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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S
55°
W
Angle STV is a right angle.
The measure of angle STW is 55°.
The measure of angle WTV is xº.
What is the value of x?
to
Х
5
=
?
Answer:
x= 35
Step-by-step explanation:
STV°= WTV° + STW°
STV°=90
WTV°=x
STW°=55
subtitute in above:
90= x + 55
x= 90-55
x= 35
Students in Ms. Bell’s geometry class created posters of geometric definitions. Which of the following is the most precise definition?
A. Parallel lines are lines that do not intersect.
B. A line segment is part of a line that has an endpoint.
C. Perpendicular lines are lines that intersect at a right angle.
D. An angle is formed by two lines, two segments or two rays in one plane.
Answer:
C
Step-by-step explanation:
D is missing 2 ideas.
An angle can be formed by a mixture of the types of figures quoted.An angle has common or shared endpoint.B: to me is unclear. A line does not have an endpoint. A ray does.
A: you need to mention that the lines are coplanar.
I think, brief though it is, C is the most complete and at the same time simplest choice.
Two angles are supplementary. The measure of the larger angle is 36 more than the measure of the smaller angle. Find their measures.
the answers are 72° and 108° but I need help showing my work
x = smaller angle
x+36 = larger angle, since its 36 degrees more than the smaller angle
The two angles x and x+36 must add to 180 if they are to be supplementary (aka form a straight line)
So this means we can say the following:
(smaller)+(larger) = 180
(x) + (x+36) = 180
2x+36 = 180
2x = 180-36
2x = 144
x = 144/2
x = 72 is the smaller angle
x+36 = 72+36 = 108 is the larger angle
As a check:
smaller+larger = 72+108 = 180
which shows they are supplementary and it confirms our answers
Step-by-step explanation:
let the smaller angle be x
then the measure of larger angle will be x+36
x+x+36=180°(being supplementary angle)
2x+36=180°
2x=180°-36
2x=144°
x=144°/2
x=72°
now,
the larger angle x+36 = 72+36=108°
write and solve an equation to find the value of X. please explain in details and show your work!
Answer:120 degrees
Step-by-step explanation:
5) If point M is (-3,-1) and point P is (2,8), what is the y-coordinate of the midpoint of MP ?
Answer:
Find the equation with a point and y-intercept.
y=(yx−5x)x+5
Step-by-step explanation:
help me plz branniest to whoever right
In a competitive examination negative marks of 2 are awarded for each wrong answers and 4 marks for every correct answer. If neerav gets 15 correct answers and 5 wrong answers and rajan gets 14 correct answers and no wrong answers, who gets more marks and by how much?
9514 1404 393
Answer:
Rajan gets 6 marks more
Step-by-step explanation:
Neerav's marks are (15)(4) +(5)(-2) = 60 -10 = 50.
Rajan's marks are (14)(4) = 56.
Rajan gets 6 more marks than Neerav.
Jasmine bought 3500g of flour. She used 3/7 of it to bake some tarts and 700g of it to bake a cake. Find the ratio of the amount of flour used for baking the cake to the amount of flour used for baking the tarts to the remaining amount of flour.
Answer: 15:13
Step-by-step explanation: 7/7=3500
1/7=3500÷7=500500x3=15001500+700=22003500-2200=13001500:130015 : 13 (if there is a need to simplify the ratio)Use the graph of f(x) to explain the relationship
between the real zeros of f(x) and its intercept(s).
4
A. f(x) has one real zero at --2 because the graph of the
function has an intercept at (0.-2).
B. f(x) has two real zeros at -4 and -2 because the
graph of the function has intercepts at (-4,0) and (0,
-2).
C. f(x) has no real zeros because the graph of the
function does not pass through (0,0).
D. f(x) has one real zero at 4 because the graph of the
function has an intercept at (-4, 0).
Answer:
D.f(x) has one real zero at 4 because the graph of the function has an intercept at (-4,0).
Solve the equation: 6/2(1+2) =?
Answer:
answer must be 9
Step-by-step explanation:
6/2×3
3×3
9 ans
Answer: 9
Step-by-step explanation:
( 6/2) = 3
( 1+2) = 3
3*3=9
can someone who's really good at math help me with this?
for f(x) evaluate each of the following:
a. f(0)
b. f(6)
show all your work
Answer:
Step-by-step explanation:
a)
f(0) is just the function f(x) evaluated at 0, meaning we need to plug in 0 to the function.
What piece of this function should we plug 0 in? Well, because 0 is less than 5, plug it into the first piece.
so f(0) = 0 + 4 = 5
b)
By similar reasoning:
f(6) = 8
because 5 <= 6 < 7
A triangle has side lengths of (7n-2p) centimeters, (2n+4q) centimeters, and (q-5p) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
It is 9n - 7p + 5q
Step-by-step explanation:
Perimeter formular:
[tex]perimeter = (side + side + side)[/tex]
substitute:
[tex]p = \{(7n - 2p) + (2n + 4q) + (q - 5p) \} \\ [/tex]
group like terms together:
[tex] = (7n + 2n) + ( - 2p - 5p) + (4q + q) \\ = 9n - 7p + 5q[/tex]
1 - 5(x+2)=10+5x
2- 7/8 (48x-8)+4=3(5x-19)
9514 1404 393
Answer:
infinite solutionsx = -2Step-by-step explanation:
1. The equation simplifies as follows:
5(x +2) =10 +5x
5x +10 = 5x +10 . . . . . eliminate parentheses, write in standard form
0 = 0 . . . . . . . . . . . . . . subtract 5x+10 from both sides
This is true for all values of x. Any value of x is a solution to this equation. There are an infinite number of solutions.
__
2. 7/8(48x -8) +4 = 3(5x -19) . . . . given
42x -7 +4 = 15x -57 . . . . . . . . eliminate parentheses
25x = -50 . . . . . . . . . . . . . add 7-15x to both sides
x = -2 . . . . . . . . . . . . . . divide by 25
Check
7/8(48(-2) -8) +4 = 3(5(-2) -19) . . . . substitute for x
7/8(-96 -8) +4 = 3(-10 -19)
7/8(-104) +4 = 3(-29)
-91 +4 = -87 . . . . . . . . . . true
please help somebodydds
Answer :
RA , TR , and HP
................
PLEASE HELP IN A RUSH
What is the least common multiple (LCM) of 4 and 7?
Answer:
The least common multiple of 4 and 7 is 28
7 - 3x = 2x + 7 – 5x
Step by step
Answer:
0
Step-by-step explanation:
7-7=2x-5x+3x
0=2x-5x+3x
A water wheel has a radius of 18 feet. the wheel is rotating at 5 revolutions per minute. find the linear speed, in feet per minute, of the water
Answer:
The linear speed is
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
we have
substitute
step 2
Find the linear speed in feet per minute
we know that
The wheel is rotating at 10 revolutions per minute
Convert revolutions to feet
Remember that
One revolution is equal to the circumference of the circle
so
10 revolutions is equal to
therefore
The linear speed is
Find the sum of the even numbers from 1 to 300
a) 14,280
b) 22,650
c) 16,100
d) 15,460
Answer:
The answer is 22,650
So, option b for you
Step-by-step explanation:
To find the sum of even numbers from 2 to 300, the formula we use is,
N ( N + 1 )
Where N is given by,
N = [( first number + last number)/2] - 1
So here, N = [ (2 + 300 ) / 2 ] - 1 = 150
And hence Sum = 150 * 151 = 22650
how to answer tyhis question plz i need help quick
√400=x² what is x? Thanks
Answer:
x=4.47213
I hope it's helps you
I NEED HELP IM DOING A EXAM
Solve the equation and check your solution.
1. 3(x+6)=18+3x
2. -2(x-1)=2-2x
3. x+4=-2+x
4. -2(x+2)=5-2x
Answer:
1.0
2.0
3.2
4.3
Step-by-step explanation:
1.3x+18-3x+18
2.-2x+2-2+2x
3.x-x+4-2
4.-2x-4+5+2x
Answer:
3x + 18 = 18 + 3x-2x + 2 = 2 - 2x4 = -2 (the statement is false)-4 = 5 (the statement is false).......
Please help with this question
Answer:
bdjjirलअाफखनल पनपअ लbबजदहडनदजडनफjnnkdffruidirbttjt tjrjnf h
Step-by-step explanation:
uuhsbd?eg\bnothing hereafter hgbg
Can a triangle be formed with side lengths of 2inches, 3 inches, and 6 inches?
Take 9 numbers forming a calendar and mark 4 number corner. Add the square of diagonal pair and difference of the sum
There are 15 people expected for a dinner. If 3 ounces of corn serve 1 person and 1 can of corn is 9 ounces, how many cans of corn should be bought for the dinner?
Answer:
5 cans
Step-by-step explanation:
First multiply 15 by 3 to see how many ounces are needed in total: 15x3=45
Then divide 45 by 9 to see the amount of cans: 45/9=5
Three times the sum of a number and 2 is the same as three-fifths of the sum of the same
number and 22. What is the number?
Answer:
3
Step-by-step explanation:
3(n+2)=3/5(n+22)
3n+6=3/5n+66/5
3n-3/5n = 66/5 - 6
2.4n = 7.2
n = 7.2/2.4
n = 3
write rhis number in standard notation. 1.342×10^-7
Answer:
0.0000001342
Step-by-step explanation:
A student says that if 5x2 = 20, then x must be
equal to 2. Do
you agree or disagree with the
student? Justify your answer.
Answer:
I agree with the student's answer. "x" cannot be -2 because then it would make -20 which is not equal to 20:
5(-2)(2) = ?
-10 x 2 = ?
? = -20
-20 ≠ 20
Step-by-step explanation:
Justificaiton:
5(x)(2) = 20
10(x) = 20
10/10(x) = 20/10
x = 2
Second Justification:
5(x)(2) = 20
5/5(x)(2) = 20/5
2x = 4
2x/2 = 4/2
x = 2
Answer:
Step-by-step explanation:
Noah bought 5 pounds of onions at $2 per pound and a bag of salad greens for $4. How much money did he spend?cant someone help me please
Suppose an ATM PIN must consist of 6 numbers from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, with repeats allowed. For example, an acceptable PIN could be 955123.
1. How many possible ATM PINs are possible?
2. If someone had one attempt to guess an ATM PIN, what is the probability they would guess correctly with one attempt?
Answer:
1) the no. of possible pins are 6×5×4×3×2×1
=720
2) the probability is 1/720