Answers
For:
[tex]8x^3+16x^2[/tex]Factor 8x² out of the expression:
[tex]8x^2(x+2)[/tex]-------------------------------------------------------------------
For:
[tex]\begin{gathered} 2x^2-x+8x-4 \\ \end{gathered}[/tex]Add like terms:
[tex]2x^2+7x-4[/tex]The coefficient of x² is 2 and the constant term is -4. The product of 2 and -4 is -8. The factors of -8 which sum to 7 are -1 and 8, thus:
[tex]\begin{gathered} 2x^2+7x-4=4(2x-1)+x(2x-1) \\ so\colon \\ 4(2x-1)+x(2x-1)=(2x-1)(x+4) \end{gathered}[/tex]Related Questions
the distance between City a and City b is 200 mi. on a certain wall map this is represented by the length of 1.7 ft. On the map how many feet would there be between City c and City d two cities that are actually 400 mi apart?
Answers
Given that:
the distance between City a and City b is 200 mi. on a certain wall map this is represented by the length of 1.7 ft.
So:
[tex]\begin{gathered} 200\text{ mi=1.7 ft } \\ 1\text{ mi=}\frac{1.7}{200}ft \end{gathered}[/tex]between City c and City d two cities that are actually 400 mi apart?:
So for 400 mi.
[tex]\begin{gathered} 1\text{ mi=}\frac{1.7}{200}ft \\ 400\text{ mi=400}\times\frac{1.7}{200}ft \\ 400mi=2\times1.7ft \\ 400\text{ mi=3.4ft} \end{gathered}[/tex]So 3.4 feet would there be between City c and City d two cities that are actually 400 mi apart
Select all the values that are equivalent to (25+9.05×10^2)/3.
Answers
We have the following:
[tex]\frac{25+9.05×10^{2}}{3}[/tex]solving:
[tex]\frac{25+9.05\cdot100}{3}=\frac{25+905}{3}=\frac{930}{3}=310[/tex]The expression is equivalent to 310
Use the unit circle to identify the reference angle for 245°
Answers
In a unit circle every angle is measured from the positive x-axis to its terminal line traveling counterclockwise; the reference angle is the smallest possible angle formed by the x-axis and the terminal line going either clockwise or counterclockwise.
Now, to find the reference angle we first need to determine in which quadrant the original angle is; then, depending on where the angle is, we calculate the reference angle by remembering the following rules:
• If the original angle is in the first quadrant then the reference angle is the same.
,• If the original angle is in the second quadrant then the refrence angle is found by the formula:
[tex]180-\theta[/tex]• If the original angle is in the third quadrant the reference angle is given by:
[tex]\theta-180[/tex]• If the original angle is in the fourth quadrant the reference angle is given by:
[tex]360-\theta[/tex]Now that we know this let's find the reference angle for 245°. This angle is in the third quadrant, and hence its reference angle is:
[tex]245-180=65[/tex]Therefore, the reference angle is 65°
translate this sentence into an equation:Four less than five times a number is equal to 11
Answers
we subtract 4 from the product between 5 and a number, and the result is 11
fifteen more than half a number is five
[tex]\frac{x}{2}+15=5[/tex]We must add 15 to the quotient between a number and two and its result is 5
Is there enough information to prove the quadrilateral is a parallelogram if so what property proves it
Answers
To solve this problem we remember the following statement: a quadrilateral that has opposite sides that are congruent and parallel can be a parallelogram, rhombus, rectangle or square.
From the figure, we see a quadrilateral with congruent opposite sides. Relating this information to the statement above, we see that this quadrilateral can be a parallelogram, rhombus, rectangle or square. So we conclude that there is not enough information to conclude that the quadrilateral is a parallelogram.
Answer
d. Not enough information
Simplify the expression. 1 3 3 m +8 4 3m 3 2 3 1 3 3 +8 4 2 (Use the operation symbols in the math palette as ne any numbers in the expression.)
