Answer:
(7,10)
Step-by-step explanation:
In a charity triathlon, Mark ran half the distance and swam a quarter of the distance. When he took a quick break to get a drink of Gatorade, he was just starting to bike the remaining 24 miles. What was the total distance of the race?
The total distance of the race is D = 96 miles
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let's denote the total distance of the race as "d" miles.
According to the given information, Mark ran half the distance and swam a quarter of the distance. This can be expressed as:
Distance Mark ran = d/2 miles
Distance Mark swam = d/4 miles
After Mark's quick break, he was just starting to bike the remaining 24 miles. Since he has already completed running and swimming, the total distance he has covered at that point is:
And this distance is equal to 24 miles, as given in the problem:
d/2 + d/4 + 24 = d
On simplifying the equation , we get
( 3/4 )d + 24 = d
Subtracting ( 3/4 )d on both sides , we get
( 1/4 )d = 24
Multiply by 4 on both sides , we get
d = 96 miles
Hence , the total distance of the race, denoted by "d", is 96 miles
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"Write two equations: one parallel, one perpendicular to (5,-2) y= 1/5x-3
Write in the form y=mx±b,y=mx±b (first the parallel, then the perpendicular)"
Answer:
For parallel:
gradient is 1/5
[tex]y = mx + c[/tex]
consider (5, -2):
[tex] - 2 = ( \frac{1}{5} \times 5) + c \\ - 2 = 1 + c \\ c = - 3[/tex]
[tex]{ \boxed{ \bf{equation : y = \frac{1}{5}x - 3 }}}[/tex]
For perpendicular:
gradient, m1:
[tex]m _{1} \times m_{2} = - 1 \\ m _{1} \times \frac{1}{5} = - 1 \\ \\ m _{1} = - 5[/tex]
gradient = -5
[tex]y = mx + c \\ - 2 = (5 \times - 5) + c \\ - 2 = - 25 + c \\ c = 23[/tex]
[tex]{ \boxed{ \bf{equation :y = - 5x + 23 }}}[/tex]
Answer:
Parallel: [tex]y=\displaystyle \frac{1}{5}x-3[/tex]
Perpendicular: [tex]y=-5x+23[/tex]
Step-by-step explanation:
Hi there!
What we must know:
Slope intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)Parallel lines always have the same slopePerpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, -6/7 and 7/6)Finding the Parallel Line
[tex]y=\displaystyle \frac{1}{5} x-3[/tex]
Given this equation, we can identify that its slope (m) is [tex]\displaystyle \frac{1}{5}[/tex]. Because parallel lines always have the same slope, the slope of the line we're currently solving for would be [tex]\displaystyle \frac{1}{5}[/tex] as well. Plug this into [tex]y=mx+b[/tex]:
[tex]y=\displaystyle \frac{1}{5}x+b[/tex]
Now, to find the y-intercept, plug in the given point (5,-2) and solve for b:
[tex]-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b[/tex]
Therefore, the y-intercept is -3. Plug this back into [tex]y=\displaystyle \frac{1}{5}x+b[/tex]:
[tex]y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3[/tex]
Our final equation is [tex]y=\displaystyle \frac{1}{5}x-3[/tex].
Finding the Perpendicular Line
[tex]y=\displaystyle \frac{1}{5} x-3[/tex]
Again, the slope of this line is [tex]\displaystyle \frac{1}{5}[/tex]. The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-5x+b[/tex]
To find the y-intercept, plug in the point (5,-2) and solve for b:
[tex]-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b[/tex]
Therefore, the y-intercept is 23. Plug this back into [tex]y=-5x+b[/tex]:
[tex]y=-5x+23[/tex]
Our final equation is [tex]y=-5x+23[/tex].
I hope this helps!
In a survey of mobile and telephone, it was found that 200 people had telephone, 25
had both, 135 did not have telephone and 300 did not have mobile.
i. How many people participated in the survey?
ii. How many people had mobile only
Answer:
a)660
b)135
Step-by-step explanation:
a)200+25+135+300=660
b) 135 because since 135 do not have telephone, they will have mobile instead.
Hope this helps! Thanks.
PLZZ HELP ME (50 POINTS)
Answer:
x = w / 57r is the answer
Find the coordinates of the point P that lies along the directed line segment from A(-2,5) and B(2,-3) and partitions the segment in the ratio of 4 to 1.
