Answers
The solution of the system of equations is (x, y) = (9/2, -7/10).
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
To solve a system of equations, we can use any of the following methods:
Substitution method,
Elimination method,
Matrix method.
Let's use the substitution method to solve the given system of equations.
We can solve the first equation for z:
z = 7 - 3x - 2y
Substituting this expression into the third equation, we get:
3x + 2y + 3(7 - 3x - 2y) = 1
This simplifies to:
-5x - 3y + 21 = 1
Adding 5x and 3y to both sides, we get:
21 = 5x + 3y + 1
Subtracting 1 from both sides, we get:
20 = 5x + 3y
Dividing both sides by 5, we get:
4 = x + 3/5 y
Substituting this expression into the first equation, we get:
3(x + 3/5 y) + 2y + 7 = 7
This simplifies to:
2y = -7/5
Dividing both sides by 2, we get:
y = -7/10
Substituting this value into the expression for x, we get:
x = 4 - 3/5(-7/10)
This simplifies to:
x = 4 + 21/10
x = 9/2
Hence, the solution of the system of equations is (x, y) = (9/2, -7/10).
To learn more about the Linear equations visit,
https://brainly.com/question/28144615
#SPJ1
Related Questions
i need help
Cerise waters her lawn with a sprinkler that sprays water in a circular pattern at a distance of 15 feet from the sprinkler. The sprinkler head rotates through an angle of 300°, as shown by the shaded area in the accompanying diagram.
What is the area of the lawn, to the nearest square foot, that receives water from this sprinkler?
Responses
a. 79 ft. 2
b. 94 ft.2
c. 707ft.2
d. 589 ft.2
Answers
A sector is a part of a circle that is bounded by an arc and two radii. Thus the area of the lawn is Option D. 589.
What is the circle about?A circle is a figure that is bounded by curved lines called circumference. Some parts of a circle are radius, sector, diameter, chord, circumference, arc etc.
A sector can be defined as a part of a circle which is bounded by two radii and an arc.
The area of a sector can be determined by;
Area of a sector = (θ/360) *r²
where: θ is the measure of the internal angle of the sector
r is the radius of the sector
In the given question, it can be observed that the area of the lawn that receives water from the sprinkler has the shape of a sector.
So that:
Area of the lawn = (300/360)*22/7 * 15²
= 589.2857
Area of the lawn = 589²
Learn more about the area of a sector of a circle at https://brainly.com/question/22972014
#SPJ1
Complete the two-column proof. Drag the missing statements into the correct order.
Given: ∠1≅∠2 ; JK║AB
Prove: ∆CDL is an isosceles triangle.
Answers
By using the property of isosceles triangle, it can be proved that-
∆CDL is an isosceles triangle
What is isosceles triangle?
At first, it is important to know about triangle.
A triangle is a two dimensional three sided figure. A triangle has three sides and three interior angles.
A triangle whose any two sides are equal are called isosceles triangle.
JK || AB [Given]
[tex]\angle 1 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 4[/tex] [Corrosponding angle]
[tex]\angle 1 \cong \angle 2[/tex] [Given]
[tex]\angle 3 \cong \angle 4[/tex] [Transitive property of congruence]
CL [tex]\cong[/tex] DL [Converse of isosceles triangle theorem]
∆CDL is an isosceles triangle [Def. of isosceles triangle]
To learn more about isosceles triangles, refer to the link-
https://brainly.com/question/1475130
#SPJ1
in a regression analysis, the standard error of the estimate is determined to be 4. in this situation, the mse
Answers
The mse will be 16 in the given case as mse is the square of standard error.
What is regression analysis ?
Regression analysis is a group of statistical procedures used in statistical modelling to determine the relationships between a dependent variable (often referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon), and one or more independent variables (often referred to as "predictors," "covariates," "explanatory variables," or "features").
Given, the standard error = 4
We know that standard error is the square root of mse ( mean squared error ).
So, mse = (standard error)^2
= 4^2
= 16.
Learn more about Regression analysis from the link given below :
https://brainly.com/question/7781679
#SPJ4
solve the following inequality 7x-3/9 ≥ 8 - 2x. Then graph the solution on the number line
Answers
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
Answers
The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations with the same solution?The equation is given as
2.3p – 10.1 = 6.5p – 4 – 0.01p
Evaluate the like terms on the right-hand side
So, we have the following representation
2.3p – 10.1 = 6.49p – 4
The above equation is an equivalent equation of the given equation
Multiply through the equation by 100
So, we have:
100(2.3p – 10.1 = 6.5p – 4 – 0.01p)
Evaluate
230p – 1010 = 650p – 400 – p
The above equation is also an equivalent equation of the given equation
Hence, the equations with the same solution are represented above
Read more about equivalent equations at
brainly.com/question/2972832
#SPJ1
The dimensions of this polygon are shown in feet (ft).
