The roots of a polynomial written in the form
[tex] (x-x_1)(x-x_2)(x-x_3)\ldots(x-x_n) [/tex]
Are exactly
[tex] x_1,\ x_2,\ x_3,\ldots x_n [/tex]
The multiplicity of a solution [tex] x_i [/tex] is how many times the parenthesis [tex] (x-x_i) [/tex] appears in the factorization of the polynomial.
So, if we write the powers explicitly, your polynomial is written as
[tex] (x + 5)^3(x - 9)^2(x + 1) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1) [/tex]
Which means that the solutions are:
-5, with multiplicity 39, with multiplicity 2-1, with multiplicity 1The roots of [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are:
-5 with multiplicity 3
9 with multiplicity 2
-1 with multiplicity 1
The given function is:
[tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex]
The roots of the function [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are the values of x that makes f(x) to be zero
To find the roots of the function [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex], equate each of the terms to zero
The multiplicity of the roots is the power of the term from which the root is gotten
Equate each of the terms to zero
[tex](x+5)^3 = 0\\x + 5 = 0\\x = -5[/tex]
Since the power is 3, the multiplicity is 3
One root is -5 with a multiplicity of 3
[tex](x-9)^2 = 0\\x - 9 = 0\\x = 9[/tex]
Since the power is 2, the multiplicity is 2
One root is 9 with a multiplicity of 2
[tex](x+1)^2 = 0\\x +1 = 0\\x = -1[/tex]
Since the power is 1, the multiplicity is 1
One root is -1 with a multiplicity of 1
Therefore, the roots of [tex]f(x) = (x + 5)^3(x-9)^2(x+1)[/tex] are:
-5 with multiplicity 3
9 with multiplicity 2
-1 with multiplicity 1
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What is the equation of the following graph in vertex form?
Courtesy of Texas Instruments (2 points)
y = (x - 3)2 - 1
y = (x + 3)2 - 1
y = (x - 4)2 - 2
y = (x - 4)2 + 8
For this case we have:
The equation in vertex form of the parabola is given by:
[tex]y = a (x-h) ^ 2 + k\\[/tex]
The vertex is (h, k) and is given by the highest or lowest point of the parabola, in this case it is observed that it is [tex](h, k) = (- 3, -1)\\[/tex]
Thus, the equation is given by:
[tex]y = a (x - (- 3)) ^ 2 + (- 1)\\\\y = a (x + 3) ^ 2-1\\[/tex]
We look for the value of a, substituting a point of the parabola in the equation in the form of vertex, we will take the point [tex](x, y) = (0,8)\\[/tex]
Substituting we have:
[tex]8 = a (0 - (- 3)) ^ 2 + (- 1)\\\\8 = a (0 + 3) ^ 2-1\\\\8 = a (3) ^ 2-1\\[/tex]
[tex]8 = 9a-1\\\\8 + 1 = 9a\\\\9 = 9a\\[/tex]
[tex]a = \frac{9}{9}\\\\a = 1\\[/tex]
Thus, the equation of the parabola is given by:
[tex]y = (x + 3) ^ 2-1\\[/tex]
Answer:
[tex]y = (x + 3) ^ 2-1[/tex]
Answer:
y = (x + 3)2 - 1
Step-by-step explanation:
What is the perimeter of the triangle shown on the coordinate plane, to the nearest tenth of a unit? A.24.8 units B.27.8 units C.28.5 units D.30.9 units
The answer is B I hope I helped
Answer:
the answer is B.28.7 hope i helped you learn something new
Step-by-step explanatio
Which of the following equations correctly describes the graphed line?
y = 2/3x - 2
y = -2/3x - 2
y = 2/3x + 2
y = -2/3x + 2
y = - [tex]\frac{2}{3}[/tex] x - 2
the equation of a line in ' slope - intercept form ' is
y = mx + c ( m is the slope and c the y- intercept ) calculate m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (0 , - 2 ) and (x₂ , y₂ ) = A( 6 , - 6 )
m = [tex]\frac{- 6+ 2}{6 - 0}[/tex] = [tex]\frac{-4}{6}[/tex] = - [tex]\frac{2}{3}[/tex]
y -intercept c = - 2 ( from graph )
y = - [tex]\frac{2}{3}[/tex] x - 2
25 Points! Pre-Calc help? Will award brainliest.
Find the solution set of the given equation for 0 ≤ x ≤ 2π.
-tanA = -1
A. pi/4, 3pi/4
B. pi4/, 5pi/4
C. 3pi/4, 5pi/4
D. 3pi/4, 7pi/4
The answer is B. If you look at a graph of -tan (which is cot), the places the graph crosses -1 are at pi/4 plus kpi. If you add pi to pi/4, you get 5pi/4, and these two answers are in B only.
Im adding an answer so the other guy that gave an answer gets his points.
Five cats each ate 1/4 cup of cat food. How much food did the five cats eat?
Answer: Five cats ate 1 and a quarter of cat food.
Step-by-step explanation
Given:-
Cat food ate by one cat = 1/4 cup
Cat food ate by five cats =[tex]5\times \frac{1}{4} \text{ [Multiplying both sides with 5 ]}\\\\=\frac{5}{4}=\frac{4+1}{4}=\frac{4}{4}+\frac{1}{4}=1+\frac{1}{4}[/tex]=1 and 1/4 cup.
Therefore cat food ate by five cats = 1 and a quarter of cup.[ here a quarter =1/4]
A cement bridge post is 24 inches square and 15 feet 9 inches in length. If the cement weighs 145 pounds per cubic foot, how much does one bridge post weigh? A. 9,280 pounds B. 9,222 pounds C. 9,135 pounds D. 8,700 pounds
Answer:
The answer is option (C), One cement bridge post weighs 9,135 pounds
Step-by-step explanation:
Step 1: Get the total volume of a cement bridge post
The cement bridge post is in the shape of a cuboid, therefor the volume of the cement bridge post can be expressed as;
Volume of cement bridge post=Base area×Length
where;
Base area=(24^2) inches square
1 foot=12 inches
Convert 24 inches to foot=24/12=2^2=4 feet²
Length=15 feet and 9 inches
1 foot=12 inches
Convert 9 inches to foot=9/12=0.75 feet
Total length=(15+0.75)=15.75 feet
replacing;
Volume of cement bridge post=(4×15.75)=63 cubic feet
Volume of cement bridge post=63 cubic feet
Step 2: Get the total weight of the cement bridge post
Total weight of the cement bridge post=Weight per cubic foot×total volume of the cement bridge post
where;
Weight per cubic foot=145 pounds per cubic foot
Total volume of the cement bridge post=63 cubic feet
replacing;
Total weight of the cement bridge post=(145×63)=9,135 pounds
One cement bridge post weighs 9,135 pounds
A survey was sent to GCA students asking the question "Who is your favorite teacher?" (Just FYI - Mrs. Parker received the most votes) What type of data was collected? Question 1 options: Quantitative Qualitative Continuous Discrete Question 2 (1 point) Question 2 Unsaved A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?" The data collected was Question 2 options: Quantitative Qualitative Continuous redundant since every student rated their AMDM teacher as a 5. Question 3 (1 point) Question 3 Unsaved You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house. 47.6 miles is an example of... Question 3 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data Question 4 (1 point) Question 4 Unsaved While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole. The number of times you were able to sink the beanbag is an example of.... Question 4 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data Question 5 (1 point) Question 5 Unsaved You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes. 57.28 minutes is an example of.... Question 5 options: Qualitative, continuous data Quantitative, discrete data Qualitative, discrete data Quantitative, continuous data
1. Qualitative
2. Quantitative
3. Quantitative, continuous data
4. Quantitative, discrete data
5. Quantitative, continuous data
Find the system determinant of the given matrix. [2, 4] [3,-9]
[tex]\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]\\\\\det\left[\begin{array}{ccc}2&4\\3&-9\end{array}\right]=(2)(-9)-(4)(3)=-18-12=-30[/tex]
Answer:
-30 will be the determinant.
Step-by-step explanation:
We have to find the system determinant of the given matrix
[tex]\begin{bmatrix}2 & 4\\ 3 & -9\end{bmatrix}[/tex]
Determinant will be = 2(-9) - (4 × 3)
= -18 -12
= -30
Therefore, as per given options by you in the comments.
option A is the answer.
A party host is making identical party bags for guests using 44 bottles of bubbles, 89 stickers, and 55 pencils. What is the greatest number of identical party bags the host can make with the least amount of items leftover? Describe the contents of each bag.
Answer: 11 party bags with 1 sticker leftover
Each bag contains 4 bubbles, 8 stickers, and 5 pencils.
Step-by-step explanation:
Find the GCF of 44 (bubbles), 89 (stickers), and 55 (pencils)
44: 2 x 2 x 11
89: prime so choose 88 with 1 leftover
88: 2 x 2 x 2 x 11
55: 5 x 11
GCF = 11
Disregard the GCF to see how many of that item should go in each bag.
Bubbles: 2 x 2
Stickers: 2 x 2 x 2
Pencils: 5
What is the slope of the line shown below?
Answer C, aka 3 is that line's slope.
Answer:
the slope of the line is 3
Step-by-step explanation:
Hello, I think I can help you with this
if you have two points of a line
[tex]P1=(x_{1},y_{1})\\ and\\P2=(x_{2},y_{2})[/tex]
you can find the slope using
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
Step 1
Let
P1( 1, 3) and P2(3,9)
put the values into the equation
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\m=\frac{9-3}{3-1}\\m=\frac{6}{2}\\ m=3[/tex]
the slope of the line is 3
I hope it helps,Have a great day.
A jet ski depreciates at 11% of its original value each year. If the jet ski was $8,000 as it’s time of purchase, what is the value of the jet ski after 5 years
f(x) = 8000 - (8000)(0.11)x
= 8000 - 880x
f(5) = 8000 - 880(5)
= 8000 - 4400
= 3600
Answer: $3,600
Answer:
$4467.25
Step-by-step explanation:
We have been given that a jet ski depreciates at 11% of its original value each year. The jet ski was $8,000 as it’s time of purchase.
We will exponential decay function to solve our given problem.
[tex]y=a\cdot(1-r)^x[/tex], where,
a = Initial value,
r = Decay rate in decimal form.
[tex]r=\frac{11}{100}=0.11[/tex]
[tex]y=\$8,000\cdot(1-0.11)^5[/tex]
[tex]y=\$8,000\cdot(0.89)^5[/tex]
[tex]y=\$8,000\cdot 0.5584059449[/tex]
[tex]y=\$4467.2475592[/tex]
[tex]y\approx \$4467.25[/tex]
Therefore, the value of ski jet after 5 years would be $4467.25.
What graph represents the inequality y≥2−2x?
[tex]y\geq2-2x\\\\\text{Let's the line}\ y=2-2x\\\\for\ x=0\to y=2-2(0)=2\to(0,\ 2)\\for\ x=1\to y=2-2(1)=0\to(1,\ 0)[/tex]
[tex]\text{draw a line and shade above the line}\\\\\text{Look at the picture}[/tex]
Answer:
Graph is attached below
Step-by-step explanation:
To graph the given inequality , replace the inequality sign by = sign
y≥2−2x
y=2−2x
Now make a table , assume some random number for x and find out y
x y=2-2x
0 2
1 0
2 -2
Now graph all the points (0,2) (1,0) (2,-2)
Now we do shading. For shading use test point (0,0)
plug in 0 for x and 0 for y
[tex]y\geq 2-2x[/tex]
[tex]0\geq 2-2(0)[/tex]
[tex]0\geq 2[/tex] is false
So shade the region that does not contain (0,0)
The graph is attached below
For y = 3x - 2x2 +5x3, show how to find the value for y, when x = 3. Show your work
Answer:
y= 126
Step-by-step explanation:
The given equation is: y= 3x-2x^2+5x^3
Substituting the value x=3 in the above equation,we get
y= 3(3)-2(3)^2+5(3)^3
⇒y= 9-2(9)+5(27)
⇒y= 9-18+135
⇒y= 126
the second longest bridge in the world, the tianjin grand bridge, is 373,000 feet long. Its length is 167,700 feet less than the length of the longest bridge in the world. What is the length of the longest bridge? Show your work.
The length of the longest bridge in the world is found by adding the length of the second longest bridge namely the Tianjin Grand Bridge, and the stated difference between the two bridges' lengths. After calculation, the length of the longest bridge in the world is found to be 540,700 feet.
Explanation:To find the length of the longest bridge in the world, we should add the length of the Tianjin Grand Bridge (the second longest in the world) and the difference between the two bridges. In this case, the length of the Tianjin Grand Bridge is 373,000 feet and it's stated that this is 167,700 less than the length of the longest bridge.
So, we have to do the following calculation: 373,000 feet (length of the Tianjin Grand Bridge) + 167,700 feet (difference in length) = 540,700 feet.
