Solution:
Factors of a number are defined as numbers that divide another number evenly or exactly without giving any remainder.
Hence,
The factors of 6 are the numbers that can divide 6 without any remainder.
[tex]\text{Factors of 6 =1,2,3,6}[/tex][tex]\begin{gathered} \text{Factors of 5=1,5} \\ \text{Factors of 20=1,2,4,5,10,20} \\ \text{Factors of 10=1,2,5,10} \\ \text{Factors of 30=1,2,3,5,6,10,15,30} \end{gathered}[/tex]From the above, we can deduce that the factors of 6 are also the factors of 30.
The corr
write a point slope equation for the line that has a slope 5and passes the point (6,22).
Solution:
The general equation of a line of slope m passing through a point A is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ (x_1,y_1)\text{ is the coordinate of the point A through which the line passes through} \end{gathered}[/tex]Given that the line has a slope of 5, and passes through the (6, 22), we have
[tex]\begin{gathered} m=5 \\ x_1=6 \\ y_1=22 \end{gathered}[/tex]thus,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-22=5(x-6) \end{gathered}[/tex]Hence, the point-slope equation for the line is expressed as
[tex]y-22=5(x-6)[/tex]
need help with this problem Its not the first one
Solution:
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints and contains every point on the line that is between its endpoints. The angle of rotational symmetry or angle of rotation is the smallest angle for which the figure can be rotated to coincide with itself.
A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation
Rotation of a line does not change the length of the line segments
Reflection does not preserve orientation.
Dilation (scaling), rotation, and translation (shift) do preserve it.
Hence,
The final answer is the THIRD OPTION
PLEASE HELP !!
When a right triangle with a hypotenuse of 1 is placed in the unit circle, which sides of the triangle correspond to the x- and y-coordinates?
The adjacent side of the central angle is the x-coordinate and the opposite side of the central angle is the y-coordinate
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The hypotenuse is the radius of a unit circle whose origin serves as its center. Allow being the central angle.
x = Adjacent Side of the central angle
y = Opposite Side of the Central angle
The x-coordinate is the central angle's adjacent side, while the y-coordinate is its opposite side.
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Given z1 = 5(cos 240° + isin 240°) and z2 = 15(cos 135° + isin 135°), what is the product of z1 and z2?
By multiplying z1 and z2, we get:
[tex]\begin{gathered} z1\times z2=5(cos240+isin240)15(cos135+isin135) \\ z1\times z2=75(cos240+isin240)(cos135+isin135) \end{gathered}[/tex]Applying the distributive property:
[tex]\begin{gathered} z1\times z2=75(cos240+\imaginaryI s\imaginaryI n240)(cos135+\imaginaryI s\imaginaryI n135) \\ z1\times z2=75(cos240\times cos135+cos240\times isin135+\mathrm{i}s\mathrm{i}n240\times cos135+\imaginaryI s\imaginaryI n240\times\imaginaryI s\imaginaryI n135) \\ z\times1z\times2=75(cos240\times cos135+cos240\times\imaginaryI s\imaginaryI n135+\imaginaryI s\imaginaryI n240\times cos135-s\imaginaryI n240\times s\imaginaryI n135) \end{gathered}[/tex]In order to simplify this, we can use the following trigonometric identities:
[tex]\begin{gathered} sin(\alpha+\beta)=sin(\alpha)cos(\beta)+cos(\alpha)sin(\beta) \\ cos(\alpha+\beta)=cos(\alpha)cos(\beta)-sin(\alpha)sin(\beta) \end{gathered}[/tex]By taking β as 135 and α as 240, we can write:
[tex]\begin{gathered} is\imaginaryI n(240+135)=isin(375)=is\imaginaryI n(240)s\imaginaryI n(135)+icos(240)s\imaginaryI n(135) \\ cos(240+135)=cos(375)=cos(240)cos(135)-s\imaginaryI n(240)s\imaginaryI n(135) \end{gathered}[/tex]Then, by grouping some terms of the expression, we get:
[tex]z\times1z\times2=75(cos(375)+isin(375))[/tex]375° is equivalent to 15° (375 - 360 = 15), then the product of z1 and z2 can be finally written as:
[tex]z1\times z2=75(cos(15)+\imaginaryI s\imaginaryI n(15))[/tex]Then, option A is the correct answer
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (0, 5) and point (3, -1) rounded to the nearest tenth?
