The slopes and the y-intercepts of two equations are different.
How to calculate the slope-intercept form of the equation?Mathematically, the slope-intercept form of a line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the y-intercept.How to determine the slopes and y–intercepts of the two equations?From the information provided, we have the following equations:
2x + y = 3 ....equation 1.
−2y = 14 − 6x ....equation 2.
In slope-intercept form, the first equation can be written by subtracting 2x from both sides as follows:
2x + y - 2x = 3 - 2x
y = 3 - 2x
y = -2x + 3
Therefore, m = -2 and c = 3.
For the second equation, we would divide both sides by -2 as follows:
−2y/-2 = 14/-2 − 6x/-2
y = -7 + 3x
y = 3x - 7
Therefore, m = 3 and c = -7.
In this context, we can reasonably and logically deduce that the slopes and the y-intercepts are quite different.
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Answer:
y = -2x + 3
y = 3x + -7
The slopes and the y-intercepts are different.
The system represents lines that Intersect at one point
Exactly one solution
Step-by-step explanation:
Edge2022
get me brainliest
Deondra read 18 pages in 2/5
of an hour. At what rate, in pages per hour, did she read?
First, reason down from 2/5
to 1/5 . Enter all values as fractions (proper or improper) or whole numbers. You will need to convert mixed numbers to improper fractions.
Deondra read at rate 40 pages per hour.
What is the meaning of the rate?
The rate at which something occurs or changes, as well as the quantity or frequency with which it does so over a period of time.
What is the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given that, Deondra read 18 pages in 2/5 of an hour.
Use unitary method to calculate the required value:
In 2/5 hour, she read 18 pages.
In 1 hour, she read 18/(2/5) pages.
In 1 hour, she read 18 × (5/2) pages = 40 pages.
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If you are dealt 3 cards from a shuffled deck of 52 cards, find the probability of getting one queen and two kings.
The probability is
(Round to six decimal places as needed.)
Answer:
0.000348 (rounded)
Step-by-step explanation:
Please tell me if this is wrong.
A standard deck of cards has 52 cards of four different suits (diamonds, spades, hearts, clubs). Each suit
consists of numbered cards 1 (Ace) to 10, followed by Jack, Queen and King (face cards). Express all your
answers as a percent rounded to the nearest tenth of a percent, if necessary. If one card is drawn randomly from a deck, what is the probability that it is not a face card?
If one card is drawn randomly from a deck, then the probability that it is not a face card is 76.9%
Probability
Probability refers the possible way of getting the required event.
Given,
A standard deck of cards has 52 cards of four different suits (diamonds, spades, hearts, clubs). Each suit consists of numbered cards 1 (Ace) to 10, followed by Jack, Queen and King (face cards).
Here we need to find the probability of getting not a face card and we have to round off the resulting value to the tenth percent.
We know that,
Total number of cards = 52
Number of suits = 4
Number of cards in each suit = 13
Number of face cards in each suit = 3
Therefore, the total number of face cards in the deck is calculated s,
=> 3 x 4
=> 12
Therefore, the probability of getting not a face card is
=> (52 - 12)/52
=> 40/52
When we simplify this one then we get,
=> 0.7692
When we convert this into percent and round of to the nearest tenth then we get the probability of getting not a face card is
=> 76.9%.
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what does (cot0)(sin0)(sec0) simplify to
Answer: c. 1
Step-by-step explanation:
[tex]\displaystyle\\(cot\theta)(sin\theta)(sec\theta)=\\\\\frac{cos\theta}{sin\theta}(sin\theta)\frac{1}{cos\theta} =\\\\\frac{cos\theta (sin\theta)(1)}{sin\theta(cos\theta)}=\\\\1[/tex]
Part A
A model car is for sale online. Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells.
If the original price of the model car was $40, how much did the car sell for to the nearest cent?
Part B
What percent discount does this represent from the original price? Round to the nearest whole percent.
