Hello, please consider the following.
[tex]\begin{aligned}5(9x^2+9x+10) &= x(9x-40)\\&=9x^2-40x\end{aligned}\\\\<=> 45x^2+45x+50=9x^2-40x\\\\<=> (45-9)x^2+(45+40)x+50=0\\\\<=> 36x^2+85x+50=0[/tex]
We can estimate the discriminant, and then, the solutions and we take the largest one.
[tex]\Delta=b^2-4ac=85^2-4*36*50=25=5^2\\\\x_1=\dfrac{-85-5}{2*36}=\dfrac{-18*5}{18*4}=\dfrac{-5}{4}\\\\x_2=\dfrac{-85+5}{2*36}=\dfrac{-80}{72}=\dfrac{-8*10}{8*9}=\boxed{\dfrac{-10}{9}}[/tex]
Thank you
PLEASE HELP!
Use the values x = -0.5,0,1 to prove your solution to the equation 5 + x - 12 = 2x - 7 . In your final answer, include all of your calculations.
Answer:
0
Step-by-step explanation:
Hello!
To solve this we put in the values given to us for x and go till we get one this is true.
The values given for x are -0.5, 0, and 1
1
5 + 1 - 12 = 2(1) - 7
Combine like terms
-6 = -5
Since -6 does equal -5 the answer is not 1
0
5 + 0 - 12 = 2(0) - 7
Combine like terms
-7 = -7
Since -7 equals -7 the answer is 0
Hope this Helps!
The following dot plot shows the number of weekly challenge questions each of the 30 members the Math Bowl team answered correctly last season. Each dot represents a different member. Which of the following is a typical number of challenge questions one member answered correctly?
Answer:
10
Step-by-step explanation:
The most number of questions answered correctly are 10 and 11.
The typical number of questions a student answered correctly can be represented by the middle most value that is common to the data set.
If the data set is distributed evenly, the median, or the middle most value will fall on the 15th and 16th dots, which represents 10 correct correct challenge questions answered.
The typical number is 10.
Answer:
[tex]10[/tex]
Please help! I’ll mark you as brainliest if correct
Answer:
3. C
Step-by-step explanation:
16 / 4 = 4 which is a counting number.
- 30 / 5 = -6 which is a integer.
-31/8 = -3.875 which is rational number
30/9 = 10/3 = 3.333333333.... which is an irrational number
So your answer is C
HELP PLEASE!! I DONT UNDERSTAND!!!!!!!!!! THANKS SO MUCH
Hello, please consider the following.
We will multiply the numerator and denominator by
[tex]4+\sqrt{6x}[/tex]
to get rid of the root in the denominator.
First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.
[tex]4-\sqrt{6x} =0<=>\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}[/tex]
We need to take any x real number different from 8/3 then and simplify the expression.
Let's do it!
[tex]\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}[/tex]
Thank you
6. What is the slope of the line given by the equation y = 4x +12?
Answer:
4
Step-by-step explanation:
y = 4x + 12
In y = mx+b
The coefficient of x (m) is the slope.
So the slope is 4
Answer:
The slope is 4
Step-by-step explanation:
y = 4x +12
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 4 and the y intercept is 12
Which function does this graph represent ?
Answer: B
Step-by-step explanation:
a is negtive bcs grph opens down. h value is -1 and k is +2
Kimberly's grade in Algebra is comprised of tests (40%), quizzes (40%), and a final project (20%). Her scores for each of the categories are 82 on tests, 100 on quizzes, and a 84 on her final project. Compute her weighted average for the class. (to the nearest tenth of a percent) A) 86.4% B) 88.6% C) 89.1% D) 89.6%
Answer:
D) 89.6 %
Average or mean of the given data = 89.6 %
Step-by-step explanation:
Step(i):-
Given data
X : 82 100 84
P(X=x) : 0.40 0.40 0.20
Step(ii)
Let 'X' be the discrete distribution
Mean of the discrete distribution = ∑ x P( x=x)
= 82 ×0.40 +100 ×0.40 +84 ×0.20
= 89.6
Final answer:-
Average of the given data = 89.6 %
The data show systolic and diastolic blood pressure of certain people. Find the regression equation, letting the systolic reading be the independent (x) variable. Find the best predicted diastolic pressure for a person with a systolic reading of 146 . Is the predicted value close to 91.0 , which was the actual diastolicreading? Use a significance level of 0.05.Systolic 117 134 150 113 138 113 144 145Diastolic 85 74 86 55 75 80 106 841. What is the regression equation? (Round to two decimal places as needed.)2. What is the best predicted diastolic pressure for a person with a systolic reading of 146 ?3. Is the predicted value close to 91.0 , which was the actual diastolic reading?A. The predicted value is very close to the actual diastolic reading.B. The predicted value is not close to the actual diastolic reading.C. The predicted value is close to the actual diastolic reading.D. The predicted value is exactly the same as the actual diastolic reading.
Answer:
ŷ = 6.69X - 706.18 ; ŷ = 270.56 ; B. The predicted value is not close to the actual diastolic reading.
Step-by-step explanation:
Systolic reading(x) :
117
134
150
113
138
113
144
145
Diastolic (y) :
85
74
86
55
75
80
106
841
Using the online regression calculator, the regression equation obtained using the data values provided above is:
ŷ = 6.69X - 706.18
Comparing with the regression equation formula: ŷ = mX + c
Where :
ŷ = predicted variable (Diastolic)
m = 6.69 = gradient or slope of the regression line
c = - 706.18 = intercept ( where the regression line intersects the y-axis).
2.) What is the best predicted diastolic pressure for a person with a systolic reading of 146
X = 146
ŷ = 6.69(146) - 706.18
ŷ = 976.74 - 706.18
ŷ = 270.56
The predicted value, 270.56 is not close to the actual Diastolic reading of 91.0
Find the sum of all $r$ such that $\frac{8r^2 - 14 r + 3}{r+5} = 4r -1$.
Answer:
8.25
Step-by-step explanation:
[tex]\frac{8r^2 - 14 r + 3}{r+5} = 4r -1[/tex]
[tex]8r^2 - 14r + 3= (4r -1)(r + 5)[/tex]
[tex]8r^2 - 14r + 3= 4 {r}^{2} + 19r - 5[/tex]
[tex]4 {r}^{2} - 33r + 8=0[/tex]
[tex]4 {r}^{2} - 32r - r + 8 = 0[/tex]
[tex]4r(r - 8) - 1(r - 8) = 0[/tex]
[tex](4r - 1)(r - 8)[/tex]
[tex]r = 8 \: or \: \frac{1}{4} [/tex]
Therefore the sum of all values of r
[tex]8 + \frac{1}{4} = 8 \frac{1}{4} [/tex]
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
Answer:
V = 150π units^3
Step-by-step explanation:
The volume of this cylinder is V = πr²h = π(5 units)^2·(6 units), or
V = 150π units^3
The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.
What is the volume of a solid?The volume of a solid is the total space it contains in the three-dimensional space.
What is the volume of a cylinder?The volume of a cylinder can be given by the formula,
V = πr²h cube units,
where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
How to solve the given question?In the question, we are asked to find the volume of the cylinder shown in the figure.
The cylinder has a base radius (r) of 5 units, and height (h) of 6 units.
So, we can find its volume using the formula,
V = πr²h cube units,
where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.
∴ The volume of the cylinder = π(5²)6 cube units
or, the volume of the cylinder = π*25*6 cube units
or, the volume of the cylinder = 150π cube units
or, the volume of the cylinder = 150*3.14 cube units = 471 cube units.
∴ The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.
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Recent census data indicated that 14.2% of adults between the ages of 25 and 34 live with their parents. A random sample of 125 young adults in this age group was selected. What is the probability that between 14 and 20 of these young adults lived with their parents?
Answer:
The probability is [tex]P(14 < X < 20 ) = 0.5354[/tex]
Step-by-step explanation:
From the question we are told that
The proportion that live with their parents is [tex]\r p = 0.142[/tex]
The sample size is n = 125
Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution
i.e
[tex]X \ \~ \ B( \mu , \sigma )[/tex]
Now the mean is evaluated as
[tex]\mu = n * \r p[/tex]
[tex]\mu = 125 * 0.142[/tex]
[tex]\mu = 17.75[/tex]
Generally the proportion that are not staying with parents is
[tex]\r q = 1 - \r p[/tex]
= > [tex]\r q = 0.858[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{n * \r p * \r q }[/tex]
[tex]\sigma = \sqrt{ 125 * 0.142 * 0.858 }[/tex]
[tex]\sigma = 3.90[/tex]
Given the n is large then we can use normal approximation to evaluate the probability as follows
[tex]P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90} <\frac{ X - \mu }{\sigma } < \frac{ 20 - 17.75}{3.90} )[/tex]
Now applying continuity correction
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )[/tex]
Generally
[tex]\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )[/tex]
[tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )[/tex]
[tex]P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )[/tex]
[tex]P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)[/tex]
So for the z - table
[tex]P( Z< 0.449 ) = 0.67328[/tex]
[tex]P(Z < -1.0897) = 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.67328 - 0.13792[/tex]
[tex]P(14 < X < 20 ) = 0.5354[/tex]
pt 3 6/7 Pleasee helpp
Answer:
7p + 4
Step-by-step explanation:
7p - (-5) + (-1)
7p + 5 -1
7p + 4
Consider the sequence {an} = {nrn}. Decide whether {an} converges for each value of r.
(a) r = 1/5
(b) r = 1
(c) r = 1/6
For what values of r does the sequence {nr^n} converges?
Answer:
a). converges
b). diverges
c). converges
Step-by-step explanation:
{ [tex]$ a_n $[/tex] } = { [tex]$ nr^n $[/tex] }
Using radio test,
L = [tex]$ \lim_{n \rightarrow \infty} |\frac{a_n + 1}{a_n}| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |\frac{(n+1)r^{n+1}}{nr^n}| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |(1+\frac{1}{n})^r| $[/tex]
= [tex]$ \lim_{n \rightarrow \infty} |r| $[/tex]
= |r|
Therefore, [tex]$a_n$[/tex] converges in |r| < 1
a). r = 1/5
[tex]$\{ a_n \}= \{\frac{1}{5}, n \}$[/tex]
This sequence is monotonically decreasing and bounded.
0 < [tex]$ a_n $[/tex] < 1
Hence, { [tex]$ a_n $[/tex] } converges.
b). r = 1
{ [tex]$ a_n $[/tex] } = { n }
This sequence is monotonically increasing sequence which is not bounded.
Hence, { [tex]$ a_n $[/tex] } diverges.
c). r = 1/6
[tex]$\{ a_n \}= \{\frac{1}{6}, n \}$[/tex]
This sequence is monotonically decreasing and bounded.
0 < [tex]$ a_n $[/tex] < 1
Hence, { [tex]$ a_n $[/tex] } converges.
For |r| < 1, the [tex]$a_n$[/tex] converges.
PLet f be a function that is defined for all real numbers x. Of the following, which is the best interpretation of the statement lim x->3 f(x)=5?
Answer:
C
Step-by-step explanation:
The definition of a limit is the value a function it is approaching as the limit approaches a certain point.
We have the limit:
[tex]\lim_{x\to3} f(x)=5[/tex]
In other words, the value of f(x) as x approaches 3 approaches 5.
We do not care what happens at x=3. Rather, the limit tells us that as x approaches or gets closer to x=3, the function f(x) gets closer to 5.
Thus, the correct answer is C.
find the x-intercept for y=x^2+4x+5
Answer: There is no x-intercept for this quadratic equation.
Step-by-step explanation:
An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.
change these percentage to decimals. 1. 40%. 2. 35%. I want to know how to solve it.
Answer:
1. 40 % is 40 / 100
by cancelling it the output is 2 /5
2. 35% is 35 / 100
7 / 20 is your answer
plz brainlist me and follow me
Help me with this please ❤️❤️
Answer:
Hey there!
The coordinates of the point Q are (0, 2)
Let me know if this helps :)
Jeff and Cameron are arguing about which one of them is faster. Jeff says I can run 7 kilometers per hour!"
and Cameron says "I can run 100 meters per minute!!
Which one is faster?
Answer:
So Jeff is faster with 7 km per hour
Step-by-step explanation:
Jeff says I can run 7 kilometers per hour!
Cameron says "I can run 100 meters per minute!!
To actually know which one of them is the fastest we will convert their speed to be in the same unit
Let's convert meters per minute to kilometers per hour
100 meters per minute= 100 M/m
100 meters per minute= 100 *60/1000
100 meters per minute= 6000/1000
100 meters per minute= 6 km /h
100 meters per minute= 6 kilometers per hour
So Jeff is faster with 7 km per hour
Answer:
Jeff is faster than Cameron. Khan Academy
Step-by-step explanation:
Simplify 16x^2 9y^2/(4x-3y)^2
Hey There!!
STEP 1:
1
Simplify ——————————
(4x + 3y)2
Equation at the end of step
(4x-3y) 1
——————————————————————————— ÷ ————————
(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2
STEP 2:
Equation at the end of step
2
:
(4x-3y) 1
——————————————————————— ÷ ————————
(((16•(x2))+24xy)+32y2) (4x+3y)2
STEP 3:
Equation at the end of step
(4x - 3y) 1
—————————————————————— ÷ ——————————
((24x2 + 24xy) + 32y2) (4x + 3y)2
STEP 4:
4x - 3y
Simplify —————————————————
16x2 + 24xy + 9y2
Trying to factor a multi variable polynomial :
4.1 Factoring 16x2 + 24xy + 9y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (4x + 3y)•(4x + 3y)
Detecting a perfect square :
4.2 16x2 +24xy +9y2 is a perfect square
It factors into (4x+3y)•(4x+3y)
which is another way of writing (4x+3y)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Equation at the end of step
4:
(4x - 3y) 1
—————————— ÷ ——————————
(4x + 3y)2 (4x + 3y)2
STEP 5:
4x-3y 1
Divide ———————— by ————————
(4x+3y)2 (4x+3y)2
5.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
4x - 3y 1 4x - 3y (4x + 3y)2
—————————— ÷ —————————— = —————————— • ——————————
(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1
Canceling Out :
5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.
Final result :
4x - 3y
Hope It Helped!~ ♡
ItsNobody~ ☆
Simplify 1 - 3s - s + 8 - 2
Step-by-step explanation:
first you group like terms.
-3s-s+8+1-2
-4s+7
Answer:
-4s + 7
Step-by-step explanation:
We need to combine like terms. Like terms are terms whose variables (and exponents) are the same (note that they could be constants as well). Basically, they are "like" each other. In this case, the like terms are -3s and - s and also 1, 8, and -2. -3s - s = -4s and 1 + 8 - 2 = 7 so the answer is -4s + 7.
If you can download 6 songs for $4.68, then how much would 10 songs cost.
Answer:
$7.80
Step-by-step explanation:
Find the cost to download 1 song. Divide 6 from 4.68
4.68/6 = 0.78
Each song costs $0.78.
Find the amount 10 songs cost. Multiply 0.78 with 10:
10 x 0.78 = 7.80
$7.80 is your answer.
~
Hi
6 = 4.68
10 = X
X = 10*4.68 /6
X = 46.8/6
X = 7.8
To which subsets of numbers does 30/15 belong?
A whole, rational
B integer, rational
C whole, integer, rational
D natural, whole, integer, rational
Answer:
Step-by-step explanation:
For
The number 30 / 15 belongs to the whole, integer, and rational numbers. the correct option is C.
What is a number system?
A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
The number set from 0 to infinity are called whole numbers. The number set from negative infinity to positive infinity are called integers.
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.
The given number 30 / 15 is in the form of a rational number that can also be written as 2. Then the number 30 / 15 can be the whole, integer, and rational number.
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subtract the sum of -1 37 and - 43 from the sum of - 103 and 27
Step-by-step explanation:
Hey, there!!
I hope you mean to subtract (-137) +(-43) from sum of -103 and 27.
First, add -103 + 27
[tex] = - 103 + 27[/tex]
[tex] = - 76[/tex]
{As ( minus + plus )= subtracts with sign which has greator value. }
now,
[tex]( - 137) + ( - 43) = - 180[/tex]
{ minus + minus = add with minus sign}.
Now, subtracting -180 from -76.
=(-76) - (-180 )
Now, multiply the sign (- × -)= +
so, -180 becomes +180
= -76+180
= 104..... is answer.
Hope it helps...
Answer:
104
Step-by-step explanation:
With what you provide, the expression would be:
[tex](-103+27)-(-137+-43)[/tex], which equals to:
[tex](-76)-(-180)= (-76)+(180)=104[/tex]. [negative minus a negative equals positive]
So, the answer would be 104.
using the number 5,647,210.392 the digit 2 is in the... place and the... place
Answer:
the 2 is in the hundreds and hundredths place
What is the prime factorization of 75?
Point r is on line segment qs. Given qr =2 and rs = 10, determine he length qs.
Answer:
[tex]\huge \boxed{\mathrm{12}}[/tex]
Step-by-step explanation:
R is a point on the line segment QS.
QR = 2
RS = 10
QS = 2 + 10
QS = 12
The length of the line segment QS is 12 units.
Given that, point R is on the line segment QS. Given QR =2 and RS = 10.
We need to determine the length of QS.
What is the line segment?A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.
Here, since R is in between QS, QS=QR+RS
=2+10=12 units
Therefore, the length of the line segment QS is 12 units.
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Describe the translation. y=(x−6)2+7 → y=(x−1)2+3
The translation of the given graph has done in two steps.
1. Horizontal shift of 5 units to the left
2. Vertical shift of 4 units in the downwards direction.
What is the translation of a graph?"The translation of a graph is its rigid movement, vertically or horizontally."
The given translation of graph is:
[tex]y = (x - 6)^{2} + 7[/tex] to [tex]y = (x - 1)^{2} + 3[/tex]
Here, two types of translation has done to the first graph.
1. First of all, there is a horizontal shift of 5 units to the left has done.
[tex]y = (x - 6)^{2}[/tex] ⇒ [tex]y = [(x - 1) - 5)]^{2}[/tex]
2.After that, there is a vertical shift of 4 units in the downwards direction.
[tex]y = (x - 6)^{2} + 7[/tex] ⇒ [tex]y = (x - 1)^{2} + 3[/tex]
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There are only HB and F type pencils in the store. The ratio of the number of HB to F is 7 : 3. If there are 15F type pencils, how many pencils are there altogether?
Answer:
50
Step-by-step explanation:
Ratio is
7 : 3Total number is
7x + 3x = 10xSince F type pencils number is known:
3x = 15 x = 15/3x = 5Then total number is:
10x = 10 *5 = 50
What is an equation of the line that passes through the point (6, -2) and is parallel
to the line 5x + 3y = 6?
Answer:
y= -5/3x + 8
Step-by-step explanation:
parallel lines have the same slope
5x + 3y = 6
3y = -5x + 6
y = -5/3x + 2
the new line will have the slope (-5/3x)
y = (-5/3x) + b
plug in the (x, y) value to find b
-2 = -5/3(6) + b
-2 = -10 + b
b = 8
your equation is: y= -5/3x + 8
. Which category(s) does 75% belong? I. Real II. Whole III.Rational IV. Integer V. Irrational VI. Natural * A. III and IV only B. I and III only C. I, II, IV, V, and VI only D. I, II, III, IV, and VI only E. I, II, and III
Answer: B.) 1 and 111 only.
Step-by-step explanation:
75% = 75/100 = 0.75
0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.
Irrational numbers are the opposite of rational numbers thus, 75% is not irrational.
All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.
Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number
Whole numbers are natural numbers including 0. (0, 1, 2,.....). Hence, 75% is not a whole number
Integer numbers are comprises of both positive and negative whole numbers. (..., - 1, - 2, 0, 1, 2,...). Hence, 75% is not an integer.