which polynomial when factored gives the zeros for the polynomial shown in the graph?
Answers
According to the given graph, the zeros of the function are x = -2 and x = 3 because the function intercepts there the x-axis.
Hence, the zeros are x = -2 and x = 3.To find the correct polynomial, we evaluate the x-values above to zero which polynomial gives a zero after evaluating it.
[tex]\begin{gathered} A\colon \\ (-2)^3+8(-2)^2+21(-2)+18=-8+32-42+18=0 \\ (3)^3+8(3)^2+21(3)+18=27+72+63+18=180 \end{gathered}[/tex][tex]\begin{gathered} B\colon_{} \\ (-2)^3-2(-2)^2-9(-2)+18=-8-8+18+18=20 \end{gathered}[/tex][tex]\begin{gathered} C\colon \\ (-2)^3-4(-2)^2-3(-2)+18=-8-16+6+18=0 \\ (3)^3-4(3)^2-3(3)+18=27-36-9+18=0 \end{gathered}[/tex]As you can observe, option C is the correct answer because it's satisfied by both x = -2 and x = 3.Related Questions
22. Distribute (c +4)(3c2-C-5).
Answers
We need to make the product of a binomial times a trinomial of the form:
[tex](c+4)\cdot(3c^2-c-5)[/tex]So we use distributive roerty, making sure that we multiply each term of the first binomial times each term of the trinomial.
We start by multiplying c times each of the three terms in the trinomial expression, and after that we do the product of "4" times each of the three terms of the trinomial:
[tex]\begin{gathered} c\cdot(3c^2)-c^2-5c+4\cdot(3c^2)-4c-20 \\ 3c^3-c^2-5c+12c^2-4c-20 \end{gathered}[/tex]and to follow this, we combine the like terms that we have produced in the product. These are the terms in c-squared, and the terms in c:
[tex]3c^3+11c^2-9c-20[/tex]Express the product of 2x2 + 3x - 10 and x +5 in standard form.
Answers
The given expression :
[tex]2x^2+3x\text{ -10 and x +5}[/tex]set up the expressions next to each other in parenthesis:
[tex](x+5)(2x^2+3x-10)[/tex]Distribute the first term in the first set of parenthesis throughout each term in the second set of parenthesis:
[tex](x+5)(2x^2+3x-10)=x(2x^2+3x-10)+5(2x^2+3x-10)[/tex]Now, distribute x over 2x^2+3x-10 and 5 too
[tex]\begin{gathered} (x+5)(2x^2+3x-10)=x(2x^2+3x-10)+5(2x^2+3x-10) \\ (x+5)(2x^2+3x-10)=2x^3+3x^2-10x+10x^2+15x-50 \\ (x+5)(2x^2+3x-10)=2x^3+13x^2+5x-50 \end{gathered}[/tex]evaluate the expression 9÷{17-8}
Answers
Solution
We have the following expression:
[tex]\frac{9}{17-8}=\frac{9}{9}=1[/tex]The reason is because we need to do the subtraction and then the division
Rewrite the following linear equation in slope intercept form. write your answer with no spaces. y-5=(x+1)
Answers
Answer:
y=x+6
Explanation:
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Given the line:
[tex]y-5=\mleft(x+1\mright)[/tex]We add 5 to both sides to obtain:
[tex]\begin{gathered} y-5+5=x+1+5 \\ y=x+6 \end{gathered}[/tex]The slope-intercept form is y=x+6.
The triangle shown is rotated 90 degrees clockwise about the origin.Next, it is translated according to the rule (x, y) -> (x-5y-2).
Answers
1ST. Rotate 90° (red)
Image of A after first transformation= (-2,2)
Next, translate 5 units to the left along the x -axis , and down to units along the y-axis. (BLUE TRIANGLE)
image of A after both tranformations= (-7,0)
my son needs help with Algebra equation for GED test
Answers
we have
3x+7=8x+24
this is an equation
Solve for x
That means
Isolate the variab;e x
so
step 1
Group terms
8x-3x=7-24
step 2
Combine like terms
5x=-17
step 3
Divide both sides by 5
5x/5=-17/5
simplify
x=-17/5Given the point slope equation: Y-2=4(x+5)What is the same equation rewritten into slope intercept form:What is the y-intercept:
Answers
The Point-Slope equation is given as
[tex]y-2=4(x+5)[/tex]STATEMENTS KLASUN What could be the final reason in the proof below? ASA HL SAS CPCTC
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Diagram
Step 02:
We must apply the properties of parallel and transversal lines.
Statements Reasons
AB || CD , AB = CD 1. Given
∠ ABD = ∠ CDB 2. Alternate interior angles
BD = DB 3. Reflexive Property
ΔABD = ΔCBD 4. Side-angle-side SAS
That is the full solution.
In the coordinate plane, the points X(−11 4) Y( 10 2) and Z(−3− 5) are reflected over the y-axis to the points X′, Y′, and Z′, respectively. What are the coordinates of X′, Y′, and Z′?
Answers
We are given the points X(-11,4), Y(10,2) and Z(-3,-5) and asked to find their reflection over the y-axis. Note that given a point of the form
when we reflect it over the y-axis, we get the red dot
Note that the reflection over the y-axis gives you a point that has the same height. This means that when we reflect over the y-axis, we fix the y coordinate of the point. What changes is the x coordinate. The change is simply obtained by multiplying the x coordinate by -1. So, we get the following table
X(-11,4)--->X'(11,4)
Y(10,2)--->Y'(-10,2)
Z(-3,-5)-->Z'(3,-5)
The digit 6 is placed in front of a 3-digit number abc, to form a 4-digit number. the sum of the 4-digit number and 300 is 8 times the original 3-digit number, find the abc
Answers
Step-by-step explanation:
abc = x
6 in front of abc means it is abc + 6000.
x + 6000 + 300 = 8x
x + 6300 = 8x
6300 = 7x
x = abc = 900
In the diagram below, describe what additional piece of information isneed to prove the triangles are congruent by SAS.
Answers
Remember that
(SAS for Similarity). In two triangles, if two sets of corresponding sides are proportional and the included angle is congruent, the triangles are similar.
so
in this problem
JK and AK ae congruent to NK and AK
is needed the measure of angle
therefore
answer is fourth optionFind 15% of $2000.00
Answers
In this question,
We need to get 15 percent of 2000 dollars,
[tex]\begin{gathered} \frac{15}{100}\text{ x }\frac{2000}{1} \\ =\text{ }\frac{30000}{100} \\ =\text{ 300 dollars} \end{gathered}[/tex]=
197Find tanexactly using an angle addition or subtraction formula.12[Hint: This diagram of special trigonometry values may help.)Choose 1 answer:3+3-3+3|--3+33+ 33 - 333-O 3 KOD3 – 33 + 3
Answers
Given:
[tex]\tan (\frac{19\pi}{12})[/tex][tex]\pi=180\text{ degre}es[/tex]So:
[tex]\begin{gathered} \tan (\frac{19\times180}{12}) \\ =\tan (\frac{3420}{12}) \\ =\tan (285) \\ =-3.732 \end{gathered}[/tex]Check the value for all opction.
(a)
[tex]\begin{gathered} =\frac{3+\sqrt[]{3}}{-3+\sqrt[]{3}} \\ =\frac{3+1.73205}{-3+1.73205} \\ =-3.732 \end{gathered}[/tex]So the first opction is equal to -3.732
Caroline likes to go to her local hair salon because she is a premier member there her membership fee cost $40 and that membership allows her to get her hair done for $24 every visit how much would it cost for two visits
Answers
From the statement, we know that:
• Carolina is a premier member, and her membership fee cost $40,
,• with the membership, she can get her hair done for $24 every visit.
If Carolina makes two visits, the cost of the visits will be: 2 * $24 = $48.
The total cost of the membership and the two visits is: $40 + $48 = $88.
Answer
Carolina must pay $88 for the two visits.
Write an equation of a line in slope-intercept form that is perpendicular to the line to y = -2x - 1 and that passes through the point (-10,4)
Answers
The slope - Intercept form of the equation of a line is written as:
y = mx + c...........................(1)
where m is the slope and
c is the intercept
the equation given in this task is:
y = -2x - 1..........................(2)
Comparing equations (1) and (2)
m = -2
That is the slope of the line = -2
A line perpendicular to the line y = -2x - 1 will have a slope:
[tex]\begin{gathered} m_1=\text{ }\frac{-1}{m} \\ m_1=\text{ }\frac{-1}{-2} \\ m_1=\text{ }\frac{1}{2} \end{gathered}[/tex]The equation of the perpendicular line will be:
[tex]y-y_1=m_1(x-x_1)[/tex]The point through which the line passes is (-10, 4)
That is, x₁ = -10, y₁ = 4
The equation of the perpendicular line becomes:
[tex]\begin{gathered} y\text{ - 4 = }\frac{1}{2}(x\text{ - (-10))} \\ y\text{ - 4 = }\frac{1}{2}(x\text{ + 10)} \\ y-\text{ 4 = }\frac{x}{2}+\text{ }\frac{10}{2} \\ y\text{ - 4 = }\frac{x}{2}\text{ + 5} \\ y\text{ = }\frac{x}{2}\text{ + 5 + 4} \\ y\text{ = }\frac{x}{2}\text{ + 9} \\ y\text{ = }\frac{1}{2}x\text{ + 9} \end{gathered}[/tex]The first two numbers in a sequence areh(1) = 4 and h(2) = 8a) If h(x) is an arithmetic sequence, write anequation:b) If h(x) is a geometric sequence, write anequation:
Answers
First term of sequence (a)=4
Second term of sequence =8
The recursive defination of arithmatic sequence is,
[tex]\begin{gathered} a_n=a_{n-1}+d \\ a_0=a=4 \\ \text{common difference d=8-4=4} \end{gathered}[/tex]The arithmatic sequence is written as,
[tex]\begin{gathered} h(x)=a_0+dn \\ h(x)=4+4n \\ h(x)=4,8,12,16 \end{gathered}[/tex]The recursive defination of geometric series is,
[tex]\begin{gathered} a_n=ra_{n-1} \\ \text{where a}_0=4 \\ 8=a_0r \\ 8=4.r \\ r=2 \\ \text{commom ratio = r=2} \end{gathered}[/tex]The geometrix series is written as,
[tex]\begin{gathered} a_n=a_{0^{}}r^n \\ h(x)=4(2)^n_{} \\ h(x)=4,8,16,\ldots\text{..} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} 1)h\mleft(x\mright)=4+4n \\ 2)h(x)=4(2)^n \end{gathered}[/tex]Question 6 of 10 If f(x) = 2x-3 -3 5 which of the following is the inverse of f(x)? > O A. f-'(x) = 5x+3 2 O B. f'(x) = 3x+2 5 O c. f'(x) 2x +3 5 O D. f-'(x) = 3x +5 2 SUBMIT
Answers
y = (2x-3)/5
To find the inverse, exchange x and y and solve for y
x = ( 2y-3)/5
Multiply each side by 5
5x = 2y-3
Add 3 to each side
5x+3 = 2y-3+3
5x+3 = 2y
Divide each side by 2
(5x+3)/2 = 2y/2
(5x+3)/2 = y
The inverse is (5x+3) /2
f^-1(x) = 5x+3
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2
A pre-image and its image have coordinates (-3,-6) and (-1, -2), respectively. Which of the following options representsthe scale factor used in the dilation?321/21/3
Answers
ANSWER
1/3
EXPLANATION
The pre-image has coordinates (-3, -6) and the image has coordinates (-1, -2)
The scale factor is the number by which the pre-image was increased or decreased in size through dilation.
To find that, we pick either of the x or y coordinates of the pre-image and image and then we have:
[tex]\text{scale factor =}\frac{coordinate\text{ of image}}{coordinate\text{ of preimage}}[/tex]Let us pick the x coordinates.
We have that the scale factor is:
[tex]SF\text{ = }\frac{-1}{-3}\text{ = }\frac{1}{3}[/tex]The scale factor is 1/3.
A person invests 4000 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5900 dollars?
Answers
Given:
A person invests 4000 dollars in a bank.
so, the initial balance = P = 4000
The interest rate = r = 5.75% = 0.0575
Compounded quarterly, n = 4
We will find the time (t) to reach 5900
We will use the following formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values then solve for (t)
[tex]\begin{gathered} 5900=4000(1+\frac{0.0575}{4})^{4t} \\ \frac{5900}{4000}=1.014375^{4t} \\ \end{gathered}[/tex]Taking the natural logarithm for both sides:
[tex]\begin{gathered} \ln \frac{5900}{4000}=4t\cdot\ln 1.014375 \\ \\ t=\frac{\ln \frac{5900}{4000}}{4\ln 1.014375}\approx6.8077 \end{gathered}[/tex]Rounding to the nearest tenth of a year
So, the answer will be t = 6.8 years
Please can someone help me draw a graph for this question
Answers
Given:
There are given the function:
[tex]f(x)=x^3+4x^2-9x-36[/tex]Explanation:
To the factor, the above function, first find the first zero of the above function:
So,
From the function:
[tex]\begin{gathered} f(x)=x^{3}+4x^{2}-9x-36 \\ f\mleft(x\mright)=(x+4)(x^2-9) \end{gathered}[/tex]Then,
[tex]\begin{gathered} f(x)=(x+4)(x^{2}-9) \\ f\mleft(x\mright)=(x+4)(x+3)(x-3) \end{gathered}[/tex]So,
The factor of the given function is shown below:
[tex]f(x)=(x+4)(x+3)(x-3)[/tex]Now,
Solve the given inequality:
[tex]x^3+4x^2-9x-36\leq0[/tex]Then,
[tex]\begin{gathered} x^3+4x^2-9x-36\leq0 \\ (x+4)(x+3)(x-3)\leq0 \\ x\leq0\text{ or -3}\leq x\leq3 \end{gathered}[/tex]Final answer:
Hence, the factor and the solution to the given inequality are shown below;
[tex]\begin{gathered} factor=(x+4)(x+3)(x-3) \\ Soution\text{ of inequality= x}\leq-4\text{ or -3}\leq x\leq3 \end{gathered}[/tex]The number line graph of the inequality is shown below:
From the above graph, we can see that the first value of x is less than and equal to -4 and for the second value, the x has lies between -3 and 3.
the variable y is directly proportional 2 x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
Answers
y is directly proportional to x, so:
y = αx
Where α = constant of proportionality
If y = -0.6 and x = 0.24:
-0.6 = α0.24
Solving for α:
α = -0.6/0.24 = -2.5
Now, if y = -31.5 :
-31.5 = -2.5*x
Solving for x:
x = -31.5/-2.5 = 12.6
david invested 89000 in an account paying an intrest rate of 3.1% compounded continuously. assuming no deposits or with drawls are made how much money to the nearest ten dollars would be in the account after 15 years?
Answers
The information we have is:
Principal, the invested amount:
[tex]P=89,000[/tex]Interest rate:
[tex]r=3.1\text{ percent }[/tex]We will need the percent as a decimal, so we divide by 100:
[tex]r=0.031[/tex]Time of the investment in years:
[tex]t=15[/tex]Since the investment is compounded continuously, we need to use the formula for continuous compounding:
[tex]A=Pe^{rt}[/tex]Where P, r, and t are the values we defined earlier. And A is the Amount after 15 years. Also, e is a mathematical constant:
[tex]e=2.7183[/tex]Substituting these values into the formula:
[tex]A=(89,000)(2.7183)^{(0.031\times15)}[/tex]Solving the operations:
[tex]\begin{gathered} A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(2.7183)^{(0.465)} \\ A=(89,000)(1.592) \\ A=141,689.7 \end{gathered}[/tex]Answer: $141,689.7
To round the answer to the nearest ten dollars, we should round the last three digits: 89.7 to the nearest tens which is 90.
So the rounded answer will be: $141,690
If a seed is planted, it has a 75% chance of growing into a healthy plant. If 8 seeds are planted, what is the probability that exactly 1 doesn't grow?
Answers
Explanation
From the question, we can see that
Probability of sucess = 0.75
Probability of failure = 1-0.75=0.25
n=8
Therefore, we will use the binomial probability distribution formula to find the probability that exactly 1 doesn't grow
[tex]P_x=(nCx)p^xq^{n-x}[/tex]For exactly one not growing we must have seven success and one failure.
[tex]\begin{gathered} P_7=8C7(0.75)^7(0.25)^1 \\ =\frac{8!}{7!1!}(0.75)^70.25 \\ =8(0.75)^7(0.25) \\ =0.2670 \end{gathered}[/tex]Answer: 0.2670
The country of Honduras has a population of 8.2 million. There were 7,172 homicide deaths there in 2014. a) Express the deaths per capita as a decimal. Round to 6 decimal places. b) Express the deaths per capita in Scientific Notation (using the digits you typed in part a). Type your answer as though you were typing it into your calculator--either with "E" or "x10^" notation-- no spaces in your answer!c) The United States has a population of about 320 million. If our homicide deaths were proportional to that of Honduras, how many deaths would we expect in the United States due to homicides? Round to the nearest person.
Answers
Population = 8.2 million = 8,200,000
Homicides = 7,172
a) Deaths per capita = Homicides / Population = 7,172 /8,200,000 = 0.000875 deaths per capita
b) 8.75 x 10 ^-4
c) Population : 320 million : 320,000,000
7,172 /8,200,000 = x / 320,000,000
Cross multiply:
320,000,000 ( 7,172 ) = 8,200,000 x
320,000,000 ( 7,172 ) / 8,200,000 = x
x = 279,883 Deaths
Use the stacked box and whisker plot in the diagram below. What conclusion can be made about the median of the two data sets?
Answers
ANSWER
The median for school #1 is greater
EXPLANATION
In a box and whisker plot, we have the following information about the data set,
The vertical line inside the box is the median.
In this problem, the median for school #1 is about 82, while the median for school #2 is about 80 (between 78 and 82). Therefore, the median for school #1 is greater.
A construction crew needs to pave a road that is 202 miles long. The crew paves 9 miles of the road each day. The length, L (In miles), that is left to be pavedafter d days is given by the following functionL (D)=202 -9DAnswer the following questions.(a) if 130 miles of the road is left to be paved, how many days has the crew beenpaving the road?1 days(b) How many miles of the road does the crew have left to pave after 13 days?
Answers
a) The crew has been paving the road for 8 days
b) The crew has 85 miles left to pave after 13 days
Explanation:The function representing the length, L (In miles), that is left to be paved
after D days is given as:
L(D) = 202 - 9D
a) If 130 miles of the road is left to be paved
L(D) = 130
Substitute L(D) = 130 into the equation L(D) = 202 - 9D and solve for D
130 = 202 - 9D
9D = 202 - 130
9D = 72
D = 72/9
D = 8
The crew has been paving the road for 8 days
b) The number of miles the crew have left to pave after 13 days
D = 13
L(D) = 202 - 9D
L(13) = 202 - 9(13)
L(13) = 85
The crew has 85 miles left to pave after 13 days 2
help!! im confused on this question of my study guide.
Answers
Solution:
Remember that corresponding Parts of Congruent Triangles are Congruent. According to this, we can conclude that the correct answer is:
CPCTC
calculate the area of a triangle with a 3.5 cm base and a 2.6 cm height
Answers
calculate the area of a triangle with a 3.5 cm base and a 2.6 cm height
the area of triangle is equal to
A=(1/2)b*h
where
b is the base and h is the height
we have
b=3.5 cm
h=2.6 cm
substitute in the formula
A=(1/2)*(3.5)*(2.6)
A=4.55 cm2
area is 4.55 square centimeters
determine whether each sequence is arithmetic geometric it neither. then find a formula for the nth term of the sequence
Answers
The sequence we are given is:
3, 5, 9, 17
and we are asked to find if it is arithmetic, geometric or neither.
To check for arithmetic we observe if there is a common difference between consecutive terms:
a(n+1) - a(n)
5-3 = 2
9-5 = 4
17-9 = 8
So clearly this is NOT an arithmetic sequence
To check for geometric sequence, we study if there is a "common ratio" by looking at the quotient of consecutive terms:
a(n+1) / a(n)
5/3
9/5
17/9
These are all different, therefore this is NOT a geometric sequence either.
Then, we answer NEITHER.
In order to find the term a(n), we notice how we build the different terms:
5 = 3 + 2
9 = 5 + 2^2
17 = 9 + 2^3
so we can try to write the a(n+1) term in terms of the previous one a(n) as:
a(n+1) = a(n) + 2^(n)
this is called a RECURRENT definition of the sequence.
Find the sum 8.7 + (-1.8)
Answers
Given data:
The given expression is 8.7+(-1.8).
The given expression can be written as,
8.7+(-1.8)=8.7-1.8
=6.9
Thus, the solution of the given expression is 6.9.