The equation of the plane that goes through these points is:
6x + 2y + z = 10.
How to find the equation of a plane given three points?The equation of the plane is found replacing the points into the following equation:
ax + by + c = z.
For point A, we have that:
3b + c = 4.
For point B, we have that:
a + 2b + c = 0.
For point C, we have that:
-a + 6b + c = 4.
Hence the system is:
3b + c = 4.a + 2b + c = 0.-a + 6b + c = 4.From the first equation, we have that:
c = 4 - 3b.
Replacing in the second, we have that:
a + 2b + 4 - 3b = 0
a - b = -4.
Replacing in the third, we have that:
-a + 6b + 4 - 3b = 4.
-a + 3b = 0.
a = 3b.
We have that a - b = -4, hence:
3b - b = -4
2b = -4
b = -2.
a = 3b, hence a = -6.
c = 4 - 3b -> c = 10.
Hence the equation is:
ax + by + c = z.
z = -6x - 2y + 10
6x + 2y + z = 10.
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To pass a course with a C grade, a student must have an average of 70 or greater. A students grades on three test are 60,71, and 63. Find what score the student must get on the next test to get a C average or better
The score the student must get on the next test to get a C average or better is 86.
How to calculate the average?From the information given the pass a course with a C grade, a student must have an average of 70 or greater and students grades on three test are 60,71, and 63.
The next score will be calculated as x.
60 + 71 + 63 + x = (70 × 4)
194 + x = 280
x = 280 - 194
x = 86
Therefore, the next score must be 96.
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The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V equals the square root of the quantity 2 times h times a end quantity where a represents the acceleration in ft/sec2. If the acceleration due to gravity is 32.2 ft/sec2, at what height should you drop an object in order for it to have a velocity of 80 ft/sec?
5,152 feet
99.4 feet
71.8 feet
1.5 feet
The object is dropped at a initial height of 99.4 feet. (Correct choice: B)
What is the final velocity of a falling object?
Herein we find the case of a specific object under free fall motion, that is, due to gravity and neglecting effects from air viscosity and Earth's rotation. The kinematic equation is presented below:
v = √(2 · a · h) (1)
Where:
v - Final velocity, in feet per second.a - Acceleration, in feet per square second.h - Initial height, in feet.If we know that a = 32.2 ft / s² and v = 80 ft /s, then the initial height of the object is:
80 = √(2 · 32.2 · h)
80 = √(64.4 · h)
80² = 64.4 · h
h = 80² / 64.4
h = 99.379 ft
The object is dropped at a initial height of 99.4 feet. (Correct choice: B)
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The first week of January, there are
49 dogs and 28 cats in an animal shelter.
Throughout the month, the ratio of dogs
to cats remains the same. The last week
of January, there are 20 cats in the
shelter. How many dogs are there?
Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange. Help pls
Answer:
The answer is that there are 18 different combinations of vehicles.
Step-by-step explanation:
We are given that the number of vehicles for his business = 3.
The vehicles are a car, truck, and motorcycle.
So we know that there is two possibilities for car: Red and yellow.
Three possibilities for truck: Black, white, and silver.
Three possibilities for motorcycle: Green, blue and orange.
So now we can make an equation of the different combinations of vehicles that Edwin have to chose from.
So 3 x 3 x 2 = 18
Therefore, there are 18 different combinations of vehicles.
I hope this helps, have a good day!! :D
Explanation? I’ll give brainliest
Answer:
Step-by-step explanation:
you add all of that up and you get your answer then you subtract that answer to 100 then that’s your answer.
Answer:
First what you want to do is start with the socks.
Socks cost $9.00 so if he is buying 3 pair you would multiply by 3.
9 times 3 is 27. = $27
He bought 2 belts and the belts cost $10.00 so you would multiply that by 2.
10 times 2 is 20. = $20
He bought 1 hoodie which amounts to $29.99 and a pair of shoe laces that amounts to $1.50.
Now what you do is add all thew prices together.
$27 + $20 + $29.99 + $1.50 = $78.49
Final, since he is paying with a hundred dollar bill you want subtract that from the total amount.
$100 - #78.49 = $21.51
So he would get back a total of $21.51.
Step-by-step explanation:
Hope it helps! =D
Find the coordinates of J if K (-5,10) is the midpoint of JL and L has coordinates of (-8,6)
A circle has a circumference of 25. Find the length of an arc whose central angle is 50
Answer:
19.625 units
Step-by-step explanation:
[tex]\text{ Arc length } = 2 \pi r \times \frac{\theta}{360}[/tex]
Substituting the given values,[tex]\begin{gathered}\text{Arc Length } = 2\times 3.14 \times 12.5 \times \frac{50}{360}\\\\\text{Arc length } = 78.5 \times \frac{1}{4}\\\\\text{Arc Length } = 19.625\end{gathered}[/tex]
Thus length of arc is 19.625 units
How many pounds of a chicken feed that is 40% corn must be mixed with 270 lb of a feed that is 80% corn to make a chicken feed that is 70% corn?
We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.
How many chicken feed must be added to a given blend?
In this problem we have to prepare a chicken feed with a given concentration by blending two chicken feeds with different concentration. The addition of chicken feed needed can be determined by weighted averages:
(70 / 100) · (270 + x) = (80 / 100) · 270 + (40 / 100) · x
0.7 · (270 + x) = 0.8 · 270 + 0.4 · x
189 + 0.7 · x = 216 + 0.4 · x
0.3 · x = 27
x = 90
We have to add 90 pounds of chicken feed that is 40 % to make a chicken feed that is 70 % corn.
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The given signs denote the following operations/relationships:
A+B means A is greater than B.
A-B means A is less than B.
A-B means A is greater than or equal to B.
A*B means A is not equal to B.
A/B means A is equal to B.
Which of the two conclusions I and II is/are definitely true based on the information
provided?
Statements:
E*F, F/G, G-H
Conclusions:
1. E*G
II. F-H
Based on the given information, the EFG GH Findings.
Refer to the symbols and their associated meanings below.
The symbols shown signify the following.
operations/relationships:
A+B denotes that A is bigger than B.
A-B indicates that A is less than B.
A is more than or equal to 8 when A=B.
A B denotes that A and B are not equal.
A = B is expressed as A/B.
Which of the two conclusions is unquestionably true?based on the details offered?
Statements: EFG GH Findings
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In a math class of 48 students, eight students are studying less than
one hour a night. Six students claim they never study. The rest say they
study more than one hour a night. What fraction of the students are
studying more than one hour each night? (2 marks)
Type a sentence answer in the field provided. Then, submit a picture of
your work to be graded by the instructor.
Fraction of the students are studying more than one hour each night is 17/24.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Total student in the class = 48
students studying less than 1 hour = 8
students that don't study at night = 6
students studying more than one hour a night = 48 - (8+6) = 34
fraction of the students studying more than one hour -
= 34/48
= 17 / 24
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If BC= 5x, CD = 8, and BD = 7x, what is BD?
Answer: 28
Step-by-step explanation:
5x + 8 = 7x
2x = 8
x = 4
BD = 7x
BD = 7(4)
= 28
please help me human to human its due in an hour I've cried help me
Answer:
The equation has one solution.
A value of x that makes the equation true is -3, which when substituted into the equation and simplified makes the equation turn into 18=18.
A value of x that makes the equation false is 0, which when substituted into the equation and simplified makes the equation turn into 0=18.
Step-by-step explanation:
Hope this helped! :)
Answer:
Step-by-step explanation:
The equation has one solution conditional equation
-6x = 18
-6x/-6 = 18/-6
x = -3
A value of x that makes the equation true is -3, which when substituted into the equation and simplified makes the equation turn into 18 = 18
-6x = 18
-6(-3) = 18
18 =18
A value of x that makes the equation false is 3, which when substituded into the equation and simplified makes the equation turn into -18 = 18
-6x = 18
--6(3) = 18
-18 = 18
The average American woman self-reports consuming 1.785×103 kcal/day. For a 147.0 lb woman, express this value in joules per second per kilogram of body mass (watts per kilogram).
Energy consumed equals 0.133 W/kg
What is energy?
Energy is described as the "capacity to accomplish work, which is the ability to apply a force that causes an object to move." Despite this perplexing terminology, the meaning is straightforward: energy is just the force that causes objects to move. Potential energy and kinetic energy are the two forms of energy.
Weight = 147 lb = 66.68 kg (since, 1 lb = 0.453 kg)
Energy consumed = 1.785 x 103 kcal/day
In Watts = 1.785 x 103 x 0.0484 = 8.9 W/day
Energy consumed watts per kilogram = 8.9/66.68 = 0.133 W/kg
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Type an equation for the following pattern.
Answer:
y=28x+0
Step-by-step explanation:
In each row of the table, y is 28 times the value of x.
What is 61 lb to g?
What is 0.11 m^3 to kg
Answer:
1. 27669.1 g
2. 110 kg
PLS HELP ASAP!!!!!!!!!!!!!!!!!!
Answer:
it A because if u apply pressure the molecules will be cramped
Step-by-step explanation:
From the equation, find the axis of symmetry of the parabola.
y=-4x² + 24x-35
a. X=1
b. x=-1
PD
Ο Α
OB
O C
OD
C.
d.
x=3
X=-3
Please select the best answer from the choices provided
The equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
We know that the method to find the axis of the symmetry of the parabola is given by:
x = - b / 2 a
We have the general equation of the parabola as:
y = a x² + b x + c
We have the equation of the parabola as:
y = - 4 x² + 24 x - 35
Comparing from this equation, we get that:
a = - 4
b = 24
c = - 35
Now, substituting the values, we get that:
x = - 24 / 2 (- 4)
x = - 24 / - 8
x = 24 / 8
x = 3
Therefore, the equation for the axis of symmetry of the parabola y = - 4 x² + 24 x - 35 is given by x = 3.
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There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=0.33c+38T=0.33c+38, where TT represents the temperature in degrees Fahrenheit and cc represents the number of times the cricket chirps in one minute. What could the number 38 represent in the equation?
The temperature at which the crickets do not chirp is represented by the number 38, which serves as the y-intercept of the linear equation.
The equation is as follows:
T = 38 + 0.3*c
The temperature is denoted by T, while the number of chirps in a minute is denoted by c.
We want to know what the number 38 means.
Take c = 0 to demonstrate this as there are no chirps.
Then:
T = 38 + 0.33*0 = 38
T = 38
This is the temperature where crickets cease to chirp.
The temperature at which the crickets do not chirp is represented by the number 38, which is the y-intercept of the linear equation.
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What is the result, when the decision is to reject a null hypothesis
The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
What is the null hypothesis?The observed difference is thought to be the sole product of chance, which is the underlying premise. Statistical testing can be used to calculate the likelihood that the null hypothesis is true.
As part of hypothesis testing, the null hypothesis is a made-up assertion that is intended to see if it can be rejected. It is incorrect to draw the conclusion that a result supports the null hypothesis when it is not extreme enough to do so.
This is because the research hypothesis is true, but the result in the particular sample was not extreme enough to enable the null hypothesis to be rejected.
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Find the value of x in the following
1101 base two + x base two + 11001 base two = 111 base two
The value of x is -101001 using the base-2 system.
What is a binary number?
A binary number is a number that is expressed in the binary system or base 2 numeral system, according to digital technology and mathematics. It uses the symbols 1 and 0 to represent different numeric values (zero). The positional notation with 2 as a radix is known as the base-2 system.
Given:
1101₂+x₂+11001₂=111₂
To find the value of x.
First, we'll write the binary numbers and multiply each digit of the binary numbers by the corresponding power of two:
1101₂+x₂+11001₂=111₂
(1×2³+1×2²+0×2¹+1×2⁰) + x₂ + (1×2⁴+1×2³+0×2²+0×2¹+1×2⁰) = (1×2²+1×2¹+1×2⁰)
Now, solve the powers.
(8+4+0+1) + x₂ +(16+8+0+1) = (4+2+1)
Simplifying we get,
13+x₂+25=7
x₂=7-48
x₂=-41
Using binary converter, we get the value of x as -101001.
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A quarterback is sacked for a loss of 7 yards. On the next play, his team loses 12 yards. Then the team gains 5 yards
on the third play. Write an expression to represent the word problem. What is the total number of yards lost or gained?
The total number of losses is 14.
What are expressions?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.So, let the total number of lost and gains be 'x'.
Then, the expression:
-7 - 12 + 5 = x- 19 + 5 = x-14 = xSo, x has a value that is negative so it is a loss.Therefore, the total number of losses is 14.
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slope-intercept form? proper fractions, and improper
Answer:
y = 3x
Step-by-step explanation:
slope intercept form is y = mx + b with m as the slope and b as the y-intercept
to find the slope you can see where the line intersects at (1, 3) and (0,0) If you look at the graph you count up three spaces over one so the slope is 3
since the y-intercept intersects at (0,0) The y-intercept is 0 and you do not have to add that to the answer
Answer:
y=3x I think if not sorry
Step-by-step explanation:
have great evening,day,night,morning!
Francesca wants to
convert 1 cubic foot to cubic centimeters. Use
what you know about customary units to explain
how she can do this.
