Given the linear function:
y = ax + b
And it undergoes a horizontal shift of 5 units
Let the original line be f(x) and the new line be g(x)
g(x) = f(x - 5)
The vertical change will be the horizontal change times a, using the definition of slope.
Thus, since the horizontal change here is 5 units, the vertical change is 5a units
ANSWER:
E) a vertical change of 5a units
in a class of 36 students, 6 are in the drama club and 12 are in the art club. if a student is selected at random, what is the probability that the selected student is in the drama club?
Total number of students = 36
Students in drama club = 6
Divide the number of students that are in the drama club (6) by the total number of students (36)
P = 6 /36 = 0.16666666 or 1/6 (fraction form)
Simplify the following trig expressions to an expression involving at most one trig function
we know that:
• cot x = adjacent /opposite
,• secx = hypotaneus / adjacent
,• cscx = hypotaneus / opposite
Therefore , our expression can be re-rewritten as follows :
(cot x * secx) /(cosec x)
→{adj /opp * hyp /adj }/( hyp/opp)... [note that adj cancels each other ]
→(hyp /opp)/ hyp/opp
→(hyp /opp) * (opp /hyp) .......( each variable cancels each other)
→1*1
= 1
write an equation in slope intercept form for the line that passes through the given point and is perpendicular to the graph of the equation. (-4,2); y= -1/2x + 6
First of all we are going to find the slope perpendicular to the equation y = -1/2 x +6.
We need to remember that two slopes are perpendicular if its product is equal to -1. Like this:
[tex]\begin{gathered} m_1\cdot m_2=-1 \\ m_1=-\frac{1}{2}_{} \\ m_2=-\frac{1}{m_1}=-\frac{1}{-\frac{1}{2}}=2 \\ m_2=2 \end{gathered}[/tex]Now, we find the equation of the line using the general form:
[tex](y-y_1)=m(x-x_1);\text{ }[/tex]m - slope
[tex](x_1,y1)=(-4,2)_{}[/tex]That was a point of the line, now:
[tex]\begin{gathered} (y-2)=2(x-(-4)) \\ y-2=2x+8 \\ y=2x+10 \end{gathered}[/tex]Finally, the equation of the line that passes through (-4,2) and is perpendicular to the equation y = -1/2x+6 is
y=2x+10
If a different number in domain of a function have different outputs the function is called?
A function is a rule that assigns each input exactly one output. We call the output the image of the input. The set of all inputs for a function is called the domain.
A function is one-to-one if no two elements in the domain correspond to the same element in the range.
Thus, if a different number in the domain of a function has different outputs the function is called a one-to-one function
x + y =5x + y =5one solution no solutions infinity many solutions
We have the same equation twice, then there are infinity many solutions
2. Solve the system of equations: *S 2x – 4y = 201x=4x = 4=
EXPLANATION
Since we have the system of equations:
(1) 2x - 4y = 20
(2) x = 4
Plugging in x=4 into (1):
2*4 - 4y = 20
Multiplying numbers:
8 - 4y = 20
Subtracting -8 to both sides:
-4y = 20 -8
Subtracting numbers:
-4y = 12
Dividing both sides by -4:
y = 12 / -4
Simplifying:
y = -3
The solution to the system of equations is (x,y) = (4,-3)
how do you do how do you point plot on a graph
To point plots on a graph, take the following steps:
1. Identify the x-coordinates and y-coordinates from the variable/data you have. It should be written in this form: (x, y)
2. Label both axes on the graph(x-axis and y-axis). The x-axis is usually on the horizontal line while the y axis is the horizontal line.
3. Start plotting your first 2 points on both axes (usually the numbers on first row). Plot the x value and also plot the y value at the appropriate points
4. Finally, Continue plotting the numbers by pointing each point on the graph (take them in rows)
If Angle A is acute and Angle B is obtuse and Angle A is 2X+5 and Angle B is 6X+55, then how many degrees would Angle A be?
Angle A is 35° and Angle B is 145°
Supplementary angles are angles that give 180° when added together
Angle A and Angle B are supplementary angles such that
∠A + ∠B = 180°
Given that ∠A is acute angle and ∠B is obtuse angle
also , ∠A = 2x+5 and ∠B = 6x+55
using supplementary angle property ,
2x+5 + 6x+55 = 180
solving for x ,
8x + 60 = 180
x = 15
8x = 180 - 60
8x = 120
∠A = 2x+5
substituting value of x
∠A = 2(15)+ 5 = 30+5
∠A = 35°
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a Density is the ratio of mass to volume. An object with a volume of 25 cubic centimeters (cm?) has a mass of 125 grams (g). What is the density, in g/cm", of the object? A 5 B. 25 C. 100 D. 3125
The density is a ratio, defined as
[tex]\rho=\frac{m}{v}[/tex]replace in the ratio of density
[tex]\rho=\frac{125g}{25\operatorname{cm}3}[/tex]the density will be
[tex]\rho=\frac{5g}{\operatorname{cm}3}[/tex]I need HELP PLS!!! ITS HARD TO DO I NEED HELP
ANSWER:
B.
[tex]x^{\frac{7}{6}}[/tex]STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\mleft(\sqrt{x}\mright)\mleft(\sqrt[3]{x^2}\mright)[/tex]We simplify and we have:
[tex]\begin{gathered} (\sqrt[]{x})=x^{\frac{1}{2}} \\ (\sqrt[3]{x^2})=x^{\frac{2}{3}} \\ \text{therefore:} \\ x^{\frac{1}{2}}\cdot x^{\frac{2}{3}}=x^{\frac{1}{2}+\frac{2}{3}} \\ \frac{1}{2}+\frac{2}{3}=\frac{1\cdot3+2\cdot2}{2\cdot3}=\frac{3+4}{6}=\frac{7}{6} \\ x^{\frac{7}{6}} \end{gathered}[/tex]$7.400 at 10.5% for 1/4 yearsTo find the ending balance from the equation given using simple interest
Given:
$7.400 at 10.5% for 1/4 years
To find:
The ending balance from the equation given using simple interest
The ending balance here the total amount that will be gotten after the duration of 1/4 years
Using simple interest formula:
[tex]\begin{gathered} \text{I = PRT} \\ I\text{ = interest = ?} \\ P\text{ = principal = \$7400} \\ R\text{ = rate = 10.5\% = 0.105} \\ T\text{ = time = }\frac{1}{4}year \end{gathered}[/tex]substitute the values in the formula:
[tex]\begin{gathered} I\text{ = 7400 }\times\text{ 0.105 }\times\text{ }\frac{1}{4} \\ \\ I=\text{ 194.25} \end{gathered}[/tex]The ending balance = Interest + Principal
[tex]\begin{gathered} The\text{ ending balance = 194.25 + 7400} \\ \\ The\text{ ending balance = \$7594.25} \end{gathered}[/tex]5 books weight a total of 6 2/5 pounds. If each book weighs the same amount, how much does each book weigh? Show your work
Hello there. To solve this question, we'll have to remember some properties about mixed fractions.
5 book weight a total of 6 2/5 pounds. If each book weighs the same amount, how much does each book weigh?
We start by converting the fraction from the mixed fraction notation to the normal notation:
Therefore we have:
Now, suppose each book weigh x pounds. 5 books weight will be equal to 5x.
If 5 books weigh 32/5, then we have the following equation:
Divide both sides of the equation by a factor of 5
To find the value of this fraction, the trick is to multiply it by 4/4 (when the denominator is 25):
Each book weighs 1.28 pounds.
Which of the following is a quadratic equation that has the roots x = 5 and x = 6?
Answer:
the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]Explanatio
We want to derive the quadratic equation that has the roots x=5 and x=6;
To derive the equation, we have;
[tex](x-5)(x-6)=0[/tex]Expanding;
[tex]\begin{gathered} x^2-5x-6x+30=0 \\ x^2-11x+30=0 \\ x^2-11x=-30 \end{gathered}[/tex]Therefore, the quadratic equation that has the roots x=5 and x=6 is;
[tex]x^2-11x=-30[/tex]5. It is an angle formed above the horizontal is called A. Depression B. Elevation C. Right D. Acute
Given
It is an angle formed above the horizontal is called ---
Find
Complete the sentence
Explanation
as we know that the angle of elevation is the angle formed by the line of sight with horizontal .
so , here the correct option is Elevation
Final Answer
Therefore , an angle formed above the horizontal is called Elevation
Solve for q.
-18q+ 18q+ 2q + 14 = 4
q=
Answer:
q = -5
Step-by-step explanation:
Collect like terms
-18q + 18q + 2q = 4 - 14
-18q + 20q = -10
2q = -10
Divide both sides by 2
2q/2 = -10/2
q = -5
the 4000N boat picks up 5 passengers who each weigh 500N. what is the total mass of the boat and passengers
The weight of the boat is 4000 N
and each passenger weigh 500 N,
then the total weigh of boat and passengers is:
4000 N + 5 * 500 N = 4000 + 2500 = 6500 N
A student has 42 coins worth a total of $5.90. Each coin is either a nickel (five cents) or a quarter (twenty-five cents). If x is the number of nickels, then x can be determined from the equation---
Given
no. of coins = 42
worth of coins = $5.90
Find
number of nickels
Explanation
The number of quaters is 42 - x
0.05x + 0.25(42 - x) = 5.9
-0.2x + 10.5 = 5.9
-0.2x = -4.6
x = 23
Final Answer
Number of Nickels, x = 23
Equation A and Equation B are Equivalent Equations.Equation A: 3/5x + 4/5 = 2Equation B: 3x + 4 = 10Explain what was done to both sides of equation A to create equation B?
You have the following equations:
3/5 x + 4/5 = 2
3x + 4 = 10
In order to show that the previous equations are equivalent equations, multiply the first equation by 5, to eliminate the denominators of the fractions:
(3/5 x + 4/5 = 2)(5)
3x + 4 = 10
Hence, it was necessary to multiply by 5 the first equation to obtain the second one
Find the measure of the following numbered angles and the feason: Measure Reason 1 1 3 1 m
Answer
Explanation
Using the image,
Kim typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
ANSWER
54 words per minute
EXPLANATION
We want to know how much words he can write in 1 minute, so we have to find the ratio of words to minutes by dividing the number of words he wrot
function notations For the function below for which values of x does f (x)=4?
Answers:
x = 3
x = 5
Explanation:
In the function, the first set represents the x and the second set represents f(x), so to find for which values of x does f(x) = 4, we need to identify the beginning of the arrows that end in the number 4.
Therefore, these numbers are 3 and 5. It means that x = 3 and x = 5 make f(x) equal to 4.
So, the answers are x = 3 and x = 5.
The table below shows the cost of a pizza based on the number of toppings. Defend your choice.
Answer: This problem can be modelled using the linear function, which is as follows:
[tex]y(x)=mx+b[/tex]Based on the information provided, the function can be constructed as follows:
[tex]C(n)=1.5(n-1)+12[/tex]Therefore the answer is Option (A).
Problem: Solve the following equations for the given variable: 1. P = 2L + 2W for W. 2. 2x + 3y = -10 for y.
EXPLANATION
Given the equations:
1. P = 2L + 2W for W. (Subtracting 2L to both sides)
P - 2L = 2l + 2W - 2l (Dividing both sides by 2)
P/2 -2L/2 = W (Simplifying and switching)
W = P/2 - L
2. 2x + 3y = -10 for y. (Subtracting 2x to both sides)
2x - 2x + 3y = -10 -2x (Simplifying)
3y = -2x - 10 (Dividing both sides by 3)
y = -2x/3 - 10/3
Travis was walking to school when hesaw some friends walking a block aheadof him. After running to catch up with hisfriends, his heart was beating 24 beatsevery 10 seconds. At this rate, how manytimes would his heart beat in 3 minutes?
his heart would beat 432 times in 3 minutes
Explanation
we can easily solve this by using a rule of three,
then
Step 1
to do that we need the same measure unit for the time, let's use seconds
so, we need to convert 3 minutes into seconds,
the equivalence is
[tex]1\text{ minute = 60 seconds}[/tex]hence, to convert from minutes into seconds just mutlply by 60
then
[tex]3\text{ minutes}\Rightarrow3\cdot60\text{ seconds=180 seconds}[/tex]Step 2
now, let's make the proportion
let x represents the number of times his heart would be in 180 seconds( 3 minutes)
so
[tex]\begin{gathered} \text{if} \\ 24\text{ beats}\Rightarrow10\text{ s} \\ \text{then} \\ x\text{ beats}\Rightarrow180\text{ s} \end{gathered}[/tex]so, the proportion is
[tex]\begin{gathered} \frac{24\text{ beats}}{10\text{ s}}=\frac{x}{180\text{ s}} \\ \frac{24}{10}=\frac{x}{180} \\ \end{gathered}[/tex]finally, to solve for x multiply both sides by of the equation by 180 and reduce
[tex]\begin{gathered} \frac{24}{10}=\frac{x}{180} \\ \frac{24}{10}\cdot180=\frac{x}{180}\cdot180 \\ \frac{4320}{10}=x \\ 432=x \end{gathered}[/tex]therefore, his heart would beat 432 times in 3 minutes
I hope this helps you
the figure below has a point marked with a large dot.first rotate the figure 90 degrees counterclockwise about the origin.then give the coordinates of the Mark point in the original figure in the final figure.
When we do a 90 degree counterclockwise rotation about the origin, a point moves from ( x,y) to ( -y,x)
Using the point with the blue dot
It is originally at (2,-3)
It will move to (3,2)
Under her cell phone plan, Ella pays a flat cost of $58.50 per month and $3 per gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would have to pay for 3 whole gigabytes.) She wants to keep her bill under $65 per month. What is the maximum whole number of gigabytes of data she can use while staying within her budget?
The maximum number of gigabytes of data she can use while staying within her budget is 2 gigabytes.
Given that Ella pays a flat cost of $58.50, and per gigabyte used have to pay $3. If she uses g gigabytes she has to pay $3xg.
Now we have to find the maximum whole number of gigabytes data, she can use within her budget.
Her budget is less than $65.
We can create a inequality expression for this, as follows.
58.50+3g< 65
Calculating further, we get
3g<65-58.50
3g<6.5
g<6.5/3
g<2.163.
Therefore, the maximum whole of gigabytes, she should use to keep the expense within budget is 2 gigabytes.
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the number of girls is 75% of the number of boys.There are 28 students altogether. how many are girls and how many are boys?use a tape diagram
Let x be the number of boys
Let the number of girls be 75% of x = 75x/100
Boys + girls = 28
75x/100 + x = 28
0.75x + x = 28
1.75x = 28
Divide both-side of the equation by 1.75
x = 16
There a
I need to make my birthday into a polynomial my birthday is 11/01/2005
EXPLANATION:
To express a number or value as a polynomial we must take into account some steps:
-The polynomial may or may not have grouping signs.
-The polynomial can have more than one variable, constants and exponents.
-A polynomial must be ordered, the monomials that form it must be written from highest to lowest degree.
Since a polynomial is an algebraic expression that shows the sum of monomials and we have 3 separate monomials, so we must do the following:
[tex]\begin{gathered} (11)\rightarrow a\text{ monomial} \\ (01)\rightarrow a\text{ monomial} \\ (2005)\rightarrow a\text{ monomial} \\ \text{Now }we\text{ add }the\text{ t}hree\text{ }monomials\colon \\ (2005+11+01);\text{ there }the\text{ poly}nomial\text{ }must\text{ be organized }from \\ highest\text{ }to\text{ lowe}st\text{ }coefficient; \\ \text{ANSWER: (2005+11+01)} \end{gathered}[/tex]twice a number is 24a. 2- n = 24b. 2 + n = 24c. 2 / n = 24 d. 2n = 24
Answer:
d. 2n = 24
Explanation:
Let the number be n
Twice the number = 2 x n
The word 'is" is the equality sign.
Therefore, the expression twice a number is 24 in mathematical symbol is:
[tex]2n=24[/tex]Find the volume of a pyramid with a square base, where the side length of the base is10 m and the height of the pyramid is 7.2 m. Round your answer to the nearesttenth of a cubic meter.
hello
to find the volume of the figure, we need to know the formula of a pyramid with a square base
once we know that, we can proceed to simply substitute the values into the equation
[tex]\begin{gathered} \text{volume}=\frac{1}{3}\times l^2\times h \\ l=\text{side length} \\ h=\text{height} \end{gathered}[/tex][tex]\begin{gathered} l=10m \\ h=7.2m \end{gathered}[/tex][tex]\begin{gathered} \text{volume}=\frac{1}{3}\times10^2\times7.2 \\ \text{volume}=\frac{100\times7.2}{3} \\ \text{volume}=240m^3 \end{gathered}[/tex]the volume of the figure is 240m^3