1|4)
4x + 3y = 4 4 (3.2) +
2X- $y = -28
20:0)
6x=
Answers
The solution to the system of equations is x = -2 and y = 4
How to solve the equation
To solve this system of equations using Cramer's rule, we need to first express the equations in standard form: Ax + By = C
According to the problem, we have the equations
4x + 3y - 4 = 0
6x = 8 - 5y.
This is the same as
4x + 3y = 4
6x + 5y = 8
The determinants required for Cramer's rule:
Coefficient matrix (D)
[tex]\[D = \begin{vmatrix} 4 & 3 \\ 6 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 6) = 20 - 18 = 2\][/tex]
For Dₓ
[tex]\[D_x = \begin{vmatrix} 4 & 3 \\ 8 & 5 \end{vmatrix} = (4 \times 5) - (3 \times 8) = 20 - 24 = -4\][/tex]
For D y
[tex]\[D_y = \begin{vmatrix} 4 & 4 \\ 6 & 8 \end{vmatrix} = (4 \times 8) - (4 \times 6) = 32 - 24 = 8\][/tex]
Using Cramer's rule:
[tex]\[x = \frac{D_x}{D} = \frac{-4}{2} = -2\][/tex]
[tex]\[y = \frac{D_y}{D} = \frac{8}{2} = 4\][/tex]
complete question
Solve the following simultaneous equations using Cramer's rule.
4x + 3y - 4 = 0
6x = 8 - 5y
Related Questions
The base of a triangle is 5 times the height. If the area is 490 square feet, then what is the height of the triangle, in feet?
Answers
Answer: 14 feet
Step-by-step explanation:
The formula for finding the area of a triangle is given as :
Area = [tex]\frac{1}{2}[/tex] x base x height
Let the height be h , then the base is 5 times the height , that is the base is 5h.
Substituting into the formula , we have
490 = [tex]\frac{1}{2}[/tex] x h x 5h
490 = [tex]\frac{1}{2}[/tex] x [tex]5h^{2}[/tex]
multiply through by 2
980 = [tex]5h^{2}[/tex]
divide through by 5
196 = [tex]h^{2}[/tex]
Therefore :
h = 14
Therefore : the height is 14 feet
what is -1 1/2 as a decimal
Answers
please help me with this problem and explain how to solve these
Answers
Option A:
The simplest radical form of x is [tex]3\sqrt{15}[/tex].
Solution:
Hypotenuse = 16 in
Two sides are 11 in and x.
To find the value of x:
Pythagoras theorem:
In a right angle triangle, the hypotenuse is equal to the sum of the other two sides.
[tex]11^2+x^2=16^2[/tex]
[tex]121+x^2=256[/tex]
Subtract 121 from both sides of the equation.
[tex]121+x^2-121=256-121[/tex]
[tex]x^2=135[/tex]
Taking square root on both sides of the equation.
[tex]\sqrt {x^2}=\sqrt {135}[/tex]
[tex]x=3\sqrt {15}[/tex]
Hence option A is the correct answer.
Hence the simplest radical form of x is [tex]3\sqrt{15}[/tex].
What fractions are equivalent to 9/24?
Answers
9/24 = 3/8 = 6/16
÷ 3/3 x 2/2
answers: 3/8, 6/16
what is 1 5/6 of $84.00
Answers
Answer:
425/2
Step-by-step explanation:
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Solve 3/2 x - 4 = 16
Answers
hope this helped!
10(a+0.50)<9.00 what is the answer I need help
Answers
Answer:
a<0.4
Step-by-step explanation:
The given inequality is
10(a+0.50)<9.00
We expand the parenthesis to get:
10*a+10*0.50<9.00
Multiply to get:
10a+5<9.00
Subtract 5 from both sides to get:
10a<9.00-5
This implies that:
10a<4
Divide both sides by 10
a<4/10
a<0.4
Please help fast!! Is it A, B, C or D?
Answers
Answer:
c
Step-by-step explanation:
3 to the power of 2 is 9. Then You do PEMDAS.
Answer:
C
Step-by-step explanation:
Use PEMDAS.
1. (21 - 3) / 3²
2. 18 / 3²
3. 18 / 9
4. 2
A stainless steel patio heater is a square pyramid. The length of one side of the base is 19.4 in.19.4 in. The slant height of the pyramid is 91.5 in.91.5 in. What is the height of the pyramid?
Answers
Answer:
89.4 inches
Step-by-step explanation:
The slant height of the square pyramid, the height of the square pyramid and half the base side of the square pyramid altogether form a right triangle.
In this right triangle, the slant height is the hypotenuse.
By the Pythagorean theorem,
[tex]91.5^2=19.4^2+h^2\\ \\h^2=91.5^2-19.4^2\\ \\h^2=8,372.25-376.36\\ \\h^2=7,995.89\\ \\h=\sqrt{7,995.89}\ in\\ \\h\approx 89.4\ in[/tex]
Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
-78x+52=-52x-78−78x+52=−52x−78minus, 78, x, plus, 52, equals, minus, 52, x, minus, 78
(Choice B)
B
52x+52=52x-7852x+52=52x−7852, x, plus, 52, equals, 52, x, minus, 78
(Choice C)
C
58x+52=78x-7858x+52=78x−7858, x, plus, 52, equals, 78, x, minus, 78
(Choice D)
D
58x+52=-78x-7858x+52=−78x−7858, x, plus, 52, equals, minus, 78, x, minus, 78
Answers
The equations which have exactly one solution are:
Choice A: [tex]-78x+52=-52x-78[/tex]
Choice C: [tex]58x+52=78x-78[/tex]
Choice D: [tex]58x+52=-78x-78[/tex]
Explanation:
Choice A: [tex]-78x+52=-52x-78[/tex]
Adding both sides by 52x, we have,
[tex]-26x+52=-78[/tex]
Subtracting both sides by 52,
[tex]-26x=-130[/tex]
Dividing both sides by -26,
[tex]x=5[/tex]
Hence, the equation [tex]-78x+52=-52x-78[/tex] has exactly one solution.
Thus, Choice A is the correct answer.
Choice B: [tex]52 x+52=52 x-78[/tex]
Subtracting both sides by 52x,
[tex]52=-78[/tex]
Since, both sides are not equal.
It has no solution.
Thus, Option B is not the correct answer.
Choice C: [tex]58x+52=78x-78[/tex]
Subtracting both sides by 78x,
[tex]-20x+52=-78[/tex]
Subtracting both sides by 52,
[tex]-20 x=-130[/tex]
Dividing both sides by -20,
[tex]x=6.5[/tex]
Hence, the equation [tex]58x+52=78x-78[/tex] has exactly one solution.
Thus, Choice C is the correct answer.
Option D: [tex]58x+52=-78x-78[/tex]
Adding both sides by 78x,
[tex]136x+52=-78[/tex]
Subtracting both sides by 52,
[tex]136x=-130[/tex]
Dividing both sides by 136,
[tex]x=-\frac{65}{68}\\x=-0.956[/tex]
Hence, the equation [tex]58x+52=-78x-78[/tex] has exactly one solution.
Thus, Choice D is the correct answer.
Answer
a
Step-by-step explanation:
it must =180
find the perimeter of a rectangle whose length is 15 cm and length of one diagonal is 17cm
Answers
Answer:
46 cmStep-by-step explanation:
first ,we use the Pythagorean theorem to determine the width:
width = √(17^2-15^2) = 8
then
perimeter = 2(width+lengt) = 2(8 + 15) = 2×23 = 46
Find the sum of - 3/7 and its opposite. [Type your answer as a number.]
Answers
Why? Because adding any number and its opposite is always going to be zero.
Consider adding the number 5 to its opposite -5
5 + (-5) = 5-5 = 0
The same applies to fractions as well. All we do is change the sign from negative to positive, or vice versa, to get the opposite number. The opposites cancel out more or less.
You can think of it as going up 5 floors (positive 5), then going back down 5 floors (negative 5). So overall you didn't change floors at all (represented by 0)
Combine the like terms to create an equivalent expression 2a + 6 + 1
Answers
Answer:
2a+7
Step-by-step explanation:
Answer:
2a+7
Step-by-step explanation:
2a+6+1=2a+7
I try doing this but am not getting the right answer please can someone help me out?
Answers
Answer:44
So you do 2 shapes and add them together
Answer:
44 square yd.
