Given
(x+6) and (x+9) are the factors of a polynomial.
To find: Which values of x would make a polynomial equal to zero?
Explanation:
It is given that,
(x+6) and (x+9) are the factors of a polynomial.
Then, the polynomial can be written as,
[tex]p(x)=(x+6)(x+9)[/tex]Also, if (x+a) is a factor of a polynomial p(x).
Then, p(-a)=0.
Therefore,
For the factors (x+6) and (x+9),
The polynomial p(x) is zero at x=-6, and x=-9.
Hence, the answer is x = -6, -9.
I need help it says identity the equivalent expression for the expression above
Given:
Expression is
[tex]=\frac{m^{\frac{1}{3}}}{m^{\frac{1}{5}}}[/tex]Required:
Equivalent expression for the given expression.
Explanation:
We will use
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]So,
[tex]\begin{gathered} \frac{m^{\frac{1}{3}}}{m^{^{\frac{1}{5}}}}=m^{\frac{1}{3}-\frac{1}{5}} \\ =m^{\frac{2}{15}} \end{gathered}[/tex]Answer:
Hence, 1st option is correct.
Evaluate 2g - 4, if the value of g=5
Put g=5 in 2g-4.
[tex]\begin{gathered} 2g-4=2\times5-4 \\ =10-4 \\ =6 \end{gathered}[/tex]The value is 6.
what is the equation for the line that passes through the given point and is parallel to the graph of y=3x-2; (3,2)
The function f(T) = a (x - h[ + k is shown in the graph below. 2 0 6 N What is the value of a? What is the value of h? 1 What is the value of k?
As we can see from the graph, the function is shifted from one unit to the right, and two units up, and it is in an inverse way.
Then, we can express this as:
[tex]-1\cdot|x-1|+2[/tex]The value for a = -1.
The value for h = 1.
And the value for k = 2.
If 36 identical motors are installed in a drying oven on blowers for that oven and the total current for all 36 motors is 85 amps, what is the approximate current for each motor? Round your answer to two decimal places.
Step 1:
Given data
Number of identical motors = 36
Total current for all 36 motors = 85 amps
Step 2: Calculate current for each motor
If the total current in all 36 motors = 85 amps
To find the current in 1 motor, you will divide the total number of current with the total number of motors.
Step 3: Final answer
[tex]\begin{gathered} \text{Current for each motor = }\frac{Total\text{ current}}{\text{Total number of motors}} \\ =\text{ }\frac{85}{36} \\ =\text{ 2.36 amps/motor} \end{gathered}[/tex]Current for each motor = 2.36 amps/motor
Which of the functions is an exponential function? F(x)=-3x^-1F(x)=-3(2)^2F(x)=-3(1)^xF(x)=-3x^2
For this problem we recall the definition of an exponential function:
[tex]\begin{gathered} f(x)\text{ is an exponential function if } \\ f(x)=a\cdot b^{kx} \\ \text{Where a}\ne0,\text{ k}\ne0\text{ and b}\ne1 \end{gathered}[/tex]Answer: F(x)= - 3 (2)^x
Hello can you help with the angles for each letter
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
diagram
Step 02:
angles:
we must analyze the diagram to find the solution.
a = (180 - 115)° = 65°
b = 115°
c = 65°
d = (180 - 135)° = 45°
f = 110°
g = (180 - 110)° = 70°
h = 110°
j = (180 - 65)° = 115°
k = (180 - 45 - 70)° = 65°
m = (180 - 42)° = 138°
n = (180 - 42 - 65)° = 73°
p = (180 - 73)° = 107°
q = (180 - 107)° = 73°
r = (180 - 68)° = 112°
s = (540 - 135 - 115 - 107 - 115)° = 68°
t = (360 - 124 - 73 - 112)° = 51°
u = 135°
v = 45°
w = (180 - 45 - 65)° = 70°
x = (180 - 65)° = 115°
That is the full solution.
