Solve the system of equations.
11x+4y=-46
7x-4y=10
The solution is x = -2 and y = -6.
What are linear equations?First-order equations are linear equations. The coordinate system defines the linear equations for lines. A linear equation in one variable is one in which there is only one variable and the equation has a homogeneous variable of degree 1. There can be more than one variable in a linear equation. When there are two variables in a linear equation, it is referred to as a "linear equation with two variables" and so on.
Given equations 11x + 4y = -46
and 7x - 4y = 10
add both equations
11x + 4y + 7x - 4y = -46 + 10
18x = -36
x = -36/18
x = -2
substitute the value of x in equation
11x + 4y = -46
11(-2) + 4y = -46
4y = -46 + 22
4y = -24
y = -6
Hence the solution for given equations is x = -2 and y = -6.
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Use the law of cosines to find the missing third side
The missing third side BC is approximately 16.93 units. To use the Law of Cosines to find the missing third side (BC), we'll use the formula:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where:
c is the side opposite angle C (BC in this case)
a and b are the known sides (AC and AB, respectively)
C is the angle opposite side c (angle BAC in this case)
Given values:
Angle BAC (C) = 54 degrees
AC (a) = 7.4
AB (b) = 15.8
Now, we can plug the values into the formula and solve for BC (c):
[tex]BC^2 = 7.4^2 + 15.8^2 - 2 * 7.4 * 15.8 * cos(54)[/tex]
To find cos(54), we can use a calculator:
[tex]cos(54 degrees) \approx 0.5878[/tex]
Now, we can continue the calculation:
[tex]BC^2 = 54.76 + 249.64 - 2 * 7.4 * 15.8 * 0.5878\\BC^2 = 54.76 + 249.64 - 17.44\\BC^2 = 286.96[/tex]
Now, find the square root of both sides to get the value of BC:
[tex]BC = \sqrt{286.96} \\BC \approx 16.93[/tex]
So, the missing third side BC is approximately 16.93 units.
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Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Answer:
THE ANSWER IS A
Step-by-step explanation:
Simplify six to the -3rd power over six to the fifth power
how do you reduce the fraction of 28/49
In a casino, the chance of winning a certain game is 14.5%. If you play the game 20 times, what’s your best estimate for the number of times you would win? Round off your answer to the nearest whole number.
if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answer:
a - √b
Step-by-step explanation:
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.x = (1/2) [ 2a +/- √(4a² - 4(a² - b)] = a +/- (1/2)*√(4b) = a +/- √bx = a + √b, or x = a - √b, as expected.
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?
What type of stock receives an equal part of the profits on each share to be distributed after all other obligations of a company have been satisfied?
Suppose you roll two standard number cubes once. Find the probability. P(7 or even)
To roll a seven you could have (1,6) (6,1) (2,5) (5,2) (3,4) (4,3)
6 different ways so 6/36 reduces to 1/6 way of getting a 7
For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 ways, probability is 18/36 reduces to ½
So for either one you now have 1/6 + 1/2 = 6+2/12 = 8/12 reduced to 2/3
25/150 in simplest form
PLease Answer!
The Mali Empire of West Africa was known far and wide for the great wealth of its rulers. The empire fell in the year 1610.
Let x represent any year. Write an inequality in terms of x and 1610 that is true only for values of x that represent years after the year the Mali Empire fell.
the answer is x>1610
If f(x)=6x and g(x) = 4x+1, find ( f o g)(x)
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone is what shape?
Answer:
The answer is a triangle.
Step-by-step explanation:
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
For better visualization, you can also see the attached image.
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
The answer is a triangle.
A cross-section of a cone taken perpendicular to the base and intersecting the apex of the cone is a triangle.
When you cut a cone perpendicular to its base and through its apex, the resulting cross-section will be a triangle. The shape of the cross-section depends on the angle at which you make the cut. If the cut is parallel to one of the sides of the cone, the cross-section will be a right-angled triangle.
If the cut is made at an angle to the sides of the cone, the cross-section will be an isosceles or scalene triangle.
In any case, the cross-section will always be a triangular shape with its vertices at the apex of the cone and the points where the cut intersects the base of the cone.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
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Write 2 expressions that represent the areas of 4 triangles
517.21 km what is the nearest 10km?
Evaluate the expression : (0.4)^3=
The expression when evaluated, can be found to be 0. 064.
How to evaluate the expression ?( 0 . 4 ) ³ means raising the number 0. 4 to the power of 3 , which is the same as multiplying 0. 4 by itself three times. This is how the expression is evaluated.
Start with:
0 . 4 * 0 . 4 * 0 . 4
Calculate each multiplication step:
1st multiplication: 0 . 4 * 0 . 4 = 0 . 16
2nd multiplication: 0 . 16 * 0 . 4 = 0 . 064
So, when you multiply 0. 4 by itself three times ( 0 . 4 * 0 . 4 * 0 . 4), you get the result of 0 . 064.
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Of the 240 shirts on a rack, 40 percent are size medium. How many shirts on the rack are size medium?
First, let’s check for the given:
Shirts on the rack = 240
Medium size shirts = 40% of 240
With the following given, we can now solve for the total
number of shirts on the rack that are size medium.
So, in order to solve for the problem, we multiply 40% to 240:
The decimal equivalent of 40% is 0.4.
240 shirts * .4 = 96 shirts
Therefore, out of 240 shirts on the rack, there are 96 shirts on the rack that are size medium.
To add, the number or ratio that represents a fraction of 100 is called a percentage.
Stuart is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%,what is the sale price of the jeans including tax?
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answer:
we can not multiply matrix A and B.
Step-by-step explanation:
We have been given that
dimension of matrix A = 3 x 2
dimension of matrix B = 3 x 2
Rule of multiplying two matrices:
Two matrix can be multiplied if the column of first matrix is equal to the row of second matrix.
column of first matrix = row of second matrix
Here, we have
Column of first matrix A = 2
Row of second matrix b = 3
Since,, column of matrix A ≠ Row of matrix B
Hence, we can not multiply matrix A and B.
What is the value of x/3y , when x = 18 and y = 3?
3/18
2
3
6
x = 18
y = 3
x/3y becomes 18/3(3) = 18/9 = 2
need help, thank you!
2x+3y=5x−y
y=0
x=?
Answer:
X=4\3
Step-by-step explanation:
A sphere has a radius of 3 and a hemisphere has a radius of 6. Compare the ratio of the volume of the sphere to the volume of the hemisphere.
-cz+6z=tz+83 solve for z
Answer:
The value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]-cz+6z=tz+83[/tex]
Subtract tz from both the sides.
[tex]-cz+6z-tz=tz-tz+83[/tex]
[tex]-cz+6z-tz=83[/tex]
Take z common.
[tex]z(-c+6-t)=83[/tex]
[tex]z(6-c-t)=83[/tex]
Divide 6-c-t from both the sides.
[tex]\frac{z(6-c-t)}{6-c-t}=\frac{83}{6-c-t}[/tex]
[tex]z=\frac{83}{6-c-t}[/tex]
Thus, the value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
A bicycle wheel makes 5 revolutions. Determine how far the bicycle travels in feet. The diameter of the wheel is 32in.
Please help!! I attached an image, will give most brainliest
Daniel and Sofia both solve this system of equations: y = -1.5x + 5.7 y = 0.5x + 0.3 Daniel's solution is (1.1, 2.4). Sofia's solution is (2.7, 1.65). They graph the equations to check their work. Based on the graph, whose solution is more likely to be correct?Daniel is more likely to be correct. The x-coordinate of the intersection is between 1 and 2 and the y-coordinate of the intersection is between 2 and 3. Sofia is more likely to be correct. The x-coordinate of the intersection is between 2 and 3 and the y-coordinate of the intersection is between 1 and 2. or niether
Answer:
Sofia is more likely to be correct
=)
Step-by-step explanation:
Sarah received $55 for her birthday. She used some of that money to buy 3 shirts priced at m dollars each.
How much money does Sarah have left?
Write your answer as an expression.
Solve 2a 2 - 3a - 2 = 0
{-1/2, 2}
{1/2, -2}
{}
Find the area of the composite figure.Use 3.14 for pi.
area for the triangle section is 1/2 x b x h: 1/2 x 16 x 10 = 80 square m
area for half circle = 1/2 x 3.14 x 8^2 = 100.48 square m
100.48 + 80 = 180.48 square meters