y = 2x + 6
y = -3x + 1
Equality
2x + 6 = -3x + 1 6 is in the left side and is positive so we substract 6 in both sides
2x +6 - 6 = -3x + 1 - 6
Simplify
2x = -3x - 5
Add -3x in both sides
2x + 3x = -3x + 3x - 5
Simplify
5x = -5
2x + 3x = 1 - 6
5x = -5
x = -5/5
This is the x-coordinate
x = -1
Which list orders the numbers from least to greatest?
[tex]\pi \: 4.3 \: 3.6 \: 13 \: \sqrt{19} [/tex]
Answer:
[tex]\pi[/tex], 3.6, 4.3, [tex]\sqrt{19}[/tex], 13
Step-by-step explanation:
[tex]\pi[/tex]≈ 3.14 This is an approximation because [tex]\pi[/tex] never repeats or terminates.
[tex]\sqrt{19}[/tex] This is also a number that never repeats or terminates. If you put this in your calculator, I estimated it to
4.359
Using this information, I put the numbers in order.
can anyone help me? solve using system of linear equations using elimination x – y - 3z = 4 2x + 3y – 3z = -2 x + 3y – 2z = -4
The solution is x = 2, y = -2 and z =0
How to solve the system of equations?The system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Start by eliminating y
To do that, we subtract (2) from (3)
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
This gives
-x + z = -2
Make x the subject in the above equation
x = z + 2
Substitute x = z + 2 in (1) and (2)
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Solve the equations
-2z - y = 2
-z + 3y = -6
Multiply -z + 3y = -6 by 2
-2z + 6y = -12
Start by eliminating z
Subtract -2z + 6y = -12 from -2z - y = 2
7y = -14
Evaluate
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the values of the variables are x = 2, y = -2 and z =0
Read more about system of equations at
https://brainly.com/question/13729904
#SPJ1
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmYou have to multiple the whole number and the fraction if you don’t know how to do it
We need to find how much spare represents the given space for vegetables.
The total are is 24 square feet and she will use 3/4 of the space for vegetables.
Then, you need to multuply the result by 3 and then, we need to divide 24 by 4.
Therefore:
24*(3/4) =72/4 = 18
Hence, she will use 18 square feet for vegetables.
Lily likes to collect records. Last year she had 12 records in her collection. Now she has 15 records. What is the percent increase of
her collection?
The percent increase of her collection is
Remember to write a let statement and answer the question. A collection of dimes abs quarters has a value of $1.35. List all possible combinations of dimes abs quarters.
Let d represents dimes and q represents quarter.
Note that a dime is 10 cent, which is same as one over ten, and a quarter is one over four
[tex]\begin{gathered} d=\frac{1}{10}=0.1 \\ q=\frac{1}{4}=0.25 \end{gathered}[/tex]Given that a collection of dimes abs quarters has a value of $1.35, then this can be represented as below:
[tex]0.1d+0.25q=1.35[/tex]Multiply through by 100 to get
[tex]\begin{gathered} 100\times0.1d+100\times0.25q=100\times1.35 \\ 10d+25q=135 \end{gathered}[/tex]To get the possible combinations of dimes and quarters, lets the try different values of that will satisfy the equation.
When q is 1,
[tex]\begin{gathered} 10d+25q=135 \\ q=1 \\ 10d+25(1)=135 \\ 10d+25=135 \\ 10d=135-25 \\ 10d=110 \\ d=\frac{110}{10}=11 \end{gathered}[/tex]Therefore, 11 dimes and 1 quarter abs is a possible combination
When q is 3
[tex]\begin{gathered} 10d+25(3)=135 \\ 10d+75=135 \\ 10d=135-75 \\ 10d=60 \\ d=\frac{60}{10} \\ d=6 \end{gathered}[/tex]Also, 6 dimes and 3 quarter abs is a possible combination
When q is 5
[tex]\begin{gathered} 10d+25(5)=135 \\ 10d+125=135 \\ 10d=135-125 \\ 10d=10 \\ d=\frac{10}{10} \\ d=1 \end{gathered}[/tex]Also, 1 dime and 5 quarter abs is a possible combination
When q is 7
[tex]\begin{gathered} 10d+25(7)=135 \\ 10d+175=135 \\ 10d=135-175 \\ 10d=-40 \\ d=\frac{-40}{10}=-4 \end{gathered}[/tex]Since negative answer was gotten for dimes, 7 quater wouldn't give any possible combination.
