Pablo draws Rectangle P. He says that the area is greater than 50 square units. What could the missing side length be? Explain. P. ? units 6 units
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Answer:
Explanation:
Here, we want to get the missing side length
From the question, it was said that the area is greater than 50 square units
What this mean is that the product of the width and length of the rectangle is greater than 50 square units
Therefore, the number in whch we will multiply by 6 must give us a result greater than 50 square units
The highest multiple of 6 closest to 50 is 48 while the closest multiple after 50 is 54
9 multiplied by 6 will give 54 square units
In essence, we can say that the missing side length is 9 square units
Related Questions
ā has an initial point, at (4,-8) and a terminal point at (5,2). Write ā in component form
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Ok, here we have this data:
I: Initial point (4,-8)
T: Terminal Point (5,2)
IT==<5-4, 2-(-8)>=<1, 10>
The component form is <1,10>
Which of the following exponential functions is represented by the data in the table?Question 12 options:A) ƒ(x) = x3B) ƒ(x) = 3xC) ƒ(x) = (1∕3)xD) ƒ(x) = x1∕3
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ANSWER:
C.
[tex]f(x)=(\frac{1}{3})^x[/tex]EXPLANATION:
Given:
To find:
The exponential function represented by the data in the given table
Let's go ahead and check each of the given functions to determine the right function;
*For the first function;
[tex]\begin{gathered} f(x)=x^3 \\ f(-3)=(-3)^3=-27 \end{gathered}[/tex]We can see that the first function is not the right function
*For the second function:
[tex]\begin{gathered} f(x)=3^x \\ f(-3)=3^{-3}=\frac{1}{27} \end{gathered}[/tex]We can see that the first function is not the right function
*For the third function:
[tex]\begin{gathered} f(x)=(\frac{1}{3})^x \\ f(-3)=(\frac{1}{3})^{-3}=27 \\ f(-2)=(\frac{1}{3})^{-2}=9 \\ f(-1)=(\frac{1}{3})^{-1}=3 \\ f(0)=(\frac{1}{3})^0=1 \\ f(1)=(\frac{1}{3})^1=\frac{1}{3} \\ f(2)=(\frac{1}{3})^2=\frac{1}{9} \\ f(3)=(\frac{1}{3})^3=\frac{1}{27} \end{gathered}[/tex]We can see that the third function is the right function
(b)A sight-seeing ship is stopped in the water for an hour, miles from the shore. Then the captain heads the ship back to the shore at a constant rate. The ship docks at the shore for a while and then returns to the open sea.Choose the graph that gives the best representation.
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We have the following information from the question:
• A sight-seeing ship is stopped in the water for an hour, miles from the shore.
,• Then the captain heads the ship back to the shore at a constant rate.
,• The ship docks at the shore for a while and then return to the open sea.
Then we have to choose the graph that best represents the situation.
To do this, we need to analyze the three situations separately by knowing that on the y-axis we have graphed a distance relative to the shore (dependent variable), and on the x-axis, we have the time as an independent variable:
1. A sight-seeing ship is stopped in the water for an hour, miles from the shore:
If we see this situation, we have to check a distance larger than zero at x = 0. Then we have to see a horizontal line for an hour since the ship is stopped in the water for an hour, and this is because the ship is stopped, and the ship remains in the same place for an hour.
2. Then the captain heads the ship back to the shore at a constant rate:
It means that the ship will shorten the distance with respect to the shore, and this will be verified at a constant rate. Then we need to check in the graph a segment with a negative slope.
3. The ship docks at the shore for a while and then return to the open sea:
We need to check on the graph that the distance from the shore will be zero, and then we will have a horizontal line since the ship will remain for a while in the shore. Then the ship will return to the open sea, and we will check that the distance to shore will increase constantly.
Therefore, the graph that gives the best representation is the second graph from the left, that is:
Therefore, in summary, the
Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 137 millimeters, and a standard deviation of 8 millimeters.If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be greater than 133.5 millimeters? Round your answer to four decimal places.
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The probability that the sample mean would be greater than 133.5 is 0.9926
Explanation:Given:
Mean = 137
Standard deviation = 8
Sample = 31
To find the probability that the sample mean would be greater than 133.5, we have:
[tex]\begin{gathered} z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}} \\ \\ =\frac{133.5-137}{\frac{8}{\sqrt{31}}}=-2.4359 \\ \\ P(X>133.5)=1-P(z<-2.4359) \\ =1-0.0074274 \\ \approx0.9926 \end{gathered}[/tex]12² × 5 + 5 .........
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The solution to the given expression will be,
[tex]12^2\times5+5=144\times5+5=720+5=725[/tex]What is the midpoint of the segment shown below?