The car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
According to the question,
We have the following information:
Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells. And the original price of the model car was $40.
The first day:
40*5/100
200/100
2
The price on the first day = $38
The second day:
38*5/100
190/100
1.9
The price on the second day = 38-1.9
The price on second day = 36.1
The third day:
36.1*5/100
180.5/100
1.805
The price on third day = $34.295 (36.1-1.805)
1 dollar = 100 cents
Price of car in cents = 3429.5 cents
B) Percent discount from the original price:
Let's take it to be x.
40 - (40x/100) = 34.295
-40x/100 = 34.295-40
-40x/100 = -5.705
40x = 570.5
x = 570.5/40
x = 14.265%
Hence, the car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
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Suppose $18,000 is deposited into an account paying 8.5% interest, compounded continuously. How much money is in the account after 10 years if no withdrawals or additional deposits are made?
This question requires you to find simple interest. Total money in the account after 10 years is $189,000
The total money can be calculated as follows:
First, multiply all the things known from the question, deposit, interest, and years of saving.Given,
=Deposit×Interest×Year
=18,000×8.5%×10
=18,000×[tex]85/100[/tex]×10
=$171,000
Next, we need to add up the deposit above with the initial deposit=$171.000+$18.000
=$189,000
Hence, the simple interest or total money in the account after 10 years without any withdrawals of additional deposits is $189,000.
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The amount of money in the account after 10 years will be $42113.64.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $18000
Rate of interest r = 8.5% = 0.085
Time t = 10
By continuous compounding interest formula,
P = (18000)[tex]e^{0.085\times10}[/tex]
P = $42113.64
Hence "The amount of money in the account after 10 years will be $42113.64".
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A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $81,000.00 for 27 years at 6.8% compounded monthly, and will make monthly payments of $546.61. (Round all answers to 2 decimal places) What is the unpaid balance after 12 months? During this period, how much interest did she pay?
1. The unpaid balance after 12 months of paying $546.61 for borrowing $81,000 for 27 years at 6.8% is $79,915.29.
2. During this period, the interest she paid was $5,474.61.
How is the unpaid balance determined?The total payment made, including interest and principal, for 12 months is the product of the monthly payments and 12 months.
From the amortization schedule from an online finance calculator at month 12, we can deduce that the loan balance is $79,915.29.
When this balance is subtracted from the loan, the difference is the principal repayment so far.
N (# of periods) = 324 months (27 years x 12)
I/Y (Interest per year) = 6.8%
PV (Present Value) = $81,000
PMT (Periodic Payment) = $-546.61
Results:
Sum of all periodic payments = $-6,559.32 ($546.61 x 12)
Total Interest for six months = $5,474.61
Amortization Schedule:1 $81,000.00 $-546.61 $459.00 $-80,912.39
2 $80,912.39 $-546.61 $458.50 $-80,824.28
3 $80,824.28 $-546.61 $458.00 $-80,735.68
4 $80,735.68 $-546.61 $457.50 $-80,646.57
5 $80,646.57 $-546.61 $457.00 $-80,556.96
6 $80,556.96 $-546.61 $456.49 $-80,466.84
7 $80,466.84 $-546.61 $455.98 $-80,376.21
8 $80,376.21 $-546.61 $455.47 $-80,285.06
9 $80,285.06 $-546.61 $454.95 $-80,193.40
10 $80,193.40 $-546.61 $454.43 $-80,101.22
11 $80,101.22 $-546.61 $453.91 $-80,008.52
12 $80,008.52 $-546.61 $453.38 $-79,915.29
Total payment at $546.61 x 12 months = $6,559.32
Principal repayment for 12 months = $1,084.71 ($81,000 - $79,915.29)
Interest paid for 12 months = $5,474.61 ($6,559.32 - $1,084.71)
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Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
(−2,3) , (−3,2)
The equation (in slope-intercept form) of the line passing through the points with the given coordinates (−2,3) , (−3,2) is y = x + 5
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slope of the lineb = y-interceptHence, let's find the slope of the line using the coordinates (-2, 3) and (-3, 2).
