D(2, –4) → D' = (-4, 2)
E(1, –1) → E'= (-1, 1)
F(5, 1) → F'=(1, 5)
What is the rule that describes a reflection across the line y = x?
rx = y(x, y)= (y, x)
The rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
What is reflection?The reflection of a plane or shape is flipping the original figure with respect to a reference line.
The following steps are used to for reflecting a shape-
Select the shape which has to be reflected.Select a base line or reference line over which the shape has to be reflected.Mark the corners of the shape at the equidistant from the reference line as the original shape has, but in the opposite direction.The reflected shape is now is facing the opposite direction.The rule that describes a reflection across the line says that when your reflect a point across the line say y=x. Then the coordinates of x and y are interchanged as,
y(x, y) → (y, x)
Now let's complete the mapping of the vertices of ΔDEF using the above rule. For this, change the places of x and y coordinate as,
D(2, –4) → (-4, 2)D'
E(1, –1) → (-1, 1)E'
F(5, 1) → (1, 5)F'
Thus, the rule which describes a reflection across the line is y(x, y) --> (y, x) and the mapping of the vertices of ΔDEF is (-4, 2)D', (-1, 1)E' , (1, 5)F'.
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The highest point in the United States is Mount McKinley in Alaska. Its summit is 20,335 feet above sea level. Badwater, a basin located in Death Valley, is the lowest point in the United States at 282 feet below sea level. How high is the summit of Denali above the Death Valley location? (How far apart are the two distances?) *
Answer:
20,053
Step-by-step explanation:
20,335 - 282 = 20,053
Answer:
20617 feet is your answer
Step-by-step explanation:
You are subtracting the two numbers. Note however, that 282 feet below the sea level = -282
Subtract.
20335 - (-282) = answer
Note that two negatives = one positive
20335 + 282 = answer
20617 = answer
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Find two numbers the exact answer is between 6 x 7,381
I got 37,286 the steps were...
2 4
7,381
× 6
---------
37,286.
Am I suppose to multiply?
What is the equation of the following line ?
y = 6x is your answer.
How to write 2.6 in word form
two - point six
is the answer
The answer you are looking for is "Two and six tenths".
The reason this is, is because 2 is left of the decimal, which makes it "two". Since 6 is to right of the decimal, you have to look at how far it is from the decimal. It being directly after the decimal, it is in the tenths place, making it six tenths. Thus meaning the answer is two and six tenths.
I hope this helps!
the room shown below right is 14ft by 10ft. Find the dimensions of each piece of furniture to the nearest tenth.
The dimension of dresser is :
Length is 6.0 feet
width is 3.0 feet
The dimension of bed is :
Length is [tex]5\sqrt{2}[/tex] = 7.1 feet
Width is [tex]4\sqrt{2}[/tex] = 5.7 feet
The dimension of table:
Length is [tex]2\sqrt{2}[/tex] = 2.8 feet
Width is [tex]2\sqrt{2}[/tex] = 2.8 feet
Answer:
A). Dimensions of the bed = 7.1 ft × 5.7 ft
B). Dimensions of table = 2.8 ft × 2.8 ft
C). Dimensions of the dresser = 6ft × 3ft
Step-by-step explanation:
Dimensions of the room are 14 ft by 10 ft.
We have to find the dimensions of each furniture.
First we take the bed.
Length of the bed = [tex]\sqrt{(5)^{2}+(5)^{2}}[/tex]
= [tex]\sqrt{25+25}[/tex]
= [tex]\sqrt{50}[/tex]
= 7.07 ft ≈ 7.1 ft
Width of the bed = [tex]\sqrt{4^{2}+4^{2}}[/tex]
= [tex]\sqrt{16+16}[/tex]
= [tex]\sqrt{32}[/tex]
= 5.7 ft
We take another furniture table which is in the square shape,
Side of the table = [tex]\sqrt{2^{2}+2^{2}}[/tex]
= [tex]\sqrt{8}[/tex]
= 2.8 ft
Therefore, each side of the table is 2.8 ft
Length of the dresser = 6 ft
Width of the dresser = 3 ft
What is the quotient 1074 divided by 26
the answer is 44.75 I would explain but ehhhhhhhhhh
What is the measure of angle a?
A. Cannot be determined
B. 45•
C. 15•
D. 60•
As all angles of the triangle have to give 180 ° and, as the triangle is equilateral (all the angles are equal), the three angles have the same amplitude. 180 ÷ 3 = 60
So, the answer is D.
The measure of angle a (x) is 60 degrees when all sides of triangle are equal The correct answer is option D: 60°.
Since all three sides of the triangle ABC have equal lengths (15 units each), we can determine that this is an equilateral triangle. In an equilateral triangle, all three angles are congruent, meaning they have the same measure.
Let's represent the measure of angle a as "x."
In an equilateral triangle, the sum of all three angles is 180 degrees. So, we can write the equation:
x + x + x = 180
Combine like terms:
3x = 180
Now, divide by 3 to solve for x:
x = 180 / 3
x = 60
Therefore, the measure of angle a (x) is 60 degrees.
The correct answer is option D: 60°.
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Oak tree is 48 feet tall.Oak tree is as 8 times tall mike.How tall is Mike?
If the oak tree is 48 feet tall, and is 8 times taller than Mike, you must divide 48 by 8 to find that Mike is 6 feet tall. To check your work, multiply 6 by 8 and see that you get 48 feet. Hope I helped!!
Please award brainliest!:)
Mike is 6 feet tall. This is determined by dividing the height of the oak tree, which is 48 feet, by 8, because Mike's height is said to be 1/8 of the oak tree's.
Explanation:The subject of this question is a basic math problem involving division. The question states that the oak tree is 8 times as tall as Mike. So, to find Mike's height, we need to divide the oak tree's height by 8.
Applying this to the details given:
Oak Tree height = 48 feet
Mike's height = Oak Tree Height/8
Mike's height = 48/8
Mike's height = 6 feet
So, Mike is 6 feet tall.
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Write the equation of the line that contains the given point and has the given slope.
a) (2, –2), slope = 1.4
b) (–1, 4), slope = –3
WILL GIVE BRAINLIEST!! 20 PT QUESTION
Hey there!!
What is slope-intercept form :
... y = mx + b
( a ) Given :
... ( 2 , -2 ) and slope=1.4
... y = mx + b
... -2 = 2×1.4 + b
... -2 = 2.8 + b
... -4.8 = b
The slope-intercept form :
... y = 1.4x - 4.8
( b ) Given :
... ( -1 , 4 ) and slope = -3.
y = mx + b
... 4 = -3×-1 + b
... 4 = 3 + b
... 1 = b
The slope-intercept form :
... y = -3x + 1
Note :
( m = slope and b = y-intercept )
Hope my answer helps!!
Answer:
... y = mx + b ( a ) Given : ... ( 2 , -2 ) and slope=1.4 ... y = mx + b ... -2 = 2×1.4 + b ... -2 = 2.8 + b ... -4.8 = b The slope-intercept form : ... y = 1.4x - 4.8( b ) Given : ... ( -1 , 4 ) and slope = -3. y = mx + b ... 4 = -3×-1 + b ... 4 = 3 + b ... 1 = b The slope-intercept form : ... y = -3x + 1 Note : ( m = slope and b = y-intercept ) Hope my answer helps more math stuff
Step-by-step explanation:
what does it mean if am equation is equivalent to 0=0? explain.
This means it has infinite solutions congrats. When solving algebraic equations you can find one solution, no solutions. When you have infinite solutions that means that equations has multiple things that can equal it.
If the equation 0=0, then its solution is that x can take any real value.
The given equation is 0=0.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
We obtain 0=0, this means the equation is in fact an identity which is true for all values of x. As an equation, its solution is that x can take any real value (assuming we are supposed to be finding real solutions).
Therefore, if the equation 0=0, then its solution is that x can take any real value.
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what is the constant of variation k of the line y=kx through (5,8)
Answer:
k= 8/5
Step-by-step explanation:
here x= 5 and y= 8
we have y=kx
k= y/x
k= 8/5 this is constant of variation
Answer:
[tex]k=\frac{8}{5}[/tex]
Step-by-step explanation:
find the constant of variation k of the line y=kx through (5,8)
Use equation of line [tex]y=kx[/tex]
k is the constant of variation
LEts find out k using the point (5,8)
x=5 and y=8, plug in the values
[tex]8=k(5)[/tex]
To get k alone, divide by 5 on both sides
[tex]k=\frac{8}{5}[/tex]
stan, a local delivery driver is paid $3.50 per mile driven plus a daily amount of $75. on monday he is assigned a route that is 30 miles long. how much is he being payed for that day?
He is paid 180 dollars for that day
the sum of 4 times a larger integer and 9 times a smaller integer is 3. the difference between 8 times the larger and 3 times the smaller is 27. Find the integers
Round 0.0695712 to 1 significant figure
It would be 7x10^-2
That number would be rounded to 0.07
Consider a function that describes how a particular car’s gas mileage depends on its speed. What would be an appropriate domain for this function?
A 0 to 100 miles per hour
B 0 to 50 miles per gallon
C times from 0 to 10 minutes
D times from –10 to 10 minutes
Answer:
A) 0 to 100 mph
Step-by-step explanation:
the range would be the mpg, and domain would be speed.
That would be the best presentation.
Blue Sky International Airport handles passenger to cargo traffic in a ratio of 8 to 5. If 45 cargo planes landed yesterday, how many passenger flights came in?
Answer:
72 passenger planes
Step-by-step explanation:
ratio passenger to cargo = 8 to 5 = 8/5
Let p = number of passenger planes.
The ratio of passenger to cargo planes that actually landed is p/45.
The ratio in general is 8/5, so 8/5 must equal p/45.
p/45 = 8/5
5p = 45 * 8
p = 9 * 8
p = 72
Answer: I'm guessing 72
Step-by-step explanation:
its says 8 to 5. If you read it correctly you will know that 8 is the number of passengers and 5 is the number of cargo. 45 ÷ 5 = 9 x 8 = 72consider the following equation: f(x)=x^2+4\4x^2-4x-8 name the vertical asymptote(s)
ANSWER
The vertical asymptotes are
[tex]\Rightarrow x=2\:or\:x=-1[/tex]
EXPLANATION
We have
[tex]f(x)=\frac{x^2+4}{4x^2-4x-8}[/tex]
For vertical asymptotes we set the denominator to zero and solve the quadratic equation;
[tex]4x^2-4x-8=0[/tex]
[tex]\Rightarrow x^2-x-2=0[/tex]
We split the middle term to obtain,
[tex]x^2+x-2x-2=0[/tex]
[tex]\Rightarrow x(x+1)-2(x+1)=0[/tex]
[tex]\Rightarrow (x-2)(x+1)=0[/tex]
[tex]\Rightarrow x=2\:or\:x=-1[/tex]
Therefore the vertical asymptotes are
[tex]x=2\:or\:x=-1[/tex]
The vertical asymptotes are x = 2 and x = -1
How to determine the vertical asymptote?[tex]f(x)=\frac{x^2+4}{4x^2-4x-8}[/tex]
Set the denominator to 0
[tex]4x^2-4x-8 = 0[/tex]
Divide through by 4
[tex]x^2-x-2 = 0[/tex]
Expand
[tex]x^2+x-2x-2 = 0[/tex]
Factorize
[tex]x(x+1)-2(x+1) = 0[/tex]
Factor out x + 1
[tex](x-2)(x+1) = 0[/tex]
Solve for x
x = 2 or x = -1
Hence, the vertical asymptotes are x = 2 and x = -1
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Find the area shaded in yellow.
Im not sure but the answer might be 52. I just found the area of the whole box, and then found the area of the red box only. I subtracted the area of the red box from the whole box and got 52.
66 square units, because you count the number of yellow squares
Al bought 24 stickers. He gave away 11 stickers. Then he bought 8 more stickers.
Write an expression that will match the words
Al bought 24 stickers, gave away 11, then bought 8 more. The numerical expression representing this situation is '24 - 11 + 8'.
Explanation:The word problem describes Al's activity concerning stickers. To turn the words into a numerical expression, each operation performed by him needs to be included. Initially, Al bought 24 stickers. Then, he gave away 11 stickers. Lastly, he bought 8 more stickers. By using these actions as a guide, the equivalent numerical expression would be '24 - 11 + 8'.
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Simplify: |4 - 2 • 1| - 17|8 - 13|
Step 1. Simplify 2 * 1 to 2
|4 - 2|-17|-13|
Step 2. Simplify 4 - 2 to 2
|2|-17|8-13|
Step 3. Simplify 8 - 13 to -5
2 - 17|-5|
Step 4. Simplify |-5| to 5
2 - 17 * 5
Step 5. Simplify 17 * 5 to 85
2 - 85
Step 6. Simplify
-83
Answer:
your answer is -83
Step-by-step explanation:
Solve 6x^2 = 12x − 20.
The answer is
3 + i √21 all divided by 3
3 + i √21/3
Hope I helped! :)
Mark brainliest
Determine the ordered pair that satisfies the equation, 6x - 3y = 5.
a-(9 ,16/3)
b- (6 , -3)
c- (1,−11/3)
d- (-2 ,−17/3)
Given the equation [tex]6x-3y=5.[/tex]
Check all options:
A. [tex]\left(9,\dfrac{16}{3}\right)[/tex], this means that [tex]x=9, y=\dfrac{16}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 9-3\cdot \dfrac{16}{3}=54-16=38\neq 5.[/tex]
This option is false.
B. [tex]\left(6,-3\right)[/tex], this means that [tex]x=6, y=-3.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 6-3\cdot (-3)=36+9=45\neq 5.[/tex]
This option is false.
C. [tex]\left(1,-\dfrac{11}{3}\right)[/tex], this means that [tex]x=1, y=-\dfrac{11}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot 1-3\cdot \left(-\dfrac{11}{3}\right)=6+11=17\neq 5.[/tex]
This option is false.
D. [tex]\left(-2,-\dfrac{17}{3}\right)[/tex], this means that [tex]x=-2, y=-\dfrac{17}{3}.[/tex] Substitute these numbers into the left side of the equation equation:
[tex]6\cdot (-2)-3\cdot \left(-\dfrac{17}{3}\right)=-12+17=5.[/tex]
This option is true.
Answer: correct choice is D.
Answer:
Option d
Step-by-step explanation:
Given is a linear equation in x and y as
[tex]6x-3y =5[/tex]
To check whether a point satisfies the equation, let us substitute and check whether the equation holds good
a) [tex]6(9)-3(16/3) = 38 \neq 5[/tex]
b) [tex]6(6)-3(-3) \neq 5[/tex]
c) [tex]6(1)-3(-11/3) = 17\neq 5[/tex]
d) [tex]6(-2)-3(-17/3) = -12+17 =5[/tex]
Since last point satisfies the equation, option d is the answer.
How do you solve 24 divided by 3/8?
The quotient from the given division is 64.
Given that, 24 divided by 3/8.
The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.
Here, 24 ÷ 3/8
= 24 × 8/3
= 8 × 8
= 64
Therefore, the quotient from the given division is 64.
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Explain and demonstrate how to change 4/20 into a percent
4/20 is equivalent to 20%.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.We have the following fraction -
4/20
We can convert it into percent as -
[x]% = (4/20) x 100
[x]% = 20%
Therefore, 4/20 is equivalent to 20%.
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The maximum safe load of a bridge is 1500kg to the nearest 10kg. An average soldier is 75kg to the nearest kilogram. Work out an estimate for the maximum number of soldiers that can safely cross the bridge at the same time
solve for x
[tex] \frac{x}{a} = \frac{x}{b} [/tex]
[tex]Domain:\ a\neq0\ \wedge\ b\neq0[/tex]
[tex]\dfrac{x}{a}=\dfrac{x}{b}\qquad|\text{cross multiply}\\\\bx=ax\qquad|\text{subtract ax from both sides}\\\\bx-ax=0\\\\x(b-a)=0\qquad|\text{divide both sides by }\ b-a\neq0\\\\x=0[/tex]
[tex]\dfrac{x}{a}=\dfrac{x}{b}\\\\if\ a\neq b\ then\ x=0\\\\if\ a=b\ then\ x\in\mathbb{R}[/tex]
An above ground swimming pool is leaking. After 1/2 hour the pool has leaked 7/8 if a gallon of water. How many gallons of water per hour is the swimming pool leaking?
There are 7/4 gallons leaking per hour. This is the same as 1.75 gallons per hour. Hope this helps! :)
Answer:
[tex]1\frac{3}{4}[/tex] gallons of water will be leaked in one hour.
Step-by-step explanation:
An above ground pool is leaking [tex]\frac{7}{8}[/tex] gallon of water in half an hour.
Therefore, amount of water leaked in one hour will be = 2 × (amount of water leaked in half an hour)
= [tex]2\times \frac{7}{8}[/tex]
= [tex]\frac{7}{4}[/tex]
= [tex]1\frac{3}{4}[/tex] gallons
Therefore, [tex]1\frac{3}{4}[/tex] gallons of water will be leaked in one hour.
Hey! I was wondering if someone could explain to me how solving two-step inequalities works. Thanks!
Here is the inequality:
[tex]-2x+6<20[/tex]
You're looking for x. To find it, you have to remove everything on the same side of the variable. The only thing with it is positive 6. To remove it, you have to do the opposite of it, which is -6, which is also the same as subtracting 6. Subtract 6 from both sides:
[tex]-2x+6-6<20-6 \\-2x<14[/tex]
Now you have -2x. When you have a negative variable, the inequality sign changes. Change the sign:
[tex]-2x<14 \rightarrow -2x>14[/tex]
You're looking for x alone. To leave x alone, you have divide both sides by -2 since the variable is -2x. Divide both sides by -2:
[tex]-2x \div -2 > 14 \div -2 \\\\x>-7[/tex]
When dividing a negative number number by a positive or vice versa, the result is ALWAYS negative. That's why in your answer, it's -7.
Your answer is x > -7
GRAPH:
Arrange the steps in order to solve this expression sin (3pi/4) cos (pi/12)
To solve sin (3\u03c0/4) cos (\u03c0/12), calculate the value of sin (3\u03c0/4), use the half-angle formula to find cos (\u03c0/12), and multiply the results.
Explanation:To solve the expression sin (3\u03c0/4) cos (\u03c0/12), we need to find the sine and cosine values of the individual angles and then multiply them together. The sine of 3\u03c0/4 is \u221a2/2 and the cosine of \u03c0/12, which is not a standard angle on the unit circle, can be calculated using the half-angle formula since \u03c0/12 is half of \u03c0/6. Therefore, once we have both values, we simply multiply them to get the result of the expression.
what is the area of the square
the area of the square would be 49
49 inches (7 multiplied by 7)