Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
x − 3y = −3
4x + 3y = 18
Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.)
(x, y) =
The system of linear equations has one and only one solution.
x = 3 and y = 2.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
x - 3y = -3 _____(1)
4x + 3y = 18 ______(2)
We will solve the equation to check its solutions.
x - 3y = -3 can be written as:
x = -3 + 3y ____(3)
Putting in (2) we get,
4(-3 + 3y) + 3y = 18
-12 + 12y + 3y = 18
15y = 18 +12
15y = 30
y = 2
Putting in (3)
x = -3 + 3 x 2 = -3 + 6 = 3
x = 3
We see that,
x = 3 and y = 2
Putting in the equation it is satisfied.
x - 3y = -3
3 - 3 x 2 = -3
3 - 6 = -3
-3 = -3
4x + 3y = 18
4x3 + 3x2 = 18
12 + 6 = 18
18 = 18
Thus,
The system of linear equations has one and only one solution.
x = 3 and y = 2.
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Using the line AB, name two line segments.ACBA,BoAB, CAC, CBCB,B
Point C is between points A and B, this point divides the line AB into two segments:
One segment goes from point A to point C and can be named line segment AC
The second segment goes from point C to point B and can be named line segment CB
The correct option is the third one AC,CB
Hey can someone please help me? I’m confused. I’ll give brainliest
Answer:
1.50t + 3 < 9
Step-by-step explanation:
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
total cost of taking and Gatorade is less than $9
Answer:
1.50t + 3 < 9
Step-by-step explanation
each taki is $1.50
each Gatorade is $3 and he only bought one so its $3.
the total cost of taking and Gatorade is less than $9
hey please help. this has to do with exponential functions. i have to do 225 problems before midnight. it’ll mean a lot!!!
Answer:
Explanation:
To complete the missing values, we have to evaluate the function at the x-values given.
For example, to find the number below x = -1, we will put in x = -1 into y = (1/6)^x.
Putting in x = - 1 in y = (1/6)^x gives
[tex]y=(\frac{1}{6})^{-1}[/tex]which simplifies to give
[tex]y=\frac{1}{1/6}[/tex][tex]\rightarrow y=6[/tex]Similarly, for the missing value below x = -2, we put in x = - 2 into y = (1/6)^x to get
[tex]y=(\frac{1}{6})^{-2}[/tex]which simplifies to give
[tex]y=\frac{1}{(1/6)^2}[/tex][tex]\begin{gathered} \rightarrow y=6^2 \\ \rightarrow y=36 \end{gathered}[/tex]Similarly, for the missing value below x = 2, we put in x = 2 in y = (1/6)^x to get
[tex]y=(\frac{1}{6})^2[/tex]which simplifies to give
[tex]y=\frac{1}{36}[/tex]Hence, the missing value to be put in is 36.
To summerise, the missing values are
x | -2
3/4 times x equals 3.45 solve for x
4.6
1) Since 3/4x = 3.45, then we can solve it for x
3/4x = 3.45 Multiply both sides by 4 to eliminate the fraction
3x =13.80 Divide both sides by 3
x= 4.6
2) So x is equal to 4.6, and that is the answer
What is the least common multiple of 4 and 8?
Enter your answer in the box.
Step-by-step explanation:
answer is 8
detail is in the picture
A restaurant serves sandwiches using slices of bread in the shape of a right triangle. If the legs of the
triangle are each 6 inches, how long is the hypotenuse in inches? Round your answer to the nearest inch.
6 inches
8 inches
10 inches
12 inches
Answer: 8 inches
Step-by-step explanation:
1) Set up the equation
If you know both sides of the triangle are 6 inches you can set a Pythagorean equation. C is the hypotenuse
[tex]6^2+6^2=c^2\\36+36=c^2\\72=c^2\\\sqrt{72} = \sqrt{c^2} \\8.485 = c[/tex]
2) Rounding
After you found 8.485, the tenth place is less the 5, so it will round down to 8 inches.
The answer is 8 inches
A manufacturer throws out gaskets with weights that have an absolute deviation of more than 0.06 pound from the mean weight of the batch. The weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. Which gaskets should be thrown out? Use an absolute value inequality to justify your answer.
If the weights (in pounds) of the gaskets in a batch are 0.58, 0.63, 0.65, 0.53, and 0.61. The gaskets that should be thrown out is 0.53 and the inequality is: 0.54 ≤ w ≤ 0.66.
Means and inequalityUsing this formula to determine the mean
Mean = ∑x/n
Mean = 0.58 + 0.63 + 0.65 + 0.53 + 0.61 /5
Mean = 3/6
Mean = 0.6
Since the mean is 0.6 the gasket that are less than 0.53 and more than 0.66 (0.6±0.06) should be thrown out which in turn means that 0.53 should be thrown out.
Inequality :
0.54 ≤ w ≤ 0.66
Therefore 0.53 should be thrown out.
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You visit your favorite restaurant and order an appetizer for $5.99, a drink for $4.50, your meal for $10.99, and dessert for $3.75. The sales tax is 9%. and you
would like to leave an 18% tip. Find the total cost of your meal.
Using percentages, we can conclude that the total cost of the meal is approximately $33.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Frequently, it is indicated by the percent sign, "%".By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the total cost of the meal:
$5.99 + $4.50 + $10.99 + $3.75 = $25.23Sales tax on the bill: 9%
25.23/100 × 9 = $2.2977Total bill printed on bill: $25.23 + $2.2977 = $27.527718% tip of the bill:
27.5277/100 × 18 = 4.954986Rounding off: $5Total cost of meal: $27.5277 + $5 = $32.5277
Rounding off: $33Therefore, using percentages, we can conclude that the total cost of the meal is approximately $33.
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can you please cancer C what is the explicit function and the relationships for the term please I dont understand
EXPLANATION
Given the sequence:
C. 3, 12, 27, 48, 75
First, we need to calculate the difference between terms:
12-3 = 9 27-12 = 15 48-27 = 21 75 - 28 = 27
Arithmetic relationship: 9, 15 , 21, 27
To obtain the sequence we use the following formula:
[tex]a_n=a_1+(n-1)d[/tex]Now, we need to calculate the appropriate difference between terms:
15-9 = 6 21-25 = 6 27 - 21 = 6
So the constant difference is 6 and the nth term will be:
nth = 6n + 3
*a1=3
So, the relationship will be:
n Value Relationship
1 12 3 + (6*1 +3)
2 27 12 + (6*2 + 3)
3 48 27 + (6*3 + 3)
4 75 48 + (6*4 + 3)
5 108 75 + (6*5 + 3)
n n-1 + (6n+3) n-1 + (6n+3)
Explicit function: y = (n-1) + (6n+3)
Create an image of rectangle ABCD that is
translated 6 units to the right and 3 units up
by plotting the corresponding vertices.
Plot the vertex that corresponds to A.
The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .
In the question ,
a rectangle is given
the vertex of the rectangle ABCD is given as
A(-10,-6) , B(-10,-2) , C(-6,-2) , D(-6,-6) .
On applying the translation 6 units to right and 3 units up ,
the rule is (x,y)→(x+6,y+3)
by applying the rule for the translation
we get image as
A'(-4,-3) ,B'(-4,+1) , C'(0,1) , D'(0,-3)
The image is plotted below .
Therefore , The image of the rectangle ABCD translated 6 units to the right and 3 units up is shown below .
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A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph what is the speed of the flying carpet
The most appropriate choice for speed will be given by-
Speed of the flying carpet is 15.2 mph
What is speed?
The distance travelled by the body per unit time is called speed of the body.
If d is the distance travelled by the body and t is the time taken, then
speed = [tex]\frac{d}{t}[/tex]
Speed is a scalar quantity as the direction is not taken into account.
Here,
Let the speed of the flying carpet be [tex]x[/tex] miles
A flying carpet flies 2.4 miles with the wind
Time taken flying with the wind = [tex]\frac{2.4}{x +4}[/tex]
The flying carpet flies 1.4 miles against the wind
Time taken flying against the wind = [tex]\frac{1.4}{x - 4}[/tex]
By the problem,
[tex]\frac{2.4}{x +4} = \frac{1.4}{x-4}[/tex]
[tex]2.4(x - 4) = 1.4(x + 4)\\2.4 x - 9.6 = 1.4 x + 5.6\\2.4 x - 1.4 x = 9.6 + 5.6\\[/tex]
[tex]x = 15.2[/tex] mph
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Find the area of the figure
Answer:
126.5 cm²
Step-by-step explanation:
Hello!
This shape can be split into a rectangle and a triangle.
The rectangle's dimensions are 8 and 11, and the base and height of the triangle are 11 and 7 respectively.
Area of Rectangle:A = b * hA = 8 * 11A = 88Area of Triangle:A = b*h/2A = 11 * 7/2A = 77/2A = 38.5The combined area is 88 + 38.5 which is 126.5 cm².
Find the value of x. Write an equation andsolve, showing ALL the work.
Given:
The objective is to find hte value of x.
The value of x can be calculated by basic proportionality theorem.
[tex]\frac{12}{14}=\frac{9}{x}[/tex]Thus, the required equation is obtained.
