Answer:
Question:
A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A.) (-1,3),(2,-1),(-1,-1)
B.) (6,0),(6,7)(0,7)
C.) (-1,-1),(-6,-13),(-9,-9)
D.) (-3,-4),(3,-4),(3,4)
Triangle and Coordinate Geometry
As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.
So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always
180
∘
.
If a triangle
A
B
C
has the sides
a
,
b
,
and
c
, then
The perimeter of the triangle:
P
=
a
+
b
+
c
In coordinate geometry, the distance between two points:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Answer and Explanation:
Given:
The perimeter of the triangle is
24
units.
There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.
Firstly we chose the option
D
:
The vertices of the triangle are:
P
(
−
3
,
−
4
)
,
Q
(
3
,
−
4
)
,
and
R
(
3
,
4
)
Using the distance formula:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
So
P
Q
=
√
(
3
+
3
)
2
+
(
−
4
+
4
)
2
=
√
6
2
+
0
=
6
u
n
i
t
And
Q
R
=
√
(
3
−
3
)
2
+
(
4
+
4
)
2
=
√
0
+
8
2
=
8
u
n
i
t
And
P
R
=
√
(
3
+
3
)
2
+
(
4
+
4
)
2
=
√
6
2
+
8
2
=
√
36
+
64
=
√
100
=
10
u
n
i
t
So
The perimeter of the triangle
P
Q
R
is:
Perimeter
=
P
Q
+
Q
R
+
P
R
=
6
+
8
+
10
=
24
u
n
i
t
s
Step-by-step explanation:
find the slope of the line that goes through the points (4,-6) and (3,7)
Answer:
m=-13
Step-by-step explanation:
the formula for getting the slope is[tex] = \frac{y 2- y1}{x2 - x1} \\ = \frac{7 - ( - 6)}{3 - 4} \\ = \frac{7 + 6}{ - 1} \\ = \frac{13}{ - 1} \\ = - 13[/tex]Hope this helpsFind the area of the quarter circle with a radius of 10 in. Use
3.14 for , and round the answer to the nearest tenth, if
necessary.
10in
The area of the quarter-circle is_______in².
Answer:
314 in²
Step-by-step explanation:
A=3.14r^2
π·10^2≈314
The area of the quarter-circle is 314 in²
Which transformation will preserve distance between points when applied to a figure
in the (x, y) -coordinate plane?
A . (x,y) → (x + 2,- 3y)
B . (x,y) → (-x+ 2, y + 7) C . (x,y) → (2x,- 3y)
D. (x,y) → (2x, y)
1 pts. PLEASE HELP FOR TEST
The transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)
How to determine the transformation will preserve distance between points when applied to a figure in the (x, y) -coordinate plane?Let the coordinate be represented as
(x, y)
For a transformation to preserve distance between points when applied to a figure in the (x, y)-coordinate plane, the transformation must be any of the following:
ReflectionRotationTranslationFrom the list of options, we have
B . (x,y) → (-x+ 2, y + 7)
This transformation is a translation
Hence, the transformation that will preserve distance between points when applied to a figure in the (x, y) -coordinate plane is B . (x,y) → (-x+ 2, y + 7)
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Write the math sentence as an equation: Negative six times the sum of a number and 16.4 is 22.8.
A.) −6r − 16.4 = 22.8
B.)−6(r − 16.4) = 22.8
C.)-−6r + 16.4 = 22.8
D.)−6(r + 16.4) = 22.8
Answer:
Negative six times the sum of a number and 16.4is22.8
Step-by-step explanation:
D. -6(r+16.4)=22.8
The sentence is that a negative is six times the sum of a number and 16.4 is 22, then in equation form, it will be -6(r + 16.4) =22.8. Hence, option D is correct.
What is an Equation?Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way.
There are many different kinds of equations, some of which include:
Liner equationQuadratic equationCubic equation.According to the question, the given statement for the equation is,
16.4 is equal to 22.8 when multiplied by a negative six.
Negative six times means -6 times to any number + 16.4.
Assume that number is r.
-6(r+16.4) = 22.8
Hence, from here it is concluded that option D is correct.
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can anyone solve this we need to simplify
Answer: x^3/3
Step-by-step explanation:
Since you have an exponent outside of your 'x' in parenthesis, you're multiplying the exponents together, that being 1 * 3.
Since the exponent of 3 is being multiplied to only the top area, your 3 stays the same, leaving you with x^3/3
If the exponent is being multiplied to the top and bottom, your answer would be x^3/3*3*3 or x^3/27.
Hope this helps!
4. MA.912.LT.4.3
Select all the conditionals and truth values implied by the following biconditional.
Two lines are parallel if and only if they do not intersect.
A. If two lines are parallel, then they do not intersect; True.
B. If two lines are not parallel, then they intersect; False.
C. If two lines do not intersect, then they are parallel; True.
D. If two lines intersect, then they are parallel; False.
E. If two lines intersect, then they are not parallel; True.
The conditionals and truth values based on the biconditional, 'Two lines are parallel if and only if they do not intersect', are;
A. If two lines are parallel, then they do not intersect; True
B. If two lines are not parallel, then they intersect; True
C. If two lines do not intersect, then they are parallel; True
D. If two lines intersect, then they are parallel; False
E. If two lines intersect, then they are not parallel; True
What are the conditionals and truth values?The given biconditional is presented as follows;
Two lines are parallel if and only if they do not intersect
Therefore;
If two lines do not intersect, then they are parallel.If two lines intersect, then they are not parallel.If two lines are not parallel, then they intersect.Which gives;
A. If two lines are parallel then they do not intersect;
The above statement is a true statement, the correct option is therefore;
True
B. If two lines are not parallel, then they intersect.
The above statement is true and the correct option is; True
C. If two lines do not intersect, then they are parallel.
The above statement is; True
D. If two lines intersect then they are parallel.
The above statement is; False
E. If two lines intersect, then they are not parallel.
The above statement is; True
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Simplify fully
4x^+ 4x/-2x^-2
Answer: -12x
Step-by-step explanation: 4x +4 −2 −2x
Calculate x to the power of 1 and get x.
4x+4×( −2 −2x )
Calculate 2 to the power of −2 and get 41.
4x+4×( − 41x)
Divide x by − 41
by multiplying x by the reciprocal of − 41 .
4x+4×( −1x×4)
Anything divided by -1 gives its opposite.
4x+4(−x×4)
Multiply 4 and −1 to get −4.
4x−4x×4
Multiply −4 and 4 to get −16.
4x−16x
Combine 4x and −16x to get −12x.
−12x
4.024 as a mixed number
Answer:
4 24/1000 simplified/reduced to 4 3/125
Step-by-step explanation:
The number 4 in .024 ends in the thousandths place so the mixed number will be ...
4 24/1000
4 24/1000 is simplified to 4 3/125 because we divide the numerator and denominator by 8 to get 4 3/125.
24 ÷ 8 3
4 ----- = 4 -----
1000 ÷ 8 125
Hope this helps :)
12 ÷ 4 + (3 − 2) × 7
Answer: step-by-step
Step-by-step explanation:
answer: 10
to solve you have to follow PEMDAS
Segment BD bisects segment AC. Solve for x. Round to the nearest tenth, if
necessary. (Image not necessarily to scale.)
B
20
x
D
7
A
The value of x when rounded of to nearest tenth is 7 units.
What happens when a line is bisected?
A line, beam, or other component that divides another line segment into two identical pieces is said to bisect. A "Bisector" in geometry is a line that splits a line into two distinct or equal sections. It is applied to angles and line segments. The term "line segment bisector" refers to a line that cuts through the middle of a line segment, whereas the term "angle bisector" refers to a line that cuts through the apex of an angle.
Given, BD bisects AC thus dividing AC into two equal parts.
Thus value of x will be equal to 7 units.
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can someone please anwser (5z+y)/7 (the number values of z and y are in the picture)
Answer:
2
Step-by-step explanation:
First substitute the values of z and y in the expression.
Use PEDMAS. We have to multiply 5 and 3, which gives 15. Subtract 1 from 15 and then divide the result by 7.
[tex]\sf \dfrac{5z + y}{7}= \dfrac{5*3 + (-1)}{7}\\\\[/tex]
[tex]\sf = \dfrac{15 - 1}{7}\\\\ = \dfrac{14}{7}\\\\= 2[/tex]
two accountants, lee and johnson, went to a business meeting together. lee drove to the meeting and johnson drove back from the meeting. if lee and johnson each drove 140 kilometers, what was the average speed, in kilometers per hour, at which lee drove? 1) the average speed at which johnson drove was 70 kilometers per hour 2) lee drove for exactly 2 hours
The average speed of Lee is 70 km/hr.
To clear up this trouble we want to understand the concept of average speed.
average speed is given while we divide the overall distance blanketed with the aid of the total time taken.
right here, it's miles given that Lee and Johnson each drove a hundred and forty Km. additionally, it's miles given that lee drove for two hours.
So, average speed of Lee = [tex]\frac{140}{2}[/tex]
= 70 km/hr
Here, the average speed at which Lee drove the car and went to business meeting is 70 km/hr.
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please solve u r the best thx
Answer:13
Step-by-step explanation:
Answer:
There are no values of f to make this equation true.
Hope this helps.
Step-by-step explanation:
In the second part of the equation, 6( 1/16f - 3 ), 6 * 1/16f is 3/8f. If both sides subtract a 3/8f and both sides add 18, you get 18.5 = 0 meaning there are no values of f to make this equation true.
I cant find my answer please help!
Answer:
Domain: 1 ≤ x ≤ 6
Range 10 ≤ M(x) ≤ 60
Step-by-step explanation:
M(x) = 10x where x represents the number of tickets bought
Assume nobody goes with Victoria. In that case she will go alone, only 1 ticket is bought and total cost = $10
Maximum 5 friends means total of 6 tickets purchased so total cost is $60
Domain refers to the possible input values ie possible x values. Here the domain is 1 ≤ x ≤ 6 also written as [1, 6]
The range is the total possible set of output values. Here output of the function is cost and cost ranges between 10 and 60 inclusive
So Range = 10 ≤ M(x) ≤60 also written as [10, 60]
how many quarts of pure antifreeze must be added to 3 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution?
1.5 quarts of pure antifreeze must be added to 3 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
Given;
Percentage of 3 quarts of antifreeze solution = 40%
We have to find,
Quarts to obtain the antifreeze solution of 60%
Now,
The 3 quarts of 40% antifreeze solution contains 0.4 x 3 = 1.2 quarts of pure antifreeze solute
Let,
x is the number of quarts of pure antifreeze needed to make a 60% solution
The equation to solve becomes, where x is the amount of pure antifreeze to be added is
(1.2 + x )/(3 + x) =0.6
(1.2 + x ) = 0.6 * (3 + x)
(1.2 + x ) = 1.8 + 0.6x
x-0.6x = 1.8 - 1.2
0.4x = 0.6
x = 1.5
Therefore,
1.5 quarts of pure antifreeze to the current solution to make a 60% solution
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Factorise the following:
a) x(squared)– 12x + 32
b) x(squared) – 14x + 48
c) x(squared) - 3x + 2
Answer: a. (x-8)(x-4)
b. (x-8)(x-6)
c. (x-2)(x-1)
Step-by-step explanation:
a. x^2-12x+32=
x^2-4x-8x+32=
x(x-4)-8(x-4)=(x-8)(x-4)
b. x^2-14x+48=
x^2-6x-8x+48=
x(x-6)-8(x-6)=(x-8)(x-6)
c. x^2-3x+2=
x^2-x-2x+2=
x(x-1)-2(x-1)=(x-2)(x-1)
[tex]\frac{11}{6}[/tex]
Answer:
1, R 5
Step-by-step explanation:
Long division
[tex]6 \times 1 = 6\\11 - 6\\= 5\\=1\:R5[/tex]
-4n algebraic expression
Answer: -1 x 2 x 2 x n
Step-by-step explanation:
-4n
factor
which leads to -1 x 2 x 2 x n
jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 what is the range of the data jonathon collected?
The range of the data collected by Jonathon is [0.25,0.98]
Given that Jonathon wanted to know how far people could swim in 30 minutes. he collected data from 10 people about how many miles they could swim in 30 minutes and obtained the following results: 0.25 0.80 0.75 0.93 0.24 0.50 0.75 0.98 0.35 0.85 and asked to find the range of the data collected by Jonathon.
The minimum value of the data collected by Jonathon is 0.25 and the maximum value of the data collected by Jonathon is 0.98
The range of the given data:(minimum value,maximum value)
Here, The minimum value of the data collected by Jonathon is 0.25
The maximum value of the data collected by Jonathon is 0.98
Therefore,The range of the data collected by Jonathon is [0.25,0.98]
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What is the value of the expression below when w=7?
w² +3w - 10
Answer:
The value of the expression is 60.
A person who weighs 100 kilograms on Earth would weigh 16.5 kilograms on the moon. Determine how much a child who weighs 30.5 kilograms on Earth would weigh on the moon. Round to the nearest hundredth if necessary.
On Earth, a child weighing 30.5 kilograms would weigh 5 kilograms on the moon.
What is the basis of the difference between the weights on earth and the moon?Our weight on the Moon is 16.5% of what it would be on Earth. In other words, if we weighed 100 kilograms on Earth, we would only weigh 16.5 kilograms on the Moon. Assume we tipped the scales at 200 pounds for you imperial folks. On the Moon, our weight would be only 33 pounds. It's due to the Moon's lower gravity. Objects on the Moon's surface experience only 16.5% of the gravity that they would on Earth. Gravity is caused by mass. The more weight we have, the more gravity will pull on us.Given:
A person who weighs 100 kilograms on Earth would weigh 16.5 kilograms on the moon.Our weight on the Moon is 16.5% of what it would be on Earth.So, we have to take out 16.5% of 30.5 kilograms.
= 30.5/100 × 16.5= 0.305 × 16.5= 5.0325After rounding off, the weight becomes 5 kilograms.
Therefore, a child who weighs 30.5 kilograms on Earth would weigh 5 kilograms on the moon.
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Given , find the average rate of change of f(x)=[tex]f(x)=\frac{1}{x+5}[/tex] on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp
The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
Given,
The function = [tex]\frac{1}{x+5}[/tex]
We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where a and b are the intervals
a= 1
b=1+h
f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]
=[tex]\frac{1}{6}[/tex]
f(b)= f(1+h)
=[tex]\frac{1}{1+h+5}[/tex]
=[tex]\frac{1}{6+h}[/tex]
f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]
[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]
Then,
[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]
[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]
Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
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a password system uses four digits from 0 to 9. how many different four-digit passwords with no digit repeated are possible?
Total 5040 passwords can be generated when no digits are repeated
• Permutation in mathematics is an arrangement of objects in an definite order. The elements or sets or things are arranged in sequential order or linear order.
• Permutation is classified into four types :
1) where repetition is not allowed
2) where repetition is allowed
3) objects that are non distinct
4) circular permutation
• The formula for calculating permutation is n!/(n-r)!
As we are given that the password uses four digits from 0-9 and repetition is not allowed.
So, n = 10 and r = 4
Using the formula for permutation we get
= 10! / (10-4)!
= 10!/6!
= 10 * 9 * 8 * 7 * 6! / 6!
= 10 * 9 * 8 * 7
= 5040
Therefore, 5040 four digit passwords are possible when no digit is repeated.
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The length of a rectangle is 4 inches more than 3 times its width. The perimeter of the rectangle is 48 inches. What are the length and width of the rectangle?
The length and width of the rectangle is found as 19 inches and 5 inches respectively.
What is defined as the perimeter of rectangle?To calculate the perimeter, or distance all around rectangle, add all four side lengths. This can be done quickly by adding the width and height and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter = 2(length + width).Now, as per the given question;
Let width of a rectangle = w inches
Then, length of a rectangle = 3w + 4
Perimeter of a rectangle = 2(length + width)
Substitute the values in the formula of perimeter.
48 = 2(3w + 4 + w)
48/2 = 4w + 4
24 = 4w + 4
20 = 4w
w = 5
Thus, the width of the rectangle is 5 inches.
Put w = 5 inches in its length.
l = 3w + 4
l = 3×5 + 4
l = 15 + 4
l = 19 inches.
Therefore, the length of rectangle is found as 19 inches.
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Evaluate 15 − 6(7 + 5) ÷ 32.
Eva’s phone is 4 times the number of songs on Hank’s phone.
• The total number of songs on both phones is 600 songs.
How many songs (N) are on Hank’s phone?
Answer:
120 songs
Step-by-step explanation:
Eva=4u
Hank=1u
Eva+Hank=5u
5u=600
1u=600/5
=120
what is 9/7 divided by 6
help please
just tell the answer get it right for brainliest!
Answer:
pretty sure its 2.9
Step-by-step explanation:
Answer:2.92 or just 3
Step-by-step explanation:
btw read your lesson and pay attentiom
PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Let f(x) be the integrand.
[tex]f(-2)=-8 \\ \\ f(0)=0 \\ \\ f(2)=8 \\ \\ f(4)=64 \\ \\ \implies \int^{4}_{-2} x^3 \text{ dx}=\approx \frac{1}{2}(2)[-8+64+2(0+8)] \\ \\ =\boxed{72}[/tex]
What is the length of the shorter leg?
____________________________
What is the length of the longer leg?
____________________________
The shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.
How to get the length of the legs of the triangle?Here we know that we have a right triangle, and we know that:The hypotenuse measures √130 units.
The perimeter measures 14 + √130 units.
If we define:
x = shorter leg.
y = larger leg.
Then, using the Pythagorean theorem, we can write:x^2 + y^2 = √130^2 = 130
And for the perimeter equation we know that:
perimeter = x + y + √130 = 14 + √130
We can simplify this equation to:x + y = 14Then we have the system of equations:
x^2 + y^2 = 130
x + y = 14
Isolating one variable in the second equation we get.
x = 14 - y
Replacing that in the other equation we get:
(14 - y)^2 + y^2 = 130
Now we can solve this for y.
196 - 28y + y^2 + y^2 = 130
2y^2 - 28y + 196 - 130 = 0
2y^2 - 28y + 66 = 0
y^2 - 14y + 33 = 0
Using Bhaskara's formula we can get:
y = (14 ± √( 14^2 - 4*1*33))/2*1y = (14 ± 8)/2
Now, remember that y is the larger leg of the triangle, then:y = (14 + 8)/2 = 11For the value of x we use:
x = 14 - y = 14 - 11 = 3x = 3the shorter leg of the right triangle measures 3 units, while the larger lag measures 11 units.
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