The value of 1 Cubic Foot is said to be 28316.85 Cubic Centimeters.
A cubic foot is a unit used to measure the volume of a cube with one foot-long sides. It is a unit to measure a unit volume and is symbolically represented as [tex]ft^{3}[/tex]. It is primarily used in the customary and imperial systems of measurement in the United States.
The volume of a cube with sides that are each one centimeter long is measured in cubic centimeters. It is a unit for measuring a unit volume that is symbolically represented as [tex]cm^{3}[/tex] and is typically used to measure lower volumes.
Conversation: The value of 1 cubic foot is approximately equal to 28316.85 cubic centimeters. So, to convert cubic feet to cubic meters, we have to multiply the given foot value by 28316.85 cubic centimeters.
Hence 1 Cubic Foot = 28316.85 Cubic Centimeters.
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Alonzo found three pieces of cable in his tool drawer. Here are their lengths (in meters).
16, 13.13, 9.7
What is the total length of the three pieces?
Given details in question are as follows :
Alonzo found three pieces of cable in his tool drawer.
Their lengths (in meters) are 16, 13.13, 9.7
What is an addition in maths?The addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum.
The Sum of all the numbers in this question is 16+13.13+9.7
=38.83
Alonzo found three pieces of cable in his tool drawer, the total length of the three pieces is 38.83
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The information that is in question is as follows:
Three cables were located by Alonzo in his tool chest.
16, 13.13, and 9.7 meters are their lengths.
What does a math addition mean?
By combining objects, we can count them as a single huge group by adding them. In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
16+13.13+9.7 is the total of all the numbers in this question.
=38.83
Alonzo discovered three cables totaling 38.83 inches in length in his tool drawer.
Manny took home a couple of his friends after soccer practice. He originally had 5 gallons of gas in his car. He used 1.03 gallons of gas to take one friend home and four fifths gallon to take the other friend home. How much gas did he have left in his car after taking both friends home?
1.04 gallons
3.17 gallons
5.8 gallons
6.03 gallons
Answer:
3.17
Step-by-step explanation:
got dat big brain
Jen made a scale drawing of a county park. The scale of the drawing was 13 inches : 6 yards. The picnic area is 42 yards wide in real life. How wide is the picnic area in the drawing?
The width of the picnic area in scale drawing is 91 inches.
How to find the width of the picnic in scale drawing?The scale of the drawing was 13 inches : 6 yards.
The picnic area is 42 yards wide in real life.
The width of the picnic area in drawing is as follows:
Therefore,
6 yards = 13 inches
42 yards = ?
cross multiply
Hence,
width of the picnic in the scale drawing = 42 × 13 / 6
width of the picnic in the scale drawing = 546 / 6
width of the picnic in the scale drawing = 91
width of the picnic in the scale drawing = 91 inches
Therefore, the width of the picnic area in scale drawing is 91 inches.
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The marching band needs to create rows for its performance. There are 48 instruments and 32 flag bearers. Only one type of performer can be in each row. What is the maximum number of performers in each row so that all the rows are equal in length?
48
32
16
2
The maximum number of performers in each row so that all the rows are equal in length is C. 16.
How to calculate the value?It should be noted that there are 48 instruments and 32 flag bearers and only one type of performer can be in each row.
The maximum number of performers in each row so that all the rows are equal in length will be the highest common factor between both numbers.
It should be noted that the highest common factor between 32 and 48 is 16
Therefore the correct option is C.
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given the rule what is the new coordinate? Show all of your work. rule: (x, y) -> (x-7.5, y+6.8) original coordinate: (5, 3)
The point (5, 3) is translated using the rule (x, y) ⇒ (x - 7.5, y + 6.8) to get the point (-2.5, 9.8)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane.
The point (5, 3) is translated using the rule (x, y) ⇒ (x - 7.5, y + 6.8) to get the point (-2.5, 9.8)
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Five more than the quotient of a number and 3 is 7
Answer:
y/3 + 5 = 7
Step-by-step explanation:
Five more would mean plus five, and in these types of equations you work almost backwards. So if you but +5 in your answer, you need to add the quotient, dividing(/) by 3, and the unknown number is y. so your finial equation would read, y divided by 3 plus 5 is equal to 7 (y/3 + 5 = 7) Hope this was helpful!
PLS PLS PLS PLS PLS PLS PLS PLS HELP ME write the ratios 25:4 and 45:10 as a complex fraction
Answer: =−13 1/3
Step-by-step explanation:
