Hannah bought pears and bananas only, so let's write the following equation:
[tex]\text{total}=\text{pears}+\text{bananas}[/tex]If the total weight bought is 5.12 and 2.5 pounds are pears, we can calculate the weight of bananas bought:
[tex]\begin{gathered} 5.12=2.5+\text{bananas} \\ \text{bananas}=5.12-2.5 \\ \text{bananas}=2.62 \end{gathered}[/tex]So Hannah bought 2.62 pounds of banana.
How do you answer these questions? How do you know whether a given value is a solution to the inequality?
We have the following inequality:
x > - 0.75
This is the same as state "x is greater than -0.75". Therefore, any value greater than -0.75 is a solution to this inequality
Considering this rule, we can answer each item:
a) The statement "-0.75 is a solution to the inequality" is FALSE, because, or rule states that x must be greater than -0.75.
b) The statement "There are many solutions to this inequality" is TRUE. Actually, there is an infinite number of solutions to this inequality (some of them can be expressed by -0.74, -0.73, -0.72...)
c) The statement "All the solutions to the inequality are negative" is FALSE, since any positive (or null) number is also greater than -0.75.
d) The statement "The inequality -0.75 < x is equivalent to the given inequality" is TRUE, since this inequality is tha same as the statement "-0.75 is less than x", which is a different form of express the original statement "x is greater than -0.75".
e) The statement "-4.5 is a solution to the inequality" is FALSE, because -4.5 is less than -0.75, which contradicts or rule.
A recipe for chocolate cupcakes makes 24 cupcakes that are 350 calories each. Instead you decideto make mini-cupcakes, and the same recipe yields 40 mini-cupcakes. If you eat four mini-cupcakes,how many calories will you eat?Enter a whole number wiha no units.
The recipe yields:
[tex]24\cdot350=8400[/tex]8400 calories in total.
Those 8400 calories are equally divided into 40 mini-cupcakes. Then, each mini-cupcake has
[tex]\frac{8400}{40}=210[/tex]210 calories for each mini-cupcake.
Therefore, 4 mini-cupcakes contain:
[tex]210\cdot4=840[/tex]The answer is 840 calories
The members of an adult soccer team are planning a party for their children. The histogram below shows the number of children each team member will bring to the party, (*If you can't see the histogram below, click on the attached pdf to view.) Members of soccer team Frequency 1 2 Number of children attending party
6The mean number of children each team member will bring
Here, we want to get the mean number of students that each team member willl bring
From the histogram, we can deduce the following;
a) 4 team members will bring no (0) children
b) 3 team members will bring 1 children each
c) 5 team members will bring 2 children each
d) 2 team members will bring 3 children each
e) 1 team member will bring 5 children
So the totla number of children at the party will be;
4(0) + 3(1) + 5(2) + 2(3) + 1(5)
= 0 + 3 + 10 + 6 + 5 = 24 children
The number of team members is 4 + 3 + 5+2 + 1 = 15
So, the mean number each will bring is; the number of children attending the party divided by the number of team members
[tex]\frac{24}{15}\text{ = 1.6}[/tex]0.6 divided by 30 I don’t know how to divide decimals to well
Given: 0.6 divided by 30
We will find the result as follows:
[tex]0.6\div30=\frac{6}{10}\times\frac{1}{30}=\frac{6}{300}=\frac{1}{100}\times\frac{6}{3}=\frac{2}{100}=0.02[/tex]So, the answer will be 0.02
please help me understand how to solve for the domain!
Given:
f(x) = x^2 + 4x + 4 and g(x) = x^2 - 2x - 8.
we are to find the domain of (f/g) (x)
before we find the domain of the function, its best we know what a domain is.
The Domain of a function is the set of all possible inputs for the function. it can also be seen as the set of input or arguement values for which the function is real and defined.
recall that we have x + 2 as our the simplest form
x - 4
so the domain we wil be looking for is x + 2
x - 4
so we have to take t denominator of the above and compare to zero
x - 4 = 0
x = 4
so this is undefined
the function domain
x < 4 or x > 4
so the domain is:
(- infinity, 4) U (4, infinity)
The correct option is A.
Fill in the table using this function rule.y= 4x-3
the initial function is:
[tex]y=4x-3[/tex]now we replace the values in x that gives the table so:
for -2:
[tex]\begin{gathered} y=4(-2)-3 \\ y=-8-3 \\ y=-11 \end{gathered}[/tex]for 0:
[tex]\begin{gathered} y=4(0)-3 \\ y=-3 \end{gathered}[/tex]for 2:
[tex]\begin{gathered} y=4(2)-3 \\ y=5 \end{gathered}[/tex]for 4:
[tex]\begin{gathered} y=4(4)-3 \\ y=13 \end{gathered}[/tex]Solve for the area of a parallelogram that has a base of 1/2 in and a height of 8 in.
The area of a parallelogram is given by the equation:
[tex]A=b\times h[/tex]Where b is the base of the parallelogram and h is the height.
In this case, b=1/2 in and h=8in, then:
[tex]\begin{gathered} A=(\frac{1}{2}in)(8in) \\ =4in^2 \end{gathered}[/tex]Therefore, the area of the described parallelogram, is:
[tex]4in^2[/tex]Solve the following equation by factoring.x? - 15x = 0Rewrite the equation in a completely factored form.
What statements are true regarding undefine terms in geometry A point has no length or width. A point indicates a location in a coordinate plane. A plane has one dimension, length A line has a define begging and end A plane consists of an infinite set of lines. A line consists of an infinite set of points
Explanation:
Question:
What statements are true regarding undefine terms in geometry
A point has no length or width.
This is true because a point cannot have a dimension
A plane consists of an infinite set of lines.
This is not true because from the definition of a plane, it must have an infinite set of lines or points.
A plane has one dimension, length
This statement is not true because a line is a one dimensional object and as such can only have one dimension which is its' length.
A point indicates a location in a coordinate plane.
This statement is true because any point located on a plane must have an ordered pair of an x and y coordinate
A line has a define begging and end
This is not true because A distance along a line must have no beginning or end.
A line consists of an infinite set of points
This is not true becaue a plane consists of an infinite set of points
Hence,
The final answers are
A point indicates a location in a coordinate plane.
A point has no length or width.
For the function f(x) = √x/2, find f-1(x).
1. replace f(x) with y:
[tex]\begin{gathered} y=\frac{\sqrt[]{x}}{2} \\ \end{gathered}[/tex]2. Replace every x with a y and replace every y with an x:
[tex]\begin{gathered} x=\frac{\sqrt[]{y}}{2} \\ \end{gathered}[/tex]3. Solve for y:
[tex]y=4x^2=(2x)^2[/tex]4. replace y with f-1(x):
[tex]f^{-1}(x)=(2x)^2[/tex]Find the Vale of X, round your awsner to the nearthest tenth
The required value of the x is given as 8.66 for the given triangle.
Given that,
A figure of the triangle is shown, with the help of trigonometric operators we have to determine x.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
Tan60 = x/ 5
x = tan60 × 5
x = 1.732 × 5
x = 8.66
Thus, the required value of the x is given as 8.66 for the given triangle.
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Michiko has one quiz each week in social studies class. The table gives the probability of having a quiz on eachday of the week. What is the probability that Michiko will not have a quiz on Wednesday? Express your answeras a percent.
Solution:
Given:
From the table, the probability that Michiko will hava a quiz on Wednesday is 0.070.
This is the probability of success.
Hence, the probability that Michiko will not have a quiz on Wednesday is the probability of failure.
Thus,
[tex]\begin{gathered} p+q=1 \\ \text{where;} \\ p\text{ is the probability of success} \\ q\text{ is the probability of failure} \\ \\ p=0.070 \\ q=\text{?} \end{gathered}[/tex][tex]\begin{gathered} p+q=1 \\ q=1-p \\ q=1-0.070 \\ q=0.93 \end{gathered}[/tex]Hence, the probability of failure (the probability that Michiko will not have a quiz on Wednesday is 0.93.
As a percent,
[tex]\begin{gathered} q=0.93\times100 \\ q=93\text{ \%} \end{gathered}[/tex]Therefore, the probability that Michiko will not have a quiz on Wednesday is 93%
C is the depth in meters and f(x) is in grams of salt kilograms of sea water approximate the salinity to the nearest hundredth) when the depth is 797 meters
Using the function f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg
How to find the salinity at the required depthThe salinity s calculated using the logarithmic function model
f(x) = 28.7 + 1.2log (x + 1)
given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters
for x = 797 meters
f(x) = 28.7 + 1.2log (x + 1)
f(x) = 28.7 + 1.2log (797 + 1)
f(x) = 28.7 + 1.2log (798)
f(x) = 28.7 + 1.2 * 2.902
f(x) = 28.7 + 3.4824
f(x) = 32.1824
f(x) = 32.18 (to the nearest hundredth)
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what is LK rounded to the nearest hundredth?what is JK rounded to the nearest hundredth?
LK = 2.91m
JK = 7.99m
Explanation:hypotenuse = 8.5m
angle = 20°
LK = side opposite the angle 20°
Since we know the hypotenuse and we need to find the opposite, we would apply sine ratio
sine ratio = opposite/hypotenuse
sin 20° = LK/8.5
LK = 8.5(sin 20°)
LK = 8.5(0.3420)
LK = 2.907
To the nearest hundredth, LK = 2.91m
JK = base = adjacent
We would apply cosine ratio
cos 20° = adjacent/hypotenuse
cos 20° = JK/8.5
JK = 8.5(cos20°)
JK = 8.5(0.9397)
JK = 7.98745
To the nearest hundredth, JK = 7.99m
please please pleaseee help mee i have to finish my credit by may 20th
Answer:
[tex]C[/tex]Explanation:
Using the graph of both equations, we want to get the correct option
We start by making a plot of the two on same axes
We have the plot of the functions as follows:
Now, let us take a look at the options:
a) This is wrong. The functions have two intersection points
b) This is incorrect. They have equal y-intercepts at y = 2
c) This is correct. The quadratic function have a greater maximum
PLS HELP ASAP!!!!!!!!!!!!!!!!
Answer: n = 42
Step-by-step explanation:
3 (42 - 6)= 126 - 18
= 108
2(42+12) = 84+24
= 108
In overall, the second equation is not greater than the first equation
Find the minimum value if f(x) = xe^x over [-2,0]
Given function:
[tex]f(x)=xe^x[/tex]The minimum value of the function can be found by setting the first derivative of the function to zero.
[tex]f^{\prime}(x)=xe^x+e^x[/tex][tex]\begin{gathered} xe^x+e^x\text{ = 0} \\ e^x(x\text{ + 1) = 0} \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} x\text{ + 1 = 0} \\ x\text{ = -1} \end{gathered}[/tex][tex]\begin{gathered} e^x\text{ = 0} \\ \text{Does not exist} \end{gathered}[/tex]Substituting the value of x into the original function:
[tex]\begin{gathered} f(x=1)=-1\times e^{^{-1}}_{} \\ =\text{ -}0.368 \end{gathered}[/tex]Hence, the minimum value in the given range is (-1, -0.368)
2. Find the difference of 6x - 3x^2 and - 5x^2 - 6x +1. Write your final solution in standard form!
To start, we need write the polynomials:
[tex]6x-3x^2and-5x^2-6x+1[/tex]Now we gonna find the difference between first polynomial and second, like this:
tip: Special care with operate signs.
[tex]\begin{gathered} 6x-3x^2-(-5x^2-6x+1);\text{ we operate with signs over here}\ldots \\ 6x-3x^2+5x^2+6x-1;\text{ We }put\text{ together terms with similar exponent in parentheses, like this:} \\ (5x^2-3x^2)+(6x+6x)-1;\text{ we operate}\ldots \\ 2x^2+12x-1. \end{gathered}[/tex]That is the final solution, you can solve that polynomial if you need.
[tex]2x^2+12x-1.[/tex]Use the given graph to create the equation for the rational function. The function is written in factored form to help you see how the given information shapes our equation.vert asymp at x=-3 opposite end behavior, vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2The numerator is: Answer (x-Answer)^2 The denominator is: (x+Answer )(x-Answer )(x-Answer )
Solution
The function is written in factored form
Using vertical asymptote at x = 3 opposite end behaviour
vert asymp at x=2 same end behavior, bounce off x axis at x=1, y int at -1/2
[tex]\begin{gathered} y=\frac{A(x-1)^2}{(x+3)(x-2)^2} \\ -\frac{1}{2}=\frac{A(0-1)^2}{(0+3)(0-2)^2} \\ -\frac{1}{2}=\frac{A}{12} \\ 2A=-12 \\ A=-\frac{12}{2} \\ A=-6 \end{gathered}[/tex][tex]y=\frac{-6(x-1)^2}{(x+3)(x-2)^2}[/tex]Therefore the numerator is : -6(x-1)²
The denominator is : (x+3)(x-2)²
Raina, Kevin, and Eric have a total of $66 in their wallets. Kevin has 3 times what Eric has. Raina has $9 less than Eric. How much does each have?
In order to determine the amount of money Rain, Kevin and Eric have, write the given situation as an algebraic equation.
If x is the money of Raina, y the money of Kevin and z the money of Eric, you have, based on the given problem, the following equations:
x + y + z = 66 All of them have a total of $66
y = 3z Kevin has 3 times what Eric has
x = z - 9 Raina has $9 less than Eric
Replace the expressions for x and y into the first equation and solve for z, as follow:
(z - 9) + (3z) + z = 66
z - 9 + 3z + z = 66
3z = 66 + 9
3z = 75
z = 75/3
z = 25
Next, replace the previous value of z into the expressions for x and y:
y = 3(25)
y = 75
x = 25 - 9
x = 16
Hence, the amount of money each of them has is:
Raina: $16
Kevin: $75
Eric: $75
Brenda had $23 to spend on two notebooks. After buying them she had $19. How much did each notebook cost
7x - 2x + 4 = 8 - 3x what's the value of x
The initial equation is:
[tex]7x-2x+4=8-3x[/tex]so we can move all term with x to the left and the constants to the right so:
[tex]\begin{gathered} 7x-2x+3x=8-4 \\ 8x=4 \end{gathered}[/tex]Now we divide by 8 bout side of the equation so:
[tex]\begin{gathered} x=\frac{4}{8} \\ x=\frac{1}{2} \end{gathered}[/tex]a line with slope of 3 and passes through the point of (0,5)
Answer: y=3x+5
Step-by-step explanation:
What is the equation of the line perpendicular to 3x+y=-8 that passes through (-3,1)?
Before we calculate the perpendicular line, let's rewrite our line equation in slope-intercept form. The slope-intercept form is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
Rewritting our equation, we have
[tex]\begin{gathered} 3x+y=-8 \\ y=-3x-8 \end{gathered}[/tex]This means the slope of our line is equal to - 3.
Two perpendicular lines are related by their slope. Let's say two lines are perpendicular, this means the slope of one of the lines is equal to minus the inverse the slope of the other. If we call the slope of one of those lines as m_1, the slope of the perpendicular line m_2 is given by
[tex]m_1=-\frac{1}{m_2}[/tex]Using this relation, we can find the slope of a perpendicular line. Since the slope of our line is equal to - 3, then, the slope of the perpendicular line is
[tex]m_{\perp}=-\frac{1}{(-3)}=\frac{1}{3}[/tex]In slope-intercept form, our perpendicular line has the following form
[tex]y=\frac{1}{3}x+b[/tex]To find our y-intercept, we can use our given point that belongs to this line.
The point is (-3, 1), evaluating this point in our equation, we have
[tex]\begin{gathered} (1)=\frac{1}{3}\cdot(-3)+b \\ \Rightarrow1=-1+b \\ \Rightarrow b=2 \end{gathered}[/tex]Then, our line is
[tex]y=\frac{1}{3}x+2[/tex]Hi, can you help me to find (if passible) the complement andsupplement of the angle 3pi/ 4.
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.
In radians this are
[tex]\begin{gathered} \frac{\pi}{2}\text{ for }90\degree \\ \pi\text{ for }180\degree \end{gathered}[/tex]To find the complement of 3π/4, subtract it by π/2
[tex]\frac{\pi}{2}-\frac{3\pi}{4}=-\frac{\pi}{4}[/tex]To find the supplement of 3π/4, subtract it by π.
[tex]undefined[/tex]60x+110y= 265 120x+90y=270
EXPLANATION
Given the system of equations:
(1) 60x + 110y = 265
(2) 120x + 90y = 270
We can apply the substraction method as shown as follows:
Multiply 60x + 110y = 265 by 2:
----> (60x + 110y = 265)*2 -------> 120x + 220y = 530
Subtract the equations:
120x + 220y = 530
- (120x + 90y = 270)
--------------------------------
130y = 260
Divide both sides by 130:
y= 260/130
Simplifying:
y= 2
Replacing on the first equation:
60x + 110(2) = 265
Applying the distributive property:
60x + 220 = 265
Subtracting 220 to both sides:
60x = 265 - 220
Subtracting like terms:
60x = 45
Dividing both sides by 60:
x = 45/60
Simplifying:
x= 3/4
The solutions to the system of equations are:
x=3/4 y=2
is the equation 2(n^2 + 6n +9) written in standard or factored form?
Standard form by definition of standard form of polynomials
What is the rule of the pattern below? 52, 48, 44, 40, 36....
Answer:
Subtract 4
Explanation:
In the number pattern:
[tex]52,48,44,40,36...[/tex]We subtract the next term from the previous term below:
[tex]\begin{gathered} 48-52=-4 \\ 44-48=-4 \\ 40-44=-4 \end{gathered}[/tex]We see that each one gives a subtraction of 4.
Therefore, the rule of the pattern is 'Subtract 4'.
which is an equation
The slope is define as the rate of y coordinate with respect to the x coordinate.
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]In the line D which is parallel to x axis has the constant y coordinate i.e
y = -3
So, for the numerator of the slop for line D is ( -3) - ( -3) = 0
Thus the slope will be express as :
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{-3-(-3)}{x_2-x_1} \\ \text{Slope}=\frac{0}{x_2-x_1} \\ \text{Slope = }0 \end{gathered}[/tex]Thus the slope of line is 0
Now, for the line A :
The line A is parallel to y axis, that is only y coorsinates are changes x is at contant position.
i.e. x = -5
So, substitute the value in the expression for the slope :
[tex]\begin{gathered} \text{Slope}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope}=\frac{y_2-y_1}{-5-(-5)_{}} \\ \text{Slope}=\frac{y_2-y_1}{-5+5_{}} \\ \text{Slope = }\frac{y_2-y_1}{0_{}} \\ If\text{ the denominater becomes zero, then the expression is not define} \\ So,\text{ slope of line A is not define} \end{gathered}[/tex]Slope of line A is not define
In the line B and C, the coordinates of x and y aixs are changes countinously
thus thier slopes will be well define.
Answer : Slope of line A is not define.
F is the midpoint of EG. If F is at (2,-4) and G is at (8,2), where is E located?
geometry homework help line
Using midpoint of a line, the point at which E is located on the coordinates is (-4, -10)
Midpoint of a LineMidpoint refers to a point that is in the middle of the line joining two points. The two reference points are the endpoints of a line, and the midpoint is lying in between the two points. The midpoint divides the line joining these two points into two equal halves. Further, if a line is drawn to bisect the line joining these two points, the line passes through the midpoint.
The formula of midpoint is given as
(x, y) = (x₂ + x₁) / 2 , (y₂ + y₁) / 2
Taking x-coordinate
x = (x₂ + x₁) / 2
2 = (8 + x₁) / 2
x₁ = -4
Taking the y - coordinate
y = (y₂ + y₁) / 2
-4 = (2 + y₁) /2
y₁ = -10
The coordinate of E is (-4, -10)
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