(14,2) is the point lies on the slope-intercept form, line .
What does the slope intercept form mean?
The formula for a straight line, written as y = mx + b, where m denotes the line's slope and b its y-intercept. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.
In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. We can observe that the line's slope is 3 from our equation, y = 3 x + 5.
All lines passing thru the origin should have a slope of y = mx + c
In this case, since the slope is 1/7 , the line will be y = 1/7x
Thus, it could observe which is the only point that satisfies this equation of the line out of all the points.
For choice "E" when x= 7 and y = 14 m = 1/7 and put the value in y = mx + c it will give 14 = 2 , which is wrong.
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Answer and explaining
Answer:
a
Step-by-step explanation:
i just took it
Joshua is driving to the store. the average distance din miles, he travels over minutes is given by the function (1) - 0.57. what is the
75 miles
7.5 minutes
7.5 miles
15 minutes
Driving to the supermarket is Joshua. He covers 7.5 miles since he goes an average of 0.56 miles per minute.
Why is mean called the average?By dividing the entire specific number by sum of all the values, the average can be obtained. A mean may indeed be calculated by adding all of the values in a sample of data. In other terms, a means is also known as the arithmetic mean. The average is referred to as having a mean.
The provided function is
d(t) = 0.5t
Simply substitute it to get the figure set t = 15
7.5 miles are equal to d (15) 0.5 (15).
To get the distance, use the range equations d = st, which says "distance equals force times time." Rate and speed are equivalent because they both indicate a specific length of distance per unit time, such like km/h or kilometers per hour. R = s = d/t is true if clip r and mobility s are equal.
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Select all the inequalities that have symbols that will be reversed when the variable is isolated.
–10. 5 < 3a
b6 ≤ 7
–4. 5c > 9
–215 ≤ –52d
e – 13 ≥ 11
Option - C and D : -4.5c > 9 and -215 ≤ -52d will have its inequalities that have symbols that will be reversed when the variable is isolated .
Anytime you are multiplying or dividing an inequality by a negative you must reverse the inequality symbol .
Inequalities in mathematics specify the connection between two non-equal quantities. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.
The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples. "A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">,",“<”, “≥”, “≤”, An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions.
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Lines Cut by a Transversal (1st Correct Answer Will be Given BRAINLIEST)
Consider parallel lines cut by a transversal.
Parallel lines q and s are cut by transversal r. On line q where it intersects line r, 4 angles are created. Labeled clockwise, from uppercase left: angle 1, angle 2, angle 4, angle 3. On lines where it intersects line r, 4 angles are created—labeled clockwise, from uppercase left: angle 5, angle 6, angle 8, angle 7.
Explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.
With the description of the parallel lines and the transversal line, the alternate exterior angles are angle 1 and angle 8 and they are equal
How to show that alternate exterior angle are equalAccording to the description
angle 1 + angle 2 = 180 degrees (angles of a straight line)
angle 4 + angle 2 = 180 degrees (angles of a straight line)
subtracting will result to
angle 1 - angle 4 = 0
angle 1 = angle 4
the vertical angle theorem
because the line is parallel
angle 1 = angle 5 (corresponding angles)
angle 4 = angle 8 (corresponding angles)
Since angle 1 = angle 4 = angle 8 then applying transitive property
angle 1 = angle 8
This completes the prove that alternate exterior angles are equal.
Another pair of alternate exterior angles are angle 2 and angle 7
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3. Find the distance between (-4, 6) and (0, 6). Round to the nearest tenth if needed.
A. 4
B. -3
C. -4
D. 3
Answer: A. [tex]4[/tex]
Step-by-step explanation:
Since the points have the same [tex]y[/tex]-coordinate, take the absolute value of the difference of the [tex]x[/tex]-coordinates. Doing so yields [tex]|-4-0|=4[/tex].
In what ratio is the line segment joining the points (- 3 1 and (- 8 9?
the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4. The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points.
5:4
Given two points, (x1, y1) and (x2, y2)
The ratio of the line segment joining the points is:
(x2 - x1) : (y2 - y1)
Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9)
The ratio of the line segment joining the points (-3, 1) and (-8, 9) is calculated by subtracting the x-coordinates and y-coordinates of the two points. Specifically, the ratio is given by the expression (x2 - x1) : (y2 - y1). In this case, the x-coordinates are -3 and -8, and the y-coordinates are 1 and 9. By substituting these values into the expression, we get ( -8 - (-3)) : (9 - 1) which simplifies to ( -5 ) : ( 8 ). Therefore, the ratio of the line segment joining the points (-3, 1) and (-8, 9) is 5:4.
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1000 kg of limestone is subjected to intense heat and high pressure to form marble. all but one of the statements applies to the formation of the marble.
a) marble is a metamorphic rock.
b) about 1000 kg of marble is produced.
c) marble is formed by recrystalization.
d) marble is formed close to earth's surface.
1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
When limestone is subjected to the heat and pressure of metamorphism, marble is created as a metamorphic rock. Calcite (CaCO3) makes up the majority of its composition, but it also frequently includes other minerals such clay, mica, quartz, pyrite, iron oxides, and graphite.
When limestone undergoes a process known as metamorphism, which involves heat and tremendous pressure, marble is created. The marble's interconnecting calcite crystals are created when the calcite limestone recrystallizes after metamorphism.
Hence, 1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
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Round to the nearest tenth if necessary
Answer:
obviously 16 meters to the west
03.06 LC)
Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 7 and b = 10?
The standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
What is Hyperbola ?
a plane curve generated by a factor so moving that the difference of the distances from two constant points is a consistent : a curve formed by way of the intersection of a double right circular cone with a plane that cuts each halves of the cone.
Given,
The standard equation of the hyperbola centered at the origin with given values a=7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
vertical axis with values a = 7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
(x^2 / 7*7) - ( y^2/ 10*10) = 1
x^2 / 49 - y^2 / 100 = 1
Hence , the standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
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whats the answer for this question
By the Pythagorean theorem, [tex]y=\sqrt{6^2-3^2}=3\sqrt{3}[/tex].
By the geometric mean theorem, [tex]y^2=3x \implies x=9[/tex].
Pat had a 12:30 pm appointment 72 miles from his office. If he averaged 48 mph for the trip and arrived ten minutes late, when did he leave his office? Show all your work and explain how you arrived at your answer.
Pat left the office at 10:50 am.
What is the relation between speed, distance, and time?
The relation between speed, distance, and time would be
distance = speed x time
We know that Pat had a 12:30 pm appointment 72 miles from his office, arrived ten minutes late, and averaged 48 mph for the trip. So we can set up the equation as:
distance = speed x time
72 = 48 x time
To solve for time, we divide both sides of the equation by 48:
time = distance / speed
time = 72 / 48
time = 1.5 hours
Since Pat arrived 10 minutes late, we need to subtract that 10 minutes from the time it took him to get to the appointment
12:30pm - 00:10 = 12:20 pm
Now, we have to subtract the time it took Pat to get to the appointment from the time he left the office
12:20 pm - 1.5 hours = 10:50 am
So Pat left the office at 10:50 am.
Hence, Pat left the office at 10:50 am.
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A particle is located at vector r = (0.54,)i + (-36m)j +(p.85m)k constant force of magnitude 2.6 N acts on the particle. Find the components of the torque about the origin when the force acts in (a) the positive x direction and (b) the negative z direction.
The components of the torque about the origin when the force acts in
(a) the positive x direction is 1.4N.
(b) the negative z direction is 2.21N.
What is constant force of magnitude?
The motion of a particle occurs on a plane and is influenced by a force of constant magnitude that is always perpendicular to the particle's velocity.
Given:
A particle is located at vector r = (0.54m)i + (-36m)j +(.85m)k constant force of magnitude 2.6 N acts on the particle.
We have to find the torque about positive x direction and negative z direction.
At the positive x direction the torque is (T)
= the x component of position vector . F
= 0.54 x 2.6
= 1.4 N
At negative z direction Torque = - (z component of position vector).F
= .85 x 2.6
= 2.21 N
Hence,
The components of the torque about the origin when the force acts in
(a) the positive x direction is 1.4N.
(b) the negative z direction is 2.21N.
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3) Five kilograms of flour can make 45 loaves of bread. How many loaves of bread can 6 kilograms make?
Answer:
54 loaves of bread
Step-by-step explanation:
45:5=9 (45 divided by 5 equals 9)
9x6=54 (9 times 6 equals 54)
What is the value of y in this triangle?
Answer:64
Step-by-step explanation: You add 79 and 37 then subtract the sum of the two numbers from 180
5. The sum of two numbers is 15. The difference between five times the first number and Three times the second number is 19. Find the two numbers.
Answer:
let the 2 unknown numbers be 'x' and 'y'
given: x+y=15 - equation 1
5x-3y=19 - equation 2
from equation 1 :
x = 15 -y
substitute this in equation 2
5(15-y) -3y = 19
75 - 5y - 3y = 19
75-8y=19
8y=56
y=7(substitute value of y in equation 1)
x+7=15
x=8
hence the two numbers are 8 and 7
Answer:
x = 8
y = 7
Step-by-step explanation:
let's assume the first number as x, and the second number as y
Now, according to the question,
x + y = 15
Moving on to the next statement,
five times the first number = 5x
three times the second number = 3y
Thus,
5x - 3y = 19
Now that we have two equations, we can either write 'x' in 'y' terms, or y in 'x' terms.
For example, from the first equation:
x + y = 15
y = 15 - x
Now, let's put this value of y into the second equation, i.e.
5x - 3(15 - x) = 19
5x - 45 +3x = 19
8x = 19 + 45
x = 64/8
x = 8
Now, let's put this value of x into the first equation, i.e.
x + y = 15
8 + y = 15
y = 7
In conclusion, the two numbers, x and y, are 8 and 7 respectively
HELP ASAP PLEASE! Find all the cube roots of -512.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The real cube root(s) of -512 is/are [}.
B. There are no real cube roots of -512.
Answer:
A; -8
Step-by-step explanation:
Well, the cube root of 512 is just 8, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -512 is just -8
jim wants to buy a 5-pound mixture of chocolates. if kind 1 sells for $1.80 per pound, and kind 2 sells for $2.30 per pound, how much of each kind can he buy for $10? i just am not really sure what the question is asking, and if i did know i'm not sure how to solve it
Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 chocolate for $10 by setting up and solving a system of equations.
The question is asking how much of each kind of chocolate Jim can buy for $10. To solve this, you can set up a system of equations.
Let x = pounds of kind 1, and y = pounds of kind 2
x + y = 5 (total pounds of chocolate)
1.8x + 2.3y = 10 (cost of chocolate)
Solving the system of equations, you get x = 3.75 pounds of kind 1 and y = 1.25 pounds of kind 2. Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 for $10.
1.8x + 2.3y = 10
1.8x = 10 - 2.3y
x = (10 - 2.3y)/1.8
x + y = 5
x = 5 - y
(10 - 2.3y)/1.8 = 5 - y
10 - 2.3y = (1.8)(5 - y)
10 - 2.3y = 9 - 1.8y
1.2y = 10 - 9
1.2y = 1
y = 1/1.2
y = 0.833 (rounded to 1.25)
x = 5 - y
x = 5 - 0.833
x = 4.167 (rounded to 3.75)
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18. 11,9, 22, 20, 33, 44, ?, ? (a) 55, 54 (b) 43,55 (c) 55,53 (d) 41, 55 (e) 42, 55
This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.
Find the sequence ?This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.
Given:
Sequence is 55, 44, 33, 22, ...
We need to find the next two terms in the sequence.
According to the question,
Now, calculating the common difference of arithmetic sequence.
d1 = 44 - 55 = -11
d2 = 33 - 44 = -11
Hence, the common difference d is -11.
Now, calculating the next two terms of given sequence.
We know that,
a5 = 55+ (4) * (-11)
a5=55-44
a5 = 11
a6 = 55+(5)*(-11)
a6 = 55- 55
a6 = 00
This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.
Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.
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Solve:
4(x - 2) - 4x = -(3x + 2)
Answer:
x = 2
Step-by-step explanation:
To solve, you have to get the variable to only be on one side by subtracting from one side.
How many 3 1/4 inch pieces of yarn can be
cut from a roll that has 52 inches of yarn?
Answer:
16 peices
Step-by-step explanation:
52/3.25 = 16
a tree limb hangs 51 feet from a telephone wire. the city trims back the branch before it grows within 2; feet of the wire. will the city allow the tree to grow 2} more feet?
No, the city will not allow the tree to grow 2} more feet.
The telephone wire is a safety hazard, so the city trims back the branch so that it does not come closer than 2 feet to the wire. To calculate if the tree can grow 2} more feet, we need to find out how far the branch is currently from the wire and subtract 2 feet.
Let x = the current distance of the branch from the wire
51 - x = 2
x = 49 feet
Therefore, the branch is currently 49 feet away from the wire, which is less than 2} feet. Since the city trims back the branch when it grows closer than 2 feet to the wire, the city will not allow the tree to grow 2} more feet.
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2(x + 3=5x + 6 - 3x true or never true
Answer:
true
Step-by-step explanation:
2(x + 3)=5x + 6 - 3x true or never true?
2(x + 3)=5x + 6 - 3x
2x + 6 = 2x + 6
2x - 2x = 6 - 6
0 = 0
a swimming pool had 2.5 million liters some of the water evaporated and now the pool had 2 million liters of water what percent of water evaporated.
show all work
Answer:
4/5 = .8. 20% evaporated
Step-by-step explanation:
2.5 million divded into fifth. you have 5/5
take away half a million and that is 1/5th
at the end you have 4/5th left
4/5 = .8 = 80% left over meaning 20% evaporated
Directions: Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Question 9
[tex]\frac{\sin x}{23}=\frac{\sin 27^{\circ}}{11}\\\\\sin x=\frac{23\sin 27^{\circ}}{11}\\\\x \approx 71.7^{\circ}, 108.3^{\circ}[/tex]
Both of these cases satisfy the angle sum of a triangle.
Question 11
[tex]\frac{\sin x}{27}=\frac{\sin 74^{\circ}}{26}\\\\\sin x=\frac{27 \sin 74^{\circ}}{26}\\\\x \approx 86.6^{\circ}, 93.4^{\circ}[/tex]
Both of these cases satisfy the angle sum of a triangle.
please answer my mock rev question !!
Answer:
(a) 8800000
(b) Barcelona had the least population in 2018
(c) The difference in population is 2.9 x [tex]10^{7}[/tex]
Step-by-step explanation:
(a) Since '10' is raised to a positive power, the decimal will be moving in the forward direction, In other words, it will move towards the right. Therefore, the decimal will be moving 6 places forward. After which, the empty slot(s) will be occupied by zeros
8.8 x [tex]10^{6}[/tex] = 8800000
(b) First notice that three out of the five cities have population expressed in [tex]10^{6}[/tex] (where 6 is the least power). Then notice that out of those three cities, the smallest number corresponds to Barcelona (i.e. 5.5).
Therefore, Barcelona had the least population in 2018
(c) Population of:
Tokyo: 3.7 x [tex]10^{7}[/tex]
Ahmedabad: 7.7 x [tex]10^{6}[/tex]
First, make sure the two numbers are expressed in the same standard form (meaning 10 is raised to the same power in both cases):
Tokyo: 3.7 x [tex]10^{7}[/tex] = 3.7 x 10 x [tex]10^{6}[/tex] =37 x [tex]10^{6}[/tex]
Ahmedabad: 7.7 x [tex]10^{6}[/tex]
Next step:
37 x [tex]10^{6}[/tex] - 7.7 x [tex]10^{6}[/tex]
= (37 - 7.7) x [tex]10^{6}[/tex]
= 29.3 x [tex]10^{6}[/tex]
= 29 x [tex]10^{6}[/tex] (Corrected to 3 significant figures)
= 2.9 x 10 x [tex]10^{6}[/tex]
= 2.9 x [tex]10^{7}[/tex]
ABCD is a regular tetrahedron. MandN are the mid points of the edges AB and CD. It the length of AB is a, then |MN|^2 = ...?
4/3 is the valve of |MN| ^2 of a given tetrahedron in which M AND N are the mid points of the edges AB and CD . is explained below:
on observing the diagram we can estimate that image of point D in the plane is given by ABC is [tex](2\sqrt{2} , 0 , -2 )[/tex] and volume of tetrahedron ACBM is 4/3
AB=BC=CD=AD =a
hence a =[tex]2\sqrt{2}[/tex] then MA =2 ; 2b^2 =4 ; therefore , b=[tex]\sqrt{2}[/tex]
then value of B ([tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] then according to the theorem we get as
[tex]MA^{2} + MB^{2} = AB^{2}[/tex] we have condition by diagram as MA ⊥ MB similarly
MA ⊥ MC , MB ⊥ MC hence , MA.MC =-2z =0
hence MB.MC= [tex]\sqrt{2x} +\sqrt{2y} =0[/tex] therefore we get y=-x and z=0 hence the coordinates for C(x ,-x ,0)
and also MC^2 =2x^2=MA^2 =4 ; x=[tex]\sqrt{2}\\[/tex] (x>0)
hence C[tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] hence
|MN|^2 = [tex]\frac{1}{6} |MA| . |MB| . |MC| = \frac{4}{3}[/tex]
hence the value of |MN|^2 = 4/3
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a standard interior staircase has steps each with a rise (height) of 22 cm and a run (horizontal depth) of 23 cm. research suggests that the stairs would be safer for descent if the run were, instead, 28 cm. for a particular staircase of total height 4.57 m, how much farther into the room would the staircase extend if this change in run were made?
The staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
To find out how much farther into the room the staircase would extend if the run were 28 cm instead of 23 cm, we need to calculate the difference in the run and then multiply it by the number of steps.
The difference in the run is 28cm - 23cm = 5cm
To find the number of steps, we need to divide the total height of the staircase by the height of each step:
4.57m / 0.22m = 20.86 steps.
So the difference in the run multiplied by the number of steps is:
5cm * 20.86 steps = 104.3cm.
Therefore, the staircase would extend 104.3cm farther into the room if the run were made 28cm instead of 23cm.
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Draw the image of A ABC under a dilation whose center is A and scale factor is 1/4
Check the picture below.
A grocer bought 4 crates of lettuce and 3 crates of cabbage. later he bought 2 crates of lettuce and 5 crates of cabbage. his first bill was $34.20 and his second bill was $31.80. find the cost for each crate of lettuce and each crate of cabbage.
Answer:
cost of 1 crate of lettuce = x
cost of 1 crate of cabbage = y
[tex]4x + 3y = 34.2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(1)[/tex]
[tex]2x + 5y = 31.8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(2)[/tex]
Multiplying eq. (2) by 2
[tex]4x + 10y = 63.6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ...(3)[/tex]
(3)-(1)
[tex]7y = 29.4 \\ y = \frac{29.4}{7} \\ y = 4.2 \\ [/tex]
Putting this in (2)
[tex]2x + 5(4.2) = 31.8 \\ 2x = 10.8 \\ x = 5.4[/tex]
.'. Cost of 1 crate of lettuce= $5.40
Cost of 1 crate of cabbage= $4.20
Answer:
Let 1 crate of lettuce be X and 1 crate of cabbage be y.
Now from question,
4 crates of lettuce and 3 crates of cabbage costs 34.20$
i.e.4x+3y=34.20----(1)
Also,
2 crates of lettuce and 5 crates of cabbage costs 31.80$
i.e. 2x+5y=31.80----(2)
Multiplying eqn (2) by 2 then subtracting from (1), we get,
4x+3y - {2(2x+5y)}=34.20-(2×31.80)
or,4x-4x+3y-10y=34.20-63.60
or,-7y= -29.40
:.y=4.20
Putting value of y in eqn 1 we get,
4x=34.20-12.60
or,4x=21.60
or,X=21.60/4
:.X=5.40
Hence,Cost of each crate lettuce i.e.X=5.40$
and,each crate cabbage i.e y=4.20$
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The length of a rectangle is 3 cm greater than its width. The perimeter is 24 cm. What are the dimensions
of the rectangle?
O width is 3.5; length is 6.5
O width is 4; length is 7
O width is 4.5; length is 7.5
O width is 5; length is 8
We can use algebra to set up and solve a system of equations to determine the size of a rectangle given the given information.
Step 1: Assign the rectangle's width and length the letters "w" and "l," respectively. We can determine the rectangle's 24 cm perimeter from the problem. The formula P = 2l + 2w = 24 cm can be used to draw up an equation since the perimeter of a rectangle is equal to the total of its four sides.
Step 2: Using the additional knowledge that the length is 3 cm longer than the width, we can construct a second equation as follows: l = w + 3 cm.
Step 3: We can change the variable "l" in the first equation to read "w + 3," making P = 2(w + 3) + 2w = 24 cm. As a result, we can calculate 2w + 2(w + 3) = 24 cm.
Step 4: Finding the value of w: 24 cm = 2w + 2w + 6.
Step 5: Condensing the formula: 4w = 18 cm.
Sixth step: multiply both sides by 4 to get w = 4.5 cm.
Step 7: Using the second equation, we can get the length now that we know the width: l = w + 3 cm = 4.5 + 3 = 7.5 cm.
Therefore the answer is option c , width is 4.5 and length is 7.5 .
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