The solution of the system of equations are x = 4 and y = 4.
What are the solutions?The system of equations would be solved using the elimination method.
−10x+2y=−32 equation 1
-2x-2y=−16 equation 2
In order to determine the value of x, take the following steps:
Add equation 2 and equation 1 together
-12x = - 48
Divide both sides of the equation by -12
x = -48 / - 12
x = 4
In order to determine the value of y, substitute for x in equation 1:
-(10 x 4) + 2y = -32
-40 + 2y = -32
Combine similar terms:
2y = -32 + 40
Add similar terms:
2y = 8
Divide both sides of the equation by 2
y = 8 / 2
y = 4
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In AJKL, JL is extended through point L to point M, m/LJK = (x+9)°,
m/JKL = (x - 2)°, and m/KLM = (5x - 11)°. Find m/LJK.
For the given triangle JKL, the value of x is 10. An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint.
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angelus, which means "corner." An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angelus," which means "corner." The two rays are known as the sides of an angle, and the common endpoint is known as the vertex.When two lines intersect at a common point, an angle is formed. They are expressed in degrees, which are denoted by the symbol °.Given information:
In ∠J K L,JL is extended through point L to point M.
[tex]$&m \angle J K L=(2 x+14)^{\circ} \\[/tex]
[tex]$&m \angle L J K=(3 x+15)^{\circ} \\[/tex]
[tex]$&m \angle K L M=(7 x+9)^{\circ}[/tex]
See the attached figure.
At point L, the measure of angle JLK will be as,
[tex]$&m \angle J L K=180-m \angle K L M=180-7 x-9 \\[/tex]
[tex]$&=(171-7 x)^{\circ}[/tex]
Now, in triangle JKL, use the angle sum property to find the value of x as,
[tex]$$m \angle J K L+m \angle L J K+m \angle J L K=180[/tex]
[tex]$$$(2 x+14)^{\circ}+(3 x+15)^{\circ}+(171-7 x)^{\circ}=180$[/tex]
-2 x+200=180
2 x=20
x=10
Therefore, the value of x for the given triangle JKL is 10.
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I need help like asap !!!
only numbers and decimal points
Answer:
a = 6.63 cm
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (12)² = a² + (10)²
→ 144 = a² + 100
→ a² = 144 - 100
→ a = √44
→ [ a = 6.63 cm ]
Hence, value of a is 6.63 cm.
x + 3y = -18 in slope intercept form
Answer:
y=1/3x+6
Step-by-step explanation:
Use the formula "Y=mx+b"
Answer:
y= -1/3x - 6
Step-by-step explanation:
x+3y = -18
3y = -x -18
y= -1/3x - 6
You and your friend went out to lunch and your total bill (before
taxes) was $36.50. You enjoyed your
service and want to leave a tip of $20%. What is your tip amount?
$7.30
$0.73
$20.00
$36.70
Answer: Your answer is $7.30
Step-by-step explanation:
Finding the amount for a tip is simple!
all that's required is multiplying the bill (36.50) by the amount you want to tip (.20, because 20% is equal to .20)
36.50×.2= $7.30
Find the LCM of
2 x 3 x 3 x 5 and 3 x 3 x 5 x 5
Answer:
LCM of 90 and 225 = 450
I'm not too sure I understand
2 x 3 x 3 x 5 = 90, and 3 x 3 x 5 x 5 = 225
90: 90, 180, 270, 360, 450
225: 225, 450
LCM = 450
What is 2/3 plus 4/8 equal to please let me know and please explain, and this is 5th grade.
5th grade
Answer: 7/6
Step-by-step explanation:
Ok so first we must take these fractions and make them have a common denominator. The best way to do this is to take 2/3 and multiply the numerator and denominator by 8 giving us 16/24. Next take 4/8 and multiply the numerator and denominator by 3 giving us 12/24. Now we have both a common denominator. Now we add the numerators of both (16+12) to get 28/24 but now we have an improper fraction divide the numerator and denominator by 4 to get us 7/6.
Hope this Helps :)
A group of friends wanted to compare their average running speeds. They recorded the distance and amount of time each person ran one Saturday morning.
Select all the runners whose speeds are in a proportional relationship with each other.
Name Time (seconds) Distance (miles)
Liam 306.6 0.5
Taylor 756.36 1.2
Sarah 504.35 0.7
Ashley 459.9 0.75
Connor 600.5 1
Nathan 942.75 1.5
Juan 827.82 1.35
Katie 429.48 0.6
The runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.