So, the length of the longest bridge in the world is 540,700 feet.
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IF WORK IS SHOWN YOU'LL BE MARKED BRAINLIEST
row #of students
1 4
2 7
3 10
4 13
Which formula can be used to find the number of students seated in any given row?
a. an= 4n
b. an= 4n – 1
c. an= n + 3
d. an= 3n + 1
I believe its asking you the formula to find the rows numbers moving forward
Examle row 5 will be 16, I believe that is B. 4n - 1
find dy/dx by implicit differentiation. 5+4x=sin(xy^2)
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. The derivative of sin(xy^2) with respect to x is cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx). Simplify the expression to find dy/dx.
Explanation:To find dy/dx by implicit differentiation, we will differentiate both sides of the equation with respect to x.
We have the equation 5+4x=sin(xy^2). Taking the derivative of both sides, the left side will be 0 since it is a constant. On the right side, we use the chain rule.
The derivative of sin(xy^2) with respect to x can be written as cos(xy^2) * (y^2 * dx/dx + x * d(y^2)/dx).
Simplifying further, dy/dx = (cos(xy^2) * (2xy^2 + x * 2y * dy/dx)) / (1 - x * 2y^2 * cos(xy^2)).
A toy jeep is 12 1/2 inches long while an actual Jeep measures 18 3/4 ft long what is the value of the ratio length of a toy Jeep to the length of a actual Jeep
The length of toy jeep = [tex]12 \frac{1}{2}[/tex]
= [tex]\frac{25}{2}[/tex] inches
The length of actual Jeep = [tex]18 \frac{3}{4}[/tex] feet
We have to find the ratio length of a toy jeep to the length of actual jeep.
Firstly, we will make the dimensions of the both the given lengths same.
As 1 foot = 12 inches
[tex]18 \frac{3}{4}[/tex] feet = [tex]18 \frac{3}{4} \times 12[/tex] inches
=[tex]\frac{75 \times 12}{4}[/tex]
= 225 inches
So, the ratio length of toy jeep to actual jeep
= [tex]\frac{25}{2} \div 225[/tex]
= [tex]\frac{25}{2} \times \frac{1}{225}[/tex]
= [tex]\frac{1}{18}[/tex]
= 1:18
So, the ratio length of a toy Jeep to the length of a actual Jeep is 1:18.
Length of toy jeep = [tex]12\frac{1}{2}=\frac{25}{2}[/tex] inches
Length of actual jeep = [tex]18\frac{3}{4}=\frac{75}{4}[/tex] feet
Now to find the ratio between the two, we must convert both of them in same units. So, lets convert the actual jeep length in feet to inches.
1 feet = 12 inches.
So, [tex]\frac{75}{4}[/tex] feet = [tex]\frac{75}{4}\times12=225[/tex] inches
Ratio of length of toy jeep to actual jeep will be =
[tex]\frac{\frac{25}{2}}{225}[/tex]
[tex]\frac{25}{2\times225}[/tex]
[tex]\frac{25}{450}[/tex] = [tex]\frac{5}{90}[/tex]
ratio is : [tex]\frac{1}{18}[/tex] or 1:18
△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .
Which statement correctly describes the relationship between △ABC and △A′B′C′ ?
A. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a rotation, which is a sequence of rigid motions.
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
C. △ABC is not congruent to △A′B′C′ because the rules do not represent a sequence of rigid motions.
D. △ABC is congruent to △A′B′C′ because the rules represent a reflection followed by a reflection, which is a sequence of rigid motions.
Answer:
B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
Step-by-step explanation:
I just took the test, good luck! Have a wonderful day! :)
Transformation involves changing the position of a shape.
The correct statement is: (b) △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.
The transformation rule is given as:
[tex]\mathbf{(x,y) \to (-x,-y)}[/tex], then:
[tex]\mathbf{(x,y) \to (x,-y)}[/tex]
The first transformation [tex]\mathbf{(x,y) \to (-x,-y)}[/tex] is 180 degrees rotation across the originThe second transformation [tex]\mathbf{(x,y) \to (x,-y)}[/tex] is a reflection across the x-axisRotation and reflection are both rigid transformation.
Hence, the correct option is (b):
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Which of the following numbers is divisible by 3 and 9?
A. 74,028
B. 40,653
C. 62,997
D. 95,376
The number that is divisible by 3 and 9 is 40,653.
What is division?The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in maths.
We may face different situations every day where we use the division technique.
Given are numbers, we need to find which of them numbers are divisible by 3 and 9,
LCM of 3 and 9 is 9,
So numbers completely divisible by 9 will also be divisible by 3.
The only number from the option which is completely divisible by 9 is 40,653.
Hence, the number that is divisible by 3 and 9 is 40,653.
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Cristoble used synthetic division to divide the polynomial f(x) by x + 3, as shown on the table. What is the value of f(−3) ? −3 2 33 36 A synthetic division setup with respective columns containing the following numbers column 1 containing -3 as the divisor, column 2 containing 2, blank and 2, column 3 containing negative 5, negative 6, negative 11, and column 4 containing 3, 33, 36.There is a line above the numbers 2, negative 11 and 36.
Answer:
Remainder is 36.
Step-by-step explanation:
We are given that f(x) is divided by x+3 using synthetic division, and we are given with table attached in the image.
In synthetic division, first row represents the coefficients of dividend. From the given table, dividend is f(x)=[tex]2x^{2}-5x+3[/tex] and since f(x) is divided by x+3, divisor is -3.
First two numbers of last row represents coefficients of quotient and last most number of third row is remainder.
And we can write f(x) as (x+3)(2x-11)+36.
Hence remainder is 36 , when f(x) is divided by x+3.
Answer:
36
Step-by-step explanation:
this i believe is the settup u were describing
joshua can wash 5 cars in 1 hour and jason can wash 3 cars in one hour. at this rate, how long will it yake joshua and jason to wash 26 cars if they work together?
The answer is 3 hours 40 minutes
Given the graph of a line y=−x. Write an equation of a line which is perpendicular and goes through the point (8,2).
When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.
To find the y-intercept, you have to substitute the point (8,2) into y = mx + b
2 = 1(8) + b
b = -6
The equation is y = x - 6
The equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6
The equation of the required line in slope-intercept form is expressed as:
y-y0 = m(x-x0) where:
m is the slope(x0, y0) is the point on the lineGiven the equation of the line as y = -x
Get the slope of the line
mx = -x
m = -1
Since the required line is perpendicular to this line, the required slope will be 1 (M = -(-1/1))
Get the required equation
Recall that;
y-y0 = m(x-x0)
y - 2 = 1(x-8)
y - 2 = x - 8
y = x - 8 + 2
y = x - 6
Hence the equation of the line which is perpendicular and goes through the point (8,2) is y = x - 6.
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Please help it would be apreacated
What is the name of the line of reflection for the pair of figures?
Enter your answer in the box.
Line ___
Hi!
Answer - Line R
Well refraction is the bending of something. I choose r because it may have refraction because of the 2 rectangles at the end of both sides.
Hope This Helps!
HELP PLEASE??
Drag and drop the answers into the boxes to correctly complete the statement.
A sequence of transformations that maps △ABC to △A′B′C′ is a _____________ followed by a _____________.
- reflection across the y-axis
- rotation of 180° about the origin
- translation 2 units right
- rotation of 90° counterclockwise about the origin
Answer:
(1) Rotation of 90° counterclockwise about the origin (2) Translation 2 units right .
Step-by-step explanation:
We have been asked to determine a sequence of transformations that maps △ABC to △A′B′C'.
To map △ABC to △A′B′C′ first of all we have to rotate △ABC 90° counterclockwise (positive rotation) about the origin. After rotating △ABC 90° our new coordinates will be A(-3,-4), B(-3,-1) and C (-1,-2).
We can see that distance between A and origin is [tex]\sqrt{5}[/tex] and distance between A' and origin is also [tex]\sqrt{5}[/tex]. Distance between A and A' is [tex]\sqrt{10}[/tex], which forms a right triangle.
To map △ABC to △A′B′C′ completely we will translate our △A′B′C' 2 units right. After translation our coordinates will be A'(-1,-4), B'(-1,-1) and C'(1,-2).
Therefore, a sequence of transformations that maps △ABC to △A′B′C′ is (1) rotation of 90° counterclockwise about the origin and (2) translation 2 units right.
Final answer:
The sequence of transformations is a rotation followed by a translation, which can map one triangle to another in the Euclidean plane.
Explanation:
A sequence of transformations that maps △ABC to △A′B′C′ can be described as a combination of basic transformations such as rotations, reflections, and translations. Based on the options given, the correct sequence to map △ABC to △A′B′C′ is a rotation followed by a translation. For example, if △ABC were rotated 90 degrees counterclockwise about the origin and then translated 2 units to the right, it could be mapped to a new position as △A′B′C′. It is important to note that the order of transformations can affect the outcome, and transformations are done in sequence.
The estimated insurance loss from a hurricane was $18.218.2 billion. This was $12.412.4 billion more than the loss from a tsunami three years later. What was the estimated insurance loss from the tsunami?
Answer:
If you are asking about the difference between the two, the difference is $5,805.80
Step-by-step explanation:
Sam initially invested $4,500 into a savings account that offers an interest rate of 3% each year. He wants to determine the number of years, t, for which the account will have less than or equal to $7,020.
Every year, Sam will have 103% of the amount from the previous year.
[tex]p\%=\dfrac{p}{100}\\\\103\%=\dfrac{103}{100}=1.03[/tex]
After the first year:
[tex]1.03\cdot\$4,500[/tex]
After the second year:
[tex]1.03\cdot1.03\cdot\$4,500=\$4,500(1.03)^2[/tex]
After the t-th year:
[tex]\$4,500(1.03)^t[/tex]
Therefore we have the inequality:
[tex]\$4,500(1.03)^t\leq\$7,020\ \ \ \ |\text{divide both sides by \$4,500}\\\\(1.03)^t\leq1.56\\\\(1.03)^{15}\approx15.56\\\\\text{therefore}\ t\leq15[/tex]
Answer: t ≤ 15.solve.
14n + 6p - 8n = 18p for n
[tex]14n+6p-8n=18p\ \ \ \ |\text{subtract 6p from both sides}\\\\14n-8n=12p\\\\6n=12p\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{n=2p}[/tex]
The correct solution for this equation is n = 2p.
I hope this helped! :)
Hayley begins solving this problem by combining like terms. 3x + 5x = 10 Which problem begins the same way? A) 5x = 20 Eliminate B) 2(x + 5) = 20 C) x 4 = 30 D) 4x ? 2x = 10
Answer:
In a linear equation of one variable there are two terms terms containing variable and constant.
Variable means term containing x,y,z which act as variables. and constant means any rational number . In higher classes you can include real number also.
The given equation is 3x + 5x = 10
So, the solution out of four options is A) 5x = 20.
Here variable is on one side of equation and constant on other side.
But Option (D) looks absolutely correct if we replace ? by either + sign or Negative (-) sign.
Answer:
D. [tex]4x-2x=10[/tex]
Step-by-step explanation:
We have been give an equation [tex]3x+5x=10[/tex]. The equation is solved by combining like terms. We are asked to choose the equation that an be solved by combining the like terms.
Let us check our given choices one by one.
A. [tex]5x=20[/tex]
We can see that equation A will be solved by dividing 20 by 5, therefore, option A is not correct choice.
B. [tex]2(x+5)=20[/tex]
We can see that equation B will be solved by dividing 20 by 5 and then subtracting 5, therefore, option B is not correct choice.
C. [tex]\frac{x}{4}=20[/tex]
We can see that equation C will be solved by multiplying 20 by 4, therefore, option C is not correct choice.
D. [tex]4x-2x=10[/tex]
We can see that equation D will be solved by combining like terms, therefore, option D is correct choice.
What are the values of m and n in the matrix addition below?
ANSWER
The correct answer is [tex]m=45,n=12[/tex].
EXPLANATION
We were given the matrix equation;
[tex]\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
We must first simplify the Left Hand Side of the equation by adding corresponding entries.
[tex]\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
That is;
[tex]\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right][/tex].
Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.
This implies that;
[tex]n-2=10[/tex]
We got this equation from row one-column one entry of both matrices.
[tex]n=12[/tex]
Also, the row three-column three entries of both matrices will give us the equation;
[tex]m-5=40[/tex]
[tex]m=45[/tex]
Hence the correct answer is [tex]m=45,n=12[/tex].
The correct option is option 2
What value of x makes the equation 3x-(7+4x)=2(5x-4)+1 true
x = 0
distribute parenthesis on both sides of the equation and simplify
3x - 7 - 4x = 10x - 8 + 1
- x - 7 = 10x - 7 ( subtract 10x from both sides )
- 11x - 7 = - 7 ( add 7 to both sides )
- 11x = 0 ( divide both sides by - 11 )
x = 0