Answer:
[tex]x>2[/tex]
Step-by-step explanation:
When given the following inequality;
[tex](x^2+x-3):(x^2-4)\geq1[/tex]
Rewrite in a fractional form so that it is easier to work with. Remember, a ratio is another way of expressing a fraction where the first term is the numerator (value over the fraction) and the second is the denominator(value under the fraction);
[tex]\frac{x^2+x-3}{x^2-4}\geq1[/tex]
Now bring all of the terms to one side so that the other side is just a zero, use the idea of inverse operations to achieve this:
[tex]\frac{x^2+x-3}{x^2-4}-1\geq0[/tex]
Convert the (1) to have the like denominator as the other term on the left side. Keep in mind, any term over itself is equal to (1);
[tex]\frac{x^2+x-3}{x^2-4}-\frac{x^2-4}{x^2-4}\geq0[/tex]
Perform the operation on the other side distribute the negative sign and combine like terms;
[tex]\frac{(x^2+x-3)-(x^2-4)}{x^2-4}\geq0\\\\\frac{x^2+x-3-x^2+4}{x^2-4}\geq0\\\\\frac{x+1}{x^2-4}\geq0[/tex]
Factor the equation so that one can find the intervales where the inequality is true;
[tex]\frac{x+1}{(x-2)(x+2)}\geq0[/tex]
Solve to find the intervales when the equation is true. These intervales are the spaces between the zeros. The zeros of the inequality can be found using the zero product property (which states that any number times zero equals zero), these zeros are as follows;
[tex]-1, 2, -2[/tex]
Therefore the intervales are the following, remember, the denominator cannot be zero, therefore some zeros are not included in the domain
[tex]x\leq-2\\-2<x\leq-1\\-1\leq x<2\\x>2[/tex]
Substitute a value in these intervales to find out if the inequality is positive or negative, if it is positive then the interval is a solution, if it is negative then it is not a solution. This is because the inequality is greater than or equal to zero;
[tex]x\leq-2[/tex] -> negative
[tex]-2<x\leq-1[/tex] -> neagtive
[tex]-1\leq x <2[/tex] -> neagtive
[tex]x>2[/tex] -> positive
Therefore, the solution to the inequality is the following;
[tex]x>2[/tex]
The tables represent the functions f(x) and g(x).
A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, f(x), has the entries, negative 5, negative 3, negative 1, 1, 3, 5. A table with 2 columns and 7 rows. The first row, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2. The second row, g(x), has the entries, negative 13, negative 9, negative 5, negative 1, 3, 7.
Which input value produces the same output value for the two functions?
Answer:
rtyujn
Step-by-step explanation:
er456y7ujm
A candy store held a contest to guess the total number of jelly beans in a jar. All of the jelly beans in the jar were either green or orange. There were 1,872 jelly beans in the jar in total. There were 12 times as many green jelly beans as orange jelly beans. How many green jelly beans were in the jar?
Answer:
Step-by-step explanation:
Let the number of orange jelly beans be x , as we do not know the exact value of it yet. There are 12 times as many green jelly beans than the orange ones. So , if the number of orange jelly beans is x , the number of green jelly beans will be = 12 times x , which can be written as 12x. Now there are a total of 1872 jelly beans , but they are either orange or green , so we already know that the number of orange jbs is x , and the number of green jelly beans is 12x. So if we the green jelly beans and orange jelly beans , it should be 1872.
Now all we need to do is to find x.
We know that ,
x + 12x = 1872
Now we add x and 12x on the left hand side
13x = 1872
Now we divide both sides by 13 to get x. (That includes 1872 as well)
x = 144
Now we have the value of x which is 144
We know that the number of green jelly beans was 12 times x
So the number of green jelly beans in numeric value is : 12 * 144
As x is equal to 144
Ans . : The number of green jelly beans is 1728.
The number of green jelly beans is 1728.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Let the number of orange jelly beans = x ,
So, the number of green jelly beans will be = 12 times x ,
which can be written as, 12x.
Now, there are a total of 1872 jelly beans , but they are either orange or green , so we already know that the number of orange is x , and the number of green jelly beans is 12x.
So if we the green jelly beans and orange jelly beans , it should be 1872.
Now, We get;
x + 12x = 1872
13x = 1872
Divide both sides by 13,
x = 144
So, the number of green jelly beans in numeric value is :
⇒ 12 × 144
⇒ 1728
Thus, The number of green jelly beans is 1728.
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Find the measure of "theta". Round all answers to the nearest tenth.
Answer:
[tex]\displaystyle \theta \approx 36.4[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentInverse TrigStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ
Opposite Leg = 31
Adjacent Leg = 42
Step 2: Find Angle
Substitute in variables [tangent]: [tex]\displaystyle tan(\theta) = \frac{31}{42}[/tex]Inverse Trig: [tex]\displaystyle \theta = tan^{-1}(\frac{31}{42})[/tex]Evaluate: [tex]\displaystyle \theta = 36.4309[/tex]Round: [tex]\displaystyle \theta \approx 36.4[/tex]which graph represents the function f(x) = |x| - 4?
Answer:
So f(x) is y
y = |x| -4
Put in some numbers for x and see which graph matches the y output.
The first graph.
ILL MARK BRAINLIEST !!!
29.
Select the three statements that are true.
a. -11 > -6
b. -5 > -7
c. -4 > -6
d. -9 > 7
e. 8 < -1
f. -5 < -4
Answer:
BCF is the correct answer
Answer:
b, c, and f
Step-by-step explanation:
because on the negative scale -5 is closer to 0 than -7, -4 is closer to 0 than -6, and -4 is closer to 0 than -5. So in this case b, c, and f are true because it is greater than. Sorry if I explained it badly, but im pretty sure its b, c, and f.
OPQR is a tetrahedron. Given that the area of its base is 12 m and its height is 4 m, find the , volume of the tetrahedron.
Answer:
[tex]16m^{3}[/tex]
Step-by-step explanation:
The volume of a tetrahedron shape is calculated by first multiplying the base area by 1/3. Then you multiply the product obtained by the height of the tetrahedron. This will give you the volume of the tetrahedron. For example, using the values provided, the volume would be the following...
(12 * 1/3) * 4 = x
4 * 4 = x
16 = x
Finally, we can see that the volume of the tetrahedron is [tex]16m^{3}[/tex]
Name the marked angle in 2 different ways.
1) angle HJI
2) angle IJH
What is the volume of a rectangle prism with a height of 6 and base dimensions 5 in and 7 in
Answer:
210
Step-by-step explanation:
5x7x6
which function is represented by the table
Answer:
f(x)=x+5
Step-by-step explanation:
x=-1 therefore -1+5=4
Answer:
Step-by-step explanation:
i need help fast in these questions.
Which graph shows the solution to the system of linear inequalities below?
y2 2x+1
y<-2x-3
Since there isn't a picture of the graphs, I attached one, of my graph, to this answer.
I'm also assuming (y2 2x+1) is actually (y< 2x+1).
Possible solutions are within the purple section of the attached image.
I hope this is helpful to you.
Graph that represents both the inequality is attached below.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
First, we make the graph,
The border of the inequality y = 2x + 1 has a slope of 2 and a y-intercept of 1. Plotting the y-intercept at (0, 1) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units up (in the positive y-direction) and one unit to the right (in the positive x-direction), we get the point (1, 3).
The answer to y < 2x + 1 may be represented by connecting these points with a dashed line and darkening the area below the line.
A boundary line for the inequality y -2x - 3 has a slope of -2 and a y-intercept of -3. Plotting the y-intercept at (0, -3) and using the slope to determine further points will allow us to draw this line.
For instance, if we move two units down (in the negative y-direction) and one unit to the right (in the positive x-direction), we get the point (1, -5).
The answer to y < -2x - 3 may be represented by connecting these points with a dashed line and coloring the area below the line.
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Find any domain restrictions on the given rational equation:
X/2x+14 + x-4/6 = 3/x^2 + 2x -35. Someone please answer I’m doing summer school not tryna redo math AGAIN
Answer:
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35; Domain \ restriction \ x \neq 0 \ or \ -7[/tex]
Step-by-step explanation:
The given rational equation is presented here as follows;
[tex]\dfrac{x}{2 \cdot x + 14} + \dfrac{x - 4}{6} = \dfrac{3}{x^2} + 2\cdot x - 35[/tex]
A domain restriction are the limits to the ranges of input values (x-values) of a function
The three main types of domain restrictions are the reciprocal function, the log function, and the root function
The form of restriction in the given rational are reciprocal form, which are;
[tex]\dfrac{x}{2 \cdot x + 14}[/tex], and [tex]\dfrac{3}{x^2}[/tex], from which the function is undefined when;
2·x + 14 = 0, therefore when x = -7, or x² = 0, when x = 0
Therefore, the domain restrictions are that the function is defines for all x, except x = -7 and x = 0
The domain restrictions are x ≠ -7 and x ≠ 0.
Answer:
it's -7 and 5
Step-by-step explanation:
used his and got it wrong
I need help with number 35 please help
Answer:
B. shelves × 51
Reason:
sum of all books= 357
sum of shelves= 17
no of shelves × 21
or, 17 × 21= 357
which is the number of books.
find the value of 525²-475² using suitable identity
Answer to this question:
I think the answer is 3
11. Kurtis is a video salesman. On each sale he earns a commission of 12%. One of
his customers bought a TV for $550 and a VCR for $400. How much did he
earn in commission?
Answer:
114
Step-by-step explanation:
550*12%=66
400*12%=48
48+66=114
What is the following sum?
[/xy)+ s(t/x+y)
o 7(1984
o 7(1024x2)
(8/643)
Answer:
Option C
Step-by-step explanation:
[tex] \sqrt[5]{x {}^{2} y} (4 + 3) \\ 7 \sqrt[5]{x {}^{2} y} [/tex]
What is the constant variation, k, of the direct variation, y= kx, through (-3,2)
Answer:
k = -2/3
Step-by-step explanation:
y = kx
plug in the x,y values
2 = k(-3)
divude both sides by-3
-2/3 = k
k = -2/3
Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a5 and 9a5.
Given:
The lengths of legs of a right triangle are [tex]12a^5[/tex] and [tex]9a^5[/tex].
To find:
The perimeter of a right triangle.
Solution:
In a right angle triangle,
[tex]Hypotenuse=\sqrt{Leg_1^2+Leg_2^2}[/tex]
[tex]Hypotenuse=\sqrt{(12a^5)^2+(9a^5)^2}[/tex]
[tex]Hypotenuse=\sqrt{144a^{10}+81a^{10}}[/tex]
[tex]Hypotenuse=\sqrt{225a^{10}}[/tex]
On further simplification, we get
[tex]Hypotenuse=\sqrt{(15a^{5})^2}[/tex]
[tex]Hypotenuse=15a^5[/tex]
Now, the perimeter of the triangle is the sum of all of its sides.
[tex]Perimeter=Leg_1+Leg_2+Hypotenuse[/tex]
[tex]Perimeter=12a^5+9a^5+15a^5[/tex]
[tex]Perimeter=36a^5[/tex]
Therefore, the perimeter of the right triangle is [tex]36a^5[/tex].
Which terms could have a greatest common factor of 5m2n2? (Two options need to be selected)
m5n5
5m4n3
10m4n
15m2n2
24m3n4
Answer:
There are two terms that could have a greatest common factor of 5m2n2, and those are 5m4n3 and 15m2n2.
The only correct option will be 5m^4n^3 since 5m²n² can go in the expression,
What is the greatest common factor?The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers
From the question, we are to find the equivalent expression that has 5m²n² as a factor
The only correct option will be 5m^4n^3 since 5m²n² can go in the expression,
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En una panadería se dispone diariamente de 80 kg de masa y de 24 kg de frutas (secas y confitadas) para preparar dos tipos de panetones: especial y Premium, según estos requerimientos: Panetón especial: 1kg de masa y 200 g de frutas Panetón Premium: 1kg de masa y 400 g de frutas Si el panetón especial se vende a $3 y el Premium a $4, ¿Cuántos panetones especiales y Premium deben hacerse para obtener el máximo ingreso?
Answer:
x₁ = 40 x₂ = 40 z (max) = 280
Step-by-step explanation:
El presente es un problema de programación lineal, este problema se resuelve por el procedimiento o Método Simplex, con programas de resolución en línea. Como en este caso se trata de que se venden unidades enteras ( es decir las variables son enteros reales) entonces hay que imponer esa condición a nivel de la solución
Para preparar:
Masa Kg Frutas Kg Precio de venta $
Panetón tipo esp. x₁ 1 0.2 3
Panetón tipo Prem x₂ 1 0.4 4
Disponibilidad 80 24
Función Objetiva
z = 3*x₁ + 4*x₂ a maximizar
Sujeto a:
Restricciones o condicionantes:
1.- Cantidad de masa 80 Kgs
1*x₁ + 1*x₂ ≤ 80
2.- Cantidad de frutas 24 kgs.
0.2*x₁ + 0.4*x₂ ≤ 24
x₁ ≥ 0 x₂ ≥0 deben ser enteros
El modelo es:
z = 3*x₁ + 4*x₂ a maximizar
Sujeto a:
1*x₁ + 1*x₂ ≤ 80
0.2*x₁ + 0.4*x₂ ≤ 24
x₁ ≥ 0 x₂ ≥0 deben ser enteros
Usando Atomzmath on-line, después de 6 iteracciones, la solución óptima es:
x₁ = 40 x₂ = 40 z (max) = 280
What is the value of x in the equation -3/4 = x/24
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{x}{24} [/tex]
➼ [tex] \: x = \frac{ - 3 \times 24}{4} [/tex]
➼ [tex] \: x = \frac{ - 72}{4} [/tex]
➼ [tex] \: x = - 18[/tex]
Therefore the value of [tex]x[/tex] is -18.
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
[tex] \frac{ - 3}{4} = \frac{ - 18}{24} [/tex]
➼ [tex] \: \frac{ - 3}{4} = \frac{ - 3}{4} [/tex]
➼ L. H. S. = R. H. S.
Hence verified.
[tex]\bold{ \green{ \star{ \orange{Mystique35♨}}}}⋆[/tex]
Hurry hurry hurry please help in 5 mins
Answer:
nkknknknjobbjojobihgghighigugyghugughuugbhibhi
Step-by-step explanation:
hibbihib
gbuhbuhb
buying hi
hnununnhon
jinonoonno
Solve for x when y = 4
2x + 2y = 20
Answer:
x=6
Step-by-step explanation:
2x + 2y = 20
Let y=4
2x +2(4) = 20
Multiply
2x+8 = 20
Subtract 8 from each side
2x+8-8= 20-8
2x = 12
Divide by 2
2x/2 = 12/2
x = 6
Answer:
[tex]x=6\\[/tex]
Step-by-step explanation:
[tex]2x+2(4)=20[/tex]
[tex]2x+8=20[/tex]
Subtract both sides by 8
[tex]2x=12[/tex]
Divide both sides by 2 to get x alone
[tex]x=6[/tex]
Hope this is helpful
answer the question below please
Answer:
A
Step-by-step explanation:
because linear modelling can include population change
X, Y and Z are three points on a map. Y is 85km and on a bearing of 190° from X. Z is on a bearing of 140°, from Y. Z is due south of X. Calculate the distance between X and Z rounded to 1 DP
Answer:
The distance between X and Z is approximately 95.99 km
Step-by-step explanation:
Given, X, Y and Z are three points on a map. Y is 85km and on a bearing of 190° from X. Z is on a bearing of 140°, from Y. Z is due south of X.(For Diagram Please Find in Attachment)
Thus, The parameters areThe distance of Y from X = 85 km
The bearing of Y from X = 190°
The bearing of Z from Y = 140°
The bearing of Z from X = 180°
Now,
In triangle XYZ, we have∠YZX = 180° - (130° + 10°) = 40°
Therefore, Apply the sine rule here, we get
(85 km)/sin(40°) = XZ/(sin(130°))
XZ = sin(130°) × (85 km)/sin(30°) ≈ 95.99 km
The distance between X and Z ≈ 95.99 km
what is the value of this expression when x = -5 and y = -3 [tex]\frac{2}{3} x^{3} y^{2}[/tex]
Answer:
y = - 750
Step-by-step explanation:
Given
y = [tex]\frac{2}{3}[/tex] x³y² ← substitute x = - 5, y = - 3 into the expression
= [tex]\frac{2}{3}[/tex] × (- 5)³ × (- 3)²
= [tex]\frac{2}{3}[/tex] × - 125 × 9 ( cancel the 3 and 9 )
= 2 × - 125 × 3
= - 750
graph y = |x| -1
graph 1- looks like an arrow pointing down (only in top quadrants)
graph 2- like an inverted checkmark (bottom point in top right quadrant)
graph 3- looks like an arrow pointing down (in all quadrants)
Answer:
It should look roughly like this
due in 30 mins help plssss
Answer:
x = [tex]7\sqrt{2}[/tex]
Step-by-step explanation:
a is the hypotenuse of the right angled triangle ehereas the other two sides are legs of a right angle triangle .
since the other two sides are equal both should be denoted as x.
now the value of a is given i.e 14 m
using pythagoras theorem,
pythagoras theorem states that sum of square of two smaller sides of a right triangle is equal to the sum of square of hypotenuse. so,
a^2 + b^2 = c^2
x^2 + x^2 = 14^2
2x^2 = 196
x^2 = 196/2
x^2 = 98
x = [tex]\sqrt{98}[/tex]
x = [tex]7\sqrt{2}[/tex]
Answer:
[tex]x=7\sqrt{2}[/tex]
Step-by-step explanation:
The given triangle is a right isosceles triangle. This means that it is a triangle with two congruent sides and a right angle (indicated by the box around one of the angles). One of the properties of a right isosceles triangle is that it follows the following sides-ratio,
[tex]x-x-x\sqrt{2}[/tex]
Where (x) represents the legs (sides adjacent to the right angle of a right triangle) or the congruent sides in this case. ([tex]x\sqrt{2}[/tex]) represents the hypotenuse or the side opposite the right angle. Form a proportion based on the given information and solve for the unknown value (x).
[tex]x=\frac{a}{\sqrt{2}}[/tex]
Substitute,
[tex]x=\frac{14}{\sqrt{2}}[/tex]
Simplify,
[tex]x=\frac{14}{\sqrt{2}}\\\\x=\frac{14*\sqrt{2}}{\sqrt{2}*\sqrt{2}}[/tex]
[tex]x=\frac{14\sqrt{2}}{2}[/tex]
[tex]x=7\sqrt{2}[/tex]
Shawn and Dorian rented bikes from two different rental shops. The prices in dollars, y, of renting bikes from the two different shops for x hours is shown. Shop Shawn used: y=10+3.5x Shop Dorian used: y=6x If Shawn and Dorian each rented bikes for the same number of hours and each paid the same price, how much did each pay for the rental? Round to the nearest dollar if necessary. 3 4 14 24
Answer: 24
Step-by-step explanation:
Since we are given the information that
Shop Shawn used: y=10+3.5x while Shop Dorian used: y=6x.
To solve the question asked, we need to equate both equations together and this will be:
10 + 3.5x = 6x
6x - 3.5x = 10
2.5x = 10
x = 10/2.5
x = 4
Therefore, we can put the value of x into any of the equation to get y. This will be:
y = 6x
y = 6 × 4
y = 24
The amount paid for the rentals is 24
Answer:
D 24
Step-by-step explanation:
Which graph represents a proportional relationship?
Answer:
top graph
Step-by-step explanation:
The graph of a proportional relationship is a straight line graph passing through the origin.
The only graph to pass through the origin is the top one