Answer:
For points : (2, 12) and (6, 11)
, option A. is correct.
For points : (6, –1) and (–3, –1), option B. is correct
Step-by-step explanation:
We are given points in both the questions and we need to find the slope.
Slope refers to steepness of curve .It is basically change in y with change in x.
For two points [tex]P\left ( x_1,y_1 \right )\,,\,Q\left ( x_2,y_2 \right )[/tex], slope of line PQ is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
For points : (2, 12) and (6, 11)
Let [tex]P\left ( x_1,y_1 \right )=(2, 12)\,,\,Q\left ( x_2,y_2 \right )=(6, 11)[/tex],
Slope is [tex]\frac{11-12}{6-2}=\frac{-1}{4}[/tex] i.e, - 1 over 4
So, option A. is correct.
For points : (6, –1) and (–3, –1)
Let [tex]P\left ( x_1,y_1 \right )=(6, -1)\,,\,Q\left ( x_2,y_2 \right )=(-3, -1)[/tex]
Slope is [tex]\frac{-1+1}{-3-6}=\frac{0}{-9}=0[/tex]
So, option B. is correct
The required slope of the lines with the given coordinates are as follow,
For first line option A. -1/4
For second line option B.0.
For the first set of coordinates of the line,
Points are (2, 12) and (6, 11)
let (x₁ , y₁ ) = (2, 12 )
( x₂ , y₂ ) = (6, 11 )
Slope of the line for the two coordinates (x₁ , y₁ ) = (2, 12 ) and
( x₂ , y₂ ) = (6, 11 ) is equal to
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value ,
m = ( 11 - 12 ) / ( 6 - 2 )
= -1 / 4
For the second set of coordinates of the line,
Points are (6, -1) and (-3, -1)
let (x₁ , y₁ ) = (6, -1 )
( x₂ , y₂ ) = (-3, -1 )
Slope of the line for the two coordinates (x₁ , y₁ ) = (6, -1 ) and
( x₂ , y₂ ) = (-3, -1 ) is equal to
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substitute the value ,
m = ( -1 - (-1) ) / ( -3 - 6 )
=0 / -9
= 0
Therefore, slope of the lines are option A. -1/4 and option B.0.
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What’s the measure of x
Answer:
[tex]\boxed {\sf x=66^o}[/tex]
Step-by-step explanation:
Apply the properties of a triangle:-
Where, the sum of all internal angles of a triangle is always equal to 180°.
[tex]\sf 90^o+x+24^o=180^o[/tex]
Combine like terms.
[tex]\sf x+90+24=180^o[/tex]
Add numbers.
[tex]\sf x+114=180^o[/tex]
Subtract 114 from both sides.
[tex]\sf x+114-114=180-114[/tex]
[tex]\sf x=66^o[/tex]
Translate (N-5)*7 turn into verbal statement
(N-5)*7
The N-5 is in parenthesis, so this needs to be done first, then the multiplication is done.
To say this verbally:
Subtract five from N, then multiply by seven.
Solve the formula for the specified variable
A=p+prt solve for r
Answer:
Step-by-step explanation:
The first step is to take p on both sides:
[tex]A - p = p + p*r*t - p[/tex]
On the right hand side, cancel p and -p, since [tex]p-p=0[/tex]. The equation will be:
[tex]A - p = p*r*t[/tex]
Then, divide both sides of the equation by p*t:
[tex]\frac{A-p}{p*t} = \frac{p*r*t}{p*t}[/tex]
On the right hand side, p*t can be cancelled:
[tex]\frac{A-p}{p*t} = r[/tex]
Answer:
r=A-p (the line is the bar so this is a-p over pt)
pt
Step-by-step explanation:
P + Prt = A
P r t=A −P isolate the term which contains r
P rt=A−P
divide pt by each side
The graph of which function(s) will contain the point (3, 6)?
y = x + 3
y = 3x
y = 2x
y = x + 6
Answer:
Step-by-step explanation:
y = x+3 because when : x = 3 y = 3+3=6
y=2x because when : x = 3 y = 2(3)=6
What is the circumference of a circle with an area of 50.24 cm²?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answer:
What is the circumference of a circle with an area of 50.24 cm²?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
25.12cm
Turn 3.45 into a mixed number write in simplest form
Answer:
3 whole number, 9/20
because if you multiply 20 by 3 and add it by 9 you get 69, so when you divide the 69/20, you get 3.45
- 3/4 (x + 2) = 6
the / is a fraction can someone help
find the coordinates of Z if Y is the midpoint of XZ , X( -10, 9) , and Y( -4,8)
Answer:
The coordinates of Z are (2,7)
Step-by-step explanation:
we know that
The formula to calculate the midpoint between two points is equal to
[tex]Y=(\frac{x1+x2}{2} ,\frac{y1+y2}{2})[/tex]
we have
X(-10,9),Y(-4,8)
Let
(x2,y2) ----> the coordinates of Z
substitute the values
[tex](-4,8)=(\frac{-10+x2}{2} ,\frac{9+y2}{2})[/tex]
Solve for x2
[tex]-4=(-10+x2)/2\\-8=-10+x2\\x2=10-8\\x2=2[/tex]
Solve for y2
[tex]8=(9+y2)/2\\16=9+y2\\y2=16-9\\y2=7[/tex]
therefore
The coordinates of Z are (2,7)
Answer: The required co-ordinates of Z are (2, 7).
Step-by-step explanation: Given that Y is the midpoint of XZ and the co-ordinates of X are (-10, 9) and the of Y are (-4, 8).
We are to find the co-ordinates of Z.
Let (a, b) represents the co-ordinates of the point Z.
We know that
the co-ordinates of the midpoint of a line segment with endpoints (x, y) and (z, w) are given by
[tex]\left(\dfrac{x+z}{2},\dfrac{y+w}{2}\right).[/tex]
So, according to the given information, we have
[tex]\left(\dfrac{-10+a}{2},\dfrac{9+b}{2}\right)=(-4,8)\\\\\\\Rightarrow \dfrac{-10+a}{2}=-4\\\\\Rightarrow -10+a=-8\\\\\Rightarrow a=-8+10\\\\\Rightarrow a=2[/tex]
and
[tex]\dfrac{9+b}{2}=8\\\\\Rightarrow 9+b=16\\\\\Rightarrow b=16-9\\\\\Rightarrow b=7.[/tex]
Thus, the required co-ordinates of Z are (2, 7).
Lyndi has started a home business
Write in slope-intercept form an equation of the line that passes through the points (−5,−3) and (3,−11)
Slope intercept form is y=-x-8.
PLEASE HELP ME!! I DO NOT UNDERSTAND PLEASE SHOW WORK THANK YOU!!
Answer:
= 10x² + 9x³
Step-by-step explanation:
I'm assuming you mean question 19
3x² + 5x³ + 7x² + 4x³ (rearrange to group like terms)
=3x² + 7x² + 5x³ + 4x³ (factor out common powers)
= (3+7)x² + (5+4)x³
= 10x² + 9x³
Rewrite the following without an exponent. (-2)^2
Answer:
(-2)(-2) or 4
Step-by-step explanation:
[tex](-2)^2=4[/tex]
What is an exponent?"It is the number of times a number is multiplied by itself. "
For given question,
We have been given a number [tex](-2)^2[/tex]
We need to write given number without exponent.
[tex](-2)^2\\=(-2)\times (-2)\\=4[/tex]
Therefore, [tex](-2)^2=4[/tex]
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[2+(-4)]+5-[(-11)x(-2)]-(-7)
Answer: -12
Step-by-step explanation:
[2+(-4)] becomes (2-4), or -2, and 5-[(-11)x(-2)]-(-7) becomes 5-22+7, so the entire thing is -2+5-22+7, so it is -12.
The given expression [2+(-4)]+5-[(-11)x(-2)]-(-7) simplifies to -12.
To simplify the given expression, we follow the order of operations (PEMDAS/BODMAS):
Step 1: Evaluate the innermost parentheses:
[2 + (-4)] + 5 - [(-11) x (-2)] - (-7)
[2 - 4] + 5 - [(-11) x (-2)] - (-7)
Step 2: Complete the operations inside the brackets:
[-2] + 5 - [22] - (-7)
Step 3: Simplify the subtraction and negation:
-2 + 5 - 22 + 7
Step 4: Perform addition and subtraction from left to right:
(5 - 2) - 22 + 7
3 - 22 + 7
Step 5: Continue performing addition and subtraction:
-19 + 7
Step 6: Final result:
-12
The expression simplifies to -12.
