The opposite of a number is the same as multiplying it by -1. any negative number, it's opposite is that same number positive. And any positive number is that same number negative.
Our number W is 5. Then, the opposite number is - 5.
To draw a point at - 5 from 5, we just need to move the difference between them to the left. The difference between 5 and -5 is given by
[tex]|5-(-5)|=|5+5|=|10|=10[/tex]Then, to draw point V we need to move 10 units to the left of Point W.
there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.
ANSWER
There are 8 kittens
EXPLANATION
If the sum of the number of adult cats, middle aged cats and kittens is 19:
[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]Convert the polar equation r=3 to a Cartesian equation.x^2+y^2=√3x^2+y^2=3x^2+y^2=9
For the given equation:
[tex]\begin{gathered} \text{Polar form: } \\ r=3 \\ \\ \text{Cartesian form:} \\ x^2+y^2=3^2 \\ x^2+y^2=9 \end{gathered}[/tex]The crew knows the amount of dirt the truck can hold each trip in cubic yards.
Given:
Measurements of hole are 48ft 39ft and and 9ft
Required:
Volume in cubic yd
total number of trip
total cost of trip
Explanation:
First we need to convert given measurements from ft to yd
[tex]\begin{gathered} 3ft=1yd \\ 48ft=16yd \\ 39ft=13yd \\ 9ft=3yd \end{gathered}[/tex]
A)
[tex]V=lhw=16*13*3=624yd^3[/tex]B)
11 cubic yd in 1 trip
then
624 cubic yd in x trip
[tex]x=\frac{624}{11}=56.7\approx57[/tex]C)
cost for 1 trip is $1175
then
cost for 57 trip is y
[tex]y=57*1175=66975[/tex]Final answer:
Volume in cubic yd is 624
total number of trips is 57
total cost of trip $66975
How do I do this, I’m unsure how to go about it
Given:
[tex]\sqrt{\frac{6}{x}}\cdot\sqrt{\frac{x^2}{24}}[/tex]Simplify:
[tex]=\sqrt{\frac{6}{x}}\cdot\frac{\sqrt{x^2}}{\sqrt{24}}=\sqrt{\frac{6}{x}}\cdot\frac{x}{2\sqrt{6}}[/tex]Apply the properties of fractions:
[tex]=\frac{\sqrt{\frac{6}{x}}x}{2\sqrt{6}}[/tex]Simplify:
[tex]=\frac{\frac{\sqrt{6}}{\sqrt{x}}x}{2\sqrt{6}}=\frac{\sqrt{6}\sqrt{x}}{2\sqrt{6}}[/tex]Eliminate common terms:
[tex]=\frac{\sqrt{x}}{2}[/tex]Answer:
[tex]\frac{\sqrt{x}}{2}[/tex]Translate the sentence into an equation,The sum of 5 times a number and 4 is 3.Use the variable b for the unknown number.
Given the sentence, the sum of 5 times a number and 4 is 3.
The information would translate to;
[tex]\begin{gathered} (5\times b)+4=3 \\ 5b+4=3 \end{gathered}[/tex]ANSWER:
[tex]5b+4=3[/tex]Lines AD and BC are parallel. What is the angle measurement of Angle DAE(Point A)?D150°45°BсFYour answer
Solution
For this case we can find the angle:
m < ECB = 30º
And we can find the angle CEB and we got:
m < CEB = 180 -30 - 45 = 105
And then the angle DAE would be:
m < DAE = 30º
Convert decimal to 0.147 to fraction ( the last digit 7 repeating)
Answer:
133/900
Explanation:
To convert the decimal 0.147777 to a fraction, we first identify the decimal part, so we have 147 as a decimal part.
Then, we subtract 14 because that part is not repeating. So:
147 - 14 = 133
Now, we need to divide by 9 to get the repeating part, but the repeating part starts at the third decimal place, so we will divide by 900 instead of 9.
Therefore, 0.147777... as a decimal is:
[tex]0.14777\ldots=\frac{133}{900}[/tex]So, the answer is 133/900
Evaluate the expression [tex]9 + 7 - 3 \times 3 - 2[/tex]
I need help with review on functions
The answer is Option 2
Its not a function
The domain and range of the function is shown at the various endpoints of the graph.
At every point you can always identify a value for x (the input value) and also a corresponding value for y (the output value).
Please note the endpoints marked in blue.
These are the endpoints, and for every point, you will have (x, y).
However, note that at the endpoints, the values of y remains the same.
For every relation to be a function, there must be exactly one corresponding y value for every x value. As shown by the blue markings on the graph, the x values on the horizontal axis both have the same y value (which is zero).
Hence, the relationship shown by the graph is not a function
A ball is kicked up in the air from the ground. The height of the ball can be modeled as a function of time in seconds. This function is represented on the graph below. Enter the average rate of change for the height of the ball, measured as feet per second, between 0 seconds and 2 seconds._[blank]_ feet per secondEnter your answer as a number, like this: 42
ANSWER:
2
STEP-BY-STEP EXPLANATION:
The average rate of change is given by the following formula:
[tex]r=\frac{f(b)-f(a)}{b-a}[/tex]Since it is between 0 and 2 seconds, the values of a and b will be these respectively, the evaluated values can be determined by the graph, therefore:
[tex]\begin{gathered} r=\frac{4-0}{2-0}=\frac{4}{2} \\ \\ r=2\text{ feet pe second } \end{gathered}[/tex]The average rate of change is equal to 2 feet per second
I need help answering the 2nd part of this question
An identity function has one output value for each input value.
G is an identity function.
To find its equation apply the slope-intercept form:
y=mx +b
Where:
m= slope ( rise / run)
b= y-intercept ( where the function crosses the y axis)
By looking at the graph we can see that it crosses (0,0) so, b= 0.
And for every unit to right along the x-axis, it goes up by 1 unit along the y axis.
So, m= 1/1 = 1
Equation:
y = x
The figure on the right is a scale drawing of the figure on the left. What is the scale factor?
In order to find the scale factor, we just need to divide one side of the right figure by the corresponding side in the left figure.
So, taking the sides SU and PR, we have:
[tex]\text{scale}=\frac{SU}{PR}=\frac{12}{8}=1.5[/tex]So the scale factor is 1.5.
2x + 4x = 3x + 3x Solve for x.
You have the following expression:
2x +4x = 3x + 3x
in order to solve for x, proceed as follow:
2x +4x = 3x + 3x simplify like terms both sides
6x = 6x
Due to the previous result is the trivial solution, it means that the equation has infinite solutions.
3(2x+4) - 2(4x-1)=20A. x=5B. x=-5C. x=3D. x=-3
we have the following:
[tex]3(2x+4)-2\left(4x-1\right)=20[/tex]solving for x:
[tex]\begin{gathered} 3(2x+4)-2\left(4x-1\right)=20 \\ 6x+12-8x+2=20 \\ -2x=20-12-2 \\ -2x=6 \\ x=\frac{6}{-2} \\ x=-3 \end{gathered}[/tex]The answer is x = -3
To make an open box from a 175cm by 100cm piece of cardboard, equal-sized squares will be cut from each of the four corners and then the sides will be folded up. What is the approximate volume of the largest possible box that can be made?Group of answer choices:A) 324,146 cm^3B)162,073cm^3C) 251,707cm^3D)189,640cm^3
Given that dimensions of the piece of cardboard are:
[tex]\begin{gathered} l=175\text{ }cm \\ w=100\text{ }cm \end{gathered}[/tex]Where "l" is the length and "w" is the width, you can determine that it has the shape of a rectangle.
You know that equal-sized squares will be cut from each of the four corners and then the sides will be folded up. Then, you can make the following drawing:
By definition, the volume of a rectangle is:
[tex]Volume=length\cdot width\cdot height[/tex]In this case, you can set up that:
[tex]\begin{gathered} length=175-2x \\ width=100-2x \\ height=x \end{gathered}[/tex]Therefore, you can write this equation:
[tex]V=(175-2x)(100-2x)(x)[/tex]Expand it:
[tex]V=(175-2x)(100x-2x^2)[/tex][tex]V=(175)(100x)-(175)(2x)-(2x)(100x+(2x)(2x^2)[/tex][tex]V=4x^3-550x^2+17500x[/tex]Now you need to derivate it using the Power Derivative Rule:
[tex]\frac{d}{dx}(x^n)=nx^{n-1}[/tex]Then:
[tex]V^{\prime}=(4)(3)x^2-(550)(2)x+17500[/tex][tex]V^{\prime}=12x^2-1100x+17500[/tex]Make the equation equal to zero and sove for "x":
[tex]12x^2-1100x+17500=0[/tex]Use the Quadratic Formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]Substituting:
[tex]\begin{gathered} a=12 \\ b=-1100 \\ c=17500 \end{gathered}[/tex]You get:
[tex]\begin{gathered} x_1\approx20.49 \\ x_2\approx71.18 \end{gathered}[/tex]Therefore, you can make the following Sign Chart:
Then, you can substitute these:
[tex]\begin{gathered} x=20 \\ x=50 \\ x=72 \end{gathered}[/tex]Into the factorize form of the derivated function:
[tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex][tex]V=(x+\frac{275-25\sqrt{37}}{6})(x-\frac{275+25\sqrt{37}}{6})[/tex]It's a gross thought, but the number (N) of bacteria in refrigerated food is given by latex- 1≤T≤20 where T is the temperature of the food in degrees Celsius. When you take the food out of the refrigerator, the temperature of the food is given by T(t)=3t+2, 0≤t≤6 where t is the time in hours. Find the composition N(T(t)) and interpret what it means in this context.
Given that the concentration of bacteria in the refrigerated food is
[tex]10T^2-20T-6----\mleft\lbrace1\mright\rbrace[/tex]and the temperature of the food is given by
[tex]T(t)=3t+2-----\mleft\lbrace2\mright\rbrace[/tex]Therefore, N(T(t) is given by
[tex]N\mleft(T(t)\mright)=10(3t+2)^2-20(3t+2)^{}-6[/tex]Then,
[tex]\begin{gathered} N(T(t))=10(3t+2)^2-20(3t+2)^{}-6 \\ =10(9t^2+6t+6t+4)-60t-40-6 \\ =10(9t^2+12t+4)-60t-46 \\ =90t^2+120t+40-60t-46 \\ =90t^2+60t-6 \end{gathered}[/tex]Answer: The composition is
[tex]N(T(t))=90t^2+60t-6[/tex]It can be interpreted as the concentration of bacteria in the food when outside of the refrigerator with time.
Suppose you have a piece of ribbon that is 6 feet long, and you cut off one piece that's 3 2/3
inches long and a second piece that's 2 5/6 inches long. How much ribbon is left in inches?
inches of ribbon left
Answer:
65 1/2 inches of ribbon is left, my exact work is shown on a piece of paper below if you need it.
Step-by-step explanation:
1 foot = 12 inches
6 x 12 = 72 inches
72 - (3 2/3 + 2 5/6) = ?
John has two apples, he gives Jane 251. How many apples does John have? Please help 2nd grade is so hard.
Solve the equation. Check your solution.20x - 4= 50x + 2x=(Simplify your answer. Type an integer or a simplified fraction.)
20x - 4 = 50x + 2
Solve for x
20x - 50x =
Sean, Kevin and Bill take classes at both JJC and CSU. Sean takes 8 credits at JJC and 4 credits at CSU; Kevin takes 10 credits at JJC and 6 at CSU: Bill takes 6 credits at JJC and 4 at CSU; the cost per credit at JJC is $103 and at CSU is $249. a) Write a matrix A that gives the credits each student is taking and B that gives the cost per credit at each school. b) Find the dimension of A and B. c) Find the product AB and the names of its rows and columns.
ANSWER:
a)
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix} \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix} \end{gathered}[/tex]b)
Dimension A = 3 x 2
Dimension B = 2 x 1
c)
Cost of credits
Sean $1820
Kevin $2524
Bill $1614
[tex]\begin{pmatrix}Sean \\ \: Kevin \\ \: Bill\end{pmatrix}\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix}[/tex]STEP-BY-STEP EXPLANATION:
With the help of the statement, we create the matrices A and B:
[tex]\begin{gathered} A=\begin{pmatrix}8 & 4 \\ 10 & 6 \\ 6 & 4\end{pmatrix}\rightarrow3\times2 \\ B=\begin{pmatrix}103 \\ 249\end{pmatrix}\rightarrow2\times1 \end{gathered}[/tex]Now, we calculate the product just like this:
[tex]\begin{gathered} \text{Product }A\cdot B=\begin{pmatrix}8\cdot103+4\cdot249 \\ 10\cdot103+6\cdot249 \\ 6\cdot103+4\cdot249\end{pmatrix}=\begin{pmatrix}1820 \\ \: 2524 \\ \: 1614\end{pmatrix} \\ \text{Product }A\cdot B=\begin{pmatrix}Sean \\ Kevin \\ Bill\end{pmatrix}\begin{pmatrix}1820 \\ 2524 \\ 1614\end{pmatrix} \end{gathered}[/tex]Michael studied the feather lengths of some adult fox sparrows.How long is the shortest feather in the data set?
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Given,
The image is attached with this.
The length of fox sparrow feathers studied by Michael.
1 sparrow with 3/4 inches of feather4 sparrows with 2 inches of feather7 sparrows with 2 1/4 inches of feather5 sparrows with 2 1/2 inches of feather3 sparrows with 2 3/4 inches of feather.We have to find the shortest feather in the data set.
Here,
3/4 inches is the shortest feather and only 1 sparrow has the shortest feather.
2 3/4 inches is the longest feather and 3 sparrows have the longest feather.
That is,
From the data set given, 3/4 is the length of the shortest feather of fox sparrow.
Learn more about length of feather here;
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