Final answer:
To solve the problem, we found the finishing time of the first competitor by subtracting the range of completion times from the last finisher's time then added 4 minutes to get Ty's finishing time, which is 2:11 p.m.
Explanation:
To determine the time Ty crossed the finish line, we first need to calculate when the first place finisher completed the race, given that the range of completion times was 2 hours and 36 minutes and the last competitor finished at 4:43 p.m. Then, we add 4 minutes to the first finisher's time to find out when Ty finished.
Let's calculate the finishing time of the first place finisher:
Convert the range of times to minutes: 2 hours and 36 minutes is (2 × 60) + 36 = 156 minutes.Subtract 156 minutes from the last competitor's finishing time (4:43 p.m.) to find the first finisher's time.4:43 p.m. is the same as 16:43 in 24-hour format.Subtracting the range in minutes: 16:43 - 156 minutes = 14:07 (2:07 p.m.).This is the time the first competitor finished the race.
Now, add 4 minutes to get Ty's finishing time:
2:07 p.m. + 4 minutes = 2:11 p.m.Ty crossed the finish line at 2:11 p.m..
The length of the base and the height of a triangle are numerically equal. Their sum is 30 less than the number of units in the area of the triangle. Find the area of the triangle.
Answer:
50 sq. units
Step-by-step explanation:
The length of the base and the height of a triangle are numerically equal.
Let us assume that, the length and height as x.
So the area of the triangle will be,
[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{x^2}{2}[/tex]
As their sum is 30 less than the number of units in the area of the triangle, so
[tex]\Rightarrow x+x=\dfrac{x^2}{2}-30[/tex]
[tex]\Rightarrow 2x=\dfrac{x^2}{2}-30[/tex]
[tex]\Rightarrow 4x=x^2-60[/tex]
[tex]\Rightarrow x^2-4x-60=0[/tex]
[tex]\Rightarrow x^2-10x+6x-60=0[/tex]
[tex]\Rightarrow x(x-10)+6(x-10)=0[/tex]
[tex]\Rightarrow (x+6)(x-10)=0[/tex]
[tex]\Rightarrow (x+6)=0,(x-10)=0[/tex]
[tex]\Rightarrow x=-6,x=10[/tex]
Neglecting negative roots,
[tex]\Rightarrow x=10[/tex]
Hence, the base and height of the triangle is 10 units, so the area will be,
[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{1}{2}\cdot 10\cdot 10=50\ unit^2[/tex]
A pair of parallel lines is cut by a transversal. One of the angles formed measures 58°.
Which statements about the other seven angles formed are true?
There are three more angles with the same measure.
All the other angles have the same measure.
The rest of the angles measure 122°.
Only three of the angles measure 122°.
Four of the angles measure 122°.
Answer:
a and e
Step-by-step explanation:
Write the coordinates for the given dilation
Answer:
D[tex]_o[/tex] of Y = (-3/2, -1)
Step-by-step explanation:
We are given three points on the graph:
X (4, 0)
Y (3, 2)
Z (2, 2)
and the scale factor of dilation which is [tex]-\frac{1}{2}[/tex].
Given that, we are to find the coordinates of Y after dilation. To find that, we will multiply the coordinates of the point Y with the scale factor.
Y = [tex](-\frac{1}{2}[/tex] × [tex]3[/tex] , (-\frac{1}{2}[/tex] × [tex]2)[/tex]
Y = [tex](-\frac{3}{2} , -1)[/tex]
The cost of going to the big playland park for a family is given by C = 15x + 50, where C represents the cost and x represents the number of family members. How much would it cost for 10 family members to go?
A) $3
B) $4
C) $100
D) $200
How many groups of 8 can you make out of 63
Factor the trinomial below 8x^2-12x-8
[tex]8x^2-12x-8=4(2x^2-3x-2)=4(2x^2-4x+x-2)\\\\=4[2x(x-2)+1(x-2)]=4(x-2)(2x+1)\\\\\boxed{ 8x^2-12x-8 =4(x-2)(2x+1)}[/tex]
Answer:
4(2x+1)(x-2)
Step-by-step explanation: I just did it
The functions f(x) and g(x) are defined below.