Hence, there are It can be found that there are there are three possible combinations, these are:
11 dimes and 1 quarter abs
6 dimes and 3 quarter abs
1 dime and 5 quarter abs
prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
First try was incorrect Fill in the blank. Constant: a number that is next to a variable.
A number that is right next to a variable. For instance,
[tex]5x+6[/tex]the number 6 is a constant.
Answer parts a through E for the function shown below
Solution
We are given the function
[tex]f(x)=x^3+4x^2-x-4[/tex]First, Let us do the simplification or factorization
[tex]\begin{gathered} f(x)=x^2(x+4)-1(x+4) \\ f(x)=(x^2-1)(x+4) \\ f(x)=(x-1)(x+1)(x+4) \end{gathered}[/tex](a).
The coefficient of x^3 is positive
(b).
So basically, we set f(x) = 0 to get the x - intercepts
[tex]\begin{gathered} f(x)=(x-1)(x+1)(x+4) \\ (x-1)(x+1)(x+4)=0 \\ x=1,-1,-4 \end{gathered}[/tex]The x - intercepts are
[tex]x=1, -1, -4[/tex]The graph of f(x) is also given below
Look at the figure below. 8 8 4 4 Which expression can be evaluated to find the area of this figure?
Answer
[tex]8^2-4^2[/tex]Step-by-step explanation
The figure consists of a square with sides of 8 units from which a square of sides of 4 units has been subtracted.
The area of a square is calculated as follows:
[tex]A=a^2[/tex]where a is the length of each side.
Substituting a = 8, the area of the bigger square is:
[tex]A_1=8^2[/tex]Substituting a = 4, the area of the smaller square is:
[tex]A_2=4^2[/tex]Finally, the area of the figure is:
[tex]A_1-A_2=8^2-4^2[/tex]When nee, a standard tire has 10/32 inches of tread. When only 2/32 inches of tread remains, tire needs to be replaced. If this occurs after 40,000, what thickness of tire rubber is lost every 1,000 miles driven? Answer in fractions of an inch.
Given:
A standard tire has 10/32 inches of tread.
The tire needs to be replaced when only 2/32 inches of tread remains left.
Here the tire is needed to be replaced after 40,000 miles.
To find:
The thickness of tire rubber lost every 1,000 miles.
Step-by-step solution:
According to the question,
The tire is replaced when only 2/32 inches of tread remain left.
The new tire has 10/32 inches of tread.
Thus tire needs to loose:
10/32 - 2/32 = 8/32 inches of tread.
This means upon traveling for 40,000 miles, 8/32 inches of tread is lost.
So their ratio equals:
40,000 = k (8/32)
k = 40,000 × 32 / 8
k = 40,000 × 4
k = 1,60,000
So to calculate for 1000 miles:
1000/x = 1,60,000
1/x = 1,60,000 / 1000
1/x = 160
x = 1 / 160 inches
Thus we can say for every 1000 miles, 1 / 160 inches of tread is lost.
Determine which of the following are true statements. Check all that apply.
Substitute in each inequality the given corresponding solution (x,y) and prove if it makes a true math expression:
1.
[tex]\begin{gathered} -5x-9y\ge60 \\ (-3,-5) \\ \\ -5(-3)-9(-5)\ge60 \\ 15+45\ge60 \\ 60\ge60 \end{gathered}[/tex]As 60 is greater than or equal to 60, (-3,-5) is a solution for the inequality.2.
[tex]\begin{gathered} 4x-3y>1 \\ (5,7) \\ \\ 4(5)-3(7)>1 \\ 20-21>1 \\ -1>1 \end{gathered}[/tex]As -1 isn't greater than 1, (5,7) is not a solution for the inequality3.
[tex]\begin{gathered} -10x+8y<12 \\ (-9,-10) \\ \\ -10(-9)+8(-10)<12 \\ 90-80<12 \\ 10<12 \end{gathered}[/tex]As 10 is less than 12, (-9,-10) is a solution for the inequality.4.
[tex]\begin{gathered} 9x+7y\le98 \\ (9,3) \\ \\ 9(9)+7(3)\le98 \\ 81+21\le98 \\ 102\le98 \end{gathered}[/tex]As 102 is not less than or equal to 98, (9,3) is not a solution for the inequalityAnswer For Brainiest!
What 3D Objects' do EACH Net Make?
Looking at the 4th net, we see it has what seems to be 4 squares in a line. And two of them are each one united into another square.
Then, when we join the left side of the left square and the right side of the right square, we obtain a 3D object with 4 square faces, and 2 empty faces also in the form of a square.
After that, we can fold down the upper square face, and fold up the other one.
We will get the following 3D object, that is a cube:
Therefore, the 4th net makes a cube.
what us the area of the triangle if the perimeter is 16
We are asked to find the area of the given triangle.
Recall that the area of a triangle is given by
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Where b is the base and h is the height of the triangle.
Let us find the base and height from the given figure.
As you can see,
base = 6
height = 4
[tex]\begin{gathered} A=\frac{1}{2}\cdot b\cdot h \\ A=\frac{1}{2}\cdot6\cdot4 \\ A=\frac{1}{2}\cdot24 \\ A=12 \end{gathered}[/tex]Therefore, the area of the triangle is 12 square units.
STRUCTURE Quadrilateral DEFG has vertices D(-1, 2), E(-2, 0), F(-1,-1) and G(1, 3). A translation maps quadrilateral DEFG to
quadrilateral D'EFG. The image of D is D'(-2,-2). What are the coordinates of E, F, and G'?
E (
FD
G' (
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Given,
Quadrilateral DEFG with vertices;
D = (-1, 2)E = (-2, 0)F = (-1,-1) G = (1, 3)We have to find the coordinates of E', F', G'.
A figure is translated when it is moved to the left, right, up, or down.
The original figure's points are all translated (moved) by the same amount and in the same direction.
Here,
Compare the coordinates of D with the coordinates of D' to determine the mapping rule that converts DEFG to D'E'F'G'.
D = (-1, 2)
D' = (-2, -2)
The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Then,
The mapping rule is:
(x, y) → (x-1, y-4)
To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
That is,
The coordinates are;
E' = (-3, -4)F' = (-2, -5)G' = (0, -1)Learn more about translation maps here;
https://brainly.com/question/13007985
#SPJ1
To graph the inequality y>-3x-4, you would draw a dashed line.O A. TrueO B. False
True.
Since it is strictly greater
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. Which probabilities correctly completethis probability distribution for the 50 pieces of fruit, in the order listed?
Given:
Total number of pieces = 50
So, the probabilities are:
Apples
[tex]P(apples)=\frac{8}{50}=0.16[/tex]Bananas
[tex]P(bananas)=\frac{10}{50}=0.2[/tex]Lemons
[tex]P(lemons)=\frac{5}{50}=0.1[/tex]Oranges
[tex]P(oranges)=\frac{15}{50}=0.3[/tex]Pears
[tex]P(pears)=\frac{12}{50}=0.24[/tex]Answer: A.
The lower quartile for wages at a coffee shop is $8.25, and the upper quartile is $10.75. What can you conclude? a. Half the workers earn between $8.25 and $10.75. b. The median is $9.50. c. The range is $2.50 H COR B
A)Half the workers earn between $8.25 and $10.75.
1) We must remember that the First Quartile responds to 25% of the data points, as well as the Third Quartile responds to 75% of the data points within this dataset.
2) Since the first quartile and the third quartiles were given, then we can tell that
Half the workers earn between $8.25 and $10.75
The median will present exactly what is the value.
Because the difference between the third and the first quartile corresponds to 50%.
Moreover to that, there's not much information about the dataset to figure the range (Highest minus lowest data point) or the median.
14) A positive number is two fifths of another positive number. The sum of the numbers is 49. What arethe two numbers?
Let's use the variable x to represent the second number. The first number is two fifths of x, so the first number is 2x/5.
