Answer:
(-4,-7)
Step-by-step explanation:
Multiply both sides of the first equation by-5 or 2 (I'll use 5) and both sides of the second equation by - 2 or 3 (I'll use -2).
3x - 2y = 2
5(3x-2y)= 5(2)
-15x - 10y = 10
2x - 5y = 27
-2(2x - 5y) = -2(27)
-4x + 10y = -54
Now you see that the absolute values of the y-values of the 2 equations match up . They are still the same equations but scaled up.
-15x + 10y = 10
-4x - 10y = -54
Add to eliminate y.
-11x = 44
Divide both sides by -11.
[tex]\frac{-11x}{-11} = \frac{44}{-11}[/tex]
x = -4
Plug back in to either equation to solve. I'll use the first equation.
3x - 2y = 2
x = - 4
3(-4) - 2y = 2
-12 - 2y = 2
Add 12 on both sides.
-12 + 12 - 2y = 2 + 12
- 2y = 14
Divide -2y on both sides.
[tex]\frac{-2y}{-2} = \frac{14}{-2}[/tex]
y = -7
(-4,-7)
Street D has a x-intercept of 5 and a y-intercept of -4. Write this street's equation in point slope form using the x-intercept as (x1,yl).
The point-slope form of the equation of Street D is; y = 0.8·(x - 5)
What is the point-slope of the equation of a straight line?The point-slope of the equation of straight line can be expressed mathematically as (y - y₁) = m·(x - x₁)
The coordinates of the point
The x-intercept of the street D = 5
The y-intercept of the street D = -4
The x-intercept is the point the graph of the equation of the street intersects the x-axis.
At the x-intercept, the y-coordinate of the point of the graph is 0, therefore, the coordinate of the x-intercept is (5, 0)
The y-intercept is the point at which the graph of the function intersects the y-axis, therefore, the x-coordinate of the graph at the y-intercept is 0
The y-intercept of the street D is therefore; (0, -4)
The slope, m, of the equation of the street is therefore;
m = (-4 - 0)/(0 - 5) = 4/5 = 0.8
The point-slope form of the equation, using the x-intercept, (5, 0) is therefore;
y - 0 = 0.8·(x - 5)
y = 0.8·(x - 5)
Learn more about the point-slope form of a straight line equation here:
https://brainly.com/question/8424741
#SPJ1
Select all of the following that are quadratic equations. 2 x2+ 12 x = 0 x2 - 2 x = 4 x + 1 x3 - 6 x2 + 8 = 0 5 x - 3 = 0 5 x - 1 = 3 x + 8 9 x2 + 6 x - 3 = 0
Answer:x2 - 2x = 4x + 1" and "9x2 + 6x - 3 = 0
Step-by-step explanation: that will be your quadratic equation
DUE ASAP PLS HELP ME!!!!!!!
Answer:
A 5 and -5
Step-by-step explanation:
You take the root of both sides to solve.
Which expression is equivalent to 3/4 divided by 5/7
Answer:
Since there are no abcd options, I'll just give the answer here: 3/4 divided by 5/7 is 21/20
Step-by-step explanation:
First, we have to convert the division sign to a multiplication sign, so we do that by using the reciprocal of the second fraction:
3/4 divided by 5/7 will turn into 3/4 * 7/5
Here is how to solve that:
3 7
-- * --
4 5
3*7 is 21, and 4*5 is 20, so the final fraction is 21/20, final answer.
What is the radius of a circle whose equation is x2 y2 8x â 6y?
The radius of a circle with equation is x² + y² + 8x - 6y + 21 = 0 is 2 units .
In the question ,
it is given that ,
the equation of circle is ⇒ x² + y² + 8x - 6y + 21 = 0 ,
we know that the general equation of the circle is x²+y²+2fx+2gy+c=0
so , the radius of the circle is calculated using the formula ,
radius = √(f² + g² - c)
On comparing the given equation with general equation
we get , the values of f as 4 and g as -3 .
So after substituting the values of f , g and c in the radius formula ,
we get ,
radius = √(16 + 9 - 21)
= √(16 + 9 - 21)
= √(25 - 21)
= √(4) = 2 .
