Answer:
[tex]g(x) = 4(x - 2)^2 -9[/tex]
Step-by-step explanation:
Given
[tex]g(x) = 4x^2 - 16x + 7[/tex]
Required
Complete the square
Rewrite so that [tex]x^2[/tex] has 1 coefficient
[tex]g(x) = 4(x^2 - 4x) + 7[/tex]
Take half of the coefficient of x
[tex]\frac{4}{2} = 2[/tex]
Square the result
[tex](\frac{4}{2})^2 = 2^2[/tex]
[tex](\frac{4}{2})^2 = 4[/tex]
Add and subtract the result in the bracket
[tex]g(x) = 4(x^2 - 4x + 4 - 4) + 7[/tex]
Expand the bracket to remove -4
[tex]g(x) = 4(x^2 - 4x + 4) - 16 + 7[/tex]
[tex]g(x) = 4(x^2 - 4x + 4) -9[/tex]
Expand the bracket
[tex]g(x) = 4(x^2 - 2x -2x+ 4) -9[/tex]
Factorize
[tex]g(x) = 4(x(x - 2) -2(x-2)) -9[/tex]
Factor out x - 2
[tex]g(x) = 4((x - 2)(x-2)) -9[/tex]
Express as square
[tex]g(x) = 4(x - 2)^2 -9[/tex]
Determine the modulus of each of the complex numbers in the matching pairs. List these moduli in order from smallest to largest. Use the letters of the matching pair in your listing.
Suppose m = 2 + 6i, and |m + n| = 3√10 , where n is a complex number.
a. What is the minimum value of the modulus of n?
√10
Provide one example of the complex number, n.
A = J → 2 + 6i
B = F →75
C = H → -3 - i
D = I → 1 + i
E = G → 5 + 5i
these are my matching pairs
Answer:
the modulus of a complex number z = a + bi is:
Izl= √(a²+b²)
The fact that n is complex does not mean that n doesn't has a real part, so we must write our numbers as:
m = 2 + 6i
n = a + bi
Im + nl = 3√10
√(a² + b²+ 2²+ 6²)= 3√10
√(a^2 + b^2 + 40) = 3√10
squaring both side
a²+b²+40 = 3^2*10 = 9*10 =90
a²+b²= 90 - 40
a²+b²=50
So,
|n|=√(a^2 + b^2) = √50
The modulus of n must be equal to the square root of 50.
now
values a and b such
a^2 + b^2 = 50.
for example, a = 5 and b = 5
5²+5²=25+25= 50
Then a possible value for n is:
n = 5+5i
Let n be x+yi
So
√(a²+b²+2²+6²)=3√10√a²+b²+40=3√10a²+b²+40=90a²+b²=50Minimum value is 5+5i as 5²+5²=50
Find the sum of the polynomials -4x^2+9x-3 and 7x^2-5x+4
Answer: the answer is 2.
Which side lengths cannot form a triangle? Select all that apply.
7 cm, 8 cm, 13 cm
16 cm, 4 cm, 18 cm
24 cm, 14 cm,9 cm
11 cm, 21 cm, 13 cm
11 cm, 22 cm, 11 cm
7cm,8cm,13cm
16cm,4cm,18cm
11cm,21cm,13cm
What is the radius, Diameter, Area, and Circumference of a 12 feet circle? (No links or fake answers, actually give me a right answer)
Answer:
12ft, 6ft, 36πft², 12πft
Step-by-step explanation:
Diameter: the distance across the circle - so 12ft
Radius: half the diameter = 0.5(12) = 6ft
Area: πr² = π(6)² = 36π ft² (substitute in 22/7, 3.14, or the exact value of π as fit)
Circumference: 2πr = πd = 12πft
A runner ran 2/3 of a race in 21 minutes. They ran the entire race at a constant speed How long did it take to run the entire race?
Answer:
31.5 minutes
Step-by-step explanation:
21 / 2 = 10.5
10.5 x 3 = 31.5
On a winter day in the Midwest, the temperature got colder than 5 degrees below zero when measured in degrees Fahrenheit. Which of these inequalities correctly represents the temperature? For each inequality, assume that x is the temperature and that the constant is the number of degrees Fahrenheit. (No links.)
A
x<−5
B
x>−5
C
x<5
D
x>5
Answer:
A
Step-by-step explanation:
The question asks us what equation would represent a temperature less than -5. The answer must then be A.
Answer:
The answer is A. x<-5
Step-by-step explain:
So the question is On a winter day in the Midwest, the temperature got colder than 5 degrees below zero when measured in degrees Fahrenheit. Which of these inequalities correctly represents the temperature? Basically It is simple you have to figure out which inequality accurately represents the temperature. What u can do is imagine x is the temperature and the 5 is the number that way it will be way easier to figure out!!!! MARK ME AS BRAINLEIST PLS??
Question 14 of 25
In a group of 40 students, the probability that at most 15 of them like to hike
is 54%. What is the probability that at least 16 of them like to hike?
O A. 38%
B. 46%
C. 55%
D. 62%
The probability that at least 16 of them like to hike would be equal to 46% So, option B is correct.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
In a group of 40 students, the probability that at most 15 of them like to hike is 54%. we need to find the probability that at least 16 of them like to hike.
The probability that at most 15 of them like to hike = 54%
Let the total possibility be 100%
then 100 - 54 = 46%
Therefore, the remaining possibility is the probability for at least 16 of them like to hike.
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Volume (look at the picture)
Answer:
192 is the volume
Step-by-step explanation:
Answer:
192 cubic (measurement you are using)
Step-by-step explanation:
Formula for the volume of a pyramid is length of base times width of height times the height of the pyramid all over 3 so it would be 8x8x9 all over 3 which is 576, and 576 divided by 3 is 192
Johnny flipped a coin 450 times. His results are:
Heads: 240
Tails: 210
What is the experimental probability that the coin lands on heads?
Please help
Brennan is wrapping a birthday present for his sister. He starts with 2 yards of ribbon. Then, he cuts off 9 inches to decorate the present. How many inches of ribbon does he have left now?
Answer:
63 inches
Step-by-step explanation:
Brennan is wrapping a birthday present for his sister. He starts with 2 yards of ribbon.
Step 1
We convert from yards to inches
1 yard = 36 inches
2 yards = x
Cross Multiply
x = 2 × 36 inches
x = 72 inches
Step 2
Then, he cuts off 9 inches to decorate the present.
The number of inches of ribbon he has left now is calculated as:
72 inches - 9 inches
= 63 inches
Therefore, he has 63 inches of ribbon left
Eva draws a line that includes the points (2,0) and (-2,2) which function gives all the points (٫) on this line
Possible answers
= -1/2 + 1
= -2 +1
= 1/2 -1
= 2 -1
Given:
A line passes through the points (2,0) and (-2,2).
To find:
The equation of the line.
Solution:
If a line passes through the two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the points (2,0) and (-2,2). So, the equation of the line is:
[tex]y-0=\dfrac{2-0}{-2-2}(x-2)[/tex]
[tex]y=\dfrac{2}{-4}(x-2)[/tex]
[tex]y=-\dfrac{1}{2}(x-2)[/tex]
[tex]y=-\dfrac{1}{2}(x)-\dfrac{1}{2}(-2)[/tex]
[tex]y=-\dfrac{1}{2}x+1[/tex]
Therefore, the required equation is [tex]y=-\dfrac{1}{2}x+1[/tex].
Note: In the options, the variables are missing.
Find the length of the missing leg of a right triangle given a leg of length 60 and a hypotenuse of length 61
Answer:
11 units
Step-by-step explanation:
61² - 60² = x²
3721 - 3600 = 121
√121 = 11
A water tank is in the shape of a right circular cylinder with a height of 20 feet a volume of 320π cubic feet. What is the diameter, in feet, of the water tank?
A, 16
B, 10
C, 8
D, 4
Answer:
c: 8
Step-by-step explanation:
What is the volume of a sphere with a diameter of 9.3 m, rounded to the nearest
tenth of a cubic meter?
The volume of a sphere with a diameter of 9.3 is 521.
what is Volume of sphere?The amount of space occupied by a three-dimensional figure as measured in cubic units.
Volume of sphere is = 4/3*π*r³
d=9.3, radius= 9.3/2
Volume of sphere = 4/3*22/7*4.65*4.65*4.65*4.65
= 421.16 m³
= 521
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If 2g - 4 = 6, then g =
Answer:
Then g = 5.
Step-by-step explanation:
The only number that fits in g is 5.
2*5 - 4 = 6
So 2 x 5 = 10.
Which the equation is now 10 - 4 = 6.
So the answer is 5.
Answer:
g = 5
Step-by-step explanation:
2g - 4 = 6
2g - 4 + 4 = 6 + 4
2g = 10
2g ÷ 2 = 10 ÷ 2
g = 5
please helpp 10 points and brainlyist if you are right.Thanks
Answer:
58
Step-by-step explanation:
A pyramid and a cone are both 8 centimeters tall and have the same volume.
What statement must be true about the two solids?
АЛ
A. The vertical cross-sections of the prisms at the same width must
have the same area.
B. The area of the cross-sections of the prisms are multiples of each
other.
C. The cross-sections of the prisms are the same shape.
D. The horizontal cross-sections of the prisms at the same height
must have the same area.
Answer:
D. The horizontal cross-sections of the prisms at the same height must have the same area.
Step-by-step explanation: I dont know what the guy above is saying but this is the right answer
Since it is given that both prisms have the same height and volume, the answer is option D. The horizontal cross-sections of the prisms at the same height must have the same area.
A solid figure is one which has surface area and volume. Examples are prisms, cube, cuboid etc. Thus cones and pyramids are solid figures.
From the given question,
Volume of a cone, V = [tex]\frac{1}{3}[/tex][tex]\pi r^{2} h[/tex]
where r is its radius, and h its height
also,
Volume of a pyramid, V = [tex]\frac{1}{3}[/tex] lwh
where l is its length, w is the base width and h is its height.
Given that: i. volume of cone = volume of pyramid
ii. height of cone = height of pyramid
Then,
[tex]\frac{8}{3}[/tex][tex]\pi r^{2}[/tex] = [tex]\frac{8}{3}[/tex]lw
[tex]\pi r^{2}[/tex] = lw
Thus it can be deduced that at the same height, the horizontal cross section of the prisms have equal area. So that option D is the appropriate answer to the given question.
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What is the range of the following data set? 60, 40, 35, 45, 39
Answer:
25
Step-by-step explanation:
35,39,40,45,60
60-35=25
how do I solve this?
Answer:
The final answer is (2,-1)
(also idek what I did in the photo but I'm positive the answer is (2,-1)
Parker borrowed some money from his friend in order to help buy a new video game system. Parker agreed to pay the friend back some amount every week until his loan was paid off. An equation representing the amount Parker owes his friend after tt weeks is L=150-25t. What is the y-intercept of the equation and what is its interpretation in the context of the problem?
Answer:
L = 150
Step-by-step explanation:
y intercept: when x = 0
Plug in x = 0 into the equation.
L = 150
This means that Parker has not yet begun to pay his friend.
The diameter of a circle is 20 m. Find its area in terms of π
Answer:
100π m^2
Step-by-step explanation:
Given data
Diameter= 20m
Radius= 10m
The expression for the area is
Area= πr^2
Area= π*10^2
Area= π*100
Area= 100π m^2
Hence the area is 100π m^2
Pls help ASAP
Are there any noticeable outliers in either of the data sets? What does this mean about the best measures to use for center and
variability?
Answer:
Yes, there are some noticeable outliers. They are in the data set from doctor A they are in the contacts section they are 92,99,93. Well for Doctor A the center for Corrective lenses is about 750, for glasses it is about 640, and for contacts it is 110. Then the Variability for doctor A for Corrective lenses is also 750 for me, for glasses it is 650 for me, and for contacts it is also 110. For doctor B for the center for Corrective lenses is 760, for glasses it is 640, and for contacts 110. For doctor B for variability for Corrective lenses it is 750, for glasses it is a 630, and for contacts it is a 110.
Step-by-step explanation:
a landscaper is fencing a triangular garden for a customer. if the fence has the dimensions shown,does triangular garden have right angle?
Answer:
e
no, the numbers are not pythagoras triple
Step-by-step explanation:
find the complete question in the attached image
If the angle is a right angle would be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
20² + 10² =
400 + 100 = 500
500 is not equal to the square of 25
so it is not a right angled triangle
Suppose a sample consists of the following data values. What is the sample
mean?
8,7, 5, 9, 4, 8, 7, 9, 9,5,7,6
Answer:
7
Step-by-step explanation:
add all then divide by amnt of numbers
In circle J with m ∠ H L K = 42 m∠HLK=42, find the m ∠ H J K m∠HJK.
Answer:
82
Step-by-step explanation:
All honesty I did 2*42=82 :) <3
A jeweler had 38 inches of silver chain. She need five times that much to make some necklaces and 3 times that amount to make some bracelets. How much silver chain does the jeweler need to make her necklaces and bracelets?
Answer:
304 IN
Step-by-step explanation:
total inches needed for necklace : 38 x 5 = 190
total inches needed for necklace : 38 x 3 = 114
190 + 114 = 304 inches
Nancy and Fabian’s dinner bill at a restaurant is $28 before tax. The tax on their meal is 2.5%.
How much is Nancy and Fabian’s final bill after tax is added?
Answer:
gtbhytyt4ff5ddtd56cc6c6c6c6f6c66ffb
The amount that Nancy and Fabian’s final bill after tax is added will be $28.70.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Nancy and Fabian’s dinner bill at a restaurant is $28 before tax. The tax on their meal is 2.5%.
Let "T" be the final bill. Then the equation is given as,
2.5% = [(T - $28) / $28] x 100
0.025 = (T - $28) / $28
T - $28 = $0.70
T = $28.70
The amount that Nancy and Fabian’s final bill after tax is added will be $28.70.
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simplify 3²×5² what is the answer
Answer:
9.25=225
Step-by-step explanation:
Can You teach english and math
The square pyramid below represents a tent that Wayne is making. The sides of the tent will be covered in blue fabric and the base of the tent will be covered in brown fabric. Find the surface area that will be covered in each color of fabric.
Answer:
The answer is below
Step-by-step explanation:
A square pyramid is a pyramid with a square base. Therefore it is composed of 4 identical triangles and a square base.
From the image attached:
Area of each of the triangle = (1/2) * 3 m * 4.5 m = 6.75 m²
Area of base = 3 m * 3 m = 9 m²
Since the sides are covered in blue fabric, hence:
Surface area of blue fabric = 4 * area of each triangle = 4 * 6.75 m² = 27 m²
The base is covered with brown fabric, hence Surface area of brown fabric = 4 * area of each triangle = 4 * 9 m² = 36 m²
Please help me with this thx need soon
Answer:
A) x = 7
Step-by-step explanation:
7x + 1 + 7x + 6 + (180° - 15x) = 180°
14x + 7 + 180° - 15x = 180°
combine like terms:
-x = -7
x = 7