Answer: [tex]y = 2x + 6[/tex]
Step-by-step explanation:
Let x represents the number of days .
Given : There are 6 quarters in a jar.
Jill adds 2 quarters to the jar every day.
Then, the number of quarters added in x days = 2x
Now, the total number of quarters in the jar after x days = 2x+6
Hence, the linear equation represents the total amount of quarters in the jar after x days will be:-
[tex]y = 2x + 6[/tex]
At 3:00 PM a man 143 cm tall casts a shadow 150 cm long. At the same time, a tall building nearby casts a shadow 180 m long. How tall is the building?
Lucas and Erick are factoring the polynomial
12x3 – 6x2 + 8x – 4. Lucas groups the polynomial (12x3 + 8x) + (–6x2 – 4) to factor. Erick groups the polynomial (12x3 – 6x2) + (8x – 4) to factor. Who correctly grouped the terms to factor? Explain.
Both students are correct because polynomials can be grouped in different ways to factor. Both ways result in a common binomial factor between the groups. Using the distributive property , this common binomial term can be factored out. Each grouping results in the same two binomial factors.
Which description represents the expression 3x + 4 ?
the sum of 3 times a number and 4
4 added to 3 plus a number
4 divided by the product of 3 and a number
4 less than 3 times a number
Answer:
first option
Step-by-step explanation:
To know this, let's begin with discarting options.
The expression is 3x + 4
This expression means that you have 3 times a number and then you add 4 to that number.
According to this, the second option states that to the number 4 you add the 3, in other words 4 + 3 and then a number. This cannot be the correct option.
The third option states a division, but we don't have in the expression any division, so, this is not the option.
The fourth option is the same as the second option with the difference that instead of adding you do a substract, which is not the case.
So with this we can conclude that the correct option is the first one, sum 3 times a number with 4.
the answer is (A) the sum of 3 times a number and 4
A circle has its center at the origin, and (5, -12) is a point on the circle. how long is the radius of the circle
Answer: 13 units.
Step-by-step explanation: A circle has its center at the origin, and the point of the circle is (5, -12). Then we have to calculate the length of its radius formula to find the length between the two points.
m<AOB = 4x - 1; m<BOC = 2x + 15; m<AOC = 8x + 8
Find the value of x.
By setting up an equation using the measures of adjacent angles AOB, BOC, and AOC, we find that the sum of AOB and BOC equals AOC. Simplifying and solving for x gives us the value of x as 3.
Explanation:To solve for the value of x given the measures of angles AOB, BOC, and AOC, we have to use the fact that the sum of the angles AOB and BOC is equal to the angle AOC since the angles are adjacent to each other.
By setting up an equation where m + m equals m, we have:
(4x - 1) + (2x + 15) = (8x + 8).
Upon simplifying, we combine like terms to get:
4x + 2x - 1 + 15 = 8x + 8,
which simplifies to 6x + 14 = 8x + 8. To solve for x, we need to move the terms involving x to one side and the constant terms to the other side. Subtracting 6x from both sides of the equation yields:
14 = 2x + 8,
and then subtracting 8 from both sides gives us:
6 = 2x,
Divide both sides by 2, and we find that:
x = 3.
if the domain of a function that is reflected over the x axis is (3,4)(2,-1)(-1,2) what is the range? answers asap plz
The range of the reflected function consists of these reflected y-values. The range of the reflected function is (-4, -2, 1).
The range of a function reflected over the x-axis can be determined by considering the y-values of the original domain. In this case, the given domain points are (3,4), (2,-1), and (-1,2). The reflected points will have the same x-coordinates but opposite y-coordinates. Therefore, the reflected range will be the set of y-values obtained by changing the signs of the y-values in the original domain.
The original domain points have y-values of 4, -1, and 2. When reflected over the x-axis, these y-values become -4, 1, and -2, respectively.
Thus, the range of the reflected function consists of these reflected y-values. The range of the reflected function is (-4, -2, 1).
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The initial amount of people that are sick with the flu is 36 and growing at a rate of 8% every day.
How many people will be sick with the flu in 11 days?
Which is the converse of this conditional?
If it is appropriate, then I play golf.
A.
If it is appropriate, then I do not play golf.
B.
If I play golf, then it is appropriate.
C.
If I do not play golf, then it is appropriate.
D.
If it is not appropriate, then I play golf.
a cable installer charges $42.50 per hour plus a $45.00 service charge. your fathers firm hires him to hook up his companys internet service. find the total charges if it takes the cable installer 5 hours to complete the task? ...?
Answer: $257.50
Step-by-step explanation:
Total charges of 5 hours paid by father = Charges of cable installer for 5 hours + Service Charge
Charges of cable installer per hour = $42.50
Charges of cable installer for 5 hours = 5 × 42.50 = $212.50
Additional service charge by him = $45.00
So, total charges of 5 hours paid by father = $212.50 + $45.00 = $257.50
Evaluate -3(-4) (-p)where p=9
In the united states sales tax is added to items that you purchase.the rate of sales tax varies by state and sometimes by country or region
What is the quotient of 6,523÷7=?
How do the prefixes in the metric system relate to the basic units?
Answer:
The prefixes in the metric system are used to modify the basic units. The prefixes either make the unit a larger measurement, as in the case of meter to kilometer, or they make the unit a smaller measurement, as in the case of meter to millimeter.
Step-by-step explanation:
What is the simplified form of the following expression? (n5)(n2)
Final answer:
The simplified form of the expression (n⁵)(n²) is found by adding the exponents since the base is the same, resulting in n⁷.
Explanation:
The simplified form of the expression (n⁵)(n²) is achieved by applying the laws of exponents. Since both terms have a common base of n, when multiplying two exponentials with the same base, we simply add their exponents.
The addition of 5 and 2 (the exponents) provides n⁵⁺² which simplifies to n⁷.
Hence, the simplified form of (n⁵)(n²) is n⁷.
Chapter 7 of the Jiuzhang suanshu presents a problem of two linear equations involving acres of land and their respective prices. One of the two equations can be translated to: 300x + y = 10000 If y = 87.5, what is the value for x? 300x + y = 10,000 300x + (87.5) = 10,000 300x + 6,250 = 10,000 x =
Answer:
12.5 :) enjoy
Final answer:
To find the value of x in the linear equation 300x + y = 10000 where y = 87.5, we substitute the value of y into the equation and solve for x. The value of x is approximately 33.04.
Explanation:
To find the value of x, we can substitute the given value of y into the equation and solve for x.
Given equation: 300x + y = 10000
Substituting y = 87.5 into the equation:
300x + 87.5 = 10000
Subtracting 87.5 from both sides:
300x = 10000 - 87.5
Simplifying the right side:
300x = 9912.5
Dividing both sides by 300:
x = 33.04
Therefore, the value of x is approximately 33.04.
What is the answer to 2a+3=9a-4
Estimate 142 to the nearest number
How to do 4 3/4 -9 2/3?
You are purchasing office supplies. Because of the volume of your orders your company receives 15% off all purchases. You buy a case of paper for $24.95 and a toner refill at $35.99. You find discontinued ink for $49.95 at 50% off. The local sales tax is 4.5%.What did you spend?
$73.03
$76.32
$85.92
$89.78
Which of the following is a factor of 2x4 + 22x3 + 60x2?
2x3
x4
x + 4
x + 5
Answer
One factor of the equation [tex]2x^{4} + 22x^{3} + 60x^{2}[/tex] is x + 5 .
Option (d) is correct.
Reason
As the equation in the question is as follows
[tex]= 2x^{4} + 22x^{3} + 60x^{2}[/tex]
simplify the above
Taking 2x² as a common part
= 2x²(x² + 11x + 30 )
= 2x² (x² + 5x + 6x + 30)
= 2x²(x(x+5) +6(x + 5))
= 2x²(x + 5)(x + 6)
Therefore the factors are 2x² , (x +5) , (x + 6) .
You roll 2 dice. What is the probability that the sum of the dice is greater than 6 and 1 die shows a 2? A 6 X 6 table of dice outcomes will help you to answer this question ...?
The perimeter of a triangular plot of land is 2400 ft. The longest feet is 200 ft less than twice the shortest. The middle side is 200 ft less than the longest side. Find the lengths of the three sides of the triangular plot. ...?
Final answer:
The lengths of the three sides of the triangular plot are 600 feet for the shortest side, 800 feet for the middle side, and 1000 feet for the longest side.
Explanation:
To find the lengths of the three sides of the triangular plot, let's define the shortest side as x. Therefore, according to the problem statement, the longest side would be 2x - 200 feet and the middle side would be (2x - 200) - 200 = 2x - 400 feet. The perimeter of the triangle is the sum of all its sides, which is given as 2400 feet.
The equation representing the perimeter of the triangle is:
x + (2x - 200) + (2x - 400) = 2400
Simplifying the equation, we get:
5x - 600 = 2400
Adding 600 to both sides:
5x = 3000
Dividing by 5 gives us:
x = 600
Thus, the shortest side is 600 feet, the longest side is 2(600) - 200 = 1000 feet, and the middle side is 1000 - 200 = 800 feet.
The lengths of the three sides of the triangular plot are 600 feet, 800 feet, and 1000 feet respectively.
Simplify.
2+{8−2[32+5(1+2)]}
Answer:
-84 is the answer.
Step-by-step explanation:
The given expression is 2 + {8 - 2[32 + 5(1 + 2)]}
We will start solving the inner most parenthesis first.
2 + {8 - 2[32 + 5×3]}
Further solve the parenthesis having the addition of 32 and 15
= 2 + {8 - 2[32 + 15]}
= 2 + {8 - 2×[47]}
Finally we will solve the last parenthesis.
= 2 + {8 - 94}
= 2 + {-86}
= 2 - 86
= -84
The function g(x) = –2x – 5. Compare the slopes.
A. The slope of f(x) is the same as the slope of g(x).
B. The slope of f(x) is less than the slope of g(x).
C. The slope of f(x) is greater than the slope of g(x).
D. The slope of f(x) is undefined and the slope of g(x) is negative.
Answer:
Option A is correct that is the slope of f(x) is the same as the slope of g(x).
Step-by-step explanation:
We have been given a function g(x)= -2x -5
And slope of f(x) can be shown from the given graph
And a line (0,3) and (1,1) is f(x)
Slope we can find in f(x) by the formula
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, in f(x) [tex]x_1=0,x_2=1,y_1=3,y_2=1[/tex]
On substituting the values we get slope of f(x) as:
[tex]slope=\frac{1-3}{1-0}=-2[/tex]
hence, slope of f(x) is -2
And slope of g(x) can be find by the formula
y= mx +c; where m is the slope on comparing the given equation with the above equation
We have slope of g(x) is -2
Hence, the slope of f(x) is the same as the slope of g(x).
Therefore, option A is correct.
A fair number cube is rolled. What are the odds in favor of rolling a 1?
A model rocket is launched with an initial upward velocity of201ft/s . The rocket's height h (in feet) after t seconds is given by the following. h=201t -16t^2
Find all values of for which the rocket's height is 93 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
...?
The values for which the rocket's height is 93 feet are t = 0.48 seconds and 12.08 seconds.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
We have:
A model rocket is launched with an initial upward velocity of 201ft/s.
The rocket's height h (in feet) after t seconds is given by the following:
h = 201t -16t²
The above equation is parabolic.
Plug h = 93 feet
93 = 201t - 16t²
16t² - 201t + 93 = 0
After solving with the quadratic formula:
[tex]\rm t_{1,\:2}=\dfrac{201\pm \sqrt{201^2-4\left(16\right)\left(93\right)}}{2\left(16\right)}[/tex]
t = 0.481, 12.081
or
t = 0.48, 12.08 secods
Thus, the values for which the rocket's height is 93 feet are t = 0.48 seconds and 12.08 seconds.
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Write log8 3 as a logarithm of base 5.
1) (log3)5/(log8)5
2) (log5)3/(log5)8
3) (log8)5/(log3)5
4) (log5)8/(log5)3 ...?
To write log8 3 as a logarithm of base 5, we can use the change of base formula: loga b = logc b / logc a. Applying this formula, we have log5 3 = log8 3 / log8 5. Therefore, the correct option is (log8)5/(log3)5.
Explanation:The expression log83 represents the logarithm of 3 with base 8. To write it as a logarithm with base 5, we can use the change of base formula:
logab = logcb / logca
Applying this formula, we have:
log53 = log83 / log85
Therefore, the correct option is (log8)5/(log3)5.
Simplify
-(2/3)(-9y)(3/2)(8x)(0)
A.
72xy
B.
–72xy
C.
72
D.
0
The inequality x + 2y ≥ 3 is satisfied by which of the following points? (Select all that apply.)
1. (1,1)
2. (-3,4)
3. (-2,2)
4. (5,-2)
Answer:
answer 1 and 2 are the correct ones.
Step-by-step explanation:
The x-intercept of the line x = 3.5 is...?