The value of x is,
[tex]\begin{gathered} x=9\cdot\frac{14}{12} \\ x=\frac{9\cdot14}{12} \\ x=\frac{126}{12} \\ x=10.5 \end{gathered}[/tex]Hence, the value of x is 10.5
Plot the point then make a staircase using the given slope connect the points to form a line answer the questions below
use the provided equation below to complete the table and graph
Answer:
Explanation:
To complete the table, we need to replace each value of x and calculate the value of y.
So, if x = - 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}x-2 \\ y=\frac{3}{8}(-16)-2 \\ y=-6-2 \\ y=-8 \end{gathered}[/tex]If x = -8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(-8)-2 \\ y=-3-2 \\ y=-5 \end{gathered}[/tex]If x = 0, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(0)-2 \\ y=0-2 \\ y=-2 \end{gathered}[/tex]If x = 8, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(8)-2 \\ y=3-2 \\ y=1 \end{gathered}[/tex]If x = 16, y is equal to:
[tex]\begin{gathered} y=\frac{3}{8}(16)-2 \\ y=6-2 \\ y=4 \end{gathered}[/tex]So, the complete table is:
x y
-16 -8
-8 -5
0 -2
8 1
16 4
Finally, we can graph the table, so:
Look at this graph: 101 9 8 7 6 5 4 3 2. 1 0 1 2 3 4 5 6 7 8 9 10 What is the slope?
The slope can be calculated as the quotient between the difference in the y-coordinates of two points, and the difference in the x-coordinates of the same two points.
We pick any 2 known points, like (0,2) and (5,4).
We calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{5-0}=\frac{2}{5}=0.4[/tex]Answer:
The slope is m=2/5=0.4
Rafael wants to construct a square inscribed in a circle. He divides the circle into six equal arcs and then draws line segments between four ofthe points. What was the first error Rafael made?:toThe first error Rafael made wasV. A square is constructed by first
The first error Rafael made was that he made six arcs instead of taking the perpendicular bisector of the diameter and then making 4 arcs.
A square is constructed first by taking the perpendicular bisector of the diameter and making the four arcs and then joining them to make the square.
48% of people in a certain country like to cook and 54% of people in the country like to shop, while 26% enjoy both activities. What is the probability that a randomly selected person in the country enjoys cooking or shopping or both? The probability that a randomly selected person in the country enjoys cooking or shopping or both is ________
The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
48% of people in a certain country like to cook.
And, 54% of people in the country like to shop, while 26% enjoy both activities.
Now,
Probability to like the cook P (C) = 48%
Probability to like the shop P (S) = 54%
Probability to like the both activity P (C∩S) = 26%
So, Probability to like the both activity P (C ∪ S) is calculated as;
P (C ∪ S) = P (C) + P (S) - P (C ∩ S)
P (C ∪ S) = 48% + 54% - 26%
P (C ∪ S) = 102% - 26%
P (C ∪ S) = 76%
P (C ∪ S) = 0.76
Thus, The probability that a randomly selected person in the country enjoys cooking or shopping or both will be;
⇒ P (C ∪ S) = 0.76
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help meeeeeee pleaseee !!!!
The function that represents the cost function is c(x) = 75 + 0.25x
What is the Cost FunctionTo find the cost function c(x), we have to write a linear equation or linear function to represent this.
Initial charge = 75charge per copy = 0.25x = number of copiesThe cost function can be expressed as a function of the number of copies made which can be represented as
[tex]c(x) = 75 + 0.25x[/tex]
The cost of printing x number of pages is c(x) = 75 + 0.25x
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Pls helppppppppppp
It’s not c
Answer: it would be D because m∠NSO+m∠OSL+m∠LSM+m∠MSN=360°
and m∠LSM+m∠SML+m∠MLS≠360° doesnt equal 360 degrees so that one is wrong ∠LSM≅∠NSM is a false statement same with m∠LSO+m∠MSO=180° its false so it would be (D)
hope i helped
Step-by-step explanation:
Write a numerical expression then match words with the expression
Numerical expression: 30 - 10 - 7
In words: Elizabeth had $30, if she spent $10 to buy some pizza and $7 on a soda, how much money does she have left?
Calculate the correlation coefficient for the given data below:
x y
2 21
3 22
48
5 11
6 15
7 14
Round your final result to two decimal places.
The correlation coefficient of the data provided is -0.52.
What is the correlation coefficient?Correlation is a measure that is used in statistics to determine the linear relationship that exists between two variables. Correlation can be positive, negative or zero.
Positive correlation is when two variables move in the same direction. Negative correlation is when two variables move in opposite directions. Zero correlation is when there is no relationship between the variables.
Correlation can be determined using a financial calculator. When the financial calculator is used, the correlation coefficient is -0.52
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A linear function r models the growth of your right index fingernail. The length of the fingernail increases 0.7 millimeter every week. Graph r when r(0)=12.
