The domain restrictions on the rational function [tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex] are (b) x = 3 or and (d) x = -4
How to determine the domain restrictions?The function as expressed in the correct format is:
[tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex]
Factorize the denominators of the fractions
[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x^2 + 4x- 3x - 12} = \frac{x}{2}[/tex]
Factor out x and -3
[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x(x + 4)- 3(x + 4)} = \frac{x}{2}[/tex]
Factor out x + 4
[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{(x- 3)(x + 4)} = \frac{x}{2}[/tex]
Set the denominators to 0
4(x - 3) = 0
(x - 3)(x + 4) = 0
Solve for x:
4(x - 3) = 0 ⇒ x = 3
(x - 3)(x + 4) = 0 ⇒ x = 3 or x = -4
This means that the domain restrictions on the rational function are (b) x = 3 or and (d) x = -4
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The formula for the distance traveled over time ttt and at an average speed vvv is v\cdot tv⋅tv, dot, t.
Amit ran for 404040 minutes at a speed of about 555 kilometers per hour
What calculation will give us the estimated distance Amit ran in kilometers?
Y intercept due today
Answer:
y intercept = 3
Step-by-step explanation:
y = 1/3x + 3
y = mx + b
where b represents the y intercept
y intercept = 3
How many combinations without repetition are possible if n = 6 and r = 3? 56 20 27 18
Answer:18
Step-by-step explanation:
n+r=9
n×r=27
r²=9
n²=36
n+n=12
r+n=9
r+r=6
The length of a rectangle is 5 feet less than its width. If the area of a rectangle is 84 square feet, find its dimensions.
Answer:
7 x 12
Step-by-step explanation:
[tex]a=l *w[/tex]
[tex]84=l*w\\w=l+5\\[/tex]
these equations we know, so we can use them like this
[tex]84=l*(l+5)\\84=l^2 +5l\\[/tex]
I then plugged this equation into the desmos calculator to get the answer
[tex]l=7[/tex]
we then plug this into a previous equation
[tex]w=l+5\\w=7+5\\w=12[/tex]
to get our answer l=7, w=12
HELPPPPPPPPPPPPPPPPpppp
This double bar graph shows the results of a survey asking girls and boys to choose their favorite subject.
Based on the information represented in the graph, which statement is true?
Exactly 50% of girls surveyed chose language arts or social studies.
The total number of students that chose language arts is greater than the total number of students that chose math.
Less than 50% of the boys surveyed chose math or science.
The total number of students that chose social studies is greater than the total number of students that chose science.
For each graphically defined function below, state the domain, the range, and the intervals on which the function is increasing, decreasing, or constant.
Domain:
Range:
Increasing:
Decreasing:
Constant Intervals?
Answer:
Domain: [tex]-3\leq x\leq 3[/tex]
Range: [tex]0\leq y\leq 1.5[/tex]
Increasing: [tex]0\leq x\leq 3[/tex]
Decreasing: [tex]-3\leq x\leq 0[/tex]
No constant intervals
Step-by-step explanation:
Hope this helped
What is the range of the function graphed below?
Picture has the stuff
Answer:
∝ < y < 2
Step-by-step explanation:
The range is negative infinity to 2.
Please help me solve for X
Answer:
[tex]\boxed{\sf x = 8.67}[/tex]
Step-by-step explanation:
[tex]\sf 6(6 + x) = 4(4 + 18)[/tex]
Use the distributive property to multiply 6 by (6+x).
[tex]\sf 36+6x=4(4+18)[/tex]
Let's add 4 and 18 = 22.
[tex]\sf 36+6x=4 \times 22[/tex]
Multiply 4 and 22 = 88.
[tex]\sf 36+6x=88[/tex]
Subtract 36 from both sides.
[tex]\sf 6x=88 - 36[/tex]
[tex]\sf 6x=52[/tex]
Divide both sides by 6.
[tex]\sf x = 8.67[/tex]
What is the equation of the circle with center (-3.2, -2.1) and radius 4.3?
The equation of the circle is : [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84
Meaning of a CircleA circle is a loci or a continuous line that equidistant from the center to any point on the line. it drawn starting from a point and ending on that same point.
The equation of a circle is an equation used to find points on a circle so the circle can be drawn with accurate measurement. it can also be used to find the missing points.
In conclusion, The equation of the circle is : [tex]x^{2}[/tex] + [tex]y^{2}[/tex] + 6.4[tex]x[/tex] + 4.2[tex]y[/tex] = 3.84
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Multiply.
(−8)⋅(−15)⋅(4)
Enter your answer in the box.
Answer:
la respuesta es 480
Step-by-step explanation:
(-8)(-15)=8*15=120
120*(4)
480
(-8)*(-15)*(4)=480
Step-by-step explanation:
(-8)*(-15)*(4)=480
** PLS HELP THIS IS GONNA AFFECT MY GRADE!! BRAINLIEST!! ANSWER ANH OF MY QUESTIONS! **
Answer:
180-108=72 72/2=36 degrees
Step-by-step explanation:
Please ad brainliest
In an effort to improve scores on college-entrance exams, the principal at a large high school chooses 35 students
at random who have already taken the exam. The students are enrolled in a six-week prep course to improve their
scores. After the prep course, the students take the college-entrance exam again. The mean difference (first-
second) in exam scores is -1.75 points with a standard deviation of 7.12 points. Assuming the conditions for
inference are met, what is the test statistic for testing the hypotheses Hoi Hoi = 0; He Moip <0?
O 1-1.75 -0
7.12
35
o
0+ 1.75
7.12
35
-1.75 -0
7.12
35
=
1.75 -0
7.12
35
Nex
Submit
Mark this and return
Using the t-distribution, it is found that the test statistic for the hypotheses test is given by:
[tex]t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}[/tex]
What are the hypotheses tested?At the null hypotheses, it i tested if the mean difference remains the same, that is:
[tex]H_0: \mu = 0[/tex]
At the alternative hypotheses, it is tested if it has decreased, hence:
[tex]H_a: \mu < 0[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The parameters are given as follows:
[tex]\overline{x} = -1.75, s = 7.12, n = 35[/tex].
Hence the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}[/tex]
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Ricki Charges $ 10.45 an hour for her new labor. This job took her 13 hours. What is the new total for the job, including material costs and labor?
For all values of x,
x² + 6x - 2 = (x+p)² + q
Find the value of p and the value of q.
Step-by-step explanation:
[tex] {x}^{2} + 6x - 2 = {x}^{2} + 2px + {p}^{2} + q[/tex]
[tex]2p = 6[/tex]
[tex] {p}^{2} + q = - 2[/tex]
[tex]p = 3[/tex]
[tex] {3}^{2} + q = - 2[/tex]
[tex]q = - 11[/tex]
p=3, q=-11
The side lengths of the equilateral triangle pictured are each 12 cm. What is the circumference of the larger circle? Round your answer to the nearest 100th.
Please awnser last question if correct we can do thisss
Answer:
B = (8,2)
C = (8,9)
D = (5,4)
Step-by-step explanation:
Hope this helps!
Answer:
Point B: (-8,2) Point C: (-8,9) Point D: (-5,4)
Step-by-step explanation:
Since you are reflecting over the y-axis, the numbers in the coordinates will be the same but they will all have a negative "x" value instead of both numbers in the coordinate being positive.
Point B: (8,2) --> (-8,2)
Point C: (8,9) --> (-8,9)
Point D: (5,4) --> (-5,4)
Can you please help answer will make you brainliest
Answer:
C
Step-by-step explanation:
given a triangle with 2 sides and the angle between them given, then the area (A) is calculated as
A = [tex]\frac{1}{2}[/tex] bc sinA
the 2 sides are b = 4, c = 6 and ∠ A = 35° , then
A = [tex]\frac{1}{2}[/tex] × 4 × 6 × sin35° = 12 × sin35° ≈ 6.9 m² ( to the nearest tenth )
15. Federico necesita resolver el problema de encontrar la medida x, en centímetros, del lado del cuadrado de
la figura.
Sabe que el área total de la figura es 45 centímetros cuadrados y determina que el problema se puede
resolver utilizando la ecuación
8x
2
= 45
Las soluciones correctas de esta ecuación son x = -9 y x = 5. Para resolver el problema inicial, de las dos
soluciones de la ecuación, Federico debe presentar como respuesta
A. -9, porque nueve es el único cuadrado perfecto en las soluciones.
B.
C.
las dos, porque al ser soluciones de la ecuación lo son del problema.
ninguna, porque la ecuación no corresponde al problema.
D. 5, porque el lado del cuadrado debe ser un valor positivo.
Al encontrar la medida x del lado del cuadrado, Federico debe presentar como solución igual a 5, ya que el lado del cuadrado debe ser un valor positivo.
¿Cómo calcular el área del cuadrado?Como el cuadrado es una figura geométrica que tiene lados iguales, para realizar el cálculo, debemos tomar la medida de uno de los lados y elevarlo al cuadrado. El cálculo se puede realizar mediante la siguiente fórmula:
A = L²Por lo tanto, la geometría plana se usa para calcular las medidas precisas de la habitación en relación con su área, longitud y altura.
La respuesta correcta es la opción D.
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write the equation of a line:
a) parallel to the line 3x+5y=-10
b) parallel to the line 2y-4x=5 and which goes through the point (3,7)
c) perpendicular to the line 8x+6y=-1 and which goes through the point (-2,1)
THANKS!!
a) Line parallel to the line 3x+5y=-10 is -6x-10y=9
b) Line parallel to the line 2y-4x=5 and which goes through the point
(3,7) is y= 2x-1.
c) Line perpendicular to the line 8x+6y=-1 and which goes through the
point (-2,1) is 4y= 3x+ 10
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y.
a) Equation parallel to 3x+5y=-10 is
-6x-10y=9
So, it satisfies: [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}[/tex]
b)given equation into the form of y=mx+c,
2y-4x=5
we can find the gradient of the line.
2y= 5+4x
y= [tex]\frac{5}{2}[/tex] + 2x
Hence, the gradient is 2.
As, Parallel lines have the same gradient
Thus the line would also have a gradient of 2.
Substitute m=2 into the equation:
y= 2x +c
To find the value of c, substitute a pair of coordinates.
When x=3, y=7,
7= 2(3) +c
7= 6 +c
c=6-7
c= -1
So, equation of line be: y= 2x-1.
c) Given: 8x+6y=-1
6y= -1-8x
y= [tex]\frac{-1}{6} -\frac{4}{3}x[/tex]
Hence, m= [tex]-\frac{4}{3}[/tex]
We know, if two lines are perpendicular have m and m' as slope then,
m*m'=-1
[tex]\frac{-4}{3} *m'=-1[/tex]
m'= [tex]\frac{3}{4}[/tex]
Now, y= [tex]\frac{3}{4}[/tex] x +c
Put x= -1 and y=1
then, 1= [tex]\frac{3}{4}[/tex] (-2) + c
c= [tex]\frac{5}{3}[/tex]
So, y= [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{2}[/tex]
4y= 3x+ 10
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Areas of Southeast Asia were very desirable, especially because of their rich soil and these lands
A. Putrid
B. Grotesque
C. Arable
Answer:If im correct the answer is C
Step-by-step explanation:
Pls help will give brainilist
Answer:
3. 26 problems left
4. $69.20
Step-by-step explanation:
1. First I divided 5 into 2 to get a decimal, 0.4, and then I multiplied 0.4 to 65.
0.4 x 65 = 26
2. It said that Luke paid 2.75 for himself and 6 other friends, which is 7 people. I then multiplied 2.75 x 7 and got 19.25. I then added 19.25 to the other amount of money, and got 69.20.
49.95 + 19.25 = 69.20
Hope this helps <3
Ryan ran 0.5 miles on july 1st. each day
thereafter, he ran 0.3 miles more than the
previous day. find the total number of
miles ran in the month of july.
Answer:
155 miles
Step-by-step explanation:
The sum of n terms of an arithmetic series is given by the formula ...
Sn = (2·a1 +d(n -1))(n/2)
__
The number of miles Ryan ran in July is described by the arithmetic series ...
0.5 +0.8 +1.1 +... (a total of 31 terms)
The first term is a1=0.5, and the common difference is d=0.3.
The total number of miles Ryan ran in July is ...
S31 = (2(0.5) +0.3(31 -1))(31/2) = (1 +9)(31/2) = 155
Ryan ran 155 miles in July.
HELP ASAP PLS
Which graph represents function gif 9(x) = ƒ(2x)?
(Purple graph is the f(x))
Answer:
A (correctly marked)
Step-by-step explanation:
The graph of g(x) = f(2x) will be the graph of f(x) horizontally compressed by a factor of 2. The horizontal compression moves each point on f(x) to a distance half as far from the y-axis.
__
The graph of f(x) shows a vertical asymptote at x=2 so the graph of g(x) will have a vertical asymptote at x=1. Only Graph A shows a vertical asymptote at x=1.
Find the Surface Area:
A) 144 in^2
B) 102 in^2
C) 17 in^2
D) 180 in^2
E) 68 in^2
Answer:
D 180 in²
Step-by-step explanation:
step 1
2 (l) (w) + 2 (l) (h) + 2(h) (w)
step 2
2×(6)×(3) + 2×(6)×(8) + 2×(8)×(3)
step 3
2×(18) + 2×(48) + 2×(24)
step4
36 + 96 + 48 = 180 in²
My question is the if the app well it be good for me or not and if the awers the this is app it give to me are they are good of not??????????? but Thx for all and for the time be here workind thank very much... ;\ LO VE THIS APP THX TO ALLL YOU WORK...
sounds nice? I'm responding to just answer a question
What are the slope and y-intercept of the line
represented by the points shown in the table?
O slope: 2, y-intercept: -20
Oslope: 2, y-intercept: 10
Oslope: 5, y-intercept: -20
O slope: 5, y-intercept: 10
The slope of the line is 2 and y-intercept is -20 and the linear equation can be framed as y = 2x—20 option first is correct.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Taking two points to find the slope of the line:
(0, -20) and (5, -10)
[tex]\rm m =\dfrac{-10+20}{5-0}[/tex]
m = 2
The straight line equation:
y = mx + c
y = 2x + c
Plug (0, -20)
-20 = c
Thus, the slope of the line is 2 and y-intercept is -20 and the linear equation can be framed as y = 2x—20 option first is correct.
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1000 ft.
Problem 3.2
100 ft.
A large rectangular swimming pool is 1000 feet long,
100 feet wide, and 10 feet deep.
The pool is filled to the top with water.
How much water does the pool hold?
Submit
Answer:
1,000,000
Step-by-step explanation:
you just get the Volume of the shape
QUESTION
Find 45% of 240.
Answer:
108
Step-by-step explanation:
Calculator
Answer:
108
Step-by-step explanation:
(45 * 240) / 100
(10,800) / 100
108
I WILL CHOOSE BRAINLYEST please asap need help
Answer:
a. is not proportional and b. is proportional
Step-by-step explanation:
a. constant is 1 and b. constant is -2
