let the three consecutive numbers are,
a , a+ 1 , a+2
sum of the numbers = -9
a + a +1 + a + 2 = -9
3a + 3 = -9
3a = -9 - 3
3a = -12
a = -12/3
a = -4
so the least number is a = -4
thus the answer is -4.
Estimate the instantaneous rate of change of the function f(x)=x2−2x+1 at x=−1 using the average rate of change over successively smaller intervals.
The instantaneous rate of change of the function f(x)=x²−2x+1 at x=−1 using the average rate of change over successively smaller intervals is 4.
What is function?A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain. A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x is the input.
Here,
x²-2x+1
x=-1
(-1)²-2*-1+1
1+2+1=4
the instantaneous rate of change=4
Using the average rate of change over successively smaller intervals, the instantaneous rate of change of the function f(x)=x²-2x+1 at x=1 is 4.
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Determine the possible numbers of positive real zeros, negative real zeros, and imaginary zeros for the function. g(x) =x^5-2x^3-x^2+6
Step-by-step explanation:
Note: The term root and zero are used interchangeably.
Use Descartes Rule of Signs,
For the function, f(x), For every sign change, we have a positive root. If we have at least 2 positive roots, we either have that said number of roots or 2 less number of roots until we reach 0.
For example if we have 8 positive roots, we either have 8,6,4,2, or 0 positive roots
For the function f(-x), For every sign change we have a negative root.. If we have at least 2 negative roots, we either have that said number of roots or 2 less number of roots until we reach 0.
For example, if we have 7 possible roots, we either have 7,5,3,1 possible negative roots.
For g(x), we have 2 sign changes, so 2 positives root or none
[tex]g( - x) = ( - x) {}^{5} - 2( - x) {}^{3} - ( - x) {}^{2} + 6[/tex]
[tex]g( - x) = - {x}^{5} + 2 {x}^{3} - {x}^{2} + 6[/tex]
We have 3 sign changes, so we have 3 or 1 negative roots.
The degree of the polynomial tells us the max possible of zeroes. So the total number of zeroes is 5. That will always be the case for this polynomial so fill every row under the total number columns as 5.
The following possible combinations
2 positive zeroes, 3 negative zeroes, 0 imaginary zeroes
2 positive zeroes, 1 negative zeroes, 2 imaginary zeroes
0 positive zeroes, 3 negative zeroes, 2 imaginary zeroes
0 positive zeroes, 1 negative zeroes, 4 imaginary zeroes
of the exterior angle of a regular octagon measures (11x+1), fond the value of x.
Recall that a regular octagon is an image with eight equal sides and equal internal angles.
So, considering that the exterior angles of any polygon should add to 360 degrees, the addition of the 8 equal exterior angles of the octogon should add to 360.
We are given the expression for each exterior angle as: (11 x + 1)
then, 8 times this should render 360 degrees, and we write an equation that gives such relationship as:
8 * (11 x + 1) = 360
use distributive property to eliminate the parenthesis
88 x + 8 = 360
subtract 8 from both sides:
88 x = 360 - 8
88 x = 352
x = 352 / 88
x = 4
Therefore please type 4 in the given box.
An automobile battery manufacturer claims that its midgrade battery has amean life of 50 months with a standard deviation of 6 months. Suppose thedistribution of battery lives of this particular brand is approximately normal.ba. On the assumption that the manufacturer's claims are true, find theprobability that a randomly selected battery of this type will last less than 48months.Your answer6b. On the same assumption, find the probability that the mean of a randomsample of 36 such batteries will be less than 48 months.
Given data:
The given mean life is m=50 months.
The given standard deviation is s=6 months.
The given value of battery life is x= 48 months.
The expression for the probability of that a randomly selected battery will last less than 48 months is,
[tex]\begin{gathered} P(Z<\frac{x-m}{s})=P(Z<\frac{48-50}{6}) \\ =P(Z<-\frac{1}{3}) \end{gathered}[/tex]Refere the Z-table the value of the above expression is 0.3707.
Thus, the probability that a randomly selected battery will last less than 48 months is 0.3707.
Write the equation of the line in slope-intercept form. Through the points (-8, 15) and (6, 15)
Question: Write the equation of the line in slope-intercept form. Through the points (-8, 15) and (6, 15)
Solution:
The equation of the line in slope-intercept form is :
y = mx + b
where m is the slope of the line, and b is the y-coordinate of the y-intercept of the line. Now, the slope of the line is given by the following formula:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]Where (X1,Y1) and (X2,Y2) are points on the line. In our case, we have that:
(X1, Y1) = (-8,15)
(X2,Y2) = (6,15)
Replacing these values in the equation of the slope we obtain:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}\text{ =}\frac{15-15}{6-(-8)}\text{ = 0}[/tex]then we have a horizontal line, because the slope is 0, for that, the equation of the line would be:
y = mx + b = 0(x) + b
then
y = b
now, take any point on the line, for example (x,y) = (6,15). Replacing this value in the previous equation, we obtain that the equation of the line is given by:
[tex]y\text{ = 15}[/tex]Chauncey is studying a 250-mg sample of a radioasubstance has a half-life of 5 days. Write an equatsubstance, s, is left after n days?aS =b= 250 (3)s = 250 (3)s = 250 (0.5)s = 250 (0.5)$5nd
Answer:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]Step by step explanation:
Exponential functions are represented by the following expression:
[tex]\begin{gathered} f(x)=ab^x \\ \text{where,} \\ a=\text{initial amount} \\ b=\text{decay factor} \\ x=\text{time(days)} \end{gathered}[/tex]Then, for this situation, we have an initial amount of 250, a decay factor of (0.5) in 5 days:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]Consider the following graph of two functions.(8-1-2)Step 3 of 4: Find (8.5(-2)Enable Zoom/Pan866) = -3010-35SG) = x + 3
The question requires that we evaluate the value of:
[tex](g\cdot f)(-2)[/tex]Recall that:
[tex]\left(g\cdot \:f\right)\left(x\right)=g\left(x\right)\cdot \:f\left(x\right)[/tex]Therefore, we have that:
[tex]\left(g\cdot\:f\right)\left(-2\right)=g\left(-2\right)\cdot\:f\left(-2\right)[/tex]We can get the values of g(-2) and f(-2) from the graph as shown below:
Therefore, we have:
[tex]\begin{gathered} g(-2)=5 \\ f(-2)=1 \end{gathered}[/tex]Hence, we can calculate the composite function to be:
[tex]\begin{gathered} (g\cdot f)(-2)=5\times1 \\ (g\cdot f)(-2)=5 \end{gathered}[/tex]write each percent as a fraction in simplest form 1. 80%=
4/5
Explanation:
80%
[tex]\begin{gathered} \frac{80}{100}=\text{ }\frac{8}{10} \\ \text{this we divided both numerator an denominator by 10 } \end{gathered}[/tex]dividing both numerator an denominator by 2:
[tex]\frac{8}{10}=\text{ }\frac{4}{5}[/tex]fraction in simplest form = 4/5
How large is the sample space when rolling a die five times?
7776
ExplanationThe size of the sample space is the total number of possible outcomes.for example, for a dice, the possible outcomes are 1, 2,3 4, 5 or 6, when rolling a dice five times we have:
Each time you roll the dice there are 6 possible outcomes. (1 of 6)
[tex]6[/tex]now, you have to roll the dice five times
then
[tex]\text{sample space=6}^5=6\cdot6\cdot6\cdot6\cdot6=7776[/tex]I hope this helps you
solve the equation by completing the square.4x(x + 6) = -40
Answer:
The solution to the equation is;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]Explanation:
Given the equation below;
[tex]4x(x+6)=-40[/tex]Expanding the bracket we have;
[tex]4x^2+24x=-40[/tex]dividing through by 4;
[tex]\begin{gathered} \frac{4x^2}{4}+\frac{24}{4}x=-\frac{40}{4} \\ x^2+6x=-10 \end{gathered}[/tex]To solve by completing the square, let us add the square of half of 6 to both sides;
[tex]\begin{gathered} x^2+6x+(\frac{6}{2})^2=-10+(\frac{6}{2})^2 \\ x^2+6x+9=-10+9 \\ x^2+6x+9=-1 \\ (x+3)^2=-1 \end{gathered}[/tex]taking square roots of both sides;
[tex]\begin{gathered} x+3=\sqrt[]{-1} \\ x+3=\pm i \end{gathered}[/tex]So;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]Therefore, the solution to the equation is;
[tex]\begin{gathered} x=-3+i \\ or \\ x=-3-i \end{gathered}[/tex]True or false: Are vertical angles only congruent if they are marked, and why ?
The vertical angles formed when two lines intersected each other at a point
The vertical angles are always equal in mesuaresSorry
So you do not want a mark to know they are equal
The answer is false
Find a cofunction with the same value as the given expression.COS(3pi/7)
We will have the following:
[tex]\cos (\frac{3\pi}{7})=\sin (\frac{\pi}{2}-\frac{3\pi}{7})[/tex][tex]=\sin (\frac{\pi}{14})[/tex]So, the cofunction with the same value as the expression gu
Translate the sentence into an inequality.Twice the difference of a number and 10 is greater than 29.
We will have the following:
[tex]2(x-10)>29[/tex]I you could just give me the answer that would be great no explanation needed:)
f(n) = -1.2n + 38.1
Hence, for an additional race
the finishing time, f(n+1), is given
f(n+1) = -1.2(n+1) + 38.1 = -1.2n + 38.1 -1.2
Which implies that
f(n+1) = f(n) - 1.2
This implies that the finishing time decreases by 1.2minutes
The model predicts that for each additional race a runner has run, the finishing time decreases by about 1.2 minutes
triangle QRS is reflected across the y axis to create triangle QRS complete the rule that describes the coordinates of triangle QRS after the reflection has occurred
The rule for describing the reflection of the given figure QRS is as follow:
If the coordinate of each point of the triangle is (x,y), then, after the reflection across the y axis the new coordinates become:
(x,y) => (-x,y)
Answer:
[tex](x',y')=(-x,y)[/tex]
A new car worth $27,000 is depreciating in value by $3,000 per year. After how many years will the car's value be $3,000?
The equation for the worth of car after x number of years is,
[tex]\begin{gathered} y=27000-3000\cdot x \\ =27000-3000x \end{gathered}[/tex]Substitute 3000 for y in the equation to obtain the value of x.
[tex]\begin{gathered} 3000=27000-3000x \\ 3000x=27000-3000 \\ x=\frac{24000}{3000} \\ =8 \end{gathered}[/tex]So after 8 years the worth of car is $3000.
To solve rational equation shown below, find the common denominator
Given:
[tex]\frac{3}{2x+1}=\frac{5}{4x+3}[/tex][tex]3(4x+3)=5(2x+1)[/tex][tex]12x+9=10x+5[/tex][tex]12x-10x=5-9[/tex][tex]2x=-4[/tex][tex]x=-\frac{4}{2}[/tex][tex]x=-2[/tex]A guidebook says that one night at a mid-range hotel the capital city, republica cost between $25 an $40 us dollars. The hotel capital city offers a one week rental for 150 rp ( republica pounds) the current exchange rate is 1=0.0147 usd ($us dollars) does the price per night at the hotel capitol suggest that it a mid range hotel?
To determine if the hotel capital suggests is a mid-range hot, we need to do the conversion:
[tex]150rp\cdot\frac{0.0147\text{usd}}{1rp}=2.2\text{ usd}[/tex]By the exchange rate 1rp=0.0147usd, notice the rental week of Hotel Capital city is $2.2
Then, for the night:
[tex]\frac{2.2}{7}=0.31[/tex]Then, a night at Hotel Capital City would be $0.31. It is not a mid-range hotel.
Which binomial is a factor of 49x2 + 84xy + 36y2?А. 7х + 6уВ. x+6yC. х- 6уD. 7х- 6уPLEASE HELP ASAP I WILL GIVE YOU BRAINLIEST!!!!!!
Factoring 2nd-degree polynomials make use of the factors of the numerical coefficient of the first and last term.
The numerical coefficient of our first term is 49. The possible factors of 49 are 1 and 49, 7 and 7, -1 and -49, and -7 and -7.
The numerical coefficient of our last term is 36. The possible factors of 36 are 1 and 36, 6 and 6, 12 and 3, 4 and 9, -1 and -36, -6 and -6, -3 and -12, and -4 and -9.
Since the choices only show 1,7 and 6,6, we will only be focusing on these factors. Our goal here would be for us to have a result of +84 when the two pairs of factors are multiplied and then multiplied to two.
The second row gives us the middle term +84. Therefore, the factors of the polynomial are (7x + 6y)(7x + 6y). The answer is Option A.
PLEAS HELP ANSWER ASAP
The slopes of a quadrilateral are -1/2, 3/2, -1/2, and 3/2. What conclusion about this shape can be made?
A. The quadrilateral is a parallelogram, because there are two pairs of equal slopes, and Thus two pairs of parallel opposite sides.
B. The quadrilateral is a trapezoid, because there are two pairs of equal slopes, and thus two pairs of parallel opposite sides.
C. The quadrilateral is a parallelogram, because there is one pair of equal slopes, and thus one pair of parallel opposite sides.
D. The quadrilateral is a trapezoid, because there is one pair of equal slopes, and thus one pair of parallel opposite sides.
Answer
the first one, A.
Step-by-step explanation:
hope this helps
Which can be the first step in finding the equation of the line passing through (5,-4) and (-1,8)
The equation of the line, in slope-intercept form, is written as
[tex]y=mx+b[/tex]wherein m is the slope of the line and b is the y-intercept.
The first step to solve the equation of the line that passes through two points is to find the slope of the line given two points. The slope of the line can be computed using the equation
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]For points (5, -4) and (-1, 8), the slope of the line is
[tex]m=\frac{8-(-4)}{-1-5}=\frac{12}{-6}=-2[/tex]Now, we have the initial equation of the line written as
[tex]y=-2x+b[/tex]To solve for the value of b, we use one of the points and substitute it on the initial equation above. In my case, I will be using points (5,-4), we have
[tex]\begin{gathered} -4=-2(5)+b \\ -4=-10+b_{} \\ b=10-4 \\ b=6 \end{gathered}[/tex]Hence, the equation of the line that passes through (5,-4) and (-1,8) is
[tex]y=-2x+6[/tex]QL An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the investment when interest is compounde monthly, (c) daily, and (d) continuously. Then find (e) the doubling time I for the given interest rate. P = $2500, r=3.95%, t = 8 yr Te luture value ore vesmen we erst is Compouleu annually iS J400.29 (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $3,427.30 (Type an integer or a decimal. Round to the nearest cent as needed.) c) The future value of the investment when interest is compounded daily is $3429.02 (Type an integer or a decimal. Round to the nearest cent as needed.) d) The future value of the investment when interest is compounded continuously is $ 3429.08 (Type an integer or a decimal. Round to the nearest cent as needed.) e) Find the doubling time for the given interest rate. T= yr (Type an integer or decimal rounded to two decimal noon
User asks to solve part e of the problem.
We are asked to find the doubling time for the interest rate in the case of continuous compounding.
Recall that the formula for the continuously compounding interest rate is:
[tex]A=P\cdot e^{(r\cdot t\}}[/tex]Then, we need to solve when the value "A" (Accrued value) doubles the principal P, that is:
[tex]2P=P\cdot e^{(r\cdot t\}}[/tex]Dividing both sides by P and then applying natural logarithms (ln) on both sides, we get:
[tex]\begin{gathered} 2P=P\cdot e^{(r\cdot t\}} \\ 2=e^{(r\cdot t)} \\ \ln (2)=r\cdot t \\ \ln (2)=0.0395\cdot t \\ t=\frac{\ln l(2)}{0.0395} \\ t=17.548 \end{gathered}[/tex]which gives us approximately 17.548 years which we round to two decimals as: 17.55 years
need help asap will give you 5 stars! need a quick worker!
Explanation
The question wants us to get the length of the missing side
To do so, we will use the trigonometric ratio:
[tex]undefined[/tex]The endpoints of AB are A(9,4) and B(5,-4). The endpoints of its image after a dilation are A'(6,3) and B'(3,-3). Find the scale factor and explain each of your steps.
It is given that the line segment AB is dilated to give another line segment A'B'.
Since it is a dilation, the length of the image will be a multiple of the length of the preimage.
To find the scale factor, divide the length of the image by the length of the preimage.
Recall that the length of a line segment with endpoints (a,b) and (c,d) is given as:
[tex]\sqrt[]{(c-a)^2+(d-b)^2}[/tex]To find the length AB of the preimage, substitute the coordinates (a,b)=(9,4) and (c,d)=5,-4) into the formula:
[tex]AB=\sqrt[]{(5-9)^2+(-4-4)^2}=\sqrt[]{(-4)^2+(-8)^2}=\sqrt[]{16+64}=\sqrt[]{80}[/tex]To find the length A'B' of the image, substitute the coordinates (a,b)=(6,3) and (c,d)=(3,-3) into the formula:
[tex]A^{\prime}B^{\prime}=\sqrt[]{(3-6)^2+(-3-3)^2}=\sqrt[]{(-3)^2+(-6)^2}=\sqrt[]{9+36}=\sqrt[]{45}[/tex]Divide the length of the image by the length of the preimage to calculate the scale factor:
[tex]\frac{A^{\prime}B^{\prime}}{AB}=\frac{\sqrt[]{45}}{\sqrt[]{80}}=\sqrt[]{\frac{45}{80}}=\sqrt[]{\frac{9}{16}}=\frac{\sqrt[]{9}}{\sqrt[]{16}}=\frac{3}{4}[/tex]Hence, the scale factor is 3/4.
The answer is 3/4.
Can someone help me with this question?
So the average decrease will be 50% for the season of 5 weeks as the definition of percent decrease will be "The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease".
What is percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease.
Here,
The percent decrease will be,
48000-24000=24000
24000/48000*100=50%
24000-12000=12000
12000/24000*100=50%
12000-6000=6000
6000/12000*100=50%
6000-3000=3000
3000/6000*100=50%
3000-1500=1500
1500/3000*100=50%
Due to the definition of percent decrease being a season of five weeks, the average decrease will be 50% "The percentage decrease is the difference between the starting and ending values. Regardless of the units, it shows a percentage decline in value relative to the starting point. The amount of decrease is the difference between the initial and final amounts ".
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Is it always, sometimes, or never true that an equation in slope-intercept form represents a direct variation? Support your answer with examples
It is always true an equation in slope-intercept form represents a direct variation.
For example, the amount of money you earn by hours.
Let:
x = Number of hours
y = Amount of money
a = Money per hour = $5
The equation will be:
[tex]\begin{gathered} y=ax \\ y=5x \end{gathered}[/tex]2. Given that the quadrilateral PQRS is a parallelogram, ST = 6x + 3 andQT= 4x + 27, what is the length of QS?161145138150None of these answers are correct
Given: The quadrilateral PQRS
To Determine: The value of QS
Solution
Please note that the diagonal of a quadrilaterals bisect each other. This is as shown below
Therefore ST equals QT
[tex]\begin{gathered} ST=QT \\ 6x+3=4x+27 \\ 6x-4x=27-3 \\ 2x=24 \\ x=\frac{24}{2} \\ x=12 \end{gathered}[/tex][tex]\begin{gathered} QS=ST+QT \\ QS=6x+3+4x+27 \\ QS=10x+30 \\ QS=10(12)+30 \\ QS=120+30 \\ QS=150 \end{gathered}[/tex]Hence QS = 150
Im trying to plot a slope function on a graph y=2x+3
1) To plot a linear equation, like y=2x +3 let's visualize the graph
2) Set this function as an equation, to find the root of that function the x coordinate
y= 2x +3 Turn this to an equation
2x +3 =0 Subtract 3 from both sides
2x +3 -3 = -3
2x+0=-3 Divide both sides by 2
x=-3/2 -3/2 = -1.5
Looking at the function, we can see that the slope m=2, m>0, and the y-intercept is 3
Now we can set a table, where we can choose any value for x and then plug it into the function
x = 0 , y = 2(0) +3 y= 3
x= 1, y = 2(1) +3 y= 5
x=-1.5 y = 2(-1.5) +3 y=0
x | y
0 3
1 5
-1.5 0
At least 3 points already determine a line
Our graph must be like this:
Evaluate expressions with parenthesesWhere can we put parentheses in 45 – 22 + 9 to make it equivalent to 14?Choose 1 answer:A45 – (22 +9)(45 – 22) +9Stuck? Review related articles/videos or use a hint.Report
Answer
45 – (22 +9)
Explanation
Given the expression
45 - 22 + 9
In order to rearrange the expression to get 14, this can be expressed as:
= 45 - (22 + 9)
= 45 - 31
= 14
Hence the required answer is 45 – (22 +9)
#14 iW Ua. Give another name for UVb. Name a ray with endpoint Xc. Match each ray with its opposite ray.
Given
Find
a) another name for UV
b) Name a ray with endpoint X
c) Match each ray with its opposite ray.
Explanation
a) another name for UV is VU
b) ray with endpoint X is UX
c)
i) UZ is opposite to UY
ii) UV is opposite to UW
iii) UX is opposite to UT
Final Answer
Hence ,
a) VU
b) UX
c) UY , UW , UT