Use the Remainder Theorem to determine if [tex]x-2[/tex] is a factor of the polynomial [tex]f(x)=3x^5-7x^3-11x^2+2[/tex].
I have a math question
For
the first question; we have a problem dealing with translations.
Our goal is to translate
the word problem into an algebraic one. So our numbers are
60, 2, and 5. Our variable, or the letter holding the unknown
number's place
value, is
N.
The
problem states that 60 is MORE THAN the PRODUCT of 5 and N. Focus
on the words I bolded and capitalized. These are your key words that
tells you what operations
you need to use. Note that 'product' signals the operation of
multiplication (Since the answer you get from multiplying numbers is
called the 'product'.) and
'more than' signals the operation of addition (Because you are left
off with more than you originally had before adding).
Now
that we know that our algebraic expression contains multiplication,
addition, letter N and the numbers 2 and 5; we can start plugging the
numbers in.
60
= 2 (more than) + (product of) 5N. The answer for the first
attachment is
B.
_____________________________________________________________
All
we need to do for the AB problem (Question 25 on your material) is
solve AB.
Note
1: When a problem has no operation separating two letters or numbers,
this means multiplication.
Note
2: A and B are variables. Variables are letters that stand for and
hold the place of our unknown quantities. However, the values are not
unknown anymore given the fact that the question tells us that A= 42
and B = 2. Thus we substitute A with 42 and B with 2, then work from
there. 42 * 2 =84. Answer = A.
____________________________________________________________________
And
finally, for question 26, we use PEMDAS. P = parenthesis (), E =
exponent x^2, M/D = x or /, A/S means + or subtraction.
According to PEMDAS, we first solve what's parenthesis, which is 77 – 32. Using mental math, 77 – 32 = 45. ( 7 – 3 = 4 and 7 – 2 = 5.). 5/9 * 45 is what we have left. 5 divided by 9 =0.5555555555555556. 0.5555555555555556 * 45 = 25. Answer is D.
Which are the solutions of the quadratic equation? x2 = –5x – 3 –5, 0 5, 0
The solutions of the quadratic equation x² = -5x - 3 are [tex]\( x = \frac{-5 - \sqrt{13}}{2} \)[/tex] and [tex]\( x = \frac{-5 + \sqrt{13}}{2} \)[/tex].
To find the solutions of the quadratic equation x² = -5x - 3, first we rearrange it to the standard form:
x² + 5x + 3 = 0
We solve this using the quadratic formula, which is given by:
x = [tex]\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
For our equation, a = 1, b = 5, and c = 3. Substituting these values in, we get:
x = [tex]\frac{-5 \pm \sqrt{5^2 - 4*1*3}}{2*1}[/tex]
x =[tex]\frac{-5 \pm \sqrt{25 - 12}}{2}\\[/tex]
x =[tex]\frac{-5 \pm \sqrt{13}}{2}[/tex]
Hence, the solutions are:
x = [tex]\frac{-5 - \sqrt{13}}{2}[/tex] and x = [tex]\frac{-5 + \sqrt{13}}{2}[/tex]
Complete question: Which are the solutions of the quadratic equation? x² = -5x - 3
-5, 0[tex]\frac{-5 - \sqrt{13}}{2}[/tex], [tex]\frac{-5 + \sqrt{13}}{2}[/tex][tex]\frac{5 - \sqrt{13}}{2}[/tex], [tex]\frac{5 + \sqrt{13}}{2}[/tex]5,0Problem 4 the measure of the largest angle of a triangle is 90◦ more than the measure of the smallest angle, and the measure of the remaining angle is 30◦ more than the measure of the smallest angle. find the measure of each angle. showyourwork in obtaining your answe
If s = -5 and t = 3, find the value of s^2t.
225
75
30
-75
Answer:
75
Step-by-step explanation:
Suppose an investment of $500 doubles in value every 15 years. How much is the investment after 30 years? 45 years?
If a solid has faces that consist of 2 equilateral triangles and 3 congruent rectangles, what type of solid is it?
A. regular hexagonal prism
B. right rectangular prism
C. right triangular prism
D. triangular pyramid
Chad owns twice as many cds as carlin owns. if you add 6 to the number of cds chad owns and then divide by 7, you get the number of cds bryce owns. bryce owns 30 cds. how many cds does carlin own?
An equation is formed of two equal expressions. The number of CDs owned by Carlin is 102.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the following points:
Chad owns twice as many CDs as Carlin owns. if you add 6 to the number of CDs chad owns and then divide by 7, you get the number of CDs Bryce owns. Bryce owns 30 CDs.Let the variables represent the following numbers as shown,
CDs owned by Chad = M.Cds owned by Carlin = NCDs owned by Bryce = OThe number of CDs owned by Chad.
M = 2N ______(1)
The number of CDs owned by Carlin.
= N ________(2)
The number of CDs owned by Bryce.
O = (6+2N) / 7
And O = 30
30 = (6 + 2N) / 7 ________(3)
From (3), the value of N can be written as,
30 = (6 + 2N) / 7
Multiply both sides by 7
30 x 7 = 6 + 2N
210 = 6 + 2N
Subtract 6 on both sides.
