Answer:
8 liters
Step-by-step explanation:
If the sum of 2 + x = 10,
then you subtract 10 - 2 = x,
to get x = 8
Complete the Square
x2 + 10x +
Answer:
( + 10)
Hope this helps you out
15. A rectangle has a length of 2x - 1 and a width of 3x + 7. Find the perimeter of this rectangle.
Then find the area of the rectangle.
Answer:
10x + 12 and 6x² + 11x - 7
Step-by-step explanation:
The perimeter (P) of a rectangle is calculated as
P = 2l + 2w ( l is length and w is width )
= 2(2x - 1) + 2(3x + 7) ← distribute parenthesis
= 4x - 2 + 6x + 14 ← collect like terms
= 10x + 12
--------------------------------------------------
The area (A) of a rectangle is calculated as
A = lw
= (2x - 1)(3x + 7) ← expand using FOIL
= 6x² + 14x - 3x - 7 ← collect like terms
= 6x² + 11x - 7
Howard worked out the problem below and his answer is below. Is Howard correct? If not, where did he make his mistake? Explain and give the right answer.
What is 40% of 140?
4.8
Answer: 56
Step-by-step explanation:
Howard is incorrect the right answer is 56.
Complete the steps to identify all potential rational roots of f(x) = 3x2 – x – 4. Values of p are factors of ✔ -4 . Values of q are factors of ✔ 3 Select all of the potential roots. \pm 4/3 \pm 2/3 \pm 3/4 \pm 2 \pm 4 \pm 3/2 I need help with the second one please <3 Thanks
Answer:
-1 and 4/3
Step-by-step explanation:
Given the quadratic equation;
f(x) = 3x^2-x-4
To get all potential roots, we will equate f(x) = 0
3x^2-x-4 = 0
3x^2-4x+3x-4 = 0
x(3x-4)+1(3x-4) = 0
(x+1)(3x-4) = 0
x+1= 0 and 3x-4 = 0
x = -1 and 3x = 4
x = -1 and x= 4/3
Hence the potential roots are -1 and 4/3
Is 5 a solution of 5a − 9 = 26
I purchased a new book that was on sale for 40% off. I saved $24.00 because of the sale. What was the original price? (6 points)
Pls Answer I need it for my test thats due Monday
Answer:
60
Step-by-step explanation:
24 dividend by 4 equals 6.
this means 10% of the original price is 6.
6 times 10 equals 60
hope this helps!!!
helps pls :-/
number 12
any help is greatly appreciated!
The data below represents the number of
runs scored in the last 14 games. Which
statement best describes the data?
A. The peak of the data is 3.
B. The data distribution is symmetrical.
C. The data distribution has several gaps.
D. The range of the data is 6.
Show that the area of triangle DEF is 11 cm2.
9514 1404 393
Explanation:
The length CD can be found from the Pythagorean theorem.
CF² + CD² = DF²
2² + CD² = (2√10)²
CD² = 40 -4 = 36
CD = √36 = 6
From here, any of several methods could be used to find the area of ΔDEF.
One of them is to subtract the areas of the triangles that are not ΔDEF from the area of the rectangle ABCD.
area ABCD = bh = (6 cm)(5 cm) = 30 cm²
area ΔADE = 1/2bh = 1/2(4 cm)(5 cm) = 10 cm²
area ΔBEF = 1/2bh = 1/2(2 cm)(3 cm) = 3 cm²
area ΔCDF = 1/2bh = 1/2(6 cm)(2 cm) = 6 cm²
Then the area of interest is ...
area ΔDEF = area ABCD -area ΔADE -area ΔBEF -area ΔCDF
area ΔDEF = (30 -10 -3 -6) cm²
area ΔDEF = 11 cm²
__
Alternate solution
If we define A as the origin of a coordinate system, then the coordinates of the vertices of ΔDEF are ...
D(0, 5), E(4, 0), F(6, 3)
The area can be computed as half the absolute value of the sum of the determinants of 2×2 matrices consisting of adjacent points.
[tex]A=\dfrac{1}{2}\left|\left|\begin{array}{cc}0&5\\4&0\end{array}\right|+\left|\begin{array}{cc}4&0\\6&3\end{array}\right|+\left|\begin{array}{cc}6&3\\0&5\end{array}\right| \right|\\\\=\dfrac{1}{2}|(0-20)+(12-0)+(30-0)|=\dfrac{1}{2}(22) = \boxed{11}[/tex]
_____
Additional comment
The solution using coordinates is effectively equivalent to the computation of the area of trapezoid ABFD, less the areas of triangles EBF and AED.
can someone please help, I've been stuck on this for hours
Answer:
i love ur profile pic
Step-by-step explanation:
and j
put a dot on 3 for the y side
Hello you have reached a reference page. The first to answer this question will get brainliest and a 5 star review. If it is incorrect you will not get the brainnliest and your answer will be deleted. Here is the question. You will also need to give a very specific explanation.
[tex]x^2-5x+6=0[/tex]
Sophia's math class has 6 fewer boys than girls, and there are g girls. Write
an expression for the number of boys.
Answer:
g-6=b
hope this helps
HELP AGAIN PLEASE REEEEEEEEEEEEE
Answer:
3. D
4. A
5. B
Step-by-step explanation:
Please help me!!!
solve for f : 5/6 f =5
1. 5
2. 4.2
3. 7.3
4. 6
Answer:
6
Step-by-step explanation:
What is the equation of the line that passes through the point (–2,1) and has a
slope of
3/2
Answer:
y = [tex]\frac{3}{2}[/tex] x + 4
Step-by-step explanation:
Find b and substitute for y = mx + b so
1 = 3/2(-2) + b
1 = -3 + b, so b = 1+3, b=4
Put it all together y = [tex]\frac{3}{2}[/tex] x + 4
Someone please help me!
Answer:
A = 58
B =:25
Step-by-step explanation:
C = A + B
83 = 9x + 4 + 4x + 1
83 = 13x + 5
13x = 78
x = 78/13
x = 6
A = 9x + 4 = 9 x 6 + 4 = 58
B = 4x + 1 = 4 x 6 + 1 = 25
What are the solutions to the system of the equations graphed below?
Answer:
D
Step-by-step explanation:
Where the graphs intersect each other is where the solution is. The graphs intersect each other at the points (0,-8) and (4,8). Hope this helps!
Annie wants to eat an entire donut. However, since she only two-years-old, the mother says she can
only have a third of the donut. If the diameter of the donut is 4 inches, how long is the outside edge of
the piece that Annie gets to eat? Round your answer to the nearest hundredth of an inch.
Answer:
4.19 inches
Step-by-step explanation:
Your goal is to find the circumference of the donut and then divide that by 3 to get 1/3 of the outer edge of the donut.
Circumference is 2[tex]\pi[/tex]r
The diameter (double the radius) is 4, so radius (r) is 2
2 * pi * 2 = 4 pi = 12.57 (round to hundredth)
12.57/3 = 4.19
keep in mind that dividing by 3 is the same as multiplying by 1/3
Need help. thank you
Answer:
x = 70.53 degrees
Step-by-step explanation:
equation:
cos-1 = [tex]\frac{adjacent}{hypotenuse}[/tex]
⇒ cos-1 x = [tex]\frac{4}{12}[/tex]
⇒ cos-1 x = 0.33
⇒ x = 70.528
round to the nearest tenth:
⇒ 70.53
Solve this equation. 1+1 = ?
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
What integer is closet to n
Answer:
Rounding to the Nearest Integer
The most common type of rounding is to round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth's place (the first digit to the right of the decimal point).
Help pls ! This is trigonometric function
Answer:
Amplitude: 4
Period: π
midline: y = 1
Step-by-step explanation:
r(x) = -4 sin(2x) + 1
r(x) = a sin(bx + c) + d where |a| is the amplitude and |b| for the period
a = -4 |a| = 4 : Amplitude = 4
b = 2 |b| = 2 period of sin(x) = 2π
period of sin(bx + c) = 2π/|b| = 2π/2 = π
range of sin(2x) ... -1 ≤ sin(2x) ≤ 1
range of -4 sin(2x) + 1: -4+1 ≤ -4 sin(2x) + 1 ≤ 4+1
-3 ≤ -4 sin(2x) + 1 ≤ 5
midline: y = (-3 + 5) / 2 = 1 y = 1
Answer:
Part A: The amplitude [tex]\displaystyle r[/tex]is [tex]\displaystyle 4.[/tex]
Part B: The period of [tex]\displaystyle r[/tex]is [tex]\displaystyle \pi.[/tex]
Part C: The equation of the midline of [tex]\displaystyle r[/tex]is [tex]\displaystyle y = 1.[/tex]
Step-by-step explanation:
[tex]\displaystyle \boxed{r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1} \\ \\ r(x) = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{\frac{\pi}{4}} \hookrightarrow \frac{\frac{\pi}{2}}{2} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
OR
[tex]\displaystyle r(x) = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\pi} \hookrightarrow \frac{2}{2}\pi \\ Amplitude \hookrightarrow 4[/tex]
Keep in mind that although this IS a sine function, if you plan on writing your equation as a function of cosine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the centre photograph displays the trigonometric graph of [tex]\displaystyle r(x) = -4cos\:2x + 1,[/tex]in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the cosine graph [centre photograph] is shifted [tex]\displaystyle \frac{\pi}{4}\:unit[/tex]to the left, which means that in order to match the sine graph [photograph on the left], we need to shift the graph FORWARD [tex]\displaystyle \frac{\pi}{4}\:unit,[/tex]which means the C-term will be positive, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{\frac{\pi}{4}} = \frac{\frac{\pi}{2}}{2}.[/tex]So, the cosine graph of the sine graph, accourding to the horisontal shift, is [tex]\displaystyle r(x) = -4cos\:(2x - \frac{\pi}{2}) + 1.[/tex]So, with all that being said, to find the period, again, take a look at the above information next to [tex]\displaystyle Wavelength\:[Period].[/tex]Now, the amplitude is obvious to figure out because it is the A-term. Moreover, the midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 1,[/tex]in which each crest is extended four units beyond the midline, hence, your amplitude. Now, there is one more piese of information you should know -- the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. Now, with all that being said, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Ximena just accepted a job at a new company where she will make an annual salary
of $50000. Ximena was told that for each year she stays with the company, she will
be given a salary raise of $3000. How much would Ximena make as a salary after 5
years working for the company? What would be her salary after t years?
Answer:
65,000
Step-by-step explanation:
3000 x 5 = $15,000
15,000 + 50,000 = 65,000
Answer:
$65000
50,000 + 3,000t
Step-by-step explanation:
Each car on a computer train holds 20 people. On a particular morning, 5 cars were 90% full and 3 cars were 65% full. If the people were rearranged to fill as many cars as possible, how many cars would be filled?
Answer:
7 cars
Step-by-step explanation:
The computation of the number of cars to be filled is shown below:
A car that is 90% full and the total people is 20 so 90% would be
= (.90)(20)
= 18
A car that is 65% full and the total people is 20 so 65% would be
= (.65)(20)
= 13
Now
Total number of people = (5)(18) + (3)(13).
= 129
Now the number of cars to be filled is
= 129 ÷ 20
= 6.45
= 7 cars
Does anyone know the answer? I would really appreciate it!!
Answer:
B
Step-by-step explanation:
The answer is B hope that help
What is the radius of the inscribed circle of HJK?
Answer:
D) 22
Step-by-step explanation:
Since it gives you two rays just set them equal and solve for X.
6x - 14 = 3x +4
+14 +14
6x = 3x + 18
-3x -3x
3x = 18
/3 /3
x = 6
Then plug x into either one of the equations
6(6) - 14
36 - 14
22
Answer:
D. 22
Step-by-step explanation:
Write an equivalent ratio described in the situation below. The ratio of boys to girls is 5/2
Answer:
5: 2 or 10: 4
Step-by-step explanation:
as a ratio, this would be 5: 2.
Im not sure if it's asking you to also make a new ratio that fits this, but if it is you could multiply both sides by 2 to get
10 : 4
What is the square root of √25
Answer:
5 is the square root of 25
Step-by-step explanation:
Have a great day!
and can I maybe please have brainliest?
Thanks!
Answer:
5 is the square root of √25
Step-by-step explanation:
hope it helps you
What is the HCF of 280, 112, and 140.
Answer:
Step-by-step explanation:
First find prime factorization of the numbers
280=2^3(5)7
112=2^4(7)
140=2^2(5)7
So the HCF is 2^2(7)=4(7)
HCF=28
Identify the expression equivalent to 16x + 24y
1. 2 (8x + 24y)
2. 8 (8x + 3y)
3. 8 (2x + 3y)
4. 4 (2x + 6y)