Only for c = 49 the given expression is the square of a binomial.
For which values of c is the given expression the square of a binomial?We want to find the values of c such that:
[tex]4x^2 + 14x + c[/tex]
Is the square of a binomial.
Remember that:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
Now we can rewrite our expression as:
[tex](2x)^2 + 2*7*x + c[/tex]
If you compare that with the general binomial expansion, we can see:
[tex]a = 2x[/tex]
[tex]b = 7[/tex]
Then c must be equal to 7 squared:
[tex]7^2 = 49 = c[/tex]
Only for c = 49 the given expression is the square of a binomial.
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sum1 please help me!
The next model of a sports car will cost 11.9% more than the current model. The current model costs $56,000. How much will the price increase in dollars? What will be the price of the next model?
Increase in price:
Price of next model:
Answer:
increase in price = $6664
price of next model = $56664
Step-by-step explanation:
(11.9 ÷ 100 ) x 56000 = $6664
56000 + 6664 = $56664
Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10
Answer:
x = -1.5 , y = 5.17
Step-by-step explanation:
Solve the system of equation using ELIMINATION (solve for x)
x + 3y = 14
-x + y = 10
Solution
x + 3y = 14 ------- equation 1 * 1
-x + y = 10 ------- equation 2 * 3
x + 3y = 14 ------- equation 3
-(-3x + 3y = 30)------ equation 4
Using the ELIMINATION METHOD.
x-(-3x) + 3y-3y = 14-30
4x = -6
x = [tex]\frac{-6}{4}[/tex]
x = -1.5
Substuting -1.5 into equation one
x + 3y = 14
-1.5 + 3y = 14
Adding 1.5 to both sides
-1.5 + 1.5 +3y = 14 +1.5
+3y = 15.5
Dividing by the coeffient of y
[tex]\frac{3y}{3} = \frac{15.5}{3}[/tex]
y = 5.166666666666
y =5.17
Therefore x = -1.5 , y = 5.17
A jar made of 1/4 inch thick glass has an inside radius of 4.7 inches and total height of 13.3 inches (including the bottom thickness of glass). What is
the volume of the glass shell of the jar (in cubic inches)?
The volume of the cylindrical jar, considering it's radius and height, is of 923 in³.
What is the volume of a cylinder?The volume of a cylinder of radius r and height h is given by:
[tex]V = \pi r^2h[/tex].
In which problem, we have that r = 4.7 in, h = 13.3 in, hence the volume in cubic inches is given by:
[tex]V = \pi \times 4.7^2 \times 13.3 = 923[/tex]
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sin^4 x+2sin^2 x-3=0
Solve by factoring on [0,2pi]
Answer:
Step-by-step explanation:x=π2,3π2
Explanation:
This can be factored as (x2+a)x2+b).⇒(sin2x+3)(sin2x-1)=0⇒
2
x
=
−
3
and
sin
2
x
=
1
⇒
sin
x
=
√
−
3
and
sin
x
=
√
1
⇒
sin
x
=
∅
and
sin
x
=
±
1
⇒
x
=
π
2
,
3
π
2
Hopefully this helps!
Which of the following formulas expresses h in terms of l and s?
(choices shown in attached image)
(picture for problem shown in attached image)
Answer: D
Step-by-step explanation:
x+x2 +2=44 solve the equation quick
Answer:
x=10.5 or x=6=x=−7
Step-by-step explanation:
x+x^2+2=44
x+x(x)+2=44
2x(x)+2=44 1. -2 on both sides
2x^2=42
2x(2x)=42
4x=42 2. /4 on both sides
x=10.5
Answer:
x = -7, 6.
Step-by-step explanation:
x+x2 +2=44
x^2 + x - 42 = 0
(x - 6)(x + 7) = 0
x =-7, 6
Evaluate the indefinite integral.
Answer:
I believe its C , i took this class
Step-by-step explanation:
Please, try to answer quickly Due in 1 hr!
Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit follow the example below and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24 (2 points: 1 point for each row)
The previous chart from question 2 is below. The chart I am trying to fill out is the bigger one That has the above question written on the picture.
All other times this question has been asked it has gone unanswered or with incorrect and incomplete answers please answer the question no matter how old it is because even if I have figured it out someone else can get help from this.
The values of the temperature in degree Celsius (12 and 24) converted to degree Fahrenheit are 53.6°F and 75.2°F respectively.
How to convert the value of temperature?In this exercise, you're required to convert the value of temperature in degree Celsius to degree Fahrenheit. Thus, we would use the following mathematical expression to do the conversion:
F(t) = 9/5C(t) + 32
When t = 12, we have:
F(t) = (9/5 × 12) + 32
F(t) = 21.6 + 32
F(t) = 53.6°F.
When t = 24, we have:
F(t) = (9⁄5 × 24) + 32
F(t) = 43.2 + 32
F(t) = 75.2°F.
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156,161,190,165,172,165,184,168,184,149,169,172,172,178,215,180,165,178,178,182,164,184,187,189,190 in order.
Answer:
least to greatest: 149,156,161,164,165,165,165,168,169,172,172,172,178,178,178,180,182,184,184,184,187,189,190,190,215
Greatest to least: 215,190,190,189,187,184,184,184,182,180,178,178,178,172,172,172,169,168,165,165,165,164,161,156,149
Step-by-step explanation:
What is the probability that this spinner will stop on orange when it is spun? write the probability as a fraction in simplest form.
Determine whether the value of each power is positive or negative.
(-10)
Positive
Negative
(-3)
(-2)
(-1)
(-6)
(-4)
Done
Intro
Answer:
answer in picture
Step-by-step explanation:
The radius of a circle is 2 inches. What is the circle's circumference?
r=2 in
Use 3.14 for pie
Answer:
6.28
Step-by-step explanation:
2×3.14 because this is just simple multiple
PLEASE HELP WILL GIVE BRAINLEST! What is the amplitude of the function graphed below?
Answer:
The amplitude is the maximum displacement/highest peek
Which is in your case = 2
GIVING BRAINLIESTT!!
Answer:
15) A
Step-by-step explanation:
4x-2 + 7x + 17 = 180
11x + 15 = 180
11x = 165
x = 15
Because the two angles (4x-2 and 7x+17) are linear, we can say that they add up to 180 degrees.
4x-2+7x+17 = 180 Now, simplify like terms
11x + 15 = 180
11x = 165
x = 15
Thus, the value of x would be 15 (choice 1)
Which ratio table below does not represent a proportional relationship between the number of laptop and desktop computers being sold at an electronics store?
Answer:
table 1
Step-by-step explanation:
a table represents a proportional relationship between the number of laptop and desktop computers ,if the ratio of the number of desktop computers to laptops is a constant (doesn’t vary)
Table1 : (does not represent a proportional relationship) because :
11÷10=1,1
46÷42=1.09...
and 1.1 ≠ 1.09
Table2 : (represents a proportional relationship) because :
3÷6=0.5
9÷18=0.5
18÷36=0.5
72÷144=0.5
Table3 : (represents a proportional relationship) because :
18÷12=1.5
36÷24=1.5
54÷36=1.5
108÷72=1.5
Table4 : (represents a proportional relationship) because :
2÷3=0.666666666667
18÷27=0.666666666667
22÷33=0.666666666667
200÷300=0.666666666667
Which expression is a cube root of -1+ i sqrt 3? (multiple choice)
Answer:
see below
Step-by-step explanation:
Find the magnitude (-1)^2 + (sqrt3)^2 = m^2 m = 2
find the angle arctan (sqrt3/-1) = 120 degrees
the cube root would then be
[tex]\sqrt[3]{2}[/tex](cos 40 + isin 40)
Which graph represents the solution set of y = x2 − 4 and x + y + 2 = 0?
A.
graph A
B.
graph B
C.
graph C
D.
graph D
Answer:
its C
Step-by-step explanation:
I used something else for it for it
Jeff has a balance of $2,513.77 on his credit card. He would like to pay off his card over the course of a year and a half by making identical monthly payments. The APR on his card is 10.66%, compounded monthly. Assuming that Jeff makes no additional purchases with his card, how much will he have to pay every month to reach his goal? (Round all dollar values to the nearest cent.) a. $151.73 b. $162.57 c. $139.65 d. $147.64 Please select the best answer from the choices provided A B C D
Using the monthly payment formula, it is found that the amount he will have to pay is given as follows:
a. $151.73.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 2513.77, r = 0.1066, n = 1.5 x 12 = 18.
Hence:
r/12 = 0.1066/12 = 0.008883.
[tex]A = 2513.77\frac{0.008883(1 + 0.008883)^{18}}{(1 + 0.008883)^{18} - 1} = 151.73[/tex]
Hence option A is correct.
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what is the measurement of angle B
Answer:
41 degrees
Step-by-step explanation:
All of the angles must add up to 360 degrees to form a circle. So we have 22 + b + 297 = 360. Solving for b, we get b = 41.
At the end of the winter, coats are on sale for 75% off. If a heavy coat was priced
at $120 after taking the discount, then how much will the coat ring up for at the register
if the tax is 6%?
Answer:
the answer is $31.80
Step-by-step explanation:
6% of $120.00 is $7.20,
75% off of 127.20= $31.80
a sheet of paper is 0.1mm thick
a) A ream of paper has 500 sheets. how thick would 1 ream of paper be?
Answer:
a) 50 mmb) 1 200 sheet of paperStep-by-step explanation:
a) the thickness of one ream of paper :
= 0.1 × 500
= 50 mm
b) 12 cm = 12 × 10 = 120 mm
Then
the number of sheets that exist in a pile of papers that has a thickness of 12 cm :
= 120 ÷ 0.1
= 1 200 sheet of paper
What is the surface area of a cube with a side length of 3 inches?
54
Step-by-step explanation:
Find the area of on side of the cube...it's a cube so all sides are the same
3x3=9
multiply the area of one face by the number of faces, 9x6=54
What percentage of people like
mushrooms?
Response Frequency
Like
19
Dislike
31
Isabella has a total of 150 music CD's.She loves rock music and alternative music. The number of alternative music CD's is three more than twice that of the rock music CD's that she owns .
(a). Write down two equations that represent this information.
(b). Draw the two graphs that represent these equations on the same set of axes .
(C). Show where you can read off how many Rock CD's Isabella owns .
The system of equations that we need to solve is:
x + y = 150y = 2x + 3And the solution is x = 49 and y = 101.
How to solve the system of equations?
Let's define the variables:
x = number of CDs of rock music.y = number of CDs of alternative music.We know that the total number of CDs is 150, then:
x + y = 150
And we know that:
y = 2x + 3
Then the two equations that represent the information (and conform a system of equations) are:
x + y = 150
y = 2x + 3
b) The graphs of the two equations can be seen below.
c) To find the solution, we just need to see where the graphs intercept.
We can see that the intercept is (49, 101), this means that:
Isabella has 49 rock music CDs and 101 alternative music CDs.
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Find the perimeter of the parallelogram whose vertices are A (-1,1), B (-9,6), C(-12,11) and D(-4,6) Give your answer correct to one decimal place
Answer: 30.5
Step-by-step explanation:
Using the equation, y=5x²−17x −12, determine the y-intercept.
A) (0, -12)
B) (4, 0)
C) (1.7, -26.4)
D ) (0, 12)
Answer:
A
Step-by-step explanation:
to find the y- intercept let x = 0 in the equation and solve for y
y = 5(0)² - 17(0) - 12 = 5(0) - 0 - 12 = 0 - 12 = - 12
then the y- intercept is (0, - 12 )
Answer:
[tex]\huge\boxed{\sf (0,-12)}[/tex]
Step-by-step explanation:
Given equation:[tex]y=5x^2-17x-12[/tex]
y-intercept is the point where x = 0
Put x = 0 in the above equation.
[tex]y=5(0)^2-17(0)-12\\\\y = 0-0-12\\\\y=-12[/tex]
So, y = -12, when x = 0.
Ordered pair = (x,y) = (0,-12)
[tex]\rule[225]{225}{2}[/tex]
Josh must submit for paintings as part of his application to art school if he has 25 to choose from how many ways can he took 4?
Regardless of how the graph is oriented in the standard
(x,y) coordinate plane, NO graph in one of the
following categories has a vertical line of symmetry.
Which one?
F. Line
G. Square
H. Pentagon
J. Parallelogram
K. Scalene triangle
Answer:
the answer is j because it's impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other
Out of the given options, the shape that does not have a vertical line of symmetry is J. Parallelogram.
The correct answer is J. Parallelogram.
A vertical line of symmetry means that if a line is drawn vertically through the shape, the two halves will be mirror images of each other.
In the case of a line (F), it is one-dimensional and does not have an area, so it does not have any symmetry.
A square (G) has four sides of equal length and four right angles. It has both vertical and horizontal lines of symmetry, dividing it into four congruent quadrants.
A pentagon (H) is a five-sided polygon. Depending on its shape and orientation, it may or may not have a vertical line of symmetry. For example, a regular pentagon does have a vertical line of symmetry, while an irregular pentagon may not.
A parallelogram (J) is a four-sided polygon with opposite sides that are parallel and equal in length. It does not have a vertical line of symmetry because its opposite sides are not mirror images of each other.
A scalene triangle (K) is a triangle with no equal sides or equal angles. It does not have a vertical line of symmetry because its sides and angles are not symmetric.
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need help on this one!!
Step-by-step explanation:
the square root of x squared is x.
this means the( cube root of x ) to the power of 6 is what we need
PLEASE HELP!!! 31 POINTS
What is the volume of this rectangular prism?
26 cubic feet
35 cubic feet
50 cubic feet
105 cubic feet
Work Shown:
Volume = length*width*height
Volume = 3*7*5
Volume = 105 cubic feet
length × breadth × height
7 × 3 × 5
105 cubic feet
hope it helps...!!!
