For this problem, we are given the expression for a quadratic equation and we need to determine the x-intercepts of its graph.
The x-intercepts coincide with the zeros of the equation, which are obtained when f(x) = 0. So we have:
[tex]x^2-4x-21=0[/tex]We need to determine the roots of the equation above.
[tex]\begin{gathered} x_{1,2}=\frac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot(-21)}}{2\cdot1}\\ \\ x_{1,2}=\frac{4\pm\sqrt{16+84}}{2}=\frac{4\pm\sqrt{100}}{2}=\frac{4\pm10}{2}\\ \\ x_1=\frac{4+10}{2}=\frac{14}{2}=7\\ \\ x_2=\frac{4-10}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]The intercepts are: (-3,0) and (7,0).
What is the average rate of change of f(x), represented by the graph, over the interval [-1, 2]?
The estimate (to one decimal place) of the average rate of change f is 2.3
How to estimate the average rate of change f?The interval is given as
[-1, 2]
This can be rewritten as
x = -1 to x = 2
This can also be represented as
(a, b) = (-1, 2)
From the attached graph, we have
f(-1) = -5
f(2) = 2
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(2) - f(-1)]/[2 + 1]
So, we have
Rate = [2 + 5]/[2 + 1]
Evaluate
Rate = 2.3
Hence, the average rate of change f is 2.3
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An investment offers a total return of 17 percent over the coming year. Powell Arms thinks the total real return on this investment will be only 12 percent. What does Powell believe the inflation rate will be over the next year?
Powell believe that the inflation rate will be 4.46% over the next year .
In the question ,
it is given that
total return offered by the investment((nominal rate) = 17% = 0.17
return according to Powell Arms(real rate) = 12% = 0.12
let the inflation rate be x.
The inflation rate over the next year can be calculated using the formula .
(1+Real rate ) = (1+nominal rate )/ (1+ inflation rate )
Substituting the values , we get
(1+0.12) = (1+0.17)/(1+x)
1.12 = 1.17/(1+x)
1+x = 1.17/1.12
1 + x = 1.0446
x = 1.0466-1
x = 0.0446
x = 4.46%
Therefore , Powell believe that the inflation rate will be 4.46% over the next year .
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(03.06) 5.)Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2OPTIONS: A.) y-6 = 1/2(x+3)B.) y = 1/2x - 6C.) y+3 = 1/2(x-6)D.) y-2y = 12I NEED THIS DONE ASAP!
Answer the point-slope form of the equation below that represents the line that passes through the point (6, -3) and has a slope of 1/2
A linear equation can have the form
y = mx + b
The slope is m
The point-slope form is
(y- y1) = m(x -x1) (1)
the point (x1, y1) = (6, -3)
______________
Replacing in (1) the slope and the point (x1, y1)
(y- y1) = m(x -x1)
(y- (-3)) = 1/2(x -6)
y+3 = 1/2(x-6)
__________________
So, checking the options the correct answer is C
A.) y-6 = 1/2(x+3)
B.) y = 1/2x - 6
C.) y+3 = 1/2(x-6)
D.) y-2y = 12
Let's call a year "nice" if its number can be represented as the difference of two powers of two. What is the next nice year? What nice year will be the first one after it?
The next nice year will be 2 nice.
The nice year that will be the first one after it is 4 nice.
What is an exponent?It should be noted that an exponent is used to express the numbers that are either too big or too small. This is usually expressed in their powers.
Fron the information, it as stated that a year is called "nice" if its number can be represented as the difference of two powers of two.
The next nice year will be the difference which will be
= (2² - 2) × nice
= (4 - 2) × nice
= 2 nice.
The one after it will be:
= 2 × 2 nice
= 4 nice.
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The answer has to be a geometric proof. Thank you!
Given data:
The given triangle in which AD is on perpendicular bisector on BC.
In triangle ABD and ACD.
[tex]\begin{gathered} \angle ADB=\angle\text{ADC}=90^{\circ} \\ BD=CD(\text{given)} \\ AD=AD\text{ (common)} \\ \Delta ABD\cong\Delta ACD(\text{SAS)} \end{gathered}[/tex]Simmilary triangle BED and triangle CED.
[tex]\begin{gathered} \angle BDE=\angle CDE \\ BD=CD \\ ED=ED \\ \Delta BED\cong\Delta CED(SAS) \end{gathered}[/tex]The fisr expression can be written as,
[tex]\begin{gathered} \Delta ABD\cong\Delta ACD \\ \Delta\text{ABE}+\Delta BED\cong\Delta ACE+\Delta\text{CED} \end{gathered}[/tex]Substitute CED in place of BED.
[tex]\begin{gathered} \Delta ABE+\Delta CED\cong\Delta ACE+\Delta CED \\ \Delta ABE\cong\Delta ACE \end{gathered}[/tex]Thus, the triangle ABE is congruent to trriangle ACE.
Independent Practice7. The original quantity is 10 and the new quantityis 13. What is the percent change? Is it anincrease or decrease?8. The original quantity is 5 and the new quantityis 3. What is the percent change? Is it an increaseor decrease?7%1310100%100%poP.P Р-P%.The percent increase is%The percent decrease is
The percentage increase or decrease can be calculated by :
[tex]\%change=\frac{New-Orig}{Orig}\times100[/tex]7. New = 13, Orig = 10
% change = [(13 - 10)/10] x 100 = 30% (Increase)
8. New = 3, Orig = 5
% change = [(3 - 5)/5] x 100 = -40% or 40% (decrease)
8.12 Midpoint formula: find the endpoint EUW
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The midpoint of PQ is M(4, 0). One endpoint is P(6, 0). Find the coordinates of the other
endpoint Q.
Write the coordinates as decimals or integers.
‹=OD
Work
The coordinates of the other endpoint Q.=(2,0)
How to calculate the coordinates of the other endpoint Q ?
Given:
Midpoint = PQ = M(4,0)
One endpoint = P = [tex](x_1,y_1)[/tex] = (6,0)
Other endpoint Q= [tex](x_2,y_2)[/tex]
We know that,
[tex]\text{Midpoint PQ}=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\=(\frac{6+x_2}{2} ,\frac{0+y_2}{2} )=(4,0)\\\\= > \frac{6+x_2}{2} =4\\\\= > 6+x_2= 8\\\\= > x_2=2[/tex]
[tex]\text{Similarly},\\\\\frac{0+y_2}{2} =0\\\\= > y_2=0[/tex]
So, the Other endpoint Q=(2,0)
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Line c has an equation of y = -5x + 3. Parallel to line c is line d, which passes through the
point (2, -6). What is the equation of line d?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Parallel lines have the same gradient so equation of line d is y = -5x + c.
Substitute (2,-6) into the equation to find c.
-6 = -5(2) + c
c = 4
Hence equation of line d is y = -5x + 4.
Solve the following equation 12+5x=2x+3
Answer:
-3
Step-by-step explanation:
im assuming u want to find x
1. move all the numbers with x to the left side to make life easier
2. 5x-2x= 3x
3. 3-12= -9
4. you want the x to be solo
5. -9/3 = -3
can someone help me? thank you so much
image has the answers
Given the right triangle ABC with altitude BD drawn to the hypotenuse AC. If AC=6 and DC=4, what is the length of BC in simplest radical form ?
This problem is an application of the Geometric mean theorem. It says that
[tex]\frac{6}{x}=\frac{x}{4}[/tex]Comment: In other words, it says that the length of BC (x) is the geometric mean between the lengths of AC and DC.
Then,
[tex]x^2=6\cdot4=24[/tex][tex]x=\sqrt[]{24}=2\cdot\sqrt[]{6}[/tex]................................................................................................................................................................
Let's talk a little about the simplest radical form of a square root
[tex]\sqrt[]{a}[/tex]The first step to finding it is to write the number within the root as a product of prime powers, such product is called its integer factorization. Let's do that for 24:
Then, the integer factorization of 24 is
[tex]24=2^3\cdot3[/tex]Thus,
[tex]\sqrt[]{24}=\sqrt[]{2^3\cdot3}[/tex]The idea now is to take out of the root all we can. The rule is that we can only take out powers of 2 (for our root is a square root). In the expression
[tex]2^3\cdot3[/tex]There is only one power of 2, within 2^3. We can write it as
[tex]2^2\cdot2\cdot3[/tex]How are we going to take out it? We are going to take out the base of the power, which is 2 in this case. Then,
[tex]\sqrt[]{24}=2\cdot\sqrt[]{2\cdot3}=2\cdot\sqrt[]{6}[/tex]In simple terms, the simplest radical form of a root is what results after taking out the root all that can be taken out.
please help tutor I will give you a good rating
Answer
Options A, D and E are correct.
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
For the first plan, there's a one time investment of 15,000 dollars and subsequent monthly payments of 500 dollars.
y = 15,000 + 500x
y = 500x + 15,000
Slope = unit rate of increase = 500
y-intercept = 15,000
For the second plan, the function is just given as
y = 12,000 + 520x
y = 520x + 12,000
Slope = unit rate of increase = 520
y-intercept = 12,000
We can see that
The two functions are increasing.
The function for plan II has a greater unit rate.
The function for plan I has a greater y-intercept.
Hope this Helps!!!
The graph shows the mass of the bucket containing liquid depends on the volume of liquid in the bucket. Use the graph to find the range of the function.
From the graph, the range of the function in the graph is; 0 ≤ M ≤ 6.5
What is the range of the graph Function?
The range of a function is the set of all possible output values for which the function still exists.
Now, from the graph, we can see that it is a linear graph that starts on the vertical axis with a coordinate of approximately (0, 1) which denotes 1 kg when the volume is 0 liters.
Now, we see that the line of the graph stops at the coordinate (7.5, 6.5) which denotes 6.5 kg when the volume is 7.5 liters.
Therefore the maximum mass is 6.5 kg while the minimum is 0 kg. Thus,;
Range; (0 ≤ M ≤ 6.5)
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Help me pls it would be nice thank youuuuu
Please answer this quickly, I don’t need no explanation or work, just the letter, thank you!
Solution:
Given the graph;
If a vertical line intersects a curve on an xy-plane more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function.
ANSWER: B
What is a number that when you divide it by 2 and subtract 3.8 from the quotient, you get 7?
Let the number x.
Then the number divided by 2 gives
[tex]\frac{x}{2}[/tex]Subtract 3.8 from the quotient gives
[tex]\frac{x}{2}-3.8[/tex]Hence,
[tex]\frac{x}{2}-3.8=7[/tex][tex]\begin{gathered} \frac{x}{2}-3.8=7 \\ \frac{x}{2}=7+3.8=10.8 \\ \Rightarrow x=2\times10.8=21.6 \end{gathered}[/tex]x = 21.6
For each scenario below, choose the graph that gives the best representation.
(a). The daily amount of calories that a rat eats increases steadily from birth to about age 3 months. Then, the amount levels off until about age 6 months, when it increases again.
(b). Jane leaves her house on her bike. She rides at a constant speed until she reaches a lemonade stand, where she parks her bike and takes a rest. Then she turns around and bikes home as fast as she can.
A) The second graph gives the best representation of the daily amount of calories consumed by the rat.
B)The fourth graph gives the best representation of Jane's journey.
The first slope of the graph represents the steady increase in the consumption of calories by the rat until the age of 3. The horizontal line represents the level off until the age of 6. The slopes after the horizontal line represent the increase in consumption of calories after age 6.
The first slope of the graph represents the steady increase in the distance from her home as she is traveling away from her home. The horizontal line that comes after the slope represents the time she rested at the lemonade stand. And the negative slope that comes after the horizontal line represents the decreasing distance to her home as she travels back to her home.
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A line that includes the point (1, 10) has a slope of 1. what is its equation in slope-intercept form?
Considering the definition of a line, the equation in slope-intercept of the line that passes through the point (1, 10) and has a slope of 1 is y=x+9.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Equation in slope-intercept form in this caseIn this case, you know:
The line has a slope of 1.The line passes through the point (1, 10).Substituting the value of the slope m, the line has a form: y=1x + b or what is the same y=x +b.
Replacing the value of the point in the expression of a linear equation, the value of the ordinate to the origin b can be obtained:
10= 1×1 + b
10= 1 + b
10 -1 = b
9= b
Finally, the equation of the line is y=x +9.
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the product of 5 and y
To get the product we multiply.
[tex] = 5 \times y \\ = 5y[/tex]
A) graph the function: f(x) = -2^xB) domain of the function?C) range of the function?D) Equation of the asymptote?E) y-intercept of the graph?
We are given the following function:
[tex]y=-2^x[/tex]Part A. We are asked to draw the graph of the function. This is an exponential function with a negative sign, this means that the graph is reflected across the x-axis. Therefore, the graph is:
Part B. The domain of a function is the values that the fuction can take as an input. Since the function is an exponential function, it can take any value of "x" therefore, the domain is all the real numbers, we write this as follows:
[tex]D=(-\infty,\infty)[/tex]Part B. The range of a function is the values that the function outputs, The range of an exponential function are the values that are greater than zero, but since the given function is reflected across the x-axis, this means that the rage is the negative real numbers, therefore, the range is:
[tex]R=(-\infty,0)[/tex]Part D. For an exponential function of the form:
[tex]y=a(b^x)[/tex]The asymptote is x-axis, since zero is never an output of the function. Therefore the equation of the asymptote is:
[tex]y=0[/tex]Part E. The y-intercept is the value of the function when "x = 0", therefore, substituting in the function we get:
[tex]f(0)=-2^0[/tex]Solving the operations:
[tex]f(0)=-1[/tex]Therefore, the y-intercept is -1
5. The following stem-and-leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress.ActorsStemsActresses2146667987532213001133444557788877654332210041112966515210601167480(a) What is the age of the youngest actor to win an Oscar? years(b) What is the age difference between the oldest and the youngest actress to win an Oscar? years(c) What is the oldest age shared by two actors to win an Oscar? years
Answer:
(a) 31 years
(b) 59 years
(c) 56 years
Step-by-step explanation:
In general, when reading a stem and leaf plot, we read firstly the number in the steam (middle) and then in the leaf.
Now, let's move on to the question:
(a) As we can see in the graph, the youngest actor has 31 years.
(b) The youngest actress is 21 years old and the oldest is 80.
So, the difference is 80 - 21 = 59 years.
(c) In this exercise, we have to look for actors who had the same age. That means, when evaluating the steam, we will have to find similar values in the leaf. The oldest age shared is 56 years.
Use the point-slope form to find the equation of each altitude of SABC. (Recall ! a triangle is the perpendicular drawn from any vertex to the opposite side.) (b) A(4,3), B(0,7). C- (a) A(1, -2), B(3,4), C(-2,6)
The rule of the slope of a line has 2 points is
[tex]m=\frac{y2-y1}{x2-x1}[/tex]A = (1, -2), B = (3, 4), C = (-2, 6)
We will take the altitude from A to the opposite side of BC
Then we will find the slope of BC first
x1 = 3 and y1 = 4. point B
x2 = -2 and y2 = 6. point C
We will substitute them in the rule above
[tex]\begin{gathered} m=\frac{6-4}{-2-3}=\frac{2}{-5} \\ m=-\frac{2}{5} \end{gathered}[/tex]The slope of BC = -2/5
Since the product of the slopes of the perpendicular line is -1, then if the slope of one is m, then the slope of the other will be -1/m, we reciprocal it and change its sign, then the slope of the altitude of BC should be 5/2
[tex]m_{\perp}=\frac{5}{2}[/tex]The form of the equation in point-slope is
y - y1 = m(x - x1)
m = 5/2
Since point A is lying on the altitude from A to BC, then
x1 = 1 and y1 = -2 point A
Substitute m and coordinates of point A in the form of the equation above
y - (-2) = 5/2 (x - 1)
[tex]y+2=\frac{5}{2}(x-1)[/tex]The equation of the altitude from A to BC is
y + 2 = 5/2 (x - 1)
if you cant read it, it says : A - is an algebraic expression that continues a variable to power of one - is an example A- is a rational number that is multiplied by aA Variable - is a number that can be written as the ratio fraction of two integers - is the expression - is an example of coefficient - are terms who variables are their exponents are the same one example is an - 7y ( - = blank ) the things you can feel in the blank is 4x, 2y, rational coefficient, like-terms, rational-number , 4, linear expression, and 6x+5
A Linear expression is an algebraic expression that contains a variable to the power of one. 3 + y is an example.
A Coefficient is a rational number multiplied by a variable. A Rational Number is a number that can be written as the ratio, or fraction or intgers.
4 in the expresson 4x is an example of a coefficient.
Like Terms are terms whose variables and their exponent are the same. One example is 9y and -7y
Find the equation of the linear function represented by the table below in slope-intercept form. X у -1 2 -8 5 -17 8 -26 Submit Answer Answer: D attempt 1 out of 2
Slope intercept form:
y = mx + b
m = (y2 - y1)/(x2 - 1) = (-8 - 1)/(2 - (-1)) = -9/(2 + 1) = -9/3 = -3
m = -3
If we take one of the point, for example (2, -8) and use it on the equation with the slope we already found:
y = -3x + b
-8 = -3(2) + b
Solving for b:
-8 = -6 + b
b = -8 + 6 = -2
b = -2
Therefore, the equation is: y = -3x -2
Answer:
y = -3x -2
The wheels on noah’s bike have a circumference of about 5 feet how many time do the wheels rotated if noah rides 40 feet
Find the constant of proportionality from a graph
Answer: 2
Step-by-step explanation:
The constant of proportionality is the same as the slope of the line. Using the slope formula with the points (0, 0) and (2, 4), [tex]\frac{4-0}{2-0}=2[/tex].
3 sisters age combined are 57. Jenny is 6 years
older then Lynn. Kim is 5 less then twice the age of
Lynn age. What are each sisters ages
Answer: Jenny = 6 | Kim = 7 | (Unknown Sister because no name) = 44
Step-by-step explanation:
Jenny = 6 years (that we already know)
6 x 2 = 12 - 5 = 7 years for Kim
7 + 6 = 13
To find the unknown age of the last sister, we will subtract 57 - 13 = 44
So the last sister is 44.
(I am very sorry if this is wrong, I am only in Middle School).
I'd angle 5=42° and angle 1=117° find the measure of angle CDF.
If angle 5= 42° and angle 1 = 117°
angle CDF = angle 5 + angle 1
=42° + 117°
=159°
What is the proportional relationship between a and bA B8. 324 940 15 Write a equation describing the relationship between a and b
Explanation:
A proportional relationship means that the two variables are related by a constant called constant of proportionality:
[tex]a=kb[/tex]k is the constant of proportionality.
To find k we have to use the values of a and b from the table:
[tex]\begin{gathered} k=\frac{a}{b} \\ k=\frac{8}{3} \\ k=\frac{24}{9}=\frac{8}{3} \\ k=\frac{40}{15}=\frac{8}{3} \end{gathered}[/tex]Answers:
• equation: ,a = 8/3 b
,• constant of proportionality:, 8/3
7. Which state had a population of eight
hundred four thousand, one hundred
ninety-four?
Answer:
I read it's south Dakota but not sure of it.
I found it from this picture