Answers
We need to simplify the following expression
[tex]\frac{3}{4}m^3+8-\frac{1}{2}m^3[/tex]We first group the similar terms, they are the first and the third one
[tex](\frac{3}{4}m^3-\frac{1}{2}m^3)+8[/tex]then we use common factor to take out the m^3 of the parenthesis
[tex]m^3(\frac{3}{4}-\frac{1}{2})+8=\frac{1}{4}m^3+8=4(m^3+2)^{}[/tex]-8-2y=10Hi I'm having a lot of trouble with problems like these.First when I go to solve this how do I know whether to add or subtract the -8 from the 10 or the 10 from the -8Also on problems like these how do I know either to add or subtract?
Answers
To solve an equation for a variable, we mean to "isolate" the variable on one side of the equation ( right or left), in order to solve for the variable we add and subtract constant terms, like 7, 8, 10, or any other constant.
In this case, we have the equation -8-2y=10, so the first step to take is to take the -8 "away" and put it to the other side of the equation ( this is the shortest way but you can take the -2y to the other side of the equation first or perform any other operation that you want that does not alter the equation, but the point is to isolate y), to put -8 in the other side of the equation we have to add it to both sides of the equation because -8+8=0:
[tex]\begin{gathered} -8-2y+8=10+8, \\ -2y=18. \end{gathered}[/tex]Now, notice that y still has a constant next to it, but the goal is to leave y alone, so we check what is it that this constant is doing to y, well -2 is multiplying y so in order to take to the other side of the equation we divide all the equation by -2, because -2/-2=1:
[tex]\begin{gathered} \frac{-2y}{-2}=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]That is how one solves an equation for a variable.
Alternative solution:
[tex]\begin{gathered} -8-2y=10, \\ -8-2y-10=10-10, \\ -18-2y=0, \\ -18-2y+18=0+18, \\ -2y=18, \\ y=\frac{18}{-2}, \\ y=-9. \end{gathered}[/tex]Solve x+1=3, for x: first I choose on which side of the equation I want x, I want x on the left side ( could be the right side, it is up to you), second, I observe the equation and notice that there is a number being added to x, the constant is +1, to get rid of the constant I must subtract the constant on both sides of the equation:
[tex]x+1-1=3-1.[/tex]The last step is to simplify:
[tex]\begin{gathered} x+(0)=3-1, \\ x=2. \end{gathered}[/tex]The function y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-8 and x=-5. Use the line segment to determine the average rate of change of the function f(x) on the interval −8≤x≤−5.
Answers
The formula for calculating the rate of change of a function is expressed as:
[tex]f^{\prime}(x)=\frac{f(b)-f(a)}{b-a}[/tex]Using the connecting points x = -8 and x = -5 on the graph, this means:
a = -8 = x1
b = -5 = x2
f(b) is f(-5) which is the corresponding y-values at x = -8
f(a) is f(-8) which is the corresponding x-values at x = -5
From the graph;
f(b) = f(-5) = -20 = y2
f(a) = f(-8) = -10 = y1
Determine the change in y and change in x
[tex]\begin{gathered} \triangle y=y_2-y_1=-20-(-10) \\ \triangle y=-20+10=-10 \\ \triangle x=x_2-x_1=-5-(-8) \\ \triangle x=-5+8=3 \end{gathered}[/tex]Find the average rate
[tex]\begin{gathered} Average\text{ rate of change}=\frac{f(b)-f(a)}{b-a}=\frac{\triangle y}{\triangle x} \\ Average\text{ rate of change}=-\frac{10}{3} \end{gathered}[/tex]For the grah , draw a line connecting the coordinate point (-5, -20) and (-8, -10)
evaluate the expression given sin u = 5/13 and cos v = -3/5 where angle u is in quadrant 2and angle v is in quadrant 2sin ( u - v )
Answers
We are given the following information
sin u = 5/13
cos v = -3/5
Where the angle u and v are in the 2nd quadrant.