Therefore,
m = 2 - 3 / -3 + 2
m = - 1 / -1
m = 1
Therefore, lets find the y-intercept using (-2, 3)
y = x + b
3 = -2 + b
b = 3 + 2
b = 5
Hence, the equation of the line in slope intercept form is y = x + 5
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NO LINKS!! Please help me with the Segment Proofs Part 2
Answer:
1. Given.
2. Definition of congruent segments.
3. Segment Addition Postulate.
4. Substitution Property of Equality.
5. Transitive Property of Equality.
6. Subtraction Property of Equality.
7. Definition of congruent segments.
Step-by-step explanation:
Statement 1
[tex]\overline{AB} \cong \overline{CD}; \; \overline{CE} \cong \overline{AE}[/tex]
Reason: Given.
Statement 2
[tex]AB=CD; \;CE=AE[/tex]
Reason: Definition of congruent segments.
Congruent segments are segments that have the same length.
Statement 3
[tex]AE+EB=AB; \; CE+ED=CD[/tex]
Reason: Segment Addition Postulate.
A line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.
Statement 4
[tex]CE+EB=CD[/tex]
Reason: Substitution Property of Equality.
For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.
Statement 5
[tex]CE+ED=CE+EB[/tex]
Reason: Transitive Property of Equality.
For all numbers a, b and c, if a=b and b=c, then a=c.
Statement 6
[tex]ED=EB[/tex]
Reason: Subtraction Property of Equality.
For all numbers a, b and c, if a=b, then a-c=b-c.
Statement 7
[tex]\overline{ED} \cong \overline{EB}[/tex]
Reason: Definition of congruent segments.
Congruent segments are segments that have the same length.
Toni runs a restaurant that receives a shipment of 200200200 oranges every day. According to the supplier, approximately 11\%11%11, percent of the population of these oranges is overripe. Suppose that Toni calculates the daily proportion of overripe oranges in her sample of 200200200. We can assume the supplier's claim is true, and that the oranges each day represent a random sample.
What will be the shape of the sampling distribution of the daily proportions of overripe oranges?
The shape of the sampling distribution of the daily proportions of overripe oranges is approximately normal.
The correct answer option is option C
What is sampling distribution?Sampling distribution refers to a probability distribution in which samples are drawn from a population which is taken from a larger population.
Types of sampling
Simple random sampling, Systematic sampling, Stratified sampling, and Cluster sampling.Shapes of sampling distribution:
SymmetricSkewed leftSkewed right Uniform distributionNormal distributionNumber of oranges Toni's restaurant receives everyday = 200
Population of overripe oranges = approximately 11%
Therefore, it the supplier's claim is true of overripe oranges is true, shape of the sampling distribution is approximately normal.
Complete question:
Toni runs a restaurant that receives a shipment of 200 oranges every day. According to the supplier, approximately 11% of the population of these oranges is overripe. Suppose that Toni calculates the daily proportion of overripe oranges in her sample of 200. We can assume the supplier's claim is true, and that the oranges each day represent a random sample. What will be the shape of the sampling distribution of the daily proportions of overripe oranges?
Choose 1 answer:
Skewed to the left
Skewed to the right
Approximately normal
Uniform
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Last week, a candy store sold 6 13 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate.
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
A)19
B)19 2/3
C)18
D)18 2/3
Answer: 25 1/3
Step-by-step explanation:
Smith forecasts that interest rates will rise over a 5-year period according to a force of interest function given by delta = .08 + .025t/(t+1) for 0<=t<=5.
Step-by-step explanation:
if p(A)=0.17, p(B)=0.42 and p(AorB)=0.59, are A and B mutually exclusive
A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles
from the ship located at point A. How far apart are the ships? Round your answer to the nearest tenth of a mile.
According to the given depression angle, ship is 4.4 miles apart from ship B.
Depression angle:
Depression angle refer an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given,
A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles from the ship located at point A.
Here we need to find the distance between the two ships.
Here we know the following,
Distance between plane and Ship A = 5 miles.
And the depression angle = 74°, 48°
Let us consider the following, that they sit on a line,
So under this situations,
=> 80 - 48 - 74 = 58 degrees.
The next thing we have to do is bring this 74 degree angle inside the diagram. Because it is congruent to this interior angle because they are alternate.
Then it can be written as,
=> x = sin 74°/5
=> x = 4.4
Therefore, the two ships are 4.4 miles apart from each other.
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A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set 327$. Find the original selling price of the ski set.
Answer:$583.93 is the original price
Suppose you invest $2000 in equipment to put pictures on T-shirts. You buy each T-shirt for $4. After you have placed a picture on a shirt, you sell it for $20. How many T-shirts must you sell to break even?
Answer:
25
Step-by-step explanation:
2000/4=500
500/20=25
Answer: 125
Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.
Solve by multiplying digits of value and filling in zeros: 25 x 10⁴
Answer: 250000
Step-by-step explanation:
multiple 10 4 times then multiply 25 at the end
For the piecewise function, find the values h(-5), h(0), h(5), and h(9).
- 3x-13, for x < -5
h(x) = 5,
h(0) =
h(-5) = (Simplify your answer.)
=(Simplify your answer.)
(Simplify your answer.)
(Simplify your answer.)
=
h(5)=
X+ 7,
h(9) =
for 5≤x<5
for x ≥ 5
2
Answer:
h(-5) = 5, h(0) = 5, h(5) = 12, h(9) = 16==========================
The given function is the combination of three lines:
h(x) = - 3x - 13, for x < - 5,h(x) = 5, for - 5 ≤ x < 5,h(x) = x + 7, for x ≥ 5.The values of the function at the given points are:
h(-5) = 5, corresponds to second equation,h(0) = 5, same as above,h(5) = 5 + 7 = 12, corresponds to third equation,h(9) = 9 + 7 = 16, same as above.Jose flies a kite 17 1/2 ft above the ground. He increases its elevation by 4 3/4 ft by letting out some strung. Then he reels in the string and changes its elevation by - 15.8 ft. After jose reels in the string, what is the kite's elevation relative to the ground?
The kite's elevation relative to the ground is 6.45 feet.
What is elevation?Elevation simply means the height above sea level.
In this case, Jose flies a kite 17 1/2 ft above the ground and he increases its elevation by 4 3/4 ft by letting out some strung. and then changes its elevation by - 15.8 ft.
This will be illustrated as:
= 17.5 + 4.75 - 15.8
= 6.45 ft
The elevation is 6.45 feet.
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find using substitution method
Answer:
x = 4 ; y = -1
Step-by-step explanation:
y = -2x + 7
x + 2(-2x+7) = 2
x -4x + 14 = 2
-3x = 2 -14
-3x = -12
-3/-3 x = -12/-3
x = 4
y = -2* 4 + 7
y = -8 + 7
y = -1
y + 2x2 + 14x = 36
help meee I need help
Answer:
ubtract
36
from both sides of the equation.
x
2
+
14
x
=
−
36
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
7
)
2
Add the term to each side of the equation.
x
2
+
14
x
+
(
7
)
2
=
−
36
+
(
7
)
2
Simplify the equation.
Tap for more steps...
x
2
+
14
x
+
49
=
13
Factor the perfect trinomial square into
(
x
+
7
)
2
.
(
x
+
7
)
2
=
13
Solve the equation for
x
.
Tap for more steps...
x
=
±
√
13
−
7
The result can be shown in multiple forms.
Exact Form:
x
=
±
√
13
−
7
Decimal Form:
x
=
−
3.39444872
…
,
−
10.60555127
…
Step-by-step explanation:
A water tank holds a total of 5,600 gallons in the tank has three pipe through which water drains what water is drained from the tank pipe B drains twice as much as pipe a pipe C drain 65 gallons more than pipe B how many gallons of water does each pipe
The amounts drained by each pipe, considering a system of equations, are given as follows:
Pipe A: 1107 gallons.Pipe B: 2214 gallons.Pipe C: 2279 gallons.What is the system of equations?The variables to the system of equations are presented as follows:
Variable x: amount of water drained by Pipe A.Variable y: amount of water drained by Pipe B.Variable z: amount of water drained by Pipe C.A water tank holds a total of 5,600 gallons, hence:
x + y + z = 5600.
Pipe B drains twice as much as pipe A, hence:
y = 2x.
Pipe C drains 65 gallons more than pipe B, hence:
z = 65 + y = 65 + 2x.
Replacing the last two equations into the first, the amount drained by Pipe A is obtained as follows:
x + y + z = 5600.
x + 2x + 65 + 2x = 5600
5x = 5535
x = 5535/5
x = 1107 gallons.
Hence the remaining amounts are given as follows:
Pipe B: y = 2x = 2 x 1107 = 2214 gallons.Pipe C: z = y + 65 = 2214 + 65 = 2279 gallons.More can be learned about a system of equations at https://brainly.com/question/24342899
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please help
Our class is studying the effects of mindfulness on mental health. To help with data collection, we will have the support of ten grade 9, eleven grade 10, twelve grade 11 and thirteen grade 12 students. Showing your calculations,how many different groups of 12 volunteers can we make if:
a) the group must have the same number of students from each grade?
b) the group must have at least two grade 9 students? [2A]
c) the group must have James and Lucy (both grade 11 students) in it? [2A]
The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the groups are taken as follows:
3 students from grade 9, from a set of 10.3 students from grade 10, from a set of 11.3 students from grade 11, from a set of 12.3 students from grade 12, from a set of 13.Hence the number of groups is:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, the total number of groups, without considering the restriction, is:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
Using complementary events, the number of groups with at least two grade 9 students is:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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PLEASE HELPP!!! QUICK!!!!!!!
To find the distance between the points shown we subtract each point and the x-axis
What is the distance between two points?Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2– x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
Since the two points are on the same coordinate on the x -axis
To find the distance between the two points we subtract the y coordinates of the two points and the x axis.
In conclusion the distance between the two points is found by subtracting the two points and the x -axis
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Ken, Mike, and Ariel are eating out at their favorite restaurant. They each order a sandwich combo and plan to split the bill evenly. The service they receive at the restaurant is amazing, so they decide to leave a 30% tip. Their bill total is $50.88 before tax. If Florida’s sales tax is 6%, how much will each person pay? Round your answer to the nearest hundredth.
Each individual paid the sum of $23.4 including state tax at the restaurant
PercentageIn mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".
In the problem, their total bill is $50.88 and they gave a 30% tip
We should fid 30% of 50.88
0.3 * 50.88 = $15.264
30% of $50.88 is $15.264
If we add this up and then find the state tax to it.
15.264 + 50.88 = 66.144.
Find 6% of 66.144 to determine the state tax.
0.06 * 66.144 = 3.96864
The total amount spent is 66.144 + 3.96864 = 70.11264
We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088
Rounding this to the nearest cent, we have 23.4.
We can say each person paid $23.4 at the end of the day
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jessie needs to borroe 12,000 from northwestern bank. they offeted her a 5 year loan with an apr of 4.98%. how much will she pay interest over the life of the loan?
