Answer:
the answer should be 19.2
a) by completing the square find in the form of the constant p the roots of the equation x^2+px+4=0
b) hence find the set of values of p for which the equation has no real roots
Answer:
a)
[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
b) p is in the interval (-4,4)
Step-by-step explanation:
Quadratic Equation
It's given the following quadratic equation:
[tex]x^2+px+4=0[/tex]
a)
It's required to complete squares and find the roots. This can be done by recalling the polynomial identity:
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
We already have the first term squared, and we need to find the second term. Rewriting the equation:
[tex]\displaystyle x^2+2(\frac{1}{2}px)+4=0[/tex]
The second term of the binomial is 1/2p, thus completing the squares with [tex]b^2[/tex]:
[tex]\displaystyle x^2+2(\frac{1}{2}px)+\left(\frac{1}{2}p\right)^2+4-\left(\frac{1}{2}p\right)^2=0[/tex]
Factoring:
[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2+4-\frac{1}{4}p^2=0[/tex]
Moving the independent term to the right side:
[tex]\displaystyle \left(x+\frac{1}{2}p\right)^2=\frac{1}{4}p^2-4[/tex]
Taking the square root:
[tex]\displaystyle x+\frac{1}{2}p=\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
Solving for x:
[tex]\displaystyle x=-\frac{1}{2}p\pm\sqrt{\frac{1}{4}p^2-4}[/tex]
b) If the equation won't have real roots, then the radicand should be negative:
[tex]\displaystyle \frac{1}{4}p^2-4<0[/tex]
Factoring:
[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]
The zeros of the left-side polynomial are:
[tex]\displaystyle \frac{1}{2}p-2=0[/tex]
[tex]\displaystyle \frac{1}{2}p=2[/tex]
p = 4
[tex]\displaystyle \frac{1}{2}p+2=0[/tex]
[tex]\displaystyle \frac{1}{2}p=-2[/tex]
p = -4
The inequality:
[tex]\displaystyle \left(\frac{1}{2}p-2\right)\left(\frac{1}{2}p+2\right)<0[/tex]
Is satisfied for values of p in the interval (-4,4)
someone please help me with this work
Answer:
-34degrees
Step-by-step explanation:
ILL MARK AS BRAINLESS PLS HELP
Answer:
5765/574
Step-by-step explanation:
there u go lol
Can somebody answer this short word problem but show the steps when u get answer thanks!
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DDDD
Answer:
8 dozen gingerbread men
Step-by-step explanation:
2 + 3 = 5
120 ÷ 5 = 24
24 x 4 = 96
96 ÷ 12 = 8
plzzz help me with my math it hard
Answer:
Step-by-step explanation:
Which statement is shown about the graphs shown?
Answer: In A it seems that everything got higher and higher by each number going up and that it kept going while in B it din't start in 0 but more between the middle of 1 and 2 and in the end of it, it doesn't go as high as A. Hope this helped
Step-by-step explanation:
Rita filled 2/5 of a jug with fruit juice. She then added 200 ml of milk to make a milkshake. At this stage, the ratio of the fruit juice to milk is 3:2
how much more liquid can the jug hold?
a)250 ml
b)300 ml
c)400 ml
d)450 ml
Answer:
250ml understand the concept please
The jug can hold 250 ml more liquid.
Let the jug can hold x ml liquid.
Given Rita filled 2/5 of a jug with fruit juice.
So, the amount of fruit juice is = 2/5 of x = 2x/5.
Then she added 200 ml milk.
Given the ratio of the fruit juice to milk is 3:2.
So,
[tex]\frac{2x}{5}:200=3:2\\\frac{\frac{2x}{5} }{200}=\frac{3}{2}\\2( \frac{2x}{5})=600\\\frac{4x}{5}=600\\ x=\frac{600*5}{4}\\x=750[/tex]
So the amount of fruit juice = [tex]\frac{2}{5}*750=300[/tex] ml.
Total amount of fruit juice and milk = 300+200=500 ml.
So the jug will hold = 750 - 500 =250 ml more.
Learn more: https://brainly.com/question/3796978
The endpoints of a segment are W(0,−9)and S(10,11). What are the coordinates of the midpoint?
a.(−5,−1)
b.(5, 10)
c.(5,1)
d.(−5,−10)
Answer:
C
Step-by-step explanation:
Unit 7 homework 1: Gina Wilson answer key
Does any one have the anwerkey?
The values for x are:
question 15 ⇒x=8
question 16⇒x=19
question 17⇒x=14
Here you should apply your knowledge about regular polygons. The question asks the values of x that is a variable for some interior angles. Then, you will find x from the sum of interior angles of each regular polygon.
Sum of Interior Angles of Regular PolygonThere is a formula that relates number of sides polygon with its sum of interior angles. See below.
S=(n-2)*180°
S=sum of interior angles of regular polygon.
n=number of sides of regular polygon.
Exercise 15First, you should find the value for the sum of interior angles. Here, the regular polygon has 4 sides. Then,
S=(n-2)*180°
S=(4-2)*180°
S=2*180°=360°
Note that only 3 interior angles are shown in the figure. Nonetheless, the question gives an external angle (71°). Thus, the internal angle will be: 180-71=109°. This is because the interior and exterior angles are supplementary.
Next step, sum of interior angles for finding x
[tex]10x+6+13x-2+109+8x-1=360\\ \\ 31x=360-112\\ \\ 31x=248\\ \\ x=\frac{248}{31} =8[/tex]
x=8
Exercise 16
First, you should find the value for the sum of interior angles. Here, the regular polygon has 6 sides. Then,
S=(n-2)*180°
S=(6-2)*180°
S=4*180°=720°
Next step, sum of interior angles for finding x.
[tex]90+9x-19+7x+3+111+5x+8+128=720\\ \\ 21x=720-321\\ \\ 21x=399\\ \\ x=\frac{399}{21} =19[/tex]
x=19
Exercise 17
First, you should find the value for the sum of interior angles. Here, the regular polygon has 5 sides. Then,
S=(n-2)*180°
S=(5-2)*180°
S=3*180°=540°
The image of the question shows the sides are congruent, consequently, the angles are equal.
Next step, sum of interior angles for finding x.
[tex]9x-18+9x-18+9x-18+9x-18+9x-18=540\\ \\ 45x=540+90\\ \\ 45x=630\\ \\ x=\frac{630}{45} =14[/tex]
x=14
Read more about sum of interior angles here:
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Anybody else have to have google teach them something? (free pts)
Like i had to google something just to understand what it was.
Answer:
sometimes
Step-by-step explanation:
Answer:
Yes! All the time!
Step-by-step explanation:
if you have 12 pounds of food and you use 3/8 of that bag of food a day how long untill its all gone how many days
Answer: 0.375 bc 3 divided by 8
Step-by-step explanation:
Helppppppppppp with 3 & 4!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3 is b
4 is also b
Step-by-step explanation:
sorry another question!
1. 6,9,12,15,18
common difference:
2. 7,7.5,8,8.5,9
common difference:
3. 10,7,4,1,−2
common difference:
4. 1,1.1,1.2,1.3,1.4
common difference:
Answer:
you start counting from left to right
when you want to calculate the difference you have to choose two numbers that are next to each other and subtract second one from first one and because the different between every 2 numbers in order are the same numbers we call it a common difference.
Step-by-step explanation:
for example for 4 :
1. we can choose two numbers next to each other like 1 and 1.1
2. subtract second from first like 1.1 - 1 = 0.1
3. 1.1 + 0.1 = 1.2
1.2 + 0.1 = 1.3
and ...
so the common difference is 0.1
Fiona doubled the original amount in her savings account, s. Which expression represents her new balance and what is that new balance if s = 160? 2 s; when s = 160 the new balance in Fiona's savings account is $80. StartFraction s Over 2 EndFraction; when s = 160 the new balance in Fiona's savings account is $320. 2 s; when s = 160 the new balance in Fiona's savings account is $320. StartFraction s Over 2 EndFraction; when s = 160 the new balance in Fiona's savings account is $80.
Answer:
C is the answer ,got it right on EDG 2020
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
What is the value of x?
(5y + 10)
(3x + 7)º
Answer:
x = 21
Step-by-step explanation:
[tex](5 y + 10) \degree = y \degree + 90 \degree \\ (vertical \: \angle s) \\ \\ (5 y + 10 - y) \degree = 90 \degree \\ \\ (4 y + 10 ) \degree = 90 \degree \\ \\ 4y + 10 = 90 \\ \\ 4y = 90 - 10 \\ \\ 4y = 80 \\ \\ y = \frac{80}{4} \\ \\ y = 20 \\ \\ (5 y + 10) \degree = (5 \times 20 + 10) \degree = 110 \degree \\ \\ (5 y + 10) \degree + (3x + 7) \degree = 180 \degree \\ (linear \: pair \: \angle s) \\ \\ 110 \degree + (3x + 7) \degree = 180 \degree \\ \\ (3x + 7) \degree = 180 \degree - 110 \degree\\ \\ (3x + 7) \degree = 70 \degree \\ \\ 3x + 7 = 70 \\ \\ 3x = 70 - 7 \\ \\ 3x = 63 \\ \\ x = \frac{63}{3} \\ \\ x = 21[/tex]
The value of x and y are 21 and 20 degrees respectively.
What is linear pair?
Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
WE are given two adjacent angle (5y + 10) and (3x + 7)º
These angles make a linear pair so,
(5y + 10) + (3x + 7)º = 180
Also, we can see that angle Y and (3x + 7)º lies on a straight line then;
y + (3x + 7)º + 90 = 180
(3x + 7)º = 180 - 90 - y
(3x + 7)º = 90 -y
Now replace (3x + 7)º by 90 - y in the first equation.
(5y + 10) + (3x + 7)º = 180
(5y + 10) + (90 - y )º = 180
Finally, simplify;
4y + 100 = 180
4y = 80
y = 20
Now, (3x + 7)º = 90 -y =90 - 20
(3x + 7)º = 70
3x = 70 - 7
3x = 63
x = 21
Hence, the value of x and y are 21 and 20 degrees respectively.
Learn more about angles;
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#SPJ2
Give me 2 exponents that equal to 8 :)
Caesar has $180 in his bank account. He needs a total of $2,000 to purchase his uncle's car. He earns $60 per day and says $50 of that amount each day. Which equation can be used to determine the number of days, D, he needs to work to reach his goal of $2,000?
Answer:
Im not 100% sure because I dont have paper, but the answer is..YELLOW and Dark blue
Step-by-step explanation:
If this isnt the answer pls forgive me, and if you can pls gimme brainliest
Maria paid $240 for a table set after a discount of 40%. What was the original price?
Answer:
The original price was 400 dollars.
Step-by-step explanation:
400 times 0.4 equals 160. 400 minus 160 equals 240. Therefore the answer is 400 dollars.
The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 129 cubic inches under a pressure of 3 pounds per square inch,
what will be its volume if the pressure is increased to 5 pounds per square inch? Round your answer to the nearest integer if necessary
Answer:
the volume is 77 in³
Which ordered pair represents y as a function of x?
A. {(−2, 0), (−1, 0), (−1, 1), (0, 2)}
A. {(−2, 0), (−1, 0), (−1, 1), (0, 2)}
B. {(0, 1), (1, 3), (2, 5), (3, 7)}
B. {(0, 1), (1, 3), (2, 5), (3, 7)}
C. {(−1, 4), (−1, 6), (0, 4), (1, 8)}
C. {(−1, 4), (−1, 6), (0, 4), (1, 8)}
D. {(9, 5), (9, −5), (11, 7), (11, −7)}
Answer:
B
Step-by-step explanation:
Here, we want to select an option that represents y as a function of x
We simply want to select an option which is a function
Now, the answer in this case is one in which there are no repeating values of x and y
What this means is that all x values and all y values exactly have a single relationship between each of them
No y values has two x values and no x values links to 2 y-values
With this in mind, the correct answer is ;
option B
What is 482.073 expressed in word form?
what 10x10x10x10x10x10x10000=
Answer:
10^6*10000=10,000,000,000
Step-by-step explanation:
Will mark Brianliest answer correctly !!!!!!!!!! Pleaseeee helpppp !!!!!!!!!!!!!!!!!
If two sides of a triangle are 4 inches and 6 inches, determine the possible lengths of
the third side.
O 4 inches < x < 6 inches
O 2 inches < x < 10 inches
O 4 inches < x < 10 inches
O 5 inches < x < 11 inches
Answer:
4 inches < X < 6 inches because it says that 1 side of the triangle is 4 inches and the other side of the triangle is 6 inches.
√ 25 –2√3 + √27 +2√ 9 Express in simplified radical
Answer:
The expression in simplified radical form is:
[tex]\sqrt{25}-2\sqrt{3}+\sqrt{27}+2\sqrt{9}=11+\sqrt{3}[/tex]
Step-by-step explanation:
Given the expression
[tex]\sqrt{25\:}\:-2\sqrt{3}\:+\:\sqrt{27}\:+2\sqrt{9\:}\:[/tex]
as
[tex]\sqrt{25}=5[/tex][tex]\sqrt{27}=3\sqrt{3}[/tex][tex]2\sqrt{9}=6[/tex]so the expression becomes
[tex]=5-2\sqrt{3}+3\sqrt{3}+6[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:-2\sqrt{3}+3\sqrt{3}=\sqrt{3}[/tex]
[tex]=5+\sqrt{3}+6[/tex]
[tex]=11+\sqrt{3}[/tex]
Thus, the expression in simplified radical form is:
[tex]\sqrt{25}-2\sqrt{3}+\sqrt{27}+2\sqrt{9}=11+\sqrt{3}[/tex]
Which of these is parallel to y= 4x-2
y=5+4x
y=4-3x
y=4x+1
y=5-4x
y=4x-4
Answer:
y=4x+5(the first one)
y=4x+1
y=4x-4
Step-by-step explanation:
If the slope is the same, it is parallel
The equation for a linear equation is y=mx+b
mx is the slope
your original equation is y=4x-2, so the slope is 4.
To find which ones are parallel, you find the ones with the slope 4x(make sure it isn't -4x).
Dan runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answer:
I think it would be 4 not sure
Is the function shown linear or nonlinear? Explain.
A. The function is linear becouse all values of x and y are positive.
B. The function is nonlinear becouse there are no negative values of x or y.
C. The function is nonlinear becouse the slope is not constant.
Answer:
C
Step-by-step explanation:
The function is nonlinear because the slope is not constant.
What can you do if your struggling in Volume in Math?
Answer:
Study Harder
Step-by-step explanation:
Solve the problems. 1 Determine if each equation is true Choose True or False for each equation. a. 4.25 X 10^6 425,000 b. 6.38 X 10^9=638,000,000,000 True False True False True False True False 5.11 X 10^-2=511 d. 2.79 x 10^-4 = 0.000279
I'll mark brainlyest
Answer:
a. False
b. False
c. False
d. True
Step-by-step explanation:
a. 4.25 x 10⁶ = 425,000 (false) should be 4,250,000
b. 6.38 x 10⁹ = 638,000,000,000 (false) should be 6,380,000,000
c. 5.11 x 10⁻² = 511 (false) should be 0.0511
d. 2.79 x 10⁻⁴ = 0.000279 (true)
Answer:
True
False
False
True
Step-by-step explanation: