The snowboarder travels 105 meters in 7 seconds.
This means that the snowboarder travels 105/7 = 15 meters per second (m/s). So, his speed is 15 m/s
Therefore, in 14 seconds, the snowboarder will travel (15 meters per second)*(14 seconds) = 210 meters.
Tom's Bakery recently spent a total of $800 on new equipment, and their average hourlyoperating costs are $10. Their average hourly receipts are $90. The bakery will soon makeback the amount it invested in equipment. What would the total expenses and receipts bothequal?Write a system of equations, graph them, and type the solutionTimelapsedPAUD1.000Smarts.com0300600Dollars (9)400200.103040HoursCESreceiptdollars
The equation for the expenses of the bakery is $800+$10t, where t is given in hours. On the other hand, the equation that models the receipts is $90t, where t is in hours.
To find the value of t such that the expenses are equal to the receipt we need to solve the equation below
[tex]\begin{gathered} 800+10t=90t \\ \Rightarrow800=90t-10t=80t \\ \Rightarrow t=10 \end{gathered}[/tex]In dollars, this is
[tex]90\cdot10=900[/tex]The answer is $900 dollars
The graph of the equations is
The green line represents the expenses and the blue one the receipts
Slope intercept formPlease Solve everything with the exception of 8
The equation of a line in slope intercept form is in the form,
[tex]y=mx+c[/tex]SOLUTION
3) 2y - 6 = -6x
Add 6 to both sides
[tex]\begin{gathered} 2y-6+6=-6x+6 \\ 2y=-6x+6 \end{gathered}[/tex]Divide through by 2
[tex]\begin{gathered} \frac{2y}{2}=-\frac{6x}{2}+\frac{6}{2} \\ y=-3x+3 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-3x+3[/tex]4) - 11x - 7y = -56
Add +11x to both sides
[tex]\begin{gathered} -11x-7y+11x=-56+11x \\ -7y-11x+11x=11x-56 \\ -7y=11x-56 \end{gathered}[/tex]Divide both sides by - 7
[tex]\begin{gathered} \frac{-7y}{-7}=\frac{11x}{-7}-\frac{56}{-7} \\ y=-\frac{11x}{7}+8 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-\frac{11x}{7}+8[/tex]The following is a list of 5 measurements.5, 17, 10, 13, 19Send data to calculatorSuppose that these 5 measurements are respectively labeled X2, X2, ..., Xs. Compute the following.5Σ (4)i=1
We will have the following:
[tex]\sum ^5_{i=1}(x_i)^2=(5)^2+(17)^2+(10)^2+(13)^2+(19)^2\Rightarrow\sum ^5_{i=1}(x_i)=944[/tex]So, the given sum is equal to 944.
1. What is the total area of this figure? How to calculate it?
Given the figure shown in the exercise, you can identify that it is formed by a triangle and a rectangle. Then, the total area of the figure will be the sum of the area of the triangle and the area of the rectangle.
• The formula for calculating the area of a rectangle is:
[tex]A_r=lw[/tex]Where "l" is the length and "w" is the width.
In this case:
[tex]\begin{gathered} l=8ft \\ w=2ft \end{gathered}[/tex]Then, by substituting the values into the formula and evaluating, you get:
[tex]A_r=\left(8ft\right)\left(2ft\right)=16ft^2[/tex]• The formula for calculating the area of a triangle is:
[tex]A_t=\frac{bh}{2}[/tex]Where "b" is the base and "h" is the height of the triangle.
In this case, you can identify that:
[tex]\begin{gathered} b=8ft \\ h=16ft-2ft=14ft \end{gathered}[/tex]See the picture below:
Knowing the base and the height of the triangle, you can substitute values into the formula and evaluate, in order to find its area:
[tex]A_t=\frac{\left(8ft\right)\left(14ft\right)}{2}=\frac{112ft^2}{2}=56ft^2[/tex]Therefore, you can determine that the total area of the figure is:
[tex]\begin{gathered} A_{total}=16ft^2+56ft^2 \\ \\ A_{total}=72ft^2 \end{gathered}[/tex]Hence, the answer is:
[tex]A_{total}=72ft^2[/tex]The graph of f(x) = (1/4)^-x is reflected about the y-axis and compressed vertically by a factor of 1/3 What is the equation of the new function, g(x)?
Given:
[tex]f(x)=(\frac{1}{4})^{-x}[/tex]f(x) is reflected about the y-axis and compressed vertically by a factor of 1/3.
Required:
We need to find the new function g(x).
Explanation:
The reflection of the function y=f(x) about y-axis is y=f(-x).
To reflect the given function f(x) about y-axis:
Replace x =-x in the given function f(x).
[tex]f(-x)=(\frac{1}{4})^{-(-x)}[/tex][tex]f(-x)=(\frac{1}{4})^x[/tex]Multiply both sides by 1/3 to get the function compressed vertically by a factor of 1/3.
[tex]\frac{1}{3}f(-x)=\frac{1}{3}(\frac{1}{4})^x[/tex]The new function is
[tex]g(x)=\frac{1}{3}(\frac{1}{4})^x[/tex]Final answer:
[tex]g(x)=\frac{1}{3}\times(\frac{1}{4})^x[/tex]
A quadrilateral with exactly one pair of parallel sides is: A. squareB. rectangleC. rhombusD. trapezoid
The parallel sides are sides that will never meet and are always the same distance apart.
Given the figures below;
The above shapes has more than a pair of parallel sides, hence they are wrong.
Also,
The trapezoid has only one pair of parallel sides.
CORRECT OPTION: D
Questionis undefined. If there's more than one value, list them9a - 11Determine the value(s) for which the rational expression-a - 9separated by a comma, e.g. a = 2,3.h
The rational expression is
[tex]\frac{9a-11}{-a-9}[/tex]The values of a which make the rational expression undefined are the values that make the denominator = 0
Then to find them equate the denominator by 0
The denominator is (-a - 9)
[tex]-a-9=0[/tex]Add 9 to each side
[tex]\begin{gathered} -a-9+9=0+9 \\ -a=9 \end{gathered}[/tex]Divide each side by -1
[tex]\begin{gathered} \frac{-a}{-1}=\frac{9}{-1} \\ a=-9 \end{gathered}[/tex]The value of a which makes the rational expression undefined is -9
The answer is a = -9
Complete the explanation to identify the set of numbers that best describes each situation.The change will be whole dollar amount which can be negative, zero, or positive. Thus the change willbe (an) ____[(a)rational, (b)integer, (c)real, (d)irrational] number.
The set of negative integers is represented below:
[tex]-\infty,\cdots-2,-1[/tex]The set of positive integers is represented as:
[tex]1,2,\cdots\infty[/tex]Combining the two sets above and adding zero (0), we have:
[tex]-\infty,\cdots-2,-1,0,1,2\cdots,\infty[/tex]The set which describes the set of negative, zero or positive whole numbers is the set of integers.
Thus the change will be an integer number.
3(3 + 6q) I need to simplify the expression
3(3 + 6q)
By expanding the bracket, we have
3(3) + 3(6q) = 9 + 18q
the area of square is 49m2.what is the length of one side
Consider that the area (A) of a square with side 's' is given by the formula,
[tex]A=s^2[/tex]Given that the area is 49 sq. meters,
[tex]A=49[/tex]Substitute the values and solve for the side 's' as follows,
[tex]\begin{gathered} s^2=49 \\ s=\sqrt[]{49} \\ s=\pm7 \end{gathered}[/tex]But 's' is the side of the square, which cannot be negative.
So we have to neglect the negative value, and consider the positive value,
[tex]s=7[/tex]Thus, the side of the given square is 7 meters .
find the equation of the images of the following lines when the reflection line is the x-axis
When the equation is reflected about the x-axis,
(x, y) → (x, - y)
The original equation is y = - x + 7
Therefore,
[tex]\begin{gathered} f(x)=-f(x) \\ replace\text{ y with -y} \\ -y=-x+7 \\ y=x-7 \end{gathered}[/tex]Slove the equation-4x + 1 = 21
We have the following:
[tex]-4x+1=21[/tex]solving for x:
[tex]\begin{gathered} -4x+1-1=21-1 \\ -4x=20 \\ x=\frac{20}{-4} \\ x=-5 \end{gathered}[/tex]The answer is -5
Match the amplitude, midline, period, and frequency for the cosine equation
Explanation
we can describe the cosine function as
[tex]y=A\cos \mleft(B\mleft(x+C\mright)\mright)+D[/tex]where
amplitude is A
Frequency is B
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
Step 1
identify
[tex]5\cos (2x)+3\rightarrow A\cos (B(x+C))+D[/tex]hence
[tex]\begin{gathered} A=5=\text{Amplitude} \\ B=2,C=0,so \\ \text{period}=\frac{2\text{ }\pi}{B}=\frac{2\text{ }\pi}{2}=\pi \\ \text{period}=\pi \\ Frequency=B=2 \\ \text{Vertical shift=D=3} \end{gathered}[/tex]Step 2
midline
The equation of the midline of periodic function is the average of the maximum and minimum values of the function.
a) we have a maximum when
[tex]\begin{gathered} \cos (2x)=1 \\ x=0,\text{ because (cos 0)=1} \\ \text{now, replace} \\ y=5\cos (2x)+3 \\ y=5\cos (2\cdot0)+3=5\cdot1+3=8 \\ y=8,\text{ so the max. is 8} \end{gathered}[/tex]b) we have a minimum when
[tex]\begin{gathered} \cos (2x)=-1 \\ x=\frac{\pi}{2},\text{ because} \\ \cos (2\frac{\pi}{2})=\cos (\pi)=-1 \\ \text{now, replace} \\ y=5\cos (2\cdot\frac{\pi}{2})+3=5\cdot-1+3=-5+3=-2 \end{gathered}[/tex]so, the midline is the average of 8 and -2
[tex]\begin{gathered} \text{midline}=y=\frac{8+(-2)}{2}=\frac{6}{2}=3 \\ y=3 \end{gathered}[/tex]I hope this helps you
1 ) At a local department store, jeans have been reduced to $5. This price is at 20% of theoriginal price for jeans. Given this, what was the original price of the jeans? Roundyour answer to the nearest whole number if necessary.
we have that
$5 ------> represents 20% of the original price
so
Applying proportion
Find out how much represent a percentage of 100%
so
5/20=x/100
solve for x
x=(5/20)*100
x=$25
the answer is $25Billy is comparing gasoline prices at two different gas stations. ·at the first gas station, the equation c = 2.80g gives the relationship between g, the number of gallon of gasoline, and c, the total cost, in dollars.·at the second gas station, the cost of 2.5 gallons of gasoline is $8.30, and the cost of 5 gallons of gasoline is $16.60.how much money, per gallon, would Billy save by going to the less expensive gas station?
For the first gas station,
[tex]c=2.80g[/tex]That is, for one number of gallon of gasoline, the cost is, 2.80
For the second gas station, cost of 2.5 gallons of gasoline is $8.30. Therefore, for one gallon if gasoline, the cost is,
[tex]\frac{8.30}{2.5}=3.32[/tex]Therefore, Billy will save, 3.32 - 2.80 = 0.52 dollars by going to the less expensive gas station.
calculate the area height 137, base 203
where b = base and h=height
so for this triangle:
[tex]area=\frac{1}{2}*137*203[/tex]The answer is 13905.5
How would you find the slope of this line and write an equation for it?
Given the points:
A (-1, 3) and B (0, 4)
slope - intercept form of an equation: y = mx + b.
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m\text{ = }\frac{4-3}{0\text{ + 1}}=\text{ 1}[/tex]Now, to find b, we can replace one point in the slope- intercept form:
4 = 1 x 0 + b
b = 4
Slope- intercept equation: y = x + 4
A random sample of n= 100 observations is selected from a population with u = 29 and o = 25. Approximate the probabilities shown below.b. P(22.1 ≤ x ≤ 26.8) (Round to three decimal places as needed.)
To be able to get the probability of a certain value to be selected, we need to convert it to a z-score or z-value. To convert that, we have the formula below:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]where:
bar x = sample mean
μ = population mean = 29
σ = population standard deviation = 25
n = sample size = 100
So, let's start determining the probabilities between 22.1 and 26.8 mean values.
x = 22.1
[tex]z=\frac{22.1-29}{\frac{25}{10}}=\frac{-6.9}{2.5}=-2.76[/tex]x = 26.8
[tex]z=\frac{26.8-29}{2.5}=\frac{-2.2}{2.5}=-0.88[/tex]Let's plot these values to the normal curve with their corresponding areas. The corresponding areas can be found using the Z Normal Distribution.
As you can see in the graph above, the area covered from 0 to -0.88 is 0.3106 while the area covered from 0 to -2.76 is 0.4971.
To get the area covered from -0.88 to -2.76, we need to subtract the two.
[tex]0.4971-0.3106=0.1865\approx0.187[/tex]Therefore, the area covered between x = 22.1 and x = 26.8 is approximately 0.187.
How to Use the Z-Table:
The above picture shows the area from 0 to 0.88. We have 0.8 as our row and 0.08 as our column. The intersection of this row and column is our area for 0.88 from the center of our normal curve. In this case, we have 0.3106.
Another example: The area to the left of -0.32 or z ≤ -0.32.
In the figure above, the area to the left of -0.32 is the one colored in green. The red area is the area from -0.32 to the center 0 which is 0.1255.
Remember, the area from the center of the normal curve is 0.5. If the red area is already 0.1255, how much is left for the green area?
[tex]0.5-0.1255=0.3745[/tex]Therefore, the area to the left of z = -0.32 is 0.3745 or 0.375.
Select the statement that best describes the pattern.4. 33- 33 = 04-4 = 05- 5 = 0A 33-33= xB X-X=0C x-0= x
X-X=0 (option B)
Explanation:
The pattern is the subtraction of the same number to get 0
33- 33 = 0
4-4 = 0
5- 5 = 0
From the options given, the one that has the difference of the same number resulting to zero is X-X=0
Hence, the statement that best describes the pattern is X-X=0 (option B)
Which of the two triangles has an area of 68 square units?
Given data:
The given area is A=68 square units.
The area of the first triangle is,
[tex]\begin{gathered} A_1=\frac{1}{2}(17)(8) \\ =68 \end{gathered}[/tex]The area of the second triangle is,
[tex]\begin{gathered} A_2=\frac{1}{2}(8)(15) \\ =60 \end{gathered}[/tex]Thus, the first triangle has an area 68 square-u
The endpoints of segment CD are C(1, 2) and D(5, 4). Graph the image of segment CD after the composition of transformations. C(1, 2) and D(5, 4) Translation: (x, y) + (x, y+ 2) Reflection: over the line y = x
Two segment points, transformation
C (1,2).
D (5,4)
FOR POINT C
Translate C , (x, y) + (x, y+ 2) = (1,2) + (1, 2+2) = (1+1, 2+2+2) = (2,6)
Reflection over y= x
change (x ,y ) in (y,x)
(x,y) = ( 6, 2)
FOR POINT D
Translate D ,(x,y) + (x , y+2) = (5,4) + (5, 4+2) = (5+5, 4+4+2) = (10, 10)
Reflection over y=x
(x,y) = (10,10). (Its same point)
DRAWING
New segment C'D' is drawed in green
In a certain experiment, a coin is tossed and this spinner is spun. Compute the probability of the event.P(heads and no blue)
Consider that the two events (tossing a coin and spinning a spinner) are independent and that the probability of landing on blue is equal to 1/3; thus,
[tex]\begin{gathered} P(heads\&no-blue)=\frac{1}{2}\cdot(1-\frac{1}{3}) \\ \Rightarrow P(heads\&no-blue)=\frac{1}{2}\cdot\frac{2}{3}=\frac{1}{3} \end{gathered}[/tex]Thus, the answer is P(heads&NoBlue)=1/3
Can you help me to solve the other half of this problem? I don’t know what I’m doing wrong
Let's start by copying the equation:
[tex]-5\cos ^2(x)+4\cos (x)+1=0[/tex]To make it easier to see, let's substitute cos(x) by "u":
[tex]-5u^2+4u+1=0[/tex]To find the values of "u", we can use Bhaskara's Equation:
[tex]\begin{gathered} u=\frac{-4\pm\sqrt[]{4^2-4\cdot(-5)\cdot1}}{2\cdot(-5)} \\ u=\frac{-4\pm\sqrt[]{16+20}}{-10} \\ u=\frac{-4\pm\sqrt[]{36}}{-10} \\ u=\frac{-4\pm6}{-10} \end{gathered}[/tex][tex]\begin{gathered} u_1=\frac{-4+6}{-10}=\frac{2}{-10}=-0.2 \\ u_2=\frac{-4-6}{-10}=\frac{-10}{-10}=1 \end{gathered}[/tex]Now, let's substitute cos(x) back:
[tex]\begin{gathered} \cos (x_1)=-0.2 \\ \cos (x_2)=1 \end{gathered}[/tex]Since it is a trigonometric solution, we have repeating values of "x" that satisfy each equation above.
The first, the one you already got, comes from
[tex]\begin{gathered} \cos (x)=1 \\ x=0+2\pi k \\ x=2\pi k \end{gathered}[/tex]The smallest non negative is for k = 0 which gives
[tex]x=0[/tex]The next following this part would be for k = 1, which gives:
[tex]x=2\pi[/tex]However, we have another equation for solutions:
[tex]\cos (x)=-0.2_{}[/tex]For this equation, the smallest "x" value can be found using arc-cossine of -0.2 in a calculator, which gives:
[tex]\begin{gathered} x=\arccos (-0.2) \\ x=1.772\ldots \end{gathered}[/tex]This is the next non-negative solution for the equation, because it is smaller than the other we found.
So the second part is x = 1.772.
describe the effect on the graph of the parent f(x)=x
we know that
the parent function is
f(x)=x
The line passes throught the origin
the slope is m=1
Find the equation of the line g(x)
mr. Patterson takes 8 minutes to run 2/3 of a Lap. How long would it take to run one full lap.
If it takes Patterson 8 minutes to run 2/3 of a lap.
Let the time to complete on one lap be x,
Then 2/3 of x = 8
cross- multiply, we have :
[tex]\begin{gathered} \frac{2}{3}x=8,_{} \\ 2x=8\times3 \\ \text{Then }x=\text{ }\frac{8\times3}{2} \\ x\text{ = 12 mins} \end{gathered}[/tex]1 - Determine whether the given function is even, odd, or neither.a. (picture 1)b. (picture 2)2 - Evaluate the piece wise function at the given value of the independent variable. (picture 3)if f(-3)
Here in this question, we want to know if either of the function is even , odd or neither
For an even function, the additive inverse of the value of the independent variable will give the same value of the dependent variable. An odd function will behave otherwise.
What this mean in plain terms is that for an even function;
f(x) = F(-x)
f(x) = 4x^2 + x^4
Let us find f(1)
f(1) = 4(1)^2 + 1^4 = 4 + 1 = 5
f(-1) = 4(-1)^2 + (-1)^4
f(-1) = 4 + 1 = 5
In this case, since f(1) = f(-1), then the function is even.
Using the image below, identify the type of angle and find the missing angle.
SOLUTION:
Step 1:
In this question, we are given the following:
Using the image below, identify the type of angle and find the missing angle:
Step 2:
The details of the solution are as follows:
[tex]Type\text{ of angle Relationship: Corresponding Angles}[/tex][tex]Missing\text{ Angle: m}\angle1\text{ = 129}^0[/tex]An end point and one arrow
An end point and one arrow is what is called a vector in mathematical terms.
The end point is where you apply the vector (that could be representing a velocity, or a force, for example.
The arrow indicates the direction of that vector quantity.
Hey! I need help finding the slope of the Tangent at a given point as depicted in the following image: (Just need help with an explanation to #5)
5.
[tex]\begin{gathered} \frac{d}{dx}(x^n)=nx^{n-1} \\ \end{gathered}[/tex]so:
[tex]\begin{gathered} f(x)=3-5x \\ f(x)^{\prime}=\frac{d}{dx}(3)-\frac{d}{dx}(5x)=\frac{d}{dx}(3)-5\frac{d}{dx}(x) \\ so\colon \\ \frac{d}{dx}(3)=0 \\ \frac{d}{dx}(x)=1x^{1-1}=1x^0=1\cdot1=1 \\ f(x)^{\prime}=0-5 \\ f(x)^{\prime}=-5 \end{gathered}[/tex]6.
[tex]\begin{gathered} g(x)=\frac{3}{2}x+1 \\ g(x)^{\prime}=\frac{3}{2}=m \end{gathered}[/tex]Juan paid $85.00 for 4 concert tickets. Each ticket cost the same amount. What was the cost of each concert ticket in dollars and cents?
Answer:
$21.25
Explanation:
The cost of 4 concert tickets = $85.00
Each ticket cost the same amount.
Thus:
[tex]\begin{gathered} \text{The cost for each concert ticket will be}=\frac{85}{4} \\ =\$21.25 \end{gathered}[/tex]