To evaluate f(x)=3x3+x2−5x−14 when x=−2, use synthetic division to divide the polynomial by -2 and find the resulting value.
Explanation:To evaluate f(x) = 3x^3 + x^2 - 5x - 14 when x = -2, we can use synthetic division. First, set up the synthetic division table with -2 as the divisor and the coefficients of the polynomial as the dividend.
Perform the synthetic division by bringing down the first coefficient, multiplying it by the divisor and adding it to the next coefficient, then continuing the process until you reach the last coefficient. The result in the last row of the table will be the evaluated value of the polynomial.
In this case, the evaluated value of f(x) when x = -2 is 0.
Final answer:
To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, use synthetic division to divide the polynomial by x + 2.
Explanation:
To evaluate f(x)=3x^3+x^2-5x-14 when x=-2, we can use synthetic division. First, write the coefficients of the polynomial in order: 3, 1, -5, -14. The divisor will be x - (-2), which simplifies to x + 2. Set up the synthetic division table and perform the division. The result will be the quotient and the remainder. In this case, the quotient is 3x^2 - 5x - 7 and the remainder is -20.
Complete the square to determine the minimum or maximum value of the function defined by the expression.
x2 − 10x + 15
A) maximum value at −10
B) minimum value at −10
C) maximum value at −15
D) minimum value at −15
Answer:
Option B) minimum value at −10
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -10x+15[/tex]
This function represent a vertical parabola open upward (because the leading coefficient is positive)
The vertex represent a minimum
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-15=x^{2} -10x[/tex]
Divide the coefficient of term x by 2
10/2=5
squared the term and add to the right side of equation
[tex]f(x)-15=(x^{2} -10x+5^2)[/tex]
Remember to balance the equation by adding the same constants to the other side
[tex]f(x)-15+5^2=(x^{2} -10x+5^2)[/tex]
[tex]f(x)+10=(x^{2} -10x+25)[/tex]
rewrite as perfect squares
[tex]f(x)+10=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}-10[/tex] ----> function in vertex form
The vertex of the quadratic function is the point (5,-10)
therefore
The minimum value of the function is -10
x-2y=-3 and 14y-7x=21
Answer:
Infinitely many solutions.
Step-by-step explanation:
x-2y=-3
14y-7x=21
-------------
simplify 14y-7x=21 into 2y-x=3
x-2y=-3
2y-x=3
--------------
x=2y+(-3)
x=2y-3
2y-(2y-3)=3
2y-2y+3=3
0+3=3
infinitely many solutions
The ratio of boys to girls on the bus is 3:2. If there are 18 boys on the
bus, how many girls are on the bus?
Answer:
12 girls 18 boys Total 30 students
Step-by-step explanation
x=number of girls
18/3 = x/2
3x=18*2
3x=36
x=12
Other proof
x= number of groups
3x +2x = 30
5x=30
x=6
3*(6) + 2*(6) = 30
18+12=30
Weat is the
The point slope form of the equation of the line that passes through (-9, -2) and (1, 3) is
slope-intercept form of the equation for this line?
o y = 2 x + 2
0 y = 2 x 4
o y = x + 2
O y = x - 2
Save and Exit
Submit
e
.
o
Answer:
The slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
Step-by-step explanation:
Here,the two given point s are A ( -9,-2) and B (1,3).
Now, the slope m of the line AB = [tex]= \frac{y_2 - y_1}{x_2 -x_1}[/tex]
[tex]\implies m = \frac{3 - (-2)}{1 - (-9)} = \frac{3+2}{1+9} = \frac{5}{10} = \frac{1}{2}[/tex]
or, the slope of line AB = 1/2
Now, the POINT SLOPE FORM of any equation with point (x0,y0) and slope m is given as :
y - y0 = m (x -x0)
So, the line equation of AB is given as :
[tex]y - 3 = \frac{1}{2} ( x-1)\\\implies y =3 + \frac{1}{2} ( x-1)\\or, y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
SLOPE INTERCEPT form is y = mx + c
Hence, the slope intercept of the given line equation AB is [tex]y = \frac{1}{2} ( x)- \frac{5}{2}[/tex]
Section 5.4 Exercise 16
The mean household income in a country in a recent year was about $69,953 and the standard deviation was about $90,000. (The median income was $55,517)
a) If a Normal model was used for these incomes, what would be the household income of the top 4%?
b) How confident should one be in the answer in part a?
c) Why might the Normal model not be a good one for incomes?
a) The income would be s
(Round to the nearest dollar as needed)
Answer:
Step-by-step explanation:
a) To find the household income of the top 4%, we can use the standard Normal distribution table or calculator to find the Z-score associated with the 96th percentile.
The Z-score corresponding to the 96th percentile is approximately 1.75. We can then use the Z-score formula to find the income value:
Z = (x - mean) / standard deviation
1.75 = (x - 69953) / 90000
x - 69953 = 1.75 * 90000
x - 69953 = 157500
x = 227453
Therefore, the household income of the top 4% is about $227,453.
b) The answer in part a should be taken with some caution as the Normal model assumes that the incomes follow a bell-shaped distribution, which may not be the case for all income distributions.
c) The Normal model may not be a good one for incomes because incomes often have a skewed distribution with a long tail to the right, meaning there are a small number of individuals with very high incomes that can greatly affect the mean and standard deviation. In addition, incomes may have outliers or gaps that are not well captured by a Normal distribution.
Use the compound interest formulas A=P(1+r/n)^nt and A=Pe^rt to solve the problem given. Round answers to the nearest cent.
Find the accumulated value of an investment of $15,000 for 6 years at an interest rate of 4% if the money is a. compounded
semiannually; b. compounded quarterly: c. compounded monthly d. compounded continuously.
Answer:
a) $19,023.63
b) $19,046.02
c) $19,061.13
d) $19,068.74
Step-by-step explanation:
P = 15000
t = 6
r = 0.04
a) Compounded semiannually means 2 times per year, so n = 2.
A = 15000 (1 + 0.04/2)^(2×6)
A = 19023.63
b) Compounded quarterly means 4 times per year, so n = 4.
A = 15000 (1 + 0.04/4)^(4×6)
A = 19046.02
c) Compounded monthly means 12 times per year, so n = 12.
A = 15000 (1 + 0.04/12)^(12×6)
A = 19061.13
d) Compounded continuously means we use the continuous equation:
A = 15000 e^(0.04×6)
A = 19068.74
The animal shelter charges $119 to adopt a pet. On Saturday, 2 dogs and 7 cats were adopted. How much money did the animal shelter receive from those adoptions?
PLEASE HELP ME FAST!
The balance in two separate bank accounts grow each month at different rates. The growth rates for both accounts are represented by the functions f(x)=3^x and g(x)=5x+25. In what month is the f(x) balance greater than the g(x) balance? Show your work!
P.S Whoever gives me a good answer and shows their work I will make as Brainliest!
Answer:
From fourth month onwards, the growth rate of [tex]f(x)[/tex] is greater than that of [tex]g(x)[/tex].
Step-by-step explanation:
Given:
The growth rates of both bank accounts are given as:
[tex]f(x)=3^x\\g(x)=5x+25[/tex]
Now, as per question, we need to find the value of 'x' when the value of [tex]f(x)>g(x)[/tex]. Or,
[tex]3^x>5x+25[/tex]
Now, we can do this by checking the values of 'x' by hit and trial method.
Let [tex]x=1[/tex]. The inequality becomes:
[tex]3^1>5(1)+25\\3>30(False)[/tex]
Let [tex]x=2[/tex]. The inequality becomes:
[tex]3^2>5(2)+25\\9>35(False)[/tex]
Let [tex]x=3[/tex]. The inequality becomes:
[tex]3^3>5(3)+25\\27>40(False)[/tex]
Let [tex]x=4[/tex]. The inequality becomes:
[tex]3^4>5(4)+25\\81>45(True)[/tex]
Therefore, the value of 'x' for which [tex]f(x)>g(x)[/tex] is 4.
So, from the fourth month onwards, the balance in [tex]f(x)[/tex] becomes greater than [tex]g(x)[/tex].
The graphical solution is shown below to support the same.
From the graph, we can conclude that after the 'x' value equals 3.4, the graph of [tex]f(x)[/tex] lies above of [tex]g(x)[/tex]. Hence, [tex]f(x)>g(x)[/tex] for [tex]x>3.4[/tex]
8 people eat at Charlie Brown's for Thanksgiving. How many different seating
arrangements can be formed around the ping pong table?
Answer: 40,320
Step-by-step explanation: Let's say that there is person A,B,C,D,E,F,G,H. and 8 chairs. For the first chair, 8 different people could potentially sit in it, making 8 different possibilities. No matter who sits there, the logic follows the next table. However, since one person is sitting in the first chair, there are 7 different possibilities about who would be sitting in the second chair. If you multiply the two together, there are 56 different possibilities just for the first and second chair. For the third chair, there are 6 different possibilities about whom could sit. Multiply 56*6 and you get 336 possibilities. Keep multiplying out and you get a grand total of 40,320 different arrangements!
Answer:
5040
Step-by-step explanation:
The answer is (8 - 1)!
The reason is that the first person is fixed. Any place is the same as any other place. After that there are 7! choices for the next position.
Answer: 5040
At a track meet, Tim ran at a constant speed of 300 meters per minute.
After 8 minutes, he still had 600 meters left to run.
The distance Tim ran was three times as long as the distance Eric ran.
What was the distance that Eric ran?
Tim ran a total of 3000 meters, which is three times the distance that Eric ran. By dividing Tim's distance by three, we find that Eric ran 1000 meters.
Explanation:To solve for the distance Eric ran, we need to first determine the total distance Tim ran and then divide that by three as Tim's distance is three times longer than Eric's.
Tim's speed is 300 meters per minute, and he ran for 8 minutes before having 600 meters left to run. To calculate the distance Tim ran:
Multiply Tim's speed by the time he ran: 300 meters/minute * 8 minutes = 2400 meters.Add the remaining distance to determine Tim's total distance: 2400 meters + 600 meters = 3000 meters.Since Tim's distance is three times Eric's distance, divide Tim's total distance by three to find Eric's distance: 3000 meters / 3 = 1000 meters.Therefore, the distance that Eric ran was 1000 meters.
Mr. Smith had 33 dozen cans. He sold 340 of them at 15$ each. He sold the remaining cans at a discount of 20% each. How much money did he collect from selling the cans.
he collected a total of $5,772 from selling all the cans.
Mr. Smith collected $5,772 from selling all the cans.
He sold 340 cans at full price for a total of $5,100.
He sold the remaining 39 cans at a discount of 20% each, for a total of $672.
Therefore, he collected a total of $5,772 from selling all the cans.
for such more question on discount
https://brainly.com/question/23865811
#SPJ3
6. Find the selling price of each of the following:
(i) a television set marked €800 + VAT at 20%
Answer:
€960
Step-by-step explanation:
€800 + VAT at 20%
€800 + 20% of €800 =
= €800 + 20% * €800
= €800 + 0.2 * €800
= €800 + €160
= €960
When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
When y is 4, p is 0.5, and m is 2, x is 2. If x varies directly with the product of p and m and inversely with y, which equation models the situation?
xpmy=8
xy/pm=8
xpm/y=0.5
x/pmy=0.5
Answer:The equation models the situation is [tex]\frac{x y}{p m}=8[/tex]
Solution:Given that
x is 2, y is 4, p is 0.5, and m is 2
x varies directly with the product of p and m
x varies inversely with y
[tex]\text {Product of } p \text { and } m=p \times m=p m[/tex]
x varies directly with the product of p and m
[tex]=>x \propto p m[/tex] ---- eqn 1
As x varies inversely with y,
[tex]=>x \propto \frac{1}{y}[/tex] ----- eqn 2
From (1) and 2, we can say that
[tex]x \propto \frac{p m}{y}[/tex]
[tex]\Rightarrow x=k \frac{p m}{y}[/tex]
where k is constant of proportionality
[tex]\Rightarrow \frac{x y}{p m}=k[/tex] ---- eqn 3
On substituting given values of x = 2, y = 4, p = 0.5 and m= 2 in eqn (3) we get
[tex]\frac{x y}{p m}=\frac{2 \times 4}{0.5 \times 2}=k[/tex]
[tex]\begin{array}{l}{\frac{x y}{p m}=\frac{8}{1}=k} \\\\ {=>\frac{x y}{p m}=8}\end{array}[/tex]
Hence correct option is second that is [tex]\frac{x y}{p m}=8[/tex]
Answer:
B
Step-by-step explanation:
what is -87 = 1 + 8x?
Answer:
-87= 1 + 8x
-88= 8x
x= -11
Basically bring over the one to the other side of the equation and solve for x by dividing.
4x+(x-y/8)=17 and 2y+x-(5y+2/4)=2 by using elimination method
Answer:
x=811/238, y=36/119. (811/238, 36/119).
Step-by-step explanation:
4x+(x-y/8)=17
2y+x-(5y+2/4)=2
-----------------------
4x+x-y/8=17
5x-y/8=17
40x-y=136
y=40x-136
------------------
2y+x-5y-2/4=2
2y-5y+x-1/2=2
-3y+x=2+1/2
-3y+x=4/2+1/2
-3y+x=5/2
-3(40x-136)+x=5/2
-120x+408+x=5/2
-119x=5/2-408
-119x=5/2-816/2
-119x=-811/2
119x=811/2
x=(811/2)/119
x=(811/2)(1/119)=811/238
y=40(811/238)-136
y=16220/119-136
y=36/119
x=811/238, y=36/119.
June is 16 less than 11 times the average number of tornado's in december
Answer:
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
Step-by-step explanation:
The complete question is
The average number of tornado's in June is 16 less than 11 times the average number of tornado's in December. If the difference between the average number of tornado's in June and December is 204,determine the average number of tornado's in December and June.
Let
x ----> the average number of tornado's in June
y ----> the average number of tornado's in December
we know that
[tex]x=11y-16[/tex] ---> equation A
[tex]x-y=204[/tex] ----> equation B
solve the system by substitution
substitute equation A in equation B
[tex]11y-16-y=204[/tex]
solve for y
[tex]10y=204+16[/tex]
[tex]10y=220[/tex]
[tex]y=22[/tex]
Find the value of x
[tex]x=11y-16[/tex] ----> [tex]x=11(22)-16=226[/tex]
therefore
The average number of tornado's in December is 22 and the average number of tornado's in June is 226
The car salesman earns $850 per week plus 20% commission for each car the salesman sells. The salesman sold a used car for $2000 last week, which represents the amount of money the salesman took home? Show Work!
(A) $850.00
(B) $860.00
(C) $1,250.00
(D) $2,850.00
Answer:
The answer is C. $1,250.00
Step-by-step explanation:
850+2,000×20%
First you add 850 and 2,000 and that will turn out to 2,850
2,850×20%
Then you take that 2,850 and multiply it by 20% and that would be 1,250
850+2,000×20%
2,850×20%
1,250
I hope that this helps and may I receive brainliest please
Kyle has a notebook for each of his 13 classes.He puts 5 stickers on each notebook.There are 10 stickers on each sheet.How many sheets of stickers will Kyle need?
13 * 5 = 65
So, he needs 65 stickers
65/10 = 6.5
He will need 7 sheets, but will only use 6 and a half sheets.
Kyle will need to buy 7 sheets of stickers to have enough for all 13 of his notebooks, given that each notebook requires 5 stickers and each sheet contains 10 stickers.
Explanation:Kyle needs a total of 65 stickers for his 13 notebooks, since he puts 5 stickers on each notebook. There are 10 stickers per sheet, so to find out how many sheets Kyle needs, we divide the total number of stickers by the number of stickers per sheet: 65 stickers ÷ 10 stickers/sheet = 6.5 sheets. Since Kyle cannot buy half of a sticker sheet, he will need to buy 7 sheets of stickers to have enough for all his notebooks.
Which equation has a graph that lies entirely above the x-axis?
Oy= -(x + 7)2 + 7
O y=(x-77²-7
y = (x – 7)2 + 7
y = (x – 7)
Answer:
y = [tex](x-7)^{2}[/tex] + 7Step-by-step explanation:
The graph that will lie above the x-axis will be having only positive values throughout its domain,
So, We have to check which graph is having y > 0 for every x.
y = -[tex](x+7)^{2}[/tex] + 7clearly y will be negative for many values of x , as coefficient of variable is negative.
y = [tex](x-7)^{2}[/tex] - 7Put x = 0, you will get y as negative .
y = [tex](x-7)^{2}[/tex] + 7Since, Square of anything will always be positive , and here constant term is also positive , so, It will always be positive .
Thus, it is having its graph always above x axis.
y = x - 7Put x = 0 , y = -7, which is negative
Answer:
Option C.
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex]
where, a is constant, (h,k) is vertex.
If a<0, then it is a downward parabola and if a>0, then it is an upward parabola.
A downward parabola never lies entirely above the x-axis.
First equation is
[tex]y=-(x+7)^2+7[/tex]
It is a downward parabola and vertex is (-7,7).
Second equation is
[tex]y=(x-7)^2-7[/tex]
It is an upward parabola and vertex is (7,-7).
Third equation is
[tex]y=(x-7)^2+7[/tex]
It is an upward parabola and vertex is (7,7).
Fourth equation is
[tex]y=(x-7)[/tex]
It is a linear equation with y-intercept -7.
Only equation 3 is an upward parabola whose vertex lies above the x-axis.
Hence the correct option is C.
Jack used 1 2 of a bag of okra to make 1 4 of a gallon of jambalaya. If Jack's recipe is for 1 gallon of jambalaya, how much okra will he need to make double the recipe? A) 1 bag of okra B) 2 bags of okra C) 3 bags of okra D) 4 bags of okra
Answer:
4 bags of okra
Step-by-step explanation:
To find the unit rate: multiply the numerator by the reciprocal of the denominator.
unit rate =
1/2 divided by 1/4
= 1/2× 4/1
=4/2
= 2 bags per gallon
Therefore, double the recipe: 2 × 2 = 4 bags of okra
HOMEWORK
Solve.
3. Henry's desk is 1 meter long. His nametag is
8 centimeters long. Henry says his nametag is
7 centimeters longer than his desk. What error
did Henry make? Explain how to correct it.
The mistake he made was that he did not consider units of measurement while comparing the lengths
He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters
Step-by-step explanation:
Length of desk = 1 meter
Henry's name tag = 8 cm
Henry says that his name tag is 7 cm longer than the desk. The mistake he made was that he did not compare the units of both quantities. He just subtracted 1 from 8 and got 7. Meter is a larger unit and centimeter is a smaller unit. In order to compare the lengths of the desk and his name tag the units have to be same.
Hence
The mistake he made was that he did not consider units of measurement while comparing the lengths
He has to convert the both quantities into the same unit to compare the lengths either centimeters to meters or meters to centimeters
Keywords: Measurement
Learn more about measurement at:
brainly.com/question/10894205brainly.com/question/10987396#LearnwithBrainly
Final answer:
Henry mistakenly claimed his nametag was 7 centimeters longer than his desk due to a unit conversion error. His desk is 100 centimeters long, and his nametag is 8 centimeters long, making the nametag 92 centimeters shorter than the desk. The error is corrected by accurately comparing lengths in the same unit.
Explanation:
The question asks to identify the error Henry made in stating that his nametag is 7 centimeters longer than his desk and to explain how to correct it. Henry's desk is 1 meter long, which is equivalent to 100 centimeters, and his nametag is 8 centimeters long. The error Henry made is in the comparison of the lengths in different units and misunderstanding of the concept of length comparison. To correct this error, both lengths should be in the same unit, and then we compare or subtract to find the difference or relation.
The correct comparison is as follows:
Desk length in centimeters: 100 cm
Nametag length: 8 cm
So, rather than the nametag being 7 centimeters longer, it is 92 centimeters shorter than the desk. The correction is understanding unit conversion and accurately comparing lengths.
The board of directors of a corporation must select a president a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board of directors
There are 9240 possible ways in which a president, a secretary and a treasurer can be selected from the 22 members on the board of directors.
Solution:Give that the board of directors of a corporation must select a president a secretary and a treasurer.
Need to calculate in how many possible ways this can be accomplished if there are 22 members on the board of directors
Here we are assuming that one person can hold only one position means one if get selected for president he is out of the race for remaining positions that are secretary and treasure
Lets for sake of understanding, we simplify our question.
Lets say there are 3 members A , B and C . In how many ways two positions of Secretary and treasurer can be filled .
So for selecting secretary we have three option that are A , B or C.
And once secretary is selected , number of option for selecting treasure is two.
So it is found that number of selecting 2 positions for 3 members is product of option available for selecting first position that is secretary multiplied by option available for selecting second position that is treasurer = 3 x 2 = 6
So now applying same logic for selecting members for 3 positions from 22 menbers we get
For selecting president members available = 22
Once president is selected, then option available for selecting a Secretary = 21
And one secretary is also selected, then option available for selecting a treasure = 20
So number of ways in which three positions can be filled by 22 member = 22 x 21 x 20 = 9240
Hence there are 9240 possible ways in which a president , a secretary and a treasurer can be selected from the 22 members on the board of directors.
what is the slope and y intercept of the function k(x)=7/9x-2
Answer:
For the given function, Slope is [tex]\frac{7}{9}[/tex] and y-intercept is -2.
Step-by-step explanation:
The given function in x is :
[tex]k(x)=\frac{7}{9}x-2[/tex] .....1
Since, we know that the general form of equation of a line is :
[tex]y=mx+c[/tex] .....2
where, y is the dependent variable, x is independent variable, m is the slope and c is the y intercept of the line.
On comparing equation 1 and 2, we get :
[tex]k(x) = y[/tex];
[tex]m = \frac{7}{9}[/tex]; and
[tex]c=-2[/tex];
Thus, we can conclude that
slope of function is [tex]\frac{7}{9}[/tex] and y-intercept is -2.
Scott buys candy that costs $8 per pound. He will buy at least 5 pounds of candy. What are the possible amounts he will spend on candy?
Use c for the amount (in dollars) Scott will spend on candy.
Write your answer as an inequality solved for c .
Answer: 8*5≥c
sorry if wrong! Not my strong suit !
Final answer:
Scott spends at least $40 on candy if buying a minimum of 5 pounds at $8 per pound.
Explanation:
Scott buys candy at $8 per pound and will buy at least 5 pounds. Let's use c for the amount he will spend on candy. The possible amounts he will spend on candy can be expressed as:
5 pounds x $8/pound ≤ c would mean $40 ≤ c
Therefore, the inequality solved for c is $40 ≤ c.
3×1+6×1/10+5×1/100+7×1/1000
Answer:
The Answer is [tex]\frac{3657}{1000} \ or \ 3.657[/tex]
Step-by-step explanation:
Given
[tex]3\times1+\frac{6\times1}{10}+\frac{5\times1}{100}+\frac{7\times1}{1000}\\[/tex]
Now Solving Above using PEDMAS rule we get;
[tex]3+\frac{6}{10}+\frac{5}{100}+\frac{7}{1000}[/tex]
Now we will make take LCM we get;
[tex]\frac{3\times1000}{1000}+\frac{6\times100}{10\times100}+\frac{5\times10}{100\times10}+\frac{7\times1}{1000}\\\\\frac{3000}{1000}+\frac{600}{1000}+\frac{50}{1000}+\frac{7}{1000}\\\\\frac{3000+600+50+7}{1000}\\\\\frac{3657}{1000} \ or \ 3.657[/tex]
Hence the answer is [tex]\frac{3657}{1000} \ or \ 3.657[/tex]
Three consecutive even integers have the property that when the difference between the first and twice the second is found, the result is eight more than the third. Find the three consecutive even integers
Consecutive even integers are -8, -6 and -4
Step-by-step explanation:
Let be the first even integer then the next two integers will be: x+2 and x+6
According to given property, we get
[tex]x - 2(x+2) = (x+4)+8\\x-2x-4 = x+4+8\\-x-4 = x+12\\-x-x = 12+4\\-2x = 16[/tex]
Dividing both sides by -2
[tex]\frac{-2x}{-2} = \frac{16}{-2}\\x = -8[/tex]
The two next integers are:
x+2 = -8+2 = -6
x+4 = -8+4 = -4
Verification:
[tex]-8-2(-6) = -4+8\\-8+12 = +4\\4 = 4[/tex]
Hence, Consecutive even integers are -8, -6 and -4
Keywords: Linear equation, Variables
Learn more about linear equation at:
brainly.com/question/10677255brainly.com/question/10689103#LearnwithBrainly
how do u slove for 3x-6=15
Add 6 on both sides, canceling out that -6
3x = 21
Divide both sides by 3 to isolate that variable and get your answer
x = 7.
Answer:
x=7
Step-by-step explanation:
3x-6+6=15+6
3x=21
3x/3=21/3
x=7
578 business and personal emails there are 30 fewer personal emails so how many personal emails
Answer:
Personal emails = 274 emails.
Step-by-step explanation:
Given,
Business and personal emails = 578
Therefore, there are two types of emails. Again, there are 30 fewer emails in personal emails.
The total number of emails after deducting the fewer personal emails = (578 - 30) = 548 emails.
Therefore, each type of email, according to the question = (548/2) = 274 emails
So, personal emails are 274. Business emails = (274 + 30) = 304 emails.
The problem involves setting up and solving an equation based on the information given: that the number of personal emails is 30 fewer than the number of business emails, and the total is 578. By doing this, we deduce that there are 274 personal emails.
Explanation:The problem tells us that there is a total of 578 emails, both business and personal combined. Furthermore, we know that there are 30 fewer personal emails than business emails. We can use this information to create an equation and solve for the number of personal emails.
First, we can represent the number of business emails as 'x'. So, the number of personal emails would be 'x - 30'. The sum of the business and personal emails is 578, so our equation is x + (x - 30) = 578.
Solving this equation gives us: 2x - 30 = 578, 2x = 608 and finally x = 304. This is the number of business emails. To get the number of personal emails, you subtract 30 from the total business emails (as the question states). So, there are 304 - 30 = 274 personal emails.
Learn more about Solving Equations here:https://brainly.com/question/14410653
#SPJ12
A backpack is normally $64.99,but sale,it is marked down to $45.49.what percent off is the sale price?
Answer:
30%
Step-by-step explanation:
Here we want to setup the equation
[tex]y = a - (a\times x)[/tex]
where y is the discounted price, a is the normal price and x is the percent off. so now we wanna plug in known values and solve for percent off.
[tex]45.49 = 64.99 - (64.99x)[/tex]
through algebra,
[tex] - 19.5 = - (64.99x)[/tex]
[tex] \frac{ - 19.5}{ - 64.99} = x[/tex]
[tex]x = .3000...[/tex]
so in percentage that is 30%
Which unit rate is higher 24 for 5 or 5 for 24
Answer:
24 for 5 is higher because you have to divide 24 by 5 and if you do that it gives you $4.8, while 5 for 24 gives you a unit rate of $0.20.