Answer:
1580.40----------------------------------
GivenLoan amount P = 12000,Rate r = 4.98% = 0.0498,Time t = 5 years,Number of compounds n = 12.Find the monthly payment[tex]M=\dfrac{P(r/n)(1+r/n)^{nt}}{(1+r/n)^{nt}-1}[/tex][tex]M=\dfrac{12000(0.0498/12)(1+0.0498/12)^{12*5}}{(1+0.0498/12)^{12*5}-1} =226.34[/tex]Find the total amount paid226.34*60 = 13580.40Find the amount of interest13580.40 - 12000 = 1580.40Answer:
$1580.69
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]
where:
PMT = Monthly payment.P = Loan amount.i = Interest rate per month (in decimal form).n = Term of the loan (in months).Given:
P = $12,000i = 0.0498/12 = 0.00415n = 5 years = 60 monthsSubstitute the values into the formula to calculate the monthly payment:
[tex]\implies \sf PMT=\dfrac{12000(0.00415)\left(1+0.00415\right)^{60}}{\left(1+0.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{49.8\left(1.00415\right)^{60}}{\left(1.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{63.84764727}{0.2820812705}[/tex]
[tex]\implies \sf PMT=226.3448656[/tex]
Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:
[tex]\implies \sf 226.3448656 \times 60=\$13580.69[/tex]
To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:
[tex]\implies 13580.69-12000=\$1580.69[/tex]
Therefore, the interest Jessie will pay over the life of the loan is $1580.69.
How does knowing how ACT essays are scored help
you with writing your own?
Answer:
Generally, more selective schools may require or recommend a writing score, while less selective ones may not (though there certainly are exceptions). It's worth noting that most schools no longer require the ACT with Writing, though many schools recommend it.
Step-by-step explanation:
find the slope of the line passing through the points (-2,2) and (-5,5)
Answer:
The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]
Step-by-step explanation:
The slope of a line can be found with the following formula
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex]x_2 > x_1[/tex]
Then substituting the values with the given ones we have
[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]
So the slope of the line passing through the given points is [tex]-1[/tex]
A is the point with coordinates(5,9)B is the point with coordinates (d,15) The gradient of the ab line is 3 Work out the value of d.
The gradient will only be equal to 3 if the value of d is 7.
How to find the value of d?
If we have two points (a, b) and (c, d), the gradient of the segment with these endpoints is:
G = (d - b)/(c - a)
Here the endpoints are (5, 9) and (d, 15), and the gradient is 3, so we can write the equation:
3 = (15 - 9)/(d - 5)
3*(d - 5) = 6
3d - 15 = 6
3d = 15 + 6 = 21
d = 21/3
d = 7
The value of d is 7.
Learn more about gradients:
https://brainly.com/question/21727173
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X:
6. A two-story building measures 21 feet from
the ground. A scale model shows the building
to be 3 inches tall. How many inches would an
84-foot building be in the model?
height:
Answer:
12 inches
Step-by-step explanation:
Let be "x" the top inches (in the model) of a eighty four foot building.
According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.
Knowing this, we can set up the following proportion: 3/21=x/84
The final step is to get to the bottom of for "x" in order to calculate its value.
Resolve:
1:3a + 2a
2:-5b -7b
3:-a² -9a²
4:3a^x-²^+5a^x-²
5:18x - 11x
6:5a - 8a + a -6a + 21a
[tex] \bold{1: 3a + 2a \: = 5a}[/tex]
[tex]\bold{2: - 5b - 7b = - 12b}[/tex]
[tex]\bold{3: - a {}^{2} - 9 a{}^{2} = - 10a {}^{2}}[/tex]
[tex]\bold{4: 3a {}^{x - 2} + 5a {}^{x - 2} = 8a {}^{x - 2}}[/tex]
[tex] \bold{5: 18x - 11x = 7x}[/tex]
[tex]\bold{6: 5a - 8a + a - 6a + 21a = 13}[/tex]
The reduction of similar terms is an operation that aims to convert two or more similar terms into a single term.
In these cases you must add or subtract either addition, subtraction or subtraction and addition, using the law of signs.
[tex]\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\bold{Law \: of \: signs: }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \end{gathered} [/tex]