A foil method is a technique where two or more binomials multiply.
FirstOuterInnerLastExample 1[tex]\tt{(b + 3) (b + 7)}[/tex]
[tex]\tt{F: (b)(b) = b^2}[/tex]
[tex]\tt{O: (b)(7) = b7}[/tex]
[tex]\tt{I: (3)(b) = 3b}[/tex]
[tex]\tt{L:(3)(7) = 37}[/tex]
[tex] \tt{=b^2 +7b+3b+21}[/tex]
[tex]= \boxed{ \tt{b^2 +10b+2}}[/tex]
Example 2[tex]\tt{(x + 3)^2}[/tex]
[tex]\tt{F: (x)(x) = x^2}[/tex]
[tex]\tt{O: (x)(3) = x3}[/tex]
[tex]\tt{I: (3)(x) = 3x}[/tex]
[tex]\tt{L:(3)(3) = 9}[/tex]
[tex] \tt{=x^2 +3x+3x+9}[/tex]
[tex] = \boxed{ \tt{x^2 +6x+9}}[/tex]
what is 100 - 100 -10 equal it does not equal -10 though that answer is wrong
Hey there!
100 - 100 - 10
= 0 - 10
START at 0 and go UP 10 spaces
= -10
Thus, yes it does equal to -10
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Find the DIAMETER of a circle for the circumference given.
circumference = 34.6 m
A) 2.3 m
C) 11 m
B) 5.5 m
D) 6.5 m
Step-by-step explanation:
2 pi r = 34.6
2 r = 34.6/3.14
d = 11 m
Diameter be d
Circumference=πdπd=34.6d=34.6/πd=11mThe functions it f and g are defined for all real values of x by f(x)=x^2+4ax+a^2 and g(x)=4x-2a where a is a positive constant. Given that fg(3)=69 find the value of a and hence find the value of x such that g^-1(x) =x
Answer:
Below in bold.
Step-by-step explanation:
We find fg(x) by replacing the x in f(x) by g(x), so:
fg(x) = (4x - 2a)^2 + 4a(4x - 2a) + a^2
fg(3) = 89 so:
(4(3) - 2a)^2 + 4a(4(3) - 2a) + a^2 = 69
(12 - 2a)^2 + 48a - 8a^2 + a^2 - 69 = 0
144 - 48a + 4a^2 + 48a - 8a^2 + a^2 - 69 = 0
-3a^2 + 75 = 0
-3a^2 = -75
a^2 = 25
a = 5.
Now g(x) = 4x - 2(5) = 4x - 10.
Finding g-1(x);
4x = g(x) + 10
x = (g(x) + 10)/4
So g-1(x) = (x + 10)/4
When g-1(x)= x
x = (x +10)/4
4x = x + 10
3x = 10
x = 10/3.
Monica bought a sweater for $48.00. A week later the sweater went on sale for 25% off the original price. If Monica needed to pay 7% sales tax on any purchase, how many dollars would Monica have saved by waiting to buy the sweater on sale?
A. $12.84
B. $12.00
C. $2.52
D. $0.84
Answer:
A $12.84
Step-by-step explanation:
Sweater was originally $48.00 before tax. $48.00 x 7% tax rate (.07) = $3.36 in tax
So the sweater originally would've cost $48.00 + $3.36 = $51.36
The sale price was 25% off the $48.00. $48.00 x 25% (.25) = $12.00
Then you subtract the $12.00 from the $48.00 to get the new price of $36.00
Now that's before tax, so $36.00 x 7% tax rate (.07) = $2.52 in tax
So the sweater would cost on sale $36.00 + $2.52 = $38.52
To figure out how much she would've saved you subtract the sale price & tax from the original price & tax $51.36 - $38.52 = $12.84
Huilan's age is three times Thomas's age. The sum of their ages is 92. What is Thomas's age?
Answer:
23
Step-by-step explanation:
Set Thomas' age to be variable x.
Since Huilan is 3 times the age of Thomas, he is 3x.
3x + x = 92 (The sum of their age)
4x = 92
4x/4 = 92/4 (Isolate x)
x = 23
Extra information: Huilan is 69 because 23 x 3 = 69
The sketch below shows a company's plans for a new billboard advertisement.
15 ft
21 ft
If the area of the billboard is 144 ft?, what is the height?
Answer:
8ft
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
For each expression, select all equivalent expressions from the list.
(a) 11x - 4x + 10x
O 7x+10x
O 17 + x
10x - 7x
0 17x
(b) 2(1 + 8y)
0 2 +1.2 + 8y
0 2 +16y
02.1+28y
2+8y
Ugh I can’t figure them all out please help me
What is the Length of the side LM?
Answer: 12
Step-by-step explanation:
GIVING BRAINLEST TO THE PERSON THAT CAN EXPLAIN HOW TO DO THIS THE BEST :)
Helppp!!! Find the value of
x
xx in the triangle shown below.
x
=
x=x, equals
∘
∘
degrees
Answer:
68
Step-by-step explanation:
Khan
A carnival game is designed so that approximately 10% of players will win a large prize. If there is evidence that the percentage differs significantly from this target, then adjustments will be made to the game. To investigate, a random sample of 100 players is selected from the large population of all players. Of these players, 19 win a large prize. The question of interest is whether the data provide convincing evidence that the true proportion of players who win this game differs from 0. 10.
The power of this test to reject the null hypothesis if p = 0. 19 is 0. 79 using a significance level of α = 0. 5. What are two ways to increase the power of this test?
Increase the sample size and increase the significance level.
Decrease the sample size and decrease the significance level.
Decrease the sample size and leave the significance level as is.
Leave the sample size as is and decrease the significance level
The two ways which can be used to increase the power of this test is to: A. increase the sample size and increase the significance level.
What is power?In Statistics, power can be defined as the probability that a deviation from the null hypothesis would be detected by a test of significance, if such a deviation exist.
This ultimately implies that, the statistical power of a hypothesis test refers to the probability of correctly rejecting the null hypothesis provided it is false.
In this cenario, the two ways which can be used to increase the power of this test is by increasing the sample size and increasing the significance level.
Read more on null hypothesis here: https://brainly.com/question/14913351
#SPJ1
Answer: A
Step-by-step explanation:
edge
What is the surface area of this rectangular prism below?
Answer:
230
Step-by-step explanation:
SA=2(lw+hw+lh), where
l=length
h=height
w=width
2(5*5+9*5+5*9) = 230
Which of the following is a solution of
[tex]\frac{7+\sqrt{13}}{6}[/tex] is the answer
Step-by-step explanation:
Can anybody pls help! Offering 25 points! This is due soon!
Answer: A' (1, 5)
B' (-3, 5)
C' (-3, 2)
D' (1, 2)
Step-by-step explanation:
To reflect across the y-axis the original point (x, y) must become (-x, y) which is essentially taking the opposite of x
We can do that with each of the point of the rectangle ABCD to make the reflect rectangle A'B'C'D'
A (-1, 5) to A' (1, 5)
B (3, 5) to B' (-3, 5)
C (3, 2) to C' (-3, 2)
D (-1, 2) to D' (1, 2)
Isabel created the table of x and y values shown here. O 2 14 6 19 Which equation represents the relationship between the x values and the y values in Isabel's table? A y = 4x + 4 C y= 2.5x + 4 B y= 2x + 4 Dy=4x+1
The equation that represents the relationship between the x values and the y values in Isabel's table is y = 5/4 x - 11.5
Linear functionsLinear functions are functions that have a leading degree of 1. The linear equation is expressed as:
y = mx + b
where:
m is the slope
b is the y-intercept
Using the coordinate points (2, 14) and (6, 19)
Determine the slope
Slope = 19-14/6-2
Slope = 5/4
For the y-intercept
14 = 5/4(2) + b
14 = 2.5 + b
b = 11.5
Determinethe required linear equations
y = 5/4 x + 11.5
Learn more on linear equation here https://brainly.com/question/1884491
Write an equation that represents a relationship between these angles. Do NOT use spaces or parentheses.
Answer:
Angle x measures 33.5 degrees.
Step-by-step explanation:
From the given picture, we can note that angle x and the angle of 23 degrees are vertical opposite angles,
Since lines l and m are perperdicular then the angle between then measures 90 degrees, so we have:
[tex]x+23+x=90[/tex]
By collecting similar terms the equation which represents a relation between these angles is:
[tex]2x+23=90[/tex]
Now, by subtracting 23 to both sides, we obtain:
[tex]2x=90-23\\2x=67[/tex]
and by dividing both sides by 2, we get
[tex]x=\frac{67}{2}[/tex]
[tex]x=33.5\\[/tex]
Then angle x measures 33.5 degrees.
& triangle is inscribed
in a rectangle, as shown below. What is the area of the shaded
region?
5 cm
3 cm
5 cm
11 cm
A. 40 cm2
C. 47.5 cm2
B. 62.5 cm2
D. 22.75 cm2
Answer: I am not really sure but I think its c
Step-by-step explanation:
we can simply get the area of the whole rectangle, that is, the rectangle including the triangle in it, and then get the area of the triangle and subtract it from that of the rectangle, what's leftover, is the part we did not subtract, namely the shaded region.
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{rectangle}{(5)(11)}~~ - ~~\stackrel{triangle}{\cfrac{1}{2}(\stackrel{b}{5})(\stackrel{h}{3})}}\implies 55~~ - ~~\cfrac{15}{2}\implies \cfrac{95}{2}\implies 47.5[/tex]
Simplify (x + y)² - (x - y)² + 2xy - 3x²
Answer:
[tex]\huge\boxed{\sf 6xy-3x^2}[/tex]
Step-by-step explanation:
Given Expression:
(x + y)² - (x - y)² + 2xy - 3x²
Formulas used:
[tex](x+y)^2=x^2+2xy+y^2[/tex][tex](x-y)^2=x^2-2xy+y^2[/tex]Expand the above expression according to the formulas
[tex]=x^2+2xy+y^2-(x^2-2xy+y^2)+2xy-3x^2\\\\= x^2+2xy+y^2-x^2+2xy-y^2+2xy-3x^2\\\\cancel \ out \ x^2 \ and \ y^2\\\\= 2xy+2xy+2xy-3x^2\\\\= 6xy-3x^2\\\\\rule[225]{225}{2}[/tex]
Please help me if you know, I would appreciate if you could explain how to do this!
In the figure, the area of the shaded region is 299π cm²
What are the exact areas of the inner and outer circles?
Also, the answers need to be in cm^2
Answer:
See answers below
Step-by-step explanation:
Entire outer circle area = pi r^2 = pi 18^2 = 324 pi cm^2
if you subtract the small unshaded circle you get 299 pi
324 pi - smaller circle = 299 pi
smaller circle = 25 pi cm^2
pls help can someone play help me giving 21 points
Answer:
42
Step-by-step explanation:
6 x 6 is 36. 3 x 2 is 6. 36 + 6 is 42.
Which expression is equivalent to (x^1/4y^16) ^1/2
Answer:
x^1/8 y^8
Step-by-step explanation:
= x^(1/4 * 1/2) y^(16 * 1/2) =
Find the surface area of the regular pyramid. HELP QUICK!! (Asking again because the commenter DankBoi18 tried to put a virus on my pc)
We will see that the surface area of the triangular pyramid is equal to 170.1 yd^2
How to get the area of the pyramid?Remember that the area of a triangle is equal to:
A = (1/2)*b*h
Where b is the base, and h is the height.
On the triangular pyramid, we have 3 faces with a base of 9 yards and a height of 10 yd, so the area of these 3 faces is:
A = (1/2)*(10 yd)*(9 yd) = 45 yd^2
Also, we can see that the bottom face has a base of 9 yards and a height of 7.8 yards, then its area is:
A' = (1/2)*(9 yd)*(7.8 yd) = 35.1 yd^2
So the total surface area of the pyramid is:
S = 3*A + A' = 3*45 yd^2 + 35.1 yd^2 = 170.1 yd^2
If you want to learn more about pyramids, you can read:
https://brainly.com/question/10042135
A taxi charges $2.25 for the initial mile and then 30 cents per each 1/4 mile. If the total charge was $11.00, how far did the taxi travel for that fare?
Answer:
8.29 miles
Step-by-step explanation:
1 mile= 4*1/4=0.30*4=1.20
11=2.25+1.20(m-1)
8.75=1.20(m-1)
7.29=m-1
8.29=m
What is the solution to −x≥−5
Answer:
x≤5
Step-by-step explanation:
When multiplying an inequality by a negative number, make sure to reverse the inequality signs. If -x has to be greater or equal to -5, then x has to be lesser or equal to 5
A 3-column table with 6 rows. Column 1 is labeled Month with entries July, August, September, October, November, December. Column 2 is labeled New with entries 35, 45, 20, 27, 51, 38. Column 2 is labeled Used with entries 62, 42, 55, 39, 12, 87.
Hector’s car dealership sells new and used cars. The table shows the number of each type of car the dealership sold by month for the last half of the year. Find the lower and upper quartiles for used cars.
Used Cars
Lower quartile =
Upper quartile =
Answer:
I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.
Hope's this helps you.
Step-by-step explanation:
Dana has 8 baseball cards, 10 football cards, 4 hockey cards, and 14 basketball cards. All the cards are the same size and shape. Dana will select one card at random.
What is the probability that the care selected will be a hockey card?
A. 1/9
B. 1/8
C. 1/4
D. 1/3
Answer:1/8
Step-by-step explanation:
well the total amount you have of cards is 36 so you will have 4/36 now you just need to reduce and you will get 1/8
What is 1/4 plus 1/2 equal to in a fraction
Answer:
[tex] \frac{3}{4} [/tex]
Step-by-step explanation:
[tex] \frac{1}{4} + \frac{1}{2} \: \: lcm \: of \: 4 \: an d \: 2 \: is \: 4 \ \\ = \frac{1 + 2}{4} = \frac{3}{4} [/tex]
Which values of c will cause the quadratic equation –x2 3x c = 0 to have no real number solutions? check all that apply.
The quadratic equation –x2+3x+c =0 does not have any real solution for c<-9/4.
The given quadratic equation is:
[tex]-x^{2} +3x+c=0[/tex]
What is a quadratic equation?Any equation is called a quadratic equation if it has a form [tex]ax^{2} +bx+c=0[/tex] and a≠0.
For no real solution, the discriminant of a quadratic equation should be less than zero.
[tex]D < 0[/tex]
[tex]3^{2} -4(-1)(c) < 0[/tex]
[tex]9+4c < 0[/tex]
[tex]c < \frac{-9}{4}[/tex]
The quadratic equation –x2+3x+c =0 does not have any real solution for c<-9/4.
To get more about quadratic equations visit:
brainly.com/question/1214333
Answer:
–5 and -9/2 or the first and second options
Find the volume of the solid produced by rotating this two-dimensional shape using the axis shown.
Please help
Check the picture below.
so the solid produced will be a cylinder with a hole in the middle, like you see in the picture, hmmm so we could get its volume by simply getting the outer cylinder and subtracting the inner cylinder, or we can just get the volume of the ring on the left and multiply it by its length, so let's do the that.
[tex]\textit{volume of a ring}\\\\ V=\pi (R^2-r^2)~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=3\\ r=1 \end{cases}\implies V=\pi (3^2-1^2)\implies V=8\pi \\\\\\ \stackrel{\textit{\large volume of the hollow cylinder}}{\stackrel{\textit{volume of the ring}}{(8\pi )}\qquad \stackrel{length}{(6)}\implies 48\pi ~~\approx~~150.80}[/tex]
A town is more than 300 feet below sea level. Sea level has an elevation of 0 feet. What is one possible elevation, in feet, of the town?
Answer:
301+
Step-by-step explanation:
The answer can be anything above 300. This means the answer could be 301, or 400, or 350000000000, any of those are correct.