Given:
The points are (0,3) and (1,-1).
To find:
The equation of line passes through these points.
Solution:
Standard form of a line is
[tex]Ax+By=C[/tex]
We know that, if a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through (0,3) and (1,-1), so the equation of the line is
[tex]y-3=\dfrac{-1-3}{1-0}(x-0)[/tex]
[tex]y-3=\dfrac{-4}{1}(x)[/tex]
[tex]y-3=-4x[/tex]
Adding 4x and 3 on both sides, we get
[tex]4x+y=3[/tex]
Therefore, the standard form of the line is [tex]4x+y=3[/tex].
Tickets for 2 adults and 4 children at a theme park cost £152.
An adult ticket costs twice as much as a child ticket.
Write and solve an equation to work out the price of an adult ticket
Step-by-step explanation:
Let x be the price of an adult ticket.
Then 0.5x is the price of a child ticket.
We have 2x + 4(0.5x) = £152, therefore 4x = £152 and x = £38.
Hence the price of an adult ticket is £38.
Answer:
Step-by-step explanation:
2a+4c=152
2c=a
4c+2a=152
2c-a=0
Use simultaneous equation
Substitute 2c=a
c=a divided by 2 in the first equation and find value of a and c
Fractions help me please
Answer: the first one
Step-by-step explanation: 9/15 is indeed less than 4/5 which u can make 12/15
Find the value of x and y in the parallelogram. Helpp
Answer:
The answer is D.
Step-by-step explanation:
In a parallelogram, lengths are parallel to each other so we can assume that AB is parallel to CD and AD is parallel to BC. In order to find the value of x and y, you have to compare the expressions :
AB // CD
x - 2 = 24
x = 26
AD // BC
y = 11
Last weekend, Joshua's parents drove 810 miles in 9 hours when they came to visit him. What was their
constant speed?
Answer:
90mph
Step-by-step explanation:
Answer:
90 miles per hour
Step-by-step explanation:
810 / 9
Given an inequality, what strategies can we use to determine where the boundary line is? Explain your strategies in detail.
4x+3y≥12
Answer:
Step-by-step explanation:
The strategy to determine the boundary line is that we need to remove the inequality sign and replace it with and equal to sign and then sketch the equation of the function which is
[tex]4x+3y=12[/tex]
to sketch the function we need the function's x-intercept which means the graphs crosses the x-axis at that specific point (x , 0) and y-intercept which means the graph crosses the y-axis at that specific point (0 , y).
Since both these points lie on line we can substitute it into the equation to find the x-y intercepts and hence sketch the line so here goes.
For x-intercept:
[tex]4x+3y=12\\4(x)+3(0)=12\\4x=12\\x=12/4\\x=3[/tex]
so the x-intercept is (3 , 0)
For y-intercept:
[tex]4x+3y=12\\4(0)+3(y)=12\\3y=12\\y=12/3\\y=4[/tex]
so the y-intercept is (0 , 4)
now we sketch these 2 points and draw a straight line joining both the points as shown in the image below.
What is the probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32? Round your answer to the nearest
tenth of a percent.
A. 84.3%
B. 82.3%
C. 83.3%
D. 81.3%
Please tell me how to do this in my calculator
Answer:
The probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32 is 81.3%
Option D is correct.
Step-by-step explanation:
We need to find the probability that a data value in a normal distribution is between a z-score of -1.32 and a z score of 1.32.
We can write it as P(-1.32 < Z < 1.32)
It is equal to : [tex]P(-1.32 < Z < 1.32)= P(Z<1.32)-P(Z<(-1.32))[/tex]
Looking at z-score tables to find value of z=1.32 and z=-1.32
P(Z<1.32)= 0.90658
P(Z<-1.32) = 0.09342
Putting values and finding answer
[tex]P(-1.32 < Z < 1.32)= P(Z<1.32)-P(Z<(-1.32))\\ P(-1.32 < Z < 1.32)=0.90658-0.09342\\P(-1.32 < Z < 1.32)=0.81316\\P(-1.32 < Z < 1.32)=81.3\%[/tex]
So, the probability that a data value in a normal distribution is between a
z-score of -1.32 and a z score of 1.32 is 81.3%
Option D is correct.
17 friends to 19 friends
The percent increase is
Answer:
the increase is by 2
Step-by-step explanation:
You can add 17 plus 2 or subtract 17 from 19.
Answer:
2?
Step-by-step explanation:
Lines / and mare parallel. Line / can be represented by the equation 3x + 4y = 8. If line m passes through the po
m?
y-5= -
(x+2)
y +5 = -
44-2)
y-5= f «+2)
y+5 = ģ«-2)
Answer:B
Step-by-step explanation:
Answer:
B y-5=- 3/4(x-2)
Step-by-step explanation:
Lucas buys sandwiches for the boys' basketball team. At the first game, he paid $85 for 17 sandwiches. At the second game, he will have to buy 21 sandwiches at the same cost per sandwich
How much will Lucas have to pay? Use any strategy to solve this problem.
O $90
O $105
O $110
O $120
Answer:
$105
Divide 85 by 17 which equals 5 so each sandwich cost $5. Then multiply 21 by 5 which is 105.
8 divided by (-1/8) please please
Answer: -64
Step-by-step explanation:
flip the fraction, and then change the sign so it turns into multiplication.
-8 x 8
multiply them after that.
-64
You want to buy some rice. An 8-ounce package costs $2.88. A 12-ounce package costs $4.56. A 26-ounce package costs $9.10. Which package is the best buy?
Divide cost by ounces. The lowest cost per ounce is the better buy.
2.88/8 = 0.36
4.56/12 = 0.38
9.10/26 = 0.35
The 26 ounce package is the better buy.
Answer:
The 26-ounce package is the best buy
Reasoning:
In order to figure out the best buy, you have to see the price-per-ounce in each option and figure out the one that costs the least. The way to do this is by dividing the decimal in the pricing by the number of ounces in the package. For example, 2.88/8 = 0.36
This tells us that the price-per-ounce in the 8-ounce package is 0.36
Repeat this process for each of the other two packages to find that
4.56/12 = 0.38 and 9.10/26 = 0.35
with this information, we can conclusively say that the 26-ounce package is the best buy, as it has the lowest price-per-ounce of all three of the packages.
Escribe la ecuación: Un balón de baloncesto cuesta 10€ menos que uno de fútbol. Si 10 balones de fútbol y 4 de baloncesto cuestan 310€.
Responder:
14x - 40 = 310
Explicación paso a paso:
Dado que:
El baloncesto cuesta 10 € menos que un balón de fútbol
10 balones de fútbol y 4 de baloncesto cuestan 310 €
Para formar una ecuación:
Deje que el costo de:
Balón de fútbol = x
Costo del baloncesto = x - 10
Por lo tanto,
Costo de 10 balones de fútbol = 10 * x = 10x
Costo de 4 pelotas de baloncesto = 4 * (x - 10) = 4x - 40
Coste total :
Coste del balón de fútbol + coste del baloncesto = 310 €
10x + 4x - 40 = 310 €
14x - 40 = 310
14x = 310 + 40
14 veces = 350
x = 25 € = coste del balón de fútbol
Coste del baloncesto = 25 € - 10 € = 15 €
The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 25° angle with the water. To the nearest foot, how far is the boat from the cliff?
Group of answer choices
75 feet
129 feet
141 feet
27 feet
The distance between a boat and a cliff is 129 feet.
TrigonometryThe trigonometric functions are used to determine the distance and angle in real-life situations.
How to find the distance between a boat and a cliff using trigonometry?Consider the following diagram.
Let the distance between a boat and a cliff be [tex]x[/tex].
[tex]tan25^{o}=\frac{40}{x}[/tex]
[tex]x=\frac{35+25}{tan25}[/tex]
[tex]x=\frac{60}{0.4663}[/tex]
[tex]x=128.67[/tex]
Therefore, the distance between a boat and a cliff is 129 feet.
Learn more about trigonometry here-
https://brainly.com/question/26719838
#SPJ2
Which would produce a larger balance: an annual interest rate of 8.05% compounded monthly or an annual interest rate of 8% compounded continuously? Explain.
Answer:
8% compounded monthly has higher yield
Step-by-step explanation:
Here, we want to compare which of the two options would give a higher yield
An interest rate of 8% compounded monthly or 8% compounded annually
Let us say we are looking at a time frame of two years
If compounded monthly, since there are 12 months in a year, there would have been a compounding of 12 * 2 = 24 times
While if it is annual, we would have only twice
The higher the number of times we compound, the more the return
Subtract (4a2b - 3ab2 + 2ab + 5) and (2a2b + 3ab2 - 7ab). Choose the
difference.
2a4b2 - 5a2b2 + 5
2a 2b - 6ab2 + 9ab + 5
2a 2b - 6ab2 - 9ab + 5
2a2b - 5ab + 5
Answer:
2a2b-6ab2+9ab+5 is right answer
PLSS HELP!! NEED ASAP!!! MARKING BRAINLIEST!!! PLS EXPLAIN!!! At the produce store you can buy 4 bags of bananas for $22.52. How much would it cost if you were to buy 2 bags?
Step-by-step explanation:
4 bags of bananas for $22.52
=> 2 bags of bananas for $22.52 * 2/4 = $11.26.
Hence it would cost $11.26.
The point A(-6, 0) is reflected over the y-axis. What are the coordinates of the resulting point, A′?
Answer:
(6, 0)
Step-by-step explanation:
Walmart is having a huge 25 % off sale!!!
If the SALE PRICE for a PS4 is $300, what was the ORIGINAL PRICE?
Answer:
$400
Step-by-step explanation:
Answer:
It would be 400
Step-by-step explanation:
If you don't believe me search it up! C: hope this helped
A, B, C, or D? Due at midnight!! Thank you
Answer:
the last one 3.7, 3 3/4, 31/8, 3.89
Step-by-step explanation:
3.7=3.7
3 3/4= 3.75
31/8=3.875
3.89=3.89
helicopter is flying at an elevation of 450 feet. It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘. Find the distance between a point on the ground directly below the helicopter and the landing pad. Round your answer to the nearest whole number.
Answer:
138 feets
Step-by-step explanation:
Given that :
Angle of depression (α) = 16°
Elevation = height = 450 feets
Appling trigonometry :
From the picture attached :
Height / elevation = 450 feets (Adjacent)
Distance = d (opposite)
Tan α = opposite / Adjacent
Tan 17 = d / 450
450 tan17 = d
450 * 0.3057306 = d
d = 137.57880
Hence, distance between a point on the ground directly below the helicopter and the landing pad 138 feets
The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.
Given that,
The helicopter is flying at an elevation of 450 feet.
It is within sight of the landing pad and the pilot finds that the angle of depression to the landing pad is 16∘.
We have to determine,
The distance between a point on the ground directly below the helicopter and the landing pad.
According to the question,
The angle of depression = 16°,
Elevation = height = 450 feet
And d is the distance,
The angle of depression is an important component used in trigonometric operations.
The angle of depression is formed when the observer stands on a ground higher than the object which he is trying to observe.
Therefore, The angle of depression is,
[tex]Tan16 = \dfrac{d}{450}\\\\0.28 = \dfrac{d}{450}\\\\d = 450 \times 0.28\\\\d = 129.03 \ feet[/tex]
Hence, The distance between a point on the ground directly below the helicopter and the landing pad is 129.03 feet.
To know more about Trigonometry click the link given below.
https://brainly.com/question/13760328
Javier and Ebony track the number of steps they walk. Javier records a walk of 6000 steps in 50 minutes. Ebony describes her step rate with the equation y=118, where y is the number of steps and x is the number of minutes she walks. This week, Javier and Ebony each walk a total of 5 hours. Who walks more steps?
Answer:
Javier walks more steps than ebony given the same minutes
Step-by-step explanation:
Javier records a walk of 6000 steps in 50 minutes.
Ebony describes her step rate with the equation y=118x
Where,
y = number of steps
x = number of minutes she walks
Javier and Ebony each walk a total of 5 hours. Who walks more steps?
5 hours = 5 × 60 minutes
= 300 minutes
Javier records a walk of 6000 steps in 50 minutes.
6000 : 50 minutes = x : 300 minutes
6000/50 = x / 300
Cross product
6000 * 300 = 50 * x
1,800,000 = 50x
x = 1,800,000 / 50
= 36,000
x = 36,000
Javier walks 36,000 steps
Ebony describes her step rate with the equation y = 118x
x = 300 minutes
y = 118(300)
= 35,400
y = 35,400
Ebony walks 35,400 steps
Therefore,
Javier walks more steps than ebony given the same minutes
Use the expression $100 + 5n to find the total price for n students to take a field trip to the science museum. If 175 students go on the field trip, how much will total cost?
Answer:
Total cost= $975
Step-by-step explanation:
Giving the following information:
Total cost= 100 + 5*n
n= number of students
The $100 is a fixed cost. It remains constant no matter the number of students. The $5 is the unitary variable cost. The total variable cost increases with the number of students.
Total cost for 175 students:
Total cost= 100 + 5*175
Total cost= $975
Please answer ASAP!
How many different arrangements of the letters of the word SCIENCE
have N as their first letter and S as their last?
Ignore this post, I have no Idea what it is, report this so it gets taken down so someone else can answer...
A box with inside area of 1.1m2 is covered with an unknown 0.163m of insulation material. Determine the thermal conductivity for the insulating material if a 62 W bulb is used to heat the box. The bulb maintains the inside temperature at 23oC higher than the outside temperature.
9514 1404 393
Answer:
0.40 W/(m·K)
Step-by-step explanation:
Units of thermal conductivity are ...
W/(m·K)
The length dimension in the denominator comes from the ratio of area to thickness. That is, we can compute the thermal conductivity from ...
(62 W)(0.163m)/(1.1 m²·23K) ≈ 0.40 W/(m·K)
Jim wants to make 2.7 quarts of a 60% alcohol solution by mixing together a 80% alcohol solution and a 20% alcohol solution. How much of each solution must Jim use?
Answer:
1.8 quartz of 80% solution and
0.9 quarts of 20% solution.
Step-by-step explanation:
Given that:
Total alcohol solution to be made = 2.7 quarts of 60% solution
Alcohol concentration in first solution= 80%
Alcohol concentration in second solution = 20%
To find:
How much of each solution must Jim use?
Solution:
Let amount of first solution to be used = [tex]x[/tex] quartz
Total amount is given as = 2.7 quarts
So, amount of second solution to be used = (2.7 - [tex]x[/tex]) quartz
As per question statement, we can write the following equation:
[tex]80\%\ of\ x +20\%\ of\ (2.7-x) = 60\%\ of\ 2.7\\\Rightarrow \dfrac{80}{100} x +\dfrac{20}{100} (2.7-x) = \dfrac{60}{100}\times 2.7\\\Rightarrow 4x+2.7-x =3\times 2.7\\\Rightarrow 3x=2\times 2.7\\\Rightarrow \bold{x =1.8\ quartz}[/tex]
First solution, 80% solution to be used = 1.8 quartz
Second solution, 20% solution to be used = 2.7 - 1.8 = 0.9 quartz
what is 1093 + 28478
Answer:
29571 is the answer welcome!!
What is the slope of the line passing through the points (-1, 3) and (4, - 7)?
A. -4/3
B. 3/4
C. 2
D. -2
Answer:
D
Step-by-step explanation:
-1,3
4,-7
-7-3=-10
4--1=5
-10/5=-2
If f(x) = 2x² then when x = 3, y will equal
Answer:
y = 18
Step-by-step explanation:
Given
f(x) = 2x² ( substitute x = 3 )
y = f(3) = 2(3²) = 2(9) = 18
0.0000000342 in scienctific notation
Answer:
3.42 to the -8 power
Step-by-step explanation:
In the accompanying diagram. altitude CD is
drawn to the hypotenuse of right triangle ABC. If
AD - 9 and AB = 13. find CD.
Someone help me please
To Find :
The value of side CD.
Solution :
Applying Pythagoras theorem in ΔABC :
[tex]AC^2 + CB^2=AB^2 \\\\AC^2 + CB^2 = 13^2[/tex] ....1)
Applying Pythagoras theorem in ΔACD and ΔCDB :
[tex]AD^2 + CD^2 = AC^2[/tex] ....2)
[tex]CD^2 + DB^2 = CB^2[/tex] ....3)
Adding equation 2 and 3, we get :
[tex]AC^2 + CB^2 =AD^2 + 2CD^2 + DB^2[/tex] ...4)
Solving equation 1) and 4), we get :
[tex]AD^2 + 2CD^2 + DB^2 = 13^2\\\\9^2 + 2CD^2 + ( 13 - 9 )^2 = 13^2\\\\2CD^2 = 72\\\\CD = 6[/tex]
Therefore, length of CD is 6 .