Given data:
The given distance covered by rat is d= 28 m.
The given time is t= 65 seconds.
The speed of the child is s'=2 m/s.
The expression for the speed is,
[tex]\begin{gathered} s=\frac{28}{65}\text{ m/s} \\ =0.43\text{ m/s} \end{gathered}[/tex]As the speed of the child is greater than speed of the rat, so child is going faste.
r
Use the following function rule to find (2). f(x) = (-5 - 2x)? ? f(2) = | Submit
To find f(2) you subtitute the value of x in the function by 2:
[tex]f(2)=-5-2(2)[/tex][tex]f(2)=-5-4[/tex][tex]f(2)=-9[/tex]Then, f(2) is -9Please look at the image below. By the way this is my homework.Use the definition of congruence to decide whether the two figures are congruent. Explain your answer. Give coordinate notation for the transformations you use.
Congruent Shapes
Two congruent shapes have the same size and shape, which means all of their side lengths are equal and all of their internal angles are congruent (have the same measure),
All of the rigid transformations map the original figure to a congruent figure. One of the transformations is the reflection.
The image shows two shapes SRQP and EDCB. They seem to have the same shape and size, but it must be proven by finding the appropriate transformation used.
Comparing the corresponding vertices we can find that out. For example, the coordinates of S are (-6,4) and the coordinates of E are (4,4). The x-coordinate of the midpoint between them is
xm = (-6+4)/2 = -1
Now analyze the points P(-8,2) and B(6,2). The x-coordinate of the midpoint is:
xm = (-8+6)/2 = -1
For the points R(-4,-6) and D(2,-6):
xm = (-4+2)/2 = -1
For the points Q(-9,-4) and D(8,-4):
xm = (-9+8)/2 = -0.5
Since this last pair of corresponding points don't have the same axis of symmetry as the others, the shapes don't have the same size and angles, thus they are not congruent
For both shapes to be congruent, the coordinates of Q should have been (-10,-4)
Answer the statistical measures and create a box and whiskers plot for the following set of data.
Solution
The picture below is the solution to the problem
Brief explanantion
From the data given, It is obvious that:
Minimum = 2
Maximum =
The total number of the data is 3, so the number 7th term is the median
Thus,
Median = 8
To find Q1
[tex]\begin{gathered} Q_1=\frac{1}{4}(n+1)th\text{ term} \\ Q_1=\frac{1}{4}(13+1)=\frac{14}{4}=3.5 \end{gathered}[/tex]Q1 is between the third and fourth term
Therefore, Q1 is
[tex]Q_1=0.5(4)+0.5(6)=5[/tex]Similarly, to find Q3
[tex]\begin{gathered} Q_3=\frac{3}{4}(n+1)th\text{ term} \\ Q_3=\frac{3}{4}(13+1)=3\times\frac{14}{4}=3\times3.5=10.5 \end{gathered}[/tex]Q3 is between the tenth and the eleventh term
Therefore, Q3 is
[tex]Q_3=0.5(11)+0.5(11)=11[/tex]how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]Select the correct answer..What is the value of i^ if the remainder of 4 is 2?OA. -i'OB.-1Ос. іOD. 1ResetNext
1) Considering that for that complex number we have the following pattern:
[tex]\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-1\cdot i=-i \\ i^4=-1\cdot-1=1 \end{gathered}[/tex]2) And that, the question asks us about the what number must be that exponent so that the remainder is 2, we can write out:
[tex]\frac{n}{4}=4d+2[/tex]which d is the divisor, so if the remainder is 2 then we can state:
[tex]i^n=i^2=-1[/tex]A person chooses a number in a set containing the first 5 cubic numbers. Find the set representing the event E of choosing a number that can be evenly divided by 2. Give your answer as a set, e.g. {1,2,3}, using the cubed number (not the base number) and do not include E= in your answer.
The first 5 cubic numbers are:
[tex]\lbrace1,8,27,64,125\rbrace[/tex]To find the set that represents event E we have to choose the numbers from the set above that are evenly divided by 2; this means that we have to choose the numbers that are multiple of 2. We notice that this numbers are 8 and 64, therefore the set that represents event E is:
[tex]\lbrace8,64\rbrace[/tex]Solve the system of two linear inequalities graphically,4x + 6y < 24(x22Step 1 of 3 : Graph the solution set of the first linear inequality.AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawn.Enable Zoom/PanChoose the type of boundary line:Solid (-) Dashed (--)Enter two points on the boundary line:10-5Select the region you wish to be shaded:
Answer:
To solve the system of two linear inequalities graphically,
[tex]\begin{gathered} 4x+6y<24 \\ x\ge2 \end{gathered}[/tex]For step 1,
Draw a line 4x+6y=24
Since the given equation has less than sign, the required region will not include the line, Hence we draw the dashed line for the line 4x+6y=24.
Since we required redion is 4x+6y<24, the points bellows the line satisfies the condition hence the required region is below the line,
Similarly for the inequality,
[tex]x\ge2[/tex]It covers the region right side of the line x=2,
we get the siolution region as the intersecting region of both inequality which defined in the graph as,
Dark blue shaded region is the required solution set for the given inequalities.
Jackson started a savings account using the bonus he received from work of $3,500. Theaccount is compounded weekly with an interest rate of 1.75% How much interest did theaccount earned in 18 years?O $1,295.65O $1,102.500 $4,795.65o $1,290
The amount compounded is given by the formula ;
[tex]A=P\lbrack1+\frac{r}{100n}\rbrack^{nt}[/tex]Here, P = $3500, r = 1.75%, n = 52 , t = 18 years.
[tex]\begin{gathered} A=3500\lbrack1+\frac{1.75}{100\times52}\rbrack^{52\times18} \\ A=4795.65 \end{gathered}[/tex]Therefore, the interest the account will earn is 4795.65-3500 = $1295.65, Option A
True or False: A power has two parts, a base and an exponent. True False
The said statement is true.
A power has two parts, a base and an exponent.
Example
[tex]2^3[/tex]The answer is TRUE
inserted a picture of the question, can you just answer the question and not ask a lot of questions yes i’m following
Step-by-step explanation:
A nonagon has 9 sides, so a regular nonagon will have vertices that are 40° apart as measured from the center. It has 9-fold rotational symmetry,
so the figure will be identical to the original when rotated multiples of 360°/9 = 40°.
[tex]\frac{360}{9}=40[/tex]Therefore the degrees will a nonagon have rotational symmetry
Hene the correct answer is Option B
Ethan found the spinner shownbelow and planned to use it for agame.2332453235After studying the spinner beforeusing it, Ethan correctly concludedthat the spinner was-A least likely to land on 2B least likely to land on 5C most likely to land on 3D most likely to land on 2
we have that
the number 3 appears 4 times
so
answer is
option C most likely to land on 3
Question 8 of 10What is the slope of the line described by the equation below?y=-x+ 8A. 8B. 1OOOC. -8O D.-1SUBMIT
We have the following equation
y = -x + 8
this equation is writen in slope intercept form
y = mx + b
where m is the slope
From the above, we can see that the slope is m = -1
11) -3(1 + 6r) = 14 - r 12) 660+6)-5=1+6v 13) -4k + 2(5k - 6) = -3k - 39 14) -16 + 5n=-71-
-3(1+6r) = 14 -r
-3-18r = 14 - r
-3-14 = -r +18r
-17 = 17r
17r/17 = -17/17
r = -1
distributive property 3x(7x+6)
By distributive property, we distribute 3x, and multiply it to each term inside the binomial (7x+6) accounting for the sign.
[tex]\begin{gathered} 3x(7x+6) \\ \Rightarrow3x(7x)+3x(6) \\ \Rightarrow21x^2+18x \\ \\ \text{Therefore, }3x(7x+6)=21x^2+18x \end{gathered}[/tex]two slices of dans famous pizza have 230 calories how many calories would you expect to be in 5 slices of pizza
We can answer this question, using proportions. We can see it graphically as follows:
Then, we have that 5 slices will have 575 calories.
After reading the question what would the inequality equation and the graph shade look like?
It is given that the one number is always less than the opposite of the other.
So the equation formed is y<-x
The graph is obtained as
Write the equation of the line that passes through the points (12, 4) and (22,9).
Given the following points that pass through the line:
Point A : 12,4
Point B : 22,9
Step 1: Let's determine the slope of the line (m).
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{ = }\frac{9\text{ - 4}}{22\text{ - 12}}[/tex][tex]\text{ m = }\frac{5}{10}\text{ = }\frac{1}{2}[/tex]Step 2: Let's determine the y-intercept (b). Substitute m = 1/2 and x,y = 12,4 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 4 = (}\frac{1}{2})(12)\text{ + b }\rightarrow\text{ 4 = }\frac{12}{2}\text{ + b}[/tex][tex]\text{ 4 = 6 + b}[/tex][tex]4\text{ - 6 = b}[/tex][tex]\text{ -2 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1/2 and b = -2 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (}\frac{1}{2})x\text{ + (-2)}[/tex][tex]\text{ y = }\frac{1}{2}x\text{ - 2}[/tex]Therefore, the equation of the line is y = 1/2x - 2.
The coordinates of triangle LMN are shown.YL(-1,4)XN (4, -1)M(-1, -3)What is the length of LM? Enter the answer in the box.unit(s)
Given data:
The given coordinate of L is (-1,4).
The given coordinate of M is(-1, -3).
The expression for LM length is,
[tex]\begin{gathered} LM=\sqrt[]{(-1-(-1))^2+(-3-4)^2} \\ =\sqrt[]{0+49} \\ =7 \end{gathered}[/tex]Thus, the LM length is 7 units.
how do i solve (4x^3 + 2x - 3) divided by (x - 3) with long division??
We want to divide 4x³ + 2x - 3 by x - 3 with the long division method
First, we rewrite the polynomial as:
4x³ + 0x² + 2x - 3
Them we divide the first term of the dividend by the highest term of the divisor:
4x²
x - 3 |4x³ + 0x² + 2x - 3
Then we multiply the divisor by this result:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
Now we subtract this result from the dividend:
| 4x²
x - 3 |4x³ + 0x² + 2x - 3
4x³ - 12x²
|12x² + 2x - 3
Now we can repeat all the previous steps using the last result as dividend:
| 4x² + 12x
x - 3 | 12x² + 2x - 3
12x² - 36x
|38x - 3
And we repeat these steps once more:
4x² + 12x + 38
x - 3 | 38x - 3
34x - 102
|99
The final term is the remainder
Then, we have:
4x³ + 2x - 3 = (x - 3)*(4x² + 12x + 34) + 99
Given sin(x)=.4 and cot(x) >0 what is cos(x)?
The cotangent is given by the cosine over the sine.
If the cotangent is positive and the sine is positive, that means the cosine is also positive.
Now, in order to find the value of cos(x), we can use the following property:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (0.4)^2+\cos ^2(x)=1 \\ 0.16+\cos ^2(x)=1 \\ \cos ^2(x)=1-0.16 \\ \cos ^2(x)=0.84 \\ \cos (x)=0.917 \end{gathered}[/tex]On the Richter Scale, the magnitude R of an earthquake of intensity I is given by the equation in the image, where I0 = 1 is the minimum intensity used for comparison. (The intensity of an earthquake is a measure of its wave energy). Find the intensity per unit of area I for the Anchorage Earthquake of 1989, R = 9.2.
we have the formula
[tex]R=\log _{10}\frac{I}{I_0}[/tex]we have
R=9.2
I0=1
substitute in the given equation
[tex]\begin{gathered} 9.2=\log _{10}\frac{I}{1} \\ 9.2=\log _{10}I \\ I=10^{(9.2)} \\ \end{gathered}[/tex]I=1,584,893,192.46
Solve the Equation , I tried multiplying that 6 to the numbers in the parentheses but i couldnt get it
To start we will do what you said, multiply the 6, so:
6*(n-4)=3n
6n-6*4=3n
6n-24=3n
6n=3n+24
6n-3n=24
3n=24
n=24/3
n=8
So the answer is: 8
fill in the table using the function rule y= 6x-3
Answer:
-9,-3,3,27
Step-by-step explanation:
Just multiply x by 6 and subtract 3 to that
2. Write a story that can be represented by the equation y = x + 1/4 x.Question 2 On a hot day a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink? Create an equation to represent this situation.
y= x+ 1/4 x
Y = dependent variable
x= independent variable
Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.
Find the total amount of money deposited (y).
add or subtract : x/4 + 3/4 =
Answer:
x + 3 / 4
Explanation:
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
98) Cost to store: $145Markup: _?Selling price:$319.
Answer: Mark up is 220%
Cost to store : $145
selling price = $319
let x = mark up
Using the below equation
[tex]\begin{gathered} \text{Part = whole x percentage} \\ \text{part = selling price} \\ \cos t\text{ to store = whole} \\ \text{Mark up = percentage} \\ 319\text{ = 145 }\cdot\text{ x\%} \\ \text{ x\% = }\frac{319}{145}\text{ x 100\%} \\ x\text{ = 2.2 x 100\%} \\ x\text{ = 220\%} \\ \text{Therefore, the mark up is 220\%} \end{gathered}[/tex]I'm not sure how to do this. This is a long one that's why.
We have the following:
For the area surface:
[tex]As=2\pi rh[/tex]repacing:
r = 1.5 in
h = 7 in
[tex]\begin{gathered} As=2\cdot3.14\cdot1.5^{}\cdot7 \\ As=65.94 \end{gathered}[/tex]The answer is 65.9 in^2
For volume:
[tex]\begin{gathered} V=\pi r^2h \\ V=3.14\cdot1.5^2\cdot7 \\ V=49.455 \end{gathered}[/tex]The answer is 49.5 in^3
Describe in words where the square root of 60 minus 11 would be plotted on a number line.
Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
Which expression has a negative value
Answer:
bottom one
Step-by-step explanation: