Answer:
7
Step-by-step explanation:
| 4x-13 | = 5x+4
Solve
Answer:
x = 1
Step-by-step explanation:
The absolute value always gives a positive value. However, the expression inside can be positive or negative , so
4x - 13 = 5x + 4 ( subtract 4x from both sides )
- 13 = x + 4 ( subtract 4 from both sides )
- 17 = x
OR
- (4x - 13) = 5x + 4 , simplify left side
- 4x + 13 = 5x + 4 ( subtract 5x from both sides )
- 9x + 13 = 4 ( subtract 13 from both sides )
- 9x = - 9 ( divide both sides by - 9 )
x = 1
As a check
Substitute these values into the equation and if both sides are equal then they are solutions.
x = - 17
left side = | 4(- 17) - 13 | = | - 68 - 13 | = | - 81 | = 81
right side = 5(- 17) + 4 = - 85 + 4 = - 81 ≠ 81
Then x = - 17 is an extraneous solution
x = 1
left side = | 4(1) - 13 | = | 4 - 13 | = | - 9 | = 9
right side = 5(1) + 4 = 5 + 4 = 9
Then solution is x = 1
Rationalise the denominator of: -7/(√11 - √5)
[tex] \sf \underline{ \red{Solution - }} \\ [/tex]
Given,
[tex] \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} }} \\ [/tex]
The denominator is √11 - √5.
We know that
Rationalising factor of √a-√b is √a+√b.
Therefore, the rationalising factor of √11-√5 is √11+√5.
On rationalising the denominator them
[tex] \longrightarrow \sf{\quad { \dfrac{-7}{\sqrt{11} - \sqrt{5}} \times \dfrac{(\sqrt{11} + \sqrt{5})}{(\sqrt{11} + \sqrt{5})} }} \\ [/tex]
Multiplying (√11 + √5) with both the numerator of the fraction.
[tex] \longrightarrow \sf{\quad { \dfrac{-7(\sqrt{11} + \sqrt{5}) }{(\sqrt{11} - \sqrt{5})(\sqrt{11} + \sqrt{5})} }} \\ [/tex]
Performing multiplication in the numerator and by using identity (a + b)(a - b) = a² - b², solving further in the denominator.
[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{(\sqrt{11})^2 - (\sqrt{5})^2} }} \\ [/tex]
Writing the squares of the numbers in the denominator.
[tex] \longrightarrow \sf{\quad { \dfrac{-7\sqrt{11} -7\sqrt{5}}{11 -5} }} \\ [/tex]
Performing subtraction in the denominator.
[tex] \longrightarrow \quad \underline{ \boxed{ \dfrac{ \textbf{ \textsf{-7 }}\sqrt{ \textbf{ \textsf{11 }}} - \textbf{ \textsf{7}}\sqrt{ \textbf{ \textsf{5 }}}}{ \textbf{ \textsf{ 6}}}} } \\ [/tex]
Hence, the denominator is rationalised.
Two-thirds of the sum of a number squared and 5 is fourteen
Answer:
2/3( x^2 + 5 ) = 14 or 2/3x^2 - 32/3
Step-by-step explanation:
Part 1:
Two-thirds ( 2/3 )
of the ( (---) )
sum ( + )
of a number squared ( x^2 ) and 5 ( + 5 )
is fourteen ( = 14 )
Part 2 (Not super confident about):
2/3( x^2 + 5 ) = 14
2/3x^2 + 10/3 = 14
2/3x^2 - 32/3
Hopefully this helps!
Brainliest please?
helppppppppppppppppp
i will give brainliest please help
Please help. Point M is the mid-point of PQ. The coordinates of P and M are given below. M (5, -2) and P (11, -10) Based on the information given, what is the coordinates of Q?
Answer:
Q(-1 , 6)
Step-by-step explanation:
Midpoint M(5 , -2)
[tex]Midpoint = \left(\dfrac{x_{1}+x_{2}}{2},\dfrac{y_{1}+y_{2}}{2} \right)\\\\P(11 , -10) \ ; x_{1} = 11 \ & \ y_{1}=-10\\\\\left(\dfrac{11+x_{2}}{2},\dfrac{-10+y_{2}}{2}\right)= \left( 5 , -2 \right )\\\\\dfrac{11+x_{2}}{2}=5 \ ; \dfrac{-10+y_{2}}{2}=-2[/tex]
11 + x₂ = 10 ; -10 + y₂ = -4
x₂ = 10 - 11 ; y₂ = - 4 + 10
x₂ = -1 ; y₂ = 6
Q(-1 , 6)
the coordinates of point Q is (-1,6)
Find the slope of the line that passes through (10,10) and (1,2)
Answer:
8/9
Step-by-step explanation:
[tex]m = \frac{10 - 2}{10 - 1} = \frac{8}{9} [/tex]
HELP PLSSS THIS IS HARD SOMEONEEE
Answer:
correct option is f(x,y) -----> ( -y,x) option 1.
Answer:
correct option is f(x,y) -----> ( -y,x) option 1.
Step-by-step explanation:
Select the correct answer. What is the slope of the line that goes through the points (-4,1) and (4,-5)?
A. -4/3
B. -3/4
C. 3/4
D. 4/3
Answer:
b
Step-by-step explanation:
edge2020
5/8-(1/4) to the power of 2
Answer:
[tex]\frac{9}{16}[/tex]
Step-by-step explanation:
[tex]\frac{5}{8}[/tex] - [tex](\frac{1}{4}) ^{2}[/tex]
= [tex]\frac{5}{8}[/tex] - [tex]\frac{1}{16}[/tex]
= [tex]\frac{10}{16}[/tex] - [tex]\frac{1}{16}[/tex]
= [tex]\frac{9}{16}[/tex]
What is the equation of the line passing through the points (1, 5) and (0, -3)
Answer:
The equation of this line is y=8x-3, I hope this helps you! :D
Answer:
y = 8x - 3
Step-by-step explanation:
The point (0, -3) is the y-intercept. You can take this and calculate the slope using the other point. Then you can form the formula y = mx+b.
I love this app can somebody please answer this question my granddaughter needs help and it will be very much appreciated❤️
Answer:
Your answer is :
A rotation Turns a shape. Shapes may be rotated clockwise or Counter-clockwise. Whenever we do a rotation, the figure must stay the same size and the same Shape. It is only turned. Figures always rotate around a Point that does not move. If a figure is rotated all the way around back to where it started, this is called a Full Rotation. Half-way around is 180°.
Step-by-step explanation:
Hope this helps!
For brainily please help
Answer:
FH is the smallest side.
Step-by-step explanation:
This is called the relation between angles and sides where the smallest angle will have the smallest side opposite one another.
That means if measure G is the smallest then FH is the smallest side as FH is the opposite of measure G.
You can also say GH is the biggest or largest side since GH is opposite of measure F and measure F has the biggest angle.
So, FH is the smallest.
g(x)=23x+1; find g (-3), g (0),and f (9x+6)
Answer:
x= -1/23
Step-by-step explanation:
Write equation in slope intercept from of the line
Answer:
y= 1/2x + 3
Step-by-step explanation:
good luck lmk if u have any more questions
Which fraction equals a repeating decimal 3/10 6/12 1/3 3/4
Answer:
1/3
Step-by-step explanation:
because 1/3 is 0.333333
Multiply.5/9 3/10 Express your answer in the simplest form.
1 23/27 15/90 1/4 1/6
Step-by-step explanation:
5/9×3/10= 15/90 simplification is 1/6
the correct is 1/6
Answer:
The 4th answer is correct
Step-by-step explanation:
[tex]\frac{5}{9} *\frac{3}{10} \\\\[/tex]
[tex]\frac{5*3}{9*10}[/tex]
[tex]\frac{15}{90}[/tex]
Now you can make the answer as the simplest form divide both sides by 15
[tex]\frac{15}{90} =\frac{1}{6}[/tex]
ANSWER IS,
[tex]\frac{1}{6}[/tex]
Hope this helps you.
Let me know if you have any other questions :-)
Put the in order 7/16 1/2 3/8 9/32 5/16 15/32 ??? Put from greatest to least
Solve for x
See the picture for problem! Please and thank you!
Answer:
x = 9
Step-by-step explanation:
( 17x + 7 )° = ( 13x + 3 )° + 40°
17x + 7 = 13x + 3 + 40
17x - 13x = 43 - 7
4x = 36
x = 9
What is the standard form of function f?
f(x)=4(x+6)+5
Substitute numerical values into the equation for a, b, and c.
Answer:
A = 4; B = -1 ; C = -29
Step-by-step explanation:
y = 4(x + 6) + 5
y = 4x + 24 +5
y = 4x + 29
Standard form: Ax + By = C
4x - y = -29
Answer:
Step-by-step explanation:
Hope this Helps ;)
A line with a slope of 2 passes through the point (-8, 2). What is its equation in
point-slope form?
Hello!
y-y1=m(x-x1)
y-2=2(x-(-8)
y-2=2(x+8)
And that's our equation in point-slope form. Hope this helps!
~Just a joyful teen
[tex]SilentNature\\(GraceRosalia)[/tex]
-3p + 8 = -13
HELLLLPP
Answer:
p=-7 :)
Step-by-step explanation:
-13-8=3p
-13+(-8)=3p
-21=3p
÷3
-7=p
Answer:
p=-32
Step-by-step explanation:
PLEASEEEEE HEELP MEEEE DO THIS WORK THANK U!
Answer:
There are no solutions.
Step-by-step explanation:
Put it in an equation
x + 5 = x − 13
Let's solve your equation step-by-step.
x + 5 = x − 13
Step 1: Subtract x from both sides.
x + 5 − x = x − 13 − x
5 = − 13
Step 2: Subtract 5 from both sides.
5 − 5 = − 13 − 5
0 = − 18
Answer:
There are no solutions.
Matt está jugando en un juego gana 7 puntos pierde 10 puntos luego vuelve a ganar 2 puntos y luego pierde 8 puntos Cuál es su puntuación final ?
Answer:
La respuesta es 3.
Step-by-step explanation: así que básicamente sus puntos finales son 3.
The sum of 8th term of an A.P is 160 while to sum of the 20th term is 880. Find the 43rd term
The value of the 43rd term of the arithmetic sequence will be 482.
What is the sum of an arithmetic sequence?Let a be the first term, L be the last term, n be the number of terms, and d be a common difference.
Then the sum of the arithmetic sequence will be
Sₙ = (n / 2)[a + L]
Sₙ = (n/2) [2a + (n − 1) d]
An A.P.'s eighth term is worth 160 while their twentieth term is worth 880.
160 = (8/2)(2a + 7d)
2a + 7d = 40 ...1
880 = (20/2)(2a + 19d)
2a + 19d = 88 ...2
From equations 1 and 2,
40 - 7d + 19d = 88
12d = 48
d = 4
Then the value of 'a' is given as,
2a + 7(12) = 40
2a = 40 - 84
2a = -44
a = -22
The value of the 43rd term is given as,
aₙ = a + (n - 1)d
a₄₃ = - 22 + (43 - 1)(12)
a₄₃ = - 22 + 42 x 12
a₄₃ = - 22 + 504
a₄₃ = 482
More about the sum of arithmetic sequence link is given below.
https://brainly.com/question/25749583
#SPJ5
Which of the following relations is a function?
O {(9,0), (10,3), (11, 6), (11, 9)}
O {(1, 1), (1, 2), (1, 3), (1,4)}
O {(1, 3), (2, 10), (6, 24), (24, 6)}
O {(0,6), (-1, 10), (-1, 14), (-3, 18)}
Answer:
O {(1, 3), (2, 10), (6, 24), (24, 6
Betty was charged 15 1/2% interest for the year
on her loan of £2 400. James was charged 12% interest for the year on his loan of £4 000.
How much more interest did James pay for the
year?
HELP PLEASE
Answer: James was charged with $180 more for the year that Betty
Step-by-step explanation: So I dont know how your money currency works sorry, also Ive never done this kind of math problem so I dont know if its right
plssssss help meh with this
Answer:
f(-9) = -263
Step-by-step explanation:
f(-9) = -3(-9)^2 - 20
= -3(81) - 20
= -243 - 20
= -263
Express (2+3)
as a trinomial in simplest form,
Answer:
A trinomial is an algebraic equation composed of three terms and is normally of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b and c are numerical coefficients. The number “a” is called the leading coefficient and is not equal to zero (a≠0). For instance, x² − 4x + 7 and 3x + 4xy – 5y are examples of trinomials.
Step-by-step explanation:
Please recheck your question.
Find the slope of the line
(2,3) (13,8)
Answer:
[tex]\boxed{m=\frac{5}{11}}[/tex]
Step-by-step explanation:
[tex]\left(2,\:3\right)\:\left(13,\:8\right)[/tex]
[tex]\mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:3\right)[/tex]
[tex]\left(x_2,\:y_2\right)=\left(13,\:8\right)[/tex]
[tex]Slope(m)=\frac{8-3}{13-2}[/tex]
[tex]m=\frac{5}{11}[/tex]
A recent report found that a local creamery has a 35% market share in a certain region. Employees in the marketing
department of the creamery conduct a survey to confirm the results by randomly selecting 300 residents from the regon
The employees asked the question which brand of ice cream do you usually purchase to each resident Use a normal
approximation to calculate the probability that at most 80 of these people will choose the creamery's brand. Use a T1-83,
83 plus, or T-34 calculator to find the probability
- Round your answer to four decimal places
Using the normal approximation to the binomial, it is found that there is a 0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
35% market share, hence [tex]p = 0.35[/tex].300 residents are surveyed, hence [tex]n = 300[/tex].The mean and the standard deviation are given by:
[tex]\mu = np = 300(0.35) = 105[/tex]
[tex]\sigma = \sqrt{np(1-p)} = \sqrt{300(0.35)(0.65)} = 8.26[/tex]
Using continuity correction, the probability that at most 80 of these people will choose the creamery's brand is [tex]P(X \leq 80 + 0.5) = P(X \leq 80.5)[/tex], which is the p-value of Z when X = 80.5, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80.5 - 105}{8.26}[/tex]
[tex]Z = -2.97[/tex]
[tex]Z = -2.97[/tex] has a p-value of 0.0015.
0.0015 = 0.15% probability that at most 80 of these people will choose the creamery's brand.
A similar problem is given at https://brainly.com/question/25298431
