An equation in point-slope form for this line is y=6x+5.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Given that;
Point on a line (-1,-1)
Slope of the line 6
Now, substituting the values in the general formula of line
y+1=6(x+1)
y+1=6x+6
y=6x+5
Therefore, the equation with the given slope will be y=6x+5.
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(Hari Bahadur sold a watch after allowing 20% discount and then adding 13% VAT. If the discount amount is Rs.192 more than VAT amount then find the marked price and selling price of the watch.)
Answer: Let's assume that the marked price of the watch is M.
The discount amount would be 20% of M, which can be calculated as:
0.2 * M = 0.2M
The selling price after the discount would be:
M - 0.2M = 0.8M
The VAT amount would be 13% of the selling price after the discount, which can be calculated as:
0.13 * 0.8M = 0.104M
Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:
0.2M = 0.104M + 192
0.096M = 192
M = 192 / 0.096 = 2000
So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.
Step-by-step explanation:
Consider function f. f(x)=square x-1 which graph represents f?
The graph that represents the function f(x) = sqrt(x - 1) is given by the following option:
C. Graph Y.
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the function is defined as f(x) = sqrt(x - 1), meaning that the parent square root function was moved one unit right, and thus the correct graph is given by graph Y.
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Linda and Rob charged a $67.44 restaurant bill on their credit card. They gave the card to the waitress, who accidentally transposed two digits and charged them $76.44. They did not notice this until they received their statement later that month. Their card has an 18% APR.
They plan to pay their monthly statement amount in full, but they need to deduct the amount they were overcharged, plus the finance charge that was based on the incorrect amount. If the overcharged amount was on their statement for 18 of the 31-day billing cycle, how much should they deduct from this monthly statement, including the amount they were overcharged?
Answer:
Step-by-step explanation:
a
All of the following constructions start with a line segment except...
O constructing a 45° angle
O constructing a 30° angle
O constructing congruent angles
• constructing equilateral triangles
All of the aforementioned structures, with the exception of creating equilateral triangles, begin with a line segment.
What is meant by line segment?The component of a line in a geometric shape, such as a triangle, circle, quadrilateral, etc., that is bordered by two (2) distinct points and usually has a definite length is referred to as a line segment.
An equilateral triangle is a particular kind of triangle with equal side lengths and identical angles at each of its three (3) internal sides.
A line segment serves as the foundation for the following angles and lines in geometry:
The process of creating a line perpendicular to a point on a line.
The creation of a 45-degree angle (45°).
The creation of a 30-degree (30-degree) angle.
Since an equilateral triangle has equal side lengths and all three of its interior angles are equal, we can reasonably and logically conclude that its construction does not begin with a line segment.
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h(n) =4n+2
g(n)= n³ +5 - 2n
Find 3h(n) + 2g(n)
The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.
Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-
E = 3h(n) + 2g(n)
E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)
E = 12n + 6 + 2n³ + 10 -4n
E = 2n³ + 8n + 6
Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.
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Suppose X is a random variable with mean X and standard deviation oXSuppose Y is a random variable with mean Y and standard deviation oY. The mean of X + Y is:a. MX+MYb.uX/oX) + (Y /oY). c. 1X+uY, but only if X and Y are independent. d (uX/oX) + (Y/oY), but only if X and Y are independent.
The answer is (a) MX + MY. Whether or not X and Y are independent, we cannot simplify (a) or (b) further.
The mean of X + Y is:
E(X + Y) = E(X) + E(Y)
So the answer is not (a) or (b).
(c) is incorrect because the formula given is only true if X and Y are independent, but no such assumption is given in the problem.
(d) is also incorrect because we cannot simply divide the means by the standard deviations to get the standard normal variables, especially when the variables X and Y have different means.
Therefore, the answer is (a) MX + MY.
Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.
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ons
Write the equation for this relationship and identify the constant of proportionality (or k value).
X
Y
28 36 40
21
27
30
56
42
There are two routes you can take from your house to the store.Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long. How much longer is Main Street thank Oak Street
The Main Street is 1/12 of a mile longer than the Oak Street
How much longer is Main Street thank Oak StreetFrom the question, we have the following parameters that can be used in our computation:
Main Street is 1/3 of a mile long. Oak Street is 1/4 of a mile long.Using the above as a guide, we have the following:
Difference = Main Street - Oak Street
substitute the known values in the above equation, so, we have the following representation
Difference = 1/3 - 1/4
Evaluate the difference
Difference = 1/12
Hence, the difference is 1/12 of a mile
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which point is a solution for the system of inequalities shown in the graph below?
Answer: The answer to your problem is choice b
Given that [tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex] , show that z lies on the x-axis.
The proof that z lies on the x-axis is shown below
How to show that z lies on the x-axis.For z to lie on the x-axis, then the coordinate must be represented as (x, 0)
Given that
[tex]\frac{|z - 5i|}{|z + 5i|} = 1[/tex]
We start by simplifying the given expression using the definition of the modulus of a complex number:
So, we have
[tex]\frac{|z - 5i|}{|z + 5i|} = \frac{\sqrt{(x - 0)^2 + (y - 5)^2}}{\sqrt{(x - 0)^2 + (y + 5)^2}} = 1[/tex]
Where
z = x + yi or z = (x, y)
Squaring both sides of the equation above, we obtain:
[tex]\frac{(x - 0)^2 + (y - 5)^2}{(x - 0)^2 + (y + 5)^2} = 1[/tex]
This gives
[tex]\frac{x^2 + (y - 5)^2}{x^2 + (y + 5)^2} = 1[/tex]
By comparison, we have
[tex](y + 5)^2 = (y - 5)^2[/tex]
Set y = 0 to test the equation
So, we have
[tex](0 + 5)^2 = (0 - 5)^2[/tex]
25 = 25 --- true
The equation is true for y = 0
This means that
z = (x, 0)
Hence, z lies on the x-axis
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PLEASE HELP ASAP
Circular pizza pies at Pat's Pizza's come in 10-inch and 16-inch diameters.
Which is closest to the difference in the areas of the pizza pies?
A
129.12 inches
B
183.46 inches
C
122.46inches
D
142.96 inches
Answer:
C
Step-by-step explanation:
The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and pi times (16/2)^2=201.06. 201.06-78.54 = about 122.52, which is closest to 122.46, or C.
What is the circumference of this circle?
Use π = 3.14
6 cm
Dodi has 2 cups of liquid starch and will use the entire amount. She plans to store the slime in containers that each hold a maximum of 6 fluid ounces how many containers will she need (hint 2 cups = 16 fluid ounces
The number of containers needed is given as follows:
3 containers.
How to obtain the number of containers needed?The number of containers needed is obtained applying the proportions in the context of this problem.
She has 2 cups, hence the number of fluid ounces that she has is given as follows:
16 fluid ounces.
Each container holds a total of 6 fluid ounces, hence the number of containers needed is given as follows:
16/6 = 3 containers.
(rounding up).
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pleas help me ill give you brainliest
Answer:
This is a Right Triangle because the last angle is 90 degrees.
in a certain test, there is a multiple choice question with the possible answers a, b, c, d, and e. By randomly guessing, the chances of getting the correct answer are stated as "1 in 5."Express the indicated degree of likelihood a a probability value between 0 and 1 inclusive
(b) At the beginning of the term, Caroline bought p notebooks and Bert bought 5 notebooks less than Caroline. During the term, Caroline gave 2 of her notebooks to her sister. Caroline then had twice as many notebooks as Bert. By writing a suitable equation, calculate the number of notebooks Caroline now has.
The number of Caroline's textbook is 8
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.
Represent the Notebook bought by Bert as q
q = p-5
p-2= 2q
p = 2q +2
substitute 2q +2
q = 2q+2-5
2q-q = 3
q = 3
substitute 3 for q
3 = p-5
p = 5+3
p= 8
Therefore Caroline's number of notebook is 8
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Can someone please help me do this
The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).
How to determine the image of a triangle set on Cartesian plane
Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:
Reflection over the y-axis:
(x, y) → (- x, y)
Dilation centered at the origin with a scale factor of 2:
(x, y) → (2 · x, 2 · y)
If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:
Reflection over the y-axis
A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)
Dilation centered at the origin with a scale factor of 2
A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)
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Verify the Identity.
Step-by-step explanation:
[tex] \frac{ \tan( \alpha ) }{1 + \sec( \alpha ) } = - \cot( \alpha ) + \csc( \alpha ) [/tex]
Multiply by 1-sec(a)
[tex] \frac{ \tan( \alpha ) (1 - \sec( \alpha ) }{(1 + \sec( \alpha ) )(1 - \sec( \alpha ) )} [/tex]
[tex] \frac{ \tan( \alpha ) - \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{1 - \sec {}^{2} ( \\ \alpha ) } - \frac{ \tan( \alpha ) \sec( \alpha ) }{1 - \sec {}^{2} ( \alpha ) } [/tex]
[tex] \frac{ \tan( \alpha ) }{ - \tan {}^{2} ( \alpha ) } + \frac{ \tan( \alpha ) \sec( \alpha ) }{ \tan {}^{2} ( \alpha ) } [/tex]
[tex] - \frac{1}{ \tan( \alpha ) } + \frac{ \sec( \alpha ) }{ \tan( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \frac{ \frac{1}{ \cos( \alpha ) } }{ \frac{ \sin( \alpha ) }{ \cos( \alpha ) } } [/tex]
[tex] - \cot( \alpha ) + \frac{1}{ \sin( \alpha ) } [/tex]
[tex] - \cot( \alpha ) + \csc( \alpha ) [/tex]
A dolphin is at the surface of the ocean.What is the dolphin’s elevation?