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Amber is an American teaching English in China, and she currently has 35,000
yuan in her bank account. If the exchange rate changes from 1 U.S. dollar =
6.83 Chinese yuan to 1 U.S. dollar = 6.96 Chinese yuan, what happens to the
value in U.S. dollars of the money in Amber's bank account?
A. It decreases by $4550.00
B. It increases by $4550.00
C. It increases by $95.71
D. It decreases by $95.71
It decreases by $95.71
Answer:
decreases by $95.71
Step-by-step explanation:
Just did test
Find the perimeter of quadrilateral ABCD. Round your answer to the nearest hundredth.
A(-5, 4)
B(0,3)
C(4,-1)
D(4,-5)
E(2,-3)
F(-2,1)
Answer:
The perimeter of quadrilateral ABCD is 27.48 units
Step-by-step explanation:
we know that
The perimeter of quadrilateral ABCD is the sum of its four length sides
so
[tex]P=AB+BC+CD+AD[/tex]
we have
A(-5, 4),B(0,3),C(4,-1) and D(4,-5)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
Substitute in the formula
[tex]d=\sqrt{(3-4)^{2}+(0+5)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(5)^{2}}[/tex]
[tex]AB=\sqrt{26}\ units[/tex]
Find the distance BC
Substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(4-0)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{32}\ units[/tex]
Find the distance CD
Substitute in the formula
[tex]d=\sqrt{(-5+1)^{2}+(4-4)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]CD=4\ units[/tex]
Find the distance AD
Substitute in the formula
[tex]d=\sqrt{(-5-4)^{2}+(4+5)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(9)^{2}}[/tex]
[tex]AD=\sqrt{162}\ units[/tex]
Find the perimeter
substitute the values
[tex]P=\sqrt{26}+\sqrt{32}+4+\sqrt{162}=27.48\ units[/tex]
see the attached figure to better understand the problem
slope 2, y-intercept at 0
Answer:
y = 2x
Step-by-step explanation:
This is what is known as direct variation.
I am joyous to assist you anytime.
Factor completely. x2 + 5x + 6 A. (x - 3)(x + 3) B. (x - 1)(x + 6) C. (x + 3)(x + 2) D. (x + 5)(x + 1)
being [tex]x^{2} +5x+6[/tex] the answer is (x-3)(x-2)
begin [tex]x^{2} -5x+6[/tex] the answer is (x+3)(x+2)
1. [tex]x^{2} +5x+6[/tex]
second grade formala is used
[tex]x= \frac{-b±\sqrt{b^{2} } -4ac}{2a}\\ x=\frac{-5±\sqrt{5^{2} } -4.1.6}{2} \\ x= \frac{-5±1}{2} \\ x_{1} =-3 \\ x_{2} =-2[/tex]
Factor out the coefficient of the variable in the expression 1/3b - 1/3
Answer:
[tex]\dfrac{1}{3} \left (\dfrac{1}{b} - 1 \right )[/tex]
Step-by-step explanation:
[tex]f(x) = \dfrac{1}{3b} - \dfrac{1}{3}[/tex]
1. Find the least common multiple of the denominators
The least common multiple of 3 and 3 is 3.
2. Factor out ⅓.
[tex]\dfrac{1}{3b} - \dfrac{1}{3} = \mathbf{\dfrac{1}{3} \left (\dfrac{1}{b} - 1 \right )}[/tex]
8. What is the prime factorization of 120?
Answer:
120 is a composite number. 120 = 1 x 120, 2 x 60, 3 x 40, 4 x 30, 5 x 24, 6 x 20, 8 x 15, or 10 x 12. Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Prime factorization: 120 = 2 x 2 x 2 x 3 x 5, which can also be written 120 = 2³ x 3 x 5.
Answer:
3 x [tex]2^{3}[/tex] x 5 = 120
Step-by-step explanation:
Use the factorization tree to answer this question.
What is 1 4/7 divided by 4 5/7
ANSWER THIS ASAP I ONLY HAVE 57 minutes LEFT PLEASE HURRY!!!!
Answer:
Step-by-step explanation:
[tex]\frac{11}{7} * \frac{7}{33}[/tex]
[tex]\frac{11 * 7}{7 * 33}[/tex]
[tex]\frac{1}{3}[/tex]
[tex]0.333[/tex]
What is greater 3/4 or 5/8 math
Answer:
3/4
Step-by-step explanation:
3/4 is equal to 6/8 which is bigger than 5/8
6/8 > 5/8
Answer: 5/8
Step-by-step explanation:
3/4=0.8
5/8=0.7
Which of the following equations has infinitely many real solutions?
A) 4x + 1 = x-1
B) 4(x-5)=4x+20
C) 4(x-5) =4x-20
D) 4x+ 1 = 4x-1
Which of the following equations has exactly one solution?
A) x + 1= x + 1
B) 7x= 7x
C) x + 1 = x + 2
D) 7x= 7
Which of the following equations has no real solutions?
A) 14x-6=14x-6
B) 4(x+8) = 4( x+4)
C) 4x-8 =4x -28
D) 8(x-6) =8x-48
Answer:
1) b 2) d 3) d
Step-by-step explanation:
Lilly and Rose are playing a game. In the game, each player starts with 0 points and the player with the most points at the end wins. Lilly gains 5 points two times, loses 12 points/ and then gains 3 points. rose loses 3 points two times, loses 1 point, gains 6 points, and then gains 7 points.
A. write and evaluate an expression to find Lillys score.
B. write and evaluate an expression to find Roses score
C. Who won the game, and why?
Answer:
Rose wins the game, with 6 points over Lilly's 1 point.
Step-by-step explanation:
Let's find Lilly's score. In this example we will add together the gains first, so we wouldn't have to deal with negative numbers, and after, we subtract the losses of each person.
Lilly's points:
[tex]0 + 5 + 5 + 3 - 12 = 1[/tex]
Rose's points:
[tex]0 + 6 + 7 - 3 - 3 - 1 = 6[/tex]
Rose wins the game with a 5 point lead.
Lilly's score is 1 and Rose's score is 6. Therefore, Rose wins the game because 6 is greater than 1.
Explanation:To find Lilly and Rose's score, we will create and solve an expression that reflects each player's game moves.
A. Lilly's score:
Lilly gains 5 points two times, loses 12 points, and then gains 3 points. We can express this as (5*2) - 12 + 3. First, we multiply 5 by 2, which equals 10. Then, we subtract 12 from 10, which gives -2. Finally, we add 3 to -2, resulting in a final score of 1 for Lilly.
B. Rose's score:
Rose loses 3 points two times, loses 1 point, gains 6 points, and gains 7 points. We can write this as (-3*2) - 1 + 6 + 7. First, we multiply -3 by 2, which equals -6. Then, we subtract 1 from -6 yielding -7. After that, we add 6 to -7, getting -1. Lastly, we add 7 to -1, resulting in a final score of 6 for Rose.
C. Game result:
Rose won the game because her final score of 6 is higher than Lilly's final score of 1.
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How did the railroad facilitate population growth in
the interior of the country? Check all of the boxes
that apply.
The railroad built towns along the railroad.
The railroad bought land from farmers,
ranchers, and business owners.
The railroad recruited settlers to form new
communities along the route.
The railroad encouraged American Indians to
settle along the route.
DONE
Answer:
1. The railroad built towns along the railroad.
and
3. The railroad recruited settlers to form new.
Step-by-step explanation:
I just took it
The railroad facilitate population growth in the interior of the country by The railroad built towns along the railroad, The railroad recruited settlers to form new.
What is the population?A population is a complete set of a group of individualists, whether that group constitutes a nation or a group of groupings with a common characteristic. In data point, a population is the pool of individuals from which a statistical sample is drawn for a study. As we see, different countries have different populations.
The construction of the transcontinental railroad boosted Western economic development and population growth. For both persons and commodities, railroad businesses offered superior transportation. Additionally, they sold the property to settlers, which prompted a Westward migration. New railroads benefited the industry.
Therefore, option (A) is correct
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Anything helps ouuuuuu:)))))))))))
Answer:
In order for the average to equal 3,000 then the total attendance must equal 9,000.
Show 1 = 2,580
Show 2 = 2,920
2 show total = 5,500
Therefore, third show total must equal 9,000 minus 5,500 =
3,500
Double-Check
2,580 + 2,920 + 3,500 = 9,000
Step-by-step explanation:
How do you reduce 16/72
Answer:
2/9
Step-by-step explanation:
16/72 = (8×2)/ (8×9)=2/9
Answer: 2/9
Step-by-step explanation:
Divide it by 2 and keep going until you can't anymore.
whats the pattern and the next 2 numbers of this question: -1, 2, 7, 17, _, _ .
Answer:
see explanation
Step-by-step explanation:
Consider the differences in the terms
2 - (- 1) = 2 + 1 = 3
7 - 2 = 5
14 - 7 = 7
The differences are 3, 5, 7 ← increasing in steps of 2
Thus the next 2 differences should be 9 and 11
Then the next 2 terms are
14 + 9 = 23
23 + 11 = 34
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have?
Answer:
The number of dimes is 42 and the number of quarters is 8
Step-by-step explanation:
Let
x -----> the number of dimes
y -----> the number of quarters
Remember that
1 dime=$0.10
1 quarter=$0.25
we know that
0.10x+0.25y=6.20 -----> equation A
x=3y+18 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (42,8)
see the attached figure
therefore
The number of dimes is 42 and the number of quarters is 8
There are 42 dimes and 8 quarters
Further explanationThe two-variable linear equation is a linear equation that has 2 variables and the exponent is one
Can be stated in the form:
[tex] \large {\boxed {\bold {ax + bx = c}}} [/tex]
x, y = variable
In this equation system there are coefficients and variables whose solutions can use:
1. substitution 2. elimination 3. graph 4. mix
We can state the problem in the form of algebraic equations
Lucinda has a pocketful of dimes and quarters with a value of $ 6.20
we translate this sentence into Algebraic expressions:
dime = D = $ 0.10
quarter = Q = $ 0.25
Then the equation becomes:
0.1D + 0.25Q = 6.20The number of dimes is 18 more than 3 times the number of quarters
we translate this sentence into Algebraic expressions:
D = 18 + Q
D - 3Q = 18
We solve the two equations with substitution and elimination
1. elimination
0.1D + 0.25Q = 6.20 x 10
D - 3Q = 18 x 1
------------------------------------
D + 2Q = 62
D - 3Q = 18
----------------------------------- -
5.5Q = 44
Q = 8
2. substitution
D - 3Q = 18
D - 3.8 = 18
D - 24 = 18
D = 42
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Find the distance between the points (a, 0) and (0, b).
Answer:
d = sqrt( a^2 + b^2)
Step-by-step explanation:
Formula
d = sqrt( (x2 - x1)^2 + (y2 - y1)^2 )
Givens
x1 = a
x2 = 0
y1 = 0
y2 = b
Solution
d = sqrt( (0 - a)^2 + (b - 0)^2 )
d = sqrt( a^2 + b^2)
which is another way of writing the Pythagorean theorem.
To find the distance between points (a, 0) and (0, b), use the distance formula which results in √(a² + b²). This involves calculating the square root of the sum of the squares of the coordinates.
Therefore, the final distance is √(a² + b²).
Finding the Distance Between Two Points
To find the distance between two points (a, 0) and (0, b), we use the distance formula:
Distance formula: d = √((x2 - x1)² + (y2 - y1)²)
Let's denote the points as:
Point 1: (a, 0)
Point 2: (0, b)
Applying the coordinates to the distance formula, we get:
d = √((0 - a)² + (b - 0)²)
Simplifying inside the square root:
d = √(a² + b²)
So, the distance between the points (a, 0) and (0, b) is √(a²+ b²).
2. Hal forgot the number of people at the
basketball game. He does remember that
the number had four digits and a 3 in the
tens place. Write a number that Hal could
be thinking of
Answer:
Well there is a lot of different numbers he could be thinking of because we are only given 2 useful pieces of information: Four Digits, and, a 3 in the tens place (30).
.
This means that the other spaces could be any number.
.
If X represents a random number it would be XX3X.
.
Eg 1234