The equation of the line is y = x/4 + 13/2 .
What is a slope?A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1/4
And (x₁ ,y₁) = (-2,6)
then the equation of line is
y - y₁ = m (x - x₁)
y - 6 = (1/4) (x +2)
y = x/4 + 13/2
Therefore, the equation is y = x/4 + 13/2.
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show that 12cos30 + 2tan60 can be written in the form Vk where k is an integer
Answer:
√192
Step-by-step explanation:
12 cos 30° + 2 tan 60°
Substitute the trig functions of the special angles.
12 (½√3) + 2 (√3)
Simplify.
6√3 + 2√3
8√3
Move under the radical.
√(8² · 3)
√192
STANDARD FORM MATHS HELP. POINTS
Answer:
1.64×10⁷ km16,400,000 km ("standard form" in the US)Step-by-step explanation:
You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:
c² = a² +b²
RQ² = PQ² +PR²
RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root
The distance between planets Q and R is 1.64×10⁷ km.
__
Additional comment
The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.
You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.
Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.
Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)
The distance QR is :
[tex] \qquad \sf \rightarrow d = \sqrt{(1.6 \times 10 {}^{7}) {}^{2} + (3.6 \times 10 {}^{6} ) {}^{2} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{2.56 \times 10 {}^{14} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{256\times 10 {}^{12} + 12.96 \times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex] \qquad \sf \rightarrow d = \sqrt{(268.96 )\times 10 {}^{12} {}^{} } [/tex]
[tex]\qquad \sf \rightarrow d = 16.4\times 10 {}^{6} {}^{} [/tex]
Point E has the same y-coordinate as point D, but the x-coordinate of point D. Plot point E and write the coordinates of point E. Then describe the type of reflection you plotted.
The coordinates of Point E are (-4,2) and Point E is a reflection of point D across the X-axis.
What is the coordinate about?Point E has the same y-coordinate as point D, which is 2. However, the x-coordinate of point E is the opposite of the x-coordinate of point D. The x-coordinate of point D is 4, so the x-coordinate of point E must be -4. Therefore, the coordinates of Point E are (-4,2).
As for the reflection, you can imagine a mirror placed on the x-axis (horizontally) and Point D and E being on the same side of that mirror.
Therefore, As Point D is reflected on the mirror, it will be flipped and the x-coordinate changes its sign and becomes -4. Therefore Point E is a reflection of point D across the X-axis.
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See full question below
Point E has the same y-coordinate as point D, but the x-coordinate of point E is the opposite of the x- coordinate of point D. Drag tiles to complete the statements. (4,2) (4,-2) (-4,2) (-4,-2) X-axis y-axis The coordinates of Point E are --- &Point E is a reflection of point D across the ---
suppose that, of people who undergo routine screening, for every two people who have colon cancer, there are 100 who do not. (that is, 2/102 people have it.) of those who undergo screening and do have colon cancer, all of them will have a positive test. of the people who undergo screening but don't have colon cancer, only 2 percent have a positive test. a random person undergoes routine screening and has a positive test. what is the probability (not odds) that this person has colon cancer? choose the range in which the answer lies.
The probability that a person has colon cancer given that they have a positive test result is approximately 0.98. The answer lies in the range [0.95, 1.00].
Let's call the probability that a person has colon cancer given that they have a positive test result "p". We can use Bayes' Theorem to find this probability.
Bayes' Theorem is: p(A|B) = (p(B|A) * p(A)) / p(B)
In this case, A is the event that the person has colon cancer, and B is the event that the person has a positive test result.
We are given that:
p(B|A) = 1 (all people who have colon cancer will have a positive test result)
p(B|~A) = 0.02 (2% of people who do not have colon cancer will have a positive test result).
We are also given that p(A) = 2/102 (2 out of 102 people who undergo routine screening have colon cancer) and p(~A) = 100/102 (100 out of 102 people who undergo routine screening do not have colon cancer).
Substituting these values into Bayes' Theorem, we get:
p(A|B) = (1 * (2/102)) / (1 * (2/102) + 0.02 * (100/102))
Simplifying, we get:
p(A|B) = 0.98
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Two of the coordinates representing the corners of Maya's rectangular driveway are (-1, 1) and (1 1\2, -8 1\2
9. Plot the other two coordinates of Maya's rectangular driveway. What are the ordered pairs that you plotted?
Answer:
the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Step-by-step explanation:
To plot the other two corners of Maya's rectangular driveway, we need to determine the coordinates of the points that are diagonally opposite to the points (-1, 1) and (1 1/2, -8 1/2).
Since the points (-1, 1) and (1 1/2, -8 1/2) are diagonally opposite, we can draw a line through the center of the rectangle that is perpendicular to the line connecting these two points. The center of the rectangle can be found by averaging the x-coordinates and the y-coordinates of the two points. The x-coordinate of the center is (-1 + 1 1/2)/2 = 1/4 and the y-coordinate of the center is (1 + -8 1/2)/2 = -3 3/4.
We can then use the center of the rectangle and the slope of the line connecting (-1, 1) and (1 1/2, -8 1/2) to find the coordinates of the other two corners. The slope of the line is (-8 1/2 - 1)/(1 1/2 - (-1)) = -17/3, so the slope of the line perpendicular to it is -3/17.
We can use this slope and the center of the rectangle to find one of the remaining corners by moving a fixed distance in the y-direction from the center. For example, if we move 2 units in the positive y-direction from the center, we will reach the point (1/4, -3 3/4 + 2) = (1/4, -1 3/4). We can then use the slope of the line to find the x-coordinate of the other corner by solving the equation y = mx + b for x, where m is the slope, x is the x-coordinate of the corner, y is the y-coordinate of the corner, and b is the y-intercept. The y-intercept is the y-coordinate of the center, so we can solve the equation as follows:
y = -3/17 * x + (-3 3/4)
x = (y - (-3 3/4))/(-3/17)
Substituting the coordinates of the corner we found earlier, we get:
x = (-1 3/4 - (-3 3/4))/(-3/17) = (2)/(-3/17) = -10/3
So, the coordinates of the other corner are (-10/3, -1 3/4).
The four ordered pairs that represent the corners of Maya's rectangular driveway are (-1, 1), (1 1/2, -8 1/2), (-10/3, -1 3/4), and (1 1/2, -1 3/4).
Angela is following this recipe to make biscuits.
Angela uses 0.9 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 10 biscuits
150 g margarine
180 g sugar
225 ml syrup
225 g oats
40 g sultanas
The amount of margarine needed in Kg for making biscuits is 0.6kg
What is proportions?In general, the term "proportion" refers to a part, share, or amount that is compared to a whole.
According to the definition of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.
How to find the amount of margarine needed in KgThe amount of margarine needed in Kg is calculated using proportions
If 225 ml or soup requires 150 g of margarine then 0.9 liters of soup will require
0.225 l = 0.15 kg
0.9 l = ?
cross multiplying
0.225 * ? = 0.9 * 0.15
? = 0.135 / 0.225
? = 0.6
Angela will require 0.6 kg of margarine
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I have this question can anyone solve
Answer:
-16Step-by-step explanation:
• 12a - 2b - 4b - 15a + 2 (a = 0, b = 3)
→ apply the values
• 12x0 - 2x3 - 4x3 - 15x0 + 2
• 0 - 6 -12 - 0 + 2
→ use BODMAS formulae
• 0 - 6 - 12 - 2
= 0 - 6 - 10
→ zero wouldn't be counted so
- 6 - 10
(-) + (-) = (+) so:
= -16
PLEASE HELP ASAP FOR MY FINALS
Answer:
A.86
is the answer will show how it's solved if necessary on comment.
hope it helps!!!
The statement for the expression 4x-10 is
Subtract 3
2y + 2xy – x + 4 from 9 - 7x + 3xy - 4
2y
Which is the midpoint of segment AB with A(-1,5) and B(6,-3)
Answer:
(2½,1)
Step-by-step explanation:
(-1+6/2,5+-3/2)
(5/2,2/2)
(2½,1)
Solve. 3 x − 9 x 2 = − 10
Answer:
below
Step-by-step explanation:
9x^2-3x-10 = 0 Use quadratic Formula with a = 9 b = -3 and c = -10
to find the zeroes are x = 1/6 ± sqrt (41) / 6
It takes 47 pounds of seed to completely plant a 5 -acre field. How many acres can be planted per pound of seed? (b)
6. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. What is the initial
height of the rocket before it is launched?
h(t) = -5t² +42t +54
Answer:
Step-by-step explanation:
The initial height of the rocket before it is launched can be found by evaluating the function h(t) at t=0. To do this, you can substitute 0 for t in the function:
h(0) = -5(0)² + 42(0) + 54
h(0) = 0 + 0 + 54
h(0) = 54
Therefore, the initial height of the rocket before it is launched is 54 meters.
Answer: 54 meters.
Step-by-step explanation: The initial height of the rocket before it is launched is represented by the constant term in the quadratic function, which is 54. This means that the rocket's height at time t = 0 (before it is launched) is 54 meters.
To confirm this, you can plug in t = 0 into the quadratic function to get:
h(0) = -5(0)² + 42(0) + 54 = 54 meters
This means that the initial height of the rocket before it is launched is 54 meters.
Solve for y in this diagram. Justify your answer.
The value of y in the given diagram is 6cm.
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
Consider, the given triangle the two base angles are same.
So, the triangle is a isosceles triangle.
Since, when the base angles of an isosceles triangle are equal, the sides that face these angles are also equal.
Hence, the value of y in the given diagram is 6cm.
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At a candy store, the price listed for 2 pounds of
chocolate is $9.95. What amount will Jerry need to pay,
if he decides to purchase 12 pounds of chocolate?
lbs
$
****
Submit
Answer:
Step-by-step explanation:
teaj
(50 points) Mariel and Sam Trent's savings account had a balance of $9,544 on May 1. The account earns interest at a rate of 5.25% compounded monthly until the end of August.
Answer:
$9,712.12 (nearest cent)
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]
Given:
P = $9,544r = 5.25% = 0.0525n = 12 (monthly)t = 4 months = 1/3 yearSubstitute the given values into the formula and solve for A:
[tex]\implies A=9544\left(1+\frac{0.0525}{12}\right)^{12 \cdot \frac{1}{3}}[/tex]
[tex]\implies A=9544\left(1.004375\right)^{4}[/tex]
[tex]\implies A=9544\left(1.017615179\right)[/tex]
[tex]\implies A=9712.119269[/tex]
The balance of the account at the end of August will be $9,712.12 (nearest cent).
△DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)° , what is the measure of one of the congruent base angles?
The measure of one of the congruent base angles is 65°.
How to illustrate the triangle?It's important to note that any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane. In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. A triangle has three sides, three angles and the sum of the angles equal 180°.
It should be noted that a triangle has 3 side, 3 angles and a sum of 180°.
In this situation, DEF is an isosceles triangle. If m∠D = (3x + 5)° , m∠E = (4x − 15)° and m∠F = (2x + 10)°.
The value will be illustrated thus:
3x + 5 + 4x - 15 + 2x + 10 = 180
Collect the like terms
9x = 180 - 5 + 15 - 10
9x = 180
x = 180 / 9
x = 20
The measure of one of the congruent base angles will be:
= 4x - 15
= 4(20) - 15
= 65°
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A right triangle has a leg length of √ and a trypolenuse length of 7. Determine the length of the other leg of the right triangle.
03
O √59
O√43
The length of the other leg is (c) √43
How to determine the length of the other legFrom the question, we have the following parameters that can be used in our computation:
Hypotenuse = 7
One leg = √6
The length of the other leg can be calculated using
The length of the other leg = √(Hypotenuse^2 - One leg^2)
So, we have
The length of the other leg = √(7^2 - √6^2)
Evaluate
The length of the other leg = √43
Hence, the length is (c) √43
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Complete question
A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.
Please help, thank you!
boston thinks that the domain is all positive real numbers between 0-4 while caleb thinks it is all whole numbers between 0-4. who do you agree with, and why?
0-4 can be the domain of positive real numbers but can not be the domain of whole numbers.
Numbers an arithmetical value used in counting and calculating that is expressed as a word, symbol, or figure that represents a specific quantity.
Let's understand what is positive real numbers.
That is all the real numbers that are greater than or equal to zero.
real numbers are numbers which include both rational and irrational numbers.
whole numbers are positive integers that mean only positive integers.
that means 0-4 can be the domain of positive real numbers but can not be the domain of whole numbers because 0.5 and 0.6 these numbers are not whole numbers.
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the population of a city was 250,000 in 1980, and it was 310,000 in 2000. what was the average rate of growth over this period?
Average rate of growth over this period is 0.4%.
Average rate of growth over a period is given by:
A=P[tex]e^{rT}[/tex] where,
A- Population at time T
P- Initial population
r-average rate of growth
T-Time period
Now, P=250,000, A=310,000 and T=21 (2000-1980+1)
therefore, putting values in the equation, we get:
310,000=250,000[tex]e^{21r}[/tex]
⇒ [tex]e^{21r}[/tex] = 1.24
⇒ 21r = log(1.24)
⇒ r = 0.0044 or 0.4%.
so, the average rate of growth over this time period is 0.4%.
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Solve for y
-x - 2y ≥ 7
Answer: [tex]y \leq -\frac{x}{2}-\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]-x-2y \geq 7\\\\x+2y \leq -7\\\\2y \leq -x-7\\\\y \leq -\frac{x}{2}-\frac{7}{2}[/tex]
. Solve for x: log₂ (x+4) + log₂ (x + 3) = 1. Pleasee
The value of x for the expression is equal to -5 and -2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the logarithmic expression is log₂ (x+4) + log₂ (x + 3) = 1. The value of x will be calculated as,
log₂ (x+4) + log₂ (x + 3) = 1
log₂ { (x+4)(x + 3) } = 1
x² + 7x + 12 = 2
x²+ 7x + 10 = 0
Solve the above quadratic equation,
x²+ 7x + 10 = 0
x² + 5x + 2x + 10 =0
x ( x + 5 ) + 2 ( x + 5 ) = 0
(x + 5 ) ( x + 2 ) = 0
x = -5 and -2
The values of x are -5 and -2.
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Which is an expression for the derivative P(x) = f(x) / —f(x)
the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
What is derivative?
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial.
given expression p(x)= f(x)/1-f(x)
The derivative of the given expression will be
p'(x) = f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))²
Hence the derivative of the expression will be f'(x)*(1-f(x)) -( f(x)*-f(x)) / (f(x))².
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The price of a coat is reduced by 17% in a sale.
The sale price is £78.85.
What was the original price of the coat?
Give your answer in pounds (£).
The required original price of the coat is given as £95.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95
Hence, the cost of the coat before the sale is £95.
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Please help meee asap please !!!????
Express cos E as a fraction in simplest terms.
Answer: cos E=
E
10
24
C
0
The trigonometric ratio, cos E of the right triangle is 5 / 13.
How to find the angles of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
A right triangle is a triangle that has one of its angles as 90 degrees.
The sides and angles of a right triangle can be found using trigonometric ratios. The sides of a right triangle base on its sides are as follows;
opposite sideadjacent sidehypotenuse sideTherefore,
cos E = adjacent / hypotenuse
Hence,
let's find the hypotenuse side using Pythagoras theorem,
24² + 10² = c²
c = √576 + 100
c = √676
c = 26
cos E = 10 / 26
Therefore,
cos E = 5 / 13
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The digits in the product of 0.48 and a decimal number between 350 and 400 are 182136. Explain how to correctly place the decimal point without knowing the other factor. Then Place place the decimal point in the product.
The decimal point is to be placed three places to the left.
What are decimal numbers?
When we divide a whole number into smaller parts, we get decimals. Then, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
Given that, in the question, the product of a decimal number between 350 and 400 and 0.48 results in the numbers 182136. As 0.48 is just 48/100, let's take a decimal number between 350 and 400.
If the number is 370.1, for example, we can write it as 3701/10 because it has one decimal point.
Our denominator will be 1000, because both the denominators are 100 and 10, which is equivalent three decimal places to the left of the result when we multiply 48/100 by 3701/10.
The result provided to us should therefore be written as 182.136, with the decimal point moved three spaces to the left.
The decimal point is to be placed three places to the left.
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A line has a slope of 2 and includes the points (
–
7,
–
10) and (0,j). What is the value of j?
Answer:
j = 4
Step-by-step explanation:
calculate the slope of the line passing through the goven points and equate to 2
calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 7, - 10 ) and (x₂, y₂ ) = (0, j )
m = [tex]\frac{j-(-10)}{0-(-7)}[/tex] = [tex]\frac{j+10}{0+7}[/tex] = [tex]\frac{j+10}{7}[/tex] then equating gives
[tex]\frac{j+10}{7}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )
j + 10 = 14 ( subtract 10 from both sides )
j = 4
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 5 ≤ x ≤9.
7
8
9
6
x
4
5
f(x)
4
8
16
32
64
medically explained PAINL X
128
Deltal/ath
The average rate of change, in simplest form, is -2/5.
What is average rate ?
Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.
The rate of change of the function is its gradient or slope.
The formula for calculating the gradient of a function is expressed as:
[tex]m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$[/tex]
Using the coordinate points from the table (0,41) and (15,35)
Substitute the coordinate into the expression:
[tex]$$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$[/tex]
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