Coordinates of point B is (-2,-6) which gives the slope of 4/3.
What is slope ?The slope formula is m=(y2-y1)/(x2-x1)
4/3 = (xy-2y-xy)/ (-4-2)
4/3 = -2y/ -6
2y = 12
y = 6
by comparing numerators x = -2
The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. The origin for this usage is unknown, however it may be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line.
The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio may occasionally be written as a quotient ("rise over run").
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Find an equation of the line that satisfies the given conditions. Through (4, 9); parallel to the line passing through (5, 7) and (1, 3)
Answer:
y = 1x + 5
Step-by-step explanation:
First, lets calculate the equation of the line passing through (5, 7) and (1, 3) in slope-intercept form
The general equation of a line in slope-intercept form is
y = mx + b
where m = slope and b = y-intercept is rise over run =
[tex]m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}[/tex]
where (x₁, y₁) and (x₂, y₂) are any two points on the line
For the line passing through (5, 7) and (1, 3) , the slope
[tex]m = \dfrac{3 - 7}{1 - 5}[/tex]
[tex]m = \dfrac{-4}{-4}[/tex]
[tex]m = 1[/tex]
To compute the y-intercept, plug in any of the two points x and y values and solve for b
Take point 5, 7 ==> when x = 5, y must be 7
We get
7 = 1 x 5 + b
7 = 5 + b
2 = b (subtract 5 from both sides)
b = 2
So the equation of the line is
y = 1x + 2
A line parallel to another line will have the same slope and a different y-intercept
Therefore a parallel line will also have slope 1 and its equation will be of the form
y = 1x + b
To calculate this b, plug in the point (4, 9) into the equation and solve for b
9 = 1 x 4 + b
9 = 4 + b
b = 5
So the equation is
y = 1x + 5
Graph attached shows the real picture
Which expression is equivalent to (5x^−5y^3)^
−2?
Solve for x
x + k
——- = r
m
So, we are to solve for x in:
[tex] \frac{x + k}{m} = r[/tex]
Cross multiply the above to solve for x
[tex]x + k = mr[/tex]
Now, collect like terms to find x
Therefore: [tex]x = mr - k[/tex]
A school's K-Pop club is learning a new dance to a Korean pop song. They pay the dance teacher from their bank account, which showed three changes this week. • First, a $60 withdrawal was represented using the number -60. • The second change was the opposite of the first. • The third change was the opposite of the second. What number represents the third change made to the account?
The number which represents the third change made to the account according to the task content is; -60.
What number represents the third change made to the account?According to the task content, the second change was the opposite of the first, -60.
Hence, the second change is; +60 which is the additive inverse.
Ultimately, since the third change was the opposite of the second, it follows that the third change is; -60.
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Answer:
Step-by-step explanation:
Answer this volume based Question. I will make you brainliest + 50 points
Answer:
1.3 m
Step-by-step explanation:
Given dimensions of rectangle ABCD:
width = xlength = (x + 4)[tex]\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\\\implies \sf Area\:of\:ABCD& = x(x+4)\\& = x^2+4x \end{aligned}[/tex]
Given dimensions of isosceles triangle ADE:
Base = DE = xHeight = AD = x[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of $\triangle$ADE}& = \dfrac{1}{2} \cdot x \cdot x\\& = \dfrac{1}{2}x^2\end{aligned}[/tex]
As the area of the portion remaining when ADE is cut off from ABCE is 6 m²:
[tex]\begin{aligned}\sf ABCD-ADE & = 6\\\implies x^2+4x-\dfrac{1}{2}x^2 & = 6\\2x^2+8x-x^2 & = 12\\x^2+8x & = 12\\x^2+8x-12 & = 0\end{aligned}[/tex]
Solve the found quadratic equation by completing the square.
Move the constant to the right side of the equation:
[tex]\implies x^2+8x-12+12=0+12[/tex]
[tex]\implies x^2+8x=12[/tex]
Add the square of half the coefficient of x to both sides:
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=12+\left(\dfrac{8}{2}\right)^2[/tex]
Simplify:
[tex]\implies x^2+8x+4^2=12+4^2[/tex]
[tex]\implies x^2+8x+16=12+16[/tex]
[tex]\implies x^2+8x+16=28[/tex]
Factor the perfect square trinomial on the left side:
[tex]\implies (x+4)^2=28[/tex]
Square root both sides:
[tex]\implies \sqrt{(x+4)^2}=\sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{28}[/tex]
[tex]\implies x+4=\pm \sqrt{4 \cdot 7}[/tex]
[tex]\implies x+4=\pm \sqrt{4}\sqrt{7}[/tex]
[tex]\implies x+4=\pm 2\sqrt{7}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm 2\sqrt{7}[/tex]
As length is positive:
[tex]\implies x=-4+ 2\sqrt{7}\:\:\sf only[/tex]
Taking the value of √7 = 2.65:
[tex]\implies x \approx -4+ 2(2.65)[/tex]
[tex]\implies x \approx -4+5.3[/tex]
[tex]\implies x \approx 1.3[/tex]
Therefore, the width of the sheet is 1.3 m.
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What is the probability of getting a 10 or a jack from a deck of pocker cards
Answer:
The probability of both outcomes is equal i.e. 50% or 1/2. So, the probability of an event is Favorable outcomes/Total number of outcomes. It is denoted with the parenthesis i.e. P(Event).
Answer: 8/52
Step-by-step explanation:
there are 4 jacks in a deck of 52 cards, and also 4 tens. The combined probability of picking a 10 or jack is 8 in 52, which is 15.38%.
A car travels at an average speed of 52 miles per hour How many miles does it travel in 4 hours and 45 minutes
Answer: 247 miles.
Step-by-step explanation: First, we need to convert the 45 minutes into hours. we know that 1 hour = 60 minutes. Dividing any number of minutes by sixty gives us the number of hours along with the remaining minutes if there are any. so 45/60 simplifies to 3/4. Now for the miles, it's given that the speed is 52 mph. So we can put into the expression 52(4+3/4)= total miles. Once we distribute 52, we get 208 + 39, which equals to 247.
Answer:
247
Step-by-step explanation:
52÷60 mins x 45= 39 miles for 45 mins
45 mins + 4 x 52 =247
95 +94/2
= 94.5
A. Identify and explain the error in this scenario.
B. Correct the error.
Answer:
did not do order of operations and added first
94/2 remember order of operations
94/2 = 47
47+95 = 142
There you go :)
24.56 divided by 1.2
Answer:20.4
Step-by-step explanation:
Change the divisor 1.2 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.
please help it's matic
Answer:
6
Step-by-step explanation:
If there are 4 in each tank, that means there are 2 tanks. 4-2 = 2. 8-2 = 6.
Answer:
There 30 fish left at the store
Step-by-step explanation:
There are 8 tanks
If there are 4 fish in each tank, the total would be 32 fish. If Dalia buys 2 fish, you would do 32 - 2 = 30 fish.
Hope this helped!! ( >ᴗ<) xx
at the valentines day dance the sponsors handed out candy kisses to each person entering the dance. one group received a total of 20 candy kisses as they entered. another group of dancers received a total of 52 candy kisses. each person received the same amount of candy. what was the greatest possible number of candy kisses each person could have received
the maximum number of candy kisses that each person could have received is 4.
What was the greatest possible number of candy kisses each person could have received?We know that each person receives the same number of candy.
Now, one group of K people receives 20 candy.Another group of N people receives 52 candy.Then the quotients between the number of candy and the number of people should give the same value:
20/K = 52/N
Let's find the common factors between 20 and 52, to do so, we need to rewrite the two numbers as a product of prime factors:
20 = 2*10 = 2*2*5
52 = 2*26 = 2*2*13
The greatest common factor between 20 and 52 is (2*2) = 4
Then, if each person receives 4 candy:
The group that receives 20 candy:
20/K = 4
20/4 = k = 5
That group has 5 people.
The group that receives 52 candy:
52/N = 4
52/4 = N = 13
This group has 13 people.
Then the maximum number of candy kisses that each person could have received is 4.
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Which expression is equivalent to one fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x?
negative two fifteenths times x minus two
two fifteenths times x minus two
negative two over fifteen times x plus two
one and one third times x plus two
The equivalent expression is,
''Negative two over fifteen times x plus two''
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
We have to given the expression as;
''One fifth times the quantity 3 times x plus 10 end quantity minus 11 over 15 times x''
Now, Write in mathematical expression as,
⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]
We can solve it as,
⇒ [tex]\frac{1}{5} (3x + 10 ) - \frac{11}{15} x[/tex]
⇒ [tex]\frac{3}{5} x + \frac{10}{5} - \frac{11}{15} x[/tex]
⇒ [tex]\frac{3}{5} x - \frac{11}{15} x+ 2[/tex]
⇒ [tex]\frac{-2}{15} x + 2[/tex]
Hence, It can be written as;
⇒ Negative two over fifteen times x plus two.
Therefore, The equivalent expression is,
''Negative two over fifteen times x plus two''.
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In a conditional statement where do you find the conclusion
Beinggreat78 is a goddess fr
Answer:
C.
Step-by-step explanation:
[tex]\frac{3}{5} = 3 \div 5 = 0.6[/tex]
Answer: A
Step-by-step explanation:
0.6 converted to a fraction is 1/6
Given: g(x)=√x-4 and h(x) = 2x - 8.
What is g(h(10))?
O 2√2
√6
√6-8
02√6-8
The value of g(h(10)) is 2√2. the correct option is A.
Given that the functions are g(x)=√x-4 and h(x)=2x-8.
A function is defined as the relationship between a set of inputs where each input has an output.
Firstly, we will find the value of h(10) by substituting x=10 in the function h(x)=2x-8.
h(10)=2(10)-8
h(10)=20-8
h(10)=12
Now, we will find g(h(10)) where h(10)=12.
By substituting h(10)=12 in g(h(10)), we get
g(h(10))=g(12).
Further, we will find g(12) by substituting x=12 in the function g(x)=√x-4, we get
g(12)=√(12-4)
g(12)=√8
g(12)=2√2
Hence, the value of function g(h(10)) when g(x)=√x-4 and h(x)=2x-8 is 2√2.
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Can someone help me please
Answer: D': (-7, -1)
E': (-6, -1)
F': (-6, -10)
G': (-7, -10)
Step-by-step explanation:
In a 90 degree clockwise rotation about the origin for this rectangle, the x and y coordinates of the rectangle's edges are swapped, but the y-coordinates are negated. This is because the transformation is happening to the 3rd quadrant, where both the x and y values will be negative.
D: (1, -7) ==> (-7, 1) ==> D': (-7, -1)
E: (1, -6) ==> (-6, 1) ==> E': (-6, -1)
F: (10, -6) ==> (-6, 10) ==> F': (-6, -10)
G: (10, -7) ==> (-7, 10) ==> G': (-7, -10)
Please answer this question asap!! And give an explanation on how you got the answer!
Answer:-5
Step-by-step explanation:
5*5*5=125
-5*-5=25
25*-5= -125
or
3√-125
An aeroplane when flying at a height of 2000m from the ground passes vertically above a helicopter at an instant when their angles of elevation from the same point on the ground are 60⁰ and 30 respectively. Find the vertical distance of the helicopter from the ground.
The vertical distance of helicopter from the ground is equal to 2000 / 3 m.
Let the distance between the two planes A and B be x.
In △ ADC, we get that:
tan 60° = 2000 / y
√3 = 2000 / y ...(1)
Now, in △ BCD, we get that:
tan 30° = 2000 - x / y
1 / √3 = (2000 - x) / y ... (2)
Divide (1) from (2):
3 = 2000 / (2000 - x)
6000 - 3 x = 2000
3 x = 6000 - 2000
3 x = 4000
x = 4000 / 3
(2000 - x) = 2000 - 4000/3 = 2000 / 3
Therefore, the vertical distance of helicopter from the ground is equal to 2000 / 3 m.
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An addition equation to find the volume of this
An addition equation for calculating volume is = 12 units cube.
What is addition equation?The fundamental addition formula, sometimes known as the mathematical equation of addition, is as follows. The addends are 5 and 3, and the sum is 8. It should be noted that an addition fact can have many addends. For instance, 5 + 7 + 9 + 3 = 24.
What is a shape's volume?Volume refers to the amount of space occupied by a 3D shape. The volume of a shape can be calculated by multiplying its height, breadth, and depth. If somehow the shape is made using cubic cm blocks, the volume can be calculated by counting the cubes.
According to the given Data:Total no. of cubes = 12
length of the one cube = 1 unit
So,
volume of the given prism = l x b x h
volume of one prism = 1 unit^3
There are 12 cube are present on adding all the units we get
volume of total cubes are = 12 unit cube.
So,
The volume is = 12 unit cube.
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-1/2n = -8 PLEASEEEEEEE
Answer:
Step-by-step explanation:
D.16
Find a. (f+g)(x) b. (f+g)(6).
f(x)=3x2−x−6, g(x)=x−4
We get that the value of (f + g)(x) is 3 x² - 2 x - 10 and (f + g)(6) is 86.
We are given the two functions:
f(x) = 3 x² - x - 6
g(x) = x - 4
We need to find:
(f + g)(x)
= f(x) +g(x)
= 3 x² - x - 6 + x - 4
= 3 x² - 2 x - 10
Now we have to find:
(f + g)(6).
Put x = 6, we get that:
= 3 (6)² - 2 (6) - 10
= 108 - 12 - 10
= 108 - 22
= 86
Therefore, we get that the value of (f + g)(x) is 3 x² - 2 x - 10 and (f + g)(6) is 86.
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2)
Ms Seow has an envelope which is 15 cm by 7cm.
What is the perimeter of the envelope?
Find the measure of RUS.
Answer:
Step-by-step explanation:
the answer is 23.
Answer:
C
Step-by-step explanation:
The Jackman & Murohv partnership has the following balances on December 31, 2024:
H: (Click the icon to view the balances.)
Jackman and Murphy share profits 1:3, respectively. Jackman and Murphy decide to liquidate the partnership. Journalize the sale of the non-cash assets for $59,000, the payment of the liabilities.
and the payment to the partners. Assume Murphy contributes cash equal to the capital deficiencv. (Record debits first. then credits. Select the explanation on the last line of the journal entry table.)
Answer:
Step-by-step explanation:
find a degree 3 polynomial having zeros, -6, 2, and 7 and the coefficient of x^3=1
The polynomial of degree 3 is given by x³-3x²-40x+84.
The degree of a polynomial is the highest degree of the variables present with non-zero coefficients.
For example the polynomial [tex]{\displaystyle 2x^{2}y^{3}+8x+10}[/tex] has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
A degree 3 polynomial having zeros α,β and γ and the coefficient of x³ equal a is
a(x-α)(x-β)(x-γ)
So the given zeroes of the polynomial are -6,8 and 7 and the coefficient of x³ is 1. So the desired polynomial is given by:
1(x+6)(x-2)(x-7)
=(x²-4x-12)(x-7)
=x³-3x²-40x+84
Hence the polynomial of degree 3 is given by x³-3x²-40x+84.
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The sum of two numbers is 15. Using x to represent the smaller of the two numbers, translate "the sum of twice the smaller number and two more than the larger num ber" into a variable expression. Then simplify.
Answer:
Step-by-step explanation: Let x be the smaller and y be the largest number.
Since x+y=13, we deduce y=13-x
Now, for the translation: "two more than the larger number" is y+2 , while "twice the smaller" is 2x
Their sum is y+2+2x
And since we know that y=13-x, we have y+2+2x=13-x+2+2=15+x
when you get on the bus to go to school there are x people on the bus. at the next stop 6 people get off the bus. write an expression to represent the remaining number of people on the bus after the first stop.
Answer:
x-6
Step-by-step explanation:
Alex wants to make a cake and has 50 1/2 cups of sugar, he needs 1/4 of a cup to make 1 cake. How many cakes can he make?
Alex makes 202 cakes with 50 (1/2) cups of sugar.
Given,
Quantity of sugar Alex with him = 50 (1/2) cups
Quantity of sugar needed for making 1 cake = 1/4 cup
We have to find the number of cakes Alex can make with 50 (1/2) cups of sugar.
Number of cakes = Quantity of sugar Alex with him / Quantity of sugar needed for making 1 cake
Number of cakes = 50 (1/2) ÷ 1/4
Number of cakes = 50 ÷ 0.25 + 0.5 ÷ 0.25
Number of cakes = 200 + 2
Number of cakes = 202
That is, Alex can make 202 cakes with 50 (1/2) cups of sugar.
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Alexandra is ordering a taxi from an online taxi service. The taxi charges $2 just for
the pickup and then an additional $1.75 per mile driven. How much would a taxi ride
cost if Alexandra is riding for 9 miles? How much would a taxi ride cost that is m
miles long?
Answer:$17.75
Step-by-step explanation:
2+1.75m
2+1.75(9)
2+15.75
17.75
4. How many terms are there in the following sequence?
19, 21, 23, ..., 53
The answer is______ terms.
Please show work
Answer:
The answer is this sequence has 18 terms
Step-by-step explanation:
As you can see, the term-to-term rule of the sequence is +2
We can use that to calculate the amount of terms.
First, calculate the distance between the first and last terms
53 - 19 = 34
Then, use this and divide the term-to-term rule.
34/ 2 = 17
Remember to add 1 at the end :)
17 + 1 = 18
There are 18 terms in this sequence.
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