Step-by-step explanation:
7yd - 4yd = 3yd
8yd × 3yd = 24 square yd
5yd × 4yd = 20 square yd
Total area = 24 + 20 = 44 square yd.
Estimate the total percentage of complaints about parking difficulties and the location of the store. (nearest whole percent)
Answers
Answer:
i got 11%
Step-by-step explanation:
The percentage complaint about parking and location is 58%. The correct option is B
From the histogram ;
Difficulty parking = 250Isolated location = 200Sum of complaints : (200 + 250) = 450
The total number of complaints :
(450) + 150 + 125 + 50 = 775Percentage about parking and location :
(450 / 775) × 100% = 58.06Hence, the percentage complaint about parking and location is 58%
Complete Question:
Customer Complaints Estimate the total percentage of complaints about parking difficulties and the location of the store. (nearest whole percent)
A 47%
B 58%
C 75%
D 68%
what is the rise,run and slope??
Answers
Answer:
y axis over x axis is the right answer
Answer:
Rise is 2 run is -1. Slope is [tex]-\frac{2}{1}[/tex].
factor this polynomial expression 2x2+12x+18
Answers
Answer:
the answer is 2 (x-3)2
Step-by-step explanation:
Answer:
(2x + 6)(x + 3)
Step-by-step explanation:
2x^2 + 12x + 18
The above equation can be factorize as follows.
First multipy the first term(2x^2) and the last term (18) together as shown below
2x^2 x 18 = 36x^2
Next we will find the factor of 36x^2 such that the sum of the two factors will result to the second term in the equation (ie 12x). This factors are 6x and 6x. Now, let us put these factors in the equation, we have:
2x^2 +12x + 18
2x^2 + 6x + 6x + 18
Now we can factorize as follows
2x(x + 3) + 6(x + 3)
Now we have same entity in the two brackets., we'll pick one
(2x + 6)(x + 3)
Where does the Parenthesis go in 12x3 to the power of 2 +36
Answers
Answer:
Around the 12x3
Step-by-step explanation:
(12x3)^2+36
A rectangular yard has a width that is 1/2 times its length and has an area of 3800 square feet. What is the length of the yard?
Answers
Answer:
712.5
Step-by-step explanation:
The length of the rectangle is 87.1 feet
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
We are given that a rectangular yard has a width that is 1/2 times its length and an area of 3800 square feet.
Length = L
Width = W
Given that
W = 1/2 L
Area = 3800 square feet
The area of the rectangle = length × Width
3800 = L x 1/2 L
L² = 7600
L = 87.1 feet
Thus, the length of the rectangle is 87.1 feet
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Help math fractions
3 2/3 - 1 11/12=
Answers
Answer:
i wrote this as a decimal so um i hope this at least helps :). 1.75
Step-by-step explanation:
There are 15 postcards in 3 equal stacks. How many postcards are in each stack Complete the bar model to solve Then write a division equation for the bar model.
Answers
Answer:
5 postcards in each stack. 15 divded by 3 equals 5.
-3 + 9 ( 102 - 4 ) (simplify)
Answers
Answer: 879
Step-by-step explanation:
The order of operations calls for Parenthesis, Multiply, Divide, Add, Subtract. From left to right.
So we do the parenthesis first (102 - 4)
-3 + 9 (98)
Next we multiply 9 and 98
-3 + 882
Lastly we add -3 and 882
879
what is the equation of the line that passes through the point (5,4) and has a slope of 4/5?
Answers
Answer:
y-4=4/5(x-5)
Step-by-step explanation:
y-y1=m(x-x1)
y-4=4/5(x-5)
The garden outside Ms.Mertz's class needs 5 liters of water a week. Jacob poured 326 millimeters of water on the garden on Monday. SEAN poured 1.5 liters of water on Tuesday. Gavin poured 2,312 ml of water on Wednesday. Stephen poured 894ml of water on Thursday. Did they pour enough water in the garden? If not, how much more water is needed?
Answers
Answer:
Enough water has been poured .
Step-by-step explanation:
The garden needed water in a week = 5 liters
Jacob poured water on Monday = 326 ml = ( 326/ 1000) liters = 0.326 liters.
SEAN poured water on Tuesday = 1.5 liters
Gavin poured water on Wednesday = 2312 ml = ( 2312/ 1000) = 2.312 liters.
Stephen poured water on Thursday = 894 ml = ( 894/ 1000) = 0.894 liters
The total amount of water poured by all these people = 0.326 + 1.5 +2.312 +0. 894 = 5.032 liters
Here we can see that water has been poured is more than the water required in a week.
After converting all the water measurements to milliliters and summing them up, the garden received 5.032 liters of water over four days, which is slightly above the required 5 liters per week. Thus, the garden received enough water.
Explanation:The question asks if the garden outside Ms. Mertz's class received enough water over a week. To determine this, we need to add up the amounts of water poured each day and compare it to the required 5 liters per week.
Jacob poured 326 milliliters (ml) on Monday.SEAN poured 1.5 liters (l), which is 1500 ml, on Tuesday.Gavin poured 2,312 ml on Wednesday.Stephen poured 894 ml on Thursday.First, we convert all measurements to the same unit (milliliters). Then we sum up all the amounts:
326 ml (Monday) + 1500 ml (Tuesday) + 2312 ml (Wednesday) + 894 ml (Thursday) = 5032 ml
Since 1 liter = 1000 milliliters, we divide 5032 ml by 1000 to convert to liters:
5032 ml = 5.032 liters
The garden received 5.032 liters over the four days, which is just above the required 5 liters of water per week.
Therefore, the garden has received enough water for the week, with a small excess of 32 ml.
u get brainiest for the right answer
Answers
Answer:
C. 40%
Step-by-step explanation:
Since 2 of the 5 sections are shaded in, 2/5 of the circle is shaded in.
Simply divide 2 by 5 to get 0.4 and multiply by 100 to get 40%.
Which equation uses the distributive property to show 6 × 78 = 468? A)6 + (70 × 8) = 468 B) 6 × (70 + 8) = 468 C) 6 + (70 + 8) = 468 D6 × (70 × 8) = 468
Answers
Answer:
[tex]6(70 + 8) = 468[/tex]
answer is b
Answer: The answer is B. hope it could help
Step-by-step explanation:
1/8 gram of copper and 1/3 of silicone is used to manufacture 30 headphones. how much silicone is used in each pair of headphones?
Answers
Answer:
0.0111 grams with the one repeating
Step-by-step explanation:
There are 0.011 grams silicone is used in each pair of headphones.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
1/8 gram of copper and 1/3 of silicone is used to manufacture 30 headphones.
Now,
Since, 1/8 gram of copper and 1/3 of silicone is used to manufacture 30 headphones.
Hence, The amount of silicone is used in each pair of headphones is,
⇒ 1/3 ÷ 30
⇒ 1/3 × 30
⇒ 1/90
⇒ 0.0111 gram
Thus, The amount of silicone is used in each pair of headphones = 0.011 g
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What is the value of (Negative 14 Superscript 0 Baseline) Superscript negative 2? Negative StartFraction 1 Over 196 EndFraction StartFraction 1 Over 196 EndFraction 0 1
Answers
Answer:
1
Step-by-step explanation:
Assuming, we want to find the value of [tex]((-14)^0)^{-2}[/tex]
Recall that: any non-zero number exponent zero is 1.
Using this property, we simplify our expression to [tex](1)^{-2}[/tex] since [tex](-14)^0=1[/tex]
Now using the property of exponents: [tex]a^{-n}=\frac{1}{a^n}[/tex]
This implies that:[tex]1^{-1}=\frac{1}{1^2}=\frac{1}{1}=1[/tex]
The correct answer is 1
Answer:
The anwser in the edge is 1.
Step-by-step explanation:
What is the slope of the line that passes through the points -10,9 and -12,7
Answers
Answer:
slope 1
Step-by-step explanation:
change in y over cahnge in x
The slope of the line that passes through the points -10,9 and -12,7 is 1.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is defined as the ratio of the rise to the run.
Given that the line passes through the points -10,9 and -12,7. The slope of the line will be calculated as,
The slope of the line is calculated by the formula given below,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 7 - 9 ) / ( -12 + 10)
Slope = ( -2 / -2 )
Slope = 1
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find the sum or difference. 8 1/6 + 7 3/8