Answer:
0
Step-by-step explanation:
surface of ocean = sea level = elevation of zero
Given parallelogram abcd, in order to prove that opposite sides are congruent, what additional segments or points will you need?.
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are congruent. To prove this, you would need to show that the following two conditions are true:
The length of one pair of opposite sides is equal.
The two pairs of opposite sides are parallel.
To show these two conditions, you may need additional segments or points such as:
Perpendicular lines or segments to the sides to help show the sides are parallel.
Diagonal segments to help show that the parallelogram is a rectangle and that the sides are equal in length.
By showing these two conditions, you can conclude that the opposite sides of a parallelogram are congruent.
09:42 Man 13 Feb
A school carried out a report on their Year 11 students to see the impact of doing homework
regularly on final grades achieved in maths. The results are presented in the frequency tree.
Get grade B or higher
Do homework
Complete the tree.
75
6
Don't do
homework
regularly
60
b
D
Get lower than grade B
Get grade B or higher
Get lower than grade B
The percentage of students who are doing their homework regularly is 75%.
What is a Universal Set?A universal set in set theory is a set that includes itself as well as all other items. A universal set's nonexistence in set theory as it is typically expressed can be demonstrated in a number of different ways. However, a universal set is a part of several unconventional set theory variations.
To find the percentage of students who are doing their homework regularly,
We find the total students and this is 75 + 5 = 80 students
The percentage is 60/80 * 100
= 75%
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Please help me with this question
Answer:
120°
Step-by-step explanation:
360 / 12
30 X (5-1)
30 X 4= 120°
Solve for x.
3/4x + 3 = 27
Answer:
x = 32
Step-by-step explanation:
First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.
3/4x = 27-3
Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3
0.75x = 24
Now we can divide 24 by 0.75 to find x
x = 32
x = 32.
Step-by-step explanation:1. Write the expression.[tex]\frac{3}{4} x+3=27[/tex]
2. Subtract "3" from both sides of the equation.[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]
3. Divide by " [tex]\frac{3}{4}[/tex] " ob both sides of the equation.[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]
4. Verify the answer.If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!
[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]
That's correct!
5. Conclude.x = 32.
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Consider the two triangles. How can the triangles be proven similar by the SSS similarity theorem?
Answer:if their corresponding sides are proportional.
Step-by-step explanation:
Amy has three times as many Star Wars toys as Carly. Total they have 312 Star Wars toys. how many Star Wars toys does Amy have?
Answer:
the answer to this question is 936
does the equation y^2-y^2x = 6 describe y as a function of x
The equation y² - y²x = 6 can be describe as a function of x as:
y = √(6/(x - x)).
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
y² - y²x = 6
Taking y² as common.
y²(1 - x) = 6
Divide both sides with (1 - x).
y² = 6/(1 - x)
Square root on both sides.
y = √(6/(x - x))
This is a function of x.
Thus,
y = √(6/(x - x)) is a function of x.
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Please help me ASAP THANKS
Answer:
i think its 1 or 3 or 5 if not what i moslty think it is is (((( 4 )))
Step-by-step explanation:
i hope this helps may luck be with YOU! :)
A. 188.5in²
B. 94.25in²
C. 133.5in²
D. 149.25in²
Answer:B
Step-by-step explanation:
area of triangle is (10*11)/2=55
area of semicircle is
[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]
f(x) = x4 - 7x3 + 2x2 + 40x ; x-5
The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5
We need to find the value of f(5)
Plug x=5 in the above function
f(x) = x⁴ - 7x³ + 2x² + 40x
f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)
=625-875+50+200
=0
Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x
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Complete question is below
f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)
An ant can travel at a constant speed of 980 inches every 5 minutes.
How far does the ant travel in 1 minute?
At this rate, how far can the ant travel in 7 minutes?
The ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
What is cross multiplication?To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
Given that the ant can travel at a constant speed of 980 inches every 5 minutes.
Thus,
5 minutes = 980 inches
1 minute = x inches
Using cross multiplication method or Butterfly method of multiplication we have:
x = 980/5
x = 196 inches.
In 7 minutes the ant can travel:
(7)(196) = 1372 inches.
Hence, the ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.
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