Answer:
D. NeitherStep-by-step explanation:
The equation that Dimitri and Jillian were trying to solve is expressed as
(x+1)(x+3) = 12. They are both solving this equation to get the value of x.
Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;
Step 1: Multiply out the expression (x+1)(x+3)
= (x+1)(x+3)
= x(x)+ 3x+x+1(3)
= x² + 3x + x + 3
= x² + 4x + 3
He got x² + 4x + 3 on expansion
Step 2: He should have rewrote the equation as shown;
x² + 4x + 3 = 12
x² + 4x + 3 -12 = 0
x² + 4x -9 = 0
Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9
x = (-b±√b²-4ac)/2a
x = (-4±√(4)²-4(1)(-9))/2(1)
x = -4±√16+36/2
x = (-4±2√13)/2
x = (-4+2√13)/2 or (-4-2√13)/2
x = -2+√13 or -2-√13
Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.
Emily's family loves to work together in the garden.They have a slight preference for flowers, as 60\%60%60, percent of their plants are flowers and 40\%40%40, percent are vegetables. They have 505050 plants growing in the garden. How many vegetable plants do they have?
50 plants total, 40% are vegetables
40% = 40/100 = 0.40
40% of 50 = 0.40*50 = 20
Answer: There are 20 vegetable plants.....................
Answer:
2nd option is the correct one
log|x|-f(x)+k
Given the function f(x) = -2c+cx-x^2, and f^-1(5) = -1, find c
Answer:
[tex]c=-2[/tex]
Step-by-step explanation:
We are given the function:
[tex]f(x) = -2c + cx - x^2[/tex]
And that:
[tex]\displaystyle f^{-1} (5) = -1[/tex]
And we want to determine the value of c.
Recall that by definition of inverse functions:
[tex]\displaystyle \text{If } f(a) = b, \text{ then } f^{-1}(b) = a[/tex]
So, since f⁻¹(5) = -1, then f(-1) = 5.
Substitute:
[tex]f(-1) = 5 = -2c + c(-1) - (-1)^2[/tex]
Simplify:
[tex]5 = -2c - c - (1)[/tex]
Combine like terms:
[tex]6 = -3c[/tex]
And divide. Hence:
[tex]c = -2[/tex]
In conclusion, the value of c is -2.
Three years from now Tom will be twice as old as Jean and two years ago the sum of their ages was 26. How old is Tom now?
Answer:
21
Step-by-step explanation:
Tom'age: a
Jean'age: b
3+a=2(b+3)
a-2+b-2=26
or
a =2b+3
2b+3-2+b-2=26
or
a=2b+3
3b=27
or
a=21
b=9
Thus the required present age of Tom and Jean is 21 years and 9 years.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the present age of Tom and Jean is x and y.
Three years from now Tom will be twice as old as Jean.
x + 3 = 2 ( y + 3 )
x = 2y + 6 - 3
x = 2y + 3 - - - - - - - - -(1)
two years ago the sum of their ages was 26.
x - 2 + y - 2 = 26
x + y = 26 + 4
x + y = 30 - - - - - - -(2)
From equation 1 put x in equation 2.
2y + 3 + y = 30
3y = 30 - 3
3y = 27
y = 9
Put y in equation 2
x + 9 = 30
x = 30 - 9
x = 21
Thus the required present age of Tom and Jean is 21 years and 9 years.
Learn more about arithmetic here:
brainly.com/question/14753192
#SPJ2
Please answer now question
Answer:
1664 yd²Step-by-step explanation:
P = 2•(¹/₂•24•16) + 2•(20•20) + 24•20 = 384 + 800 + 480 = 1664 yd²
Determine if the following table represents a quadratic function.
x 1 2
3 4 5
y 13 22 37 58 85
(1 point)
Answer:
The options are not visible enough (See Explanation)
Step-by-step explanation:
Given
x:- 1 || 2 || 3 || 4 || 5
y:- 13 || 22 || 37 || 58 || 85
Required
Determine if the function is quadratic
Calculate the difference between the values of y
[tex]Difference = 22 - 13 = 9[/tex]
[tex]Difference = 37 - 22 = 15[/tex]
[tex]Difference = 58 - 37 = 21[/tex]
[tex]Difference = 85 - 58 = 27[/tex]
The resulting difference are: 9 || 15 || 21 || 27
Next; Calculate the difference between the difference of values of y
[tex]Difference = 15 - 9 = 6[/tex]
[tex]Difference = 21 - 15 = 6[/tex]
[tex]Difference = 27 - 21 = 6[/tex]
The resulting difference are: 6 || 6 || 6
For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.
(3,y) (1,4) m= -2 what is the value of y if the line through the two given points is to have indicated slope
Answer:
y=0
Step-by-step explanation:
The equation for the slope is
m = ( y2-y1)/(x2-x1)
-2 = (4-y)/(1-3)
-2 = (4-y)/-2
Multiply each side by -2
4 = 4-y
Subtract 4 from each side
4-4 = 4-y-4
0 = -y
0=y
Will give brainliest. Find the length and measure of each arc. Show your work.
Answer:
exact arc length = 21pi
approximate arc length (using calculator) = 65.9734457253857
approximate arc length (using 3.14 for pi) = 65.94
units are in feet
============================================
Work Shown:
L = (x/360)*2*pi*r
L = (315/360)*2*pi*12
L = 21pi = exact arc length in terms of pi
If you use your calculator's stored version of pi, then L is approximately
L = 21pi
L = 65.9734457253857
Or if you end up using pi = 3.14, then
L = 21*pi
L = 21*3.14
L = 65.94
Fairly close to the other approximation though a bit off because pi = 3.14 is just a rough approximation.
What is the perimeter of the figure shown?
Answer:
[tex]\boxed{16 units}[/tex]
Step-by-step explanation:
Hey there!
Well since all the sides are congruent and there are 8 sides we can make the following expression,
P = 2*8
P = 16
Hope this helps :)
Answer:
16
Step-by-step explanation:
The sides of this figure are equal to each other .
the permiter is the sum of the sides
The figure has 8 sides.
● P = 8 × 2
● P = 16
A student says that the function f (x) = –x² – 9 has the x-intercepts (-3,0) and (3,0). Is the student correct? If not, expl.
why.
Answer:
No
Step-by-step explanation:
The student is wrong because the function has no solutions.
You cannot factor it because the x² is negative.
If it was x² - 9 instead, you could factor it into (x-3)(x+3) which would get you the x-intercepts (-3,0) and (3,0).
But instead, -x² - 9 cannot be factored at all and has no x-intercepts/solutions.
express each of the following numbers as power of 5... (a) 0.2, (b) 125
Answer:
(a).
[tex]0.2 = {5}^{ \frac{1}{3} } [/tex]
(b).
[tex]125 = {5}^{3} [/tex]
Tricks for solving trigonometry proof question easily ??
Answer: do do that you need a firm understanding of trig. once you do, you can see all the steps and solve a trig proof problem easily. So go back to solving regular trig questions, and keep asking yourself why this formula works. once you have understanding of that, you can solve trig proof problems with ease.
Step-by-step explanation:
I need the answers for Q10 part b and Q11 ASAP!!!
Answer:
Q10ii: x axis horizontal, y axis vertical, a straight line through the origin and point (5,20)
Q11i: z = 8y
Q11ii: y axis horizontal, z axis vertical, a straight line through the origin and (6,48)
Step-by-step explanation:
Linear proportions will always produce straight lines when graphed. Also, they will have to go through the origin when there is not some kind of offset.
5 ratio 4 = 35 ratio x
Answer:
5 ratio 4 is
35 ratio 28
they both multiply by 7.....
Answer:
[tex]\large \boxed{x=28}[/tex]
Step-by-step explanation:
[tex]5:4=35:x[/tex]
Ratios can be expressed as fractions.
[tex]5/4=35/x[/tex]
Cross multiply.
[tex]5 \times x = 4 \times 35[/tex]
[tex]5x=140[/tex]
Divide both sides by 5.
[tex](5x)/5=140/5[/tex]
[tex]x=28[/tex]
An online company wants to establish ratings for the products they provide. To do so, they ask visitors to their website to evaluate the products and leave a "thumbs up" or a "thumbs down." What type of sample is this? Explain why.
Answer:
This is a group specific influence sample, it only shows a demographic sample of those that are influenced by the reviews in the first place.
Step-by-step explanation:
1/4(12x – 16) = 4 is equivalent to 3x – 16 = 4.
O False
O True
Hi there!
»»————- ★ ————-««
I believe your answer is:
O False
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Simplifying the Equation Given...}}\\\\\frac{1}{4}(12x-16)=4 \\---------------\\\\\rightarrow \left \{ {{\frac{1}{4} * 12 = 3} \atop {\frac{1}{4}*-16 = -4}} \right.\\\\\rightarrow \boxed{3x - 4 = 4}\\\\\\\rightarrow\boxed{3x - 4 = 4\neq 3x - 16 = 4} \leftarrow\\\\\text{The 'simplified' equation is not distributed correctly.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
What is the distance between (1, 9) and (1, -4)? Use the distance formula.
D=(x2-x1)2+(y2-y1)2
Answer:
D. 13
Step-by-step explanation:
You just have to plug in numbers then solve.
(1,9) and (1,-4). Every coordinate is placed as (x,y)
(1,9) is labeled as (x1, y1)
(1,-4) is labeled as (x2,y2)
Now plug in the numbers.
d= Square root of (1-1)^2 + (-4-9)^2
d= Square root of 1^2 +-13^2
d= Square root of 1+169
d= Square root of 170
d= 13.04
Rounded to a whole number, the answer is 13
Answer:
D
Step-by-step explanation:
you have to substitute the values in the distance formula,in this case x2 is 1,x1 is 1,y2 is -4 and y1 is 9
d=√(x2-x1)²+(y2-y1)²
=√(1-1)²+(-4-9)²
=√(0)²+(-13)²
=√169
=13
I hope this helps
Solve for x. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answer:
Hey there!
Angles in a triangle add to 180 degrees.
24+134+2x=180
158+2x=180
2x=22
x=11
Let me know if this helps :)
2. Calculate the amount of gallons needed to fill the pool shown below. (3 points)
Answer:
52,322 gal
Step-by-step explanation:
will make it simple and short.
vol = ( a + b ) * h/2 times the depth
vol = (10 + 4) x (40/2) x 30 = 8400 cu. ft. ---------->>> then convert to gal.
6.2288 gal
vol = 8400cu.ft. x ----------------- = 52,322 gal
1 cu.ft.
Can you give me same question like this..please
Q. Amina thinks of a number and subtracts 5/2
from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
Answer:
Three more than twice a number is equal to four less than the number. find the number.
What is 100,000+4,000+800+5 in standard form
Answer: 104,805
Step-by-step explanation:
just add
Answer:
104,805
Step-by-step explanation:
add it in each placement form
i need your help guys
Answer:
It is 3^6
Step-by-step explanation:
[tex]{ \tt{ {9}^{7} \div {3}^{8} }} \\ = { \tt{( {3}^{2}) {}^{7} \div {3}^{8} }} \\ = { \tt{ {3}^{14} \div {3}^{8} }} \\ = { \tt{ {3}^{(14 - 8)} }} \\ = { \tt{ {3}^{6} }}[/tex]
[tex]{ \underline{ \sf{ \blue{christ \: † \: alone}}}}[/tex]
In Exercise 4, find the surface area of the solid
formed by the net.
Answer:
535.2 cm²
Step-by-step explanation:
The surface area the solid formed by the net in exercise 4 can be calculated by finding the area of each part that makes up the net.
The net consists of 2 triangles and 3 rectangles.
Each triangle has a base (b) of 8 cm and a height (h) of = √(8² - 4²) (using Pythagorean theorem)
height = 6.9cm
Each rectangle has length (l) of 20cm, and width (w) of 8cm
Therefore, Surface Area (S.A) = area of 3 rectangles + area of 2 triangles
S.A = 3(l*b) + 2(½*b*h)
S.A = 3(20*8) + 2(½*8*6.9)
S.A = 3(160) + (1*8*6.9)
S.A = 480 + 55.2 = 535.2 cm²
A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with µ = 30 and σ = 18. This sample mean corresponds to a z-score of z = –1.00.
Answer:
True
Step-by-step explanation:
Given that:
M = 27, sample of n = 36 scores, µ = 30 and σ = 18.
The z score is used in statistics to determine by how many standard deviations the raw score is above or below the mean. If the z score is positive, the raw score is greater than the mean and if the z score is negative the raw score is less than the mean. The z score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that M = 27, this means that x = 27. Therefore:
[tex]z=\frac{x-\mu}{\sigma}\\\\for \ a\ sample\ size(n):z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\z=\frac{27-30}{18/\sqrt{36} } =\frac{-3}{3}=-1[/tex]
This sample mean corresponds to a z-score of z = –1.00.
Last year, Marla planted x rows of tomatoes in her garden, and each row has (x + 5) tomatoes. This year she increased the number of rows by 3 and doubled the number of tomatoes in each row. How many more tomatoes did Marla plant this year than last year?
Answer:
8
Step-by-step explanation:
rows=x
each row=(x+5) tomatoes
she increased the number of rows by 3
and doubled the number of tomatoes in each row
3multiplied by x=3x
(2x+10) because she doubled them
3x+10÷2x
=8
I've tried I hope this helps
Esmereldas family went out to dinner paying 20% tip at the end of the meal. Their credit card was charged $51.00. What was the amount on the bill without the tip
Answer:
42.50
Step-by-step explanation:
bill + tip = total bill
The tip is based on the bill
tip = bill * 20%
tip = bill * .20
Replace in the original equation
bill + .20 bill = total bill
Combine like terms
1.20 bill = total bill
The total bill was 51 dollars
1.20 bill = 51
Divide each side by 1.20
1.20 bill / 1.2 = 51/ 1.2
bill =42.50
Answer:
$42.50
Step-by-step explanation:
If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:
0.2x+x=51
1.2x=51
x=42.5
Therefore, the bill (w/o tip) was $42.50
p.s.Please give me brainliest. Thank you! :)
2. What is the volume of the regular pyramid to the nearest whole number?
14 cm
12 cm
WILL MARK BRAINLIEST !! find the coordinates F after a dilation about the origin of 2.5 write your answer in AB form
Explanation:
Point F is located at (2,0)
Multiply each of those coordinates by the scale factor 2.5
2.5*2 = 52.5*0 = 0This means point F(2,0) moves to F ' (5,0) after applying the dilation, where the dilation is centered at the origin.
Please answer it now
━━━━━━━☆☆━━━━━━━
▹ Answer
435.20 square cm
▹ Step-by-Step Explanation
Diameter = 12
Radius = 1/2d
Radius = 1/2 * 12
Radius = 6
A = πr(r +√h² + r²) =
A = π · 6·(6 + √16²+6²)
≈ 435.19869 → 435.20 square cm
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
In a given set of items, the mode is items which ?
a. appears first
b. appears fewest
c. appears farthest
d. appears most
Answer:
d. appears most
Step-by-step explanation:
Mode is the number that appears the most often in a set of data