Answer:
The number is 2
Step-by-step explanation:
product of two numbers is -28 one of the numbers is -7 and should be sq of some number. Hence number is 2
sq of 2 is 4
multiplying 4 and -7 we will get -28
7-×^(2)sq=-28
A circle’s circumference is 600 m.
What is a good approximation of the circle’s area? 1. 300\ m^{2} 2. 3,000\ m^{2} 3. 30,000\ m^{2} 4. 300,000\ m^{2}
The area of the circle is approximately 30,000 [tex]m^{2}[/tex]
The circumference of the circle is given as 600m.
And we know that circumference = [tex]2\pi r[/tex] where r is the radius of the circle.
Therefore,
[tex]2\pi r = 600[/tex]
[tex]r = \frac{600}{2\pi }[/tex]
[tex]r = \frac{300}{\pi }[/tex]
Now, we know that area of the circle = [tex]\pi r^{2}[/tex]
Putting the value of r in this, we get
area = [tex]\pi (\frac{300}{\pi } )^{2}[/tex]
area = [tex]\pi.\frac{300}{\pi } .\frac{300}{\pi }[/tex]
Therefore, area of the circle = 28,647.889 [tex]m^{2}[/tex]
Therefore, the correct answer is 30,000 [tex]m^{2}[/tex]
To learn more about circle and it's area, refer to:
https://brainly.com/question/16125353
This Is a Math Test. Help please ASAP! 30 POINTS!
Use the following model to answer the question.
3 groups are shown. Each group shows 2 tens rods and 6 ones cubes.
Which division problem is shown by the model?
A. 0.66÷3=0.22
B. 0.66÷3=0.26
C. 0.78÷3=0.62
D. 0.78÷3=0.26
Answer:
D
Step-by-step explanation:
well, it all starts with a check, what calculations in the answer options are even correct.
A. is correct. 0.66/3 = 0.22
B. is incorrect
C. is incorrect
D. is correct. 0.78/3 = 0.26
so is it A or B ?
one group of 2 tens and 6 ones : how much is that ?
2×10 + 6×1 = 20 + 6 = 26
3 groups of 26 means
3×26 = 78
so, the combination of the 3 groups would either show that
3×26 = 78
or
78/3 = 26
and that is the same as showing
0.78/3 = 0.26
because
0.78 = 78/100
0.26 = 26/100
therefore
78/100 / 3 = 26/100
78/100 = 3×26/100 = 78/100
correct.
z/2>2
hey help me please
Answer:
Z > 4
Step-by-step explanation:
When do you use the RECIPROCAL of a fraction?
Group of answer choices
-When dividing fractions.
-When adding fractions.
-When multiplying and dividing fractions.
-When multiplying fractions.
Thank u!
The reciprocal of a fraction is used when:
Dividing fractions
Which expression has like terms?
Group of answer choices
8x - 4y
8x - 4x
13c + 13d
4 + 4y
thx!
HELP I NEED AWNCERS ASAPPPP!!!!!!!!!!!! I GIVE BRAINLIST
Question 1 (1 point)
Why does an eclipse happen?
a
A celestial object moves into the shadow made by another celestial object.
b
The Sun burns out quickly and reignites due to changes in magnetic energy.
c
Stars twinkle which creates a delay in light transfer.
d
The planets Mars and Venus interfere with Earth's orbit.
Question 2 (1 point)
The picture below shows a globe with the location of Barrow, Alaska circled. For almost three months, mid-May to mid-August, the Sun never sets in Barrow, Alaska.
Which is themost likelyreason for the Sun always shining in the summer in Barrow?
a
Earth only rotates on its axis during the winter, so the same part of Earth faces the Sun all summer.
b
Only the middle of Earth rotates around its axis, so the top of Earth always faces the Sun.
c
Earth's axis is tilted, so sometimes parts of Earth face the Sun for the entire daily rotation.
d
The Sun's axis is tilted, so sometimes parts of Earth face the Sun for the entire daily rotation.
Question 3 (0 points)
The diagram shows Earth in its yearly orbit around the Sun.