Suppose sin(A) 2/5 Use the trig identity sin(A) + cos(A) = 1 and the trig identity tan(A)= sin(A)/cos(A) to find can(A) in quadrant I. Round to ten thousandth.
Trigonometric identity is tanθ ≅ 0.4364
[tex]$\sin A=\frac{2}{5}$[/tex]
[tex]$\cos ^2 A=1-\sin ^2 A=\frac{21}{25}$[/tex]
[tex]$\cos A=\frac{\sqrt{21}}{5}$[/tex]
[tex]$\tan A=\frac{\sin A}{\cos A}=\frac{\left(\frac{2}{5}\right)}{\left(\frac{\sqrt{21}}{5}\right)}=\frac{2}{\sqrt{21}} \cong 0.4364$[/tex]
Sine, cosine, tangent, cosecant, secant, and cotangent are the functions. All of these trigonometric ratios are defined using the sides of a right triangle, specifically the adjacent, opposite, and hypotenuse sides.
The even-odd identities relate the value of a trigonometric function at a given angle to the value of the function at the opposite angle. tan ( − θ ) = − tan θ tan ( − θ ) = − tan θ cot ( − θ ) = − cot θ cot ( − θ ) = − cot θ sin ( − θ ) = − sin θ sin ( − θ ) = − sin θ csc ( − θ ) = − csc θ csc ( − θ ) = − csc θ
To learn more about Trigonometric identity visit:https://brainly.com/question/24377281
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Zoe and Marsden are working with expressions with rational exponents. Zoe believes V2+ V8 is equivalent to 2.21. Marsden believes v2 + V8 is equivalent to 3.21. Use the properties of exponents to decide who is correct. Write the correct answer in the space provided.
Explanation
the properties of exponents
[tex]\begin{gathered} \sqrt[n]{a}=a^{\frac{1}{n}} \\ \sqrt[n]{a^{n^{}}b^n}\text{ = ab} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}[/tex]Step 1
Zoe believes
[tex]\sqrt[]{2}+\sqrt[]{8\text{ }}=\text{ 2.21}[/tex]Marsden Believes
[tex]\sqrt[]{2}+\sqrt[]{8}=3.21[/tex]Step 2
[tex]\sqrt[]{8}=\sqrt[]{4}\cdot\sqrt[]{2}=\text{ 2}\sqrt[]{2}[/tex]then
[tex]\begin{gathered} \sqrt[]{2}+\sqrt[]{8}=\text{ }\sqrt[]{2}+2\sqrt[]{2}=3\sqrt[]{2} \\ \text{also } \\ \sqrt[]{2}=\text{ 1.4142} \\ so, \\ \sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24 \end{gathered}[/tex]then
[tex]\sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24[/tex]I hope this helps you
For each system of equations below, determine whether it has one solution, no solution, or infinite solutions. 4x+9y=1510x+15y=25
Let's solve the system of linear equations
[tex]\begin{gathered} 4x+9y=15 \\ 10x+15y=25 \end{gathered}[/tex]Using the z score formula use the information below to find the value of
Explanation
Given that
[tex]\begin{gathered} z=-4.80 \\ x=23.55 \\ \mu=32.67 \end{gathered}[/tex]Using the z-score formula;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ -4.80=\frac{23.55-32.67}{\sigma} \\ -4.80\sigma=-9.12 \\ \sigma=\frac{-9.12}{-4.80} \\ \sigma=1.9 \end{gathered}[/tex]Answer: 1.9
give the following five-number summary, find the interquartile range. 29, 37, 50, 66, 94
we have the data set
29, 37, 50, 66, 94
step 1
Order the data from least to greatest
so
29, 37, 50, 66, 94
step 2
Find the median
29, 37, 50, 66, 94
the median is 50
step 3
Calculate the median of both the lower and upper half of the data
29, 37, 50, 66, 94
the lower half ------> (29+37)/2=33
upper half -------> (66+94)/2=80
step 4
The IQR is the difference between the upper and lower medians
so
80-33=47
the answer is 47Show work and/or describe how the expression for the completing the square method and the expression associated with the quadratic formula are equivalent.
Given a general quadratic expression:
[tex]ax^2+bx+c=0[/tex]firs, lets divide both sides of the equation by 'a' :
[tex]\begin{gathered} (\frac{1}{a})(ax^2+bx+c=0)^{} \\ \Rightarrow\frac{a}{a}x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x+\frac{c}{a}=0 \end{gathered}[/tex]next, we can move the term c/a to the right side of the equation:
[tex]\begin{gathered} x^2+\frac{b}{a}x+\frac{c}{a}=0 \\ \Rightarrow x^2+\frac{b}{a}x=-\frac{c}{a} \end{gathered}[/tex]now we are ready to complete the square on the left side. What we have to do, is to take the constant that is multiplying x (in this case,b/a), and first, we divide it by 2, and then elevate to the square the result:
[tex]\begin{gathered} \frac{b}{a}\frac{\cdot}{\cdot}2=\frac{b}{2a} \\ \Rightarrow(\frac{b}{2a})^2=\frac{b^2}{4a^2} \end{gathered}[/tex]then, adding this number on both sides of the equation, we get:
[tex]x^2+\frac{b}{a}x+\frac{b^2}{4a}=-\frac{c}{a}+\frac{b^2}{4a^2}[/tex]which we can write like this:
[tex](x+\frac{b}{2a})^2=\frac{-4ac+b^2}{4a^2}_{}[/tex]applying the square root on both sides,we get the following:
[tex]\begin{gathered} \sqrt[]{(x+\frac{b}{2a})^2}=\sqrt[]{\frac{b^2-4ac}{4a^2}}=\pm\frac{\sqrt[]{b^2_{}-4ac}}{2a} \\ \Rightarrow x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]finally, we can solve for x:
[tex]\begin{gathered} x+\frac{b}{2a}=\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]as we can see, if we have a general quadratic equation, we can us the completing the square method to deduce the quadratic formula
A composite figure is shown. 10 ft А 6 ft - 10 ft तो 12 ft B C 12 ft 4 ft Determine whether each statement about the composite figure is correct. Choose True or False for each statement. a. The area of region B is the same as the area of region C. True False b. The area of region A is double the area of region C. True False C. The area of the composite figure is 180 square feet. True False True False d. The sum of the areas of regions B and C is less than the area of region A.
ANSWERS
a. True
b. False
c. True
d. False
EXPLANATION
a. Regions B and C are both rectangles with the same side lengths. Therefore, they are congruent rectangles, so the areas must be the same.
b. For this item we have to find the areas of region A and C.
Region A is a trapezoid. The area is:
[tex]A_A=\frac{(10+18)}{2}\times6=84ft^2[/tex]The area of region C is:
[tex]A_C=12ft\times4ft=48ft^2[/tex]Two times the area of region C is 96ft², so this statement is false.
c. In the previous item we found the area of regions A and C. From item a we know that the area of region C is the same area of region B. The area of the figure is:
[tex]A=A_A+A_B+A_C=84+48+48=180ft^2[/tex]This statement is true.
d. Since regions B and C have the same area, saying 'the sum of the areas of regions B and C' is the same as saying 'double the area of region C'. From item b, we know that the sum of areas B and C is 96ft², and area A is 84ft².
Area A is less than the sum of areas B and C. Therefore this statement is false.
whats my test mean by Match the two numbers with their least common multiple (LCM). MatchTermDefinition 8 and 4A) 40 8 and 6B) 24 8 and 10C) 8
LCM of 8 and 10 = 40 ((option C)
LCM of 8 and 4 = 8 (option B)
LCM of 8 and 6 = 24 (option A)
Explanation:We find each of the least common multiple (LCM) of the numbers then we match the result.
We pick the common numbers in both. Then multiplied by other numbers not common to both
8 = 2 × 2 × 2
4 = 2 × 2
LCM of 8 and 4 = 2×2×2
LCM of 8 and 4 = 8 (option B)
8 = 2 × 2 × 2
6 = 2 × 3
LCM of 8 and 6 = 2×2×2×3
LCM of 8 and 6 = 24 (option A)
8 = 2 × 2 × 2
10 = 2 × 5
LCM of 8 and 10 = 2 × 2 × 2 × 5
LCM of 8 and 10 = 40 ((option C)
Can someone help me with these geometry questions sorry it’s a two parter.
In this problem, we are trying to choose between using a permutation and a combination.
The main difference between the two is the order.
In a combination, order doesn't matter, but it does matter in a permutation. Since the coach is choosing people based on how they performed, this will be a permutation.
For the first box on your screen, you should drag and drop the "P" variable for permutation.
Next, we need to apply the permutation formula:
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]I'm assuming there are a total of 14 players on the team? So we will let
[tex]\begin{gathered} n=14 \\ r=3 \end{gathered}[/tex]Where n represents the total number of players, and r represents the number of people being chosen based on performance. Then we have:
[tex]\frac{14!}{(14-3)!}=\frac{14!}{11!}[/tex]You can drag the 14! to the numerator and the 11! to the denominator.
Finally, we need to simplify to get the final answer. We can always use a calculator, but I'll show the steps for simplifying here:
[tex]\begin{gathered} \text{ Rewrite}14! \\ \frac{14\cdot13\cdot12\cdot11!}{11!} \end{gathered}[/tex][tex]\begin{gathered} \text{ Cancel the }11! \\ \\ \frac{14\cdot13\cdot12\cdot\cancel{11!}}{\cancel{11!}} \end{gathered}[/tex]Multiply the remaining values:
[tex]14\cdot13\cdot12=2184[/tex]The coach has 2184 ways to choose a player.
Given the function g(x) =x^2 +9x+18, determine the average rate of change of the function over the interval -8_
The given function is:
[tex]undefined[/tex]Sam bought a stereo that listed for $795. He saved 20% of the originalcost by buying it at a sale and paying cash. How much did he pay for thestereo?a. $159b. $636c. $63.60d. $795
Given:
a.) Sam bought a stereo that was listed for $795.
b.) He saved 20% of the original cost by buying it at a sale and paying cash.
We will be using the following formula:
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex]We get,
[tex]\text{ Discounted price = Original Price x (}\frac{100\text{\% - \% Discount}}{100})[/tex][tex]\text{= 795 x (}\frac{100\text{\% - 20\%}}{100})[/tex][tex]\text{ = 795 x (}\frac{80}{100})[/tex][tex]\text{ = 795 x 0.80}[/tex][tex]\text{ Discounted Price = \$}636.00[/tex]Therefore, Sam paid $636 for the stereo.
The answer is letter B.
What is the quotient and the remainder of 491÷3
To find the quotient of 491 by 3,
We have to divide 491 by 3
So,
[tex]\frac{491}{3}=163.66[/tex]Answer : 163.66
Verify my answer an explanation on how to do this
Given:
In the California Community Colleges an undergraduate student survey was taken that compares the class of the student to their opinion on whether or not they favor or oppose same sex marriages . The following data is a summary of the survey taken by questioning 500 undergraduate students.
Required:
If a student from the survey is selected at random , then we need to find the probability that the student favors same sex marriages , given that the student is not a Senior
Explanation:
Here we need the probability in which students are in the favor of sex marrige but noe senior
[tex]276-53=223[/tex]so 223 students are in the favors sex marrige but not seniors
so the probability is
Final answer:
[tex]\frac{223}{500}[/tex]shania traveled 310 miles in 5 hours. if she remain at a constant rate , how many miles can she travel in 1 hour
A kitche sa tabletop that is a rectangle 24 in long and 18 in wide.Rita is an interior designer and wants to cover the tabletop in small tiles.She knows the area each bag of tiles covers, but only in square centimeters.(a) Find the area of the tabletop in square centimeters. Do notround intermediate computations and round your finalanswer to two decimal places. Use the table of conversionfacts, as needed.cm(b) The designer wants to cover the tabletop with tiles. Shedoesn't have any to begin with and she can't buy partialbags of tiles. Each bag of tiles covers 260 cm². How manywhole bags of tiles does the designer need to buy tocompletely cover the tabletop?bags(c) If each bag of tiles costs $3.76, how much will she need tospend on tile? Write your answer to the nearest cent.ExplanationCheckConversion facts for length2.54 centimeters (cm)= 30.48 centimeters (cm)≈ 0.91 meters (m)1 inch (in)1 foot (ft)1 yard (yd)1 mile (mi)XNote that means "is approximately equal to".For this problem, treat as if it were = .1.61 kilometers (km)5?I need help with this math problem.
Given: a tabletop that is a rectangle 24 in long and 18 in wide.
Find: (a) the area of the tabletop in square centimeters
(b) The designer wants to cover the tabletop with tiles. She doesn't have any to begin with and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm². number of bags of tiles does the designer need to buy to completely cover the tabletop
(c)If each bag of tiles costs $3.76, how much will she need to spend on tiles.
Explanation: (a)
[tex]1\text{ inch= 2.54cm}[/tex]so the length of the tabletop in cm will be
[tex]24\times2.54=60.96cm[/tex]and the breadth of the tabletop in cm will be
[tex]18\times2.54=45.72cm[/tex]the area of the tabletop will be
[tex]\begin{gathered} l\times b \\ =60.96\times45.72 \\ =2787.09cm^2 \end{gathered}[/tex](b) The designer wants to cover the tabletop with tiles and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm² so the numbe rof bags designer needs to buy to cover the tabletop is
[tex]\begin{gathered} \frac{2787.09}{260} \\ =10.71 \end{gathered}[/tex]it means that designer needs to buy 11 bags of tiles to cover the tabletop.
(c) If each bag of tiles costs $3.76.the the total cost will be equal to
[tex]3.76\times11=41.36\text{ \$}[/tex]Is Rashida’s work correct? If not, what is the first step where Rashida made a mistake?- Her work is correct - First mistake was in Step 1- First mistake was in Step 2- First mistake was in Step 3*pls help!*
Answer:
First mistake was in Step 1
Explanation:
If f(x) = x² - |x| and we find f(-x), we get:
f(-x) = (-x)² - | - x |
f(-x) = x² - | x |
Therefore, her first mistake was in Step 1 because she changed the sign of |x| and
|x| = |-x|
So, the answer is:
First mistake was in Step 1
identify all expressions equivalent to the given expressions. 2/3 • 9 ÷ 3 - 1 ANWSER: 6 ÷ 2 - 1 + 2 3 • 2/3 -12/3 • 9 ÷ 1
Simplify each expression and find if the simplified form is the same.
[tex]2/3\cdot9\div3-1[/tex]This can also be writen as:
[tex]=\frac{2}{3}\cdot9\div3-1[/tex]Multiply 2/3 by 9:
[tex]=6\div3-1[/tex]divide 6 by 3:
[tex]=2-1[/tex]Substract 1 from 2:
[tex]=1[/tex]Now, check each option:
6 ÷ 2
Divide both numbers:
[tex]\frac{6}{2}=3[/tex]This is NOT equivalent to the given expression.
- 1 + 2
Add the numbers:
[tex]-1+2=1[/tex]This IS equivalent to the given expression.
3 • 2/3 -1
First, multiply 3 times 2/3:
[tex]3\cdot\frac{2}{3}-1=2-1[/tex]Then, add both numbers:
[tex]2-1=1[/tex]This IS equivalent to the given expression.
2/3 • 9 ÷ 1
Perform the operations from left to right:
[tex]\begin{gathered} \frac{2}{3}\cdot9\div1=6\div1 \\ =6 \end{gathered}[/tex]This is NOT equivalent to the given expression.
Therefore, the expressions that are equivalent to the given one, are:
[tex]\begin{gathered} -1+2 \\ 3\cdot2/3-1 \end{gathered}[/tex]Given h(x) = 5x – 3 and m(x)= -2x^2 what (h o m)(-1)=
Let's begin by listing out the information given to us:
[tex]\begin{gathered} h\mleft(x\mright)=5x-3 \\ m\mleft(x\mright)=-2x^2 \\ \mleft(h^om\mright)\mleft(x\mright)=5(-2x^2)-3 \\ (h^om)(1)=-10x^2-3=-10(-1^3)-3 \\ (h^om)(1)=10-3=7 \\ (h^om)(1)=7 \end{gathered}[/tex]A day of the week is chosen at random. What is the probability that it is a Wednesday or Saturday?A.2/7B.1/7C.2/14D. 2
ANSWER
[tex]A)\frac{2}{7}[/tex]EXPLANATION
There are 7 days in a week.
The probability that a chosen day of the week is Wednesday or Saturday is the sum of the probability that the day is a Wednesday and the probability that the day is a Saturday.
Since there is only one Wednesday in a week, the probability that the day is a Wednesday is:
[tex]P(W)=\frac{1}{7}[/tex]The same rule applies for Saturday:
[tex]P(S)=\frac{1}{7}[/tex]Therefore, the probability that the day is a Wednesday or a Saturday is:
[tex]\begin{gathered} P(W-or-S)=\frac{1}{7}+\frac{1}{7} \\ P(W-or-S)=\frac{2}{7} \end{gathered}[/tex]-7 x -10 y equals -83 4x - 10 y equals 16
Answer:
Subtract to eliminate y.
Step by step explanation:
[tex]\begin{gathered} -7x-10y=-83 \\ 4x-10y=16 \end{gathered}[/tex]Since we have the same negative coefficient for y, we can subtract them to eliminate y.
-10-(-10)=0.
Choose whether the number given in specific notation is representing a large or small number.
Given:
[tex]\begin{gathered} a)1.2\times10^3 \\ b)7.5\times10^^{-4} \end{gathered}[/tex]To find:
The number given in a specific notation is representing a large or small number.
Explanation:
a) It can be written as,
[tex]\begin{gathered} 1.2\times10^3=1.2\times1000 \\ =1200 \end{gathered}[/tex]So, it is a large number.
b) It can be written as,
[tex]\begin{gathered} 7.5\times10^{-4}=7.5\times\frac{1}{10^4} \\ =\frac{7.5}{10000} \\ =0.00075 \end{gathered}[/tex]So, it is a small number.
Final answer:
a) Large
b) Small
18. A line has slope = -9 and goes through the point (-4,-2). What is the equation of this line in point-slope forma A. y + 2 = -91X - 4) B. Y-2= -9(x-4) C. y 2 = -91x + 4) D. y - 2= -9(x +4)
The straight line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. In our case m=-9. Hence, our line
equations has the form
[tex]y=-9x+b[/tex]In order to find b, we must use the given point (-4,-2) and substitute it and the last equation.
It yields,
[tex]-2=-9(-4)+b[/tex]hence, we have
[tex]\begin{gathered} -2=36+b \\ -2-36=b \\ b=-38 \end{gathered}[/tex]Finally, the answer is
[tex]y=-9x-38[/tex]Now, we can rewrite this equation as
[tex]\begin{gathered} y=-9(x+4)-2 \\ \text{which is equal to} \\ y+2=-9(x+4) \end{gathered}[/tex]then, the answer is C.
Find x and y without a calculator! No Desmos! Make sure that this one is on your work that you are uploading.
Given:
Given the system of equations:
[tex]\begin{gathered} y=4x \\ 2x+3y=-28 \end{gathered}[/tex]Required: Values of x and y
Explanation:
Substitute 4x for y into the equation 2x + 3y = -28.
[tex]\begin{gathered} 2x+3\cdot4x=-28 \\ 14x=-28 \\ x=-2 \end{gathered}[/tex]Plug the obtained value of y into y = 4x.
[tex]\begin{gathered} y=4(-2) \\ =-8 \end{gathered}[/tex]Solution is (x, y) = (-2, -8).
Final Answer: Solution is (-2, -8).