The distance between the points is 6.7 units
What is distance?The distance between two points is the number of points between them
How to determine the distance?The points are given as
(0, 5) and (3, -1)
The distance formula is given as
d = √(x2 - x1)^2 + (y2 - y1)^2
Substitute the given points in the above distance formula
So, we have
d = √(0 - 3)^2 + (5 + 1)^2
Evaluate the difference and the sum
d = √(-3)^2 + 6^2
Evaluate the exponents
d = √9 + 36
Evaluate the sum
d = √45
This gives
d = 6.7
Hence, the distance is 6.7 units
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When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows
–
$30, which of these describes the transaction?
The next transaction statement can be described through option A) Thirty dollars was withdrawn if the next transaction on his statement shows –$30.
What is a Transaction statement?The term "Transaction Statement" refers to a statement that the lender may from time-to-time issue to any borrower, at the borrower's reasonable request or at the lender's option, listing the loans made, the inventory and accounts receivable they financed, as well as the terms and conditions of repayment.
A transaction can be said as a unit of work that is thus performed against a database. These transactions are units or mostly sequences of work that are accomplished in a logical order.
You can find your most recent statement via your bank branch because most banks allow you to generate statements through your online banking platform.
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Complete Question
When Levi deposited $40 into his savings account, his bank statement showed the transaction as $40.
If the next transaction on his statement shows –$30, which of these describes the transaction?
A) Thirty dollars was withdrawn
B) Money was neither deposited nor withdrawn
C) $30 was deposited
D) Seventy dollars was deposited
four inches of a (somewhat magnified ) ruler is shown. use the ruler to give the length of the gray bar, to the nearest sixteenth of an in. write answer as a mixed #. (simplify as much as possible)
We have the following:
We have that 4 is equal to 64/16
[tex]\frac{4\cdot16}{1\cdot16}=\frac{64}{16}[/tex]Thefore:
The bar is found in 2 and 15 more lines, each line is 1/16
[tex]\frac{2\cdot16}{1\cdot16}+\frac{15}{16}=\frac{32}{16}+\frac{15}{16}=\frac{47}{16}=2\frac{15}{16}[/tex]The manager of a new restaurant plans on ordering place-mats for the maximum number of diners, which is 279. Suppose the place-mats come in boxes of 24. Write a division expression that could be used to determine the number of boxes he needs to order.\
The number of boxes he needs to place = 279÷ 24 = 11.625 ≈ 12.
What is meant by division ?Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
In the aforementioned scenario, you would need to place four donuts in each group in order to divide 12 donuts into three similar groups. Thus, 12 divided by 3 will result in the number 4.
Dividend: Divisor x Quotient + Remainder
Given : Number of diners = 279
And the number of boxes = 24
Thus to find out the number of boxes he needs to place = 279÷ 24 = 11.625 ≈ 12.
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solve the equation for x
6x + 8 = 50
Answer:
x=7Step-by-step explanation:
To solve the equation for x, isolate it on one side of the equation.
6x+8=50Subtract by 8 from both sides.
6x+8-8=50-8
Solve.
50-8=42
6x=42
Divide by 6 from both sides.
6x/6=42/6
Solve.
Divide.
42/6=7
[tex]\Rightarrow \boxed{\sf{x=7}}[/tex]
Therefore, the solution is x=7, which is the correct answer.
I hope this helps, let me know if you have any questions.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6x + 8 = 50}[/tex]
[tex]\large\text{SUBTRACT \boxed{\textsf 8} to BOTH SIDES}[/tex]
[tex]\mathsf{6x + 8 - 8 = 50 - 8}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{8 - 8}} because it gives you 0}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{50 - 8}} because it help solve for the x-value}[/tex]
[tex]\mathsf{6x = 50 - 8}[/tex]
[tex]\large\text{New equation: } \mathsf{6x = 42}[/tex]
[tex]\large\text{DIVIDE \boxed{\mathsf{6}} to BOTH SIDES sides}[/tex]
[tex]\mathsf{\dfrac{6x}{6} = \dfrac{42}{6}}[/tex]
[tex]\large\text{CANCEL out: \boxed{\mathsf{\dfrac{6}{6}}} because it gives you 1}[/tex]
[tex]\large\text{KEEP: \boxed{\mathsf{\dfrac{42}{6}}} because it gives you the x-value}[/tex]
[tex]\mathsf{x = \dfrac{42}{6}}[/tex]
[tex]\mathsf{x = 7}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 7}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Need help with his practice problem, having troubleIt has an additional picture of a graph. Please help me with the graph, I will send a pic
Given the function:
[tex]f(x)=\sin (\frac{\pi x}{2})[/tex]To graph the function, we will identify the maximum and the minimum points
As we can see, the coefficient of the function = 1
So, the maximum will be at f = 1
And the minimum will be at f = -1
The period of the function will be as follows:
[tex]p=\frac{2\pi}{\frac{\pi}{2}}=4[/tex]So, beginning from the point (0, 0) then rise till we reach the maximum at ((1, 0) then complete the sine wave
The graph of the function will be as shown in the following picture:
What is the end behavior of the polynomial function?
Drag the choices into the boxes to correctly describe the end behavior of the function.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
f(x)=6x9−6x4−6 f(x)=−3x4−6x+4x−5
The end behavior of each function is given as follows:
f(x) = 6x^9 - 6x^4 - 4, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> ∞.f(x) = -3x^4 - 6x + 4x - 5, as x -> -∞, f(x) -> -∞ and as x -> ∞, f(x) -> -∞.End behavior of a functionThe end behavior of a function is given by the limits of the function as x goes to infinity, both negative and positive infinity, giving how the function behaves to the left and to the right of the graph.
For a polynomial function, only the term with the highest exponent is considered for the calculation of the limit, which is a standard rule for limits when x goes to infinity.
The first function is given by:
f(x) = 6x^9 - 6x^4 - 4.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ x^9 = (-∞)^9 = -∞.lim x -> ∞ x^9 = (∞)^9 = ∞.The second function is given by:
f(x) = -3x^4 - 6x + 4x - 5.
Then the limits that define the end behavior of the function are given as follows:
lim x -> -∞ -x^4 = -(-∞)^4 = -∞.lim x -> ∞ -x^4 = -(∞)^4 = -∞.A similar problem, also about the end behavior of a function, is presented at https://brainly.com/question/28884735
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jk has midpoint M(–17, 16.5) and endpoint K(–12, 4). What are the coordinates of endpoint J?
The coordinates of endpoint J which has the midpoint M(–17, 16.5) and endpoint K(–12, 4) is (-22,29)
Mid point:
Midpoint means the point that is in the middle of the line joining two points.
Given two points A (x)1, (y)1 and B (x)2, (y)2, the midpoint between A and B is given by,
M(x)3, (y)3 = [(x)1 + (x)2]/2, [(y)1 + (y)2]/2
where, M is the midpoint between A and B, and (x)3, (y)3 are its coordinates.
Given,
JK has midpoint M(–17, 16.5) and endpoint K(–12, 4).
Here we need to find the coordinates of endpoint J.
We know that formula of mid point through the given definition,
So let us consider
(x1, y1) = (a, b)
(x2, y2) = (-12,4)
Now we have to apply the values on the formula in order to solve it,
Therefore,
(-17, 16.5) = (a + (-12))/2 , (b + 4)/2
Compare the values individually, then we get,
-17 = (a - 12) / 2
-17 x 2 = a - 12
- 34 = a - 12
a = -34 + 12
a = -22
Similarly, when we take the second part,
16.5 = (b+4)/2
16.5 x 2 = b + 4
33 = b+ 4
b = 33 - 4
b = 29
Therefore, the coordinate end points of J is (-22, 29).
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Which is the solution to the equation: 0.435 + x = 0.92*x = 1.355O x= 0.595x = 0.4950 x = 0.485Send me a copy of my responses.
