on the goal of the post. If the goal is to reach a larger audience quickly, then having more friends initially but fewer shares like Carter is preferable. But if the goal is to reach a smaller audience but with a more engaged audience, then having fewer friends initially but more shares like Amber is preferable.
What is exponential function examples?An exponential function is one in which the variable is an exponent. Mathematically, it is defined as f of R in R, such that f(x) = ax, where a ϵ R, a > 0 and a ≠ 1. The graph of this function is a curve obtained by finding some ordered pairs that belong to the function and drawing this curve that passes through them.
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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.
-15 POINTS-
A.
B.
C.
Answer:
Trapezoid
Step-by-step explanation:
The math
true or false 3 times the speed will have 9 times the force of impact
Answer: true
Step-by-step explanation:
Which graph represents the solutions to this equation?
X²+8x=-20
Answer:
The one with the vertex of (-4,4)
Step-by-step explanation:
how to work out the area of a parallelogram
the base timed by the height
least common number
( sorry i forgot what its called )
of 598 and 45
The least common multiple of 598 and 45 is 26, 910
How to find the least common multiple ?To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.
This gives:
598 prime factorization :
2 x 13 x 23 = 598
45 prime factorization :
3 x 3 x 5 = 45
The least common multiple is;
= 2 x 13 x 23 x 3 x 3 x 5
= 26, 910
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A _____ is a flat surface that has no thickness.
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.
Find the measure of angle A,
The value of the Angle A is 74.3°.
What is Relation between angle and Side of a triangle?The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.
The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.
We know:-AB/sin(c)=AC/sin(a)=BC/sin(b)
8/sin(a)=5/Sin37°
Angle= 74.3°.
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Identify each angle pair as Complementary, Supplementary, Adjacent, or Vertical. Select from the drop
down menu. Select the most specific choice.
Answer:
A. Adjacent
B. Complementary
C. Complementary
Step-by-step explanation:
Select largest number from 16,48,8
Answer:
48.
Step-by-step explanation:
8 < 16 < 48
48 > 16 > 8
Answer:
Step-by-step explanation:
Select largest number from 16,48,8
A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
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Triangle ABC has vertices A(-3, 3), B(2, 5), and C(4, - 3).
a. What is the x-coordinate of the centroid of triangle ABC?
(-,5/3)
Answer:
Step-by-step explanation:
To find the x-coordinate of the centroid of triangle ABC, we need to take the average of the x-coordinates of the three vertices of the triangle. The x-coordinates of the vertices of triangle ABC are -3, 2, and 4, so the average of these three numbers is (-3 + 2 + 4) / 3 = (3) / 3 = 1.
Therefore, the x-coordinate of the centroid of triangle ABC is 1. The correct answer is (-,1). The given answer (-,5/3) is not the correct x-coordinate of the centroid.
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
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
10,14,18,22,26 find the 12 term of the sequence
Answer:
30,34,38,42,46,50,54,58,62,66,70
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]
Manicure sets at nails by Nina are marked up 47% from the cost of $8.36. What does a manicure set cost in Nina’s store?
Answer:
The cost of a manicure set in Nina's store is $12.30.
Step-by-step explanation:
To find the cost of the manicure set in Nina's store, you can use the following formula:
Selling price = Cost + Cost * Markup percentage
Substituting the given values into this formula, you get:
Selling price = $8.36 + $8.36 * 47%
To find the value of the markup percentage, you can convert 47% to a decimal by dividing it by 100: 47/100 = 0.47
Then you can use this value in the formula to find the selling price:
Selling price = $8.36 + $8.36 * 0.47