Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
What is EQUATIONS?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The meanings of the word equation and its cognates in various languages can vary slightly.
For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfill the equality are known as the equation's solutions.
Equations come in two varieties: identities and conditional equations.
Hence, Jon still needs to travel miles to Sacramento, according to a linear equation: Y=-55x +600 .
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What is the solution to this system of linear equations?
2x + y = 1
3x - y = -6
Answer:
x = -1
y = 3
Step-by-step explanation:
2x + y = 1
3x - y = -6
Let's find x first by adding both equations
5x = -5
x = -1
Now put -1 in the spot of the variable x
2(-1) + y = 1
-2 + y = 1
y = 3
a line with a slope of 2 passes through the points (10,8) and (w,6). what is the value of w?
Answer:
w = 9
Step-by-step explanation:
Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.
(8-6)/(10-w) = 2
2/(10-w) = 2
Cross-multiply.
2 = 2(10-w)
Distributive property
2 = 20 - 2w
Add 2w
2 + 2w = 20
Subtract 2
2w = 18
divide by 2
w = 18/2 = 9
Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1
select the correct answer from each drop down menu
choices: the rate of function eight is (greater than), (less than), (equal to) the rate of change a function b
(neither function is ), (only function b is) , (only function a is) , (both functions are) increasing.
The y intercept of function a is (less than) , (greater than), (equal to) the y-intercept of function B
whatever is in the parentheses are the choices. please help
The rate of change of function A is greater than the rate of change of function B.
The y-intercept of function A is less than the y-intercept of function B.
How to calculate the rate of change of the function?The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.
For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;
Rate of change = (y₂ - y₁)/(x₂ - x₁)
Rate of change = (-3 - 3)/(-1 - 2)
Rate of change = -6/-3
Rate of change = 2
For function B, we are given that the equation of the line is;
y = ¹/₂x + 2
Now, formula for equation of a line in slope intercept form is;
y = mx + c
where ;
m is slope and c is y-intercept
Thus, slope is 1/2 and y-intercept is 2
For function A, we can find the y-intercept as;
3 = 2(2) + c
c = 3 - 4
c = -1
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For a recipe, harris uses 2 cups of sugar for each cup of flour. how many cups of flour does harris need when he uses 1 cup of sugar?
Answer:
1/2 a cup of flour
Step-by-step explanation:
Sugar to flour ratio:
2 to 1
That means for every 2 sugar Harris needs 1 cup flour
There are twice as many cups of sugar of cups of flour
Since 1/2 times 2 is 1 that means the ratio is ture
2 to 1 = 0.5 to 1
Hope this helps :) im kinda bad at explaining
In a company, 80% of the workers are men. If 780 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
There are [enter your response here] workers in all.
Answer:
3900
Step-by-step explanation:
20%=1/5
780 is 20%
780x5 equals total since 20% 80% is 3120
Which graph represents function f?
f(x) = 2|x − 1|– 3
Answer:
graph D
Step-by-step explanation:
if x = 0
y = 2 |-1| - 3
y = 2 (1) - 3
y = 2 - 3
y = -1
A (0, -1)
if x = 1
y = 2 |1-1| - 3
y = 2 (0) - 3
y = -3
B (1,-3)
a company wants to encrypt a document containing important passwords. to do this, the sum of two positive numbers will need to be minimized. if the product of both numbers is 47, what is the minimum sum?
The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.
To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).
The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:
AM ≥ GM
For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).
Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).
Using the AM-GM inequality:
(a + b) / 2 ≥ √(ab)
Substitute ab = 47:
(a + b) / 2 ≥ √47
Now, let's solve for the minimum sum (a + b):
a + b ≥ 2(√47)
a + b ≥ 2 * √(47)
a + b ≥ 13.711.
Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.
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Joseph is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. Let CC represent the total cost of the gym membership over t months. A graph of CC is shown below. Write an equation for CC then state the slope of the graph and determine its interpretation in the context of the problem.
Answer:
The equation for the total cost of the gym membership over t months is CC = Jo + M * t, where Jo represents the one-time fee to join, M represents the monthly fee to remain a member, and t represents the number of months for which the membership is valid.
The slope of the graph is M, the monthly fee to remain a member. The interpretation of the slope in the context of the problem is that it represents the cost per month of remaining a member of the gym.
Select the correct answer from each drop-down menu. which formulas return true, if the value in cell b4 is 12 and the value in c4 is 29? and return true, if the value in cell b4 is 12 and the value in c4 is 29.
the correct answer from each drop-down menu. which formulas return true,.if the value in cell b4 is 12 and the value in c4 is 29.: A. =B4=12 AND C4=29
The correct answer is A. =B4=12 AND C4=29, as this is the only formula that returns true if the value in cell b4 is 12 and the value in c4 is 29.
Both B. =(B4=12) AND (C4=29) and D. =(B4+C4)=41 are correct, but they do not fit the given criteria.
C. =B4+C4=41 does not return true for the given values, as 12 + 29 does not equal 41.
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A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.
What is the slope of line t?
–0.75
What is the y-intercept of line t?
2
What is the equation in slope-intercept form of line t?
y = –0.75x + 2
The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The line t that passes through the points (0, 2) and (8, -4) is given as,
(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)
y - 2 = - 0.75x + 0
y = -0.75x + 2
The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.
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please help me with this
Answer: The first one is equivlent because you move the variable to the left collect like terms and then divide both terms.
Step-by-step explanation:
pool workers conducted a chi-square goodness-of-fit test at the 5% significance level. the chi-square value is 1.3892 and the p-value is 0.7081. what can the pool workers conclude?
The pool workers can conclude that there is not a statistically significant difference between the expected and observed results.
The chi-square value is 1.3892 and the p-value is 0.7081 The p-value of 0.7081 is greater than the 5% significance level, meaning that the null hypothesis can not be rejected.
This means that the difference between the expected and observed results is not statistically significant, and the observed results are likely due to random chance. This means that there is not a significant difference in the observed results from the expected results, and the null hypothesis is accepted.
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a cylindrical water tank with its circular base parallel to the ground is being filled at the rate of 4 cubic feet per minute. the radius of the tank is 2 feet. how fast is the level of the water in the tank rising when the tank is half full? give your answer in feet per minute.
In the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.
What is a cylinder?One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.
It is regarded as a prism with a circle as its base in basic geometry.
In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.
So, we know that:
The rate at which water is being filled is 4 ft³.
The radius of the cylinder is 2 ft.
Now, the time in which the level of water in the tank rises when the tank is half full:
Area of cylinder: πr²
πr² = 12.566 ft³
Next, multiply 4 by 12.566 to get how quickly the water is rising:
12.566 ft³/4 ft³/min = 3.14 m
According to this, a foot of water rises every roughly 3.14 minutes, or 1/3.14 - 0.318 ft/min, or 3.82 in/min.
Therefore, in the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.
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identify the value of f(x) and x from the given coordinates
Answer:
1
Step-by-step explanation:
For function f(x), the average rate of change from x = a to x = b is:
average rate of change = (f(b) - f(a))/(b - a)
Here we have:
f(a) = f(-3) = -2.88
f(b) = f(2.5) = 2.62
average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1
Establish the identity.
1+ tan^2 (-0) = sec^2 0
Which of the following four statements establishes the identity?
pls help asap i can’t pass this class without passing this test :(
The correct statement that establishes the identity is the third one: "The reciprocal of the cosine of an angle is equal to the secant of the angle."
Here's how you can prove this using the other three statements:
"The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle."
"The reciprocal of the sine of an angle is equal to the cosecant of the angle."
"The reciprocal of the cosine of an angle is equal to the secant of the angle."
"The reciprocal of the tangent of an angle is equal to the cotangent of the angle."
To prove the identity, we can start by substituting the first statement into the equation on the left side of the identity:
$1 + \tan^2 (-0) = 1 + \left( \frac{\sin (-0)}{\cos (-0)} \right)^2 = 1 + \frac{\sin^2 (-0)}{\cos^2 (-0)}$
Next, we can use the fourth statement to write the right side of the identity in terms of the cotangent:
$1 + \frac{\sin^2 (-0)}{\cos^2 (-0)} = 1 + \frac{1}{\cot^2 (-0)} = \frac{1}{\cot^2 (-0)}$
Now we can use the second statement to write the right side of the identity in terms of the cosecant:
$\frac{1}{\cot^2 (-0)} = \frac{1}{\frac{1}{\sin^2 (-0)}} = \csc^2 (-0)$
Finally, we can use the third statement to write the right side of the identity in terms of the secant:
$\csc^2 (-0) = \frac{1}{\sec^2 (-0)} = \sec^2 (-0)$
Therefore, the third statement establishes the identity.
8.