Which expression is equal to f(x) · g(x)?
none of the above
Step-by-step explanation:This question wants you to see that the radical can be simplified because it is ...
[tex]f(x)=\sqrt{(x+6)^2}[/tex]
The answer choices show you are expected to simplify this to ...
... f(x) = x +6
Then
... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C
_____
However,
... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x
so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.
The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).
solve equation for n
Simplify 2/3 + n + 6 to n + 20/3
n + 20/3 = 3/4
Subtract 20/3 from both sides
n = 3/4 - 20/3
Simplify 3/4 - 20/3 to - 71/12
n = -71/12
John must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70. Which inequality will tell him at least how many more points he needs to pass the class? A. 72 + 78 + 70 + x 289 B. 72 + 78 + 70 + x > 289 C. 72 + 78 + 70 + x < 289 D. 72 + 78 + 70 + x 289
B. 72 + 78 + 70 + x > 289
Please show steps so I understand.
Rearrange the equation so X is the independent variable. 6x+y=4x+11
Y=______________
6x+y=4x+11
y=4x+11-6x
y=-2x+11
[tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
To rearrange the equation [tex]\(6x + y = 4x + 11\)[/tex] so that (x\) is the independent variable and (y) is dependent, we need to isolate (y) on one side of the equation.
Start with the given equation: [tex]\(6x + y = 4x + 11\)[/tex].
Subtract (4x) from both sides to move all terms involving (y) to one side: [tex]\(6x - 4x + y = 11\).[/tex]
Simplify the left side by combining like terms: 2x + y = 11.
To isolate y, subtract 2x from both sides: 2x + y - 2x = 11 - 2x.
Simplify: [tex]\(y = 11 - 2x\)[/tex].
So, the rearranged equation with (x) as the independent variable is y = 11 - 2x.
Detailed calculation:
Starting equation: (6x + y = 4x + 11)
Subtract (4x) from both sides:
[tex]\(6x - 4x + y = 4x - 4x + 11\)[/tex]
[tex]\(2x + y = 11\)[/tex]
Subtract (2x) from both sides:
[tex]\(2x + y - 2x = 11 - 2x\)[/tex]
[tex]\(y = 11 - 2x\)[/tex]
Therefore, [tex]\(y = 11 - 2x\)[/tex] is the rearranged equation with [tex]\(x\)[/tex] as the independent variable.
-3 (e - 6)= 39 please show work
Hey there!
[tex]-3(e-6)= 39[/tex]
First, [tex]distribute[/tex][tex]-3(e)[/tex] [tex]+[/tex] [tex]-3(-6)[/tex] [tex]= 39[/tex]
[tex]-3(e) = -3e[/tex][tex](-3)(-6 = 18)[/tex] [tex]\boxed{-3e+18=39}[/tex]Second, [tex]subtract[/tex] by [tex]18[/tex] on each of your sides [tex]-3e + 18[/tex] [tex]-18[/tex] [tex]= 39- 18[/tex][tex]Cancel: 18 - 18[/tex] because it gives you the result of [tex]0[/tex][tex]Keep: 39 - 18[/tex] because it helps us get closer to our answer ( is a step to find our answer) [tex]39-18=[/tex][tex]21[/tex][tex]\boxed{-3e = 21}[/tex]Third, [tex]divide[/tex] by [tex]-3[/tex] on each of your sides[tex]\frac{-3e}{-3}[/tex][tex]= \frac{21}{-3}[/tex][tex]Cancel: \frac{-3e}{-3}[/tex] because it gives you the result of [tex]-1[/tex][tex]Keep: \frac{21}{-3}[/tex] because it gives you the result of [tex]e[/tex][tex]\Boxed{\frac{21}{-3}= -7 }[/tex]Forth, your [tex]answer[/tex][tex]\Boxed{Answer: e = -7}[/tex]Good luck on your assignment and enjoy your day!
~[tex]LoveYourselfFirst:)[/tex]
Simplify the expression
3(2+q)+15 simplified is
What is the full price of 90 tablets of "Drug Y", assuming your cost for 500 tablets is $425.00 with a 28% markup and a dispensing fee of $4.85 ?
Answer: Full price of Drug Y = $98.793
Step-by-step explanation:
Cost of 500 tablet = $425
28% markup = 425 * 28/100
= $119
Cost + markup = $425 + $119 = $544
Cost + markup + dispensing fee = $544 + $4.85 = $548.85
Full price of 500 tablet = $548.85
Full price of 1 tablet = $548.85/500
=$1.0977
Full price of 90 tablet = $1.0977 * 90
= $98.793
You have just accepted a job at Wonders Day Camp for the summer. The camp will pay you $48.23 each day for 8 weeks. If you work 5 days each week, how much money will you make this summer?
Answer:
$192.20
Step-by-step explanation:
8 x 5=40 48.32x40=192.20
Answer:
You will make $1929.20 this summer.
Step-by-step explanation:
You have just accepted a jab at Wonders Day Camp for the summer.
The camp will pay for each day for 8 weeks = $48.23
You work 5 days each week.
So total days of work = 8 × 5 = 40 days
You earn $48.23 for one day.
For 40 days you will earn = 40 × 48.23 = $1,929.20
You will make $1929.20 this summer.
what is the domain of f(x) = (1/3)^x ?
Answer:
B
Step-by-step explanation:
There isn't any number that x can't be. Start with a graph to show how this could be so.
It is easy to see that x > 0 gives a line that goes very near the x axis. It is not quite so easy to see that it never touches the x axis. But if you recreate the graph in Desmos, you will see that is true if you spread the x's out.
It is not quite so easy to see that when x<0 the graph tips upward very quickly but again if you move the values of the axis around you will see there is no value that x cannot be.
Answer:
B:All real numbers
Sierra sells book .This month she sold 683 books,which is 96 books more than she sold last month .Which equation can be be used to find the number of books she sold last month
help me on this math question thank you
Answer:
C for question 1 A for question 2Step-by-step explanation:
First Question
What you need to do here is pick an answer that will result in a decrease. If you have something like 1.3 * e ^ (0.038 * t), what will happen when t = 20
P = 1.3 * e^(0.038*20) = 1.3*e^0.76 = 2.77 which is getting bigger not smaller.
So what you want is something like 1.3 * e^-0.76 = 0.67
So which question is configured that way?
It's either C or D. but which one? It cannot be D. 0.38 is far too big: it does not represent 3.8%
C does represent 3.8% as a decimal. It is the correct answer.
Answer: C
Second Question
Every time she sells a ticket, the total that she gets is 4 more than what she had before.
The variation is a direct one. It is y = k*x. But what is k? Is it 4 or is it 1/4?
Read the first sentence above. She gets 4 dollars more, not 1/4 of a dollar.
C and D are both wrong because those equations think she is getting 1/4 more.
B is wrong because it says that the relationship is inverse. It is not. It is direct.
The answer is A
PLZ HELP!!!!!!!!!!!!!!!!! Pick either one prime number or one composite number and create a rectangle diagram to show that it is prime or composite. You can draw the image by hand on a grid and photograph it, make a slide, or use other software to create your diagram. Post your diagram to the discussion board. B. Review posts from two other students. Choose a post that has no responses or only one response first. In your comment, assign the original poster a new number to diagram. Be sure to switch it up between prime and composite numbers!
Answer:
your answers are 2,and 18
Step-by-step explanation:
Urgent
What is the equasion,Can anybody awnser the question attached Please help
Answer:
x=6 ; y=1
Step-by-step explanation:
Let 'y' stand for the speed of the wind and 'x' stand for the speed of Santa. We will use the general equation (distance)=(rate)(time) to write two equations from the given information:
With the wind:
35=(x+y)(5)
Against the wind:
35=(x-y)(7)
Now we have two equations and two unknowns so we can solve for x and y. We get:
x=6 miles/min
y=1 miles/min
what % is 9 of 27? I am really, really, really confused about this question
To find the percent, divide 9 by 27 to get a decimal, then multiply the decimal by 100 to get the percent:
9 / 27 = 0.333
0.333 x 100 = 33.3%
Answer:
33.33%
Step-by-step explanation:
9/27*100
=0.3333*100
=33.33%
A recipe for one batch of KFC buttermilk biscuits calls for 1 ½ cups all-purpose flour, 1 teaspoon salt, 1 tablespoon sugar, 1 tablespoon baking powder, 1/3 cup vegetable shortening, and ⅔ cup buttermilk.
What happens when we double the recipe?
Cup all-purpose flour _____
Teaspoon salt _____
tablespoon sugar ______
Baking Powder _______
Answer:
See below.
Step-by-step explanation:
Original Doubled Ingredient
1½ c ⟶ 3 c all-purpose flour (2×1½ = 2×1 + 2×½ = 2+1 = 3)
1 tsp ⟶ 2 tsp salt
1 Tbsp ⟶ 2 Tbsp sugar
1 Tbsp ⟶ 2 Tbsp baking powder
⅓ c ⟶ ⅔ c vegetable shortening
⅔ c ⟶ 1⅓ c buttermilk (2×⅔ = ⁴/₃ = 1⅓)
A radio station have free tickets to 10% of the people attending a concert. The radio station gave 640 people free tickets. What is the total number of people who attended the concert?
Answer:
6400 people.
Step-by-step explanation:
If 640 is 10%. You multiply 640 by 10 to get 6400 or 100% of the people.
Simplify 4(x + 7) – 7x + 2
Answer:
(-3x+30)
Step-by-step explanation:
We first distribute: 4(x+7) = 4x+28
Then, we bring it down.
4x+28-7x=2
Combine like terms.
4x+(-7x) = -3x ... 28+2 = 30.
Combine both results.
-3x+30
Answer:
[tex]-3x+30[/tex]
Step-by-step explanation:
We have been given an expression [tex]4(x+7)-7x+2[/tex]. We are asked to simplify our given expression.
Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:
[tex]4*x+4*7-7x+2[/tex]
[tex]4x+28-7x+2[/tex]
Combine like terms:
[tex]4x-7x+2+28[/tex]
[tex]-3x+30[/tex]
Therefore, the simplified form of our given expression would be [tex]-3x+30[/tex].
a regular size chocolate bar is 5 4/9 inches long. the king size bar is 3 times as long as the regular size bar. how long is the king size bar
Answer:
15 4/9 inches long
Step-by-step explanation:
5 4/9 × 3
When lining them vertically the 3 ends up under 5 in which you multiply and transfer the 4/9 next to the product of 15. Hope that helped!
The king size chocolate bar is three times as long as the regular bar, so given that the regular bar is 5 4/9 inches long, the king size bar is 16 1/3 inches long.
Explanation:The problem involves a regular size chocolate bar that is 5 4/9 inches long and a king size bar that is three times as long. Given the length of the regular bar, our objective is to find out how long the king size bar is.
We start by converting the mixed number 5 4/9 into an improper fraction which gives us 49/9 inches. We then multiply 49/9 by 3 to get the length of the king size bar which is 147/9 inches. Converting this improper fraction back into a mixed number, we get 16 1/3 inches. Therefore, the king size bar is 16 1/3 inches long.
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Can you help?
: 46 × 12 = 46 × (10 + ? )
= ( ? × 10 ) + ( ? × 2)
= ? + 92
= ?
Thank you :D
46 × 12 = 46 × (10 + 2) =
= (46 × 10 ) + (46 × 2)
= 460 + 92
= 552
Identify the angle that is vertical to angle 1 choose all answers that are correct.
Answer:
WTH IDOT SCR*W YOU
Step-by-step explanation:
SOMEONE FILL IN THE BLANK PLEASE!! The diameter of a sphere is 16 cm. The volume of the sphere is _____
Answer:
2144.66cm I think
Step-by-step explanation:
A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top travelling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Answer: 25 miles
Step-by-step explanation:
Since, the total distance = 31 miles.
Let he walks x miles at the rate of 4 miles per hour.
⇒ he walks remaining (31-x) miles at the rate of 50 miles per hour.
According to the question,
[tex]\frac{x}{4} + \frac{31-x}{50} = 2[/tex]
⇒ [tex]\frac{25x}{100} + \frac{62-2x}{100} = 2[/tex]
⇒ [tex]\frac{25x+62-2x}{100}= 2[/tex]
⇒ [tex]\frac{23x+62}{100}= 2[/tex]
⇒ [tex]23 x + 62 = 200[/tex]
⇒ [tex]23 x = 200 - 62[/tex] ( by subtracting 62 on both sides )
⇒ [tex]23 x = 138[/tex]
⇒ [tex]x=\frac{138}{23}[/tex] ( Dividing both sides by 23 )
⇒ [tex]x = 6[/tex]
Thus, the distance he pays to the cab driver = 31-x= 31 - 6 = 25 miles.
Therefore, He pays to the cab driver for 25 miles.
Distance that must be paid to the taxi = 25 miles
Further explanationLinear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
• At constant velocity motion:
the speed of vo = v = constant
acceleration = a = 0
Δx = vt or x = xo + vtAn equation of constant velocity motion
[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]
x = distance = m
v = speed = m / s
t = time = seconds
so
[tex]\rm t=\dfrac{x}{v}[/tex]
A mountain path is 31 miles long
The distance traveled by tourists = x1
The distance traveled taxi = x2, such that
x1 + x2 = 31
x1 = 31-x2
total travel time (t) = 2 hours
tourist speed = v1 = 4 mph
taxi speed = v2 = 50 mph
time taken by tourists = t1
[tex]\rm \dfrac{x1}{v1}=\dfrac{x1}{4}[/tex]
the time taken by taxi = t2
[tex]\rm \dfrac{x2}{v2}=\dfrac{x2}{50}[/tex]
total time = t1 + t2
[tex]\rm 2=\dfrac{x1}{4}+\dfrac{x2}{50}\\\\2=\dfrac{25x1+2x2}{100}\\\\200=25(31-x2)+2x2\\\\200=775-25x2+2x2\\\\575=23x2\\\\x2=\boxed{\bold{25~miles}}[/tex]
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Write the equation of a parabola with vertex at (0,0) and directrix of y=-3
Answer:
x^2=12y
**C on edge
The equation of a parabola with its vertex at (0,0) and directrix at y=-3 is y = 1/12 x².
Explanation:To write the equation of a parabola, we are given that its vertex is at (0,0) and its directrix is y=-3. The equation of a parabola with the vertex at (0,0) and the focus at (0,p) or a directrix at y=-p is given as y = 1/4p x². Considering the distance from the vertex to the directrix is the same as the distance from the vertex to the focus, the value of p in this case will be 3. Therefore, the equation of this parabola is y = 1/12 x².
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36x+45y=123
46x+15y=23
Elimination Method
[tex]\left\{\begin{array}{ccc}36x+45y=123&\text{divide both sides by (-3)}\\46x+15y=23\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-12x-15y=-41\\46x+15y=23\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad34x=-18\qquad\text{divide both sides by 34}\\.\qquad\qquad x=-\dfrac{18}{34}\to\boxed{x=-\dfrac{9}{17}}\\\\\text{Put the value of x to the second equation.}\\\\46\left(-\dfrac{9}{17}\right)+15y=23[/tex]
[tex]-\dfrac{414}{17}+15y=\dfrac{391}{17}\qquad\text{add}\ \dfrac{414}{17}\ \text{to both sides}\\\\15y=\dfrac{805}{17}\qquad\text{divide both sides by}\ 15\\\\y=\dfrac{805}{255}\\\\\boxed{y=\dfrac{161}{51}}\\\\Answer:\ \boxed{x=-\dfrac{9}{17}\ and\ y=\dfrac{161}{51}}[/tex]