Checking if the results of the following divisions are true or false.
a) -5/-1 = 5 ↔ True
The fraction, (remembering that it is a division), -5/-1 can be simplified to 5 by removing the negative sign from the numerator and denominator.
b) (0/-4) = 0 ↔ True
We know that any number divided by zero, the result will always be zero.
c) -3/1 = -3 ↔ True
Any number divided by one equals the same number.
d) -8/0 = 0 ↔ False
A normal number simply cannot be divided by 0.
The three previous divisions are true, that is, your answers are correct. While the last one can't, since it can't be divided by 0, this one is false.
-|4-7|+3 whats the answer to this question?
The answer to the question -|4-7|+3 is 0 .
The Absolute Value of x denoted by |x| is the non negative value of , without regarding its sign .
For example the absolute value of -3 will be |-3| = 3 .
and absolute value of |-2| = 2 .
In the question ,
it is given that
the question is -|4-7|+3 .
and we have to find the answer of -|4-7|+3 .
let the answer be "y"
So , y = -|4-7|+3
= -|-3| + 3
On further simplification ,
we get ,
= -(3) + 3 because |-3| = 3
= -3 +3
= 0
Therefore , The answer to -|4-7|+3 is 0 .
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Bette used 3 jumbo cans of frosting to frost 105
cupcakes for the cupcake challenge at her school
and 5 jumbo cans of frosting to frost an
additional 175 cupcakes. How many jumbo cans
of frosting would she need to frost 280
cupcakes?
The number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.
Given that, Bette used 3 jumbo cans of frosting to frost 105 cupcakes and 5 jumbo cans of frosting to frost an additional 175 cupcakes.
What are proportions?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Let number of jumbo cans of frosting would she need to frost 280 cupcakes be x.
Now the proportion is
3/105 = 5/175 = x/280
⇒ 5/175 = x/280
⇒ 175x = 280 × 5
⇒ x = 1400/175
⇒ x = 8
Therefore, the number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.
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Which equation could possibly represent the graphed function?
A polynomial function graph where the solid line intersects X-axis on (minus 4,0), (minus 2,0) and (4,0). The same line intersects Y-axis at (minus 30, 0) and (2, minus 48)
A. f(x) = (x − 4)(x + 2)(x + 4)
B. f(x) = (x − 4)2(x − 2)
C. f(x) = (x + 4)2(x + 2)
D. f(x) = (x − 4)(x − 2)(x + 4)
Answer:
answer is A
as the graph cuts the x axis at 4 which is shown by (x-4). and cut by -2 and -4 which is shown by (x+2) and (x+4).
What is the end behavior of the graph of the polynomial function f(x) = -x5 + 9x4 - 18x³?
O As x→-co, Y→→co and as x→co, y →-00
As x→-co, Y→→∞ and as x→co, y →∞
ය.
O As x→-co, Y→co and as x→co, y →→∞0
O As x→-co, y →co and as x→co, y → co
The option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is f(x) = -x⁵ + 9x⁴ - 18x³.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The polynomial function is:
f(x) = -x⁵ + 9x⁴ - 18x³
After plotting the graph of the polynomial function:
From the graph;
x → -∞, f(x) → ∞
x → ∞, f(x) → -∞
Thus, the option (A) x → -∞, f(x) → ∞ and x → ∞, f(x) → -∞ if the polynomial function is f(x) = -x⁵ + 9x⁴ - 18x³.
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A company that manufactures bicycles has a fixed cost of $90,000. It costs $200 to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable costs Write the total cost, C, as a
function of the number of bicycles produced, x Then, find and interpret C(100)
The total cost function is C(x)=
Answer:
Total cost: C(x) = 90,000 + 200x in dollars
C(100) = $110,000
This means that the total cost for the company when it produces 100 bikes would be $110,000
Step-by-step explanation:
First, you have a fixed cost, so you would start by setting C(x) to that:
C(x) = 90,000
Then, you have a cost of $200 PER bike that is made. The amount of bikes is represented by x. So you will have to multiply cost per bike by how many bikes are manufactured:
200x
Add this variable cost to the function underlined above.
C(x) = 90,000 + 200x
This is your function C(x).
Now for C(100), PLUG IN 100 for x:
C(100) = 90,000 + 200(100)
Multiply out:
C(100) = 90,000 + 20000
Then add these together to get the value:
C(100) = 110,000
This is the amount of money it would cost to make 110000 bikes, as interpreted above.
Kamryn’s doctor recommended that she drink 64 fluid ounces of water every day. There are about 30 milliliters in 1 fluid ounce. Which measurement represents the number of milliliters in 64 fluid ounces?
HELP PLEASE DUE IN 10 MINS
64 fluid ounces contain 1920 milliliters.
64 oz of liquid is what?Oz to Half Gallon Conversions
A half gallon is equal to 64 ounces in a gallon measurement.
OZ or ML: Which is bigger?
A milliliter is equal to how many ounces. The conversion factor from fluid ounces to milliliter is 1 fluid ounce = 30 milliliter.
64 ounces is equal to how many glasses of water?This equates to eight 8-ounce glasses or 2,000 ml (approximately 64 ounces) for a person who consumes 2,000 calories per day.
Given: She regularly drinks 64 fluid ounces of water.
1 fluid = 30 milliliters
=> 30 × 64 = 1920 milliliters
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place the numbers in order from least to greatest…PLS HELP!
Answer:
If the numbers are arranged from the least to the greatest, then it is called ascending order. In this form, the numbers are in increasing order. The first number should be lesser than the second number. If the numbers are arranged from the greatest to the least, then it is called descending order.
Absolute Value Calculator: Heron's Calculator
Coterminal Angle Calculator: Graphing Functi...
Step-by-step explanation:
The sum of an integer and 2 times the next consecutive integer is -22. Find the value of the lesser integer
Answer: gurl you think i know
Step-by-step explanation:
ben is making a dessert that requires 212 lb of strawberries and 112 lb of blueberries. strawberries cost $1 less per pound than blueberries. ben spent a total of $9.50 on the fruit. what is the price per pound of each type of fruit?
Answer:
Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.
Explanation :
Given data ;
Weight of strawberries required for dessert = 212 lb
Weight of blueberries required for dessert = 112 lb
Total cost spent = $9.50
Let,
Cost of blueberries per pound =x
Cost of strawberries per pound = (x-1)
We know that,
Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.
x(112) + (x-1)212 = 9.50
112x + 212x – 212 = 9.50
324x = 221.5
X = 221.5/324
X = $0.6836
So, (x-1) = $-0.31635
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Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
Given that ;
Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.
So according to the question get the price per pound of each type of fruit;
Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.
By assuming the following equations;
212x - 112y = 1 → ( I )
212x + 112y = 9.5 → ( II )
By solving above equations ( I ) ( II ) we get;
424x = 10.5
x = 10.5/424
x = 0.02476
224y = 8.5
y = 8.5/224
y = 0.03794
Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794
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Milly and Lotte are knitting scarves. For every 6 cm that Milly knits, Lotte knits 11 cm. If Milly knits a scarf that is 1.2 m long, how long will Lotte's scarf be in metres?
If Milly knits a scarf that is 1.2 m long then Lotte's scarf be 2.20 in metres.
We will use unitary method to solve this problem.
We know, Milly and Lotte are knitting scarves.
For every 6 cm that Milly knits, Lotte knits 11 cm. This can also be written as,
6 cm Milly knits ----------------> 11 cm Lotte knits
1 cm Milly knits ----------------> (11/6 ) cm Lotte knits
We know, 1m = 100cm. So, we can write
120 cm Milly knits ----------------> ( 11/6 ) × 120 cm Lotte knits
120 cm Milly knits ----------------> 220 cm Lotte knits
120 cm Milly knits ----------------> 2.20 m Lotte knits
Thus, we can conclude that if Milly knits a scarf that is 1.2 m long then Lotte knits 2.20 metres scarf .
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4(a-c)+2(a-b)
x(x-y)+y(y-x)
Answer:
hi how are you . i cant find the answer youre looking for
Answer:
1) 6 ( a - b )
2) x² - 2xy + y²
Step-by-step explanation:
1) 4 ( a - c ) + 2 ( a - b )
First, solve the brackets.
4a - 4c + 2a - 2b
Combine like terms.
6a - 6b
Take the common factor out.
6 ( a - b )
2) x ( x - y ) + y ( y - x )
First, solve the brackets
x² - xy + y² - xy
Combine like terms.
x² - 2xy + y²
this is a pre for something later on in the future please help me i will give brainliest and dont make it sound to smart or use big words becausee i dont type like that
Using the Pythagorean Theorem, it is found that:
The length of the bar is of c = 8.73 ft.The amount of netting needed is of 132.76 ft².Pythagorean TheoremThe Pythagorean Theorem is a geometry axion relates the length of the sides [tex]l_1[/tex] and [tex]l_2[/tex], which are the separated by the angle of 90º, of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
For the netting, it is found that:
The legs are of 8 ft and 3.5 ft.The hypotenuse is of c.Hence the measure c, representing the length of the bar, is calculated as follows:
c² = 8² + 3.5²
c = sqrt(8² + 3.5²)
c = 8.73 ft.
The amount of netting needed is the area of the entire goal, composed by:
A rectangle of dimensions 12 ft and 8.73 ft.Two right triangles of dimensions 8 ft and 3.5 ft.Hence:
A = 12 x 8.73 + 2 x 1/2 x 8 x 3.5 = 132.76 ft².
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what is the first quartile of this data set?
11,12,15,16,17,19,22,24,29,33,38
The first quartile of the given data set would be 15 which is The middle of the numbers from the beginning up.
What is the first quartile of the data set?When data points are organized in ascending order, the first quartile, or lower quartile, (Q1), is the value at which 25% of them are located.
The given data set is:
11,12,15,16,17,19,22,24,29,33,38
Since the number of elements in the data set is 11. As a result, the data are divided into two equal parts by the sixth term. The median of the data is 19.
The middle of the numbers from the beginning up to and including the first middle value: 11,12,15,16,17.
The middle value is 15.
Therefore, the first quartile of this data set would be 15.
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graph the equation, y=x/3-4
Step-by-step explanation:
With the equation
y
=
|
−
x
+
3
|
−
4
, we know that the term inside the absolute value mark will never be less than zero, which means the smallest
y
can be is
y
=
−
4
. This value is achieved with
|
−
x
+
3
|
=
0
, putting
x
=
3
. So that is our first point,
(
3
,
−
4
)
.
We're dealing with
x
terms (versus
x
2
or
√
x
or any other form of
x
), so the graph coming off
(
3
,
−
4
)
will be lines. Since there the coefficient of the
x
term is 1, the slope of those lines will be 1 and
−
1
(with the x term inside the absolute value, we look at both
±
1
).
The standard graph for an absolute value graph is for it to be in the shape of a V. And so we can expect our graph to have points
(
4
,
−
3
)
and
(
2
,
−
3
)
- and we can plug in those values to prove it:
y
=
|
−
x
+
3
|
−
4
−
3
=
|
−
4
+
3
|
−
4
−
3
=
|
−
1
|
−
4
−
3
=
1
−
4
−
3
=
−
3
and
−
3
=
|
−
2
+
3
|
−
4
−
3
=
|
1
|
−
4
−
3
=
1
−
4
−
3
=
−
3
The graph itself will look like this:
graph{abs(-x+3)-4 [-10, 10, -5, 5]}
34=−2x34 I don’t understand
this problem
HELP PLEASEEEE
Suppose that y varies directly with x and that y=84
when x=7
. What is the value of x when y=108
?
Suppose that y varies directly with x and that y=84 when x=7. What is the value of x when y=108?
when y=84 and when x=7, x to y in proportion is 1:12. Keeping the ratio of x to y at 1 to 12, when y = 108, x = 9.
jeremy sells strawberries 5 pounds for $7.50. what is the cost for 1 pound of strawberries?
Question 3 (10 points)
Answer:
11
Explanation:
if you want to find the answer to a question like this just put the square root symbol on to your calculator before you type the number it wants you to get an answer for and the correct answer will appear
hope this helps:)
Answer:
11
Step-by-step explanation:
[tex]\sqrt{121} = \sqrt{11^{2} } = 11[/tex]
Find the y-intercept and the slope of the line. 3x+4y=-7
Answer: m(slope) = -3/4, b(y-int) = -7/4
Answer:
The slope is -3/4 and the y intercept is 74.
Step-by-step explanation:
I just know I had this question.
Combine like terms, if possible. Write the result with descending powers. -7x^4 + 4x^4 - 6x^4
Select the correct choice below and fill in the answer box to complete your choice.
A. The polynomial can be simplified. -7x^4 + 4x^4 - 6x^4 =
B. The polynomial cannot be simplified. The polynomial written in descending powers is =
The polynomial can be reduced to -9x^4
Addition of Polynomial
To solve this, we can simply add the similar polynomials or polynomials with the same power. This will help us simplify the polynomial to the lowest possible value.
[tex]-7x^4 + 4x^4 -6x^4 = -9x^4[/tex]
The polynomial given is simplified to become -9x^4
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a particular fruit's weights are normally distributed, with a mean of 717 grams and a standard deviation of 18 grams. if you pick 12 fruits at random, then 16% of the time, their mean weight will be greater than how many grams? give your answer to the nearest gram.
If the mean is 7171 grams, the standard deviation is 18 grams and 12 fruits are selected at random. Then, the mean weight will be 734.901 grams greater.
Let X be the random variable of the fruit's weight.
We have, the mean and standard deviation as 717 grams and 18 grams respectively.
We want to find the specific gram value for which 16% of the fruits are heavier, i.e. the 84th percentile of X's normal distribution
Now, Solving for x:
P( X < x ) = Normal( 717, 18 ), Z = 0.84
So,
P( [X - 717] / 18 < [x - 717] / 18 ) = P( Z < [x - 717]/18 ) = 0.84, where Z is a standard normal random variable
Now,
Standard Normal CDF( [x - 717]/18 ) = 0.84
Then, from the standard normal table: [x - 717]/18 = Inverse Standard Normal CDF( 0.84 ) = 0.9945
Therefore,
[ x - 717 ] / 18 = 0.9945
Multiplying 18 on each side of the equation,
x - 717 = 0.9945 × 18
x - 717 = 17.901
Adding 717 on each side of the equation,
x - 717 + 717 = 17.901 + 717
x = 734.901
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the null and alternative hypotheses are given. determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. what parameter is being tested? 105
The hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
What is a null and alternative hypotheses?
A null hypothesis predicts no effect between variables while an alternative hypothesis predict an effect or relationship between variables of the study.
What is the given hypothesis test?
In the question, the given hypothesis test includes "H0: σ=110" and "H1: σ<110"
Hence, based on the test above, the hypothesis test is a Left-tailed test and the parameter being tested is known as a Population mean.
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A building company employs 3 labourers 12 joiners 8 electrician 4 plumbers. For a job, the company needs one of each type of worker in how may ways can the company choose four workers
The number of ways that the company can choose four workers is 40920 ways.
How to calculate the number?From the information, the building company employs 3 laborers 12 joiners 8 electrician 4 plumbers. The total number of workers will be:
= 3 + 12 + 8 + 4
= 27 workers
It should be noted that combination will be used to choose the 4 workers. This is illustrated as
Combination formula
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
where n = 33
r = 4
ⁿCr = n! / ((n – r)! r!)
³³C₄ = 33! / (33 - 4)! 4!
= 33! / 29! 4!
= 33 × 32 × 31 × 30 / 4 × 3 × 2
= 40920 ways
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The value of [tex]\tan 1^{\circ}\tan 2^{\circ}+\tan 2^{\circ}\tan 3^{\circ}+\tan 3^{\circ}\tan 4^{\circ}+\cdots+\tan 88^{\circ}\tan 89^{\circ}[/tex] can be expressed in the form [tex]\cot^2 1^{\circ}-n[/tex]. What is the value of [tex]n[/tex]?
Answer:
n = 89Step-by-step explanation:
Use of identitiestan (x - y) = (tan x - tan y)/(tan x tan y + 1) 1/tan x = cot xtan (90 - x) = cot xtan (- x) = - tan xConvert the first one above:
tan x tan y = (tan x - tan y) / tan (x - y) - 1Apply this to each term of the given expression to get:
tan1°tan2° + tan2°tan3° + ... + tan88°tan89° = (tan1° - tan2°)/(tan-1°) - 1 + (tan2° - tan3°)/(tan-1°) - 1 + ... + (tan88° - tan89°)/(tan-1°) - 1 = (tan1° - tan2° + tan2° - tan3° + ... + tan88° - tan89°)/(tan-1°) - 88 = (tan1° - tan89°)/(tan-1°) - 88 = tan1°/ (tan-1°) - tan89°/tan-1° - 88 = - 1 - cot1*(- cot1°) - 88 = cot² 1° - 89The value of n is 89.
Answer:
n = 89
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan double angle identity}\\\\$\tan (A - B)=\dfrac{\tan A - \tan B}{1 + \tan A \tan B}$\\\end{minipage}}[/tex]
Rewrite the tan double angle identity to isolate tanAtanB:
[tex]\implies 1 +\tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}[/tex]
[tex]\implies \tan A \tan B=\dfrac{\tan A- \tan B}{\tan (A - B)}-1[/tex]
Therefore:
[tex]\implies \tan 1^{\circ} \tan 2^{\circ}+\tan2^{\circ}\tan3^{\circ}+...+\tan88^{\circ}\tan89^{\circ}[/tex]
[tex]\implies \left(\dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (1 - 2)^{\circ}}-1\right)+\left(\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (2 - 3)^{\circ}}-1\right)+...+\left(\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (88 - 89)^{\circ}}-1\right)[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}-1+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}-1+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-1[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}}{\tan (-1)^{\circ}}+\dfrac{\tan 2^{\circ}- \tan 3^{\circ}}{\tan (-1)^{\circ}}+...+\dfrac{\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 2^{\circ}+\tan 2^{\circ}- \tan 3^{\circ}+...+\tan 88^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}- \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{\tan (-1)^{\circ}}-\dfrac{ \tan 89^{\circ}}{\tan (-1)^{\circ}}-88[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{ \tan(-x)=-\tan(x)}:[/tex]
[tex]\implies \dfrac{\tan 1^{\circ}}{-\tan 1^{\circ}}+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies -1+\dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-88[/tex]
[tex]\implies \dfrac{ \tan (90-1)^{\circ}}{\tan 1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\tan(90-x)=\cot(x)}:[/tex]
[tex]\implies \dfrac{\cot1^{\circ}}{\tan1^{\circ}}-89[/tex]
[tex]\implies \cot 1^{\circ} \cdot \dfrac{1}{\tan1^{\circ}}-89[/tex]
[tex]\textsf{Apply the identity}\quad \boxed{\dfrac{1}{\tan(x)}=\cot(x)}:[/tex]
[tex]\implies \cot 1^{\circ} \cdot \cot 1^{\circ}-89[/tex]
[tex]\implies \cot^21^{\circ}-89[/tex]
Therefore, n = 89.
What is an equation of the line that passes through the points (-2, 5) and (−2,−8)?
The equation of the line that passes through (-2, 5) and (−2,−8) is: x = -2.
What of the Equation of a Line?The equation of a line that passes two given points on the line, can be expressed in slope-intercept form as y = mx + b. In this form, the variable "m" represents the slope of the line, while the "b" represents the y-intercept.
Find the slope using the two points (-2, 5) and (−2,−8):
Slope (m) = change in y / change in x = (-8 - 5)/(-2 -(-2))
Slope (m) = -13/0 [cannot divide]
The slope of the line is undefined. This means the line is a vertical line that intercepts the x-axis at -2.
The equation of the vertical line would therefore be: x = -2.
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-4/0 divided by 5 11/14
Answer: undefined
Step-by-step explanation:
tony buys 6 packages of cookies. each package of cookies cost $2.50. how much will he spend
Answer:
Tony will spend 15$.
Step-by-step explanation:
2.50 * 6= 15($)
Which ordered pairs represent points on the graph of this equation? Select all that apply. x= – 1 /2 y
The ordered pairs that represent points on the graph of the equation 3x + 2y = -12. is; point (-4,0)
What is the ordered pair on the graph?An equation of the line is defined as the linear equation that has a degree of one. The equation of the line contains two variables x and y. Thus, the third parameter will be the slope of the line which represents the elevation of the line.
The general form of the equation of the line is y = mx + c
where;
m is the slope
c is the y-intercept
We will find the ordered pair that satisfies the equation with each pair of points as;
3(-6) + 2(7) = -4
3(-4) + 2(0) = -12 YES
3(0) + 2(7) = 14
3(3) + 3(-3) = 0
3(6) + 2(0) = 18
The only ordered pair that satisfies the given linear equation is (-4, 0)
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Complete question is;
Which ordered pairs represent points on the graph of this equation? Select all that apply.
3x + 2y = -12
(-6, 7)
(7, 6)
(-4,0)
(0,7)
(3,-3)
(6,0)
The formula C=3.14d can be used to approximate the circumference of a circle given its diameter. Company A manufactures and sells a certain washer with an outside circumference of 4 centimeters. The company has decided that a washer whose actual circumference is in the interval 3.9≤C≤4.1 centimeters is acceptable. Use a compound inequality and find the corresponding interval for diameters of these washers.
1.242 ≤ d ≤ 1.305 is the corresponding interval for the diameter of the washer.
Given that,
Company A makes and sells a washer having a 4-centimeter outer radius. The corporation has decided on a washer with an actual radius in the range of 3.9 ≤ C ≤ 4.1.
Inequality is defined as the connection of an equation having the symbol ( ≤, ≥, <, >) in place of the assignment operator.
Here,
C = 3.14d
Given inequality,
3.9 ≤ C ≤ 4.1
3.9 ≤ 3.14d ≤ 4.1
dividing both sides of the inequality by 3.14,
1.242 ≤ d ≤ 1.305
As a result, the needed matching spacing for the washer's diameter is 1.242 ≤ d ≤ 1.305.
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Given the function f(x)=x^2+7x+6f(x)=x
2 +7x+6, determine the average rate of change of the function over the interval −4≤x≤−1.
The average rate of change of the function f( x ) = x² + 7x + 6 at the interval of −4 ≤ x ≤ −1 is 2
What is the average rate of change the function?The average rate of change the function is simply the change in y-values of the two points divided by the change in x-values of the two points.
It is expressed as;
Given the data in the question;
f( x ) = x² + 7x + 6Interval: −4 ≤ x ≤ −1 ⇒ [-4.-1]Average rate of change = ( f(-1) - f(-4) ) / ( (-1) - (-4) )
Average rate of change = ( (-1)² + 7(-1) + 6 ) - ( (-4)² + 7(-4) + 6 ) ) / ( (-1) - (-4) )
Average rate of change = ( (1 + -7 + 6 ) - ( 16 - 28 + 6 ) ) / (-1 + 4 )
Average rate of change = ( ( 0 ) - ( -6 ) ) / (-1 + 4 )
Average rate of change = ( 0 + 6 ) / ( 3 )
Average rate of change = 6 / 3
Average rate of change = 2
Therefore, the average rate of change of the function is 2.
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