If the sum of the numbers is 49, we can write the following equation:
[tex]\frac{2}{5}x+x=49[/tex]Now, solving the equation for x, we have:
[tex]\begin{gathered} \frac{2}{5}x+\frac{5}{5}x=49\\ \\ \frac{7}{5}x=49\\ \\ \frac{1}{5}x=7\\ \\ x=7\cdot5\\ \\ x=35 \end{gathered}[/tex]Let's calculate the first number:
[tex]\frac{2}{5}x=\frac{2}{5}\operatorname{\cdot}35=2\cdot7=14[/tex]Therefore the numbers are 14 and 35.
Jordan owns a house painting service. For each house, they charge $95 plus $60 per hour of work. A linear equation that expresses the total amount of money Jordan earns per house is y=60x+95. What are the independent and dependent variables? What is the y-intercept and the slope?
Answer:
The slope is 60
The y intercept is 95
The independent variable is x (the number of hours)
The dependent variable is y (The amount earned.)
Step-by-step explanation:
Question 1-3
The distance traveled by car, for a duration of time, can be modeled with the equation s= 45t, where s is the distance, in miles, and it is
the time, in hours. Which graph represents this proportional relationship correctly?
120
105
90
Distance (mi)
Distance (mi)
75
60
45
120
30
105
90
15
75
60
45
30
0
15
2
Time (hr)
Time (hr)
100
lon
3
+X
X
120
105
90
Distance (mi)
75
60
45
30
15
0
1
2
Time (hr)
co
X
The equation s = 45t, where s is the distance in miles and it is the time in hours, can be used to simulate the distance driven by a car over a period of time then the car will travel 135 hours in 3 hours.
What is meant by the constant of proportionality?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.
Given: The distance traveled by car at a constant rate is proportional to the time spent driving.
In the equation d = 45 t, d denotes the distance (in miles) and t denotes the time (in hours).
d / t = 45 miles per hour
The constant of proportionality = 45 miles per hour.
Also, the distance traveled by car in 1 hour = 45 miles
The distance traveled by car in 3 hours = 3 × 45 = 135 miles
Therefore, a car will travel 135 hours in 3 hours.
The complete question is:
The distance traveled by car at a constant rate is proportional to the time spent driving. In equation d = 45t, d represents the distance (in miles) and t represents the time (in hours).
A. What is the constant of proportionality? _____ miles per hour
B. How far will the car travel in 3 hours? _______ miles
To learn more about constant of proportionality refer to:
https://brainly.com/question/28413384
#SPJ13
Simplify using the laws of exponents. Use the box to the right of the variable as it’s simplified exponent.
Given:
[tex](15m^8)\placeholder{⬚}^3[/tex]To find:
to simplify using laws of exponents
First, we need to expand the expression:
[tex]\begin{gathered} In\text{ exponent laws, a}^3\text{ = a }\times\text{ a }\times\text{ }a \\ \\ Applying\text{ same rule:} \\ (15m^8)\placeholder{⬚}^3\text{ = \lparen15m}^8)\times(15m^8)\text{ }\times(15m^8) \\ =\text{ 15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\times\text{15 }\times\text{ }m^8\text{ } \\ \\ collect\text{ like terms:} \\ =\text{ 15 }\times\text{ 15 }\times15\text{ }\times m^8\times\text{ }m^8\times\text{ }m^8\text{ } \end{gathered}[/tex][tex]\begin{gathered} Simpify: \\ 15\times15\times15\text{ = 3375} \\ \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8 \\ when\text{ multiplying exponents with same base, } \\ \text{we will pick one of the base and add the exponents together } \\ m^8\text{ }\times\text{ m}^8\text{ }\times\text{ m}^8\text{ = m}^{8+8+8} \\ =\text{ m}^{24} \end{gathered}[/tex][tex]\begin{gathered} 15\times15\times15\times m^8\times m^8\times m^8\text{ = 3375 }\times\text{ m}^{24} \\ \\ =\text{ 3375m}^{24} \end{gathered}[/tex]An auto mechanic recommends that 3 ounces of isopropyl alcohol be mixed with a tankful of gas (14 gallons ) to increase the octane of the gasoline for better engine performance. At this rate, how many gallons of gas can be treated with a 16-ounce bottle of alcohol (You don’t need to translate or understand just solve the word problem please )
Let be "x" the number of gallons of gas that can be treated with a 16-ounce bottle of alcohol.
According to the information given in the exercise, 3 ounces of isopropyl alcohol should be mixed with 14 gallons of gas.
Then, you can set up the following proportion:
[tex]\frac{14}{3}=\frac{x}{16}[/tex]Now you have to solve for "x":
[tex]\begin{gathered} (16)(\frac{14}{3})=x \\ \\ \frac{224}{3}=x \\ \\ x\approx74.67 \end{gathered}[/tex]Therefore, the answer is:
[tex]\approx74.67\text{ }gallons[/tex]Square ABCD is inscribed in a circle with radius 20 m . What is the area of the part of the circle outside of the square
ANSWER:
456 square meters
STEP-BY-STEP EXPLANATION:
The first thing is to represent the problem in the following figure:
To calculate the area of the part of the circle outside of the square, we must calculate the area of the circle and subtract the area of the inscribed square.
To calculate the area of the square, we plant the following, taking into account that the diagonal of the square is equal to twice the radius and the sides equal to the radius times the root of two, like this:
Knowing the value of the side of the square, we can directly calculate the area of the part of the circle outside of the square, subtracting the corresponding areas like this:
[tex]\begin{gathered} A=A_C-A_S_{} \\ A=\pi\cdot r^2-\mleft(r\cdot\sqrt{2}\mright)^2 \\ \text{replacing} \\ A=3.14\cdot20^2-\mleft(20\cdot\sqrt{2}\mright)^2 \\ A=1256-800 \\ A=456 \end{gathered}[/tex]The area of the part of the circle outside of the square is equal to 456 square meters
Pls someone help me! Giving brainless
Answer:
ANSWER=5
Step-by-step explanation:
GIVEN=8+(-3)
(+)×(-)=(-)
SO 8-3=5
PLEASE MARK ME AS BRILLINT
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Order the numbers from least to greatest
Answer:
-1, √4/5, -6/5, √3, 2, -3√9, 2√125
Step-by-step explanation:
A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 5 millimeters long, and the height of the equilateral triangle is 4.3 millimeters. The pyramid's slant height is 3 millimeters. What is its surface area?
The surface area of the triangular base pyramid is 19.75 mm².
How to find the surface area of a pyramid?The surface area of a triangular pyramid is the sum of the area of the whole sides of the triangular pyramid.
Therefore,
Surface area of a triangular pyramid = base area + 1 / 2 (perimeter × slant height)
The base of the triangular pyramid is an equilateral triangle. An equilateral triangle has congruent sides.
Therefore,
base area = 1 / 2 × 5 × 4.3
base area = 10.75 mm²
Hence,
perimeter of the base = 5 + 5 + 5 = 15 mm
Surface area of a triangular pyramid = 10.75 + 1 / 2 (15 × 3)
Surface area of a triangular pyramid = 10.75 + 1 / 2(18)
Surface area of a triangular pyramid = 10.75 + 9
Surface area of a triangular pyramid = 19.75 mm²
learn more on pyramid here: https://brainly.com/question/16472037
#SPJ1
estimate 1/4% of 798
Solve the method.simultaneous equation by graphicaly + 3x = 6y - 2x = 1
The equations given are
[tex]\begin{gathered} y+3x=6............1 \\ y-2x=1............2 \end{gathered}[/tex]The graph of the equations will be shown below
Hence, the solution to the equations is the point where the two equations intersect.
Therefore, the solution is
[tex](1,3)[/tex]Maya started to run on a treadmill after setting its timer for 96 minutes. The display says that she has finished 47% of her run. How many minutes have gone by? Round your answer to the nearest tenth.
Answer:
45.1
Step-by-step explanation:
96 x .47 = 45.12
Rounded to the nearest tenth is 45.1
Percent means per hundred [tex]\frac{47}{100}[/tex] to divide by 100 you move the decimal place to places to the left.