A (1.6, -1.2)
B (1, 4.5)
C (1.2, -1.4 )
D (9, -2)
Part B
Find the coordinates of the point P that lies along the directed line segment from A(-3,-4) and B(5,0) and partitions the segment in the ratio of 2 to 3.
Group of answer choices
(-2.4, 0.2)
(0.2, -2.4)
(-0.2, 0.4)
(-0.4, 6)
Answer:
help
Step-by-step explanation:
A survey was conducted to see which of four major sports American college students prefer to watch: baseball, basketball, football, or soccer. Of those surveyed, 53% said they prefer football, 26% chose basketball, and 15% preferred baseball. If there were 1,000 American college students in a room, how many would you expect to prefer soccer?
Answer:
Step-by-step explanation:
53+26+15=94
94-100=6
So I'm just gonna assume that 6% of people prefer to watch soccer.
Now to solve how many people out of 1000 would watch soccer we'd have to multiply 1000 by 0.09 which gives us 90.
So 90 people out of 1000 would prefer to watch soccer.
Please help me I don’t understand how to do it. If you can please use a data table to explain how to do it.
Answer:
The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.
Step-by-step explanation:
Let us have x liters of the .7 mixture and y liters of the .6 mixture.
We want total liters to be 3.5 which means we need x+y=3.5 . I don't like the decimal in the equation so I'm going to multiply both sides by 10: 10x+10y=35
We also need the .7x+.6y=.62(3.5) . I hate the decimal business going on in this question so I'm going to multiply by 1000 which gives 700x+600y=62(35) .
So we have the system
700x+600y=62(35)
10x+10y=35
I'm going to setup this up for linear combination/elimination.
Multiply bottom equation by 60.
700x+600y=62(35)
600x+600y=60(35)
Subtract equations (bottom from top):
(700-600)x+(600-600)y=35(62-60)
Simplify:
100x+0y=35(2)
100x=70
Divide both sides by 100:
x=70/100
x=7/10
Going back to x+y=3.5 along with x=7/10 or .7 liters to find y.
y=3.5-x with x=.7
y=3.5-0.7
y=2.8
The 70% mixture makes up 0.7 liters of the solution whereas the 60% mixture makes up 2.8 liters of the solution.
Pic added.
Another way to do problem:
.7x+.6(3.5-x)=.62(3.5)
Multiply and distribute:
.7x+2.1-.6x=2.17
Combine like terms on left:
.1x+2.1=2.17
Subtract 2.1 on both sides:
.1x=.07
Multiply both sides by 10:
x=0.7 liters
Now the other acid solution is 3.5-0.7 which is 2.8 litera.
after a 20% reduction, you purchase a television for $336. What was the television's price before the reduction?
What is the value of 6 (2b-4) When b=5
Answer:
36
Step-by-step explanation:
Replace the 2b with 10 and then do the parenthesis, so 10-4=6
now multiply it with the 6 outside the parenthesis and you get 36
Hi! I'm happy to help!
First of all, we need to substitute b into the expression.
6(2b-4)
6((2×5)-4)
Now we use the order of operations, or PEMDAS (Parenthesis, Exponents, Multiplication or Division, and Addition or Subtraction) to finish simplifying.
We see that 2×5 is inside two sets of parenthesis, so we solve that first
6((2×5)-4)
6((10)-4)
We cam remove the extra set of parenthesis because there isn't an expression inside of it any more.
6(10-4)
Now, we look inside of the parenthesis again and we see 10-4
6(10-4)
6(6)
The six next to the parenthesis has no sign next to it, which means to multiply.
6×(6)
Now we can remove the parenthesis.
6×6
Now, we just simply multiply.
6×6
36
To sum it up: The value of 6 (2b-4) When b=5 is 36
I hope this was helpful, keep learning! :D
Matrix addition is shown here.
([3,-2,3],[-5,2,11])=([-5,-4,4],[-4,2,-1])=([m,-6,-2],[-9,7,5])
Enter the value of s
Answer:
The value of s=10
Step-by-step explanation:
11+(-1)=10
INSTRUCTIONS: This is a numerical series. Find the missing item
10.0.18 0.36 0.72|?|2.88
A. 0.9
B. 1.26
C. 1.44
D. 1.62
Answer: C. 1.44
Step-by-step explanation:
Each number gets multiplied by 2, so it's an exponential series in a way.