To answer this question, we need to subtract 0.435 to both sides of the equation as follows:
[tex]0.435-0.435+x=0.92-0.435\Rightarrow x=0.485_{}[/tex]Therefore, the solution for x in this equation is x = 0.485 (last option).
For triangle ABC, a = 7.7 , b = 17.0 , c = 12.7. Find m∠C.
The triangle can be drawn as shown below:
The Cosine Rule can be applied in this case. It is given to be:
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \cos C=\frac{a^2+b^2-c^2}{2ab} \end{gathered}[/tex]From the question, we have the following measures:
[tex]\begin{gathered} a=7.7 \\ b=17.0 \\ c=12.7 \end{gathered}[/tex]Therefore, we can substitute and solve as shown below:
[tex]\begin{gathered} \cos C=\frac{7.7^2+17.0^2-12.7^2}{2\times7.7\times17.0} \\ \cos C=\frac{187}{261.8} \\ \cos C=0.714 \end{gathered}[/tex]Therefore, the measure of angle C will be gotten to be:
[tex]\begin{gathered} C=\cos ^{-1}0.714 \\ m\angle C=44.4\degree \end{gathered}[/tex]The measure of angle C is 44.4°.
Which answer choice shows two hundred and two thousandths?A) 200.02B) 200.202C) 202.02D) 202.002
Given
two hundred two and two thousandths.
Answer
202.002
Option D is correct
8/11 when rounded is closer to 1 than 0? True False
Answer: False?
Step-by-step explanation:
Answer:
It is closer to [tex]1[/tex] than [tex]0[/tex], so the statement is True.
Step-by-step explanation:
Step 1: Finding the decimal form of [tex]\frac{8}{11}[/tex]
Upon simplification on a calculator, we can see that the exact value of [tex]\frac{8}{11}[/tex] is:
[tex]0.7272727273[/tex]
Let's round this to [tex]0.73[/tex] for an easier time.
Step 2: Identifying the value's difference from 1 and 0
We have found the value of the fraction to be [tex]0.73[/tex].
If we subtract the value from [tex]1[/tex], we get:
[tex]1-0.73\\=0.27[/tex]
If we find the difference between it and [tex]0[/tex], we get:
[tex]0.73-0\\=0.73[/tex]
As we can see, the value is [tex]0.27[/tex] units away from [tex]1[/tex], but is [tex]0.73[/tex] units away from [tex]0[/tex].
We can clearly see that it is closer to [tex]1[/tex], so the statement is True.
2^3= 8 is equivalent to log, C = D.cand D
we have
2^3= 8
Applying log both sides
log(2^3)=log(8)
Apply property of log
3log(2)=log(8)
therefore
C=3 and D=log(8)
A right triangle has an area of 54 ft2 and a hypotenuse of 25 ft long. What are the lengths of its other two sides?
By theorem we have the following:
[tex]h^2=a^2+b^2[/tex]And, we are given:
[tex]A=\frac{a\cdot b}{2}\Rightarrow2A=a\cdot b[/tex]Then:
[tex]\Rightarrow4A^2=a^2b^2\Rightarrow4A^2=a^2(h^2-a^2)[/tex][tex]\Rightarrow a^4-h^2a^2+4A^2=0[/tex]Now, we replace h and A:
[tex]a^4-(25)^2a^2+4(54)^2=0[/tex]And solve for a:
[tex]a^4-625a^2+11664=0[/tex]Then, the possible values for a are:
[tex]a=\begin{cases}a_1=-\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_2=\frac{29}{2}-\frac{\sqrt[]{409}}{2} \\ a_3=\frac{\sqrt[]{409}}{2}-\frac{29}{2} \\ a_4=\frac{29}{2}+\frac{\sqrt[]{409}}{2} \\ \end{cases}[/tex]We can see that a1, and a2 are not solutions, therefore a2 and a4 are.
So, the two possible b sides are then:
[tex]b_2=\sqrt[]{25^2-(\frac{29}{2}-\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_2\approx24.99[/tex]and:
[tex]b_4=\sqrt[^{}]{25^2-(\frac{29}{2}+\frac{\sqrt[]{409}}{2})^2}\Rightarrow b_{4\approx}15.50[/tex]So, the lengths of the two sides can be:
a = 4.38 and b = 24.99
or
a = 24.61 and b = 15.50
What is the slope of the line passing through (3, 0) and (4, 0) ?
A) 0
B) 3/4
C) 4/3
D) Undefined
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{0-0}{4-1} \\m=\frac{0}{1} \\m=0[/tex]
⇒0 divided by any number is 0
OPTION A IS THE ANSWER.
Answer:
A
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 0 ) and (x₂, y₂ ) = (4, 0 )
m = [tex]\frac{0-0}{4-3}[/tex] = [tex]\frac{0}{1}[/tex] = 0
standard form and contain only positive exponents 21c^10d^3+56c^6d^2-7c^2d------------------------------------------- 7c^2d
To solve this problem it is necessary to simplify the expression.
Step 1. Write the equation as a sum of homogeneous fractions:
[tex]\frac{21c^{10}d^3+56c^6d^2-7c^2d}{7c^2d}=\frac{21c^{10}d^3}{7c^2d}+\frac{56c^6d^2}{7c^2d}-\frac{7c^2d}{7c^2d}[/tex]Step 2. Simplify the obtained expressions:
[tex]\begin{gathered} \frac{21c^{10}d^3}{7c^2d}=3c^8d^2 \\ \frac{56c^6d^2}{7c^2d}=8c^4d \\ \frac{7c^2d}{7c^2d}=1 \end{gathered}[/tex]Step 3. Rewrite the expression using the simplified terms:
[tex]3c^8d^2+8c^4d-1[/tex]Which number line shows all the values of x that make the inequality - 3x +1 <7 true?A2-5-4--3-2-10123B.5in-4-3-2-1012.34С5-5-4-3-2-1012345D-4-3-2.12345
First let's solve the given inequality:-
[tex]\begin{gathered} -3x+1<7 \\ -3x<6 \\ x>-2 \end{gathered}[/tex]So the correct option is (D).
I couldn’t fit all the answers on the screen but the fourth option is all positive numbers
Answer:
Alternative C - All real numbers.
Step-by-step explanation:
The domain of an function is the set of all possible numbers which x can assume.
As we can see, we have no restrictions for x.
So, the domain is all real numbers.
Answer: Alternative C - all real numbers.
A certain television is advertised as a 5-inch TV. If the width of the TV is 4 inches, how many inches tall is the TV
Answer:
The TV is 3 inches tall.
[tex]3\text{ inches}[/tex]Explanation:
Given that the width of the TV is
[tex]4\text{ inches}[/tex]And the TV is 5 inch TV, which means its diagonal is;
[tex]d=5\text{ inches}[/tex]The height of the TV can be calculated using the Pythagoras Theorem;
[tex]\begin{gathered} c^2=a^2+b^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]substituting the diagonal and the width;
[tex]\begin{gathered} b=\sqrt[]{5^2-4^2} \\ b=\sqrt[]{25-16} \\ b=\sqrt[]{9} \\ b=3\text{ inches} \end{gathered}[/tex]Therefore, the TV is 3 inches tall.
[tex]3\text{ inches}[/tex]1. m/ASN = 63°
m/GSN =
The measure of angle ∠GSN is 27°.
What do we mean by angles?An angle is a figure in plane geometry that is created by two rays or lines that have a common endpoint. The Latin word "angulus," which means "corner," is the source of the English word "angle." The common endpoint of two rays is known as the vertex, and the two rays are referred to as the sides of an angle.So, a measure of ∠GSN:
The given angle ASG is 90° (Given)∠ASN = 63°Then, ∠GSN will be:
∠ASN + ∠GSN = ∠ASG63 + ∠GSN = 90∠GSN = 90 - 63∠GSN = 27°Therefore, the measure of angle ∠GSN is 27°.
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which variable has a set of zero pairs as a coefficients? (x or y)2x + 3y=20-2x + y=4
Answer:
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]Explanation:
We want to find the variable that has a set of zero pairs as a coefficients.
Zero pair is a pair of number that sum up to give zero.
Given the system of equation;
[tex]\begin{gathered} 2x+3y=20 \\ -2x+y=4 \end{gathered}[/tex]The pair of coefficient of x is;
[tex]\begin{gathered} 2\text{ and -2} \\ 2+-2=2-2=0 \end{gathered}[/tex]The pair of coefficient of y is;
[tex]\begin{gathered} 3\text{ and 1} \\ 3+1=4 \end{gathered}[/tex]So, since the coefficient of x sum up to give zero.
The variable that has a set of zero pairs as a coefficients is;
[tex]x[/tex]These two equations look very similar at first. What is the difference in how you would solve them?
`\frac{x-2}{3}=5` `\frac{x}{3}-2=5`
The difference in how we would solve them is that there is a different order of steps.
We are given two equations.The two equations look similar, but there is a different order of steps in order to solve them.The first equation is :(x-2)/3 = 5Multiply both the sides by 3.x-2 = 15Add 2 on both sides.x = 17Hence, the solution of the first equation is x = 17.The second equation is :(x/3)-2 = 5Add 2 on both sides.x/3 = 7Multiply both the sides by 3.x = 21Hence, the solution of the second equation is x = 21.To learn more about equations, visit :
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Find the length of the third side. If necessary, round to the nearest tenth.914
The given trinagle is a right angle triangle. let the missing side be x. To find x, we would apply the pythagorean theorem which is expressed as
hypotenuse^2 = one leg^2 + other leg^2
From the triangle,
hypotenuse = 14
one leg = 9
other leg = x
Thus, we have
[tex]\begin{gathered} 14^2=9^2+x^2 \\ 196=81+x^2 \\ x^2\text{ = 196 - 81 = 115} \\ x\text{ = }\sqrt[]{115} \\ x\text{ = 10.72} \end{gathered}[/tex]To the nearest tenth, the length of the third side is 10.7
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative. This eliminates all of the options except for d.
Sydney purchased a $50.00 gift for a baby shower. She uses a coupon that offers 20% off. How much will Sidney spend on the gift after the coupon?
From the scenario, the following are the pieces of information being given:
Price of Gift = $50
Discount Coupon used = 20% Off
Let's compute how much will Sidney spend on the gift after the coupon.
Step 1: Let's determine the equivalent amount of the discount.
[tex]\text{ Amount to be Discounted = Price of Gift x }\frac{Percentage\text{ of Discount}}{100}[/tex][tex]\text{ = \$50 x }\frac{20}{100}\text{ = \$50 x 0.20}[/tex][tex]\text{ = \$10}[/tex]Step 2: Let's deduct the equivalent amount of 20% to the actual price of the gift.
[tex]\text{ = \$50 - \$10}[/tex][tex]\text{ = \$40}[/tex]Therefore, Sydney will spend $40 on the gift after the coupon.
13. Write an equation of the line that passes through the points (-7, 6) and (3, -4 )in slope-
intercept form.
Answer:
Firstly we need to find the gradient of give two points as follows;
M= y
Answer:
Answer: y = -x - 1
Step-by-step explanation:
- Consider a straight line passing through (x, y) from the origin (0, 0). That line with a positive gradient of m and meets at a point (0, c) [y-intercept]
- It has a general equation as below;
[tex]{ \rm{y = mx + c}} \\ [/tex]
- So, consider the line given in our question; Let's find its slope m first;
[tex]{ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ [/tex]
- From the points given in the question, (-7, 6) and (3, -4)
x_1 is -7x_2 is 3y_1 is 6y_2 is -4[tex]{ \rm{m = \frac{ - 4 - 6}{3 - ( - 7)} }} \\ \\ { \rm{m = \frac{ - 10}{10} }} \\ \\ { \underline{ \rm{ \: m = - 1 \: }}}[/tex]
- Therefore, our equation so far is y = -x + c. Our line has a negative slope that means it slants from top to bottom, its origin is its y-intercept
- Consider point (3, -4);
[tex]{ \rm{y = - x + c}} \\ { \rm{ - 4 = - 3 + c}} \\ { \rm{c = - 1}}[/tex]
- y-intercept is -1
hence equation is y = -x - 1
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]