Answers
Answer:
x = 27
Step-by-step explanation:
2/3x - 1/9x + 5 = 20
Subtract 5 from each side
2/3x - 1/9x + 5 -5= 20-5
2/3x - 1/9x = 15
Get a common denominator on the left side
2/3 *3/3 x - 1/9x = 15
6/9x - 1/9x = 15
5/9 x = 15
Multiply each side by 9/5
9/5 * 5/9x = 15 * 9/5
x = 15/5 *9
x = 3*9
x = 27
Answer:
x=27
Step-by-step explanation:
2/3 x -1/9 x+5=20
2/3x -1/9 x=20-5 common denominator
(6x-1x)/9=15 multiply each side by 9
(5x)=135
5x=135
x=135/5=27
x=27
Related Questions
Please help Asap, will give brainiest only if answer correctly with a good explanation
Answers
Answer:
D, or the last option.
Step-by-step explanation:
See how the rotation does not say whether it is Clockwise or Counterclockwise?
Now, what that means, is that it will, default, be CCW. I don't know why, but math teachers are like that.
Now, 80* and 10* add up to 90* (because they are both unmarked and going to the same direction).
So, 90* rotation CCW. Simple! Thus, the last option should be correct.
Hope this helps!
P.S. Stay Safe!
c) Bhurashi can do 1/3 part of a work in 6 days.
(1) In how many days would she complete the whole work?
(ii) How much work does she do in 1 day?
m) How much work is left to do if she worked only for 9 days?
Answers
Answer:
i. 18 daysii.[tex] \frac{1}{18} [/tex] part of workiii. [tex] \frac{1}{2} [/tex] part of workStep-by-step explanation:
i.
[tex] \frac{1}{3} [/tex] part of work can be done in 6 days.
Days taken to complete the whole work:
= 6 * 3
= 18 days
ii. Whole work will be done in 18 days.
So, 1 day work = [tex] \frac{1}{18} [/tex]
iii. Work done in 9 days :
[tex] \frac{1}{18} \times 9 [/tex]
[tex] = \frac{1}{2} [/tex]
So, remaining work :
[tex]1 - \frac{1}{2} [/tex]
[tex] = \frac{1 \times 2 - 1}{2} [/tex]
[tex] = \frac{2 - 1}{2} [/tex]
[tex] = \frac{1}{2} [/tex] part of work
Hope this helps...
Good luck on your assignment..
The television show Lett3rs has been successful for many years. That show recently had a share of 24, meaning that among the TV sets in use, 24% were tuned to Lett3rs. Assume that an advertiser wants to verify that 24% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Find the probability that none of the households are tuned to Lett3rs. P(none) =
Find the probability that at least one household is tuned to Lett3rs. P(at least one) =
Find the probability that at most one household is tuned to Lett3rs. P(at most one) =
If at most one household is tuned to Lett3rs, does it appear that the 24% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?)
Answers
Answer:
(a) P(none) = 0.0488
(b) P(at least one) = 0.9512
(c) P(at most one) = 0.2186
(d) No, it doesn't appear that the 24% share value is wrong.
Step-by-step explanation:
We are given that among the TV sets in use, 24% were tuned to Lett3rs.
A pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Let X = Number of households that are tuned to Lett3rs
The above situation can be represented through binomial distribution;
[tex]P(X = r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]
where, n = number of samples (trials) taken = 11 households
r = number of success
p = probability of success which in our question is % of
households that were tuned to Lett3rs, i.e; 24%
So, X ~ Binom{n = 11, p = 0.24}
(a) The probability that none of the households are tuned to Lett3rs is given by = P(X = 0)
P(X = 0) = [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}[/tex]
= [tex]1\times 1 \times 0.76^{11}[/tex]
= 0.0488
(b) The probability that at least one households are tuned to Lett3rs is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.0488
= 0.9512
(b) The probability that at most one households are tuned to Lett3rs is given by = P(X [tex]\leq[/tex] 1)
P(X [tex]\leq[/tex] 1) = P(X = 0) + P(X = 1)
= [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}+\binom{11}{1}\times 0.24^{1} \times (1-0.24)^{11-1}[/tex]
= [tex]1\times 1\times 0.76^{11}+11\times 0.24^{1} \times 0.76^{10}[/tex]
= 0.2186
No, it doesn't appear that the 24% share value is wrong because the probability that at most one household is tuned to Lett3rs is somewhere close to 24% and this probability is also not unusual as it is way more than the criteria of more than 5%.
Beth says that the graph of g(x)=x-5+1 is a
Translation of 5 units to the left and 1 unit up of
F(x)=x
She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x) is Beths description of the transformation correct? Explain
Answers
Answer:
(-15,3)
Step-by-step explanation:
Answer:
No, Beth is not correct. The function g(x) has an h value of 5 and a k value of 1. This would be a horizontal translation of the square root function of 5 units to the right, rather than the left. Beth was correct about the vertical translation of the square root function of 1 unit up. The point (0, 0) from the square root function would be translated to the point (5, 1) on the graph of g(x).
Step-by-step explanation:
This came right from Edg
A cake mix calls for these ingredients. 2 cups of sugar 7 cups of flour 3 cups of milk 1 cup of oil Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios?
Answers
Answer:
Ratio of sugar and flour
2:7
Ratio of milk and oil
3:1
Step-by-step explanation:
Here in this question, we shall be writing ratios based on the given number of cups in the question.
We start with ratio of sugar to flour.
We have;2 cups of sugar and 7 cups of flour. Thus we have the ratio of sugar to flour as 2:7
Also we want the ratio of milk and oil
we have 3 cups of milk and 1 cup of oil
So the ratio of milk and oil is 3:1
Answer: TO be short for it its B! :D
A cake mix calls for these ingredients.
2 cups of sugar
7 cups of flour
3 cups of milk
1 cup of oil
Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios?
3/7 > 2/1
2/7<3/1
7/1<2/3
3/2>1/7
2
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2/7<3/1
with 2 cups of sugar to 7 cups of flour that is a small ratio/ fraction while as
3 cups of milk to 1 cup of oil is a larger ratio/fraction.
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Answer: The correct option is (B).
The ratio of sugar to flour is and the ratio of milk to oil is
Step-by-step explanation: Given that a cake mix calls for the following ingredients:
2 cups of sugar , 7 cups of flour , 3 cups of milk and 1 cup of oil.
We are given to write the ratios of sugar to flour and milk to oil and select the correct comparison of the ratios.
The ratio of sugar to flour is given by
and the ratio of milk to oil is given by
Since
so have
Thus, the ratio of sugar to flour is and the ratio of milk to oil is The correct comparison is
Option (B) is CORRECT.
Step-by-step explanation:
HIIIIII 2 QUESTIONS IN THE 2 PICS HELP PLS
Answers
Answer:
(1)C- Trapezoid
(2)D-20 square feet
Step-by-step explanation:
Question 1
A cross-section of a rectangular pyramid cut perpendicular to the base but not passing through the top will have two parallel sides where one of the sides will be longer. Therefore, the shape which describes the cross-section will be a trapezoid.
Question 2
The base of the Triangle = 5 feet
Height of the Triangle = 8 feet
[tex]\text{Area of a triangle}=\dfrac12 \times $Base \times Height\\=\dfrac12 \times 5 \times 8\\=20 ft^2[/tex]
Usando a fatoração com fator comum em evidência, fatore o seguinte polinômio: x3 + x2 + x
Answers
Answer:
x(x^2 + x + 1)
Step-by-step explanation:
x^3 + x^2 + x = x(x^2 + x + 1)
The function d(s) = 0.0056s squared + 0.14s models the stopping distance
of a car, d(s), in metres, and the speed, s, in kilometres per hour. What
is the speed when the stopping distance is 7 m? Use a graph to solve.
Answers
Answer:
The car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
Step-by-step explanation:
Let be [tex]d(s) = 0.0056\cdot s^{2} + 0.14\cdot s[/tex], where [tex]d[/tex] is the stopping distance measured in metres and [tex]s[/tex] is the speed measured in kilometres per hour. The second-order polynomial is drawn with the help of a graphing tool and whose outcome is presented below as attachment.
The procedure to find the speed related to the given stopping distance is described below:
1) Construct the graph of [tex]d(s)[/tex].
2) Add the function [tex]d = 7\,m[/tex].
3) The point of intersection between both curves contains the speed related to given stopping distance.
In consequence, the car must have a speed of 25 kilometres per hour to stop after moving 7 metres.
On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2). Which statement best explains the relationship between lines FG and HJ? They are perpendicular because their slopes are equal. They are perpendicular because their slopes are negative reciprocals. They are not perpendicular because their slopes are equal. They are not perpendicular because their slopes are not negative reciprocals.
Answers
Answer:
They are not perpendicular because their slopes are not negative reciprocals.
Step-by-step explanation:
Well first we need to find slope.
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
Line HJ)
(-4,-2) , (0,4)
y2 is 4 y1 is -2, so 4 - -2 = 6
0 - -4 = 4
6/4 -> 3/2
Due to the point (0,4) having no x value 4 is the y intercept.
Hence, y = 3/2x + 4 is the slope of line HJ
Line FG)
(-4,1) , (0,-2)
y2 is -2 y1 is 1, so -2 - 1 = -3
0- -4 = 4
Because (0,-2) is missing an x value -2 is the y intercept,
Equation: y = -3/4x - 2
They are not perpendicular because their slopes are not negative reciprocals.
The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).
Recall:
Lines that are parallel will have the same slope.Lines that are perpendicular to each other will have slope values that are negative reciprocal of each other.Slope (m) = [tex]\frac{y_2- y_1}{x_2 - x_1}[/tex]Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:
Slope of line HJ:
[tex]Slope (m) = \frac{-2 - 4}{-4 -0} = \frac{-6}{-4} = \frac{3}{2}[/tex]
Slope of HJ is 3/2Slope of line FG:
[tex]Slope (m) = \frac{-2 - 1}{0-(-4)} = \frac{-3}{4} = -\frac{3}{4}[/tex]
Slope of FG is -3/4Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).
Learn more here:
https://brainly.com/question/18975049
Answers
Answer:
????
Step-by-step explanation:
Where is the question????
hey loves!!! PLz help me
Answers
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)
George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first 1/2 mile at a speed of only 2 miles per hour. At how many miles per hour must George run the last 1/2 mile in order to arrive just as school begins today?
Answers
Answer:
George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today
Step-by-step explanation:
Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.
Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.
Mathematically;
time = distance/speed
He walks 1 mile at 3 miles per hour.
Thus, the total amount of time he spend each normal day would be;
time = 1/3 hour or 20 minutes
Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.
Let the unknown speed be x miles/hour
Mathematically;
We shall be using the formula for time by dividing the distance by the speed
1/3 = 1/2/(2) + 1/2/x
1/3 = 1/4 + 1/2x
1/2x = 1/3 - 1/4
1/2x = (4-3)/12
1/2x = 1/12
2x = 12
x = 12/2
x = 6 miles per hour
Please answer this now in two minutes
Answers
Answer:
[tex] s = 14.1 [/tex]
Step-by-step explanation:
Find s using the Law of Cosines:
m < S = 31°
SR = q = 21
SQ = r = 9
QR = s = ?
Thus,
[tex] s^2 = r^2 + q^2 - 2(r)(q)*cos(S) [/tex]
[tex] s^2 = 9^2 + 21^2 - 2(9)(21)cos(31) [/tex]
[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]
[tex] s^2 = 522 - 324.0216 [/tex]
[tex] s^2 = 197.9784 [/tex]
[tex] s = \sqrt{197.9784} [/tex]
[tex] s = 14.07 [/tex]
[tex] s = 14.1 [/tex] (to the nearest tenth)
Please answer this in two minutes
Answers
Answer:
366.6 mm²
Step-by-step explanation:
Step 1: find XY using the Law of sines.
Thus,
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
m < W = 180 - (70+43) (sum of angles in a triangle)
W = 180 - 113 = 67°
WY = 24 mm
X = 43°
XY = ?
[tex] \frac{XY}{sin(67)} = \frac{24}{sin(43)} [/tex]
Cross multiply:
[tex] XY*sin(43) = 24*sin(67) [/tex]
[tex] XY*0.68 = 24*0.92 [/tex]
Divide both sides by 0.68 to solve for XY
[tex] \frac{XY*0.68}{0.68} = \frac{24*0.92}{0.68} [/tex]
[tex] XY = 32.47 [/tex]
XY ≈ 32.5 mm
Step 2: find the area using the formula, ½*XY*WY*sin(Y).
Area = ½*32.5*24*sin(70)
Area = ½*32.5*24*0.94
= 32.5*12*0.94
Area = 366.6 mm² (nearest tenth)
If some of the omitted variables, which you hope to capture in the changes analysis, in fact change over time within entity, then the FE estimator a. will be unbiased only when allowing for heteroskedastic-robust standard errors. b. may still be biased. c. will only be unbiased in large samples. d. will always be unbiased.
Answers
Answer:
d. will always be unbiased.
Step-by-step explanation:
When some of variables are omitted the estimator on indulge charge regressor may still be unbiased. If there is a special case where T = 2 then the FE estimator will be unbiased. Fixed effect regression model has different intercepts.
2. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a
shadow 30 m long. Determine the height of the tower.
Answers
Answer:
The height of the tower is:
24 meters
Step-by-step explanation:
1 meter = 100 centimeters
10 centimeters = 10/100 = 0.1 meters
8 centimeters = 8/100 = 0.08 meters
On a three rule:
0.1 meters is to 0.08 meters
30 meters is to A meters
A = 30*0.08/0.1
A = 24 meters
Related task:
https://brainly.lat/tarea/14821170
how to solve for x?Knowledge and Understanding
Answers
Answer:
x = 25°Step-by-step explanation:
The figure above is a quadrilateral
Angles in a quadrilateral add up to 360°
To find x add up all the angles and equate them to 360°
That's
6x + 4x + 3x + x + 10 = 360
14x = 350
Divide both sides by 14
x = 25°
Hope this helps you
a football is fired upward with an initial speed of 800 feet per second. It is given that h=-12t^2+360t (h is the height of the football at any given time).what will you set h equal to in the equation to to find how many seconds it takes the football to hit the ground?
Answers
Answer:
30 s
Step-by-step explanation:
When the ball hits the ground h=0. To find the time t when this happens we must solve the equation h=0.
●h= 0
● -12t^2+360t =0
● t(-12t +360) = 0
● t = 0 or -12t +360 =0
● t=0 or -12t = -360
● t=0 or 12t =360
● t=0 or t=360/12
● t=0 or t= 30
The equation has two solutions.
The ball was fired with an initial speed of 800 feet per second so it cannot hit the ground at t=0.
So the ball hits the ground after 30 s.
What is 5/7 subtracted by 2/5
Answers
Answer:
11/35
Step-by-step explanation:
what is the value of X when f(x)=g(x) ?
Answers
Answer:
x=3
Step-by-step explanation:
We want to find the value of x where the two graphs intersect
The graphs intersect at ( 3,8)
The value of x is 3
When using a calorimeter, the initial temperature of a metal is 70.4C. The initial temperature of the water is 23.6C. At the end of the experiment, the final equilibrium temperature of the water is 29.8C. What is the final temperature of the metal? C What is the temperature change of the water? C What is the temperature change of the metal? C
Answers
Answer:
29.8C6.2C-40.6CStep-by-step explanation:
a) "Equilibrium" means the final temperatures of everything in the calorimeter are the same. The final temperature of the metal is the same as that of the water: 29.8C.
__
b) The temperature change of the water is ...
final temp - initial temp = 29.8C -23.6C = 6.2C
__
c) The temperature change of the metal is ...
final temp - initial temp = 29.8C -70.4C = -40.6C
Answer:
29.8C
6.2C
-40.6C
Step-by-step explanation:
Valerie had a jug that contained 128 fl oz of salsa to put into bowls at a restaurant. She filled each bowl with 6 fl oz of salsa until there was not enough salsa left in the jug to completely fill another bowl. How many fluid ounces of salsa were left in the jug?
Answers
Answer: 2 fl oz
Step-by-step explanation:
Division with remainders
128/6=21.33333..
[tex]21\cdot 6=126[/tex]
128-126=2
2 fl oz was left in the jug
StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negative 0.08 x + 0.10 y = 0.10 EndLayout
Answers
Answer:
[tex]x = 1.25[/tex]
[tex]y = 0[/tex]
Step-by-step explanation:
Given
[tex]4x - 5y = 5[/tex]
[tex]0.08x + 0.10y = 0.10[/tex]
Required
Determine the solution
Make x the subject of formula in: [tex]4x - 5y = 5[/tex]
[tex]4x = 5 + 5y[/tex]
Divide both sides by 4
[tex]\frac{4x}{4} = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5y}{4}[/tex]
Substitute [tex]x = \frac{5 + 5y}{4}[/tex] in [tex]0.08x + 0.10y = 0.10[/tex]
[tex]0.08(\frac{5 + 5y}{4}) + 0.10y = 0.10[/tex]
Solve the fraction
[tex]0.02(5 + 5y) + 0.10y = 0.10[/tex]
Open the bracket
[tex]0.1 + 0.1y + 0.10y = 0.10[/tex]
[tex]0.1 + 0.2y = 0.10[/tex]
Subtract 0.1 from both sides
[tex]0.1-0.1 + 0.2y = 0.10 - 0.1[/tex]
[tex]0.2y = 0[/tex]
Divide both sides by 0.2
[tex]y =0[/tex]
Substitute 0 for y in [tex]x = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5*0}{4}[/tex]
[tex]x = \frac{5 + 0}{4}[/tex]
[tex]x = \frac{5 }{4}[/tex]
[tex]x = 1.25[/tex]
WILL MARK BRAINLIEST!! PLZ HELP!!
Answers
Answer:
The answer is D.
Step-by-step explanation:
When x=0, then y=300, so it has to be more than that.
When x=25, y=300, so it has to be less than that.
Find HY if YL=9. nobody has shown me how to do this the last two weeks
Answers
Step-by-step explanation:
(a) Your computer may be programmed to allocate borderline cases to the
next group down, or the next group up; and it may or may not manage
to follow this rule consistently, depending on its handling of the numbers
involved. Following a rule which says 'move borderline cases to the next
group up', these are the five classifications.
(i) 1.0-1.2 1.2-1.4 1.4-1.6 1.6-1.8 1.8-2.0 2.0-2.2 2.2-2.4
6 6 4 8 4 3 4
2.4-2.6 2.6-2.8 2.8-3.0 3.0-3.2 3.2-3.4 3.4-3.6 3.6-3.8
6 3 2 2 0 1 1
(ii) 1.0-1.3 1.3-1.6 1.6-1.9 1.9-2.2 2.2-2.5
10 6 10 5 6
2.5-2.8 2.8-3.1 3.1-3.4 3.4-3.7
7 3 1 2
(iii) 0.8-1.1 1.1-1.4 1.4-1.7 1.7-2.0 2.0-2.3
2 10 6 10 7
2.3-2.6 2.6-2.9 2.9-3.2 3.2-3.5 3.5-3.8
6 4 3 1 1
(iv) 0.85-1.15 1.15-1.45 1.45-1.75 1.75-2.05 2.05-2.35
4 9 8 9 5
2.35-2.65 2.65-2.95 2.95-3.25 3.25-3.55 3.55-3.85
7 3 3 1 1
(V) 0.9-1.2 1.2-1.5 1.5-1.8 1.8-2.1 2.1-2.4
6 7 11 7 4
2.4-2.7 2.7-3.0 3.0-3.3 3.3-3.6 3.6-3.9
7 4 2 1 1
(b) Computer graphics: the diagrams are shown in Figures 1.9 to 1.11
angle x and y are complementary angles . angle y measure 37 plzz help asap
Answers
Answer:
53 degrees
Step-by-step explanation:
Complementary angles add to 90 degrees
a+b = 90
a=37
37+b = 90
Subtract 37 from each side
37+b-37 = 90-37
b =53
Answer: 53 degrees
Step-by-step explanation: We can find the measure of <b by taking 90 minus the measure of <a which is 90 - 37 or 53 degrees.
simplify: m–(a–k–b) HElp!
Answers
Answer: m-a+k+b
Step-by-step explanation:
m-(a-k-b)= m+-1*(a-k-b). Then, simply use distributive property to simplify the equation into m-a+k+b
Hope it helps <3
Please answer this question now only answer if you know the answer
Answers
Answer:
v = 10.997
Step-by-step explanation:
For this, simply use the law of cosines.
v^2 = (16)^2 + (6)^2 - 2(16)(6)cos(27)
v^2 = 256 + 36 - 171.073
v^2 = 120.927
v = 10.997
Cheers.
Answer:
[tex]\boxed{11}[/tex] unitsStep-by-step explanation:
To solve the length of UW, you can use the Law of Cosines for a SAS case:
[tex]\boxed{v^2=\sqrt{u^2+w^2-2(uw)cos(V)} }[/tex]
Substitute the values and solve with a calculator:
[tex]\boxed{\sqrt{16^2+6^2-2(16*6)cos(27)} = 10.99666983 \approxeq 11}[/tex]
The length of UW is 11 units.
The roots of \[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of \[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[tex]The roots of\[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of\[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[/tex]
Answers
By the factor theorem, we have
[tex]x^2+5x+3=(x-p)(x-q)\implies\begin{cases}3=pq\\-5=p+q\end{cases}[/tex]
[tex]x^2+bx+c=(x-p^2)(x-q^2)\implies\begin{cases}c=p^2q^2\\-b=p^2+q^2\end{cases}[/tex]
Then
[tex]c=p^2q^2=(pq)^2=3^2=9[/tex]
and
[tex]p+q=-5\implies(p+q)^2=p^2+2pq+q^2=25\implies b=-(p^2+q^2)=-19[/tex]
So we have b + c = -19 + 9 = -10.
The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.
What are the sum and product of the roots of a quadratic equation?If the quadratic equation ax² + bx + c = 0, has roots as α and β, then:
Sum of the roots, α + β = -b/aProduct of the roots, αβ = c/aHow to solve the given question?In the question, we are informed that the roots of the expression x² + 5x + 3 = 0 are p and q, and the roots of the expression x² + bx + c = 0 are p² and q².
We are asked to find the value of b + c.
Since the roots of the equation x² + 5x + 3 = 0 are given as p and q.
So, we can say that:
Sum of the roots, p + q = -5Product of the roots, pq = 3Now, we are informed that the roots of the equation x² + bx + c = 0 are p² and q². So, we can say that:
Sum of the roots, p² + q² = -b, or, (p + q)² - 2pq = -b, or, (-5)² - 2(3) = -b, or, 25 - 6 = -b, or, 19 = -b, or, b = -19.Product of the roots, p²q² = c, or, (pq)² = c, or, 3² = c, or, c = 9.∴ b + c = -19 + 9 = -10.
∴ The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.
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4. The difference between twice a number and
half the number is 30. What is the number?
Help me please
Answers
Answer:
20
Step-by-step explanation:
let the number be n then twice the number is 2n and half the number is [tex]\frac{1}{2}[/tex] n
Then the difference is
2n - [tex]\frac{1}{2}[/tex] n = 30 ( multiply through by 2 to clear the fraction )
4n - n = 60, that is
3n = 60 ( divide both sides by 3 )
n = 20