We need to select all the runners whose speeds are in a proportional relationship with each other.
We find the speed using formula, speed = distance / time
Name Time (seconds) Distance (miles) Speed(mps)
Liam 306.6 0.5 0.5/306.6 = 0.0016
Taylor 756.36 1.2 1.2/756.36 = 0.0016
Sarah 504.35 0.7 0.7/504.35 = 0.0014
Ashley 459.9 0.75 0.75/459.9 = 0.0016
Connor 600.5 1 1/600.5 = 0.0017
Nathan 942.75 1.5 1.5/942.75 = 0.0016
Juan 827.82 1.35 1.35/827.82 = 0.0016
Katie 429.48 0.6 0.6/429.48 = 0.0014
Therefore, the runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
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A line is drawn through (–7, 11) and (8, –9). The equation y – 11 = y minus 11 equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus 7 right-parenthesis.(x + 7) is written to represent the line. Which equations also represent the line? Check all that apply.
y = y equals StartFraction negative 4 Over 3 EndFraction left-parenthesis x plus StartFraction 5 Over 3 EndFraction.x +
3y = –4x + 40
4x + y = 21
4x + 3y = 5
–4x + 3y = 17
The equivalent linear equation in standard form is 4x + 3y = 5
How to determine the equivalent equations?From the question, we have the following parameters that can be used in our computation:
Points = (-7, 11) and (8, –9)
Point-slope form is y - 11 = -4/3(x + 7).
Recall that the point-slope form is y - 11 = -4/3(x + 7).
So, we have
y - 11 = -4/3(x + 7).
Multiply through both sides by 3
This gives
3y - 33 = -4(x + 7).
Open the brackets
3y - 33 = -4x - 28
Evaluate the like terms
3y = -4x + 5
Add 4x to both sides
4x + 3y = 5
Hence, the equation is 4x + 3y = 5
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What two numbers = -48 (multiply) and does the two numbers = -13
Answer:
The two numbers are [tex]3[/tex] and [tex]-16[/tex].
Step-by-step explanation:
Two numbers that, when multiplied, result in a product of [tex]-48[/tex]:
[tex]x \cdot y = -48[/tex]
Same two numbers when added get a sum of [tex]-13[/tex]:
[tex]x + y = -13[/tex]
Solve for x in the summation identity:
[tex]y = -13 - x[/tex]
Plug the value back into the product identity and solve for [tex]x[/tex]:
[tex]x \cdot (-13-x) = -48\\-13x - x^2 = - 48\\x^2 + 13x = 48\\x^2 + 13x - 48 = 0\\(x-3)(x+16) = 0[/tex]
The roots we found for [tex]x[/tex] were:
[tex]x = 3\\x = -16[/tex]
Our two numbers are [tex]3[/tex] and [tex]-16[/tex]. We can test this:
[tex]3 + (-16) = -13\\3 * -16 = -48[/tex]
which proportion is equivalent to the original equation
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
As given in the question,
Given equation is :
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x
Simplify the original equation to get the equivalent equation
Least common multiple is 2 and 2x is equal to 2x
Original equation (1/2) + (1/2x) = (x² -7x +10)/4x is Equivalent to the proportion is given by:
( x + 1) / 2x = (x² -7x +10)/4x
Therefore, original equation (1/2) + (1/2x) = (x² -7x +10)/4x is equivalent to the proportion (x+1)/2x = (x² -7x +10)/4x.
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Multiply and simplify: 3i(4 - 3i) - i (2 + i)
10 + 10i
Apply Multiplicative Distribution Law: 12i - 9 x i^2 - 2i - i^2
Rewrite by definition: i^2 = -1:12i - 9 x (-1) -2i - (-1)
Remove the parentheses: 12i + 9 - 2i + 1
Combine like terms: 10 + 10i
Answer 10 + 10i
Answer:
10 + 10i
Step-by-step explanation:
Given expression:
[tex]3i(4 - 3i) - i (2 + i)[/tex]
Expand:
[tex]\implies 12i-9i^2-2i-i^2[/tex]
[tex]\implies 12i-2i-9i^2-i^2[/tex]
[tex]\implies 10i-10i^2[/tex]
Apply the imaginary number rule i² = -1 :
[tex]\implies 10i-10(-1)[/tex]
Simplify:
[tex]\implies 10i+10[/tex]
Rewrite in standard complex form a + bi:
[tex]\implies 10+10i[/tex]
A line passes through point (-2, 8) and has a slope of -5. Write an equation in Ax + By =C form for this line. Use integers for A, B, and C.