A nail's length in x weeks of m=0.7 slope with a growth rate of mm per week b starting length follows.
The slope-intercept form of a straight-line equation is indicated by y = mx + b. X and y denote the line's distance from the x- and y-axes, respectively. When x = 0, the value of b equals y, and m indicates how steep the line is.
Given, r(0) = 12
According to the question, fingernail increases by 0.7 millimeters every week. So, m = 0.7 which is the slope of the equation of a straight line.
r(0) = 12 is the b of the y = mx + b.
Now, the final equation is:
r(x) = 0.7x + 12
As a result, the slope of r(x) length of a nail in x number of weeks of m=0.7, with growth rate in mm per week b starting length.
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hey there Ms or Mr could you help me out with this please?
If a quadrilateral is a parallelogram, then its opposite sides are congruent therefore:
[tex]\begin{gathered} GH\cong JI \\ and \\ GJ\cong HI \end{gathered}[/tex]Using the distance formula:
[tex]\begin{gathered} GH=\sqrt[]{(5-1)^2+(3-1)^2} \\ GH=\sqrt[]{16+4} \\ GH=\sqrt[]{20} \\ JI=\sqrt[]{(0-4)^2+(3-5)^2} \\ JI=\sqrt[]{16+4} \\ JI=\sqrt[]{20} \\ GH\cong JI \end{gathered}[/tex][tex]\begin{gathered} GJ=\sqrt[]{(0-1)^2+(3-1)^2} \\ GJ=\sqrt[]{1+4} \\ GJ=\sqrt[]{5} \\ HI=\sqrt[]{(4-5)^2+(5-3)^2} \\ HI=\sqrt[]{1+4} \\ HI=\sqrt[]{5} \\ GJ\cong HI \end{gathered}[/tex]Step 2:
The diagonals are given by:
[tex]\begin{gathered} JH=\sqrt[]{(0-5)^2+(3-3)}^2 \\ JH=\sqrt[]{25} \\ JH=5 \\ GI=\sqrt[]{(4-1)^2+(5-1)^2} \\ GI=\sqrt[]{9+16} \\ GI=\sqrt[]{25} \\ GI=5 \\ JH=GI \\ 5=5 \\ so\colon \\ JH\cong GI \end{gathered}[/tex]I'll give brainliest!
Answer:
9 is the answer
Answer: 9 cubes
Step-by-step explanation:
9 * 9 is 81 which makes the floor of it
since its a cube, we multiply 81 by 9, giving 729
Assume that Lines L and M are parallel. Find a pair of acute, corresponding angles.
Select all that apply.
A. q and w
B. r and y
C. x and s
D. q and y
E. s and y
F. r and x
G. t and w
H. t and z
Answer:
Choice E and F
Step-by-step explanation:
acute = less than 90
What will it cost to buy fencing to go around a rectangular garden with a length of 25 ft. and a width of 30 ft.? The fencing costs $3.17 per linear foot.
It will cost $348.7 to buy fencing to go around the rectangular garden.
The length of the rectangular garden is 25 feet.The width of the rectangular garden is 30 feet.The cost of fencing per linear foot is $3.17.We need to buy fencing to go around the whole rectangular garden.This means we need the total length of the boundary.The boundary is the same as calculating the perimeter of the rectangular garden.The perimeter of the rectangular garden is two times the sum of its length and its breadth.The perimeter is 2*(25+30) = 110 feet.The total cost of fencing the whole rectangular garden is the product of the cost of fencing per foot and its perimeter.The total cost of fencing the rectangular garden is 3.17*110 = $348.7.To learn more about perimeter, visit :
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In 2017 the population of Rexburg, Idaho was 28,337 people. The population was expected to grow at a rate of about 1.21% per year. Based on these numbers, what would we predict the population of Rexburg will be in the year 2020?
Answer:
29,378 people
Step-by-step explanation:
[tex]28337 \times {1.0121}^{3} = 29378[/tex]
Mowgli usually walk from home to the beach, and returns on an elephant It takes him 40 minutes altogether. One day he traveled on the elephant from homebto the beach and back, which took 32 minutes. How much time would he need to travel the same distance on foot?
The time it would take Mowgli from the home to the beach and from the beach to the home on foot is 48 minutes.
What is the time it would take to travel on foot?Based on the assumption that the average speed that Mowgli travels from the home to the beach and from the beach to the home is constant, the time it takes from the home to the beach and from the beach to the home should be equal.
Time from the home to the beach = 32 /2 = 16 minutes
The time it took Mowgli to walk from the home to the beach = 40 - 16 = 24 minutes
Time it would take Mowgli to travel from the home to the beach and from the beach to the home = 24 x 2 =48 minutes
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