Are the two ratlos below proportional? *
5
15
6' 18
Mark only one oval.
a. No, because the unit rates are not equal.
b. Yes, because the unit rates are the same.
c. No, because the rates are the same.
d. Yes, because the unit rates are not equal.
2 points
Made possible via methods. In light of this, 5, 6, 15, and 18 are in proportion. The same unit rates prove that.
Rates and proportions are they equivalent?A ratio, on the other hand, is the comparison of the sizes of two values, whereas a proportion is a part, share, or quantity in relation to an overall total. Each of the three measures has unique characteristics, and a rate is just one number divided by another.
The same units apply to proportions, or not?Due to the consistency of the units and their equivalent, each ratio compares the same units—inches and feet—and is therefore similar. Compare two ratios using the same units when using proportions.
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How do I solve for x in #34 and #35?
Answer:
34. x = 3 1/3
35. x = 5.2
Step-by-step explanation:
Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.
In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.
34.Using the angle bisector relation, you have ...
QP/PT = QS/ST
x/3 = 5/ST ⇒ x = 15/ST
Using the parallel segment relation, you have ...
PT/QR = ST/SR
3/2 = ST/3 ⇒ ST = 9/2
Using the value of ST in the equation for x gives ...
x = 15/(9/2) = 30/9 = 10/3
x = 3 1/3
35.Using the angle bisector relation, you have ...
EF/ED = CF/CD
7.2/9 = CF/6 ⇒ CF = 6(7.2/9) = 4.8
Using the parallel segment relation, you have ...
CB/BA = CF/FE
x/7.8 = 4.8/7.2
x = 7.8(4.8/7.2)
x = 5.2
__
Additional comment
In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.
please solve theta
csc^2 theta=cot theta+3
The value of θ will -45° or 26.56°
What are trigonometric identities?Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.
Given that, cosec²θ = cotθ + 3
Solving for θ,
∵ cosec²θ = cot²θ+1
∴ cot²θ+1 = cotθ + 3
cot²θ-cotθ-2 = 0
Factorizing and solving, we get
(cotθ+1)(cotθ-2) = 0
cotθ+1 = 0
cotθ = -1
θ = -45°
or, cotθ-2 = 0
cotθ = 2
θ = 26.56°
Hence, The value of θ will -45° or 26.56°
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What is 1x1 because I do not know what is it
Answer:
The answer is 1
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
find the number a such that the limit exists. lim x→−2 4x2 + ax + a + 12 x2 + x − 2
The limit exists and equals -4 when a = 28.
How to illustrate the limit?From the information, we want to find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2.
It should be noted that this will be illustrated as:
(4x² + ax + a + 12) / (x² + x − 2)
We will substitute x = -2 into the value of x in the Illustration. This will be:
(16 - 2a + a + 12) / (4 - 2 - 2)
16 - 2a + a + 12 = 0
-a = -28
a = 28
Using lhopital rule, we'll find the derivative. This will be:
8x + a / 2x + 2
Substitute x = -2
(-16 + 28) / (-4 + 1)
= 12 / -3
= -4
Therefore the limit exists and equals -4 when a = 28.
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Complete question
find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2
[tex]\sqrt{x} \sqrt{x} 100\\[/tex]
Answer:
100 isn't under the root, so the roots over the x cancel and you have 100x as the answer
Step-by-step explanation:
100 isn't under the root, so the roots over the x cancel and you have 100x as the answer
Please help! Its algebra!
Step-by-step explanation:
don't panic. just read carefully and write equations for every relation described in the text.
perimeter = 34 cm = side 1 + side 2 + side 3
side 1 = 2×side 3
side 3 = (side 1) / 2
side 2 = (side 1) + 4
now we use the last 2 equations in the first :
34 = side 1 + ((side 1) + 4) + (side 1)/2
68 = 2×(side 1) + 2×((side 1) + 4) + side 1
68 = 2×(side 1) + 2×(side 1) + 8 + side 1
68 = 5×(side 1) + 8
60 = 5×(side 1)
side 1 = 60/5 = 12 cm
side 2 = (side 1) + 4 = 12 + 4 = 16 cm
side 3 = (side 1)/2 = 12/2 = 6 cm
you see ? it is all just straight forward. no mystery.
the only trick is to find forms of the various equations to have only one variable in the main equation. like we did here with side 1 and side 3.
(93 points) Eloise bought 2 boxes of crackers to share with her friends. Her friends ate 12 of the first box and 34 of the second box.
A. 1/2 box
B. 2/3 box
C. 3/4 box
D. 1 1/3
Answer:
The answer is C, 3/4 of a box
Write an equation that represents the line.
Use exact numbers.
answer : y = 4/5x - 22/5
y = mx + b
get m or slope (aka "rate" or "speed")
(fun fact : see how the graph is a straight line? a lot of calculus is trying to get the rate or speed or slope of a curved graph)
(-3,-6) (2,-2)
(y2 - y1)/(x2-x1)
-2 + 6/2 + 3
m = 4/5
(if you make the 2 points a triangle bottom is 5 and the right side is 4)
line formula
y - y1 = m (x - x1)
y + 6 = 4/5 ( x + 2 )
y = 4/5x + 8/5 - 6
y = 4/5x + 8/5 - 30/5
y = 4/5x - 22/5
side note : since the graph doesnt go thru (0,0) the graph is NOT PROPORTIONAL
A bag holds 23 cups of sugar. A recipe for chocolate chips cookies uses 1 cups of sugar. How many batches of chocolate chip cookies can be made with one bag of sugar?
Please have a step by step explanation so I can mark you as Brainliist.
Answer: 1 batch
Step-by-step explanation:
1 batch = 24 - 36 cookies
So here we have 23 cups of sugar, and we know that each chocolate chip cookie uses 1 cup, so we can only make 23 cookies
Which is only 1 batch of cookies can be made.
Answer:
23 batches of cookies
Step-by-step explanation:
I think this problem is kind of straightforward:
1 bag = 23 cups
1 batch = 1 cup
We need to find how many batches = 1 bag
To find that out, we have to divide bags by batches, but we don't know the number of batches yet. (Also, they're not the same units)
Instead, we can use the respective cups of sugar to divide (because they do have the same units)
So we divide the number of cups of sugar in a bag (23) by the number of cups in a batch (1):
23 ÷ 1 = 23 batches
I hope this explanation was simple enough
What is x+3y ≥ 3
Help?
Answer: x
≥
3
−
3
y
Step-by-step explanation:
There are 30 giraffe and 6 penguin at the zoo. Which tatement correctly compare the two quantitie?
To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.
To compare the two quantities, you need to divide the number of giraffes by the number of penguins.
30 giraffes / 6 penguins = 5
This means that there are 5 times as many giraffes as penguins at the zoo.
There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.
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You know distance and speed and want to find the time
You know time and distance and want to find the speed
You know speed and time and want to find the distance
Answer:
time=speed÷distance
speed=distance×time
distance=speed ÷time
Step-by-step explanation:
from the answers we get a relationship between speed,distance and time.there by when with two you can find the other
If k is a negative integer, which of these is DEFINITELY NEGATIVE? A. k* (k-1) * (k - 2) B. k* (k+1) C. k* (-50) D. (50-k)
Answer:
only A ans bellow
Step-by-step explanation:
let k= -4
A. k * (k - 1) * ( k - 2)
= -4 * (-4 -1) * ( -4 -2)
= -4* (-5) * (-6)
= 20*-6
= -120
B. k * ( k+1)
= -4 * ( -4+1)
= -4 * (-3)
= + 12
C. k * (-50)
= -4 * (-50)
= + 200
D . (50 - k)
= 50 - (-4)
= 50 + 4
= + 54
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if k is negative then k(k-1)(k - 2) will be definitely negative.
What is Number system?A number system is defined as a system of writing to express numbers.
Given that k is a negative integer.
We need to find which of the given options are defnitely negative.
Let us consider k as -3.
k(k-1)(k - 2)
-3(-3-1)(-3-2)
-3(-4)(-5)=-60
Which is negative.
k(k+1)=-3(-3+1)=6 +ve
k (-50)=-3(-50)=150 +ve
(50-k)=50-(-3)=53 +ve.
Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.
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What is the 5th term in this sequence? 1, -8, -17
The value of the fifth term in the given sequence as represented in the task content is; -35.
What is the value of the fifth term in the sequence as given?It follows from the task content that the value of the fifth term in the given sequence is to be determined.
On this note, it follows from the observation that the given sequence is arithmetic and the nth term, T (n) = a + ( n - 1 ) d.
where, a = first term = 1
and d = common difference = -8 - 1 = -17 - (-8) = -9.
Therefore, the fifth term is given as;
T (5) = 1 + ( 5 - 1 ) -9
= 1 + (4 × -9)
= 1 - 36
= -35.
On this note, the fifth term of the sequence as required is; -35.
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