25 points
The equation of line with a slope of -5 and which passes through point (-2, 8) is 5x + y = -2.
What is the equation of line with the given point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Point (-2,8)
x = -2y = 8Slope m = -5First, we determine the y-intercept 'b'. Plug the coordinates and slope into the equation of line formula and solve for b.
y = mx + b
8 = (-5)(-2) + b
8 = 10 + b
b = 8 - 10
b = -2
Now, plug values of slope m and y-intercept b into y = mx + b to determine the equation of the line.
y = mx + b
y = (-5)x + (-2)
y = -5x - 2
Convert to standard form; Ax + Bx = C
y = -5x - 2
Reorder the equation
5x + y = - 2
Therefore, the equation of the line is 5x + y = - 2.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
The value of sec θ is ____
, and the value of cot θ is _____
.
The value of sec θ is -5/3 ,and the value of cot θ is 3/4 in the unit circle.
Given:
The point -3/5 , -4/5 in the third quadrant corresponds to angle θ on the unit circle.
here x = -3/5 and y = -4/5
radius r = [tex]\sqrt{(-3/5)^{2}+(-4/5)^{2} }[/tex]
= [tex]\sqrt{9/25 + 16/25}[/tex]
r = 1.(which is hypotenuse in unit circle).
sec θ = hypotenuse / adjacent
= 1/-3/5
sec θ = -5/3
cot θ = adjacent / opposite
= -3/5 / -4/5
= 3*5/5*4
= 15/20
cot θ= 3/4
Therefore the value of sec θ is -5/3 ,and the value of cot θ is 3/4.
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Given
a = -4, b = -4 and c = -5
work out
b² - 2ac
Answer:
-24
Step-by-step explanation:
b²-2ac
(-4)²-2(-4)(-5)16-40-24⇒Plug in the values given in places and simplify.
[tex]=(-4)^{2} -2(-4)(-5)\\=16-2(20)\\=16-40\\=-24[/tex]
-24 is the answer after substitution of the known values.
How do I find the missing angle of an intersecting line?
Answer:
Read the given problem, look at the given figure of intersecting lines, and identify the angle given and the unknown angles.
Step-by-step explanation:
6. According to Statistics Canada, the number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003. What was the mean number of new subscribers per month during that year?
The mean number of new subscribers per month during that year is 242000.
What is a mean?A mean simply means the average of the numbers given.
The number of cable television subscribers increased from about 1 151 000 in 2002 to about 1 393 000 in 2003.
The mean number of new subscribers will be:
= Change in numbers / Number of years
= (1393000 - 1151000) / 1
= 242000 / 1
= 242000
Therefore, the mean is 242000.
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Which table represents an exponential function of the form y = b when 0
Second table represents an exponential function of the form y = b when 0
Define exponential function.A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered. In addition to many other applications, exponential functions are used to estimate populations, carbon date artefacts, assist coroners in determining the time of death, compute investments, and many more. Three of the most popular applications—population expansion, exponential decay, and compound interest—will be covered in this session.
Given,
Second table represents an exponential function of the form y = b when 0
Function: y = bˣ
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Someone help me with this please
Answer:
C
Step-by-step explanation:
C has a directly proportional relationship. 27 glasses are in 9 cases, and 81 glasses are in 27 cases. Directly proportional since 9×3=27 (cases) and 27×3=81 (glasses)
simplify the following
2²y + 3x² + 4y + 3x²y + 2y
Answer:
10y+3x^2+3x^2y
Step-by-step explanation:
^2 means square
2^2 is 4 and different variable cannot be added.
2x + 4y < 20 what is the inequality simplifies
Answer:
x < 10 - 2y
Step-by-step explanation:
Identify the domain of the function shown in the graph
The domain of the graph is (d) all set of real values
How to determine the domain of the relation in the graph?The graph represents the given parameter
This graph represents a function
Say the graph represents the function f(x)
The x values represent the domain
i.e domain = Set of all x values
On the graph, we can see that the graph extends across the x-axis till infinity on both sides
This means that
Domain = All set of real values
Hence, the domain of the relation is (d) all set of real values
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A garden designer designed a square decorative pool. The pool is surrounded by a walkway. On two opposite sides of the pool, the walkway is 8 feet. On the other two opposite sides, the walkway is 10 feet. The final design for the pool and walkway covers a total area of 1,440 square feet. ---------- a. The side length of the square pool is x. Write an expression that represents: 1. The total length of the rectangle (including the pool and walkway) 2. The total width of the rectangle (including the pool and walkway) 3. The total area of the pool and walkway b. Write an equation of the form: your expression = 1,440. What does a solution to the equation mean in this situation?
Part 1: The total length of the rectangle; 20 + x (Expression).
Part 2: The total width of the rectangle; 16 + x (Expression).
Part 3: The total area of the pool along with walkway; (20 + x)(16 + x).
Define the term area of the rectangle?The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.The data for the question is given as-
The boardwalk around the pool is 8 feet long and on two different sides. The walkway is 10 feet wide on either two opposite sides. The pool and walkway's final design takes up a total of 1,440 square feet.The side length of the square pool is x.The expressions for the given cases are-
Part 1: The total length of the rectangle;
The total length of the rectangle = 10 + 10 + x
The total length of the rectangle = 20 + x (Expression)
Considering; 10 + 10 > 8 + 8
Part 2: The total width of the rectangle;
The total width of the rectangle = 8 + 8 + x
The total width of the rectangle = 16 + x (Expression)
Part 3: The total area of the pool along with walkway.
Area = length x breadth
Area = (20 + x)(16 + x).
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im stumped please help
cómo se saca el porcentaje
Answer:
Step-by-step explanation:
Para determinar el porcentaje, tenemos que dividir el valor por el valor total y luego multiplicar el resultado por 100.
3
6
Find the value of x.
x
x = [?]
For the given triangle, the value of x would be 12.
What is the geometric mean theorem of a triangle?
According to the geometric mean theorem, the length of an altitude drawn from a triangle's right angle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
For the given triangle, we can apply the geometric mean theorem,
By the geometric mean theorem, we can write
6² = 3 * x
36 = 3 * x
⇒ x = 36/3
⇒ x = 12.
Hence, for the given triangle, the value of x would be 12.
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As the diameter (d) of a circle increases in size, the circumference (C)
increases Likewise, as the diameter decreases in size, so does the circumference,
The constant of variation between Cand dist. Describe the kind of variation
between eireumference and diameter Write the equation.
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Considering the triangle with exterior angles and interior angles as described. The statements that are true include
m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°How to determine the statements that are correctThe problem is solved considering this 3 theorems about triangles
exterior angle of a triangle theoremlinear pair theoremsum of angles in a triangleexterior angles theorem: m∠2 + m∠3 = m∠6
If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
Linear pair theorem: m∠5 + m∠6 =180°
Linear pairs are particular instances of supplementary angles that only involve two neighboring angles.
Sum of angles in a triangle is equal to 180 degrees:
m∠2 + m∠3 + m∠5 = 180°
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Factor x^2-x-72 Please
Answer:
(x+8)(x-9)
Step-by-step explanation:
1. Use the sum-product pattern
x²-x-72
x²+8x-9x-72
2. Find the common factor from the 2 pairs
x²+8x-9x-72
x(x+8)-9(x+8)
3. Rewrite in factored form
x(x+8)-9(x+8)
(x-9)(x+8)
Solution to problem: (x-9)(x+8)
Solve 15+ax/5= 10 for x.assume that a=0
The solution for x in the expression given as 15 + ax/5 = 10 is x = -25/a
How to determine the solution to the variable x in the expression?From the question, the algebraic expression is given as
15 + ax/5 = 10
There is a constant to add to or subtract from the expression
So, the we subtract 15 from both sides
- 15 + 15 + ax/5 = 10 - 15
Evaluate
ax/5 = -5
Multiply both sides of the equation by 5
This gives
5 * ax/5 = -5 * 5
Evaluate the products
So, we have the following equation
ax = -25
Multiply both sides of the equation by 1/a
This gives
1/a * ax = -25 * 1/a
Evaluate the products in the above expression
x = -25/a
Hence, the solution is x = -25/a
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List the independent and dependent variables
H(x)=3+0.5x
x is the independent variable and H(x) is the dependent variable
How to determine independent and dependent variables?
A dependent variable is a variable whose value depends upon independent variables.
An independent variable is a variable that does not depend on any other variable for its value.
For example, in an expression, y = 3x + 2, x is an independent and y is a dependent variable because y depends on x for its value
Given: H(x) = 3+0.5x
Therefore, x is the independent variable and H(x) is the dependent variable because it is a function of x
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