210 - 6 = 6 + 2N - 6
204 = 2N
Divide both sides by 2.
102 = N
N = 102
Thus, the number of CDs owned by Carlin is 102.
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How many yards equals 765 inches?
1 yard = 3 feet
1 foot = 12 inches
so 36 inches = 1 yard
765 / 36 = 21.25 yards
What is the solution of the system of equations?
-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9
Answer:
Given equations have no solution
Step-by-step explanation:
Given -
Three set of equations -
[tex]-3x-4y-3z=-7\\2x-6y+2z=3\\5x-2y+5z=9[/tex]
We will now equate "x" in the first equation in terms of "y" and "Z" and put it in second equation -
[tex]-3x-4y-3z=-7\\x = \frac{1}{3} (-4y -3z+7)\\\frac{2}{3}(-4y -3z+7) -6y+2z=3\\-8.667 y = -1.667\\y = 0.192\\[/tex]
We will substitute the value of y in the under given equation-
[tex]x = \frac{1}{3} (-4y -3z+7)\\x = \frac{1}{3} (-4*0.192 -3z+7)\\x= 2.077-z[/tex]
substituting the derived values in last equation, we get -
[tex]5x-2y+5z=9\\5(2.077-z)-2(0.192)+5z=9\\10.385-5z-0.384+5z=9\\0=-1[/tex]
Hence, the given equations have no solution
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
The dot plot below was made to represent the data.
For which number is the data plotted incorrectly?
2 3 4 5
Answer:
Number 4 plot incorrectly represent on dot plot.
C is correct
Step-by-step explanation:
The following data show the number of questions different students of a class could answer in a quiz competition:
2, 4, 2, 5, 1, 4, 5, 7, 3, 5, 6, 2, 2, 5, 5, 5, 4, 6
We are given the dot plot of the data set.
Data : 1 2 3 4 5 6 7
Frequency : 1 4 1 3 6 2 1
We need to choose which data number plot incorrectly.
For 2: Number of dot should be 4, In graph also 4, 4=4 (True)
For 3: Number of dot should be 1, In graph also 1, 1=1 (True)
For 4: Number of dot should be 3, In graph also 2, 3≠2 (False)
For 5: Number of dot should be 6, In graph also 6, 6=6 (True)
Hence, number 4 plot incorrectly
What are the missing parts that correctly complete the proof?
The missing parts of the question is required.
The blanks are
2 Definition of bisector
3 Definition of perpendicular
4 [tex]\angle AXP=\angle AXQ[/tex]
6 SAS congruence postulate
7 Corresponding parts of congruent triangles
In the given figure.
Line AX is a perpendicular bisector of PQ.
This means [tex]PX\cong QX[/tex]
[tex]\angle AXP=\angle AXQ=90^{\circ}[/tex]
[tex]AX\cong AX[/tex] because it is the same side.
[tex]\triangle AXP\cong \triangle AXQ[/tex] because of the above three points SAS congruence.
[tex]AP\cong AQ[/tex] because they are corresponding parts of congruent triangles
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Find an equation of a line whose graph intersects the graph of the parabola y=x^2 at (a) two points, (b) one point, and (c) no point.
Which mathematical symbol would best fill in the blank to compare the two real numbers?
square root of 7 blank 14 over 5
<
>
=
≈
Answer: The correct option is (A) < .
Step-by-step explanation: We are given to select the correct mathematical symbol that would best fill in the blank to compare the following two real numbers :
[tex]\sqrt7~~~?~~~\dfrac{14}{5}.[/tex]
First , we need to find the values of both the real numbers in decimal form.
We have
[tex]\sqrt7=2.64575...,\\\\\dfrac{14}{5}=2.8.[/tex]
Since, [tex]2.64575<2.8,[/tex] so we get
[tex]\sqrt7<\dfrac{14}{5}.[/tex]
Thus, the correct mathematical symbol is <.
Option (A) is CORRECT.
During summer months, one ice cream trucks come 4 days another 5 days. If both trucks came today, when is the next time both would be here on the same day?
Plz help with math. will reward.
A meteor crater is 3000 feet in diameter. Approximate the distance around the crater use 3.14 for pi
f(x)=2x + 1 and g(x) = -3x+4. Find f(x) + g(x)
1. What point is the image of (4,5) with a translation of right 2 and down 3?
2. Find B' in a reflection of Triangle ABC when A(3,6), B(-4,2), C(-1,-3) over the y axis.
3. Which axis is (0,7) on?
A. X axis
B. Y axis
Triangle XYZ is located at X (−2, 1), Y (−4, −3), and Z (0, −2). The triangle is then transformed using the rule (x−1, y+3) to form the image X'Y'Z'. What are the new coordinates of X', Y', and Z'?
Please Help Me
the volume of the sphere is increased by 72.8%. what is the percentage increase in the radius?
Final answer:
The volume of a sphere increases by 72.8%, which after calculations, results in a 20% increase in the radius of the sphere.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. An increase in volume by 72.8% implies that the new volume V' is equal to 1.728 times the original volume V. To find the percentage increase in the radius, we use the relationship between volume and radius:
V' = (4/3)πr'^3, where r' is the new radius after increase. Since V' = 1.728V, we have:
1.728 (4/3)πr³ = (4/3)π[tex]r'^3[/tex]Therefore, [tex]r'^3[/tex] = 1.728r³.After taking the cube root of both sides, we obtain:
r' = ∛1.728 * r ≈ 1.200 * rThus, the new radius is approximately 120% of the original radius, which means there is a 20% increase in the radius.
Final answer:
To calculate the percentage increase in the radius of the sphere when the volume is increased by 72.8%, we can use the formula for volume and solve for the new radius in terms of the original radius. The percentage increase in radius is then calculated by comparing the new and original radius.
Explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. If the volume of the sphere is increased by 72.8%, we can calculate the new volume by multiplying the original volume by 1 + 0.728. Let's denote the original radius as r1 and the new radius as r2.
The formula for volume can be written as V = (4/3)πr³. Substituting r1 and r2 into the formula, we get:
Original volume: V1 = (4/3)πr1³New volume: V2 = (4/3)πr2³Since the two volumes are related by the percentage increase (1 + 0.728), we can write the equation:
(1 + 0.728)V1 = V2
Now, let's solve for r2 in terms of r1:
(1 + 0.728)V1 = (4/3)πr2³
r2 = ([(1 + 0.728)V1] * (3/4π))^(1/3)
Finally, we can calculate the percentage increase in the radius by comparing r2 to r1:
Percentage increase in radius = (r2 - r1) / r1 × 100%
A negatively skewed curve represents a distribution in which there are very few scores on the right side of the distribution.
The area of a round mat is 64 pi square inches. what is the diameter of the mat
Which of the following shows the length of the third side, in inches, of the triangle below?
A right triangle is shown. One side of the triangle is labeled shown as 97 inches. The height of the triangle is labeled as 65 inches.
Square root of 32
72
Square root of 13634
16
97^2 = 65^2 +x^2
9409 = 4225 +x^2
9409 -4225 = 5184
Sqrt(5184) = 72
length of missing side = 72 inches
*PLEASE HELP* BRAINLIEST* A 10% discount is offered on a certain item that sells for $10.95. How much is the discount and what is the discounted sales price?
Amount of discount =
Discounted sales price =
The amount of discount is $1.095 and the discounted sales price is $9.855.
We need to calculate the amount of discount and then subtract it from the original sales price to find the discounted sales price.
First, we calculate the amount of discount. A 10% discount on an item selling for $10.95 means we need to find 10% of $10.95. To find 10% of a number, we can multiply the number by 0.10 (which is the decimal equivalent of 10%).
Amount of discount = 10% of $10.95
= 0.10 [tex]\times[/tex] $10.95
= $1.095
Now that we have the amount of discount, we can calculate the discounted sales price by subtracting the discount from the original sales price.
Discounted sales price = Original sales price - Amount of discount
= $10.95 - $1.095
= $9.855
i think of a number, multiply it by 3 and add 4 and i get 22
form an equation, using x for the unknown number and then solve it
The student's clues form the equation 3x + 4 = 22. When solved, this equation reveals that the original number x is 6.
Explanation:The student is creating an algebraic equation to find an unknown number. Starting with the clues given:
They think of a number (which we represent with x)Multiply the number by 3 (3x)Add 4 (3x + 4)The result is 22 (3x + 4 = 22)Now, we can solve this equation to find x:
Start by subtracting 4 from both sides of the equation (3x + 4 - 4 = 22 - 4)Simplify to get 3x = 18Then divide both sides by 3 (x = 18/3)This gives us x = 6 as the unknown numberLearn more about Algebra here:https://brainly.com/question/24875240
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Write down in the terms of n, an expression for the nth term of the following sequences:
a.) 23, 20, 17, 14, 11
b.) 36, 30 24, 18, 12
Give an example of a linear equation perpendicular to y=5
Final answer:
A linear equation perpendicular to y=5 is a vertical line, expressed as x=c, where c is any real number. For instance, x=2 is perpendicular to y=5.
Explanation:
A linear equation perpendicular to y=5 would need to have an undefined slope, meaning it's a vertical line. Since y=5 is a horizontal line, a perpendicular line will have no slope value that we can put in terms of y=mx+b, where m represents the slope and b represents the y-intercept. Thus, the equation will be of the form x=c, where c is any real number. This represents a vertical line that crosses the x-axis at the point (c,0).
For example, the linear equation x=2 is perpendicular to y=5 and crosses the x-axis at the point (2,0).
Solve this Multi-Step Equation: (Show your work)
-3(t + 5) + (4t + 2) = 8
2 questions
4. Each small square is 1 in². Which estimate best describes the area of this figure? (first image)
a. 10 in²
b. 15 in²
c. 20 in²
d. 35 in²
5. Which estimate best describes the area under the curve in square units? (second image)
a. 20 units²
b. 25 units²
c. 35 units²
d. 40 units²
Answer: here are the correct answers for the k12 test. Have a great day!!!
Step-by-step explanation: