The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B
if m<10=77 ,m<7=47 and m<16=139, find the missing measure of m<2=?
Note that a and b are parallel lines with a transversal line of c.
<10 is congruent to <8
so :
<8 = 77
<2 and <8 are supplementary (sum of 180 degrees)
<2 + <8 = 180
<2 + 77 = 180
<2 = 103
The answer is :
<2 = 103 deg
I'll just send you the picture. there's too much to type
ANSWER
[tex]\text{ \$278.75}[/tex]EXPLANATION
We have that Sammi has $125.75 in her account and deposits (adds) $25.50 every month for 6 months.
To find how much is there after 6 months, first, find out how much she added to the account and then add that to the initial amount that was there.
After 6 months she deposited:
[tex]\begin{gathered} 6\cdot25.50 \\ \text{ \$153} \end{gathered}[/tex]Now, add that to the initial amount there:
[tex]\begin{gathered} 125.75+153 \\ \text{ \$278.75} \end{gathered}[/tex]That is the amount in the account at the end of 6 months.
Plot the inequality on the given number line. Toggle the "Dot" or "Open Dot" button to place the correct dot on your line before you submit your answer.x<0Write the inequality using interval notation. Use "oo" (two lower case o's) for∞.
Answer:
(b) (-oo, 0)
Explanation:
Given the inequality:
[tex]x<0[/tex](a)The inequality is plotted on the number line below:
Note: An open circle is used for the inequalities, < and >.
(b)The inequality written using the interval notation is:
[tex](-\infty,0)[/tex]The sum of two numbers is at least 8, and the sum of one of the numbers and 3 times the second mumber isno more than 15.
As given by the question
There are given that the sum of the two numbers is at least 8.
Now,
Let the unknown numbers be x and y
Then,
If the sum of the two numbers is at least 8 then:
[tex]x+y\ge8[/tex]Similarly, the sum of one of the numbers and 3 times the second number is no more than 15
Then,
[tex]x+3y\leq15[/tex]Now,
From the both of the inequality:
[tex]\begin{gathered} x+y\ge8 \\ x+3y\leq15 \end{gathered}[/tex]Then, find the first and second nuber:
So,
[tex]\begin{gathered} x+y\ge8 \\ x\ge8-y\ldots(a) \end{gathered}[/tex]Then, Put the value of x into the second equation
Then,
[tex]\begin{gathered} x+3y\leq15 \\ 8-y+3y\leq15 \\ 8+2y\leq15 \\ 2y\leq15-8 \\ y\leq\frac{7}{2} \\ y\leq3.5 \end{gathered}[/tex]Then,
Put the value of y into the equation (a)
[tex]\begin{gathered} x\ge8-y \\ x\ge8-3.5 \\ x\ge4.5 \end{gathered}[/tex]Hence, the first number and second number is shown in below:
[tex]\begin{gathered} x\ge4.5 \\ y\leq3.5 \end{gathered}[/tex]The graph of the given result is shown below:
what will be the cost of material if the volume is 180in^3 and the surface area is 258in^2 and the cardboard cost $0.05 per square inch.cost of material is?
A material in the shape of a rectangular prism (cuboid) is given.
The volume and the surface area are given to be 180in³ and 258in², respectively. The cost of the material per square inch is given to be $0.05.
It is required to find the cost of the material.
To do this, since the cost per square inch is given, multiply the surface area by the cost per square inch:
[tex]258\times0.05=\$12.9[/tex]The cost of the material is $12.9.
In 9-16, estimate each product. 9. 0.12 x 105 10. 45.3 x 4 11. 99.2 x 82 12. 37 x 0.93 13. 1.67 X4 14. 3.2 x 184 15. 12 x 0.37 16. 0.904 x 75
9.
[tex]\begin{gathered} 0.12\cdot105=12.6 \\ 10.\text{ 45.3}\cdot4=181.2 \\ 11.\text{ 99.2}\cdot82=8134.4 \\ 12.\text{ 37}\cdot0.93=34.41 \\ 13.\text{ 1.67}\cdot4=6.68 \\ 14.\text{ 3.2}\cdot184=588.8 \\ 15.\text{ 12}\cdot0.37=4.44 \\ 16.\text{ 0.904}\cdot75=67.8 \end{gathered}[/tex]Find the center that eliminates the linear terms in the translation of 4x^2 - y^2 + 24x + 4y + 28 = 0.(-3, 2)(-3,- 2)(4, 0)
Step 1
Given;
[tex]4x^2-y^2+24x+4y+28=0[/tex]Required; To find the center that eliminates the linear terms
Step 2
[tex]\begin{gathered} 4x^2-y^2+24x+4y=-28 \\ 4x^2+24x-y^2+4y=-28 \\ Complete\text{ the square }; \\ 4x^2+24x \\ \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=4 \\ b=24 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\frac{24}{2\times4} \\ d=\frac{24}{8} \\ d=3 \end{gathered}[/tex][tex]\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{24^2}{4\times4} \\ e=0-\frac{576}{16}=-36 \end{gathered}[/tex]Step 3
Substitute a,d,e into the vertex form
[tex]\begin{gathered} a(x+d)^2+e \\ 4(x+_{}3)^2-36 \end{gathered}[/tex][tex]\begin{gathered} 4(x+3)^2-36-y^2+4y=-28 \\ 4(x+3)^2-y^2+4y=\text{ -28+36} \\ \\ \end{gathered}[/tex]Step 4
Completing the square for -y²+4y
[tex]\begin{gathered} \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=-1 \\ b=4 \\ c=0 \end{gathered}[/tex][tex]\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\text{ }\frac{4}{2\times-1} \\ d=\frac{4}{-2} \\ d=-2 \end{gathered}[/tex][tex]\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{4^2}{4\times(-1)} \\ \\ e=0-\frac{16}{-4} \\ e=4 \end{gathered}[/tex]Step 5
Substitute a,d,e into the vertex form
[tex]\begin{gathered} a(y+d)^2+e \\ =-1(y+(-2))^2+4 \\ =-(y-2)^2+4 \end{gathered}[/tex]Step 6
[tex]\begin{gathered} 4(x+3)^2-y^2+4y=\text{ -28+36} \\ 4(x+3)^2-(y-2)^2+4=-28+36 \\ 4(x+3)^2-(y-2)^2=-28+36-4 \\ 4(x+3)^2-(y-2)^2=4 \\ \frac{4(x+3)^2}{4}-\frac{(y-2)^2}{4}=\frac{4}{4} \\ (x+3)^2-\frac{(y-2)^2}{2^2}=1 \end{gathered}[/tex]Step 7
[tex]\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \text{This is the }form\text{ of a hyperbola.} \\ \text{From here } \\ a=1 \\ b=2 \\ k=2 \\ h=-3 \end{gathered}[/tex]Hence the answer is (-3,2)
Evaluate the following numerical expressions.a. 2(5+(3)(2)+4)b. 2((5+3)(2+4))c. 2(5+3(2+4))Can the parentheses in any of these expressions be removed without changing the value the expression?
So,
We're going to evaluate each expression as follows:
Let's begin with a:
[tex]\begin{gathered} 2(5+(3)(2)+4) \\ 2(5+6+4) \\ 2(15) \\ =30 \end{gathered}[/tex]Now, b:
[tex]\begin{gathered} 2((5+3)(2+4)) \\ 2((8)(6)) \\ =2(48) \\ =96 \end{gathered}[/tex]And, finally, c:
[tex]\begin{gathered} 2(5+3(2+4)) \\ 2(5+3(6)) \\ 2(5+18) \\ 2(23) \\ =46 \end{gathered}[/tex]Notice that if the parentheses change, the results wouldn't be the same.
a bike path is 8 miles. Max is 375% of the way to the end. How far is max on the path?
hello
the distance or length of the path is 8 miles.
Max is 375% of the way to the end. Let's find he distance of 375% on 8 miles
[tex]\begin{gathered} 375\text{ \% of 8} \\ \frac{375}{100}=\frac{x}{8} \\ \text{cross multiply both sides} \\ 100\times x=375\times8 \\ 100x=3000 \\ \frac{100x}{100}=\frac{3000}{100} \\ x=30 \end{gathered}[/tex]from the calculation above, Max is 30 miles away from the path
pls help i give brainliest
Answer: They bought 2 adult tickets and 3 children's tickets.
Step-by-step explanation: If you multiply the adult tickets, (5.10,) by 2, and then multiply the children's tickets (3.6), you will then add the products together. Your answer should come up as 21.00 dollars.
What is the density, in grams/cubic inch, of a substance with a mass of 6 grams filling a rectangular box with dimensions 2 in x 6 in x 3 in?6 8 0.11 0.17
Consider tha the density is calculated by using the following formula:
[tex]D=\frac{M}{V}[/tex]D is the density, M is the mass and V the volume. In this case, you have;
M = 6 g
V = 2 in x 6 in x 3 in = 36 in^3
Replace the previous values of the parameters into the formula for D:
[tex]D=\frac{6g}{36in^3}\approx0.17\frac{g}{in^3}[/tex]Hence, the density of the given substance is approximately 0.17 g/in^3
Solve the equation. – 4y - 37 = 6y + 13 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. y= (Type an integer or a simplified fraction.) B. The solution is all real numbers. C./ There is no solution.
solve for y:
add 4y to both sides:
[tex]\begin{gathered} -4y-37+4y=6y+13+4y \\ -37=10y+13 \end{gathered}[/tex]Subtract 13 from both sides:
[tex]\begin{gathered} -37-13=10y+13-13 \\ -50=10y \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10y}{10}=-\frac{50}{10} \\ y=-5 \end{gathered}[/tex]If the equation 6X equals 84, what is the next step in the equation solving sequence?
Answer: We have to find the next solution step for the following equation:
[tex]6x=84[/tex]The solution steps are:
[tex]\begin{gathered} 6x=84 \\ \\ \text{ Divide both sides by 6} \\ \\ \frac{6x}{6}=\frac{84}{6}\Rightarrow x=\frac{84}{6}=14 \\ \\ x=14 \end{gathered}[/tex]If Joey worked for himself and called his company “Joey’s Construction Company” and made $20,750 per year, how much would he pay per year in total Social Security and Medicare tax?
He would pay $3,154 in Social Security and Medicare tax
Explanation:Given that Joey worked for himself, he must pay doule the amount of Social Security and Medicare taxes to the government.
This makes 15.2% of $20,750
[tex]\begin{gathered} =\frac{15.2}{100}\times20750 \\ \\ =3154 \end{gathered}[/tex]He would pay $3,154 in total Social Security and Medicare tax
I am having trouble trying to figure out letter B
The confidence level is [0.1883, 0.3866] and the 95% confidence interval for the cost is [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
n = 80
a) p = 23/80 = 0.2875
% = 95
Standard error SE = √(p(1 - p)/n = √(0.2875(1 - 0.2875)/80)
z - score = 1.9599
Width of the confidence level = z x SE = 1.95996 x 0.05060 = 0.0991
Lower level of the confidence level = p - width = 0.2875 - 0.099177 = 0.1883
upper level of the confidence level = p + width = 0.2875 + 0.099177 = 0.3866778
The confidence level is [0.1883, 0.3866]
b) The 95% confidence level for the number of such customers = [0.1883 x 3000, 0.3866 x 3000] = [564.9, 1160.1]
The 95% confidence interval for the cost = [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
Therefore, the confidence level is [0.1883, 0.3866] and the 95% confidence interval for the cost is [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
To learn more about confidence level refer here
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2,-2,-6,-10,-14, ...how do I go about finding the explicit formula?
According to the given sequence, the difference is -4, because it's decreasing with that difference: 2-2 = -2; -2-4 = -6; and so on.
To find the explicit formula, we use the arithmetic sequence formula.
[tex]a_n=a_1+(n-1)d[/tex]Replacing all the given information, we have.
[tex]\begin{gathered} a_n=2+(n-1)\cdot(-4) \\ a_n=2-4n+4 \\ a_n=6-4n \end{gathered}[/tex]This explicit formula we can also express as
[tex]f(n)=6-4n[/tex]Find the terminal point on the unit circle determined by 4pi/3 radians
Given:
A terminal point on the unit circle determined by 4pi/3 radians
The unit circle has a radius = 1
the terminal point (x,y) will be calculated using the following formulas:
[tex]\begin{gathered} x=cos(\theta) \\ y=sin(\theta) \end{gathered}[/tex]Substitute θ = 4pi/3
[tex]\begin{gathered} x=cos(\frac{4\pi}{3})=-\frac{1}{2} \\ \\ y=sin(\frac{4\pi}{3})=-\frac{\sqrt{3}}{2} \end{gathered}[/tex]So, the answer will be:
[tex](x,y)=(-\frac{1}{2},-\frac{\sqrt{3}}{2})[/tex]find the average rate of change from x= -2 to x =1
We have the graph of a function of third grade and need to find the average rate of change between x=-2 and x=1.
We can see that:
[tex]\begin{gathered} \text{The rate of change is:} \\ \frac{dy}{dx} \\ \end{gathered}[/tex]So, the average between x=-2 and x=1 is:
[tex]undefined[/tex]The height and weight of adults can be related by the equation y = 48.3x 127 where a is height in feet and y is weight in poundsWhat does the slope of the line represent?A. the number of pounds heavier an adult one foot taller would weighB. the height of an adult weighing zero poundsOC. the average number of pounds per foot tallD. the number of adults in the sampleReset SelectionviousNext
The slope of the line y = 48.3x - 127 represents the number of pounds heavier an adult one foot taller would weigh .
The given line is y = 48.3x - 127
So we can use this equation to find the weight of various people of different heights.
At x = 6 , y = 48.3 × 6 - 127 = 162.8 pounds
At x = 7 , y = 48.3 × 7 - 127 = 211.1 pounds
Difference of the two weights = 211.1 - 162.8 = 48.3
The slope of something like a line in the plane consisting of the x and y axes is typically denoted by the letter m. This slope is calculated by dividing the linear change in the y coordinate between two separate points on the line by the equivalent change in the x coordinate.
Hence the slope which is 48.3 represents the difference in height of people who are a feet taller.
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20. You want to take your family on a two week vacation this summer, which is 5 months away The total cost for the vacation is $2,245. You work extra hours at your job at $11.25 per hour. Fifteen percent of your earnings go to taxes, and the rest goes toward the expenses for this vacation. Over next five months, what is the fewest number of extra hours per month you could work and still me enough money to take this vacation? A 35 ( C. 47 E.235 8.40 D. 200 AIS rregues stepl. In this ques we are given that guastotares family to go for at Vacation this summes need atat sum 15 Then, you need to hours at your sub this vacation
Assuming that all 5 months have 30 working days.
Let us assume that you need to do 'x' hours per month to get the extra money for vacation.
Given that overtime wage is $11.25 per hour, the wage (in $) for monthly overtime is obtained as,
[tex]\begin{gathered} \text{Monthly Overtime Wage}=\text{ Monthly overtime hours}\times\text{ Wage per hour} \\ \text{Monthly Overtime Wage}=x\times11.25 \\ \text{Monthly Overtime Wage}=11.25x \end{gathered}[/tex]Then the total amount (TA) earned in 5 months of overtime work is calculated as,
[tex]\begin{gathered} \text{ Total Amount}=\text{ Amount per month}\times\text{ No. of months} \\ \text{Total Amount}=11.25x\times5 \\ \text{Total Amount}=56.25x \end{gathered}[/tex]Given that the 15% of this amount earned goes for the tax, so the net amount earned is given by,
[tex]\begin{gathered} \text{Net Amount Earned}=(1-\frac{15}{100})\times56.25x \\ \text{Net Amount Earned}=(\frac{85}{100})\times56.25x \\ \text{Net Amount Earned}=47.8125x \end{gathered}[/tex]This net amount must be sufficient to cover the total cost of vacation $2245,
[tex]\begin{gathered} \text{ Net Amount Earned}=\text{ Expense on vacation} \\ 47.8125x=2245 \\ x=\frac{2245}{47.8125} \\ x=46.95 \\ x\approx47 \end{gathered}[/tex]Thus, you have to work 47 hours of overtime monthly to cover the cost of the vacation in 5 months.
Answer:
this guy is right
Step-by-step explanation:
Given P = 2L + 2W. Solve for W if P = 52 and L 18 W
First begin by making w the subject of formula
p = 2l + 2w
p-2l = 2w ( moving 2l to the left hand side )
[tex]\begin{gathered} \\ \frac{p\text{ - 2l}}{2}\text{ = w ( now we've made w the subject )} \end{gathered}[/tex]next substitute in your values p = 52 and l = 18
[tex]w\text{ = }\frac{p\text{ - 2l}}{2}\text{ = }\frac{52\text{ - 2(18)}}{2}\text{ = }\frac{52\text{ - 36}}{2}\text{ = }\frac{16}{2}\text{ = 8}[/tex]
Therefore the value for w in the expression is 8
If w = 18, what is the value of 3w − 11?
(A) 307
(B) 65
(C) 43
(D) 10
Answer: 43 ==>
Step-by-step explanation: 3w − 11=3(18)-11=54-11=43 ==> C.
Given that,
w = 18
3w - 11 = ?
3(18) - 11
54 - 11
43
correct option is (c) 43
Evaluate the equation: -9w = -54
Solution:
Given the equation:
[tex]-9w=-54[/tex]To solve for the unknown (w), we divide both sides of the equation by the coefficient of w.
The coefficient of w is -9.
Thus,
[tex]\begin{gathered} -\frac{9w}{-9}=-\frac{54}{-9} \\ \Rightarrow w=6 \end{gathered}[/tex]Hence, the value of w is
[tex]6[/tex]make a triangular garden in the backyard. you know that one side of your yard (ac) is 100 yards long and another side (ab) is 250 yards. in order for the garden to fit and not cross into the neighbor's yard, what must be the measure of angle b if angel c measures 95 degrees?
Law of sines for the given triangle:
[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]Use the equation above and the given data to solve angle B:
[tex]undefined[/tex]Find the value of n.1 x 4 = n
n = 4
The value of n is 4
TIME SENSITIVE The first step in solving this equation is to (BLANK) the second step is to (BLANK) solving this equation for X initially yields (BLANK) checking solution shows that (BLANK= 0 and 2 are valid solutions)
Give
[tex](4x)^{\frac{1}{3}}-x=0[/tex]
Procedure
The first step in solving this equation is to add x to both sides
[tex](4x)^{\frac{1}{3}}=x[/tex]The second step is to cube both sides
[tex]4x=x^3[/tex]solving this equation for X initially yields in three solutions
[tex]\begin{gathered} x(4-x^2)=0 \\ x(2-x)(2+x)=0 \end{gathered}[/tex]checking solution shows that x = 0, x = -2 and x = 2
The dot plot below shows 6 data points with the mean of 16What is the absolute deviation at 19?○3○4○7○8
we have that
The mean is 16
Find the difference between each data point and the mean
so
16-12=4
16-13=3
16-15=1
17-16=1
19-16=3
20-16=4
Find the average of these values
(4+3+1+1+3+4)/6
=16/6
=2.67
In the form (x+4)(x-2)=1, the zero-factor property can or cannot be used to solve equation?
The zero-factor property is
[tex](x+a)(x+b)=0[/tex]Then we equate each factor by 0 and find the values of x
The given equation is
[tex](x+4)(x-2)=1[/tex]Since the right side is not equal to 0, then
We can not use the zero-factor property to solve the equation
The answer is
zero-factor property cannot be used
Hello, I need help on the following question (it’s one problem but with multiple parts):
Part i. We are told that the cost for 3 throws is 1 dollar. This means that if "x" is the number of throws then the total cost must be:
[tex]C(x)=\frac{1\text{ dollar}}{3\text{ throws}}x[/tex]We can rewrite it in a simpler form as:
[tex]C(x)=\frac{1}{3}x[/tex]If we purchased the armband then this cost is equivalent to (1/6) of a dollar per throw plus the cost of the armband, we get:
[tex]C_2(x)=\frac{1}{6}x+10[/tex]Part ii. The graph of the two equations are two lines in the plane, like this:
In the graph, the red line represents the cost without the armband and the blue line represents the cost with the armband.
Part iii. We can see from the graph that if the number of throws is smaller than 60, then the cost is smaller without the armband, but if the cost is greater than 60 then the cost is smaller with the armband. Therefore, it makes sense to buy the armband if the number of throws is going to be greater than 60.
I need help with this question. Including the breakdown. Thank you
Let
x -------> the height of the tower
y -----> the height of the guy wire
we have that
x=y-3 ------> equation 1
y=9 m
substitute the value of y in equation 1
x=9-3
x=6 m
therefore
the height of the tower is 6 meters