Answer:
The number of runners that finished in first place , second place and third place are 7 , 13 and 10 respectively.
Step-by-step explanation:
Let the no. of runners fished at first place be x
Let the no. of runners fished at second place be y
Let the no. of runners fished at third place be z
We are given that Lakeland High School had 30 individual- event placers
So, x+y+z=30 -----1
First-place finishers score 7 points
So, Total score of x runners = 7x
Second-place finishers score 4 points
So, total score of y runners = 4y
Third-place finishers score 1 point.
So, total score of z runners = z
We are given that 30 individual- event placers score a total of 111 points
So, 7x+4y+z=111 ----2
We are also given that The number of first- and second-place finishers was twice the number of third-place finishers.
x+y=2z ---3
Substitute the value from 3 in 1
x+y+z=30
2z+z=30
z=10
Substitute the value of z in 1 and 2
x+y=20 ----4 and 7x+4y=101 ---5
Substitute the value of x from 4 in 5
7(20-y)+4y=101
140-7y+4y=101
140-3y=101
39=3y
`13=y
Substitute the value of y and z in 1
x+13+10=30
x=7
Hence the number of runners that finished in first place , second place and third place are 7 , 13 and 10 respectively.
why is 2 times 3/4 less then 2
since 3/4 is less than one. if the number is less than one, it will always result in a smaller number. And anything multiplied to one is the other number.
EX: 1*3=3
3/4*3= 9/4= 2 1/4= 2.25
Because linear pairs are complementary, the remaining two angles must also be right angles. true or false?
[tex]\large\boxed{\textsf{False.}}[/tex]
[tex]\Large\underline{\textsf{What are Linear Pairs?}}[/tex]
[tex]\textsf{Linear Pairs are 2 angles that form a straight angle.}[/tex]
[tex]\textsf{Straight angles are equal to 180}^{\circ}.[/tex]
[tex]\textsf{Complementary angles are 2 angles that form a right angle.}[/tex]
[tex]\textsf{Right angles are equal to 90}^{\circ}.[/tex]
[tex]\textsf{Because Linear Pairs are equal to 180}^{\circ}, \textsf{Linear Pairs are Supplementary.}[/tex]
[tex]\textsf{For this problem, if linear pairs are complementary, the other 2 angles will be 90}^{\circ}?[/tex]
[tex]\textsf{False, assuming we are referring to angles that add up to 360}^{\circ}.[/tex]
[tex]\textsf{The angles would add up to 270}^{\circ} \ \textsf{instead.}[/tex]
Line m passes through (5,-3) and is parallel to a line that passes through (1,-4) and (9,-2).
The required equation of the line is given as y =1/4x -17/4.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
Substitute the value in the above equation,
m = -2 + 4 / 9 - 1
m = 2 / 8
m = 1/4
Since the slope of the parallel lines is equal,
The equation of the parallel is given as,
y - y₁ = m (x - x₁)
Substitute the point in the equation,
y + 3 = 1/4(x - 5)
y = 1/4x - 5/4 -3
y =1/4x -17/4
Thus, the required equation of the line is given as y =1/4x -17/4.
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Which value of x satisfies the equation |-2x|=10
Answer:
Step-by-step explanation:
First you will divide I-2xI on both sides that should look like this:
-2x/-2 = 10/-2
when you divide it your -2‘s should cancel out and you should be left with
-x=10/-2
when You divide 10/-2 you should get -5
10/-2= -5
your answer should look like this then
-x=-5
-5 is just one of your answers the other is 5
To get rid of the negative on the -X you have to didvide it by both sides
-x/-x=-5/-x
your answer should be
X= 5
your final answers are
-5 or 5
The value of x is "5".
Equation:[tex]|-2x|=10[/tex]
x=?
[tex]\to |-2x|=10\\\\\to 2x=10\\\\\to x=\frac{10}{2}\\\\\to x= 5[/tex]
Therefore, the final answer is "5".
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1/2x + 24 = 6X-6
Help me
Answer:
x=5.45
Step-by-step explanation:
Answer:
answer
Step-by-step explanation:
Exact form: 60/11
Decimal form: 5.45
Mixed form: 5 5/11
Hope it answers your question
John puts $300 into a savings account. He puts more money into the account each month. After 12 months he has $1500 in his savings account. At this rate, how much will he have in his savings acount after 24 months?
Answer:
7200
Step-by-step explanation:
I'm not going to explain but i will say that you should multiply 300x 24 to get you answer
Answer:
[tex]y= 100x +300[/tex]
[tex]x=[/tex] How many months
Step-by-step explanation:
In this equation a
We are solving to find after 24 months you want to plug 24 in to where X is and solve the eqaation from there.
Hope this helps!!
PLEASE HELP!!
What value of x makes this equation true?
5-2(x + 8) = 6x + 7
Answer:
Step-by-step explanation:
5-2x+16=6x+7
-2x-6x=7-5-16
-8x=-28
x=28/8=14/4=7/2=3.5
will be nice if you give me brainlies.Good luck!
I WILL AWARD BRAINLIEST
Answer:
Choice 2 and 4
Step-by-step explanation:
3x-1>2
+1 +1
3x>3
x>1
8-4x<4
-8 -8
-4x<-4
x>1
Help please ASAP! THANKS!!!!
Answer:
(3,1)
Step-by-step explanation:
Which property is used in the following equation (3•4)•5-3•(4•5)
Answer:
8
Step-by-step explanation:
help meee please :))))
Answer:
90°
Step-by-step explanation:
Find the slope of the line
y = –3/8x − 6/5
Answer:
-3/8
Step-by-step explanation:
This equation is formatted as y=mx+b where m is the slope of the line, x is the x value, and b is the y-intercept. When finding the slope of such an equation, just find what the coefficient of x in the function is. So, this equation is y = -3/8x - 6/5 and m is -3/8, so your slope is -3/8. Hope that helps!
Marissa's piggy bank has 42 coins in dimes and quarters. The combined value is $7.35. How
many coins of each type are there?
Answer:
21 quarters and 21 dimes
Step-by-step explanation:
21 quarters = 5 dollars and 25 cents
21 dimes = 2 dollars and 10 cents
add together and you get the total
21 quarters and 21 dimes
Triangle ABC is a scaled copy of triangle DEF. Side AB measures 12 cm and is the longest side of ABC. Side DE measures 8 cm and is the longest side of DEF.
Triangle ABC is a scaled copy of triangle DEF with what scale factor?
Answer: scale factor = 1.5
Step-by-step explanation:
[tex]\text{Scale factor}=\dfrac{\text{Side length of image}}{\text{Side length of original figure}}[/tex]
Given: Triangle ABC is a scaled copy of triangle DEF.
Side AB = 12 cm and is the longest side of ABC.
Side DE = 8 cm and is the longest side of DEF.
[tex]\text{For similar triangles, Corresponding sides are proportional.}[/tex]
AB is corresponds DE (longest side of both triangles)
So, [tex]\text{Scale factor}=\dfrac{\text{AB}}{\text{DE}}=\dfrac{12}{8}=1.5[/tex]
Hence, the scale factor = 1.5.
1.) A ladder is leaning against the side so that the distance on the ground between
the base and the house is 7 feet.
If the ladder is 15 feet long, then what is the angle at which the ladder is leaning?
Answer:
62.182°
Step-by-step explanation:
Using cos and sin you are able to find the height of the ladder from the bottom of the house to the place the top of the ladder is. You can do this by making a triangle. By using the lengths and angles already present you are able to find all angles of the triangle.
The angle at which the ladder is leaning is 62.18°.
What is trigonometry?Trigonometry is the branch of mathematics that deals with calculating the angles of triangles or the lengths of their sides. It mainly concerned on the properties of right angled triangle.
For the given situation,
The length of the ladder = 15 feet
The distance between the house and the ladder base = 7 feet
The angle at which the ladder is leaning can be found by using trigonometric ratio, cos θ.
we know that, [tex]cos[/tex] θ = [tex]\frac{Base}{Hypotenuse}[/tex]
The figure below shows the relationship between the sides.
⇒ [tex]cos[/tex] θ = [tex]\frac{7}{15}[/tex]
⇒ θ = [tex]cos^{-1}(\frac{7}{15} )[/tex]
⇒ θ = [tex]62.18[/tex]
Hence we can conclude that the angle at which the ladder is leaning is 62.18°.
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On a treasure map, the actual distance varies
directly to the scaled distance. If 15 actual
miles is represented by 3 centimeters on the
map, then how many centimeters on the map
are equivalent to 135 actual miles?
(A) 27 centimeters
(B) 32 centimeters
(C) 529 centimeters
(D) 675 centimeters
Answer:
Step-by-step explanation:
10 actual miles 2 cm 120 actual miles
If line b is perpendicular to line a, and line c is
perpendicular to line a, what is the slope of line c?
mc=
Answer:
y=x-2.5
Step-by-step explanation:
If it is perpendicular to a, just like b, it has the same slope, but, it has a y-intercept of 2.5, unlike b, which has a y-intercept of 1
Answer:
mc= 1
Step-by-step explanation:
correct on edge 2020
solve for x geometry
Answer:
Step-by-step explanation:
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
ln
(
6
x
)
=
ln
(
66
)
Expand
ln
(
6
x
)
by moving
x
outside the logarithm.
x
ln
(
6
)
=
ln
(
66
)
Divide each term by
ln
(
6
)
and simplify.
Tap for more steps...
x
=
ln
(
66
)
ln
(
6
)
The result can be shown in multiple forms.
Exact Form:
x
=
ln
(
66
)
ln
(
6
)
Decimal Form:
x
=
2.33829083
…
Answer:
X=19
Step-by-step explanation:
A full line must be 180 degrees and you already know that part of the line is 66 degrees. You do 180 minus 66 which gives you 114. That is the other unknown angle but it is asking for x, not the angle. You do 114 divided by 6 to get 19. Therefore, x=19.
How do you find the prime factorization of 72?
Step-by-step explanation:
explanation:
Divide the number to be factored by the prime numbers in turn. Test that result is a natural number. If so, it is a prime factor. Continue until the factorisation is complete.
— Зу + 5х = 26
- 2 - 5x = -16
y =
Answer:
y= -4
Step-by-step explanation:
-3y + 5x = 26
0y -5x = -14
____________
-3y = 12
y = -4
The diagram shows a figure made of two right rectangular prisms.
3 yd
9 yd
4 yd
8 yd
6 yd
22 yd
What is the total volume of the figure?
O A. 52 cubic yards
B. 108 cubic yards
O c. 1,056 cubic yards
O D. 1,164 cubic yards
O E. 1,584 cubic yards
Answer: O A.52 cubic yards
Step-by-step explanation: if u add 3+9+4+8+6+22= 52 cubic yards in the total volume of the figure :>
Evaluate 2n + t2 when n =-4 and t = -10
Answer:
92
Step-by-step explanation:
Given
2n + t² ← substitute n = - 4 and t = - 10 into the expression
= 2(- 4) + (- 10)² = - 8 + 100 = 92
Answer: -28
Step-by-step explanation: 2x-4=-8 and -10x2=-20 -8+-20=-28
pls mark brainiest thanks
name an angle complementary to
HQG because it is 55 degrees and 55 + 35 is 90, and complementary angles add up to 90 degrees.
Angle HQG
A square sand box has an area of 58 square meters. Which is the best estimate of the length of one side of the sand box ?
A 8.0 meters
B 5.6 meters
C 7.6 meters
D 7.0 meters
Answer:
Step-by-step explanation:
A 8.0
figure B is not a correct rotation of figure A
Not an answer. There should be a question here? I didn’t see one
Draw and find the value of the missing segment below.
Answer:
7
Step-by-step explanation:
-1/2 + 4/5v=-5/3 solve for V
Answer:
v = -35/25 or -1 11/24
Step-by-step explanation:
First, isolate the variable. We should add 1/2 on both sides of the equation to get 4/5v = -7/6. Then we divide 4/5 on both sides to get v = -35/24!
hope this helped!! <3
Multiplication Property of Equality
If 4x divided by 2=4 then______
A function that changes in the same way all the time is?
Answer:
A function that changes the same way can be a linear function.
y = a*x + b.
Where the rate of change (this is, how much changes y when x increases or decreases) is defined by the coefficient a, that is constant.
for example, suppose that when x = x0, we have y = y0
y0 = a*x0 + b.
Now x0 increases by one unit, to (x0 + 1)
y = a*(x0 + 1) + b = (a*x0 + b) + a = y0 + a.
Then if x increases (or decreases) 1 unit, y increases (or decreases) a units.
Now, we can define the rate of change of a function as it's derivate with respect to some variable.
In this case, if we derive with respect to x, we have:
y' = a
Then the rate of change is constant.
whats the mass of 9.4 x 10^25 atoms of lithium
I NEEDDD HELP