Therefore , the radius of given circle is 2 units .
The given question is incomplete , the complete question is
What is the radius of a circle whose equation is x² + y² + 8x - 6y + 21 = 0 ?
Learn more about Circles here
https://brainly.com/question/5720980
#SPJ4
answer these questions and get 30 points
Answer: 5/4, -7/11, 1/2
Step-by-step explanation:
Slope of ordered pairs (y2-y1/x2-x1): -5/4
Y intercept (b in y=mx+b): (0, -7/11)
Slope of graph (rise over run) : 1/2
Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What
percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.
Answer:
12%
Step-by-step explanation:
Christy Peterson's total income last year was $77,340. Of that amount, she spent $7,240 on transportation costs and $2,100 on clothing. What percent of Christy's total income did she spend on transportation and clothing combined? Round your answer to the nearest percent.
7,240 + 2,100 = $9,340
9,340 / 77,340 = 0.120765
0.120765 * 100 = 12.0765%
rounded = 12%
How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
[tex]f(x)=x^3[/tex]
If something is subtracted from variable [tex]x[/tex] it means the graph shifted toward right and something is added to [tex]y[/tex] value then the graph is shifted up.
[tex]f(x)=(x-8)^3[/tex]
graph shifted toward right by [tex]8[/tex] units right
[tex]f(x)=(x-8)^3+3[/tex]
graph shifted toward right by [tex]3[/tex] units up
Thus the new function is:
[tex]g(x)=(x-8)^3+3[/tex]
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
6
Step-by-step explanation:
The y intercept is when x=0
Help me please!! Ill rate 5/5 for whoever answers first
Answer:
7) d (21)
6) a (102)
Step-by-step explanation:
For the first question, we should start with what we know first:
When angles are complementary then, their angles add up to 90.
So here we have 69 + something = 90.
We find out that the missing angle (angle B) is 21.
For this second question, we know that a straight line has an angle of 180. Here we have a straight line, but only part of the angle in which we only have 78.
Since we know 78 + x = 180
Then we can figure out that x = 102.
Shen and Linda are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.
Answer:
a. shen's car
8 gallons
b. 400 miles
shen's car
FIRST PERSON GETS BRAINLIEST! Identify the measure of angle x
Answer:
Step-by-step explanation:
180=28+73+x
180-28-73=79
79=x
A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 320 yards wide. What is the area of the actual park, in square yards?
PLEASE HELP!!!!! 20 POINTS
The area of the rectangular park is 143360 square yards.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 minute = 60 second
1 km = 1000 m
We have,
Scale drawing of a rectangular park:
Wide = 5 inches
Length = 7 inches
Actual rectangular park:
Wide = 320 yards
Length = 448 yards
Now,
5 inches = 320 yards
7 inches = 7/5 x 320 yards
7 inches = 7 x 64 yards
7 inches = 448 yards
Now,
The area of the actual park.
= Length x Wide
= 448 x 320
= 143360 square yards.
Thus,
143360 square yards is the area of the actual park.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ1
△ABC has the verticies at A(4,5) B(-3,6) and C(-1,8)
the following transformations have been done to the triangle in that order...
rotated 90 degrees
reflected across the line y=0
then translated according to the rule (x+3,y-3)
The required coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3) are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].
To determine the coordinates of the vertices of △ABC after it has been rotated 90 degrees, reflected across the line y=0, and then translated according to the rule (x+3,y-3), we need to apply these transformations to the coordinates of the original vertices in the order given.
First, we rotate the triangle 90 degrees counterclockwise around the origin. This transformation can be represented by the matrix:[cos(90) -sin(90)][sin(90) cos(90)]
Applying this matrix to the coordinates of the vertices of △ABC, we get:A' = [-5, 4]B' = [6, -3]C' = [8, -1]
Next, we reflect the triangle across the line y=0.
This transformation can be represented by the matrix:[-1 0][0 1]
Applying this matrix to the coordinates of the vertices of △ABC', we get:A'' = [5, 4]B'' = [-6, -3]C'' = [-8, -1]
Finally, we translate the triangle according to the rule (x+3,y-3).
This transformation can be represented by the matrix:[1 0][0 1]
Applying this matrix to the coordinates of the vertices of △ABC'', we get:A''' = [8, 1]B''' = [-3, -6]C''' = [-5, -4]
Therefore, the coordinates of the vertices of △ABC after given transformations are A''' = [8, 1], B''' = [-3, -6], and C''' = [-5, -4].
To learn more about the transformations click here :
https://brainly.com/question/28029674
#SPJ1
find the gradient of the line below
The gradient of the line in the given graph is 1/2.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the graph, let us consider two points from where the line is passing.
(-2, 3) and (2, 5).
Gradient is nothing but slope of the line.
m=5-3/2-(-2)
=2/4
=1/2
Hence, the gradient of line in the given graph is 1/2.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ1
a bakery sells 5800 muffins in 2010. the bakery sells 7420 muffins in 2015. write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
The required linear model is y = 5800 + 324x.
What is a linear equation?
Equations whose variables have a power of one are called linear equations.
Given, a bakery sells 5800 muffins in 2010
the bakery sells 7420 muffins in 2015
So, the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Then, the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Then our linear model will be:
y = 5800 + 324x
Hence, the required linear model is y = 5800 + 324x.
To learn more about the linear model
https://brainly.com/question/28860456
#SPJ4
initially alex, betty, and charlie had a total of 444444 peanuts. charlie had the most peanuts, and alex had the least. the three numbers of peanuts that each person had formed a geometric progression. alex eats 55 of his peanuts, betty eats 99 of her peanuts, and charlie eats 2525 of his peanuts. now the three numbers of peanuts each person has forms an arithmetic progression. find the number of peanuts alex had initially.
The number of peanuts that Alex had initially will compute to a total of 108 in the observations of the situation provided above.
The computation of the peanuts in the hands of Alex can easily be ascertained using the given information, and input of values from the same into the generalized formula, as shown below,
Let p be the number of peanuts. Thus, it can be stated that
3p = 444 – 9 – 25 – 5
3p = 409
p = 409/3 = 135.3
Now, it can also be stated that
p+9=144
[tex]\[\dfrac{144}{k} + 144 + k \cdot 144 = 444 \\\\ \\\dfrac{144}{k} + k \cdot 144 = 300\\\\ \\ \dfrac{12}{k} + k \cdot 12 = 25\\\\\\k= \dfrac{4}{3} \\\\\\\\ \dfrac {144\cdot 3}{4} =108}\][/tex]
Therefore, Alex has a total of 108 peanuts initially.
Learn more about computation here:
https://brainly.com/question/28171935
#SPJ4
Complete question
Initially, Alex, Betty, and Charlie had a total of 444 peanuts. Charlie had the most peanuts, and Alex had the least. The three numbers of peanuts that each person had formed a geometric progression. Alex eats 5 of his peanuts, Betty eats 9 of her peanuts, and Charlie eats 25 of his peanuts. Now, the three numbers of peanuts each person has forms an arithmetic progression. Find the number of peanuts Alex had initially.
A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75. If the
manager spent a total of $38.50, how many pens did the store manager purchase?
The number of pens the store manager purchase, if A store manager purchased a total of 15 pens and markers, is 7.
What is the 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.
Given:
A store manager purchased a total of 15 pens and markers. Each pen cost $3.50, and each marker cost $1.75, the manager spent a total of $38.50,
Write the equation of the statement as shown below,
x + y = 15 and 3.5x + 1.75y = 38.5
Here, x is the number of pens and y is the number of markers,
Solve the equations by using the elimination method,
x = 7, y = 15 - 7 = 5
To know more about equation:
https://brainly.com/question/12788590
#SPJ1
Please help me! It’s so hard
The range of the data-set in this problem has a value given as follows:
7.7.
How to calculate the range of a data-set?The range of a data-set is calculated as the difference between the largest value of the data-set and the smallest value of the data-set.
The data-set in this problem is defined as follows:
{6.2, 9.1. 2.9, 1.6, 9.3, 5.5, 8.3}
Hence to obtain it's range we have to obtain the smallest and the highest values from these values between the brackets.
The smallest value of the data-set and the highest value of the data-set are defined as follows:
Smallest value: 1.6.Highest value: 9.3.Hence the range of the data-set is given by the difference of 9.3 and 1.6, as follows:
Range = 9.3 - 1.6 = 7.7.
More can be learned about the range of a data-set at https://brainly.com/question/24326172
#SPJ1
Please help, it’s asap!
The population standard deviation of the data is gotten from using the sum of squares and count which gave us 1.5
Population Standard DeviationStandard deviation is used to find the values of a particular data that is dispersed or scattered. Standard deviation can be defined as the deviation of the values or data from an average mean. Lower standard deviation assumes that the values are very close to their average. Meanwhile higher values mean the values are far from the mean value. Note that the value of standard deviation value can never be negative.
The data given is
5, 8, 8, 5
The formula is given as
δ = standard deviationμ = sum of squaresn = countδ = √(μ / n)
δ = √(9/4)
δ = √2.25
δ = 1.5
The standard deviation is 1.5
Learn more on population standard deviation here;
https://brainly.com/question/26941429
#SPJ1
write a liner function f with the given values
f(0) = -4; f(10) = -12
f(x)=
Answer:
f(x) = - x - 4----------------------
Linear function is:
f(x) = mx + b, where m- slope, b- y-interceptGiven points:
f(0) = - 4 and f(10) = - 12The first point represents the y-intercept, b = - 4.
Find the slope:
m = (-12 - (-2)) / (10 - 0) = - 10/10 = - 1The function is:
f(x) = - x - 4horace horsecollar is interested in the opinion of vacationers at disney world. he creates a short survey and administers it to every 1000th person to enter the park, starting with the 364th person. what method did horace use to select his sample?
The method used by Horace to select his sample is Systematic Sampling.
A form of probability sampling technique called systematic sampling selects sample members from a broader population using a predetermined, periodic interval in addition to a random beginning point. The population size is divided by the intended sample size to arrive at this range, which is known as the sampling interval.
Horace desires to select every 1000th person to enter the park, starting with the 364th person. So he selects the 364th person, 1364th person, 2364th person, and so on. This is a perfect situation for Systematic Sampling.
To read more about Systematic Sampling, visit https://brainly.com/question/24317913
#SPJ4
2300 people attended a football game. If 25% of the people who attended were teenager, how many teenager attended the game? Divide/cale down to olve for the miing percent
The teenager whom attended a football game will be 575 people.
How to calculate amount of teenager?It shown that all the people whom attended a football game about 2300 people.And has been written that amount of teenager is 25% from 2300 people whom attended.Then we should know amount of 25% from 2300.We can solve it by, 2300 × 25% = 575.Then we can assume that amount of teenager whom attended there were 575 teenager.It can proved by, 25% is 1/4 from 100%. Then 575 must be 1/4 from total audience, then 575 can be multiple by 4.575 × 4 = 2300, then the answer is appropriate.Learn more about the percentage here: brainly.com/question/28144353
#SPJ4
Point M is the midpoint of PQ , and LM is the perpendicular bisector of PQ . Write a two-column proof to show that LP=LQ .
The two-column proof shows that LP = LQ
LP = √(LM² + PM²)
LQ² = √(LM² + PM²)
LP = LQ
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Point M is the midpoint of PQ.
This means,
PM = QM ______(A)
LM is the perpendicular bisector of PQ .
L
/ | \
/ | \
/ | \
P M Q
Applying the Pythagorean theorem.
Triangle LMP is a right triangle.
LP = LM² + PM² _____(1)
Triangle LMQ is a right triangle.
LQ² = LM² + QM² _____(2)
Thus,
From (A), (1), and (2) we get,
LP = √(LM² + PM²)
LQ² = √(LM² + PM²)
LP = LQ
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ1
How do you find the equation of a line with 2 lines?
By entering the values of m and b into the slope-intercept form of a line (y = mx + b), you may obtain the equation for the line.
Given,
Equation of a line;
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
We have to find the equation of a line with 2 points;
Here,
Using the slope formula, determine the slope.Slope, m = (y₂ - y₁) / (x₂ - x₁)
To find the y-intercept, use the slope and one of the points (b).The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.
Therefore,
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx + b).
Learn more about equation of line here;
https://brainly.com/question/259557
#SPJ4
Jimm tossed a die several times. He got the number "3" on 8 of the tosses. What is the best estimate of the total number of times he tossed the die?
The number of times to get a 3 will be 24 times.
What is the best estimate of the total number of times he tossed the die 64 times?It should be noted that the expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables
In this case, Jimm tossed a die several times and he got the number "3" on 8 of the tosses.
Therefore, when there are 64 tosses, the estimate will be:
= 3/8 × 64
= 3 × 8
= 24
The number of times is 24.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Jimm tossed a die several times. He got the number "3" on 8 of the tosses. What is the best estimate of the total number of times he tossed the die 64 times?
a rectangle is bounded by the -axis and the semicircle (see figure). what length and width should the rectangle have so that its area is a maximum?
Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.
From the question, we have
Area = A = xy
A = xsqr(9-x^2)
Taking the derivative and set = 0
A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0
A' = -x^2 + 9 -x^2 = 0
-2x^2 =-9
x^2 = 9/2
x = 3/sqr2 = (3/2)sqr2 = 4.242
y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121
Dimensions of the rectangle are 4.242 and 2.121 respectively
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Complete question:
A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ4
The slope of line p q is (v – z) divided by . the slope of line p prime q prime is divided by (w a) – (x a). both lines have a slope that is divided by . therefore, the lines are .
The slope of Line P Q is (v - z) divided by (w - x). The slope of Line P prime Q prime is
(v + b) - (z +b) divided by (w + a) - (x + a). Both lines have a slope that is (v - z) divided by (w - x). Therefore, the lines are parallel.
Slope of line :
Line slope is a measure of the slope and direction of a line. Finding the slope of a line in the coordinate plane helps predict whether the line is parallel or perpendicular without actually using a compass. The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.
The formula for the slope is
m = (y₂ - y₁)/ (x₂ - x₁)
Where (x₁, y₁) and (x₂, y₂) are the points
We have given a line PQ passing through points (x,z ) and (w,v) then slope of line is
m = ( v- z)/(w-x) --(1)
that is line lie in XZ- plane .
The slope of line p prime and q prime
m' = (( v- b) - (z-b))/(w-a)- (x-a)
= (v -b -z + b) /(w-a -x + a)
= (v-z)/(w-x) --(2)
from (1) and (2) we get , m = m'
So, both lines are parallel lines .
To learn more about Slope of line, refer:
https://brainly.com/question/16949303
#SPJ4
Complete question:
The slope of Line P Q is (v - z) divided by ________. The slope of Line P prime Q prime is _________ divided by (w + a) - (x + a). Both lines have a slope that is _______ divided by _______. Therefore, the lines are _______.
Answer: in the picture
Step-by-step explanation:
how many eight digit numbers contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes? leading 0s are allowed.
0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.
According to collect from the data
Let us assume that the data as followed by
How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.
Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.
2,3,3,4,4,4
now then:
= 8!/2!3!3!4!4!4!
= 8.7.6.5.4!/2×6×6×24×24×4!
= 35/864
Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .
Learn more about Permutations and combinations here:
brainly.com/question/4658834
#SPJ4
What do we use SSS SAS ASA and AAS to prove?
The rules SSS SAS ASA and AAS are the rule that is used to prove the congruence of the triangle
The rules SSS SAS ASA and AAS are used to prove the congruence of the triangles .
The congruence means if shape and size of the one shape is same as the shape and size of the another shape, then we can say that both the shapes are congruent
If you consider the case of triangle, two triangle can be prove as congruent if the specifics sides and angles of the triangle is equal to the other triangles.
The rules that used to prove the congruence of the triangles are
SSS - side-side-side rule of congruence
SAS = side-angle-side rule of congruence
ASA = angle-side-angle rule of congruence
AAS = angle-angle-side rule of congruence
Therefore, these rules are used to prove the congruence of the triangle
Learn more about congruence rule here
brainly.com/question/29548914
#SPJ4