-10
(-8,-7)
(-7,-8) -10-
10
OA (-15-15)
A.
O B. (-15,-15)
O C. (-15, -15)
OD. (-15, -15)
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Remember that the formula to calculate the midpoint between two points is given by
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]substitute given coordinates
[tex]\begin{gathered} M(\frac{-8-7}{2},\frac{-7-8}{2}) \\ \\ M(-\frac{15}{2},-\frac{15}{2}) \end{gathered}[/tex]The answer is option BWhat are all the zeros of the function f(x)= x^2 −x−56=0
Answers
The Solution.
The given function is
[tex]f(x)=x^2-x-56=0[/tex]Solving quadratically using the factorization method, we get
[tex]f(x)=x^2-8x+7x-56=0[/tex][tex]f(x)=x(x-8)+7(x-8)=0[/tex][tex](x+7)(x-8)=0[/tex][tex]\begin{gathered} x+7=0,\text{ or x -8 =0} \\ x=-7,\text{ or x = 8} \end{gathered}[/tex]Hence, the zeros of the function are -7 or 8
What is the amplitude of the sine funtion y=2 sin(4x)
A. 4
B. 2
C. r/2
D. r/4
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Answer:
it´s C
Step-by-step explanation: Just took the test trust
A set of data items normally distributed with a mean of 60. Convert the data item to a z-score, if the data item is 47 and standard deviation is 13.
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To answer this question, we need to remember what the z-score is. The formula for it is as follows:
[tex]z_{\text{scorre}}=\frac{x-\mu}{\sigma}[/tex]We have that:
• mu is the population mean
,• x is the raw score we want to normalize or convert into a z-score
,• sigma is the population standard deviation.
Then, since we have that the mean is equal to 60, the raw score, x, is equal to 47, and the standard deviation is 13, then, we have that the z-score is:
[tex]z_{\text{score}}=\frac{47-60}{13}=\frac{-13}{13}\Rightarrow z_{score}=-1[/tex]Then, the z-score is equal to -1. That is, x is one standard deviation below the population mean.
Determine the equation in slope intercept form
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Isabelle is designing a sandbox for her backyard. the sandbox will be a regular pentagon 3 ft each side. how much wood does she need to enclose the entire sandbox? how many square ft will the sandbox take up?
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Area of rectangular Pentagon = 5 * s^2 / (4tan(36°)) =5 × (3)^2 / (4*tan(36) ) = 17.73
the sides of the box are squares. their sides are 3 ft long. So the area of each square is 25 ft^2
Now, there are 5 sides, so if we mutiply 5 * 25 ft^ = 125 ft^2
So the answers are:
She needs 125 ft^2 to enclose the entire sandbox
and it would take up 142.73 ft^2
write an equation of the circle
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Take into account that the general equation of a circle is given by:
(x - h)² + (y - k)² = r²
where h and k are the values of the coordinates of the point (h,k), which is the center of the circle in the coordinate system.
You can notice in the given image, that the center of the circle is the point (5,4), then, the values of k and h are:
h = 5
k = 4
moreover, you can notice that the radius of the circle is 4, then
r = 4
replace the values of h, k and r in the equation of a circle:
[tex]\begin{gathered} (x-5)^{2}+(y-4)^{2}=4^{2} \\ (x-5)^{2}+(y-4)^{2}=16 \end{gathered}[/tex]The last equation is the required expression for the equation of the given circle.
The cost of a pound of nails increased from $2.40 to $2.53. What is the percent of increase to the nearest whole-number percent?
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The formula to find the percent increase of two values is:
[tex]\text{ Percent Increase }=\frac{\text{ New price - Old price}}{\text{ Old price}}\cdot100[/tex]In this case, we have:
[tex]\begin{gathered} \text{ Old price }=\text{ 2.40} \\ \text{ New price }=\text{ 2.53} \end{gathered}[/tex][tex]\begin{gathered} \text{ Percent Increase }=\frac{2.53-2.4}{2.4}\cdot100 \\ \text{ Percent Increase }=\frac{0.13}{2.4}\cdot100 \\ \text{ Percent Increase }\approx0.054\cdot100\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'} \\ \text{ Percent Increase }\approx5\% \end{gathered}[/tex]Therefore, the percent of increase to the nearest whole-number percent is 5%.
what is the experimental probability of selecting the name Alex?
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We can calculate the probability as the ratio between the positive outcomes (selecting Alex, in this case) and the total possible outcomes.
In one draw, Alex has a chance of 1 in 4, as only one of the four papers has his name on it.
The probability is 1/4 or 0.25.
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 7 4√2
Answers
9
1) In this right triangle we can find the missing leg by using the Pythagorean Theorem.
2)
a² = b² + c² Note that the hypotenuse is unknown so far
a² = 7² + (4√2)²
a² = 49 +(16 x2)
a² = 49 +32
a² =81 Take the square root on both sides
√a² = √81
a = -9, 9 Negative numbers for dimensions are not convenient.
a = 9
3) Hence, the answer is 9
The graph of the function()=1/ has origin symmetry as well as which of the following symmetries?A. y-axisB. x-axisC. y=x
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We will graph a plot of this expression, we have:
[tex]undefined[/tex]The graph is neither symmetric to the x-axis nor the y-axis. Hence, y = x
Rashad is having a picnic for 62 guests. He plans to serve each guest at least one hamburger. Ifeach package, p, contains eight hamburgers, wirte the inequality that could be used to determinehow many packages of hamburgers Rashad will need to buy.a. What are the key words and information needed to solve this problem? (2 points)b. Write the inequality that describes this situation. (2 points)C. How many packages of hamburgers will Rashad need to purchase to feed his guests? Work outthe problem, showing all of your work, including computation and explanation. (4 points)
Answers
a. What are the keywords and information needed to solve this problem?
The keywords are the words that allow us to solve the problem, So they are:
The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. Write the inequality that describes this situation.
Now, we can formulate an equation for the number of hamburgers H that each guest is going to receive if Radash buys p packages:
H = 8p/62
Because 8p is the number of total hamburgers and there are 62 guests.
Then, we know that H needs to be at least 1, so:
H ≥ 1
8p/62 ≥ 1
c. How many packages of hamburgers will Rashad need to purchase to feed his guests?
Then, we need to solve for p as:
Multiplying by 62 on both sides:
(8p/62)*62 ≥ 1 * 62
8p ≥ 62
Dividing by 8:
8p/8 ≥ 62/8
p ≥ 7.75
Therefore, Radash needs to buy at least 8 packages of hamburgers.
Answers:
a. The picnic is for 62 guests
Each guest will receive at least 1 hamburger
Every package contains 8 hamburgers
b. 8p/62 ≥ 1
c. At least 8 packages
What is the m stand for in -3 = m-14
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Step 1:
Write the equation
- 3 = m - 14
Step 2: Collect similar terms
- 3 = m - 14
m = -3 + 14
m = 11
Final answer
m = 11
Given that events A and B are independent with P(A)=0.55 and P(B)=0.72P determine the value of P(A|Brounding to the nearest thousandth
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f(x) = x +4g(x) = 3x2 – 7Find (f .g)(x).A. (f-9)(x) = 3.73 – 28O B. (f.g)(x) = 3x2 + 12x2 – 7x - 28OC. (f.g)(x) = 3.r3 +28O D. (f.g)(x) = 3.7° + 12.2 - 72 +28
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Recall that:
[tex](f\cdot g)(x)=f(x)\cdot g(x)\text{.}[/tex]Substituting f(x)=x+4 and g(x)=3x²-7 we get:
[tex]\begin{gathered} (f\cdot g)(x)=_{}(x+4)(3x^2-7), \\ (f\cdot g)(x)=3x^3-7x+12x^2-28, \\ (f\cdot g)(x)=3x^3+12x^2-7x-28. \end{gathered}[/tex]Answer: Option B.
I need help with a algebra 1 testThe graph of linear f passes through the point (1,-9) and has a slope of -3what is the zero of fanswers are24-6-2
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hello
to solve this question, we can simply use the equation of a slope on this
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ y=y-\text{coordinate} \\ x=x-\text{coordinate} \end{gathered}[/tex]now we can simply bring out our data and then proceed to input in and solve for c
[tex]\begin{gathered} y=mx+c \\ y=-9 \\ x=1 \\ m=-3 \\ y=mx+c \\ -9=-3(1)+c \\ -9+3=c \\ c=-6 \end{gathered}[/tex]from the calculations above, the answer to this question is -6 which corresponds to option c.
NB; the point at which is referred as the zero of a graph is known as the intercept. This is the point at which graph crosses the x-axis
Find the slope and y-intercept write y-intercept as order pair
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The slope and y-intercept of a line.
The equation of a line can be expressed as:
y = mx + b
Where m is the slope and b is the y-intercept. The slope of a line that passes through the points (x1,y1) and (x2,y2) is calculated as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The figure shows a horizontal red line. We only need two points (or ordered pairs) to calculate the slope. Let's get them from the graph: (0,-5) and (2,-5).
Calculate the slope:
[tex]m=\frac{-5-(-5)}{2-0}=\frac{-5+5}{2}=0[/tex]The slope is 0.
The y-intercept, as shown in the equation of the line, is the value of y when x=0.
Looking at the graph, we can identify the value of y=-5 when x=0. In fact, y=-5 for any value of x.
Thus, the y-intercept as an ordered pair is (0,-5)
1 2 4 5 6 7 9 10 Write 3 and 2 fifths as an improper fraction and as a mixed number. 17 3 2 b. 15 2 3 5 13 3. 3 5. 2 5. 5. a. d. 17 5 Please select the best answer from the choices provided A С . D
Answers
To write three and two fifths
Solution:
Three is a whole number and two-fifths is a proper fraction
[tex]\begin{gathered} \text{Thr}ee\text{ = 3} \\ Two-fifths=\frac{2}{5} \\ \text{Thr}ee\text{ and two-fifths = 3}\frac{2}{5} \end{gathered}[/tex]Therefore, three and two-fifths as a mixed number is;
[tex]3\frac{2}{5}[/tex]As an improper fraction,
[tex]\begin{gathered} 3\frac{2}{5}=\frac{(5\times3)+2}{5} \\ =\frac{15+2}{5} \\ =\frac{17}{5} \end{gathered}[/tex]Therefore, three and two-fifths as an improper fraction is 17/5.
Th
The price of a toy is increased by 20%. The resulting price is later decreased by $40.00. If the original price of the toy is $60.00, what is the final price of the toy ?
Answers
Answer
Final price of the toy = $32.00
Explanation
The price of a toy is increased by 20%
The resulting price is then decreased by $40.00
Original Price = $60.00
The price of a toy is increased by 20%
Resulting price after this increase = 1.2 (60) = $72
The resulting price is then decreased by $40.00
Final Price = 72 - 40 = $32.00
Hope this Helps!!!
Multiply the following polynomials: i) (3x-8)•(4x+7)= ii) (4x + 7)² = iii) (3x –8)•(3x+8)=
Answers
Multiply the following polynomials;
(1)
[tex]\begin{gathered} (3x-8)\times(4x+7) \\ =(3x\times4x)+(3x\times7)-(8\times4x)-(8\times7) \\ =12x^2+21x-32x-56 \\ =12x^2-11x-56 \end{gathered}[/tex](2)
[tex]\begin{gathered} (4x+7)^2 \\ =(4x+7)(4x+7) \\ =(16x^2+28x+28x+49) \\ =16x^2+56x+49 \end{gathered}[/tex](3)
[tex]\begin{gathered} (3x-8)(3x+8) \\ =9x^2+24x-24x-64 \\ =9x^2+0-64 \\ 9x^2-64 \end{gathered}[/tex]What is the LCM needed to find a common denominator for 5/6 + 3/8 quick
Answers
Answer:
Step-by-step explanation:
The lowest common denominator of 38 and 56 is 24. This allows us to convert the two fractions into 924 and 2024 for the purpose of adding and subtracting them.
The LCM is 24
Reason: 6*8/2 = 48/2 = 24
We multiply the denominators 6 and 8, then divide by 2 which is the GCF of the denominators.
Then we can use this to add the fractions
5/6 + 3/8
(5/6)*(4/4) + (3/8)*(3/3)
20/24 + 9/24
(20+9)/24
29/24
Therefore, 5/6 + 3/8 = 29/24
area of the square is 81 square inches. length of one side is represented by X. what is the value of x?
Answers
The area of a square is given by:
[tex]A=l^2[/tex]Where:
l = length of one of its sides:
Since the area is 81, and the length of one of its sides is x, then:
[tex]81=x^2[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{81}=\sqrt[]{x^2} \\ 9=x \\ x=9 \end{gathered}[/tex]There are 39 fewer 2nd graders than 3rd graders. There are 67 2nd graders. How many 3rd graders are there?
Answers
ANSWER
106 3rd graders
EXPLANATION
Let the number of 2nd graders be x.
Let the number of 3rd graders be y.
We have that there are 39 fewer 2nd graders than 3rd graders. This means that:
x = y - 39
There are 67 2nd graders. This means that:
x = 67
This means that:
67 = y - 39
y = 67 + 39
y = 106
Therefore, there are 106 3rd graders.
I need help with my math
Answers
Let's evaluate the point into the equation in order to check if it satisfies it.
[tex]\begin{gathered} y=4x+2;_{\text{ }}(2,10) \\ x=2,y=10 \\ so\colon \\ 10=4(2)+2=8+2=10 \\ 10=10 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}[/tex]Therefore, the ordered pair is a solution to the equation
Which best describes one way to show 1/3 shaded.
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Draw a circle, cut into 3 equals parts and shade 1 part