My answer would be the fourth one... 2/14
Solve for x, assuming a, b, and c are negative constants.
(ax + b)/c ≤ b
Solving for some variable means finding its value for which the given statement is true. Thus, the solution to given inequality is [tex]x \leq \dfrac{b(c-1)}{a}[/tex] (if a/c is non-negative)or [tex]x \geq \dfrac{b(c-1)}{a}[/tex] (if a/c is negative)
What type of operations are allowed in inequality?All such operations such that inequality doesn't gets modified( for example, if left expression is bigger than right one, then that expression cannot go bigger than the later expression).
For the given case, the inequality given is:
[tex](ax+b)/c \leq b[/tex]
Its solution can be found by doing operations which doesn't modify the inequality and takes all the terms such that one side is 'x' and other side are constants.
[tex](ax+b)/c \leq b\\\\\dfrac{a}{c}x + \dfrac{b}{c} \leq b\\\\\text{Subtracting b/c from both the sides}\\\\\dfrac{a}{c}x \leq b - \dfrac{b}{c}\\\\\text{Supposing that a/c is non-negative, multiplying both sides by c/a}\\\\x \leq \dfrac{c}{a} \times \dfrac{bc - b}{c} = \dfrac{b(c-1)}{a}\\\\x \leq \dfrac{b(c-1)}{a}[/tex]
(i assumed a/c non-negative, since multiplying with negative quantity can modify the sign of inequality, so ≤ would have become ≥ )
If a/c is negative, then:
[tex]x \geq \dfrac{c}{a} \times \dfrac{bc - b}{c} = \dfrac{b(c-1)}{a}\\\\x \geq \dfrac{b(c-1)}{a}[/tex]
Thus, the solution to given inequality is [tex]x \leq \dfrac{b(c-1)}{a}[/tex] (if a/c is non-negative)
or [tex]x \geq \dfrac{b(c-1)}{a}[/tex] (if a/c is negative)
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Final answer:
To solve for x, we can multiply both sides of the equation by c, subtract b from both sides, and then divide both sides by a to isolate x. The solution is x ≤ (bc - b)/a.
Explanation:
To solve for x in the equation (ax + b)/c ≤ b, we can first multiply both sides of the equation by c to eliminate the denominator:
ax + b ≤ bc
Next, we can subtract b from both sides:
ax ≤ bc - b
Finally, we divide both sides by a to isolate x:
x ≤ (bc - b)/a
Since a, b, and c are negative constants, the values of b and c are negative. Therefore, the numerator of the inequality will always be negative, resulting in a positive value for x. So the solution is:
x ≤ (bc - b)/a
Marjorie consumed 1.5 gallons of water in one day. How many milliliters are equal to 1.5 gallons, if 1 liter = 1,000 milliliters and 1 gallon = 3.785 liters? (3 points)
5.6775 milliliters
567.75 milliliters
5,677.5 milliliters
56,775 milliliters
The amount of water consumed each day is 1.5 gallons = 5667.5 millilitres. The correct option is C.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The amount of water in millilitres will be calculated as,
1 Gallons = 3.785 litres
1.5 Gallons = 3.785 x 1.5 litres
1.5 Gallons = 5.6775 litres
1.5 gallons = 5.6775 x 1000 mililitres
1.5 Gallons = 5677.5 mililitres
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What is 76912 divided by 92
Pilar used five reusable shopping bags recent purchase she made at a grocery store. Each bag decreased the amount she spent by 10 cents. What was the change to the amount Pilar spent at the grocery state by using the reusable bags?
Pilar saved a total of $0.50 by using five reusable shopping bags, with each bag providing a $0.10 discount on her purchase.
Pilar used five reusable shopping bags for a recent purchase she made at a grocery store, where each bag decreased the amount she spent by $0.10. To calculate the total amount saved by Pilar, we must multiply the number of bags by the savings per bag. So the calculation is as follows:
Number of reusable bags = 5
Savings per bag = $0.10
Total savings = Number of reusable bags imes Savings per bag = 5 imes $0.10 = $0.50
Therefore, by using the reusable bags, Pilar saved a total of $0.50 on her grocery purchase.
What are the opposites of the whole numbers from 35 to 45
The opposites of the whole numbers from 35 to 45 are; -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45.
How to label number opposites?
The opposite of a number is the opposite sign of that same number. Thus;
Opposite of a is -a.
Opposite of -b is b.
Now; Numbers from 35 to 45 are; 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45.
Thus, their opposites are; -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45.
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a cricket chirps 40 times a minute when the temperature is 50 degrees. write an equation representing the temperature in terms of number of chirps per minute
The relationship between temperature and the number of chirps per minute can be represented by the equation C = 0.8T, where C is the number of chirps per minute and T is the temperature.
Explanation:The relationship between the temperature and the number of chirps per minute can be represented by an equation.
Let's assume that the temperature is denoted by T and the number of chirps per minute is denoted by C. According to the given data, when the temperature is 50 degrees, the cricket chirps 40 times per minute. We can use this information to write the equation as:
C = kT
where k is a constant.
To solve for the value of k, we can substitute the temperature and the number of chirps per minute into the equation:
40 = k * 50
Dividing both sides by 50 gives us:
k = 40/50 = 0.8
Therefore, the equation representing the temperature in terms of the number of chirps per minute is:
C = 0.8T
PLEASE HELP ME ASAP! I HAVE A UNIT TEST! Jessica is filling glasses with water. Each glass holds 3/5 cup of water. She pours 4 1/5 cups of water into the glasses. How many glasses does she fill with water?
It was estimated that a giraffe would be 15.5 feet tall when fully grown. its actual height was 16.25 feet. what was the percent error between the actual and estimated values of height
which of these skills do you need more help with select all that apply
A. finding the square and square roots of numbers
B. idrntifying rational and irrational numbers
C. comparing values of rational and irrational numbers
D. evaluating perfect squares and cubes
E. using roots to represent solutions to equations
This grid shows the location of four animals.
Where is Chewy located?
A:(3, 6)
B:(5, 1)
C:(6, 3)
D:(1, 5)
write the product of 7×7×7×7 in exponential form
Product of 7×7×7×7 is 7⁴ in exponential form.
What is exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴
Given expression,
7×7×7×7
7 is multiplied to itself 4 times
= 7⁴
Hence, 7⁴ is the product of 7×7×7×7 in exponential form
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8.50 as a rational number?
An investment is currently worth 1.035×108 dollars . Thirty years ago, the investment was worth 2.3×105 dollars. How many times greater is the value of the investment today than the value of the investment thirty years ago? A. 0.45 B.450 C.4500 D. 45,000
The correct option is: B. 450
Explanation
Current value of the investment is [tex]1.035\times 10^8[/tex] dollars and 30 years ago, the value of the investment was [tex]2.3\times 10^5[/tex] dollars.
Suppose, the value of investment today is [tex]n[/tex] times greater than the value of the investment thirty years ago.
So, the equation will be........
[tex]n(2.3\times 10^5)=1.035\times 10^8\\ \\ n= \frac{1.035\times 10^8}{2.3\times 10^5}=0.45\times 10^3 = 450[/tex]
Thus, the value of the investment today is 450 times greater than the value of the investment thirty years ago.
Answer: B. 450
Step-by-step explanation:
Given: An investment is currently worth =[tex]1.035\times10^8[/tex] dollars .
Thirty years ago, the investment was worth =[tex] 2.3\times10^5[/tex] dollars.
Now, the number of times the value of the investment today than the value of the investment thirty years ago is given by :-
[tex]n=\frac{1.035\times10^8}{2.3\times10^5}\\\\=0.45\times10^{8-5}........\text{Since }a^na^m=a^{m+n}\\\\=0.45\times10^3\\\\=0.45\times1000=450[/tex]
Hence, the value of the investment today is 450 times greater than the value of the investment thirty years ago.
Drag and drop a phrase to make the statement true.
Triangles ABC and DEF are .
similar triangles or not similar triangles
Since m<B is equal to m<E, hence the angles are similar triangles
To determine if both triangles are similar, all the interior angles of the triangles must be equal to each other that is;
m<B = m<Em<C = m<FGet the measure of angle B
The measure of the interior angle of the triangle is 180 degrees
m<D + m<E + m<F = 90
90 + m<E + 55 = 180
m<E = 180 - 145
m<E = 35 degrees
Since m<B is equal to m<E, hence the angles are similar triangles
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Helpppp meeeeeee eeeeeee
Answer:
no
Step-by-step explanation:
The selling price of an item is $650 It is marked down by
10%, but this sale price is still marked up from the cost of $450
Find the markup from cost to sale price.
Answer:
10%×$650=$585
$585-$450=$135 Mark up.
Step-by-step explanation:
The markup from cost to sale price is $135.
What is the cost price?Cost price, for instance, equals selling price plus profit ( when selling price and profit is given ) Cost is equal to Selling price plus Loss ( when selling price and loss is given )
Cost price = 100 Selling Price + 100 + Profit (where the Selling Price and Profit Percentage are supplied)
Given the selling price of item = $650
The cost = $450
Therefore,
10% × $650 = $585
$585-$450=$135
Hence, the markup from cost to sale price is $135.
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What is the value of the expression? Drag and drop the answer into the box to match the expression. 0.9(1/2−2)+0.6
Joanna joins a CD club. She pays $7 per month plus $10 for each CD that she orders. Write an inequality to find how many CDs she can purchase in a month if she spends no more than $100. Identify what your variable represents.
140% or 0.14 which is greater?
Naomi drank 3/4 of a 20.8 ounce container of apple juice. How much ounces of apple juice did Naomi drink????
What is the simplified value of the expression below? 8.5+(12+4)x2-7
A. 10.5
B. 33.5
C. 88.5
D. 97.5
Answer:33.5
Step-by-step explanation:
What is the product in simplest form? −8/9⋅5/6
A.−1
B.−13/15
C.−20/27
D.−15
)Maya is showing her work in simplifying (5.2 − 4.5) − 5.5 + 4.8. Identify any error in her work or reasoning.
Step 1: (5.2 − 4.5) − 5.5 + 4.8
Step 2: 5.2 + (− 4.5 − 5.5) + 4.8 (identity property)
Step 3: 5.2 − 10 + 4.8
Step 4: 5.2 + 4.8 − 10 (commutative property)
Step 5: 10 − 10 = 0
Answers:
A. She wrote identity instead of commutative in Step 2.
B. She wrote commutative instead of distributive in Step 4.
C. She wrote identity instead of associative in Step 2.
D. She wrote commutative instead of associative in Step 4.
Hello,
The correct answer is C) She wrote identity instead of associative in Step 2.
Hope this helps!!!! :)
**(Vanessa)**
Find a report in a newspaper magazine or on the Internet that uses results from a servery. Evaluate how the survey uses ratios to reach
conclusion
What is the product in simplest form? −5/12 ⋅ 8/13 Please answer
simplify rational expression
In order to simplify, we want to change the 10 - x to an x - 10.
To do that, we can factor out a -1.
So we have -1(x - 10)/(x - 10).
Now our x - 10's cancel leaving us with -1.
last year there were 20 girls on the volleyball team this year the number of girls decreased by 10% how many girls are on the volleyball team this year
Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first orange, 3/10 cups from the second orange, 9/20 cups from the third orange, 3/11 cups from the fourth orange, and 7/15 cups from the fifth orange. Patel estimates that he needs 2 cups of orange juice for his family. About how much more orange juice does he need?
The amount of juice needed is about 0.487 cups
Amount of oranges squeezed :
First orange = 4/17 cups
Second orange = 3/10 cups
Third orange = 9/20 cups
Fourth orange = 3/11 cups
Fifth orange = 7/15 cups
Total amount of oranges needed = 2 cups
The amount of extra orange needed = x
Adding :
(4/17 + 3/10 + 9/20 + 3/11 + 7/15) + x = 2
(13200 + 168300 + 252450 + 153000 + 261800) / 561000
(848750 / 561000) + x = 2
1.5129 + x = 2
x = 2 - 1.5129
x = 0.4871 cups
The amount of juice needed is about 0.487 cups
Doug is twice Anne's age. Doug is 34 years old. How old is Anne
What is true about the product, a fraction less than 1 is multiplied by 9/10