You must multiply .72 by 2 to get 1.44.
What is 5.67 written in standard form?
Answer:
0.567 X 10
Step-by-step explanation:
5.67 in standard form is 0.567
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x):
Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (2 points)
Part B: Solve for k in each type of transformation. (4 points)
Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (4 points)
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) to the left or shift it up
Part B
f(x+k) for a shift to the left
f(x) + k for a shift up
Part C
Looking at shifting f(x) to g(x) by going left, we are shifting 6 units to the left
f(x+6) will shift f(x) 6 units to the left
g(x) = f(x+6)
We can all shift f(x) up, we can shift up 18 units
f(x) +18 will shift the function up 18 units
g(x) = f(x) +18
Help me please! What shape is it?
You're a square !!!1!!!!!!!!11
Jordan has $20 to share among three people Jordan types 20÷3 into his calculator and gets 6.666666667 where should Jordan round
Answer: to the nearest tenth i believe, 6.8
Step-by-step explanation:
The round off should be ones place.
What is Rounding Off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.
Given:
20÷3
The resulting value is 6.666666667.
So, divide the money it should be round off to ones place to get a whole number which can make it easy to divide.
Hence, the round off should be ones place = 7
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simplify the expression 44=5g-8-g
Answer:13
Step-by-step explanation:
What’s the answer for 5g=20
Given that LMN and PQR are
complementary angles, find the measures
of the angles if the m LMN = 8x + 1 and
the m PQR = 2x + 9.
Answer:
∠ LMN = 65° , ∠ PQR = 25°
Step-by-step explanation:
Complementary angles sum to 90°
∠ LMN + ∠ PQR = 90° , that is
8x + 1 + 2x + 9 = 90
10x + 10 = 90 ( subtract 10 from both sides )
10x = 80 ( divide both sides by 10 )
x = 8
Then
∠ LMN = 8x + 1 = 8(8) + 1 = 64 + 1 = 65°
∠ PQR = 2x + 9 = 2(8) + 9 = 16 + 9 = 25°
1- Operations with Fractions
2 1/2 - 5/3
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{5}{6}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Solving the Problem...}}\\\\2\frac{1}{2} -\frac{5}{3}\\\\----------------\\\rightarrow \text{LCM} (2,3): 6\\\\\rightarrow 2\frac{1}{2}=\frac{5}{2}=\frac{5*3}{2*3}=\frac{15}{6}\\\\\rightarrow \frac{5}{3}=\frac{5*2}{3*2} =\frac{10}{6}\\\\\\\rightarrow \frac{15}{6} - \frac{10}{6}\\\\\rightarrow \boxed{\frac{5}{6}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Matrix addition is shown here.
-5 -4 t
W -6 -2
3 -2 3
+
-5 z 11
=
21
-4 2-1
-9 7 s
Enter the value of s, t, w and z
Answer:
I haven't learned matrix sorry
from 8 abc subtract abc. from 8 abc subtract 8
4. 2) 836
does anyone know this?
Answer:
418
Step-by-step explanation:
2) 836 = 836/2
=418
•°•2) 836=418
Answer:
836/2=418,Hope it helps.
a cylindrical barrel contains 42 gallons of oil the diameter is 18 inches. determine the radius of a barrel in centimetres
Is [tex] \frac{1}{ \sqrt{5} } [/tex] a rational or a non-rational number
Answer:
yes it is a rational number..
ans all these questions please
Answer:
the answer is in picture
if(2x-y)=4 then (6x-3y)=?
Answer:
12
Step-by-step explanation:
(2x-y)=4
Multiply the first equation by 3
3*(2x-y)=3*4
6x -3y = 12
2+3+4+6+6+5+8+9+4+3+5+8+9=
Answer:
72
Step-by-step explanation:
5,9,15,21,26,34,43,47,50,55,63,72
Answer: it's 72
ok!! hope it helps
what is the 30th square number
plz tell the answer
Answer:
900
.........................
Answer:
900
Step-by-step explanation:
30 square is like 30×30=900
Find the length of segment GH.
21
12
F
Answer:
GH = 9
Step-by-step explanation:
FH=FG+GH
21= 12+GH
GH = 21-12 =9
I hope I helped you^_^
brainiest to whoever right
Answer:
The area is 7.5 square units