Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so gradient of line is -3.
Equation of line is y = -3x + c.
Substitute C(2,7) into the equation to find c.
7 = -3(2) + c
c = 13
Hence, equation of line is y = -3x + 13.
susan has an ear infection. The doctor prescribes a course of antibiotics. Susan is told to take 250mg dose of the antibiotic regularly every 12 hours for 20 days. Susan is curious and wants to know how much of the drug will be in her body over the course of the 20 days. She does some research online and finds out that at the end of 12 hours, about 4% of the drug is still in the body.
Answer:
400 mg
Step-by-step explanation:
There are 24 hours in a day. 250mg every 12 hours is 250x2=500.
500×20=10,000
10,000x.04=400
You estimate that your car gets 28 miles per gallon. The cost of gas per gallon is shown. How much does it cost you to travel 455 miles? Round to the correct number of significant figures.
The estimate of the cost to travel 455 miles as required in the task content is; $63.4.
What is the cost of travelling 455 miles as given in the task content?It follows from the task content that the cost of travelling 455 miles is to be determined from the given information.
Hence, this is two-step problem.
First, since the car gets 28 miles per gallon, the amount of gas needed to travel 455 miles by proportion is;
455/28 = 16.25 gallons.
Also, since the cost per gallon as in the complete task content is; $3.899.
The cost of 16.25 gallons is; 16.25 × $3.899
= $63.4.
Remarks: Gas costs $3.899 per gallon.
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bro can someone help please i’ve been struggling all day
Answer:
x = 7
Step-by-step explanation:
solve the quadratic equation [tex]3x^{2} +x-5=0[/tex]
give your answers to 2 decimal places
Answer:
-1.47, 1.14 to 2 decimal places.
Step-by-step explanation:
3x^2 + x - 5 = 0
3(x^2 + 1/3x) - 5 = 0
Completing the square on the expression in the parentheses:
3[(x + 1/6)^2 - 1/36) - 5 = 0
3(x + 1/6)^2 - 1/12 - 5 = 0
(x + 1/6)^2 = 61/12 / 3
(x + 1/6)^2 = 61/36
(x + 1/6) = +/-√61 / 6
x = -1/6 +/- √61 / 6
x = 1.135, -1.468
Solve for x. PLS HELP MEEE
Answer: ask candice
Step-by-step explanation:
Answer:
x = 75
Step-by-step explanation:
The triangle on the right is an equilateral triangle. This means each angle is 60 degrees.
The bottom angle which goes over both triangles is marked as a right angle (90 degrees). Given that the part of that angle in the equilateral triangle is 60 degrees, the rest of the angle (i.e. the part of the angle in the other triangle) is 30 degrees.
It is implied by the markings that the angle x = the other angle at the top (although this should be clearer). Assuming this is the case, we can use the rule that angles in a triangle sum to 180 degrees, to say that:
x + x + 30 = 180
Combine like terms, rearrange and simplify:
2x + 30 = 180
2x = 150
x = 75
Find the value of z.
Answer:
it depends on what is z for, if it's for the whole triangle then i would think it would be 2z - 4 10 and 7 added or multiplied. Or it could be 2z -4 witch would be z = 2
Please help me fast I will mark brainliast
Answer:
See attached worksheet.
Step-by-step explanation:
Given f(x) = 3x³ + kx- 10, and x - 2 is a factor of f(x), then what is the value of k?
Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems. Therefore, the value of k is -7.
What are Polynomials?A polynomial is an expression in mathematics made up of coefficients and indeterminates, which are also known as variables. It can only be solved using the addition, subtraction, multiplication, and powers of positive-integer variables. For instance, x3 + 2xyz2 yz + 1 has three indeterminates. Value In both mathematics and science, polynomials are widely used. For instance, they are used to define polynomial functions, which can be found in a variety of contexts, from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions. If f(x) = 3x³ + kx- 10 , If x -2 is a factor of the given equation, then,x - 2 = 0 ⇒ x = 2, On substituting, x =2, f(x) = f (2) = 0.So, f (2) = 3(2) ³ + k2- 10 = 0⇒ 24 + 2k -10 = 0 and 2k = -14⇒ k = -14/2, so k = -7In higher mathematics, polynomials are employed to build algebraic varieties and polynomial rings, which are fundamental ideas in algebra and algebraic geometry.To learn more about Polynomials, refer to:
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There may be more then one answer
Will give brainlest
What is the 10th term of the sequence 5,2, 4/5,….
Good evening,
Answer:
-512/390625
Step-by-step explanation:
an=a1 •r^n-1
a10=5 • -0.4^10-1
a10=5 • -0.4^9
a10=5 • -512/1953125
a10= -512/390625
Please someone help help me
Answer:
y - axis
Step-by-step explanation:
point moves from right to left
When comparing functions, such as Seth’s scenarios for travelling to school, will the function with the greatest initial value continue to be the greatest as time increases?
No. The pace of change affects the y-value, therefore having a higher beginning value does not guarantee it. The output may decrease if the function with the bigger beginning value has a slower rate of change.
This is further explained below.
What are functions?Generally, No. Even if the function had a higher beginning value, it does not always follow that it would always have a higher y-value. This is because the y-value also relies on the rate of change.
In conclusion, If the function with the higher beginning value has a slower rate of change, it is possible that the output may become smaller at some time in the future as a consequence of this.
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Simplify: -42 30(cubed) / 12 10 (cubed)
The fundamental guidelines and procedures to simplify any algebraic statement are as follows:By multiplying factors, remove any grouping symbols like brackets and parenthesis.
If the words contain exponents, use the exponent rule to eliminate grouping.Add or subtract like terms to combine them.
Simplify: -42 30(cubed) / 12 10 (cubed)?
By removing the denominators, convert fractions to integers.
Because the denominators of our two fractions differ, we must calculate the Least Common Denominator and rewrite our fractions using the common denominator as needed. LCD(-42/30, 12/10) = 30
Now that the denominators of our two fractions are similar, we may multiply them both by 30 to get rid of the denominators.
The final result is: -42/30: 12/10 = -42: 36
With the highest common factor, attempt to further reduce the ratio (GCF).
GCF is 6 for -42 and 36.
Divide both terms by the GCF, 6, as follows: -7 36 6 = 6; -42 6 =
By dividing both parts by the GCF = 6, the ratio -42:36 can be reduced to its smallest terms: -42:36 = -7:6.
Therefore:
-42/30 : 12/10 = -7 : 6
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If ST = 65, TR= 40, and WU = 16, find the length of VW. Round your
answer to the nearest tenth if necessary.
Answer:
ST/VW = TR/WU
40/16 = 65/VW
2.5 = 65/VW
2.5VW = 65
VW = 65/2.5
VW = 26
What is the x-intercept for function f? f(x) = −2/3x + 8
Answer:
x = 12 is the x-axis intercept
Step-by-step explanation:
'x-intercept' is short for 'x-axis intercept' <==== when the graph crosses the x axis, y = 0 so put y = 0 in the equation
y = -2/3 x + 8
0 = -2/3 x + 8
-8 = - 2/3x
x = 8 * 3/2 = 12
The stock of Company A gained $6.65 throughout the day and ended at a value of $101.65. By what percentage did the stock rise?
help please please help thanks
F(2,9) after a reflection over the y-axis.
Answer:
(-2, 9)
Step-by-step explanation:
hope it helped <3333 :D
y=x² + 2x - 2
iii) Find the values of x
when y = 2
Answer: 1.236, -3.236 or [tex]-1-\sqrt{5} and -1+\sqrt{5}[/tex]
Step-by-step explanation:
2 = x^2 + 2x -2
x^2 + 2x - 2 -2
x^2 +2x -4
put into quandratic formula
(a) The perimeter of a rectangular garden is 292 m.
If the length of the garden is 89 m, what is its width?
Width of the garden: ?
(b) The area of a rectangular window is 7968 cm².
If the width of the window is 83 cm, what is its length?
Length of the window: ?
Answer:
(a) Let width of garden be w m.
Perimeter = length + width + length + width
Substitute the values into the equation.
89 + w + 89 + w = 292
Simplify and solve for w.
2w + 178 = 292
2w = 114
w = 57
Hence, width of garden is 57 m.
(b) Let length of window be L cm.
Area = length × width
Substitute the values into the equation.
L × 83 = 7968
Simplify and solve for L.
83L = 7968
L = 96
Hence, length of window is 96 cm.
Write the equation of a parabola with x-intercepts at (3, 0) and (9, 0) that
passes through the point (10, -7).
The parabola's equation is y = -x2 + 12x - 27.
A parabola is a point's location where the focus and a fixed point's distance from a fixed line, known as the directrix, are the same.
A parabola's equation is in quadratic form.
Thus, it is stated as:
Y = Ax2, Bx, and C
Located at (3, 0):
0 = a(3²) + b(3) + c
9a + 3b + c = 0 (1) (1)
Located at (9, 0):
0 = a(9²) + b(9) + c
81a + 9b + c = 0 (2) (2)
Located at (10, -7):
-7 = a(10²) + b(10) + c
100a + 10b + c = -7 (3) (3)
Equations 1, 2, and 3 are solved to yield: a = -1, b = 12, and c = -27.
Consequently, the parabola's equation is y = -x2 + 12x - 27.
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Find the circumference.
Use 3.14 for π.
G
r = 3 ft
C = [?] ft
C = πd
Answer:
c=2πr
c=2π3
put it in calculator
=18.8ft (1dp)
One side of an envelope is 3 inches longer than the other side. The area of the envelope is 108 in²Determine the dimensions of the envelope.
Dimensions of envelope will be Length will be (x + 3) = (9 + 3) = 12 and Breadth will be x = 9.
Envelope can be considered as the shape of rectangle.
Rectangle has length and breath which can be considered as the sides of envelope.
Now we have given one side of envelope is 3 inches longer than the other side of envelope.
let side of envelop be x inches than other side will be (x + 3) inches.
Now we have also given that the area of envelop is 108 in².
The Area of rectangle = (length)(breadth).
let length of envelop be (x+3) as its bigger than its breadth x.
∴ Substitute area of rectangle with the area of envelope.
∴ (x + 3)(x) = 108.
∴ x² + 3x = 108.
∴ x² + 3x - 108 = 0.
∴ x² + 12x -9x - 108 = 0
∴ x(x + 12) -9(x +12) = 0
∴ (x-9) (x +12) = 0
∴ (x-9) = 0 and (x +12) = 0
∴ x = 9 and x = -12
Now as dimensions cannot be negative ∴ x = -12 is rejected.
∴ x = 9 is considered
∴ Length will be (x + 3) = (9 + 3) = 12.
∴ Breadth will be x = 9.
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Select ALL expressions equal to: -8(5y - 9)
The expression -8 (5y - 9) is equals to - 40y + 72
How to find equivalent expression?In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.).
In other words, a mathematical expression is any combination of numbers, letters, and relational operators.
Therefore, the following expression can be express in an equivalent form as follows:
Equivalent expressions are expressions that work the same even though they look different.
Hence,
-8 (5y - 9)
open the bracket
-8 (5y - 9) = - 40y + 72
Therefore, the equivalent expression of -8 (5y - 9) is - 40y + 72
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How many circular tiles are needed to make pattern number 20
Answer:
84 circle for pattern 20
Step-by-step explanation:
we know that by studying the first 3 patterns we know that the corner pieces (that have multiple circles on them) has 3 circlesThe edge pieces (the ones with 1 circle on them) we now know what to doFor each pattern number that is how many squares (x) are [tex]x^{2}[/tex] to find how many squares in totalWe know we need to find square pattern 20We now know how many squares are gonna be on each side (20)look at attachment1 for referencenow we are gonna look atttachment2now we are gonna count the edges on each side (the blue) we get 18 on each side so we do 18*4 and that is 72now we know that the edges only have one circle on it so for the edges we have 72now for the corners, we know that there are 3 per corner piecenow we count the corners ( there are 4 in total)now we do 4*3 and that is 12now we add the total circles for the corners (12) and the edges (72) 12+72= 84pattern 20 has 84 circlesDon’t have to do that graphing just need the slope please
The slope and y-intercept of each line are:
13. slope = 1/2; y-intercept: 0.
14. slope = 3; y-intercept: 0.
15. slope = -2/5; y-intercept = 0.
16. slope = -1; y-intercept = 1.
17. slope = -2/3; y-intercept = -4.
18. slope = 1; y-intercept = 0.
19. 7/9
20. 3/5
How to Determine the Slope and the Y-intercept of a Line?The slope and y-intercept of a line can be determine from the given equation of a line in slope-intercept form, y = mx + b, where:
Y-intercept is represented as b.Slope is represented as m.13. y = 1/2x,
The slope = 1/2
The y-intercept of the equation is: 0.
14. y = 3x,
The slope = 3
The y-intercept of the equation is: 0.
15. y = -2/5x,
The slope = -2/5
The y-intercept of the equation is: 0.
16. y = -x + 1
The slope = -1
The y-intercept of the equation is: 1.
17. y = -2/3x - 4,
The slope = -2/3
The y-intercept of the equation is: -4.
18. y = x,
The slope = 1
The y-intercept of the equation is: 0.
19. Slope = change in y / change in x = (18 - 11)/(19 - 10)
Slope = 7/9
20. Slope = change in y / change in x = (2 -(-1))/(9 - 4)
Slope = 3/5
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21 El Carro de la maestra mago
recorre 95km con
Solo
tiene
201 de gasolina sl
17 Litros ¿cuantos km recorre
The distance it travel in 17litres petrol: 8.024km
What is Distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
Given,
The distance traveled in 201 petrol = 95km
The distance traveled in 1 liter = 95/201
= 0.472km
Now, we have to find out how many km does it travel in 17liter:
The distance traveled in 17liters = 17 x 0.472
= 8.024km
Hence, it travels 8.024km in 17 liters petrol
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The PTA at a school want to sell chocolate bars to support the school PTA. They asked a random sample of 10 students how many chocolate bars they would be willing to buy at a price of $2 for each bar. Their responses are summarized in the following dot plot:
If there are a total of 250 students at the school and the sample is representative of the entire school's population of students, which of the following is the most reasonable estimate of the total number of chocolate bars the PTA can expect to sell to all the students of the school? A. 250
B. 500
C. 600
D. 750
Answer:
B
Step-by-step explanation:
the most answered was 2. 2x250=500
Make an equation for the first question
Then use the equation to find the cab fare if zarela has a 1.8 mile commute to work
The two equations are : 6x + m = F
and 6x + 1.8 m = F
How to solve a linear equations ?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b)
Let the total time be x
Given distance Zarela travels is m
Thus the total cab fare = F
Therefore the equation becomes;
6x + m = F
In the second part of the question it is given that Zarela travels for 1.8 mile
thus the equation becomes
6x + 1.8 m = F
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A monopoly player claims that the probability of getting a when rolling a six-sided die is because the die is equally likely to land on any of the six sides. Is this an example of a theoretical probability or an empirical probability? explain.
It is an illustration of theoretical probability.
Theoretical probability establishes the probability of certain events occurring.
The ratio of the entire number of conceivable possibilities to the intended outcome is known as theoretical probability.
In this case, the intended consequence is earning a 2, which is only one of the six potential possibilities. The possibility of receiving a 2 is.
Observance determines empirical probability. Nothing about the observing of the specified episode is indicated in the question, hence it is not an empirical probability.
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