10ft/3ft/4ft/8ft
What is the area, in square feet, of the polygon?
Answers
The required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².
Given that,
The dimensions of this polygon are shown in feet (ft). 10ft/3ft/4 ft/8 ft. The area, in square feet, of the polygon is to be determined.
A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc
Here,
Assumed that all the polygons are square,
The area of the square is given as (side)².
1,
Side = 10 ft
Area of the square = [10 ft]² = 100 ft²
Similarly,
For side 3 areas is 9 ft²,
For side 4 areas is 16 ft²,
For side 8 areas is 64 ft²,
Thus, the required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².
Learn more about polygon here:
https://brainly.com/question/24464711
#SPJ1
Write your answer in interval notation.
3x + 4 < - 17 OR 2x + 2 > - 4
Answers
Answer:
x < 3 or x ≥ 11
Step-by-step explanation:
(-∞, 3) or [11, ∞)
Step-by-step explanation:
subtract 4 from each side
2x < 6 . or . 3x ≥ 33
x < 3 or x ≥ 11
make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then
she used the graphing tool to find the equation of the line of best fit:
y = -29 202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
A. 10
B. 89
C. 118
D. 208
Answers
89.086 milliliters of juice will be in a glass with 7 ice cubes.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Equation of line: y = -29 202x + 293.5.
So, for 7 ice cubes i.e., x= 7
The amount of juice is
y= -29.202 (7)+ 293.5
y= -204.414+ 293.5
y= 89.086
Hence, the juice is 89.086 milliliters
learn more about Algebra here:
https://brainly.com/question/24875240
#SPJ1
Help please will mark brainiest!
Answers
Answer:
A = 12cm^2 B = 18cm^2 C = 54cm^2
Step-by-step explanation:
area = side 1 x side 2
A triangle has vertices at F (6, 3), G (3, 4), and H (1, 7). What are the coordinates of each vertex if the triangle is rotated 180° about the origin counterclockwise?
Answers
To rotate a triangle 180° about the origin counterclockwise, we can take each vertex of the triangle and reflect it across the origin. This will produce a new set of coordinates for each vertex that is the same distance from the origin as the original, but on the opposite side of the origin.
For example, the vertex F has coordinates (6, 3). If we reflect this point across the origin, we get the new point (-6, -3). Similarly, the vertex G has coordinates (3, 4), which become (-3, -4) when reflected across the origin, and the vertex H has coordinates (1, 7), which become (-1, -7) when reflected across the origin.
Therefore, the coordinates of each vertex of the triangle after rotating it 180° about the origin counterclockwise are as follows:
F: (-6, -3)G: (-3, -4)H: (-1, -7)Note: When rotating a point about the origin, the direction of rotation (clockwise or counterclockwise) is important. If we had rotated the triangle 180° about the origin clockwise instead of counterclockwise, the new coordinates of each vertex would have been the same as the original, since the triangle would be reflected across the origin and end up in the same position as it started.
Please give me brainliest for more high quality answers! - longstretch
Which choice shows (50+30) + 40 correctly rewritten using the associative property and then correctly simplified"
50+40+30= 90+30= 120
(30+50) + 40 = 80+ 40 = 120
50+ (30+40) = 50 + 70 = 120
O 50+(30+40) = 80 + 40 = 120
Answers
The required simplified value of the given expression is 120.
Given that the expression as;
(50 + 30) + 40.
What is simplification?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here, we have;
= (50 + 30) + 40
Now, using associative property, in parenthesis 50 + 30 become 80.
= 80 + 40
Then using associative property, 80 + 40 become 120
= 120
Thus, the simplified value is 120.
Learn more about simplification here:
brainly.com/question/12501526
#SPJ1
please help geometry
Answers
Answer:
Based on my estimates, Thy answer shall be the letter known as C
What is the slope of a line that is perpendicular to y=4/5x+15 and passes through point (-3,4)?
Answers
Answer:
Below
Step-by-step explanation:
The slope of the given line , m = 4/5
perpendicular slope is - 1/m = - 5/4
What is the value of r in the equation below? Give your answer as a
decimal.
10r - 1.5 = 12.5
3
Answers
+1.5
14/10. Answer is 1.4=r
1.4 is the value of r in the equation given.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. For solving equations The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.
In the given equation,
10r -1.5 = 12.5
Simplifying using PEMDAS
add 1.5 on both sides
10r = 14
divide by 10 into both sides
r = 14/10 = 1.4
Therefore, The value of r in the given equation is 1.4.
Learn more about equations here:
https://brainly.com/question/29657983
#SPJ2
Pls Help ASAP) Willing to give 25 points) Pls show your work) If you don't know pls don't answer.
Answers
The graph of the absolute function g(x) = -|x + 3| - 4 has vertex at (-3, -4) and touches the y -intercept at (0, -7)
Graph of an Absolute FunctionThe graph of an absolute value function is called an absolute value graph. The absolute value graph depicts the distance of a number from the origin. The graph of the absolute value function is symmetric about the y -axis. The graph of the absolute value function makes a right angle at the origin.
In this problem the function given is
g(x) = -|x + 3| - 4
To graph this function, we can use a graphing calculator which will enable us to plot all points accurately.
The graph touches the y -axis at (0, -7)
Learn more on graph of absolute function here;
https://brainly.com/question/22214776
#SPJ1
Seven percent of people receiving your email opened it. Two percent of people receiving your email clicked a link. Of those who opened the email, what percent clicked a link?.
Answers
Therefore, percentage of those who opened the email , clicked a link is 28.57%
What is percentage ?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
Here,
Let the amount of people receiving your email is x
The amount of people receiving your email opened it is 7%
7/100 * x = 0.07x
The amount of people receiving your email clicked a link is 2%
So,
2/100 * x = 0.02x
Therefore,
percent of those who opened the email , clicked a link is
=> 0.02x/0.07x * 100
=> 2/7*100 = 28.57%
Therefore, percentage of those who opened the email , clicked a link is 28.57%
To know more about percentage , visit
https://brainly.com/question/12715980
#SPJ4
What is the image of (5,-4)(5,−4) after a dilation by a scale factor of 33 centered at the origin?
Answers
The new coordinate of point (5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132)(165,132)
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
Given the coordinate (5,-4),(5,-4)
If we apply a scale factor by 33 on any general coordinate (x,y)
Then,
x → 33x and y → 33y
Similarly
5 → 33(5) = 165
-4 → 33(-4) = -132
So the new coordinate will be (165,-132)(165,-132)
Same step apply once more for (5,-4) the coordinate of other is same
Hence "The new coordinate of point (5,-4)(5,-4) after dilation by a scale factor of 33 centered at the origin is (165,-132),(165,-132)
To learn more about scale factor refer to :
https://brainly.com/question/2826496
#SPJ1
When Karen went to bed, there were 234 birds on the lake. When she woke up in the morning, there were 751 birds on the lake. How many birds landed on the lake overnight?
please help
Answers
Answer:
517 birds
Step-by-step explanation:
Subtract 234 from 751, to find how many birds landed on the lake overnight.
Help with is ixl please
Answers
Answer:
q=82
Step-by-step explanation:
The line is equal to 180 degrees, and we have three angles and two have numbers, so this will be easy.
Add 58+40 to get 98, now subtract 98 from 180.
180-98=82
Use the table to determine the location with the greatest amount of rainfall and the location with the least amount of rainfall.
a. Using complete sentences, identify the city with the greatest amount of rainfall and the city with the least amount of rainfall, and express the ratio of their respective rainfalls as a decimal number, rounded to the nearest hundredth.
b. Describe what this ratio tells you.
Answers
The region with the most rainfall is Beaumont, and the region with the least is El Paso.
How can I find the locations with the most and least rainfall?
Making sure to utilize the same units is the first step. Let's convert everything to meters as a result.
Austin equals 0.8687 m
Beaumont = 1.534 meters.
Galveston = 1,095 meters
El Paso equals 0.246 m
Del Rio equals 0.4953 m
South Padre=0.655 meters
Based on this, El Paso has the least amount of rainfall, while Beaumont has the most.
How are the two locations connected?
These locations have a ratio of 1.5 to 0.2, or 1.5/ 2 = 0.7. According to this ratio, the amount of rainfall in these locations varies by 0.7 meters.
Visit brainly.com/question/12907709 to learn more about rainfall.
#SPJ1
HELP ASAP PLS
Answers
Directions: simply ugly each expression by combining like terms
10x-16x
Answers
Answer: -6x
Step-by-step explanation:
Just subtract the coefficients:
The coefficient of 10x is 10
The coefficient of 16x is 16
now do ten minus 16 (TIP: if you don't really like negative numbers, then an easy way of subtracting 10-16 is 16-10=6, then add the negative sign to 6; -6)
10 - 16 = -6
Now put the x back: -6 = -6x
The correct answer is -6x
does 3+4x is less than or equal to 2(1+2x have a solution
Answers
Answer:
NO
Step-by-step explanation:
You need x on one side of the equation.
3+4x ≤ 2(1+2x)
3+4x ≤ 2+4x
-4x -4x
3 ≤ 2
Since there is no x value there is no solution
Reuben added 8 fish to his pond each day for 48 days. what was the total change in the number of fish in the pond
Answers
Answer:sd
Step-by-step explanation:
8(48)=384
The formula for the volume of
a square pyramid is V = 1/3s(2 squared) h.
Rewrite the formula in terms of h.
Then find the height of a square
pyramid with volume V = 400 cm3
and side length s = 10 cm.
Answers
Therefore , the height of the given square pyramid is 12 cm.
What is the plain meaning of volume?The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.
Here,
To calculate a square pyramid's volume in terms of h, use the formula h = [tex]\frac{3V}{s^{2} }[/tex]
With V = 400 and s = 10 cm, a square pyramid's height is 12 cm.
The equation for calculating the volume of a square pyramid is:
=> 1/3 [tex]s^{2}[/tex]h =V
=> h = [tex]\frac{3V}{s^{2} }[/tex]
Therefore we can rewrite the formula in terms of h you need to:
=> h = [tex]\frac{3V}{s^{2} }[/tex]
You must substitute these numbers into the following formula to determine the height of a square pyramid with volume V = 400 and side lengths s = 10 cm:
=> h = 3 * 400 / [tex]10^{2}[/tex]
=> 3* 400/100
=> 3*4
=> 12
Therefore , the height of the given square pyramid is 12 cm.
To know more about volume , visit
https://brainly.com/question/13338592
#SPJ1
A computer store buys a computer system at a cost of $605.25. The selling price was set at $807, but after a year the computer did not sell. The store then advertises a 25% markdown on the $807 computer system. Find the sale price.
PLS HELP
Answers
Answer: $605.25
Step-by-step explanation:
100% - 25% = 75%
807 times 0.75 = $605.25
The sale price is $ 605.25
GCF of 10 y 5 + 30 y 3 − 15 y
Answers
Answer:
5 y (2 y^4 + 6 y^2 - 3)
Step-by-step explanation:
The given input is 10y^5+30y^3-15y
10y^5+30y^3-15y has factors i.e 5 y (2 y^4 + 6 y^2 - 3)
By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 5 y (2 y^4 + 6 y^2 - 3) and simplified as 10 y^5 + 30 y^3 - 15 y
Help me!
I don’t know what it’s asking and im scared
What do I do in here
Answers
Using the scale factor, the length of the new figures are as 21 inches, 21 inches and 36 inches.
How to find the length of the new figure using scale factor?Bill drew a scale drawing of the figure using a scale factor of 3.
A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
The length of the drawing are 7 inches , 7 inches and 12 inches . The length of the new figure can be found as follows.
using the scale factor
length 1 = 7 × 3 = 21 inches
length 2 = 7 × 3 = 21 inches
length 3 = 12 × 3 = 36 inches
learn more on scale factor here: https://brainly.com/question/29464385
#SPJ1
In trapezoid ABCD(AB ∥CD), point M∈AD, so that AM:MD=3:5. Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N ,respectively. Find AC:PC.
please answer soon will give brainiest if correct.
Answers
AC:PC.= 3/5, as Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N.
What is Trapezoid?A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides.
The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.
A trapezoid is a closed, four-sided, two-dimensional figure that has both a perimeter and an area.
The bases of the trapezoid are the two sides of the shape that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the shortest distance between two parallel sides.
According to our question-
Consider about the triangles ACB and PCN.
These triangles contain
Since angle C is the common angle and the transversal BC cuts two parallel lines PN and AB, angles ABC and PCN are congruent as equivalent angles by virtue of the reflexive property.
In light of the AA Similarity Theorem, triangles ACB and PCN are comparable.
Similar triangles have matching sides that are proportionate, thus
3/8 / 5/8= 3/5
Hence, Due to the fact that Line l AB and goes via point M to intersect Leg BC and the diagonal AC at points P and N, AC:PC.= 3/5.
learn more about trapezoid click here:
https://brainly.com/question/1410008
#SPJ1
Subtracting a number is the same as adding its additive inverse. For which elevation do we need to find the additive inverse? What is the additive inverse of that elevation?
Answers
Yes subtracting a number is the same as adding its inverse. We have to find the additive inverse of a function.
What is additive inverse?The additive inverse of a number is the number which when we add to the number results zero.
How to find additive inverse?Complex numbers are made up of both real and fictitious numbers. A + iB, where A is the real number and B is the imaginary number, is a complex number.
The additive inverse of A + iB should now be a value that, when added to a given complex number, produces the result zero. It will therefore be -(A + iB).
Suppose we have to find additive inverse of 5.
Let the additive inverse of 5 be x.
So,5+x=0
x=-5
So the additive inverse of 5 is -5.
Hence to find additive inverse of a positive number we have to just put a negative mark and for a negative number we have put positive mark in front of the number.
Learn more about additive inverse here:
https://brainly.com/question/1548537
#SPJ1