Statement: Two planes intersect to form a point
This is false. Two planes intersect to form a single straight line.
-----------------
Statement: two lines intersect to form a point
This is true assuming the two lines have different slopes
-----------------
Because the first statement is false, the overall argument is false.
Final answer:
The intersection of two planes is a line, not a point, which makes the statement false. Two lines intersecting in a point is true provided they are not parallel.
Explanation:
The statement that the intersection of two planes is a point is false. According to geometric principles, specifically the line of intersection of two planes, when two planes intersect, they do so along a line, not just a single point. This line of intersection is represented by the points where their respective great circles cross. The intersection of two lines, however, is indeed a point, provided that the lines are not parallel. This is in agreement with Theorem 1, which states that two straight lines of a plane have either one point or no point in common; similarly, two planes have no point in common or a straight line in common.
Relevant Theorems on Intersections
Theorem 1 and Theorem 2 outline the foundational concepts regarding intersections in geometry. Understanding these theorems helps explain why two intersecting planes result in a line and not a single point.
Can anyone figure this out ??
Identify a pattern and find the next number in the pattern
Answer:
(-0.8)×4=(-3.2)
(-3.2)×4=(-12.8)
(-12.8)×4=(-51.2)
(-51.2)×4=(-204.8)
anser is -204.8
Step-by-step explanation:
Please answer this as quick as possible. Really need help.
Systems of equations have one solution. (5 points)
Always
Sometimes
Never
Answer:
Sometimes
Step-by-step explanation:
When you deal with a system of equations, there may be no solution; there may be one solution; there any positive integer number of solutions; there may be an infinite number of solutions.
The answer is : sometimes
Answer:
sometimes, I got it right on the quiz I just took :)
Step-by-step explanation:
solve each equation check your solution. 2/7y + 5 = -9
[tex]\frac{2}{7}y + 5 = -9\ /\cdot7\\2y+35=-63\\2y=-63-35\\2y=-98\ /:2\\y=-49\\ \\ \\\frac{2}{7}\cdot(-49)+5=-14+5=-9[/tex]
On a piece of paper, graph y≤ -2x.Then determine which answer matches the graph you drew.
A.(-2,4) (3,-6)
B.(-2,4) (1,2)
C.(-2,-6) (1,3)
D.(-2,-6) (1,3)
Answer:
The correct option is A.
Step-by-step explanation:
The given inequality is
[tex]y\leq -2x[/tex]
The sign of inequality is ≤, it means the points on relation line lie in the solution set.
The related equation of the inequality is
[tex]y=-2x[/tex]
At x=0,
[tex]y=-2(0)=0[/tex]
At x=1,
[tex]y=-2(1)=-2[/tex]
Plot the points (0,0) and (1,-2) on a coordinate plane.
The sign of inequality is ≤, it means we have shade below the line.
The point (-2,4) and (3,-6) are in solution set because,
[tex]4\leq -2(2)\Rightarrow 4\leq 4[/tex] (True)
[tex]-6\leq -2(3)\Rightarrow -6\leq -6[/tex] (True)
Therefore option A is correct.
The points (1,2) and (1,3) are not in the solution set because,
[tex]2\leq -2(1)\Rightarrow 2\leq -2[/tex] (False)
[tex]3\leq -2(1)\Rightarrow 3\leq -2[/tex] (False)
Therefore options B,C and D are incorrect.
Answer: (1,2) (-2,-4)
Step-by-step explanation:
tell whether the ratio is in simplest form, if not, then write it in simplest form 1)8:6 2)48/28 3)7 to 9
8/6= 1 1/3
48/28= 1 4/7
7/9 is in simplest form
Miriam poured 4 cans of fruit juice into rhe pitcher. Each can contained 1 1/2 cups of juice. How many pints of juice did she pour into the pitcher?
Answer:
She poured 3 pints
Step-by-step explanation:
If x= -5+6i and y= 3-2x, then which of the following is the value of the expression 4x-y
[tex]y=3-2x\\\\4x-y=4x-(3-2x)=4x-3+2x=6x-3\\\\\text{Put}\ x=-5+6i\ \text{to the expression}\ 6x-3:\\\\6(-5+6i)-3\qquad\text{use distributive property}\\\\=(6)(-5)+(6)(6i)\\\\=-30+36i\\\\Answer:\ \boxed{4x-y=-30+36i}[/tex]
You are helping a classmate edit this story. Your classmate decides to change the point of view and write the story from the third person point of view as if the story happened to a group of friends. What change is necessary? Names of the friends should be included. The pronoun we should be changed to they. The pronoun we should be changed to I. Explain in more detail the lesson the friends learned.
To change the story from first person to third person point of view, first-person pronouns like 'I', 'me', and 'we' should be changed to third-person pronouns such as 'they', 'he', 'she', or the friends' names.
Explanation:To change the point of view of the story from first person to third person, it is necessary to change the pronouns used in the narration. If the original story used first-person pronouns such as I, me, and we, these would need to be changed to third-person pronouns such as they, he, she, or the friends' names to reflect the third person point of view.
For example, a sentence that originally reads "We went to the park after school" would change to "They went to the park after school" in the third person point of view. This shift enables the story to be told as if an outside observer is describing the events that happen to the group of friends, rather than the friends themselves narrating the story.
the rectangular floor of a classroom is 36 feet and in length and 32 feet in width a scale drawing of the floor has a length of 9 inches what is the area in square inches of the floor and the scale drawing
Answer:
Area of the floor of the classroom is 72 inch².
Step-by-step explanation:
We are given the dimensions of the rectangular floor as,
Length = 36 feet and Width = 32 feet
Since, the scale drawing have the length = 9 inches
This gives, the ratio of the actual length to the scale drawing length = [tex]\frac{36}{9}[/tex]
Thus, we have,
[tex]\frac{36}{9}=\frac{32}{x}[/tex], where x is the width in the scale drawing.
So, on solving,
[tex]x=\frac{32\times 9}{36}[/tex] i.e. x= 8 inches
Since, Area of the rectangle= Length × Width
Thus, area of the rectangular floor = 9 × 8 = 72 inch².
Thus, the area of the floor of the classroom is 72 inch².
The area of the floor of the scale drawing and the scale factor are 72 in² and 1/4 respectively
Actual Length = 36 feets Actual width = 32 feets Model width = 9 inchesThe scale factor = 9 / 36 = 1/4
The length of the model canbe calculated thus :
Actual Length × scale factorModel width = 32 × 1/4 = 8 inches
The Area of a rectangle can be calculated using the relation :
Area = Length × widthArea of floor = 8 inches × 9 inches = 72 inch²
Therefore, the area of the floor of the scale drawing is 72 in²
Learn more : https://brainly.com/question/18796573
half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories 1/4 of a pepperoni pizza plus a whole ham and pineapple pizza contains 745 calories how many calories are in a whole pepperoni pizza and how many calories are in a whole ham and pineapple pizza
a) 600 calories, 550 calories
b) 480 calories, 640 calories
c) 520 calories, 680 calories
d) 660 calories, 580 calories
Answer:
Correct choice is D (In a whole pepperoni pizza are 660 calories, in in a whole ham and pineapple pizza are 580 calories).
Step-by-step explanation:
Let x calories be the number of calories a whole pepperoni pizza contains and y calories be the number of calories a whole ham and pineapple pizza contains.
1. If half a pepperoni pizza plus three fourths of a ham and pineapple pizza contains 765 calories, then
[tex]\dfrac{1}{2}x+\dfrac{3}{4}y=765.[/tex]
2. If 1/4 of a pepperoni pizza plus a whole ham and pineapple pizza contains 745 calories. then
[tex]\dfrac{1}{4}x+y=745.[/tex]
3. Multiply each equation by 4 and get a system of two equations:
[tex]\left\{\begin{array}{l}2x+3y=3060\\x+4y=2980\end{array}\right.[/tex]
From the second equation [tex]x=2980-4y[/tex], then
[tex]2(2980-4y)+3y=3060,\\ \\5960-8y+3y=3060,\\ \\-8y+3y=3060-5960,\\ \\-5y=-2900,\\ \\y=580.[/tex]
Then
[tex]x=2980-4\cdot 580=2980-2320=660.[/tex]
The whole pepperoni pizza contains 660 calories and the whole ham and pineapple pizza contains 580 calories. These values are obtained using a system of two equations obtained from the given statements.
Explanation:Let's denote 'P' as the calories in a whole pepperoni pizza, and 'H' as the calories in a whole ham and pineapple pizza. We can then interpret the problem as two equations based on the given information.
First equation (from the first sentence in the question): 0.5P + 0.75H = 765.
Second equation (from the second sentence in the question): 0.25P + H = 745.
Now we just need to solve this system of equations. Multiply the second equation by two to match the 'P' terms in both equations: 0.5P + 2H = 1490.
Subtract the first equation from this new equation: 0.5P + 2H - (0.5P + 0.75H)= 1490 - 765. This simplifies to: 1.25H = 725, meaning H = 580 calories.
We can then substitute H = 580 into the first original equation to solve for P: 0.5P + 0.75*580 = 765. Solving this gives P = 660 calories.
So, a whole pepperoni pizza contains 660 calories, and a whole ham and pineapple pizza contains 580 calories. This corresponds to the option d) in the given list.
Learn more about Equations here:https://brainly.com/question/9585437
#SPJ12
Kate had 50 50 tickets to use for rides at the fair. She lost some of them. Her dad doubled the tickets she had left. Kate wrote the expression 2(50−t) 2 ( 50 - t ) to find the number of tickets she has now, where t t is the number of tickets she lost. Jack correctly wrote another expression, 100−2t 100 - 2 t , to find the number of tickets Kate has now. Use the drop-down menus to explain what each part of Kate's and Jack's expressions mean.
Answer: Kate expression: 2(50-t)
2 : represents twice,
50 : represents Initial number of tickets Kate has,
t : The lost tickets
50-t : represents Number of ticket Kate has After loosing t tickets
Jack expression: 100 - 2t
100 : Twice of initial ticket Kate has,
t : The lost tickets
2t : represents twice of the lost tickets,
100-2t : represents Final number of ticket Kate has.
Step-by-step explanation:
Since, According to the question,
Initially Kate has 50 tickets.
She lost tickets = t
And, after losing t ticket she has tickets = 50 - t
But, His father doubled the amount, Thus she has final tickets = 2(50-t)= 2×50 -2× t = 100 - 2t
Final answer:
Kate's expression, 2(50−t), represents the number of tickets she has now by doubling the tickets she had left after losing some. Jack's expression, 100−2t, represents the number of tickets Kate has now by subtracting twice the number of tickets she lost from the total number of tickets she initially had.
Explanation:
Kate wrote the expression 2(50−t) to find the number of tickets she has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: multiply 2 by the quantity (50−t). This means that Kate's dad doubled the tickets she had left after losing some tickets.
Jack's expression, 100−2t, also determines the number of tickets Kate has now. In this expression, t represents the number of tickets she lost. The expression is simplified as follows: subtract 2 times the quantity t from 100. This means that Jack found the number of tickets Kate has by subtracting twice the number of tickets she lost from the total number of tickets she initially had.
[tex]1 = \frac{u}{2} - 1[/tex]
Multiply by 2:
2=u-2
4=u or u=4.
Train A departs station one traveling at 75 mph. Train N departs station two 30 minutes later traveling at 45 mph. The stations are 300 miles apart. The equation below gives the distance between the trains, D, in miles as a function of, T, the time after Train B departs. D=|262.5-120T| For which two values of T will D=50? Round to the nearest tenth.
A)1.8 and 2.6
B)0.2 and 0.3
C)-17.8 and 26.0
D)-1.8 and 1.8
Final answer:
The equation given to calculate the distance between the trains is D = |262.5 - 120T|. To find the values of T for which D = 50, substitute 50 for D in the equation and solve for T. By solving the equations, we find that T is approximately 1.8 and 2.6.
Explanation:
The equation given to calculate the distance between the trains is D = |262.5 - 120T|, where T is the time after Train B departs. To find the values of T for which D = 50, substitute 50 for D in the equation and solve for T.
50 = |262.5 - 120T|
To remove the absolute value, we can split the equation into two cases:
262.5 - 120T = 50-(262.5 - 120T) = 50Solving these equations will give us the values of T for which D = 50.
By solving both equations, we find that T is approximately 1.8 and 2.6, so the answer is A) 1.8 and 2.6.
Kaylee found the surface area, in square inches of a rectangular prism by using formula. 2(5×3)+2(5×8)+2(3×8) What is the surface area of the prism, in square inches?
Answer:
158
Step-by-step explanation:
Simplify the following:
2×5×3 + 2×5×8 + 2×3×8
5×3 = 15:
2×15 + 2×5×8 + 2×3×8
5×8 = 40:
2×15 + 2×40 + 2×3×8
3×8 = 24:
2×15 + 2×40 + 2×24
2×15 = 30:
30 + 2×40 + 2×24
2×40 = 80:
30 + 80 + 2×24
2×24 = 48:
30 + 80 + 48
| 8 | 0
| 4 | 8
+ | 3 | 0
1 | 5 | 8:
Answer: 158
Kaylee is using the formula for the surface area of a rectangular prism. She calculates it as 2(5×3) + 2(5×8) + 2(3×8), which adds up to 158 square inches, representing the total surface area of the prism.
Kaylee is calculating the surface area of a rectangular prism using a mathematical formula. The formula comprises three terms, each representing the area of a pair of opposite faces. Let's break down the calculation:
The first term is 2(5×3), representing the top and bottom faces of the prism.The second term is 2(5×8), representing the front and back faces of the prism.The third term is 2(3×8), representing the left and right faces of the prism.When Kaylee calculates these areas and adds them together, she gets:
2(5×3) + 2(5×8) + 2(3×8) = 2(15) + 2(40) + 2(24) = 30 + 80 + 48 = 158 square inches.
Thus, the total surface area of the rectangular prism is 158 square inches.
Which of the following represents the zeros of f(x) = x3 − 5x2 − 3x + 15?
A) 5, square root of 3, −square root of 3
B) −5, −square root of 3, −square root of 3
C) 5, −square root of 3, −square root of 3
D) −5, square root of 3, square root of 3
Answer: Variant A
Step-by-step explanation:
ANSWER QUICK PLEASE
If f(x) = |x – 5| + 3, find f(2).
Answer:
SO if f(x)= |x-5|+3 then F(2)= 6
Step-by-step explanation:
These signs | | mean that it is an absolute value equation. SO that means any negative will automatically change to positive values and positive values will stay at positive values. You are supposed to substitute 2 in for x and if you do 2-5 then that is negative 3 but it changes to positive 3 and add three and then f(2)= 6
Kenneth is making chocolate cakes. For each cup of milk uses, he needs to use one and 3/4 cups of flour. For each cup of flour he uses, he needs to use 3/7 cup of cocoa powder.kenneth is making enough cakes that he needs to use 4 cups of milk. How many cups of cocoa powder does Kenneth need to use?
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
1 milk = 1 3/4 cup of flour
1 flour = 3/7 cup of cocoa powder
4 cups of milk = 1 3/4 x 4 = 7/4 x 4/1 = 7 cups of flour
7 cups of flour = 7 x 3/7 = 7/1 x 3/7 = 3 cups of cocoa powder
Kenneth needs 3 cups of cocoa powder for the chocolate cakes he is making with 4 cups of milk.
To find out how many cups of cocoa powder Kenneth needs for his chocolate cakes, we should first determine how much flour is necessary for 4 cups of milk and then how much cocoa powder is needed for that amount of flour. Kenneth uses one and 3/4 cups of flour for each cup of milk. So for 4 cups of milk, he needs:
1 ¾ cups of flour/cup of milk x 4 cups of milk = 7 cups of flour
Next, for every cup of flour, Kenneth needs 3/7 cup of cocoa powder. Therefore, to find out the total cups of cocoa powder for 7 cups of flour, the calculation is:
3/7 cups of cocoa powder/cup of flour x 7 cups of flour = 3 cups of cocoa powder
So Kenneth needs a total of 3 cups of cocoa powder for his cakes.
Jeremy is driving on the interstate highway, and he just saw a sign that said Montpelier was 52 miles away. If he's driving at 65 miles per hour, how many minutes will it take him to get to Montpelier?
Answer:
48 min
Step-by-step explanation:
1 h = 60 min
It takes 60 min to go 65 mi.
Time = 52 × 60/65
Time = 48 min
Answer:
48min
Step-by-step explanation:
I used this question and got it right on my test. :)
Solve y = x - 5 if the domain is -3
Answer:
y = -8
Step-by-step explanation:
The domain is the x values so x=-3
y = x-5
Substituting x=-3
y = -3-5
y=-8
Step-by-step explanation:
[tex]\sf \longmapsto{y = - 5 + - 3} \\ \\ \sf \longmapsto{y = - 5 + - 3 = \red{ - 8}} \\ \\ \sf \longmapsto \boxed{ \sf\: y = - 8}[/tex]
a train traveled 1/5 of the distance between two cities in 3/4 of an hour ,at this rate what fraction of the distance between two cities can the train travel in one hour
sorry, put the wrong answer and cant delete
Answer:
4/15 distance
Step-by-step explanation:
We can use ratio's to solve this, putting distance over time
1/5 distance x distance
---------------- = ----------------------
3/4 hour 1 hour
Using cross products
1/5 * 1 = 3/4 x
1/5 = 3/4 x
Multiply by 4/3 to isolate x
1/5 * 4/3 = 4/3 * 3/4x
4/15 = x
The train can travel 4/15 of the distance in 1 hour
what is the range if the function in this table?
The range of a function is the set of y-values the function contains. Thus, in this case, the range would be the set of values under the y column, as this represents the y-values the function produces.
We see "2, 3, 4, 2" under the y column. Since we are establishing a set of values, we are going include all the values under the column, which includes 2, 3, and 4. We are not going to repeat the second 2 because it isn't necessary, as 2 is already in the set thus.
Thus, the final set for the range of the function is {2, 3, 4}, or Choice A.
Solve −3x2 − 4x − 4 = 0.
A) x equals quantity of 2 plus or minus 4i square root of 2 all over 3
B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3
C) x equals quantity of negative 2 plus or minus 2i square root of 2 all over 3
D) x equals quantity of negative 2 plus or minus 4i square root of 2 all over 3
Answer:
The correct answer is B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3.
Step-by-step explanation:
We are given the following quadratic equation:
[tex]-3x^2-4x-4 = 0[/tex]
Since, it cannot be factorized so we will use the quadratic formula:
x = [tex]\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Substituting in the values of a, b and c in the above formula to get:
x = [tex]\frac{-(-4)+-\sqrt{(-4)^2}-4(-3)(-4) }{2(-3)}[/tex]
x = [tex]-\frac{2}{3} +i \frac{2\sqrt{2} }{3}[/tex], x = [tex]-\frac{2}{3} -i \frac{2\sqrt{2} }{3}[/tex]
Therefore, the correct answer option is B) x equals quantity of 2 plus or minus 2i square root of 2 all over 3.
What is the product 4n/4n-4 n-1/n+1
Jackson deposited $5,000 at 3.8% interest, compounded continuously, when he was 18 years old. How much will be in the account when he is 40 years old if he made no other deposits or withdrawals?
$19,000.19
$11,535.60
$10,691.38
$8,800.00
Answer:
$11535.60 will be in his account when he is 40 years old
Step-by-step explanation:
Jackson deposited $5,000 at 3.8% interest, compounded continuously, when he was 18 years old
Time period is from 18 years to 40 years
t= 40 - 18 = 22
For compounding continuously we use formula
[tex]A= Pe^{rt}[/tex]
P = initial amount deposited = 5000
r= rate of interest = 3.8% = 0.038
t= time period = 22 years
now plug in all the values and find out A final amount
[tex]A= 5000e^{0.038*22}[/tex]
[tex]A= 5000e^{0.836}[/tex]
A= 11535.60
Moira simplifies the expression 6y4+3y4 to 9y8. Use the drop-down menus to complete the statements below to explain why Moira's solution is correct or incorrect.
When adding like terms, they simply add together:
6y + 3y = 9y
The rule of adding two powers are as follows:
[tex]x^{a} + x^{b} = x^{a+b}[/tex]
So:
[tex]y^{4} + y^{4} = y^{4 + 4} = y^{8}[/tex]
So 6y⁴ + 3y⁴ = 9y⁸
Answer:
Moira's solution is..... incorrect
6y4+3y4 is the same as...... (6*y^4) + (3*y^4)
9y8 is the same as...... 9y*y*y*y*y*y*y*y
6y4+3y4 simplifies to..... 9y^4
A motor running at 4500 RPM, revolutions per minute, is actually revolving at how many revolutions per second?
Answer:
A motor running at 75 revolutions per second.
Step-by-step explanation:
Given statement: A motor running at 4500 RPM, revolutions per minute.
⇒ In one minute , a motor running at 4500 revolutions.
Use conversion:
[tex]1 min = 60 sec[/tex]
We have to calculate how many revolutions per second.
in 60 sec , a motor running at 4500 revolutions
then,
in 1 sec , a motor running at [tex]\frac{4500}{60} = 75[/tex] revolutions.
Therefore, a motor running at 75 RPS, revolution per second.
Answer:
Motor run in 1 second = 75 revolution.
Step-by-step explanation:
Given : A motor running at 4500 RPM, revolutions per minute,
To find : how many revolutions per second.
Solution : We have given
Motor run in minute = 4500 revolution.
1 minute = 60 second .
Then ,
Motor run in 60 second = 4500 revolution.
Motor run in 1 second = [tex]\frac{4500}{60}[/tex] revolution.
Motor run in 1 second = [tex]\frac{450}{6}[/tex] revolution.
Motor run in 1 second = 75 revolution.
Therefore, Motor run in 1 second = 75 revolution.
What is the equation of the line passing through the points (3,-1) and (4,2)
Answer:
c is the answer
Step-by-step explanation:
(3,-1) and (4,2)
find the slope y2-y1 over x2-x1
so 2 and -1 is 2+1 = 3 and
4-3 = 1
so 3/1 = 3 so it is c
Solve the system using elimination.
2x + 3y = 17
x + 5y = 19
[tex]\left\{\begin{array}{ccc}2x+3y=17\\x+5y=19&|\text{multiply both sides by (-2)}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+3y=17\\-2x-10y=-38\end{array}\right}\qquad\text{add both sides of equations}\\.\qquad\qquad-7y=-21\qquad\text{divide both sides by (-7)}\\.\qquad\qquad \boxed{y=3}\\\\\\\text{Substitute the value of y to the second equation}\\\\x+5(3)=19\\\\x=15=19\qquad\text{subtract 15 from both sides}\\\\\boxed{x=4}\\\\Answer:\ x=4\ and\ y=3.[/tex]
Find the slope of the line represented by the table of values.
A) 1/2
B) 2
C) −1/2
D) −2
Answer:
D) -2
Step-by-step explanation:
Answer:
D- -2
Hope this helps :)