Answer:
5 meters/second
Step-by-step explanation:
100meters/20 seconds gives the average of 5 m/s
Final answer:
The runner's speed in the hundred meter race completed in 20 seconds is 5 meters per second. To calculate this, divide the total distance (100 meters) by the total time (20 seconds).
Explanation:
To calculate the speed of the runner in meters per second, we divide the distance travelled by the time it took to complete that distance. In this case, the runner completed a 100 meter race in 20 seconds. Using the formula speed = distance/time, we find that the speed is 100 meters / 20 seconds = 5 meters per second.
If the sprinter accelerates for the first 20 meters and then maintains that speed for the remainder of the 100-meter dash, we must first calculate the acceleration period's average speed. As it takes 20 seconds to run 100 meters, the speed over those 20 meters is also 5 meters per second. Once the sprinter reaches this speed at 20 meters, he will continue at this constant speed for the remaining 80 meters. Thus, the time to complete the race is the time taken to accelerate for 20 meters plus the time taken to run the remaining 80 meters at 5 m/s.
the slope is 35. The y-intercept is 550. what can you conclude?
If you are given the slope and y-intercept of a line, you can conclude several things about the line and use them to write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
For the values you've given:
- The slope (m) is 35.
- The y-intercept (b) is 550.
From these pieces of information, you can conclude:
1. **Slope (Steepness and Direction):** Since the slope is 35, this tells us that the line is relatively steep and rises quickly. The slope is positive, which means the line slants upwards from left to right. Specifically, for every one unit that x increases, y increases by 35 units.
2. **Y-intercept (Starting Point):** The y-intercept is where the line crosses the y-axis. Since the y-intercept is 550, it indicates that the line will cross the y-axis at the point (0, 550). This is the starting point of the line if you begin plotting from the y-axis.
With these conclusions, you can write the equation of the line in slope-intercept form:
\[ y = 35x + 550 \]
This equation allows you to predict or calculate the value of y for any given value of x along the line. It also enables you to graph the line by plotting the y-intercept and using the slope to determine the direction and steepness of the line. Remember, a line extends infinitely in both directions on the graph, so the portion you draw depends on the context or constraints of the particular situation you are modeling with the line.
Given the following sequence {a^k} beginning with a0=4
4,11,18,25,32,39
What is the value of a4?
==================================
Explanation:
Simply pair each value given in the sequence with a0,a1,a2,etc like so
a0 = 4
a1 = 11
a2 = 18
a3 = 25
a4 = 32
a5 = 39
Miami and Orlando are 205 miles apart. If a map shows them as 5 inches apart, give the scale.
Answer:
1 inch = 41 miles
Step-by-step explanation:
205 / 5 = 41
1 inch = 41 miles
Answer:
41 miles per inch
could be answered as 41/1 or 41:1
Step-by-step explanation:
Use a ratio to find the scale.
205/5
Divide the numerator and denominator by 5 to simplify.
41/1
csc^2x – 5 csc x = 0
The solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]
To find the solutions for [tex]\( \csc^2x - 5\csc x = 0 \)[/tex], we can factor the expression:
[tex]\[ \csc x (\csc x - 5) = 0 \][/tex]
This equation is satisfied when either [tex]\(\csc x = 0\) or \(\csc x - 5 = 0\)[/tex].
1. For [tex]\(\csc x = 0\)[/tex], we know that [tex]\(\csc x\)[/tex] is the reciprocal of the sine function, and sine is 0 at multiples of [tex]\(\pi\)[/tex]. Therefore, [tex]\(x = n\pi\)[/tex] where n is an integer.
2. For [tex]\(\csc x - 5 = 0\)[/tex], solving for [tex]\(\csc x\)[/tex] gives [tex]\(\csc x = 5\)[/tex], and the sine of an angle is the reciprocal of its cosecant. Therefore, [tex]\(x = \sin^{-1}(1/5)\).[/tex]
In summary, the solutions are [tex]\(x = n\pi\) and \(x = \sin^{-1}(1/5)\).[/tex]
The complete question is probably:
What are the solutions for \( \csc^2x - 5\csc x = 0 \)?
There are less than 200 apples in a box. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?
Answer:
There can be 180 apples in that box.
Step-by-step explanation:
1. Let's review the information given to answer the question correctly:
Number of apples in a box < 200
2. It is known that 2, 3, 4, 5, or 6 kids can share these apples evenly. How many apples can be in that box?
The answer is that the number of apples that can be in the box is the highest multiple of 2, 3, 4, 5, and 6 that is close to 200.
The common multiples for this set of numbers are 60, 120, 180, 240, 300 and so on with 60 as the constant.
Therefore, the highest number that is multiple for this set of numbers and at the same time lower than 200 is 180.
There can be 180 apples in that box.
Answer:
120 or 180 apples
Step-by-step explanation:
It hasd to be divisible by 5 so it can only end in fives and zeroes next it has to be divisible by 2 so that narrows it tdown to only number that end in zero the it has to be divisible by 3 once yo find that you have two answers
120 or 180 and that is how many apples can be in the box
Find the equation of a line (5,-2) (-3, -2)
Answer:
y=-2
Step-by-step explanation:
y-y1=m(x-x1)
m=slope & (x1, y1) is a point on the line
m=(y2-y1)/(x2-x1)
m=(-2-(-2))/(-3-5)
m=(-2+2)/(-8)
m=0
y-(-2)=0(x-5)
y+2=0
y=0-2
y=-2
Sandwiches
Veggiburger....... .........03.25
Roast BeetWrap............ $4.50
Ham and Cheese..............$3.75
Side Orders
Steak Fries.....
..$1.50
Salad........
...$2.50
Soup.
$2.25
Beverages
Cola
Ice Tea.
Coffee......
Water...
..$1.50
..$1.75
...$0.90
$1.00
If you and a friend order 2 veggiburgers, one salad, one fries and 2 coffees, what is the total bill
with 4% tax and 15% tip?
$13.70
0
$16.43
$15.67
•
$14.64
Thing
The total bill is $14.64 ⇒ last answer
Step-by-step explanation:
The given is;
Sandwiches
Veggieburger................$3.25Roast Beet Wrap.............$4.50Ham and Cheese....... ....$3.75Side Orders
Steak Fries.......$1.50Salad..................$2.50Soup...................$2.25Beverages
Cola...................$1.50Ice Tea..............$1.75Coffee...............$0.90Water.................$1.00∵ You order 2 veggieburgers, one salad, one fries and 2 coffees
∵ The price of the 1 veggieburgers = $3.25
∵ The price of the 1 salad = $2.5
∵ The price of the 1 fries = $1.5
∵ The price of the 1 of one coffee = $0.9
∴ The cost of the order = 2(3.25) + 1(2.5) + 1(1.5) + 2(0.9)
∴ The cost of the order = 6.5 + 2.5 + 1.5 + 1.8 = $12.3
∵ There is a tax 4%
∴ The tax = 4% × 12.3 = [tex]\frac{4}{100}[/tex] × 12.3 = $0.492
∵ There is a tip 15%
∴ The tip = 15% × 12.3 = [tex]\frac{15}{100}[/tex] × 12.3 = $1.845
To find the total bill add the cost of the order, the tax and the tip
∵ The total bill = cost of the order + tax + bill
∴ The total bill = 12.3 + 0.492 + 1.845
∴ The total bill = $14.637 ≅ $14.64
The total bill is $14.64
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A recipe for 12 servings of soup calls for 8 cups of chicken broth. How
many cups of broth are needed to make 30 servings of the soup?
Answer:
20 cups of broth are needed to make 30 servings of the soup.
Step-by-step explanation:
This is a typical proportion math problem.
Just set up the proportion and solve for the unknown variable, let it be x, because it's simple to use.
12/8=30/x
simplify 12/8 to 3/2,
3/2=30/x
cross product,
2*30=3*x
60=3x
x=60/3
x=20
Number of cups of broth needed for making 30 servings is 20.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
We have,
Cups of broth needed for 12 servings of soup = 8 cups
Let cups of broth needed for 30 servings of soup = x cups
Using the concept of proportion,
12 / 8 = 30 / x
Doing the cross multiplication,
12x = 8 × 30
12x = 240
x = 240 / 12
x = 20
Hence 20 cups of broth are needed to make 30 servings of the soup.
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Solve the equation.
a² = 100
Enter the correct answer in the boxes.
a = 10 or a = ?
A positive number is multiplied by itself and then 7 is added. The answer is 16. What is the number?
Answer:
3
Step-by-step explanation:
To solve this you have to work backwards with what you are given.
16-7=9
Then we know that a number has to be multiplied by itself to equal nine the only number that follows that criteria is 3
3*3=9+7=16
Answer:
3
Step-by-step explanation:
Work backwards. 16 Subtract 7. Take square root. We take the square root because that is how to undo a number that was multiplied by itself.
16-7=9 √(9)=3
Check this by going through the same steps listed in the question:
A positive number is multiplied by itself. then 7 is added. the answer is 16
3×3=9
9+7=16
A triangle has two sides of length 40 cm and an angle of 110°.
a) Determine the length of the third side. Then find the perimeter of the triangle.
47
b) Determine the area of the triangle
Answer:
a) c = 65.532 cm
P = 145.532 cm
b) A = 751.754 cm²
Step-by-step explanation:
This is an isosceles triangle. The given angle is obtuse, so it must be the vertex angle.
a) One way to find the length of the third side is law of cosine:
c² = a² + b² − 2ab cos C
c² = 40² + 40² − 2(40)(40) cos 110°
c = 65.532
Another way is to cut the triangle in half and use sine.
sin (110°/2) = (c/2) / 40
c = 80 sin 55°
c = 65.532
The perimeter is the sum of the sides:
P = 40 + 40 + 65.532
P = 145.532
b) You can find the area using the SAS equation:
A = ½ ab sin C
A = ½ (40)(40) sin 110°
A = 800 sin 110°
A = 751.754
Another way is to split the triangle in half, find the height using cosine, then use half the base times height.
cos (110°/2) = h / 40
h = 40 cos 55°
h = 22.943
A = ½ ch
A = ½ (65.532) (22.943)
A = 751.754
Help?! Can somebody tell me the answer and can they explain how to do it?
Answer:
[tex]15x^7y^5[/tex]
Step-by-step explanation:
Given
[tex]5x^3y^2\times 3x^4y^3[/tex]
Rewrite it as
[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)[/tex]
Use power property:
[tex]a^m\cdot a^n=a^{m+n},[/tex]
so
[tex]x^3\cdot x^4=x^{3+4}=x^7\\ \\y^2\cdot y^3=y^{2+3}=y^5[/tex]
Then
[tex](5\cdot 3)\times (x^3\cdot x^4)\times (y^2\cdot y^3)=15\times x^7\times y^5=15x^7y^5[/tex]
If 2a = 80 and b = c, what is the measure of b
A.) 40
B.) 50
C.) 80
D.) 100
Answer:
From what I can tell from the image, b is equivalent to B.) 50°
Step-by-step explanation:
So to start off 2a=80° there is 2 a's. so you subtract 80° from 180° to get 100°.
now b=c and their is 100° left over. So 100°/2 is 50° because if b=50° and c=50° both angles equal 100°.
Answer : The correct option is, (B) 50
Step-by-step explanation:
As we are given :
2a = 80
b = c
As we know that:
The sum of interior angles of a triangle is equal to [tex]180^o[/tex].
That means,
[tex]\angle A+\angle B+\angle C=180^o[/tex]
[tex]80^o+\angle B+\angle C=180^o[/tex]
and, [tex]\angle B=\angle C[/tex]
So,
[tex]80^o+2\angle B=180^o[/tex]
[tex]2\angle B=180^o-80^o[/tex]
[tex]2\angle B=100^o[/tex]
[tex]\angle B=\frac{100^o}{2}[/tex]
[tex]\angle B=50^o[/tex]
Thus, the value of 'b' is [tex]50[/tex]
A bookcase has 3 shelves with a total of 24 books. The top shelf has 8 mystery books. The middle shelf has 10 math books. The bottom shelf has 6 science books. Two books are now taken off each shelf. What fraction of the books remaining on the three shelves are math books? Express your answer as a common fraction.
Answer:22/24 or 11/12
Step-by-step explanation:
Answer:
Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.
Step-by-step explanation:
4/9
A total of 814 tickets were sold for the school play. They were either adult tickets or student tickets. There were 64 more student tickets sold than adult tickets. How many adult tickets
Answer:
STUDENT TICKETS SOLD = 439ADULT TICKETS SOLD = 375814 - 64 = 750
750 ÷ 2 = 375
375 + 64 = 439
The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.
Explanation:The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.
According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).
With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.
To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.
So, 375 adult tickets were sold.
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Enter an equation in point-slope form for the line.
Slope is O and (6, 7) is on the line.
Answer:
[tex]\displaystyle y = 7[/tex]
Step-by-step explanation:
Since the rate of change [slope] is zero, that automatically makes our equation set equal to the y-coordinate of the ordered pair, which in this case is the y-intercept.
I am joyous to assist you anytime.
need some help with this please
Answer:
40 and 50
Step-by-step explanation:
We know that River's mom drove for 45 minutes. Furthermore, at x miles per hour for a time amount y, she drove 10 miles, and at x+10 miles per hour for time amount z, she drove 25 miles. We can set up the equations like this:
x*y = 10
(x+10)*z = 25
y+z = 0.75
I knew to include time as the variable because time was given at the end, and is the only way possible to solve this. Furthermore, we can multiply x and y because we drive for x miles per hour for y hours, so
[tex]\frac{x miles}{hours} * \frac{yhours}{1} = xmiles*y[/tex]
I turned 45 into 0.75 as 45 is 3/4 of an hour, and y and z are in hours.
We're kind of stuck here, so it would be nice if we could limit the variables in an equation. One way to do this would be to solve for y in the first equation, so x=10/y. Then, we can plug that into the second equation to get
(10/y+10)*z=25
Combining that with the third equation, we can solve for z in the second equation to get that 25/(10/y+10)=z, and then plug that into the third to get that
y+25/(10/y+10) = 0.75
Multiplying both sides by 10/y+10 to get rid of the denominator, we get
10+10y+25=7.5/y+7.5
Then we multiply by y to get rid of the denominator
10y+10y²+25y=7.5+7.5y
Subtracting 7.5+7.5y to get everything on one side for a quadratic equation
10y²+27.5y-7.5=0
Plugging this into the quadratic equation, we get than y either equals -3 or 0.25. It's clear that you can't have negative time, so y = 0.25
Then, 0.75-0.25=0.5=z, and 10/0.25=40, so x=40, and x+10=50 for the 2 driving speeds
A Shark Weighs 405 kilograms and 68 grams a second shark weighs 324 kilograms and 75 grams how much more does the first shark weigh in grams than the second shark
Answer:
7 grams
Step-by-step explanation:
If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!
Answer:
7 grams
Step-by-step explanation:
Find three solution of equation - 4X+2Y-5=0
(x,y) =
(x,y) =
(x,y) =
Answer:
(0,2.5), (-1.25,0) and (3,8.5)
Step-by-step explanation:
we have
[tex]-4x+2y-5=0[/tex]
This is a linear equation (equation of a line)
If a ordered pair is a solution of the linear equation, the the ordered pair must satisfy the linear equation
1) Find the y-intercept
The y-intercept is the value of the y when the value of x is equal to zero
For x=0
substitute the value of x in the linear equation and solve for y
[tex]-4(0)+2y-5=0[/tex]
[tex]2y=5[/tex]
[tex]y=2.5[/tex]
The ordered pair is (0,2.5)
2) Find the x-intercept
The x-intercept is the value of the x when the value of y is equal to zero
For y=0
substitute the value of y in the linear equation and solve for x
[tex]-4x+2(0)-5=0[/tex]
[tex]-4x=5[/tex]
[tex]x=-1.25[/tex]
The ordered pair is (-1.25,0)
3) Assume any value of x or y and solve for the other variable
For x=3
[tex]-4(3)+2y-5=0[/tex]
[tex]-12+2y-5=0[/tex]
[tex]2y=17[/tex]
[tex]y=8.5[/tex]
The ordered pair is (3,8.5)
M=x1+x2/2 solve for x1
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Step-by-step explanation:
Given formula is:
[tex]M = \frac{x_1+x_2}{2}[/tex]
In order to solve for x1, we have to isolate x1 on one side of the equation
So,
Multiplying the whole equation by 2:
[tex]2M = \frac{x_1+x_2}{2} * 2\\2M = x_1+x_2[/tex]
Subtracting x2 from both sides
[tex]2M-x_2 = x_1+x_2-x_2\\2M-x_2 = x_1[/tex]
so,
After solving for x1, we get
[tex]x_1 = 2M-x_2[/tex]
Keywords: Formulas, Solving for a variable
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By what number should -15 raise to -1 be divided so that the quotient may be equalto -15 raise to -1
Answer:
[tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex]
Step-by-step explanation:
Given:
Dividend = [tex](-15)^{-1}[/tex]
Quotient = [tex](-15)^{-1}[/tex]
We notice that the dividend and the quotient are equal. This means the divisor is 1.
By identity property of 1, any number divided by 1 is equal to the same number or the quotient of a number divided by 1 is equal to the number itself.
So, we can write this as:
[tex]\frac{(-15)^{-1}}{1}=(-15)^{-1}[/tex]
Thus [tex](-15)^{-1}[/tex] must be divided by 1 in order to have the quotient as [tex](-15)^{-1}[/tex] (Answer)
help me with this geometry question with proofs
Answer:
m ∠ AMC = 75°
Step-by-step explanation:
Given:
In Δ ABC, m ∠C=90°
m∠ B =30°
CM is angle bisector
We need to find m ∠AMC
In Δ ABC Sum of all angle is 180° so we get,
[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]
Now we know that CM is angle bisector of ∠C
∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]
Now in Δ ACM we know that Sum of all angles is 180
[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]
Hence m ∠ AMC = 75°
Which ordered pair would form a proportional relationship with the point graphed below?
(10, –20)
(–30, 20)
(–10, 5)
(35, –20)
Answer:
I think it would be either (-10, 5) or (35, -20)
Step-by-step explanation:
Answer:
It Is C
Step-by-step explanation:
Edg 2020
What is the y-intercept of the function f(x) = –negative StartFraction 2 Over 9 EndFraction.x + ?
The y-intercept is 1/3
Explanation:I'll assume the function is the following:
[tex]f(x)=-\frac{2}{9}x+\frac{1}{3}[/tex]
As you can see, this is the equation of a line written in Slope-intercept form. The general rule of writing lines in this form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept, which is the point at which [tex]x=0[/tex]. By comparing our function with the written rule, we can say that the y-intercept is:
[tex]\boxed{b=\frac{1}{3}}[/tex]
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Answer:
[tex]b=\frac{1}{3}[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-\frac{2}{9}x +\frac{1}{3}[/tex]
This given function is a linear function, because its variables have one as exponent, we can also say that its variables are linear.
This function, as a linear one, it's represented as a line.
Additionally, the form of this function is called slope-intercept form as
[tex]f(x)=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
So, in this case
[tex]m=-\frac{2}{9}[/tex] and [tex]b=\frac{1}{3}[/tex]
Therefore, the y-intercept of the given function is
[tex]b=\frac{1}{3}[/tex]
plzzz help !!!!!!!!!!!!!!!!!!!!!!!
Answer:
Y = - 2
Step-by-step explanation:
Put your finger at x= 0 or (0,0) and go down until you hit the black line, thats your y
The school principal determined that 1/4 of the original student school desks would need to be replaced this year. 50 teachers would also receive new, improved desks. A total of 295 student and teacher desks were purchased.
How many original student desks were there before the
purchase was made?
There were 980 student desks originally before the purchase was made.
Step-by-step explanation:
Total desks purchased = 295
As 50 new desks are for teachers, therefore, we will subtract this amount from total;
Desks purchased for students = 295-50 = 245
Let,
x be the number of original student desks, therefore,
[tex]\frac{1}{4}\ of\ x=245\\\frac{x}{4}=245[/tex]
Multiplying both sides by 4
[tex]4*\frac{x}{4}=245*4\\x=980[/tex]
There were 980 student desks originally before the purchase was made.
Keywords: subtraction, fractions
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Let x represent one number and let y represent the other number. The sum of two numbers is -11 if one number is subtracted from the other their difference is -3 use the given conditions to write of the equation and solve the system find the numbers
Answer:
look at above image for answer. thank you for the question
Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.
We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.
adding the first and second equation:
(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7
We can then substitute the value of x back into one of the original equations to solve for y:
-7 + y = -11
y = -11 + 7
y = -4
Thus, the two numbers are -7 and -4.
a punch recipe calls for equal amounts of orange and pineapple juice. pineapple juice comes in 6 ounce cans and orange juice comes in 10 ounce cans what is the least amount of each kindof juice that can be mixed with out having any left over?
Answer:
0.6 ounces
Step-by-step explanation:
Answer each question and explain your reasoning. How long is 50% of 60 minutes? How long is 10% of 60 minutes? How long is 75% of 60 minutes?
Answer:
Step-by-step explanation:
50% of 60? 0.5*60=30
10% of 60? 0.1*60=6
75% of 60? 0.75*60=45
50percent of 60 minutes is 30 minutes, 10percent of 60 minutes is 6 minutes, and 75percent of 60 minutes is 45 minutes.
50percent of 60 minutes: 50percent of 60 minutes is half of 60, which equals 30 minutes.
10percent of 60 minutes: 10percent of 60 minutes is 6 minutes (10percent of 60 is 6).
75percent of 60 minutes: 75percent of 60 minutes is 45 minutes (75percent of 60 is 0.75 * 60 = 45).
Sin 60 is what? Exact value please
Answer: 0.8660254038