Inequality is a statement of an ordered relationship
The value of x as inequality is less than -3.
x < -3 is our answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
Example:
x > 3
y < 5
x ≤ 6
y ≥ 2
We have,
-32 > -5 + 9x
Add 5 on both sides.
-32 + 5 > -5 + 9x + 5
[ -32 + 5 = -27 ]
-27 > 9x
Divide both sides by 9.
-27/9 > 9x/9
-9 x 3 / 9 > 9x / 9
-3 > x
This can be written as:
x < -3
Thus,
The value of x as inequality is less than -3.
i.e x < -3
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I need help... please...
A scale drawing of a kitchen is shown below. The scale is 1 : 20.
Show your work to determine the area of the room in square feet.
scale of 1:20 means for every 1 inch on the drawing it is 20 inches in real life
5 inches * 20 = 100 inches = 8.33 feet
4 inches *20 = 80 inches = 6.67 feet
8.33 * 6.67 = 55.56 square feet
What are the solutions of the equation x4 + 95x2 – 500 = 0? Use factoring to solve.
x=+- sqrt 5 and x = ±10
x=+- sqrt i5 and x = ±10i
x=+- sqrt 5 and x = ±10i
x=+- sqrt i5 and x = ±10
Given
The equation in the form
[tex]x^{4}+95x^{2}-500 =0[/tex]
Find the factor of the above equation
To proof
factoring the above equation
we get
[tex]x^{4}+100x^{2}-5x^{2}-500 =0\\\\x^{2}(x^{2}+100)-5(x^{2}+100)=0\\\\(x^{2}-5)(x^{2}+100)=0[/tex]
now sloving the equation we get the value
x² = 5
x² = -100
[tex]x =\pm \sqrt{5}\\\\ x=\sqrt{-100}[/tex]
The factor of the equation is
[tex]x=\pm \sqrt{5}\\\\ x= \pm 10i[/tex]
Hence proved
What is the value of the expression when n=3?
–2n(5 + n – 8 – 3n)
When n=3, the value of the expression is 54.
Explanation:To find the value of the expression when n=3, we substitute n=3 into the expression: –2n(5 + n – 8 – 3n).
First, we simplify the expression:
–2n(5 + n – 8 – 3n) = –2(3)(5 + 3 – 8 – 3(3))
= –2(3)(5 + 3 – 8 – 9)
= –2(3)(-9)
= –2(-27)
= 54.
Therefore, when n=3, the value of the expression is 54.
Eight people compete in a downhill ski race assuming that there are no ties in how many different orders can skiers finish
There are a total of 8! different orders in which a skier can finish the race.
What are Permutations and Combinations?
Objects from a set may be chosen in a variety of ways, usually without replacement, to create subsets. These methods are known as permutations and combinations. When the order of selection is a consideration, this process of choosing subsets is known as a permutation; when it is not, it is known as a combination.
In the given question, we have 8 people, who compete in a downhill ski race.
Also, It is also given that there are no ties in the race.
So, There will be only one person among 8 people, who will rank 1,
Similarly, There will be only one person who will rank 2, and so on till rank 8.
So, The total number of orders a skier can finish the race will be:
Total number of ways = [tex]1 \times 2 \times 3 \times 4 \times 5 \times 6 \times7 \times 8[/tex]
The total number of ways is 8!
Hence, The total number of different orders that a skier can finish will be 8!.
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the graph below represents y=x. If the slope of the above equation is changed from 1 to 4 which graph best represents the new equation
Answer:
The graph of the new equation is shown in figure 2.
Step-by-step explanation:
Consider the provided function.
[tex]y=x[/tex]
The graph of the above function is shown in figure 1.
The slope intercept form is:
[tex]y=mx+c[/tex]
Where m is the slope and c is the y intercept.
Now, compare the slope intercept form with the provided function.
By the comparison it can be conclude that the slope of the provided function is 1 and y intercept is 0. As the coefficient of x is 1.
We need to change the slope from 1 to 4.
So change the coefficient of x from 1 to 4.
Thus, the required function is [tex]y=4x[/tex]
The graph of the new equation is shown in figure 2.
Mr. Gonzalez earns his living as a salary plus commission employee. His annual salary is $18,000. He makes 4% commission on all of his sales. Mr. Gonzalez wants to earn $60,000 this year. If his earnings are divided evenly throughout the year, how much in monthly sales would Mr. Gonzalez need to have?
a.
$37,500
b.
$87,500
c.
$100,000
d.
$125,000
In order for Mr. Gonzalez to reach his goal of $60,000, if his base salary is $18,000 and he earns a 4% commission on sales, he would need to make about $87,500 in sales per month.
Explanation:In this question, Mr. Gonzalez has a base salary of $18,000 and wishes to earn a total of $60,000 for the year. This means he needs to earn an additional $42,000 ($60,000 - $18,000) from sales commission.
The commission rate is 4%, which means for every $100 he sells, he earns $4. Therefore, to find out how much he needs to sell to make the required commission, we require to divide the target commission by the commission percentage.
Therefore, he will need to sell $42,000 / 0.04 = $1,050,000 for the whole year. If this is divided evenly over the year for monthly targets, then it would be $1,050,000 / 12 (months), which results in approximately $87,500 per month.
So, the correct answer option should be b. $87,500 per month.
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A culture of 2.4×1011 bacteria is in petri dish A. A culture of 8×109 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
The number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
What is bacteria?Bacteria are small single-celled organisms. Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.
Given is a culture of 2.4 × 10¹¹ bacteria is in petri dish 'A' and a culture of
8 × 10⁹ bacteria is in petri dish B.
Number of bacteria's in petri dish A = n[A] = 2.4 × 10¹¹ bacteria
Number of bacteria's in petri dish B = n[B] = 8 × 10⁹ bacteria
For comparison, lets assume that -
k = n[A]/n[B]
k = 2.4 × 10¹¹ / 8 × 10⁹
k = 240 / 8
k = 30
n[A] = 30 n[B]
Therefore, the number of bacteria's in petri dish 'A' are 30 times more than the bacteria's in petri dish 'B'.
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If the sum of five consecutive even integers is t, then, in terms of t, what is the greatest integer?
The greatest integer is t/5 + 4 in terms of t.
What are Integers?Integers are numbers which includes the set of natural numbers, o and the negatives of all those natural numbers.
Set of integers are usually denoted as Z.
Let the first even integer be x.
Then the consecutive even integer is x + 2.
Integers are x, x + 2, x + 4, x + 6 and x + 8.
Given, sum of five consecutive even integers is t.
x + x + 2 + x + 4 + x + 6 + x + 8 = t
5x + 20 = t
5 (x + 4) = t
x + 4 = t / 5
Greatest integer is x + 8.
x + 8 = (x + 4) + 4 = t/5 + 4
Hence the greatest integer is t/5 + 4.
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what is the union of the two sets R= {10, 11, 13, 15, 17} T= {5, 7}?
Which of these triangle pairs can be mapped to each other using a single translation?
pls help need it fast
Answer:- D shows the triangle pairs which can be mapped to each other using a single translation.
Explanation:-
Translation is a rigid transformation which creates a congruent image as that of the original figure such that the distance between the each point of the original figure and the image is fixed and same.
The translation mapping is given by (x,y)→(x+h,y+k) ,where h is the distance of the x coordinate of the each point of the original figure to the image and k is the distance of the y coordinate of the each point of the original figure to the image.
In figure D we can see that the distance between each point of ΔCED is equal to the distance between each point of ΔMPN. Thus it shows the triangle pairs which can be mapped to each other using a single translation.
The Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
Further explanation:
Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.
Explanation:
The angle MNP is equal to the angle CDE.
The side PN is equal to the side ED.
The side MN is equal to the side CD.
The translation mapping of a single translation can be expressed as follows,
[tex]\left( {x,y}\right) \Rightarrow \left({x + h,y + k} \right)[/tex]
Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.
In Figure 1 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 2 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 3 the triangle MNP and CDE cannot be mapped to each other using a single translation.
In Figure 4 the triangle MNP and CDE can be mapped to each other using a translation.
Hence, the Figure 4 is correct as the triangle MNP and CDE can be mapped to each other using a translation.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides.
to find the weight of the golden 22 karat gold object
Brent has $3.35 in quarters and dimes. if he has 23 coins in all, find the number of quarters and dimes.
what is the solution of sqrt(2x+4)-sqrt(x)=2 A. x = 0 B. x = 0 and x = 16 C. x = 0 and x = –16 D. x = 16 and x = –16
Erica has found a pair of running sneakers that she likes, costing $150. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford the sneakers?
B) 18
C) 22
D) 14
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture. Given: Point B is in the interior of \(\angle ADC). Conjecture: ∠ADB≅∠BDC
Answer:
Just because it is in the interior doesn't mean it is on the bisecting line, and ADB could be an obtuse angle
Step-by-step explanation:
Suppose △DEF≅△MNO. Which congruency statement is true?
EF¯¯¯¯¯≅MN¯¯¯¯¯¯¯DE¯¯¯¯¯≅MN¯¯¯¯¯¯¯DF¯¯¯¯¯≅NO¯¯¯¯¯¯EF¯¯¯¯¯≅MO¯¯¯¯¯¯
Answer:
DE≅MN
Step-by-step explanation:
We know that corresponding parts of congruent triangles are congruent (CPCTC). Using the congruence statement we can match up the corresponding sides.
From the statement, ∠D matches ∠M, ∠E matches ∠N, and ∠F matches ∠O.
We also see that DE matches MN, EF matches NO, and DF matches MO.
Thus we have that DE≅MN.
If 100C2 has a value of 4,950, what is the value of 100C98? A. 4,950 B. 99,000 C. 49,500 D. 9,900
Susan divides the fraction 5/8 by 1/16 . Her friend Robyn divides 5/8 by 1/32 predict which person will get the greater quotient . Explain and check your prediction
Answer:
Robyn will get the greater quotient
Step-by-step explanation:
Prediction: Since 1/16 >1/32
So, it will prove the smaller quotient
Susan divides the fraction 5/8 by 1/16 .
Calculation : [tex]\frac{5}{8} \div \frac{1}{16}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{16}}[/tex]
[tex]\frac{5}{8} \times 16[/tex]
[tex]10[/tex]
Robyn divides 5/8 by 1/32
Calculation : [tex]\frac{5}{8} \div \frac{1}{32}[/tex]
[tex]\frac{\frac{5}{8}}{\frac{1}{32}}[/tex]
[tex]\frac{5}{8} \times 32[/tex]
[tex]20[/tex]
So, The prediction is true.
Robyn will get the greater quotient
In a 10 x 10 grid that represents 800, one square represents
Find the percent change from 48 to 228. Tell whether it is a percent increase or decrease. If necessary, round your answer to the nearest percent.
There is an increase in percentage from 48 to 228 is 375%.
Given that, the percent change from 48 to 228.
What is the percent change?Percentage change calculator determines the difference in values and the percent change from the original value to the new value.
Here, the difference in values = 228-48 = 180
We know that, percentage increase = Increase ÷ Original Number × 100
Now, 180/48 × 100
= 3.75 × 100
=375%
Therefore, there is an increase in percentage from 48 to 228 is 375%.
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The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards. What is the football’s maximum height? Round to the nearest tenth. yds. How far is the football kicked? yds.
Answer:
Maximum height achieved by football = 25.5 yards.
Distance traveled by football 51 yards.
Step-by-step explanation:
Path of a football kicked by a field goal kicker can be modeled by the equation y = -0.03x² + 1.53x.
Where x represents horizontal distance and y represents height of the football.
For maximum, height we will find the [tex]\frac{dy}{dx}[/tex] ( derivative ) of the equation and equate it to zero.
[tex]\frac{d(y)}{dx}[/tex] = [tex]\frac{d}{dx}[/tex] (-0.03x² + 1.53x )
[tex]\frac{dy}{dx}[/tex] = -0.03 × 2x + 1.53
By putting [tex]\frac{dy}{dx}[/tex] = 0
-0.06x + 1.53 = 0
0.06x = 1.53
x = [tex]\frac{1.53}{0.06}[/tex] = 25.5 yards
Therefore, maximum height achieved by the ball is 25.5 yards.
Now for horizontal distance covered by ball y should be 0
-0.03x² + 1.53x = 0
x ( 1.53 - 0.03x ) = 0
0.03x = 1.53
x = [tex]\frac{1.53}{0.03}[/tex] = 51 yards.
Football was kicked 51 yards.
Factor the expression. 6g^2+11g-35
Answer:
=(3g-5)(2g+7)
Step-by-step explanation:
We have f '(x) = 6x2 + 6x − 432, so f ''(x) = 12x+6 correct: your answer is correct. , which equals 0 when
To find the values of x where f ''(x) equals 0, solve the quadratic equation 12x + 6 = 0 by setting it equal to zero and solving for x: x = -1/2.
Explanation:To find the values of x where f ''(x) equals 0, we need to solve the quadratic equation 12x + 6 = 0. To do this, we set the equation equal to zero and solve for x:
12x + 6 = 0
12x = -6
x = -6/12
Simplifying, we find that x = -1/2.
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A mother is 4 times as old as her daughter. in 3 years, the mother will be 3 times as old as her daughter. how many years old is the daughter now?
What is the sum on 1/9, 2/3, and 5/18?
a. 12/9
b. 19/18
c. 8/30
d. 4/15
Which expression is equivalent to −4.7+(−0.3)+(−1.4) ?
A.) (4.7+0.3)+(−1.4)
B.) −4.7−(0.3−1.4)
C.) −4.7+(0.3+1.4)
D.) −(4.7+0.3+1.4)
How do you write an equation in slope intercept form when the slope is undefined?
When the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.
When the slope of a line is undefined, it means that the line is vertical. In the slope-intercept form of a linear equation, y = mx + b, m represents the slope of the line. However, when the slope is undefined (infinite), you cannot express it as a finite value m.
For a vertical line passing through a point (a, b), the equation can be written as: x = a.
In this case, there is no slope term, because the line is vertical and does not have a slope in the traditional sense. Instead, the equation simply states that for all points on the line, the x coordinate remains constant at a.
Thus, when the slope is undefined, write the equation as x = c, where c is the constant value of the x-coordinate for all points on the vertical line.
Carrie is an American teaching English in Mexico, and she currently has 45,000 pesos in her bank account. If the exchange rate changes from 1 U.S. dollar = 12.94 Mexican pesos to 1 U.S. dollar = 13.09 Mexican pesos, what happens to the value in U.S. dollars of the money in Carrie's bank account?
Answer:
Because of change in conversion rates, the value in Carrie's account decreases by $39.85.
Step-by-step explanation:
Total money in Carrie's bank account = 45000 pesos.
If exchange rate is 1 USD = 12.94 pesos, then in dollars the money in account is :
[tex]\frac{45000}{12.94}[/tex] = $3477.588 ≈ $3477.59
If exchange rate is 1 USD = 13.09 pesos, then in dollars the money in account is :
[tex]\frac{45000}{13.09}[/tex] = $3437.738 ≈ $3437.74
Now, if the conversion rate is 12.94 pesos then the amount in dollars is more, than when the conversion rate is 13.09 pesos.
The difference is [tex]3477.59-3437.74=39.85[/tex] dollars.
So, because of change in conversion rates, the value in Carrie's account decreases by $39.85.
to convert 3 square feet to square centimeters multiply 3 by 9.29 x 10^-2
Answer:
9.29 x 10^-2 it's wrong. It's 9.29 x 10^2 (positive)
Step-by-step explanation:
You can "move" or change the measure of everything using some scales based on specific boards.
There's a way to move from the imperial system (yards, feet, inches) to the metric system ( centimeters, meters, kilometers)
1 square foot = 929.03 square centimetre
929.03 can be written with the scientific notation, taking care of the significant figures like [tex]9.29x10^{2}[/tex]
3 [tex]feet^{2}[/tex] = 2787.09 [tex]cm^{2}[/tex] or [tex]27.87x10^{2}[/tex] [tex]cm^{2}[/tex]
The given line segment has a midpoint at (3, 1).
What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
y = x
y = x – 2
y = 3x
y = 3x − 8
The equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.
What is the Slope-intercept Form of an Equation?The slope-intercept form is given as, y = mx + b.
b is y-intercept, and m is the slope.
Slope = change in y/change in x.
The slopes of two lines that are perpendicular to each other are negative reciprocal of each other.
Thus, let's find the slope of the blue line:
Slope = (-2 - 4)/(4 - 2) = -3
Therefore, the slope of the line perpendicular to it would be, 1/3.
Equation of the perpendicular bisector that passes through (3, 1):
Since slope (m) is 1/3, find b by substituting m = 1/3 and (x, y) = (3, 1) into y = mx + b.
Thus:
1 = 1/3(3) + b
1 = 1 + b
1 - 1 = b
b = 0.
Substitute b = 0, and m = 1/3 into y = mx + b:
y = 1/3x + 0
y = 1/3x
Therefore, the equation, in slope-intercept form, of the perpendicular bisector is: y = 1/3x.
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