Earth is moving from Position B to Position C. Which statement correctly identifies the season in the Northern Hemisphere when Earth is in Position C?
a
It is fall because the Northern Hemisphere is tilting away from the Sun and receiving less direct sunlight than Position B.
b
It is fall because the Northern Hemisphere is tilting toward the Sun and receiving more direct sunlight than Position B.
c
It is spring because the Northern Hemisphere is tilting toward the Sun and receiving more direct sunlight than Position B.
d
It is spring because the Northern Hemisphere is tilting away from the Sun and receiving less direct sunlight than Position B.
Question 4 (1 point)
The map shows the United States.
Which city will most likely experience the mildest winters?
a
Tallahassee, FL, because it is closest to the equator and receives the most direct sunlight.
b
Harrisburg, PA, because it is located in the southern hemisphere.
c
Helena, MT, because it is closest to the equator and receives the most direct sunlight.
d
Des Moines, IA, because it is closest to the poles and receives the least direct sunlight.
Question 5 (1 point)
What can happen when Earth, the Sun, and the Moon line up in a straight line?
a
a lunar or solar eclipse
b
decreased planetary rotation
c
a change in the order of Moon phases
d
a reversal in the orbital direction
Question 6 (1 point)
Use the diagram below to answer the question.
Which point indicates the location of the Moon that is the best for viewing a lunar eclipse from Earth?
a
N
b
P
c
O
d
M
Question 7 (1 point)
Why can a solar eclipse only happen during a new moon?
a
During a new moon, Earth does not receive the light created by the Moon.
b
During a new moon, Earth is between the Moon and the Sun.
c
During a new moon, the Moon is fullest and blocks the sunlight best.
d
During a new moon, the Moon is between the Sun and Earth.
Answer:
An eclipse happens when a celestial object moves into the shadow made by another celestial object. In the case of a solar eclipse, the Moon moves into the shadow of the Earth, and in the case of a lunar eclipse, Earth moves into the shadow of the Moon.
The most likely reason for the Sun always shining in the summer in Barrow, Alaska is that Earth's axis is tilted, so sometimes parts of Earth face the Sun for the entire daily rotation.
When Earth is in Position C in the diagram, it is spring in the Northern Hemisphere because the Northern Hemisphere is tilting toward the Sun and receiving more direct sunlight than Position B.
The city that will most likely experience the mildest winters is Tallahassee, Florida because it is closest to the equator and receives the most direct sunlight.
When Earth, the Sun, and the Moon line up in a straight line, a lunar or solar eclipse can happen.
The point that indicates the location of the Moon that is the best for viewing a lunar eclipse from Earth is P.
A solar eclipse can only happen during a new moon because, during a new moon, the Moon is between the Sun and Earth. This allows the Moon to block the sunlight and create an eclipse.
Answer:
During a total lunar eclipse, Earth blocks sunlight from reaching the Moon. Earth casts a shadow onto the Moon. The Moon can look reddish orange.An eclipse occurs when one heavenly body such as a moon or planet moves into the shadow of another heavenly body. Let’s learn about the two types of eclipses on Earth.What Is a Lunar Eclipse?The Moon moves in an orbit around Earth. At the same time, Earth orbits the Sun. Sometimes Earth moves between the Sun and the Moon. When this happens, Earth blocks the sunlight that normally is reflected by the Moon. (This sunlight is what causes the Moon to shine.) Instead of light hitting the Moon's surface, Earth's shadow falls on the Moon. This is an eclipse of the Moon, or a lunar eclipse. A lunar eclipse can occur only when the Moon is full.A lunar eclipse can be seen from Earth at night. There are two types of lunar eclipses: Although the Moon is in Earth's shadow, some sunlight reaches the Moon. The sunlight passes through Earth's atmosphere, which filters out most of the blue light. This makes the Moon appear red to people on Earth.Earth's shadow passes in front of the Moon until it turns red or orange.A partial lunar eclipse happens when part of the Moon enters Earth's shadow. In a partial eclipse, Earth's shadow appears very dark on the side of the Moon facing Earth. What people see from Earth during a partial lunar eclipse depends on how the Sun, Earth and Moon align.A lunar eclipse usually lasts for a few hours. At least two partial lunar eclipses happen every year, but total lunar eclipses are rare. It is safe to look at a lunar eclipse.
help me, please!!!!!!!!
Answer:
$160
Step-by-step explanation:
C = 40 · 4
C = $160
"Based on the table, which best predicts the end behavior of the graph of f(x)?"
How do I figure out the answer to this question? I need a step-by-step explanation to the answer of the question.
Answer: How you figure out the answer to this question is figure out if it's a line by a constant rate of change
Step-by-step explanation: Because you gotta make sure before you plug in an answer you need to make sure it's a line
SOMEONE HELP ME PLEASE I DONT KNOW HOW TO DO THIS!!!
if you're a tad confused, o represents one of the options and you're supposed to fill it in. x represents number for bags
A coffee shop sells bags of coffee for a regular price of $8 per bag. Chang bought some bags and used a coupon for $10 off his entire purchase. After applying the coupon, he paid $30.
How many bags of coffee did he buy?
(a) Write an equation to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
(The variable x is used to represent the number of bags.)
ox+o=o OR o×-o=o
(b) Write an expression to help answer the question above.
Choose the correct form below and fill in the blanks using only 8, 10, and 30.
o+o/o OR o-o/o
(c) How many bags of coffee did Chang buy? answer: _x_ bags
If the number of bags is x, the cost of them is 8x.
After applying a $10 coupon the total was $30.
Part (a)Set equation:
8x - 10 = 30Part (b)Solve it for x:
8x = 30 + 108x = 40x = 40/8x = 5Part (c) Answer: 5 bagsWhich expression is equivalent to 2E-3/2E-5
a. 2E2
b. 1/2E2
c. 2E8
d. 1/2E8
E=exponent
Answer:
a 2E2
Step-by-step explanation:
[tex]\frac{2^{-3} }{2^{-5} }[/tex] When powers have the same bases and you are dividing, you subtract the exponents.
[tex]2^{-3 - -5}[/tex] = [tex]2^{-3+5}[/tex] = [tex]2^{2}[/tex]
The zoom feature on a copier sets the percent size of a copy. Lebron wants to make a 200% copy of a photograph. The original photo has a width of 5 in. What width will the copy be?
a) 2.5in
b) 10in
c) 25in
d) 100in
HELP I NEED THESE AWNSERD ASAP !! I GIVE BRAINLYIST PT 2
Question 8 (1 point)
Which of the following statements is correct?
a
Lunar eclipses can be viewed from more places on Earth than solar eclipses.
b
Lunar eclipses are easier to see during the day than at night.
c
Solar eclipses last longer when they happen during a full moon.
d
Solar eclipses produce a larger shadow than lunar eclipses.
Question 9 (1 point)
Which of the following is affected by the amount of sunlight that strikes different parts of Earth due to Earth's tilt on its axis?
a
the types of landforms on Earth
b
the locations of the poles on Earth
c
the changes of the seasons on Earth
d
the lengths of the months on Earth
Question 10 (1 point)
This diagram shows Earth, the Moon, and the Sun.
Kinesha and her friend were watching a solar eclipse. Kinesha explains to her friend that a solar eclipse means that Earth is located between the Sun and the Moon. Her friend tells Kinesha that her explanation is incorrect. Why?
a
Kinesha is incorrect because a solar eclipse occurs when the Moon is directly below Earth and the Sun.
b
Kinesha is incorrect because a solar eclipse occurs when the Moon is directly between the Sun and Earth.
c
Kinesha is incorrect because a solar eclipse occurs when the Moon is directly above Earth and the Sun.
d
Kinesha is incorrect because a solar eclipse occurs when the Sun is directly between the Moon and Earth.
Question 11 (1 point)
During which phase does the Moon appear to be unlit by sunlight?
a
third quarter
b
new moon
c
first quarter
d
full moon
Question 12 (1 point)
Which of these would be best to use to model the Moon's phase changes?
a
glowing star stickers placed against a black background
b
a flashlight for the Moon and a foam ball for Earth
c
two different sized foam balls to represent Earth and the Moon and a light source to represent the Sun
d
a photograph of the Moon
Question 13 (1 point)
In what order are the Moon, Earth, and the Sun aligned during a total eclipse of the Sun?
a
in the order of Earth, the Sun, and the Moon in a straight line
b
in the order of the Sun, Earth, and the Moon in a straight line
c
in the order of the Sun, the Moon, and Earth in a straight line
d
in the order of the Moon, Earth, and the Sun in a straight line
Question 14 (1 point)
The pictures shows a diagram of the Earth on its axis.
Which position of Earth is correct if the state of Georgia is experiencing spring?
a
Z
b
Y
c
W
d
X
Question 15 (1 point)
A student creates two models to demonstrate phases of the Moon. The models are shown.
Which moon phases can the models be used to demonstrate?
a
Model 1 can be used to demonstrate a full moon, and Model 2 can be used to demonstrate a new moon.
b
Model 1 can be used to demonstrate a new moon, and Model 2 can be used to demonstrate a third quarter moon.
c
Model 1 can be used to demonstrate a full moon, and Model 2 can be used to demonstrate a waning crescent moon.
d
Model 1 can be used to demonstrate a first quarter moon, and Model 2 can be used to demonstrate a waxing gibbous moon.
Question 16 (1 point)
The picture shows the equator of Earth and the location of South Africa.
Which statement best compares the climate near the equator to the climate in South Africa?
a
The equator receives more direct sunlight through all the seasons of the year and this produces a warmer climate than South Africa.
b
The equator receives more direct sunlight in spring and summer so it is hotter than South Africa.
c
The equator receives less direct sunlight in spring and summer so it is colder than South Africa.
d
The equator receives less direct sunlight through all the seasons of the year and this produces a colder climate than South Africa.
Question 17 (1 point)
What would an observer standing on the Moon see during a solar eclipse if she was looking back towards Earth?
a
The Earth fully covered by the Moon's shadow.
b
The Earth partially covered by the Moon's shadow.
c
The Sun fully covered by the Moon's shadow.
d
The Sun partially covered by the Moon's shadow.
AND 100 POINTS!(if you awncer all)
The correct answer is a) Lunar eclipses can be viewed from more places on Earth than solar eclipses. This is because lunar eclipses are visible from any location on the night side of Earth, whereas solar eclipses are only visible from certain locations along the Moon's shadow path.
The correct answer is c) the changes of the seasons on Earth. The amount of sunlight that strikes different parts of Earth due to Earth's tilt on its axis affects the seasons on Earth because it determines the length of the days and the angle at which sunlight hits the Earth, which in turn affect the temperature and weather patterns in different regions.
The correct answer is b) Kinesha is incorrect because a solar eclipse occurs when the Moon is directly between the Sun and Earth. A solar eclipse occurs when the Moon is directly between the Sun and Earth, and the Moon's shadow is cast on Earth. In this configuration, Earth is not located between the Sun and the Moon.
The correct answer is b) new moon. During the new moon phase, the Moon is positioned between the Earth and the Sun, and its illuminated side is facing away from Earth. As a result, the Moon appears to be unlit by sunlight from Earth's perspective.
The correct answer is c) two different sized foam balls to represent Earth and the Moon and a light source to represent the Sun. This model would allow an observer to see the relative positions of Earth, the Moon, and the Sun, and how they change as the Moon goes through its phases.
The correct answer is d) in the order of the Moon, Earth, and the Sun in a straight line. During a total eclipse of the Sun, the Moon is positioned directly between the Sun and Earth, and its shadow is cast on Earth. In this configuration, the Moon, Earth, and the Sun are aligned in a straight line, with the Moon in the middle.
The correct answer is b) Y. If the state of Georgia is experiencing spring, then Earth must be in a position where the northern hemisphere is tilted towards the Sun. In the diagram, this is represented by position Y, where the northern hemisphere is pointing towards the Sun and the southern hemisphere is pointing away from the Sun.
The correct answer is c) Model 1 can be used to demonstrate a full moon, and Model 2 can be used to demonstrate a waning crescent moon. Model 1 shows the Moon with its illuminated side facing towards the observer, which is what happens during a full moon. Model 2 shows the Moon with a small part of its illuminated side visible, which is what happens during a waning crescent moon.
The correct answer is a) The equator receives more direct sunlight through all the seasons of the year and this produces a warmer climate than South Africa. The equator is located at 0 degrees latitude, where the Sun's rays are directly overhead throughout the year. This means that the equator receives more direct sunlight than other latitudes, which produces a warmer climate. In contrast, South Africa is located at about 30 degrees latitude, where the Sun's rays are less direct, which produces a cooler climate.
An observer standing on the Moon during a solar eclipse would see the Earth fully covered by the Moon's shadow. This is because the Moon's shadow is cast on Earth during a solar eclipse, and from the Moon's perspective, the Earth would be fully within the shadow.
Need Answered ASAP. As part of the training for the cross-country team, you must run a total of 20 miles per week. You ran 6.3 miles in the first two days of the week. If you run the same amount each day for the remaining five days, how many miles must you run per day to complete the 20 miles?
Write and solve an equation to determine the number of miles, m, you must run per day.
Answer: 1.48 miles
Step-by-step explanation:
6.3 x 2 = 12.6
20 - 12.6 = 7.4
7.4/5 = 1.48
Write the mixed number 4 ⅜ as an improper fraction.
Thank u!
Answer:
[tex]\frac{35}{8}[/tex]
Step-by-step explanation:
Another name for 1 is [tex]\frac{8}{8}[/tex] so 4 can be [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] + [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{8}[/tex]. we can now add this to [tex]\frac{3}{8}[/tex]
[tex]\frac{32}{8}[/tex] + [tex]\frac{3}{8}[/tex] = [tex]\frac{35}{8}[/tex]
Simplify the expression
[tex]\frac{-4(1 - \sqrt[3]{8}*5)}{3}[/tex]
Which story problem can be solved using the expression 5 divided by ¼?
Group of answer choices
-Alex cuts ¼ of a pizza into 5 slices. What part of the pizza is one of the slices he cuts?
-Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
-Suzy needs 5 pieces of ribbon that are each ¼ yard long. What is the total length of the ribbon?
-Sammy pours ¼ cup of honey equally into 5 teacups. How much honey does he pour into each teacup?
Thank u! <3
Answer: Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
Step-by-step explanation:
Nicole cuts 5 feet of string into ¼ - foot pieces. How many pieces does she cut?
When you cut one piece of string into smaller pieces, that is the same as dividing.
5/1/4 is the same as 5*4/1
=20
4x-2=7x+8-3x-6
infinite many solutions
one solutions
no solutions
two solutions
Answer:
no solutions
Step-by-step explanation:
4x-2=7x+8-3x-6
4x-7x+3x = 8-6+2
0 = 4
Since 0 = 4 is a false statement, there is no solution.
Which table shows a function that is decreasing only over the interval (–1, ∞)?
What answer is it and why? To me it seems it can either be C or D (One all the way to the right on the top row and one all the way to the bottom right), but I'm not sure why it would be either one over the other and would need an explanation. If it is neither C nor D I need an explanation on how to solve this question correctly.
Answer: The table to the farthest right the last one.
Explanation:
The interval (-1, ∞) represents x-values anywhere from -1 and higher.
As such, you are looking for a table with y-values that decrease as the x-values increase.
Starting from -1 -
The first option: -5, -2, -1, 2. This is increasing.
The second option: -7, -6, 1, -1. This increases from -7 to -6 to 1.
The third option: -1, 2, 1, -6. This increases from -1 to 2.
The fourth option: 1, 0, -4, -8. This decreases across all coordinates in the range specified.
Answer:
The last graph (d) represents it
Need Answered ASAP. Rewrite 12x^4y^3 − 48x^3y^4 using a common factor.
Answer:
Step-by-step explanation:
12x^2y^3-36x^5y^3-48x^4y4
factor out 12
12(x^2y^3-3x^5 y^3 - 4x^4 y^4
consider X^2 y^3 - 3x^5 y^3
4x^4 y^4 Factor out x^2y^3
x^2 y^3 (1-3x^3 -4x^2 y)
Rewrite the complete factored expression
12x^2 y^3 (1-3x^3-4x^2y)
Evaluate the expression: 2 × 14 ÷ (3² − 2)
Group of answer choices
3
8
4
6
Answer: 4
Step-by-step explanation:
2 × 14 ÷ (3² − 2)
28 / (9-2)
28/7
4
[tex]2\times14\div(3^2-2)[/tex]
[tex]14\times2=28[/tex]
[tex](3^2-2)=7[/tex]
[tex]28\div7[/tex]
[tex]=\fbox{4}[/tex]
20 points to whoever answers this asap <3
Joe and Andrew shot baskets in a school fair. Joe made 9 baskets, which is 2 baskets more than Andrew. Supply the correct numbers to complete the equation that can be used to determine the number of baskets, b, that Andrew made.
Answer:
The answer to the question is 7. This is the number of baskets that Andrew made, as calculated using the equation b = 9 - 2.
Step-by-step explanation:
If x and y vary directly and y is 40 when x is 10, find y when x is 15.
Answer:
y is 60 when x is 15
Step-by-step explanation:
the ratio of x to y is 1:4
Help please help help
Answer:
Question 13
89.75
Question 14
39
Question 15
403
Answer:
13: 89.75
14: 39
15: 403
DISCLAIMER: This is all in EXACT answers
Step-by-step explanation: I hope this helps! (Not rounded; exact answers) I used long division.
TIP: Round up (or down) to find the rounded number. Remember, the number in the one's place between 0-4, you round down. You round up when the number in one place is 5-9. So,
718 rounded = 720
156 rounded = 160
3627 rounded = 3630
Now, divide the rounded answers by the number on the right, so the REAL answers are:
13: 90
14: 40
15: 403.3 (3 repeats forever)
I hope this helps ;)
An equation is written in standard form, match each word with the expression that is used to find it.
Answer:
slope : opposite of a
y-intercet:b/c
x-intercet:a/b
Step-by-step explanation:
Help, i have to do this in the next like 30 seconds -_-
I think your answer is 2/3
I am not sure
Find the next two numbers in the pattern. -800, 400, -200, 100
PLEASE EXPLAIN HOW TO DO IT!
This sequence follows a pattern of dividing by two each time. So, you would divide 100 by two, and the resulting number would be divided by two as well. The next occurring numbers would be 50 and 25. I hope this helps! :)
ok, my let’s try this again. can someone please help fill out the ? for this table.
Answer:
60 months
$9,000
4.6%
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5cm}\underline{Simple Interest Formula}\\\\$ A = P(1 + rt)$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
A = $5,000P = $4,000r = 5% = 0.05Substitute the given values into the formula and solve for t:
[tex]\implies 5000=4000(1+0.05t)[/tex]
[tex]\implies \dfrac{5000}{4000}=1+0.05t[/tex]
[tex]\implies1.25=1+0.05t[/tex]
[tex]\implies 0.05t=1.25-1[/tex]
[tex]\implies 0.05t=0.25[/tex]
[tex]\implies t=\dfrac{0.25}{0.05}[/tex]
[tex]\implies t=5\; \rm years=60\; months[/tex]
Given:
A = $11,160r = 8% = 0.08t = 36 months = 3 yearsSubstitute the given values into the formula and solve for P:
[tex]\implies 11160=P(1+0.08 \cdot 3)[/tex]
[tex]\implies 11160=P(1.24)[/tex]
[tex]\implies P=\dfrac{11160}{1.24}[/tex]
[tex]\implies P=\$9000[/tex]
Given:
A = $3,207P = $3,000t = 18 months = 1.5 yearsSubstitute the given values into the formula and solve for r:
[tex]\implies 3207=3000(1+r \cdot 1.5)[/tex]
[tex]\implies \dfrac{3207}{3000}=1+1.5r[/tex]
[tex]\implies 1.069=1+1.5r[/tex]
[tex]\implies 1.5r=1.069-1[/tex]
[tex]\implies 1.5r=0.069[/tex]
[tex]\implies r=\dfrac{0.069}{1.5}[/tex]
[tex]\implies r=0.046[/tex]
[tex]\implies r=4.6\%[/tex]
Therefore, the completed table is:
[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \vphantom{\dfrac12} \rm BALANCE & \rm PRINCIPAL & \rm INTEREST \; RATE & \rm TIME \\\cline{1-4} \vphantom{\dfrac12} \$5,000 & \$4,000 & 5\% & \rm 60 \; months\\\cline{1-4} \vphantom{\dfrac12} \$ 11,\!160 & \$9,000 & 8\% & \rm 36 \; months \\\cline{1-4} \vphantom{\dfrac12} \$3,207 & \$3,000 & 4.6\% & \rm 18 \; months\\\cline{1-4} \end{array}[/tex]
Please help me with this
Answer:
z 21
Step-by-step explanation:
Write the point-slope form of the equation of a line that passes through the point (−1, 6)and is parallel to the line that passes through the points (6, 2) and (2, 4).
In order to solve this problem, we need a few formulas to help us get to the answer:
The first formula we need is the Slope Formula:
[tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where (x₁, y₁) and (x₂, y₂) are two different points.
The second formula we need is Point-Slope Form:
[tex]\displaystyle y - y_0 = m(x - x_0)[/tex]
where (x₀, y₀) is a given point on the line and m is the slope.
DefiningNow, we can organize and define what the problem has given us:
We are first given information that a line passes through the points (6, 2) and (2, 4).
We are also given that the parallel line passes through (-1, 6).
WorkLet's first find the slope of the line that passes through two points:
[tex]\displaystyle\begin{aligned}m & = \frac{4 - 2}{2 - 6} \\& = \frac{2}{-4} \\& = \boxed{ - \frac{1}{2} } \\\end{aligned}[/tex]
∴ we know that the slope is equal to negative one-half.
Let's substitute in our slope into Point-Slope Form since parallel lines have the same slope:
[tex]\displaystyle y - y_0 = m(x - x_0) \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0)[/tex]
Recall that we were given the initial point (-1, 6). Let's also substitute this into Point-Slope Form:
[tex]\displaystyle \begin{aligned}y - y_0 = m(x - x_0) & \Rightarrow y - y_0 = - \frac{1}{2} (x - x_0) \\& \Rightarrow y - 6 = - \frac{1}{2} (x - -1) \\& \Rightarrow \boxed{ y - 6 = -\frac{1}{2}(x + 1) } \\\end{aligned}[/tex]
Answer∴ we have found that the point-slope form of the equation of a line that passes through the point (-1, 6) and is parallel to the line that passes through the points (6, 2) and (2, 4) is equal to:
[tex]\displaystyle \boxed{ y - 6 = -\frac{1}{2}(x + 1) }[/tex]
Hope this helps!
#Brainlystudentskeeponlearning
___
Learn more about writing equations: https://brainly.com/question/9972577
Learn a little more about Algebra here: https://brainly.com/question/17011730
Hey, while you're at it, why not take a sneak peak of higher-level math here?: https://brainly.com/question/28758158
If x and y vary directly and y is 6 when x is 8, find y when x is 12.
Answer:
If x and y vary directly and y is 6 when x is 8, y is 9 when x is 12.
Step-by-step explanation:
In the given problem, it is known that when x is 8, y is 6, so the constant of proportionality in this case is k = y/x = 6/8 = 3/4. This means that the relationship between x and y can be written as y = (3/4)x.
To find the value of y when x is 12, we can plug this value into the equation to get y = (3/4) * 12 = 9. Therefore, if x and y vary directly and y is 6 when x is 8, y is 9 when x is 12.
Answer:
y is 9 when x is 12
Step-by-step explanation:
the ratio of x to y is 4:3