Given a principal P, compounded anually at r% for t years. Then the
How does a graph of quadratic function (f(x) = ax2 + bx + c) vary when the a,b, c changes from -1 to +1?
When a, b, c changes from -1 to +1, the parabolas opens and widens.
Given,
The quadratic function, f(x) = ax² + bx + c
We have to find the change in graph when a, b, c changes from -1 to 1.
First lets consider:
a and b as constants and c is varying.
That is,
x² + x + c
Then, the parabola will move up and down.
Now, lets consider:
a and c as constants and b is varying.
That is,
x² + bx + 1
Then, the vertex will move but all parabolas passes through the points (0, c)
Now, we can move to the question.
What happens to graph when +1 changes to -1.
So,
b and c should keep constant and a is varying.
Then,
ax² + x + 1
Here, the parabolas opens and widens.
That is,
When a, b, c changes from -1 to +1, the parabolas opens and widens.
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use matrices D, E, and F to find each sum or product
Problem
Solution
5. E-D
Procedure
-3-2 =-5
-4-1=-5
0-7=-7
1-5=-4
2-3=-1
6- (-4)=10
And the answer would be:
-5 -5
-7 -4
-1 10
6. 3F
Procedure
3* -2=-6
3 *5 = 15
3* 1= 3
3*3 = 9
3*14=12
3 * -6= -18
And the answer would be:
-6 15 3
9 12 -18
Put the following equation of a line into slope-intercept form, simplifying all fractions.
3y-3x=15
Answer:
[tex]y=x+5[/tex]
Step-by-step explanation:
[tex]3y-3x=15 \\ \\ y-x=5 \\ \\ y=x+5[/tex]
Which quadrant has ordered pairs (-x,-y)?
ANSWER
Quadrant III
STEP-BY-STEP EXPLANATION:
Firstly, we need to draw the cardinal points and label each quadrant on it
Looking at the ordered pair (-x, -y), you will see that the x and y-values both fall on the negative side of the x-ais and y-axis
Hence, it falls on the quadrant III
2) From an elevation of 38 feet below sea level, Devin climbed to an elevation of 92 feet abovesea level. How much higher was Devin at the end of his climb than at the beginning?
Ok, so he started at 38 feet below and ended at 92 feet above. 38 below = -38.
The difference in the height is given by
92-(-38) =
92+38 =
130 feet
Devin was 130 feet higher at the end of climbing.
Ms. Bell's mathematics class consists of 6 sophomores, 13 juniors, and 10 seniors.
How many different ways can Ms. Bell create a 3-member committee of sophomores
if each sophomore has an equal chance of being selected?
The number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
What is termed as the combination?Selections are another name for combinations. Combinations are the selection of items from a given collection of items. We need not aim to arrange anything here. Combinations do seem to be selections made by having taken some or all of a set of objects, regardless of how they are arranged. The amount of combinations of n things taken r at a time is denoted by nCr and can be calculated as nCr=n!/r!(nr)!, where 0 r n.0 ≤ r ≤ n.For the given question;
Ms. Bell's mathematics class consists -
6 sophomores, 13 juniors, and 10 seniors.Ms. Bell create a 3-member committee of sophomores with unbiased outcomes.
The section of 3 sophomores can be done as;
⁶C₃ = 6!/3!(6-3)!
⁶C₃ = 6/3!.3!
⁶C₃ = 20 ways.
Thus, the number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
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How to put 7^3/4 in radical form
Given:
[tex]7^{\frac{3}{4}}[/tex]Resolving it to its radical form can be gotten based on the general laws of indices.
We have:
[tex]A^{\frac{x}{y}}=\sqrt[y]{A^x}[/tex]I.e. the number is raised to the power of the numerator and then we get the denominator's root of the number obtained.
Thus:
[tex]\begin{gathered} 7^{\frac{3}{4}}=\sqrt[4]{7^3}=\sqrt[4]{343} \\ \sqrt[4]{343}=343^{\frac{1}{4}}=343^{(\frac{1}{2}\times\frac{1}{2})} \\ =343^{(\frac{1}{2}\times\frac{1}{2})}=\sqrt[]{343^{\frac{1}{2}}} \end{gathered}[/tex]Now, we have our value in the square root form as:
[tex]\sqrt[]{343^{\frac{1}{2}}}=\sqrt[]{7^{\frac{3}{2}}}[/tex]hello and thank you for helping me and this is a trigonometry question bit for the question has give exact value and it won't accept decimals as an answer and thank you for your time.
1) In this question let's calculate the sin(θ) and cos(θ)
Given that
[tex]\begin{gathered} \text{If }\sin (\theta)=\frac{5\pi}{4} \\ \sin (\theta)\text{ }\Rightarrow\sin (\frac{5\pi}{4})\text{ }=-\frac{\sqrt[]{2}}{2} \\ \cos (\frac{5\pi}{4})=-\frac{\sqrt[]{2}}{2} \end{gathered}[/tex]2) In this question, we're calculating the value of the sine and the cosine in radians.
We must remember that 5π/4 ⇒ to 225º, and that it's in the Quadrant III
If we subtract
225 -180 =45 So the sine of 5π/4 is -√2/2 and the cosine (5π/4 ) = -√2/2
2.3) The sign of the Quadrant
Since 225º is in Quadrant III both results are negative ones.
I need help with question 12 please in a hurry I understand already
Trigonometric Ratios
The figure is a triangle with hypotenuse of h = 25 feet. The angle of elevation is 35°.
Solve this system of linear equations. Separatethe x- and y-values with a comma.6x + 20y = -623x - 9y = -12Enter the correct answerDONE
Given the following systems of linear equations,
6x + 20y = -62 (Equation 1)
3x - 9y = -12 (Equation 2)
Step 1 : Solve 6x+20y=−62 for x:
6x + 20y + (−20y) = −62 + (−20y) (Add -20y to both sides)
6x = −20y −62
6x/6 = (−20y −62)/6 (Divide both sides by 6)
x = (-10y/3) + (-31/3)
Substitute to Equation 2:
3x−9y=−12
3[(-10y/3) + (-31/3)] - 9y = -12
−19y−31=−12 (Simplify both sides of the equation)
−19y−31+31=−12+31 (Add 31 to both sides)
−19y=19
-19y/-19 = 19/-19 (Divide both sides by -19)
y= −1
Step 2: Substitute −1 for y in x =(-10y/3) + (-31/3)
x =(-10(-1)/3) + (-31/3)
x = -7
Answer:
x=−7 and y=−1
Which number can be inserted into the parentheses to make a true statement?-10°C<( )A. -12° CB. -18° CC. -3°CD. -10° C
Answer:
[tex]-3\degree C[/tex]Explanation:
Here, we want to get the number that could be inserted into the parentheses to make it true
From the logical operator given, we can see that we need a number greater than -10
From the options given, only -3 is greater than -10, which makes it the correct answer choice
Katherine bought à sandwich for 5 1/2 dollar and a adrink for $2.60.If she paid for her meal with a $ 10 bill how much money did she have left?
To find out how much Katherin have left we need to substrac the amount she spent:
[tex]10-5\frac{1}{2}-2.6=10-5.5-2.6=1.9[/tex]Therefore she has $1.9 left.
To do this same problem in fraction form we need to convert the 2.6 in fraction, to do this we multiply the number by 10 and divided by ten. Then:
[tex]2.6\cdot\frac{10}{10}=\frac{26}{10}=\frac{13}{5}[/tex]then we have:
[tex]\begin{gathered} 10-5\frac{1}{2}-\frac{13}{5}=10-\frac{11}{2}-\frac{13}{5} \\ =\frac{100-55-26}{10} \\ =\frac{19}{10} \end{gathered}[/tex]Therefore, the answer in decimal form is 19/10 dollars.
Let log, A = 3; log, C = 2; log, D=5 D? what is the value of
Evaluate the value of expression.
[tex]\begin{gathered} \log _b\frac{D^2}{C^3A}=\log _bD^2-\log _bC^3-\log _bA \\ =2\log _bD-3\log _bC-\log _bA \\ =2\cdot5-3\cdot2-3 \\ =10-6-3 \\ =1 \end{gathered}[/tex]So answer is 1.
A 65 ft tree casts a 13 ft shadow. At the same time of day, how long would the shadow of a 20 ft building be? (Draw a diagram to help you set up a proportion)
height of tree = 65 ft
length of shadow = 13 ft
Let draw a diagram to illustrate the question effectively
The proportion can be set up below
[tex]\begin{gathered} \frac{65}{20}=\frac{13}{x} \\ \text{cross multiply} \\ 65x=260 \\ x=\frac{260}{65} \\ x=4\text{ ft} \end{gathered}[/tex]Th shadow will be 4 ft. do you
distribute and simply 5(3x+1)-6x
A wheel is rotating 600 times per minute. Through how many degrees does a point in the edge of the wheel move in 1/2 seconds.
The wheel is rotating 600 times per minute, find how many times rotate in 1 second:
1 minute = 60 seconds
[tex]600\frac{times}{\min}\cdot\frac{1\min}{60s}=10\frac{times}{s}[/tex]Then, if in 1 second it rotates 10 times in 1/2 seconds it rotates:
[tex]\frac{10\frac{times}{s}}{2}=5\text{times}[/tex]Multiply the number of times it rotates (5 times) by 360 (a wheel has 360º)
[tex]5\text{times}\cdot\frac{360º}{1\text{time}}=1800º[/tex]Then, a point moves 1800º in 1/2 seconds(4,0) and (0,2) write an equation in standard form for the line that passes through the given points
We have the following:
The first thing is to find the slope of the line, like this:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]replacing:
[tex]m=\frac{2-0}{0-4}=\frac{2}{-4}=-\frac{1}{2}[/tex]now, the equation has the following form:
[tex]y=mx+b[/tex]for b,
m = -1/2
y = 2
x = 0
replacing:
[tex]\begin{gathered} 2=-\frac{1}{2}\cdot0+b \\ b=2 \end{gathered}[/tex]Therefore, the equation in standard form is:
[tex]\begin{gathered} y=-\frac{1}{2}x+2 \\ y+\frac{1}{2}x=2 \\ 2y+x=4 \end{gathered}[/tex]Use log, 20.356, log, 3 0.503, and log, 5 0.835 to approximate the value of the given logarithm to 3 decimal places. Assume that b>0 and b + 1.
log, 625
X
A
Answer:
3.34
Step-by-step explanation:
625 is 5^4
Using the log rule [tex]log_b(x^a)=alog_b(x)[/tex],
log_b(5^4) = 4*log_b(5)
4*0.835 = 3.34
Create a table of values to represent the equation y = x - 9
Answer:
Explanation:
Here, we want to create a table of values to represent the given equation
To do this, we need to select a range of values for x
This can be a range of any set of numbers
With respect to this question, we shall be choosing -2 to +2 with an increment of 1
The values of x are thus: -2,-1 , 0, +1 and +2
So, now let us get the corresponding y-values using the equation rule
Now, let us get the y-values
when x = -2
y = -2-9 = -11
when x = -1
y = -1-9 = -10
when x = 0
y = 0-9 = -9
when x = 1
y = 1-9 = -8
when x = 2
y = 2-9 = -7
Thus,we have the table of values as follows:
Select the three expressions that are equivalent to 410
Answer:
A, C, E
Step-by-step explanation:
4^10 = 1048576
A: (4^5)^2 = 1048576
C: 4^20 / 4^10 = 1048576
E: (4^2 x 4^3)^2 = 1048576
In triangle ABC, angle A is 44 degrees and angle B is 76 degrees. What is the measure of the third angle?
Answer:
60 degrees
Step-by-step explanation:
Total of angles of a triangle is 180
180-76-44= 60
Write a quadratic function in intercept form whose graph passes through the points (-5,0)(-1,0) and (-7,-24)
EXPLANATION
The intercept-form of a quadratic function is as follows:
y = a(x - p)(x - q)
Now, as the roots are (-5,0)
Since the parabola passes through the point (−5,0), then 0=25a−5b+c
Since the parabola passes through the point (−1,0), then 0=a−b+c.
Since the parabola passes through the point (−7,−24), then −24=49a−7b+c.
Thus, we have obtained the following system:
Solving it we get that a=−2, b=−12, c=−10.
Thus, the equation of the parabola is y=(−2x−10)(x+1)
I need help please. I don’t know what to do.Number 6
By definition, a relation is a function if each input value (x-value) has one and only one output value (y-value).
In this case, you have the following relation:
[tex]\mleft(1,5\mright)\mleft(3,1\mright)\mleft(5,0\mright)\mleft(-2,6\mright)[/tex]Notice that each ordered pair has this form:
[tex](x,y)[/tex]Where "x" is the input value and "y" is the output value.
You can identify that each input value has one and only output value. Therefore, you can conclude that this relation is a function.
Hence, the answer is: It is a function.
hey i need help giving 10 points
Answer:
B(2) = -1
Step-by-step explanation:
Assuming each division on the grid is 1 unit
Locate 2 on the x-axis. That is two divisions to the right of the origin. The y value corresponding to this is -1
Rewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=-5(x+1)
The given equation is
[tex]y-4=5(x+1)[/tex]To write the equation in standard form, first, we have to use the distributive property.
[tex]y-4=5x+5[/tex]Now, we subtract 5x and 5 on both sides.
[tex]\begin{gathered} y-4-5x-5=5x+5-5x-5 \\ -5x+y-9=0 \end{gathered}[/tex]Now, we add 9 on each side
[tex]\begin{gathered} -5x+y-9+9=0+9 \\ -5x+y=9 \end{gathered}[/tex]Therefore, the standard form of the given equation is[tex]-5x+y=9[/tex]Where A = -5, B = 1, and C = 9.Complete a two-column algebraic proof.Given: x – 4 = (8x+6) + 4xProve: x = -1
To perform a two column proof, we should give a statement and give a reason of it.
So we start with the initial statement.
1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given
Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.
2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.
Now, on the right we can add 4x with 4x, due to the associative property of additon, we get
3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.
Now, we can subtract x on both sides, so we get
4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.
By the same reason, we should subtract 3 on both sides. We get
5. Statement: -7 = 7x. Reason: Subtraction property of equality.
Finally, we divide by 7 on both sides, so we get
6. Statement: -1=x. Reason: Division property of equality.
7. Statement: x=-1. Reason: Symmetric property of equality.
Sketch the graph of each line.
24)
y=3/5x-4
The graph of the given line is attached below.
We are given the line:-
y = (3/5)x - 4
We will find the x and y intercepts of the line to plot in the graph.
As the equation is already in the slope intercept form, we can write,
The y-intercept of the line is -4.
Hence, the coordinates of the point will be (0,-4).
To find the x - intercept of the line we will put y = 0 in the given line.
0 = (3/5)x - 4
4 = 3x/5
x = 20/3
The coordinates of the point will be (20/3,0).
We can plot these points to get the desired graph.
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A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance traveled is 75.897 miles.
part A. We are given that a hiker will increase the distance covered by 10% each day. Let "S" be the distance, then on the first day the distance is:
[tex]S_1[/tex]On the second day, we must add 10% of the first day, we get:
[tex]S_1=S_1+\frac{10}{100}S_1[/tex]Simplifying we get:
[tex]S_2=S_1+0.1S_1=1.1S_1[/tex]On the third day, we add 10% of the second day, we get:
[tex]S_3=S_2+0.1S_2=1.1S_2=(1.1)(1.1)S_1=(1.1)^2S_1[/tex]On the fourth day, we add 10% of the third day, we get:
[tex]S_4=S_3+0.1S_3=1.1S_3=(1.1)^3S_1[/tex]If we continue this pattern and we set "n" as the number of days, then a formula for the distance after "n" days is:
[tex]S_n=(1.1)^{n-1}S_1[/tex]Now, we are given that for n = 7 the distance is 75897, therefore, we substitute n = 7 in the formula:
[tex]S_7=(1.1)^{7-1}S_1[/tex]Substituting the value of the distance:
[tex]75897=(1.1)^{7-1}S_1[/tex]Now we can solve for S1, we do that by dividing both sides by 1.1 together with its
exponent:
[tex]\frac{75897}{(1.1)^{7-1}}=S_1[/tex]Now we solve the operations:
[tex]\frac{75897}{(1.1)^6}=S_1[/tex]Solving the operations:
[tex]42842=S_1[/tex]Therefore, the distance the first day was 42842 miles.
part B. The formula for Sn is the given previously but we replace the known value of S1:
[tex]S_n=42842(1.1)^{n-1}[/tex]Part C. To determine the distance after 10 days, we substitute the value n = 10 in the formula, we get:
[tex]S_{10}=42842(1.1)^{10-1}[/tex]Solving the operations we get:
[tex]S_{10}=101019.19[/tex]Therefore, the distance after 10 days is 101019.19 miles.
8x - 3x + 4x = -36x = ?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
8x - 3x + 4x = -36
x = ?
Step 02:
We must apply the algebraic rules to find the solution.
8x - 3x + 4x = -36
12x - 3x = - 36
9x = - 36
x = - 36 / 9
x = - 4
The answer is:
x = - 4
Can you help me solve my homework question I will follow along the steps
Notice that both fractions have the same denominator, therefore, we can simply add the numerators:
[tex]\frac{-5a-3x-2a+9x}{6a}.[/tex]Adding like terms, we get:
[tex]\frac{-7a+6x}{6a}.[/tex]Answer: [tex]\begin{gathered} \frac{-7a+6x}{6a},\text{ or equivalently} \\ -\frac{7}{6}+\frac{x}{a}. \end{gathered}[/tex]