[tex]\begin{gathered} \cos\theta=\frac{adjacent}{hypotenuse} \\ \sin\theta=\frac{opposite}{hypotenuse} \end{gathered}[/tex]Let us find cos u
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=13^2-5^2 \\ a^2=169-25 \\ a^2=144 \\ a=\sqrt{144} \\ a=12 \end{gathered}[/tex]Cos u = 12/13
Now, let us find sin v
Apply the Pythagorean theorem to find the 3rd side.
[tex]\begin{gathered} a^2+b^2=c^2 \\ b^2=c^2-a^2 \\ b^2=5^2-(-3)^2 \\ b^2=25-9 \\ b^2=16 \\ b=\sqrt{16} \\ b=4 \end{gathered}[/tex]Sin v = 4/5
Recall the formula for sin (A - B)
[tex]\sin(A-B)=\sin A\cos B-\cos A\sin B[/tex]Let us apply the above formula to the given expression
[tex]\begin{gathered} \sin(u-v)=\sin u\cdot\cos v+\cos u\cdot\sin v \\ \sin(u-v)=\frac{5}{13}\cdot-\frac{3}{5}+\frac{12}{13}\cdot\frac{4}{5} \\ \sin(u-v)=\frac{33}{65} \end{gathered}[/tex]Therefore, sin (u - v) = 33/65
what is 1.8333333 as a fraction
Answers
This is a periodic decimal, which means a fixed part of the number will repeat forever, this part is called period. In this case the period is equal to 3. To convert a periodic decimal to a fraction we need to do as below.
We need to subtract the part of the number that doesn't repeat with one period of that part that repeats without the dot, which would be "183" and subtract it with the part that doesn't repeat without the dot "18". This would be "183 - 18 = 165". We then count the number of algarisms in the period of the number, in this case we only have one, which is "3". For every algarism in the period we add a "9" to the denominator. If there are numbers on the decimal part that don't repeat we add "0" after the 9. So we have the following fraction.
[tex]1.833333\ldots\text{ = }\frac{183-18}{90}\text{ = }\frac{165}{90}[/tex]A carpenter is working with a beam that is 10 feet long and in the shape of a rectangular prism. He cuts the beam in half. What happens to the surface area and the volume of the beam?
Answers
For this problem, we are provided with the image of a beam and its dimensions, we are then informed that the beam was cut in half, and we need to compare the surface area and volume of the beam before and after the cut.
The surface area of a rectangular prism can be calculated with the following expression:
[tex]A_{\text{surface}}=2\cdot(\text{width}\cdot\text{height}+\text{width}\cdot\text{length}+\text{height}\cdot\text{length)}[/tex]The volume of a rectangular prism can be calculated with the following expression:
[tex]V=\text{width}\cdot\text{height}\cdot\text{length}[/tex]We can use these formulas to calculate the characteristics of the beam before the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(10\cdot1+1\cdot1+1\cdot10)=42\text{ square ft} \\ V=10\cdot1\cdot1=10_{}\text{ cubic ft} \end{gathered}[/tex]Now we can calculate the characteristics of the beam after the cut:
[tex]\begin{gathered} A_{\text{surface}}=2\cdot(5\cdot1+1\cdot1+1\cdot5)=22\text{ square ft} \\ V=5\cdot1\cdot1=5\text{ cubic ft} \end{gathered}[/tex]With this, we can conclude that:
The surface area of the cut beam is 20 sq ft smaller than the original beam.
The volume of the cut beam is half the volume of the original beam.
Solve the system of linear equations using the substitution method. 4x+4y=12x=-2y+8
Answers
Hello there. To solve this question, we'll need to isolate a variable, substitute its expression into the other equation and find both values.
4x + 4y = 12
x = -2y + 8
Plug x = -2y + 8 in the first equation. Before doing so, divide both sides of the first equation by a factor of 4
x + y = 3
-2y + 8 + y = 3
Subtract 8 on both sides of the equation and add the values
-2y + y = 3 - 8
-y = -5
Multiply both sides of the equation by a factor of (-1)
y = 5
Plug this value into the expression for x
x = -2 * 5 + 8
Multiply the values
x = -10 + 8
Add the values
x = -2
These are the values we're looking for.
The solution for this system of equation is given by:
S = {(x, y) in R² | (x, y) = (-2, 5)}
Answer:
x = -2
y = 5
Step-by-step explanation:
Solving system of linear equations by substitution method:4x + 4y = 12
Divide the entire equation by 4,
x + y = 3 -------------(I)
x = -2y + 8 ------------(II)
Substitute x = -2y + 8 in equation (I)
-2y + 8 + y = 3
-2y + y + 8 = 3
Combine like terms,
-y + 8 = 3
Subtract 8 from both sides,
-y = 3 - 8
-y = - 5
Multiply the entire equation by (-1)
[tex]\sf \boxed{\bf y = 5}[/tex]
Substitute y= 5 in equation (II),
x = -2*5 + 8
= - 10 + 8
[tex]\sf \boxed{\bf x = -2}[/tex]
A triangle has sides measuring 5 inches and 8 inches. If x represents the length in inches of the third side, which inequality gives the range of possible values for x? OA. 3< x< 13 B. 5< x< 8 OC. 3
Answers
Explanation
Step 1
then
If a,b,c are the sides of a triangle it MUST exist these equality:
each side must be less then the sum of the others sides.
[tex]\begin{gathered} then \\ x<5+8 \\ x<13 \\ \end{gathered}[/tex]Also
[tex]\begin{gathered} x+5>8 \\ x>8-5 \\ x>3 \end{gathered}[/tex]then,the answer is
[tex]33a + 9 > 21 or -2a +4 > 16
Answers
We will look at how to evaluate inequalities in terms of a number line solution.
We have the following two inequalities:
[tex]3a\text{ + 9 > 21 or -2a + 4 > 16}[/tex]We will first solve each inequality separately for the variable ( a ) as follows:
[tex]\begin{gathered} 3a\text{ > 12 or -2a > 12} \\ \textcolor{#FF7968}{a}\text{\textcolor{#FF7968}{ > 4 or a < -6}} \end{gathered}[/tex]Now we will plot the solution on a number line as follows:
What is the simplest form of the radical expression? 3 3 √ 2 a − 6 3 √ 2 a
Please show the steps to help me understand this process.
Answers
Simplest form of the radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.
As given in the question,
Given radical expression is equal to :
3 ∛2 a − 6 ∛2 a
Simplify the given 3 ∛2 a − 6 ∛2 a radical expression to get the simplest form ,
3 ∛2 a − 6 ∛2 a
Write all the prime factors of the number we have,
= 3∛2 a - ( 3 × 2) ∛2 a
Take out the common factor from the given radical expression we have,
= 3∛2 a ( 1 - 2 )
= 3∛2 a (- 1)
= -3∛2 a
Therefore, simplest form of the radical expression 3 ∛2 a − 6 ∛2 a is given by -3∛2 a.
The complete question is:
What is the simplest form of the radical expression? 3 ∛2 a − 6 ∛2 a
Please show the steps to help me understand this process.
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RmZR = 130 and mZS = 80. Find the mZT7mZT =Ilo mas rapido posible
Answers
The given figure is a Kite. A Kite is symmetrical about its main diagonal. This means that the diagram of the kite could be drawn a
Which point is located at (-1, -3)?A.point AB.point DC.point ED.point F
Answers
SOLUTION
We are asked which point is located at (-1, -3)
From the diagram given, the point located on (-1, -3) is point E.
Hence option C is the correct answer
What is the inverse of the following statement If M is the middle point of PQ then PM is congruent to QM
Answers
To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.
Given statement:
If M is the mid-point of PQ then PM is congruent to QM.
The inverse statement would be:
If M is not the mid-point of PQ, then PM is not congruent to QM
Answer:
Option A
Katie had to buy snacks for her son’s upcoming football game. She is considering buying 1 ounce bags of chips that came in a variety of carton sizes. One carton had 18 bags of chips that sold for $5.97. Another carton had 12 bags for $3.59. If she needed a total of 36 bags of chips for all of the players, how much money would she save by buying the carton with the best overall price?
Answers
The money would she save by buying the carton with the best overall price is $1.14
One carton had 18 bags of chips that sold for $5.97
Price of 18 bags of chips is sold for $5.97
Price of 1 bag of chips is sold for = 5.97/18 = 0.331
For 36 bags it would cost her 36 x 0.331 = 11.91
.Another carton had 12 bags for $3.59.
Price of 12 bags for $3.59.
Price of 1 bags for $3.59/12 = 0.299 = 0.3
For 36 bags it would cost her 36 x 0.3 = 10.77
money saved = 11.91 - 10.77 = 1.14
Therefore, the money would she save by buying the carton with the best overall price is $1.14
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Which expression is equivalent to -1/2(6x - 12)A. 6x + 6B. 3x - 12C. 3X-6D. 3x + 6
Answers
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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Answer:
The expression is 3x-6
From the question, we have
1/2(6x - 12)
=1/2*6x-1/2*12
=3x-6
Step-by-step explanation:
Find the difference: 8.02 - 0.003A) 7.990B) 8.017C) 8.019D) None of these choices are correct.
Answers
Given:
[tex]8.02-0.003[/tex][tex]8.02-0.003=8.017[/tex]Option B is the final answer.
Hans cell phone plan cost $200 to start, then there is a $50 charge each month.a. what is the total cost ( start-up fee and monthly charge) to use the cell phone plan for one month? b. what is the total cost for x months?c. graph the cost of the cell phone plan over a. Of 2 years using months as a unit of time. Be sure to scale your access by labeling the grid line with some numbers.(pt2 to letter c) what are the labels for the axes of the graph (for x and y)d. is there a proportional relationship between time and the cost of the cell phone plan?Explain how you know!e. Tyler cell phone plan cost $350 to start then there is a $50 charge each month on the same grid as Hans plan in part C above graph the cost of Tyler cell phone plan over Of 2 yearslastly, describe how hans and Tyler's graphs are similar and how they are different..
Answers
We know that
• The cost is $200 to start and $50 per month. This can be expressed as follows.
[tex]C=200+50m[/tex](a) The cost for one month would be
[tex]C=200+50\cdot1=200+50=250[/tex](b) The cost for x months is
[tex]C=200+50x[/tex](c) To graph the equation, we use the month as a unit of time, the table values would be
m C
1 250
2 300
3 350
4 400
5 450
6 500
7 550
8 600
9 650
10 700
11 750
12 800
Now, we graph all of these points.
The x-axis label is Months, and the y-axis label is Cost.
(d) The given situation does not show a proportional relationship because a proportional relationship is modeled by the form y = kx, which we do not have in this case.
(e) If the initial fee is $350, the equation is
[tex]C=350+50m[/tex]Let's graph it.
The graphs are similar because they have the same slope but they are different because they have different y-intercepts.
Luis purchased a laptop computer that was marked down by 2/5of the original price. What fractional part of the original price did Luis pay?
Answers
Problem
Luis purchased a laptop computer that was marked down by 2/5
of the original price. What fractional part of the original price did Luis pay?
Solution
For this case we can express the total as 1 and then we can do the following operation:
[tex]1-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]And we can conclude that Luis paid 3/5 of the original price for this case
The sales S (in billions of dollars) for Starbucks from 2009 through 2014 can be modeled by the exponential functionS(t) = 3.71(1.112)twhere t is the time in years, with t = 9 corresponding to 2009.† (Round your answers to two decimal places.)a) Use the model to estimate the sales in 2015 in billions of dollars.b) Use the model to estimate the sales in 2024 in billions of dollars.
Answers
a) Use the model to estimate the sales in 2015 in billions of dollars
Evaluate the function for t=15
[tex]\begin{gathered} S(15)=3.71(1.112)\placeholder{⬚}^{15} \\ \\ S(15)\approx18.24 \end{gathered}[/tex]The sales in 2015 will be $18.24 billionb) Use the model to estimate the sales in 2024 in billions of dollars
Evaluate the function for t=24
[tex]\begin{gathered} S(24)=3.71(1.112)\placeholder{⬚}^{24} \\ \\ S(24)=47.41 \end{gathered}[/tex]The sales in 2024 will be $47.41 billionClint is making a 10-lb bag of trail mix for his upcoming backpacking trip. Thechocolates cost $3.00 per pound and mixed nuts cost $6.00 per pound and Clint has abudget of $5.10 per pound of trail mix. Using the variables c and n to represent thenumber of pounds of chocolate and the number of pounds of nuts he should userespectively, determine a system of equations that describes the situation.Enter the equations below separated by a comma.How many pounds of chocolate should he use?How many pounds of mixed nuts should he use? Pls see the picture
Answers
Since c represents the number of pounds of chocolates
Since n represents the number of pounds of nuts
Since Clint is making 10 pounds of them, then
[tex]c+n=10\rightarrow(1)[/tex]Since the cost of 1 pound of chocolates is $3.00
Since the cost of 1 pound of nuts is $6.00
Since the Clint budget is $5.1 per pound, then
[tex]10\times5.1-\text{ \$51}[/tex]Multiply c by 3 and n by 6, then add the products and equate the sum by 51
[tex]\begin{gathered} 3(c)+6(n)=5.1 \\ 3c+6n=51\rightarrow(2) \end{gathered}[/tex]The system of equations is
c + n = 10
3c + 6n = 51
Let us solve them
Multiply equation (1) by -3 to make the coefficient of c equal in values and different in signs
[tex]\begin{gathered} -3(c)-3(n)=-3(10) \\ -3c-3n=-30\rightarrow(3) \end{gathered}[/tex]Add equations (2) and (3)
[tex]\begin{gathered} (3c-3c)+(6n-3n)=(51-30) \\ 0+3n=21 \\ 3n=21 \end{gathered}[/tex]Divide both sides by 3 to find n
[tex]\begin{gathered} \frac{3n}{3}=\frac{21}{3} \\ n=7 \end{gathered}[/tex]Substitute n by 7 in equation (1)
[tex]c+7=10[/tex]Subtract 7 from both sides
[tex]\begin{gathered} c+7-7=10-7 \\ c=3 \end{gathered}[/tex]He should use 3 pounds of chocolate
He should use 7 pounds of nuts
If his budget is $51
A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t - 6t^2 meters in t seconds. How high does the rock go? How long does it take the rock to reach its highest point?1190 m, 10 sec600 m, 10 sec1200 m, 20 sec2280 m, 20 sec
Answers
Substitute t = 10, and t = 20, to the given equation and we get
[tex]\begin{gathered} \text{If }t=10 \\ s=120t-6t^2 \\ s=120(10)-6(10)^2 \\ s=1200-6(100) \\ s=1200-600 \\ s=600 \\ \\ \text{If }t=20 \\ s=120t-6t^{2} \\ s=120(20)-6(20)^2 \\ s=2400-6(400)^2 \\ s=2400-2400 \\ s=0 \end{gathered}[/tex]We therefore have t = 10 as the time it takes to reach the highest point, with the rock reaching 600m.
Therefore, we choose second option.
what's the equation of the line that passes through the points (-9,-8) and (-6,6) in point slope form
Answers
The equation of the line passing through the given points in the point slope form is;
[tex]y-6\text{ = }\frac{14}{3}(x\text{ + 6)}[/tex]Here, we want to find the equation of the line that passes through the given points
Mathematically, we can write the equation of a line as follows in point slope form;
[tex]y-y_1=m(x-x_1)[/tex]m here represents the slope of the line
To calculate m which is the slope, we use the slope equation as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ m\text{ = }\frac{6-(-8)}{-6-(-9)}\text{ = }\frac{6\text{ + 8}}{-6\text{ + 9}}\text{ = } \\ =\text{ }\frac{14}{3} \end{gathered}[/tex]To write the equation, we use any of the two given points.
Thus, we have;
[tex]\begin{gathered} y-6\text{ = }\frac{14}{3}(x-(-6)) \\ \\ y-6\text{ = }\frac{14}{3}(x\text{ + 6)} \end{gathered}[/tex]6. x^2-10x+21Factors:(__________________________)(_____________________)
Answers
Factorising the given expression through sum-product pattern and grouping the factors, we find out that the factors of the given expression are (x-7) and (x-3).
The given expression is -
[tex]x^{2} -10x+21[/tex] ---- (1)
We have to find out the factors of the given expression.
Now, from equation (1), we have
[tex]x^{2} -10x+21[/tex]
This can also be written in the form of sum-product pattern as -
[tex]x^{2} -10x+21\\=x^{2} -7x-3x+21\\[/tex]
Now, grouping the common factors together, we can rewrite it as -
[tex]x^{2} -7x-3x+21\\=x(x-7)-3(x-7)\\=(x-7)(x-3)[/tex](Rewriting in factored form)
Thus, factorising the given expression through sum-product pattern, we find out that its factors are (x-7) and (x-3).
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Deon will choose between two restaurants to purchase pizzas for his party. The first restaurant charges a delivery fee of $2 for the entire purchase and $10 perpizza. The second restaurant charges a delivery fee of $5 for the entire purchase and $9 per pizza.Let x be the number of pizzas purchased.(questions included in photo)
Answers
a) We have to write an expression of the total charge for each restaurant.
The first reastaurant has a fixed charge of $2 and then $10 per pizza.
Then, if x is the number of pizzas, we can express the total charge as:
[tex]C_1(x)=2+10x[/tex]The second restaurant has a fee of $5 and charges $9 per pizza, so thetotal charge will be:
[tex]C_2(x)=5+9x[/tex]b) If the total charge is equal for both restaurants, we can write:
[tex]\begin{gathered} C_1(x)=C_2(x) \\ 2+10x=5+9x \end{gathered}[/tex]We can solve it for x as:
[tex]\begin{gathered} 2+10x=5+9x \\ 10x-9x=5-2 \\ x=3 \end{gathered}[/tex]Answer:
a) Total charge for the first restaurant = 2+10x
Total charge for the second restaurant = 5+9x
b) 2+10x = 5+9x
Hello! I need help solving and answering this practice problem. Having trouble with it.
Answers
In this problem, we have an arithmetic sequence with:
• first term a_1 = -22,
,• common difference r = 5.
The terms of the arithmetic sequence are given by the following relation:
[tex]a_n=a_1+r\cdot(n-1)\text{.}[/tex]Replacing the values a_1 = -22 and r = 5, we have:
[tex]a_n=-22+5\cdot(n-1)=-22+5n-5=5n-27.[/tex]We must compute the sum of the first 30 terms of the sequence.
The sum of the first N terms of a sequence is:
[tex]\begin{gathered} S=\sum ^N_{n\mathop=1}a_n=\sum ^N_{n\mathop{=}1}(5n-27) \\ =5\cdot\sum ^N_{n\mathop{=}1}n-27\cdot\sum ^N_{n\mathop{=}1}1 \\ =5\cdot\frac{N\cdot(N+1)}{2}-27\cdot N. \end{gathered}[/tex]Where we have used the relations:
[tex]\begin{gathered} \sum ^N_{n\mathop{=}1}n=\frac{N\cdot(N+1)}{2}, \\ \sum ^N_{n\mathop{=}1}1=N\text{.} \end{gathered}[/tex]Replacing the value N = 30 in the formula for the sum S, we get:
[tex]S=5\cdot\frac{30\cdot31}{2}-27\cdot30=1515.[/tex]Answer
sum = 1515