Answer:
9.9924 liters
Step-by-step explanation:
there are 3.785 liters in one gallon
multiply 3.785 liters times 2.64
that comes out to 9.9924 liters
Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6y=−18.
Answer:
a. No solution, parallel lines.
b. One solution.
Step-by-step explanation:
Given the system of equations:
a. [tex]2x-4y=12[/tex]
[tex]-3x+6y=-15[/tex]
b. [tex]2x-4y=12[/tex]
[tex]-5x+3y=10[/tex]
To give a geometric description of the given system of equations.
The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.
i.e.
Number of planes = Number of variables
Number of lines = Number of equations in the system.
Here, we are given 2 variables and 2 equation in each system.
So, they can be represented in the xy-coordinates plane.
And the number of solutions to the system depends on the following condition.
Let the system of equations be:
[tex]A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0[/tex]
1. One solution:
There will be one solution to the system of equations, If we have:
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
2. Infinitely Many Solutions: (Identical lines in the system)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}[/tex]
3. No Solution:(Parallel lines)
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Now, let us discuss the system of equations one by one:
a. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-3x+6y=-15[/tex] OR [tex]-3x+6y+15=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15[/tex]
Here, the ratio:
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}[/tex]
Therefore, no solution i.e. parallel lines.
b. [tex]2x-4y=12[/tex] OR [tex]2x-4y-12=0[/tex]
[tex]-5x+3y=10[/tex] OR [tex]-5x+3y-10=0[/tex]
[tex]A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10[/tex]
[tex]\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}[/tex]
[tex]\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}[/tex]
So, one solution.
Kindly refer to the images attached for the graphical representation of the given system of equations.
Drag each equation to the correct to the correct location on the table
Answer:
x=3
2(2x-3)=65x - (3x-1)=75x-2x-4=5x=2
5(x+3)=254x-(2x+1)=3x+2x+3=9
Answer:
x=3
2(2x-3)=6
5x - (3x-1)=7
5x-2x-4=5
x=2
5(x+3)=25
4x-(2x+1)=3
x+2x+3=9
Find the approximate side length of a square game board with an area of 155in2.
The side of a square is the square root of the area.
Side = sqrt(155)
Side = 12.45 inches. (Round answer as needed)
Need to know asap. If m<8=23°, find the measure of each missing angle. Give your reasoning.
Answer:
157
23
157
23
157
23
157
Step-by-step explanation:
a straight line is 180 degrees. angle 8 is 23 degrees. we want to know the rest of the angles measures. 180-23=157. angles directly across the vertex are the same measure. and since the lines are parallel 2,4,6,and 8 all have the same measure and 1,3,5,and 7 have the same measure.
look at attached photo
The measures of two supplementary angles are 8w + 58 and 16w + 14. Find the measures of the angles
Answer:
34
Step-by-step explanation
The base of 14-foot ladder is 6 feet from a building. If the ladder reaches the flat roof, how tall is the building?
Answer:
Approximatly 12.65
Step-by-step explanation:
You would use the pythagorean Theoram for this.
[tex]a^{2}+6^{2}=14^{2}[/tex]
[tex]a^{2}+36=196[/tex]
Subtract 36 from both sides:
[tex]a^{2}=160[/tex]
Square 160 to remove the exponent on "a":
[tex]a=\sqrt{160}[/tex]
[tex]a≈ 12.65[/tex]
If the ladder reaches the flat roof, then the height of the building will be 12.65 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The base of 14 feet ladder is 6 feet from a building. Then the length of the hypotenuse is 14 feet and the base is 6 feet. Then the height of the building will be given by the Pythagoras theorem.
If the ladder reaches the flat roof, then the height of the building will be
H² = P² + B²
14² = P² + 6²
196 = P² + 36
P² = 196 - 36
P² = 160
P = 12.65 feet
If the ladder reaches the flat roof, then the height of the building will be 12.65 feet.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ2
I’m not understanding this question at all. WILL GIVE BRAINLY!! (6 is not the answer)
Answer:
-8.
Step-by-step explanation:
Substitute BC with the -4 and 2, as you were given those values to substitute with B and C. Multiply those two values. You get -8.
Which graph shows the solution of the following system of inequalities :
F
G
H
J
Help me please!!!!!!!!!!!!!
Answer:
x = 12
Step-by-step explanation:
Given that AB = 2, AD = x, BC = 2, CD = -16 + 2x, since A, B, C, D are said to be collinear, therefore:
AB + BC + CD = AD
2 + 2 + (-16 + 2x) = x
Use this equation to solve for x
2 + 2 - 16 + 2x = x
-12 + 2x = x
Subtract 2x from both sides
-12 + 2x - 2x = x - 2x
-12 = -x
Divide both sides by -1
[tex] \frac{-12}{-1} = \frac{-x}{-1} [/tex]
12 = x (negative cancels negative)
x = 12
A political scientist surveys 38 of the current 153 representatives in a state's congress.
Answer:
What is the question? Is this a true or false question ?
Step-by-step explanation:
The percentage of surveys done if, A political scientist surveys 38 of the current 153 representatives in a state's congress is 25%.
What is percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
The number of surveys done = 38,
The representatives in a state's congress = 153,
Calculate the percentage as shown below,
Percentage of survey = The number of surveys done / total representative × 100,
Percentage of survey = 38 / 153 ×100
Percentage of survey = 0.25 × 100
Percentage of survey = 25 %
To know more about percentages:
https://brainly.com/question/26080842
#SPJ2
The complete question is: A political scientist surveys 38 of the current 153 representatives in a state's congress. Calculate the percentage of the survey.
Which pair of points has a slope of 4? Question 4 options: (0, 4), (4, 0) (3, 0), (–1, –1) (1, 4), (–1, 4) (0, –3), (1, 1)
Answer:
(0,-3) and (1,1)
Step-by-step explanation:
In order to have a slope of 4, the y coordinates need to differ by 4, and the x coordinates by 1. This is because slope is equal to rise/run. Rise being difference in y value and run difference in x.
In this pair of coordinates, the y coordinates differ in +4 (-3 and 1) and the x coordinate differs by 1 (0 and 1).
Therefore this is the pair of points with a slope of 4.
Hope this helped!
The pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
The formula for calculating the slope of a line passing through two points is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We need to get which of the coordinates will result in a slope of 4.
Using the coordinate points (0, –3), (1, 1)
[tex]m=\frac{1-(-3)}{1-0}\\m=\frac{1+3}{1}\\m=\frac{4}{1}\\m=4[/tex]
Hence the pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
Learn mroe here: https://brainly.com/question/23935638
12. Determine whether the given number belongs
to each set.
te?
Whole
Numbers
Integers
Rational
Numbers
es
- 34
Answer:
The number -34 belongs to:
✔️Integers and
✔️Rational numbers
Step-by-step explanation:
-34 is an integer because it can written without a fractional or decimal part.
Rational numbers are said to numbers that can actually be expressed as a fraction with integers. They have no fractional part.
For example, −34 is a rational number because it can be written as - 34/1.
-34 can be expressed as -34/17, given an integer.
-34 is NOT a whole number because whole numbers are positive numbers.
ANSWER FAST!!!!!! 25 POINTS!!!!!!!!
Answer:
X,Z,Y
Step-by-step explanation:
9π=28.27
√3/2=0.866
z=27.5
remember all are in cm^2 so no conversion is needed
Answer:
Circles X, Z, Y.
A small apple weighs 4.5 ounces. If it is divided into 4 equal pieces, how much does each piece weigh?
Find an equation for the surface obtained by rotating the line x = 6y about the x-axis.
Answer:
[tex]\frac{x^2}{36}=y^2+z^2[/tex]
Step-by-step explanation:
If we loo at the xy plane and consider the point (6y, y, 0), it looks like a circular path that is a cone as the curve is rotated about the x axis. The equation of the cone has the form:
[tex]\frac{x^2}{c^2}=\frac{y^2}{a^2}+\frac{z^2}{b^2}[/tex]
Given that x = 6y, to make the equation to be in the form as seen above, we square x = 6y, hence:
x² = (6y)²
x² = 36y²
The path parallel to yz axis are circles, so the equation should be as that of a circle. We need to add 36z², hence:
x² = 36y² + 36z²
[tex]\frac{x^2}{36}=y^2+z^2[/tex]
[tex](\frac{x}{6})^2=y^2+z^2[/tex]
This equation is that of a circle with radius of r = y = x/6, the resulting surface is that of a cone
HELP ASAP PLS pls help with all the questions thank you!
answer 2. min= 30.5
max=31.5
answer 3. 5 s.f
answer 4. False
Answer:not an answer but do you go to Cwcs because I go there too
Step-by-step explanation:
Ben works at a mobile phone store, where he earns a flat $80 for each 8-hour shift. He also earns a commission of $20 for each phone that he sells. If e stands for Ben's earnings and m is the number of mobile phones he sells, which of the following equations describes the amount of money that he earns in one shift? Question 6 options: A) e = m + 100 B) e = 20m + 80 C) e = –20m + 80 D) e = m + 80
Answer:
b
Step-by-step explanation:
he makes 80 dollars for a normal shift
20 dollars for every phone he sells 20m
and e is the total amount
e=20m+80
How do you breakdown the quotient for 814÷3.7
Answer:
move the decimal to the end and add a zero to 814 i think
Step-by-step explanation:
the low temperature in Anchorage, Alaska today was -4°F. The low
temperature in Los Angeles, California was 63°F. What is the difference in
the two low temperatures?
Answer:
67°F
Step-by-step explanation:
-4-63 = - 67°F
Therefore temperature difference=67
plane. Explain your reasoning.
MOVIES An online DVD rental company charges $15 a month for unlimited rentals. Determine whether the total paid after each month is
proportional to number of months by graphing on the coordinate plane. Explain your reasoning.
In
hu
Oa. No, because the graph of the line does not pass through the origin.
Ob. Yes, because the graph is a straight line that passes through the origin.
Oc. No, because the graph of the line passes through the origin.
Od. Yes, because the graph is a straight line that does not pass through he origin.
hu
Thu
"hu
es
Res
Answer: Yes, because the graphic is a straight line that passes the through the origin.
Step-by-step explanation: Ik the answer because I have the answer key.
A football field is 120 yards by 53.333 yards. What is the area of the football field in acres if 1 acre
Answer:
Area in acres = 1.322 acre (Approx)
Step-by-step explanation:
Given:
Length of field = 120 yards
Width of field = 53.333 yards
Finds:
Area in acres
Computation:
1 acre = 4840 square yard
Area = 120 × 53.333
Area = 6,399.96 yard² = 6,400 yard²
Area in acres = 6,400 yard² / 4840
Area in acres = 1.322 acre (Approx)
MULTIPLE CHOICE QUESTION
What type of exponent needs absolute value bars?
link
odd
even
Answer:
even
Step-by-step explanation:
Simplify. 1/3(1−1/4)^2 please
Answer:
3/16
Step-by-step explanation:
1/3(1-1/4)^2
1/3(3/4)^2
1/3(9/16)
3/16
Answer:
[tex]\huge \boxed{\frac{3 }{16}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{3} (1-\frac{1}{4} )^2[/tex]
Solving for brackets:
[tex]\displaystyle \frac{1}{3} (\frac{4}{4} -\frac{1}{4} )^2[/tex]
[tex]\displaystyle \frac{1}{3} (\frac{3}{4} )^2[/tex]
Squaring the fraction:
[tex]\displaystyle \frac{1}{3} (\frac{3^2 }{4^2 } )[/tex]
[tex]\displaystyle \frac{1}{3} (\frac{9 }{16} )[/tex]
Multiplying the fractions:
[tex]\displaystyle \frac{1 \times 9 }{3 \times 16}[/tex]
[tex]\displaystyle \frac{9 }{48}[/tex]
Simplifying the fraction:
[tex]\displaystyle \frac{3 }{16}[/tex]
[tex]\rule[225]{225}{2}[/tex]
There are 67 questions on an exam. If you miss 8 of these questions your grade is _______ %.
Answer:
88%
Step-by-step explanation:
There are 67 questions on an exam
You miss 8 questions
The first step is to calculate the number of correct questions
= 67-8
= 59
Therefore the grade can be calculated as follows
= 59/67 × 100
= 0.880 × 100
= 88%
Hence the grade is 88%
25×3/5×1/12 Multiply and simplify
[tex]25 \times \frac{3}{5} \times \frac{1}{12} = [/tex]
[tex]5 \times \frac{3}{1} \times \frac{1}{12} = [/tex]
[tex]5 \times \frac{1}{1} \times \frac{1}{4} = [/tex]
[tex]5 \times 1 \times \frac{1}{4} = [/tex]
[tex]5 \times \frac{1}{4} = [/tex]
[tex] \frac{5}{4} = 1 \frac{1}{4} [/tex]
Thank you.
Answer:
1.25
Step-by-step explanation:
We can start by multiplying the top part of the fraction. On the top, we have 25, 3, and 1. 25x3x1=75
Now we do the bottom. We have 5 and 12. 5x12=60
Now that we have both parts, we put it back into the fraction.
75/60
75/60=1.25
I'm thinking of a number.My number is a whole number.My number is larger than 100.My number mod 17 = 9.My number is smaller than 200.What could be number be? (Give one possible answer. There are several correct answers.)
Answer:
the number could be any of these numbers (111, 128, 145, 162, 179, 196)
Step-by-step explanation:
From the given information, let the number that I'm thinking of to be p
p is > 100
p is < 200
and p = 9 (mod 17)
This implies that 17 ÷ p -9
p - 9 = 17q
here;
q is an integer
p = 9 + 17q
However,
100 < p < 200
= 100 < 9+17q < 200
= 100 - 9 < 17q < 200 -9
= 91 < 17q < 191
Dividing both sides by 17; we have:
= [tex]\dfrac{91}{17}< q < \dfrac{191}{17}[/tex]
= 5.45 < q < 11.24
thus the possible values of q are between 6,7,8,9,10 and 11
The possible values of p can now be:
p = 9 +17(q)
p = 9+17(6), 9+17(7), 9+17(8), 9+17(9), 9+17(10), 9+17(11)
p = 111, 128, 145, 162, 179, 196
Therefore, the number could be any of these numbers (111, 128, 145, 162, 179, 196)
What is the profit percentage if the selling price is Rs 3000 and the cost price is RS 2000? * 5% 15% 50% 100%
Answer:
100% 50% 5% RS2000 Rs 3000
What's the difference between 2x+2 and 2x+2=10?
Answer:
10Step-by-step explanation:
Given both expression
2x+2 and
2x+2=10
the difference inlvosves basically the subtraction of one expression from the other expression.
now before we perform the subtraction operation, let us do some preprocessing.
let us equate the first and second expression to zero
2x+2=0 and
2x+2-10=0
we can now subtract
(2x+2)-(2x+2-10)=0
open bracket
2x+2-2x-2+10=0
collect like terms
2x-2x+2-2+10=0
0+0+10=0
the answer is 10
train A arrives at the station at 11:50 Am and leaves the station at 1:50 PM.how long does it stay in the station?
Answer:
2 hrs.
Step-by-step explanation:
11:50am ----> 12:50pm (1 hr.)
+
12:50pm ---> 1:50pm (1 hr.)
= 2 hrs
Triangle ABC has coordinates A(2, -5), B(1, -3), and C(6, 1). If the triangle is
rotated 180° clockwise about the origin, what are the coordinates of A'?
Answer:(2,5)
Step-by-step explanation: