Answer:
[tex]\begin{gathered} \text{Lian - 1 hour} \\ \text{Sam - 1}\frac{1}{9}\text{ hours} \end{gathered}[/tex]
Explanation:
Here, we want to calculate the time taken for each of the boys to finish the race
From what we have, the total distance traveled is 2 miles (1 mile up , 1 mile down)
The general formula to get time from speed and distance is:
[tex]\text{time = }\frac{dis\tan ce}{\text{speed}}[/tex]Kindly understand that the journey is in two phases, the leg up and the leg down. The time spent on each will be summed to give the total time spent on the race
Let us start with Lian. We have it as:
[tex]\frac{1}{2}\text{ + }\frac{1}{2}\text{ = 1}[/tex]Lian took one hour
For Sam, we have it that:
[tex]\frac{1}{9}+\text{ }\frac{1}{1}\text{ = }\frac{1\text{ + 9}}{9}\text{ = }\frac{10}{9}\text{ = 1}\frac{1}{9}\text{ hours}[/tex]Can three segments with lengths 8,15, and 6 make a triangle? Explain your answer.
Answer:
No
Explanation:
Given three segments with lengths 8, 15, and 6
We check if the sum of two sides is greater than the third.
[tex]8+6=14[/tex]Since 14 is less than 15, the three segments cannot make a triangle.
keisha eric and carlos served a total of 120 orders monday at the school cafeteria. eric served 3 times as many orders as carlos. keisha served 10 more orders than carlos. how many orders did they each serve
Let the number of orders served by Carlos be x, so
Eric = 3x
Keisha = 10 + x
then, we have:
[tex]\text{Carlos + Eric+ Keisha = 120 }[/tex]so
[tex]\begin{gathered} x+3x+10+x=120 \\ 5x+10=120 \\ 5x+10-10=120-10 \\ 5x=110 \\ \frac{5x}{5}=\frac{110}{5} \\ x=22 \end{gathered}[/tex]therefore, the answer is:
Carlos = 22 orders
Eric = 3(22) = 66 orders
Keisha = 10 + 22 = 32 orders
Find the common difference for the arithmetic sequence.-49, -42, -35, -28...
The set of numbers shown is a sequence, an arithmetic sequence. The common difference is the number which you must add to an existing term in order to get the next one. That means the common difference is what was added to -49 in order to arrive at -42. Lets calculate the common difference, d;
[tex]\begin{gathered} -49+d=-42 \\ \text{Add 49 to both sides of the equation (so as to eliminate it from the left side} \\ -49+49+d=-42+49 \\ 0+d=49-42 \\ d=7 \end{gathered}[/tex]What is the intermediate step in the form (x + a)2 = b as a result of completing thesquare for the following equation?6x2 +962 - 13 = -132.Submit Answerattempt 1 out of 2
First step is to separate the terms with variables from the constant terms.
Add 13 to both sides of the equation :
[tex]\begin{gathered} 6x^2+96x-13=-13 \\ 6x^2+96x-\cancel{13}+\cancel{13}=-13+13 \\ 6x^2+96x=0 \end{gathered}[/tex]Divide both sides by 6 :
[tex]\begin{gathered} 6x^2+96x=0 \\ x^2+16x=0 \end{gathered}[/tex]Next step, completing the square by adding this term to both sides of the equation :
[tex](\frac{b}{2a})^2[/tex]From the equation,
a = 1
b = 16
So it follows that :
[tex](\frac{b}{2a})^2=(\frac{16}{2\times1})^2=(8)^2[/tex]Adding this to both sides of the equation :
[tex]\begin{gathered} x^2+16x=0 \\ x^2+16x+8^2=8^2 \end{gathered}[/tex]And you will get a perfect square trinomial on the left side of the equation in the form :
[tex]x^2+bx+c^2[/tex]It can be factored as :
[tex]x^2+bx+c^2=(x+c)^2[/tex]So the equation will be :
[tex]\begin{gathered} x^2+16x+8^2=8^2 \\ (x+8)^2=8^2 \\ (x+8)^2=64 \end{gathered}[/tex]The answer is :
[tex](x+8)^2=64[/tex]round 1,587,966 to nearest ten thousand.
Answer:
Step-by-step explanation:
1,590,000
Marcos is building a dog run for his new puppy. He has enough money to buy 75 feet of fencing. He wants to fence in a rectangulararea and it should be at least twice as long as it is wide. Which system of inequalities represents the possible lengths L and widths Wfor his dog run?
Let the length of the fence be L
Let the wide of the fence be W
Since, he can afford 75 feet fencing
Therefore, the perimeter of the fence = 75
Perimeter = 2( L + W)
The length of the fence should be twice as long as the wide
W = 2L
P = 75
2(L + 2L) < = 75
2 WRITE THE RULE FOR THE TRANSLATION. (x Y Y D A c
This figure was translated 1 unit to the right and 4 units down, so the rule of translation will be:
(x + 1, y - 4)
Answer the questions by drawing on the coordinate plane below. You may need to print the test and graphthe images by hand.
From the figure, we have the following coordinates of the vertices :
[tex]\begin{gathered} Q(-4,2) \\ R(-1,1) \\ S(-2,4) \end{gathered}[/tex]a. Rotation of 180 degrees about the origin has a rule of :
[tex](x,y)\rightarrow(-x,-y)[/tex]The sign of the coordinates will change from positive to negative or negative to positive.
The new coordinates will be :
[tex]\begin{gathered} Q(-4,2)\rightarrow Q^{\prime}(4,-2) \\ R(-1,1)\rightarrow R^{\prime}(1,-1) \\ S(-2,4)\rightarrow S^{\prime}(2,-4) \end{gathered}[/tex]The graph will be :
b. Reflection across the x-axis has a rule of :
[tex](x,y)\rightarrow(x,-y)[/tex]Only the y coordinate will change its sign.
So from the coordinates we got in a.
[tex]\begin{gathered} Q^{\prime}(4,-2)\rightarrow Q^{\doubleprime}(4,2) \\ R^{\prime}(1,-1)\rightarrow R^{\doubleprime}^{\prime}(1,1) \\ S^{\prime}(2,-4)\rightarrow S^{\doubleprime}(2,4) \end{gathered}[/tex]The graph will be :
determine if the triangles are congruent byASA,SSS,SAS,AAS,HL or not congruent
Consider the given triangles.
Two triangles are said to be congruent, if all the sides are equal or all the angles are equal.
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
SSS - All the sides are equal.
SAS - Two sides and included angle are equal.
ASA - Two angles and included sides are equal.
AAS - Two angles and non included angle are equal.
HL (right angled trianles) - the same length of hypotenuse and the same length for one of the other two legs.
In the given traingles, it is given that,
SIde, EN = PR
Side EM = PQ
Therefore, we can say that the traingles are not congruent.
Find the missing side using Pythagorean theorem, than find the surface area
Given:
Consider the triangular part in the given figure.
To find the third side of right triangle. Use pythagorean theorem,
[tex]\begin{gathered} x^2=3^2+4^2 \\ x^2=9+16 \\ x^2=5^2 \\ x=5 \end{gathered}[/tex]The missing side of triangle is 5 cm.
Now to find the surface area of triangular prism.
Note that the height of the right triangle is 4 cm and base is 3 cm.
[tex]s_1=3,s_2=4,s_3=5,l=6,h=4,b=3[/tex]First calculate the area of each side,
[tex]\begin{gathered} \text{Area of one triangle=}\frac{1}{2}(4\times3)=6 \\ \text{Area of second triangle}=\frac{1}{2}(4\times3)=6 \\ \text{One rectangle =4}\times6=24 \\ \text{second rectangle}=3\times6=18 \\ \text{Third rectangle =}5\times6=30 \end{gathered}[/tex]So, the surface area is,
[tex]SA=6+6+24+18+30=84[/tex]Answer: surface area is 84 square cm.
Gretchen's gross annual salary is $34,788. What is the maximum amount of rent shecan afford to pay per month? Round answer to the nearest whole number.
Given:
Grethen's gross annual salary = $34, 788
The maximum amount of rent she can afford to pay per month can be found using the formula:
[tex]\text{Max amount of rent she can pay = }\frac{Gross\text{ annual salary}}{Number\text{ of months in a year}}[/tex]Applying the formula:
[tex]\begin{gathered} \text{Max amount of rent she can pay= }\frac{34788}{12} \\ =\text{ \$2899} \end{gathered}[/tex]Hence, the maximum amount of rent she can afford to pay per month is $2899
Answer: $2899
Which representation shows a nonproportional relationship between x and y? 6 4 2 1 FA 11 3 y = -X -9-8-7-6-5-4-3-2-1 334 5 6 7 8 9 5 19 9 y у у -4 -1.6 -5 -1 B - 2 -0.8 -3 -0.2 1 0.4 2. 1.8
proportional relationships have constant ratios.
the graph is a line, so it is a proportional relationship. (A)
the function is in the form y=kx (proportional function) (C)
Find the ratio of the tables: (B)
[tex]m=\frac{-0.8-(-1.6)}{-2-(-4)}=0.4=\frac{0.4-(-0.8)}{1-(-2)}=\frac{1.2-0.4}{3-1}=[/tex]D
[tex]m=\frac{-0.2-(-1)}{-3-(-5)}=0.4=\frac{1.8-(-0.2)}{2-(-3)}=\frac{3-1.8}{5-2}[/tex]All represent a proportional relationship
Using a given zero to a polynomial as a product of linear factors complex zeros
When we have a polynomial of higher degree bu we know some of its zeros, we can use synthetic division to factor the polynomial and solve the remaining factors.
We have apolynomial of fourth degree, and we know that 1 is a zero with multiplicity two, that is, the polynomial have two factors (x - 1), so it can be rewritten as:
[tex]x^4-6x^3+22x^2-30x+13=(ax^2+bx+c)(x-1)(x-1)=(ax^2+bx+c)(x-1)^2[/tex]To find out the quadratic fator, we can do the synthetic division by 1 twice.
To do this, e start by writing 1 and the coefficients of the polynomial:
1 | 1 -6 22 -30 13
|
| 1
The leading coefficient was also copied to the last row. Now, we will do the following repeatedly:
- multiply the number on the last row of the column we are by the divisor "1" and put the result under the next coefficient (the column to the right).
- add the two rows of this next coefficient and put the result in the last row.
- repeat
So:
1 | 1 -6 22 -30 13
| 1
| 1 -5
1 | 1 -6 22 -30 13
| 1 -5
| 1 -5 17
1 | 1 -6 22 -30 13
| 1 -5 17
| 1 -5 17 -13
1 | 1 -6 22 -30 13
| 1 -5 17 -13
| 1 -5 17 -13 0
Now, the 4 first numbers in the last row are the coefficients of the polynomial that is the result, and the last is the remainder, which is zero because 1 is a zero of the original polynomial.
Now, we can rewrite the polynomial as:
[tex]x^4-6x^3+22x^2-30x+13=(x^3-5x^2+17x-13)(x-1)[/tex]Now, we take this third degree polynomial and divide again by 1:
1 | 1 -5 17 -13
|
| 1
1 | 1 -5 17 -13
| 1
| 1 -4
1 | 1 -5 17 -13
| 1 -4
| 1 -4 13
1 | 1 -5 17 -13
| 1 -4 13
| 1 -4 13 0
Now, we can rewrite the third degree polynomial as:
[tex]x^3-5x^2+17x-13=(x^2-4x+13)(x-1)[/tex]So, the original becomes:
[tex]x^4-6x^3+22x^2-30x+13=(x^2-4x+13)(x-1)^2[/tex]Now, to finish the factoring, we can find the zeros of the quadratic factor, which we can do by using the quadratic formula:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(13)}}{2(1)}=\frac{-4\pm\sqrt[]{16-52}}{2} \\ x=\frac{-4\pm\sqrt[]{-36}}{2}=\frac{-4\pm6i}{2}=-2\pm3i \\ x_1=-2-3i \\ x_2=-2+3i \end{gathered}[/tex]So, we can write the quadratic factor as:
[tex]x^2-4x+13=(x-(-2-3i))(x-(-2+3i))=(x+2+3i)(x+2-3i)[/tex]So, the original polynomial as a product of linear factors is:
[tex]f(x)=(x+2+3i)((x+2-3i)(x-1)^2[/tex]3.) If f(x)=-|x| is graphed on a regular coordinate grid, does the graph form an acute, right, or obtuse angle at its vertex? a. Acute b. Right c. Obtuse d. There is no vertex
The given function is an absolute value function with vertex at the origin (0,0).
It is important to know that an absolute value function has a v-form where the lines are perpendicular because the lines have opposite slopes.
Hence, the right answer is B there is a right angle between the lines.(8.76*10*9)(6.52*10*-3) /13.27*10*5 =
What’s the exponential function of g?X 0,1,2,3,4 g(x) 1,3,9,27,81
In order to find the exponential function g(x), let's use the model below for an exponential function:
[tex]g(x)=a\cdot b^x[/tex]Using the points (0, 1) and (1, 3), we have:
[tex]\begin{gathered} (0,1)\colon \\ 1=a\cdot b^0 \\ a=1 \\ \\ (1,3)\colon \\ 3=1\cdot b^1 \\ b=3 \end{gathered}[/tex]Therefore the equation is g(x) = 3^x.
What is the equation of the line that passes through (-1,8 and (1, -4)?
Using slope-intercept form, an equation of a line can be written as
[tex]y=mx+c[/tex]Find the slope using the two-point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-8}{1-(-1)} \\ =\frac{-12}{2} \\ =-6 \end{gathered}[/tex]Substitute -6 for m into y = mx + c.
[tex]y=-6x+c[/tex]Now, to find the y-intercept,c, substitute any given point into the equation.
[tex]\begin{gathered} 8=-6(-1)+c \\ 8=6+c \\ c=2 \end{gathered}[/tex]Thus, y = -6x + 2, which is the required equation of the line passing through (-1,8) and (1,-4).
by the following expression using distributive property of division (30x-15)/3
we have the following:
[tex]\begin{gathered} \frac{30x-15}{3}=\frac{30x}{3}-\frac{15}{3} \\ 10x-5 \end{gathered}[/tex]therefore, the answer is 10 x - 5
Arrange the systems of equations in order from least to greatest based on the number of solution for each system. NEED FAST HELP
On solving equations in the box 1:
-5x+y=10 -> 1
-25x+5y=50 ->2
div by -5 on equation 2.
so we get as 5x-y=-10 ->3
so solving 1 and 3 we get the equations cancel each other.so x and y are not true.They dont have any solutions.
On solving the equations in the box 2:
3x -7y =9 -->1
-4x +5y =1 -->2
so lets multiply equation 1 by 4 and euqation 2 by 3 so we get
12x-28y=36
-12x+15y=3
on solving we get -13y=39
y=-3 ,we can get x value by putting y value in any of the above equations.
3x-7(-3)=9
3x+21=9
3x=-12
x=-12/3
x=-4 so we get x=-4 and y=-3
On solving the equations in the box 3:
y=6x-2
by re-arranging we get -6x+y=-2 ---> 1
y=6x-4
on re arranging we get -6x+y=-4 ----->2
multiplying equation 2 by -1
so we get 6x-y=4 ---> 3
on solving 1 and 3 we get them cancel eachother so they have no solutions.
so finally analyzing all the boxes we can conclude that box 2 more number of solutions
Question is in the photo. Disregard checked answer I just guessed don’t know if it’s right or wrong
Answer:
0, 3, and 6
Explanation:
Given the second derivative of the function, f(x) below:
[tex]f^{\prime}^{\prime}(x)=x^2(x-3)(x-6)[/tex]To find the x-coordinate of the point of inflection, set the second derivative of the function equal to zeroand solve for x:
[tex]\begin{gathered} x^2(x-3)(x-6)=0 \\ \implies x^2=0,x-3=0,x-6=0 \\ \implies x=0,3,6 \end{gathered}[/tex]The x-coordinates of the point of inflection are 0, 3, and 6.
If the average-size man with a parachute jumps from an airplane, he will fall12.5(0.2^t– 1) + 21t feet in t seconds. How long will it take him to fall 170 feet?(Round your answers to two decimal places.)=_______sec
The equation relating time and fall height is given by
[tex]h(t)=12.5(0.2^t-1)+21t[/tex]We want to find out how long will it take him to fall 170 feet?
Let us substitute h(t) = 170
[tex]170=12.5(0.2^t-1)+21t[/tex]Now let's solve the equation
[tex]\begin{gathered} 170=12.5(0.2^t-1)+21t \\ 170=2.5^t-12.5+21t \\ 170+12.5=2.5^t+21t \\ 182.5=2.5^t+21t \end{gathered}[/tex]Taking log on both sides
[tex]\ln (182.5)=\ln (2.5^t)+\ln (21t)_{}[/tex]When triangles ABC is reflected across line AB, the image is triangle ABD. Why is angle ACD congruent to angle ADB?
When we reflect the triangle ABC across AB, segments AD and AC are equal in length. Therefore, triangle ADC is an Isosceles triangle as it has two sides of the same measure.
Then, AC and AD are the legs of an Isosceles triangle; thus, angles The answer is An isosceles triangle has a pair of congruent angles.
Complete the equation for the piece wise function graphed below.
Answer:
[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,if-6\le x\le-2 \\ -3,if-2Explanation:For the value of x such that: -6≤x≤-2
We have the endpoints (-6,0) and (-2, -2).
We determine the equation in the slope-intercept form, y=mx+b.
[tex]\begin{gathered} \text{Slope,m}=\frac{0-(-2)}{-6-(-2)} \\ =\frac{2}{-6+2} \\ =\frac{2}{-4} \\ m=-0.5 \end{gathered}[/tex]The equation then becomes:
[tex]y=-0.5x+b[/tex]Using the point (-6,0)
[tex]\begin{gathered} 0=-0.5(6)+b \\ b=3 \end{gathered}[/tex]Therefore: f(x)=-0.5x+3, -6≤x≤-2
Next, f(x)=-3 for -2
Finally, for 1The endpoints are (1,-4) and (6,1)
[tex]\text{Slope,m}=\frac{-4-1}{1-6}=\frac{-5}{-5}=1[/tex]Using the point (1,-4)
[tex]\begin{gathered} y=mx+b \\ -4=1(1)+b \\ b=-4-1=-5 \end{gathered}[/tex]Therefore, f(x)=x-5, for 1
The completed function will now be:
[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,-6\le x\le-2 \\ -3,-2lf the sum of two angles is 180, which condition MUST be true?
By definition, if the sum of two angles is 180 degrees then they are called supplementary.
Answer: That the angles are supplementary. Two angles are supplementary if the sum of their measures is 180.
Step-by-step explanation:
Which equation models this situation?The sum of 22 and a number is 41.A. 22 + 41 = × B. 22 - × = 41C. 41 + × = 22D. 22 + × = 41
The sum of 22 and a number is 41.
Let x represent the number.
To represent the statement above as an equation, we have:
22 + x = 41
ANSWER:
D. 22 + x = 41
a. Deshaun's test score average increased by 8 points this semester. Write a signed number to represent this change in average. b. Ali lost 75 dollars from his pocket. Write a signed number to represent this change.
We have the following:
"Deshaun's test score average increased by 8 points this semester. Write a signed number to represent this change in average."
Because it is an increase, the sign is positive
The answer is +8
Ali lost 75 dollars from his pocket. Write a signed number to represent this change.
Because it is a loss, the sign is negative
The answer is -75
Find the a1 and d for the arithmetic where Sn=187, n=17, and a17 = -13
The sum of n terms is:
[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]For n = 17, a17 = -13 and Sn = 187, then:
[tex]\begin{gathered} 187=\frac{17}{2}(2a_1+(17-1)d) \\ 187\cdot\frac{2}{17}=2a_1+16d \\ 22\text{ = }2a_1+16d \end{gathered}[/tex]Arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]Replacing with n = 17 and a17 = -13:
[tex]\begin{gathered} -13=a_1+(17-1)d_{} \\ -13=a_1+16d \end{gathered}[/tex]Subtracting this equation to the previous one
[tex]\begin{gathered} 22-(-13)=2a_1-a_1+16d-16d_{}_{}_{} \\ 35=a_1 \end{gathered}[/tex]Then d is equal to:
-13 - 35 = 16d
-48/16 = d
-3 = d
12, 10, 23 15, 6.2, 6.24.6, 8.2, 3.812, 5, 7which could be the length of three sides of a triangle ?
We would apply the traingle inequality theorem which states that the sum of the length of two sides of a triangle is greater than the length of the third side. Thus,
For the first option
12 + 10 = 22 and it is less than 23. It can't form the length of the three sides of a triangle
For the second option
6.2 + 6.2 = 12.4 and it is less than 15. It can't form the length of the three sides of a triangle
For the third option,
4.6 + 3.8 = 8.4 and it is greater than 8.2. It can form the length of the three sides of a triangle
For the fourth option
5 + 7 = 12 and it is equal to 12. It can't form the length of the three sides of a triangle
Thus, the correct option is 4.6, 8.2, 3.8
On each right triangle ,find the tangent of each angle that is not the right angle.Number 2.
Given the triangle ABC, you know that:
[tex]\begin{gathered} AB=10 \\ AC=6 \\ BC=8 \end{gathered}[/tex]You can identify that the small square in the vertex C of the triangle is a Right Angle (an angle that measures 90 degrees). Therefore, you have to find the tangent of the other two angles:
[tex]\begin{gathered} \angle A \\ \angle B \end{gathered}[/tex]By definition:
[tex]tan\theta=\frac{opposite}{adjacent}[/tex]Then:
- For angle A, you can identify that:
[tex]\begin{gathered} \theta=A \\ opposite=BC=8 \\ adjacent=AC=6 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} tan(A)=\frac{8}{6} \\ \\ tan(A)=\frac{4}{3} \end{gathered}[/tex]- For angle B:
[tex]\begin{gathered} \theta=B \\ opposite=AC=6 \\ adjacent=BC=8 \end{gathered}[/tex]Therefore, you get:
[tex]\begin{gathered} tan(B)=\frac{6}{8} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]\begin{gathered} tan(A)=\frac{4}{3} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]for the given function, state the amplitude and the minimum output for the function.
Let the following function:
[tex]f(x)=A\cos(Bx\text{ -C})\text{ + D}[/tex]by definition, the amplitude of this function is the absolute value of A.
Now, consider the following function:
[tex]f(t)=3\cos(\frac{6}{5}t)[/tex]then, by definition, the amplitude of this function would be:
[tex]|3|\text{ = 3}[/tex]now, to find the minimum output of the given function we can use the first derivative criterion:
Notice that the critical points would be:
[tex]t=\frac{5\pi}{3}n,\text{ t=}\frac{5\pi}{6}+\frac{5\pi}{3}n[/tex]now, the domain of f(x) is:
[tex]\text{ -}\infty\text{ < t <}\infty[/tex]thus, the interval where the function is decreasing is:
[tex]\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{6}+\text{ }\frac{5\pi}{3}n[/tex]and the interval where the function is increasing is:
[tex]\frac{5\pi}{6}+\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{3}n\text{ + }\frac{5\pi}{3}[/tex]thus, we can conclude that the minimum output occurs when
[tex]t=\text{ }\frac{5\pi}{6}+\frac{5\pi}{3}n[/tex]and this output would be - 3.
Then, the correct answer is:
Answer: