The answer is true, our inequality has a solution of x > 13. Our final answer is: 4(x^2 - x - 12) > (101 - 2x)^2
To create a radical inequality that has a solution of x > 13 and has at least 4 terms in it, we can start with the basic inequality x > 13 and add terms to both sides to create a more complex equation. For example:
√(x + 3) + 2 > √(x - 4) + 12
Now, we can rearrange the terms and square both sides to get rid of the radicals:
√(x + 3) - √(x - 4) > 10
(√(x + 3) - √(x - 4))^2 > 10^2
x + 3 - 2√(x + 3)(x - 4) + x - 4 > 100
2x - 2√(x + 3)(x - 4) > 101
Now, we can isolate the radical term and square both sides again:
-2√(x + 3)(x - 4) > 101 - 2x
4(x + 3)(x - 4) > (101 - 2x)^2
4(x^2 - x - 12) > 10201 - 404x + 4x^2
0 > 3x^2 - 403x + 10237
Since we want the solution to be x > 13, we can plug in 13 for x and see if the inequality is true:
0 > 3(13^2) - 403(13) + 10237
0 > 507 - 5239 + 10237
0 > 4505
Since this is true, our inequality has a solution of x > 13. Therefore, our final answer is:
4(x^2 - x - 12) > (101 - 2x)^2
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Use substitution to solve
The solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We can solve this system of equations using substitution. Solving the second equation for y, we get:
y = 3x - 3
Substituting this expression for y into the first equation, we get:
9x - 3(3x - 3) = 9
9x - 9x + 9 = 9
Therefore, the equation is true for any value of x.
Hence, the solution for this system of equations is any ordered pair of the form (x, 3x-3), where x is any real number.
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A deli owner has room for 65 containers of shredded Parmesan cheese. He has 5-oz and 10-oz containers, and a total of 400 oz of cheese. If 5-oz containers sell for $7 and 10-oz containers sell for $13, how many of each should he sell to maximize his revenue? What is his maximum revenue?
He should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
What is cοntainer?A cοntainer is a standard unit οf sοftware that packages up cοde and all its dependencies sο the applicatiοn runs quickly and reliably frοm οne cοmputing envirοnment tο anοther. Cοntainers are a sοlutiοn tο the prοblem οf hοw tο get sοftware tο run reliably when mοved frοm οne cοmputing envirοnment tο anοther. This cοuld be frοm a develοper’s laptοp tο a test envirοnment, frοm a staging envirοnment intο prοductiοn, and perhaps frοm a physical machine in a data center tο a virtual machine in a private οr public clοud.
Corner point (x, y) Value of 8x+14y
0(0,0) 0
A(65,0) 520
B(50, 15) 610
C(0,40) 560
So, the maximum value is 610
Therefore, the maximum point is B(50, 15)
∴ x = 50, y = 15
So, the maximum value is
Therefore, the maximum point is
Hence, he should sell 50 5-oz containers and 15 10-oz containers to maximize his revenue.
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How many liters of water must be evaporated from 10L of a 40% salt solution to produce a 50% solution?
2L of water must be evaporated from the 10L of 40% salt solution to produce a 50% solution.
To produce a 50% salt solution from a 40% salt solution, we must evaporate some water to increase the concentration of the salt. We can use the formula:
C1V1 = C2V2
Where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
Plugging in the given values:
0.40(10L) = 0.50(V2)
Simplifying:
4L = 0.50V2
Dividing both sides by 0.50:
V2 = 8L
So the final volume of the solution must be 8L in order to have a 50% concentration of salt. To find the amount of water that must be evaporated, we can subtract the final volume from the initial volume:
10L - 8L = 2L
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CEREAL A company claims that its boxes of cereal contain 19.1 ounces of
cereal. The actual amount of cereal in the box can be within 0.5 ounce of the
advertised amount. What is the range of possible amounts of cereal c in a box?
ctIONS through a given point with a given slope ope -(2)/(3) passing through the point (3,4)
The equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6. To find the equation of a line that passes through a given point with a given slope, we can use the point-slope formula. The point-slope formula is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point that the line passes through. In this case, the slope is -(2)/(3) and the point is (3, 4).
Plugging these values into the point-slope formula, we get:
y - 4 = -(2)/(3)(x - 3)
We can then rearrange the equation to get it into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y - 4 = -(2)/(3)x + 2
y = -(2)/(3)x + 6
So, the equation of the line with slope -(2)/(3) passing through the point (3, 4) is y = -(2)/(3)x + 6.
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Two trains, Train A and Train B, weigh a total of 437 tons. Train A is heavier than Train B. The difference of their weights is 415 tons. What is the weight of each train?
Step-by-step explanation:
A + B = 437
A - B = 415 (for that sequence it is important to know that A is larger than B).
A = 415 + B
that we use now in the first equation :
415 + B + B = 437
2B = 22
B = 11
A = 415 + B = 415 + 11 = 426 tons
B = 11 tons
PLEASE HELP
what is 7.5% of 48.30? show your working out pls.
Answer:
3.6225
Step-by-step explanation:
7.5% = 0.075
48.30 x 0.075 = 3.6225
So, 7.5% of 48.30 is 3.6225
Select all the equations that are equovalent to 52= -4 (2n +1)
The equation that is equivalent to 52 = -4 (2n + 1) is C) -52/4 = 2n + 1.
Starting with the given equation:
52 = -4 (2n + 1)
First, we can simplify the right-hand side of the equation by distributing the -4:
52 = -8n - 4
Then, we can isolate the variable (n) by adding 4 to both sides of the equation:
56 = -8n
Finally, we can solve for n by dividing both sides by -8:
-7 = n
Therefore, we have found that the solution to the equation 52 = -4 (2n + 1) is n = -7.
Now, let's check each of the answer choices to see if they are equivalent to this solution:
A) 13 = -2 (2n + 1)
If we simplify the right-hand side of this equation, we get:
13 = -4n - 2
Then, if we add 2 to both sides and divide by -4, we get:
-3.75 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
B) -7 = -2 (2n + 1)
If we simplify the right-hand side of this equation, we get:
-7 = -4n - 2
Then, if we add 2 to both sides and divide by -4, we get:
1.25 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
C) -52/4 = 2n + 1
If we simplify the left-hand side of this equation, we get:
-13 = 2n + 1
Then, if we subtract 1 from both sides and divide by 2, we get:
-7 = n
This solution is equivalent to n = -7, so this equation is equivalent to the original equation.
D) -13 = -4 (2n + 1)
If we simplify the right-hand side of this equation, we get:
-13 = -8n - 4
Then, if we add 4 to both sides and divide by -8, we get:
1.875 = n
This solution is not equivalent to n = -7, so this equation is not equivalent to the original equation.
Therefore, the equation that is equivalent to 52 = -4 (2n + 1) is C) -52/4 = 2n + 1.
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Find the size of angle x. 65° X 35°
The value of 'x' using the Triangle sum theorem is found as: x = 80°.
Explain about the Triangle sum theorem?According to the triangle sum theorem, all of a triangle's inner angles add up to 180 degrees. It is also known as the triangle's angle sum property.The triangle sum principle states that the sum of another three angles of any triangle is 180 degrees. According to their sides and angles, triangles can be classified into various mathematical kinds. These triangles are all three-sided and adhere to the triangle sum concept.Given that the triangle in the image is a triangle and that two of its angles is 65° and 35°.180° = 65°+35°+x
180° = 100°+x
180° - 100° = x
x=80° (value of x)
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The diagram for the question is attached:
What is the probability that a person who test positive actually has the disease? What is the probability that a person does not test positive?
The probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.
What are restrictions on applying Bayes' theorem?The Bayes theorem's assumption that the prior probabilities are known with certainty is one of its limitations. These probabilities, however, could not be known or be impossible to predict precisely in many real-world settings. Moreover, Bayes' theorem makes the assumption that each occurrence is independent, which may not necessarily be true in real-world circumstances.
Given that,
P(D) = 0.001
P(D') = 1- 0.001 = 0.999
P(T|D) = 0.99 (the test is 99% effective in detecting the disease)
P(T'|D') = 0.995
The Baye's theorem is given as follows:
P(A|B) = P(B|A) * P(A) / P(B)
Substituting the values:
P(T) = (0.99 * 0.001) + (0.005 * 0.999) = 0.00594
P(D|T) = (0.99 * 0.001) / 0.00594 ≈ 0.166
Hence, the probability that a person has the disease given that his test result is positive is approximately 0.166 or 16.6%.
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The complete question is:
WHAT IS THE VOLUME DK THATS WHY I NEED MORE HELP PLEASE AND THANK YOU LAST ONE I SWEAR THANK YOU GUYSS
The total volume is 5760cm^3
What is the volume?Here we have a composite figure that can be decomposed into two simpler ones, such that the simpler ones are rectangular prisms of:
12 cm by 20 cm by 8 cm
12 cm by 40 cm by 8cm
We know that the volume is equal to the product between the dimensions, then the volumes are:
v1 = 12cm*20cm*8cm = 1,920 cm^3
v2 = 12cm*40cm*8cm = 3,840cm^3
The total volume is the sum of these two:
V = 1920cm^3 + 3840cm^3 = 5760cm^3
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Use the calculator to approximate the trig function of the given angle. Round answer to the fourth decimal place. sin 58°
Based on the provided information The result of rounding to four integer places is sin 58° ≈ 0.8480.
How would you define "rounding"?Making a number easier while maintaining a value that is near to what it was is known as rounding. Although less precise, the outcome is simpler to use. For instance, 73 is 70 when adjusted to the closest ten, since 70 is closer to 73 than 80 is.
Using a calculator, we can approximate sin 58° as follows:
sin 58° ≈ 0.8480
Rounding to four decimal places, we get:
sin 58° ≈ 0.8480
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Evaluate log3 3^(2x+1)
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1[/tex]
4K + 12 = -36
solving 2 step equations
Step-by-step explanation:
[tex]4k + 12 = - 36 \\ 4k = - 36 - 12 \\ 4k = - 48 \\ k = - \frac{48}{4} \\ k = - 12[/tex]
#hope it's helpful to you
y=5x2+3x-2 maximum minimum?
Answer:
its 0183
Step-by-step explanation:
jfirst queal then u have to divided then zjs
Answer: It is a minimum
Step-by-step explanation:
It is a minimum because the coefficient (5) is positive.
An item on sale costs 5% of the origional price.origional price was $75.00. Find the sale price.
Answer:
If it costs 5% of $75 it would be $3.75
If it is 5% off $75 it would be $71.25
How we find the answer.
To find 10% of an item you move the decimal point once to the right
If we do this to 75.00 it would be 7.500
We can remove the two 0's
7.5
We are not looking for 10% though we are looking for 5%
Half of 10 = 5 so half 7.5
3.75 is 5% of 75
---------------------------------------
Now if we want to find out 5% off of 75 we subtract
75.00 - 3.75
71.25
Hope i could help
Answer:
$3.75
Step-by-step explanation:
If the item was on sale and cost 5% of its original price, to find the answer we would have to find 5% of 75 and to do this we have to do 5 ÷ 100 × 75
5 ÷ 100 = 0.050.05 × 75 = 3.75This means that the price would be $3.75
Hope this helps, have a lovely day! :)
A sports camp places it's participants on teams. Each team will have 8 members. There are 3208 people registered to participate.
The number of teams that can be formed is 401
Finding the number of teams:
To determine the number of teams that can be formed with the given number of participants, we need to divide the total number of participants by the number of members per team.
Here we have
Number people registered = 3208
Number of members each team will have is 8 members
The number of teams that can be formed is equal to 3208 ÷ 8
Number of teams = 3208/8 = 401
Therefore,
The number of teams that can be formed is 401
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Judy bought 1 pound 6 ounces of almonds, 2 pounds 3 ounces of walnuts, and 8 ounces of cashews. What was the total weight of the nuts (in pounds and ounces)?
By answering the above question, we may state that This expression's equation evaluation results in: r = 8.5 ft
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A formal statement that proves the equality of two calculations is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two phrases that are inscribed on opposite sides of a letter. Frequently, the logo and indeed the particular software are identical. like in 2x - 4 = 2, for example.
The following is the formula for a circle's circumference:
C = 2πr
where is a mathematical constant that is roughly equivalent to 3.14159, C is the circumference, r is the radius, and.
The circle's circumference is stated to be 17 feet. In order to find r, we may put this equal to the circumference formula as follows:
17π = 2πr
When we divide both sides by 2, we obtain:
r = 17π / (2π)
Units cancel out, leaving:
r = 17 / 2
This expression's evaluation results in:
r = 8.5 ft
As a result, the circle's radius is 8.5 feet.
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A linear equation that is equivalent to the equation 0=-7 is a conditional equation.
No, a linear equation that is equivalent to the equation 0=-7 is not a conditional equation. Instead, it is an inconsistent equation.
A conditional equation is an equation that is only true for certain values of the variable. For example, the equation 2x+3=7 is a conditional equation because it is only true when x=2.
An inconsistent equation, on the other hand, is an equation that has no solution. The equation 0=-7 is an example of an inconsistent equation because there is no value of x that will make the equation true.
Therefore, a linear equation that is equivalent to the equation 0=-7 is an inconsistent equation, not a conditional equation.
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Can someone help plsss help me in math 50 pointssssd
Yes, an A is received on the test.
What is an inequality?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
As per the given data:
x = number of multiple choice questions.
x = 20
y = correctly answered questions.
y = 18
Inequality for receiving A:
3x + 2y ≥ 93
For receiving A, x and y must satisfy the inequality:
3x + 2y ≥ 93
3(20) + 2(18) ≥ 93
96 ≥ 93
Hence, Yes, an A is received on the test.
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Set up the trigonometric ratio for right triangles that yoa would ase to fisd
x
. Yeu are aar mied ap lad
x
. 1. a. b. Find
x
to the nearest tenth of a degree. Show your wark. Set up the trigonometric ratio for right triang gkes that you would use to find
x
. You are ase aulend to find
x
, 3. a. b. 4 Approximate
x
to the nearest lenth of a degroe. 5. Consider the following right triangle. Set up the trigonometric ratio for right triangles that you would use to find
x
. Then find
x
.
The key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.
To find the value of x in a right triangle, we can use the trigonometric ratios of sine, cosine, and tangent. The ratio we choose depends on the information given in the question and the sides and angles we are trying to find.
To find x to the nearest tenth of a degree, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given. For example, if we are given the opposite side and the hypotenuse, we would use the sine ratio.
c. Set up the equation and solve for x. For example, if we are using the sine ratio, the equation would be sin(x) = opposite/hypotenuse.
d. Use a calculator to find the value of x to the nearest tenth of a degree.
To find x using the aulend method, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Use the Pythagorean theorem, a^2 + b^2 = c^2, to find the missing side.
c. Use the appropriate trigonometric ratio to find the value of x.
To approximate x to the nearest tenth of a degree, we can use a calculator to find the value of x and then round to the nearest tenth.
To find x in the given right triangle, we can use the following steps:
a. Identify the sides of the triangle that are given and the side we are trying to find.
b. Choose the appropriate trigonometric ratio based on the sides given.
c. Set up the equation and solve for x.
d. Use a calculator to find the value of x.
Overall, the key to finding the value of x in a right triangle is to choose the appropriate trigonometric ratio based on the sides given and to use a calculator to find the value of x to the nearest tenth of a degree.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
[tex] \sf \: x = 5[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 11 + 2x = 3(x + 2)
Then the value of x will be,
→ 11 + 2x = 3(x + 2)
→ 11 + 2x = 3x + 6
→ 2x - 3x = 6 - 11
→ -x = -5
→ [ x = 5 ]
Hence, the value of x is 5.
[tex] \: [/tex]
To find:-[tex] \textrm{the value of x = ?}[/tex][tex] \: [/tex]
Solution:-[tex] \textrm{11 + 2x = 3( x + 2 )}[/tex][tex] \: [/tex]
[tex]\textrm{11 + 2x = 3x + 6}[/tex][tex] \: [/tex]
[tex]\textrm{2x - 3x = 6 - 11}[/tex][tex] \: [/tex]
[tex]\textrm{-1x = -5}[/tex][tex] \: [/tex]
[tex]\rm{x = \cancel\frac{ - 5}{ - 1} }[/tex][tex] \: [/tex]
[tex]\underline { \boxed{\textrm{\purple{x = 5}}}}[/tex][tex] \: [/tex]
The value of x is 5 !
━━━━━━━━━━━━━━━━━━━━━━━
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What does a dot plot show us that a box and whisker doesn't?
The dot plot allows us to know the exact data we are graphing.
What does a dot plot show us that a box and whisker doesn't?In a dot plot, we have the different possible values on the horizontal axis, and dots above each of these values that count how many times that value has appeared in an experiment.
Instead, in a whisker plot or a box plot we have a representation in a kinda of "rectangle with whiskers".
This type of plot is usefull to find the quartiles of the data set, but not to know exactly how many of each data points we have, like in the dot plot.
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Perform the addition or subtraction and simplify.
x
x2 + x − 2
−
9
x2 − 5x + 4
The final simplified expression turns out to be "-8x^2 + 6x - 6"
To perform the addition or subtraction and simplify the expression, we need to combine like terms and simplify the expression. First, we need to subtract the second expression from the first one:
x^2 + x − 2 - (9x^2 − 5x + 4)
Next, we need to distribute the negative sign to each term in the second expression:
x^2 + x − 2 - 9x^2 + 5x - 4
Now we can combine like terms:
-8x^2 + 6x - 6
This is the simplified expression. Therefore, the answer is:
-8x^2 + 6x - 6
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Determine if the expression -p^5√7 is a polynomial or not. If it is a polynomial, state
the type and degree of the polynomial.
The expression is not a polynomial, as it's exponent is not an integer number.
When does an expression represent a polynomial?An expression represents a polynomial when these following conditions are satisfied:
The expression consists of one or more terms.Each term contains a variable raised to a non-negative integer power, multiplied by a numerical coefficient.The exponents on the variable in each term are all whole numbers (i.e., integers).The coefficients can be any real number, including zero.The exponent for this problem is of [tex]5\sqrt{7}[/tex], which is a non-integer exponent, hence the expression is not a polynomial. Any integer exponent would make the expression in fact represent a polyonomial.
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A dealer sold a car to a man and made a profit of 15percent .The man then sold it to a woman for 120175 naira at a loss of 50percent . how much did the dealer buy the car
The dealer bought the car, which he sold to a man and made a profit of 15 percent at $209,000.
How is the dealer's purchase price determined?To compute the dealer's purchase price, we use backward calculations and percentages.
First, the man's purchase price is determined as $240,350 since he incurred a loss of 50% amounting to $120,175.
By equating the proportional loss to the selling price, we can determine the purchase price paid by the man as $240,350.
Since the dealer generated a profit of 15% on $240,350, we determine his cost as $209,000 based on the profit percentage.
The dealer's profit percentage = 15%
The man's loss percentage = 50%
The selling price by the man to the woman = $120,175
The purchase price by the man = $240,350 ($120,175/50%)
The dealer's purchase price = $209,000 ($240,350/1.15)
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Solvex + 4 - 5 = 6.
A. x = -7 and x
-15
B. x = 7 and x = -7
C. x = -7 and x = 15
D. x = 7 and x = -15
Option:-
[tex] \underline{\sf \color{brown}{ B ) x = 7 nd \: x = -7}}[/tex][tex] \: [/tex]
Given:-
[tex] \sf x + 4 - 5 = 6[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \: x + 4 - 5 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x + 4 = 6 + 5[/tex][tex] \: [/tex]
[tex] \sf \: x + 4 = 11[/tex][tex] \: [/tex]
[tex] \sf \: x = 11 - 4[/tex][tex] \: [/tex]
[tex] \boxed { \sf \blue{x = 7}}[/tex][tex] \: [/tex]
or
[tex] \sf \: x + 4 - 5 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x - 1 = 6[/tex][tex] \: [/tex]
[tex] \sf \: x = 6 + 1[/tex][tex] \: [/tex]
[tex] \boxed{ \sf { \color{skyblue}x = 7}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
For the given word problem, write a system of equations, clearly define any variables, and show work for full credit.
A photographer is mixing 5% acetic acid solution with a 10% acetic acid solution to get two liters of a 7% solution.
How many liters of each solution should he add?
Answer:
Let x be the amount (in liters) of the 5% acetic acid solution to be added.
Let y be the amount (in liters) of the 10% acetic acid solution to be added.
The system of equations is:
x + y = 2 (the total amount of solution is 2 liters)
0.05x + 0.10y = 0.07(2) (the amount of pure acetic acid in the final solution is 7% of 2 liters)
Simplifying the second equation:
0.05x + 0.10y = 0.14
5x + 10y = 14 (multiplying both sides by 100)
We now have a system of two equations with two variables. We can solve it by substitution or elimination. Here, we'll use substitution:
x + y = 2 => x = 2 - y (subtracting y from both sides)
Substituting x in the second equation:
5(2 - y) + 10y = 14 (replacing x by 2 - y)
10 - 5y + 10y = 14
5y = 4
y = 0.8
So the photographer should add 0.8 liters of the 10% acetic acid solution and 2 - 0.8 = 1.2 liters of the 5% acetic acid solution. We can check that this solution satisfies both equations:
0.05(1.2) + 0.10(0.8) = 0.06 + 0.08 = 0.14
1.2 + 0.8 = 2
Therefore, the answer is:
The photographer should add 0.8 liters of the 10% acetic acid solution and 1.2 liters of the 5% acetic acid solution.
Use the compound interest formula \( A=P e^{\lambda t} \) to solve. Round to two decimal places. Find the accumulated value of an investment of \( \$ 5,000 \) at \( 9 \% \) compounded continuously for
The accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
The accumulated value of an investment of $\$ 5,000$ at 9% compounded continuously for 4 years is $7,311.12.
This can be calculated using the compound interest formula
\(A=P e^{\lambda t}\).
In this equation, A is the accumulated value of the investment, P is the principal investment amount (which is $\$ 5,000$), $\lambda$ is the interest rate per compounding period (which is 0.09) and t is the number of compounding periods (which is 4 years).
Therefore, the accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.
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a printer makes more than three copies of labels every hour graph the number of books made in 2 hours.
