Answer:
g(x) has greatest y-intercept.
Step-by-step explanation:
We are given a table of values for function f(x) as:
x y=f(x)
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6
We know that the y-intercept of a function is a point where the x-value is zero.
i.e. the input value is zero.
Hence, after looking at the table of values of the function f(x) we have the y-intercept of the function f(x) is:
y=3
Also we are given function g(x) as:
g(x) = 3 cos(2x) + 1
Hence, we calculate the y-intercept of the function g(x) by taking x=0
on taking x=0 we have:
g(0)=3 cos(0)+1
g(0)=3+1=4
Hence, the y-intercept of function g(x) is 4.
Hence, g(x) has the greatest y-intercept.
round 421,906 to the nearest hundred thousand and to the nearest thousand
Two-thirds a number plus 4 is 7
At a store clearance, a women spent less than $200 on shirts that were labeled $15 each . How many shirts did she buy? Identify the numbers that are included in the solution set .
A union charges monthly dues of $6.00 plus $0.15 for each hour worked during the month.A union member's due for march were $33.00.How many hours did the union member work during the month of march?
A rectangle's width is one-fifth it's length, and it's perimeter is 180m. Find the dimensions of the rectangle. The length is M and the width is m
The dimension of the rectangle will be 15 meters (width) and 75 meters (length).
What is the perimeter of the rectangle?The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.
Then the perimeter of the rectangle will be
Perimeter of the rectangle = 2(L + W) units
The length is M and the width is m. A rectangle's width is one-fifth its length, and its perimeter is 180 metes. Then the equation will be
m = (1/5)M
m = M/5
M = 5m
Then the perimeter of the rectangle will be
P = 2(m + M)
180 = 2(m + 5m)
90 = 6m
m = 15 meters
Then the length of the rectangle will be
M = 5m
M = 15 x 5
M = 75 meters
The dimension of the rectangle will be 15 meters (width) and 75 meters (length).
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Which is the graph of f(x) = 100(0.7)x?
Answer:
a
Step-by-step explanation:
If it is 5 degrees outside and the temperature will drop 17 degrees in the next 6 hours how cold will it get?
a baker makes cakes and sells them at county fairs his initial cost was $45 to reserve a booth and $25 traveling expenses. He figures that it costs $1.75 to make each cake and he charges $6.50 per cake. Let x represent the number of cakes sold. Express the revenue R and Cost C as functions of x. Then find how many cakes will he need to sell before he will make a profit
Final answer:
The baker's revenue R can be expressed as R = x * 6.50, and the cost C can be expressed as C = 45 + 25 + (x * 1.75). To find the number of cakes he needs to sell before making a profit, we set the revenue equal to the cost and solve for x. The baker will need to sell at least 15 cakes before making a profit.
Explanation:
To express the revenue R as a function of x, we can use the equation R = x * 6.50. This is because the revenue is the number of cakes sold multiplied by the price per cake. So, every cake sold contributes $6.50 to the revenue.
To express the cost C as a function of x, we can use the equation C = 45 + 25 + (x * 1.75). The initial fixed costs of $45 for reserving a booth and $25 for traveling expenses are added to the variable costs of $1.75 per cake multiplied by the number of cakes sold.
To find the number of cakes he needs to sell before making a profit, we need to set the revenue equal to the cost and solve for x:
R = C => x * 6.50 = 45 + 25 + (x * 1.75)
Combining like terms, we get:
4.75x = 70
x = 70 / 4.75
x ≈ 14.74
Since you cannot sell a fraction of a cake, the baker will need to sell at least 15 cakes before making a profit.
A college student borrow $1,500 for 3 months to pay for a semester of school. If the interest is $30.94, find the monthly payment (Round to the nearest cent.)
Answer:
Hence, the monthly payment to the nearest cent is 510.31
Step-by-step explanation:
Consider the provided information,
A college student borrow $1,500 for 3 months to pay for a semester of school.
Let us consider the monthly payment is $x.
If he pay $x for next 3 months, then the total amount student paid in 3 month is: 3x
The interest is $30.94 for 3 months.
Student pay all the borrowed money and interest in 3 months.
That means he pay $1,500 + $30.94 in 3 months while the monthly payment was 3x.
This can be written as:
[tex]3x = 1500+30.94[/tex]
[tex]3x = 1530.94[/tex]
[tex]x = \frac{1530.94}{3}[/tex]
[tex]x = 510.31[/tex]
Hence, the monthly payment to the nearest cent is 510.31
If y= -6 when x= -24 what is the value of x when y= -7
Determine whether the equation defines y as a function of x. y equals = 8 Over x Does the equation define y as a function of x?
Yes, the equation defines y as a function of x.
Yes, the equation defines y as a function of x.
A function is a relation where each input x corresponds to exactly one output y. In this equation, y is defined as 8 over x. For any given value of x, the equation will give us a unique value for y. For example, if we plug in x = 2, y = 8/2 = 4. If we plug in x = 4, y = 8/4 = 2.
Thus, this equation defines y as a function of x.
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At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
The temperature at 4:00 pm will be 66° F.
What are Integers?
An integer is a number with no decimal number or fractional part.
Given that;
At 4:00 am the outside temperature was 28*F. By 4:00 pm that same day it rose to 38 degrees.
Now, The temperature at 4:00 pm is calculated as;
= 28° F + 38° F
= 66° F.
Thus, The temperature at 4:00 pm will be 66° F.
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The complete question is this;
At 4:00 am, the outside temperature was 28*F. By 4:00 P.M. it rose 38 degrees. What was the temperature at 4:00 P.M. ?
Make s the subject of the formula t to the power of 2
= 2p+as
Which answer is a reasonable estimate to the following problem? 94 · 689
60,000
70,000
600,000
700,000
The reasonable estimate for multiplying 94 by 689 is found by rounding the numbers to the nearest convenient figures, which gives an estimated result of 70,000.
Explanation:To estimate the product of 94 and 689, you can round each number to its nearest simple form and then multiply. Round 94 to 100 because it is close to that multiple of ten. Round 689 to 700, as it is close to this hundred mark. When you multiply 100 by 700, you get 70,000.
This process of rounding to the nearest convenient number simplifies the multiplication and gives us an answer that is easy to calculate and understand. Hence, by rounding the numbers before multiplying, the reasonable estimate for the problem 94 · 689 is 70,000.
Final answer:
By rounding the numbers and multiplying, a reasonable estimate for the product of 94 and 689 is 70,000.
Explanation:
To estimate the product of 94 · 689, we can round the numbers to the nearest ten or hundred and then multiply. For estimation purposes, we can approximate 94 to 100 (since it's closer to 100 than 90) and 689 to 700 (since it's closer to 700 than 600).
Multiplying these rounded figures: 100 × 700 equals 70,000. Therefore, 70,000 is a reasonable estimate for the product of 94 and 689.
What is the area of a circle 3.102 cm in diameter? (note: the units will be cm2, you only need to enter the number)?
find two consecutive integers such that the larger is nine more than twice the smaller
Two consecutive integers are - 7 and - 8.
Here,
We have to find the two consecutive integers.
What are Integers?
An integer is a number which includes negative and positive numbers, including zero.
Now,
Let the smaller number is x.
Then, the larger is nine more than twice the smaller.
So, Larger number = 2x + 9
Since, The difference of two consecutive number are always 1.
So,
2x + 9 - x = 1
x + 9 = 1
x = -8
Therefore, The larger number = 2x + 9 = 2*-8 + 9 = -16 + 9 = -7
Hence,
Two consecutive integers are - 7 and - 8.
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What is the volume of a frustum of a right pyramid with the area of the lower base equal to 100 square inches, the area of the upper base equal to 25 square inches, and the altitude equal to 12 inches?
A. 560 in^3
B. 700 in^3
C. 420 in^3
D. 750 in^3
Where B₁ and B₂ are the areas of the bases, the volume of the frustum is given by
... V = (1/3)(B₁ +B₂ +√(B₁B₂))h
For your dimensions, the volume is
... V = (1/3)(100 + 25 + √(100·25))·12 = (1/3)·175·12 = 700
The appropriate choice for the volume of the frustum is
... B. 700 in³
Mt. Everest, the highest elevation in Asia, is 29,028 feet above sea level. The Dead Sea, the lowest elevation, is 1,312 feet below sea level. What is the difference between these two elevations?
area of rectangular window is 360 square centimeters if the length of the window is bigger than the width of the window by 4 centimeters what are the dimensions
What is the prime factorization of 15
Answer: 3 × 5
Step-by-step explanation: To find the prime factorization of 15, first create a factor tree with two branches.
Since 15 divided by 3 gives us 5, we know that and 5 are factors of 15. This means that we can write 3 and 5 at the bottom of our branches.
While 1 and 15 are also factors of 15, we don't use them in our factor tree. This because when finding a prime factorization, we only want factors other than 1 and the number itself.
Next, we circle any prime numbers in our factor tree. Since 3 and 5 are both prime numbers, we circle both 3 and 5. Since we have circles at the bottom of our branches, we are finished.
Therefore, the prime factorization of 15 is 3 × 5.
What Is 1,270 rounded to the nearest hundred?
the product of two numbers is 14. One of the numbers is d. What expression represents the other number
please help me what is 1462 ÷ 58 as a mixed number then put it in simplest form
The expression 40x2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?
Answer:
Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Step-by-step explanation:
Given Expression of the Sum of the all interior angles of a regular polygon
40x² - 65x + 50
We need to find expression representing the measure of the two angles.
We know that regular polygons have all side and all angles equal.
Number of side or angles in regular polygon = 5
So, when we divide given expression by 5 we get expression for an angle of the regular polygon.
[tex]\frac{40x^2-65x+50}{5}=\frac{5(8x^2-13x+10)}{5}=8x^2-13x+10[/tex]
Expression for an angle of regular pentagon = 8x² - 13x + 10
Now, For 2 angles = 2( 8x² - 13x + 10 ) = 16x² - 26x + 20
Therefore, Expression representing the measure of the two angles of the given regular polygon is 16x² - 26x + 20.
Priscilla has 56 stickers in her collection. Write the prime factorization of 56
Answer:
Prime factorization: 56 = 2 x 2 x 2 x 7.
Step-by-step explanation:
Given : 56
To find : Write the prime factorization.
Solution : We have given number 56.
Prime factorization : Factors of 56 as prime number
56 = 56 = 1 x 56, 2 x 28, 4 x 14, or 7 x 8.
Prime factorization: 56 = 2 x 2 x 2 x 7
Therefore, Prime factorization: 56 = 2 x 2 x 2 x 7.
evaluate the expression of 8+(-1)+(-3)
The cost of a 12.95 pizza was shared evenly by 5 friends. How much did each person pay?
in slope intercept form, what is the equation of the line passing through the points (3,17) and (7, 25)
A. y=-2x+23
B. y=2x+11
C. y=-3x+26
D. y=2x-11
Answer:
B
Step-by-step explanation:
To write the equation of the line, use the slope formula to find the slope. Then substitute the slope and a point into the point slope form. Simplify using the distributive property to write in slope intercept form.
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{25 - 17}{7-3} = \frac{8}{4} = 2[/tex]
Using the point slope form of a line equation, substitute m = 2 and the point (3,17).
[tex]y - y_1 = m(x-x_1)\\y -17 = 2(x - 3)\\y - 17 = 2x - 6 \\ y = 2x - 6 + 17 \\ y = 2x + 11 [/tex]
The number 3.453 has two 3s why does each 3 have a different value
Can someone PLEASE help me with this? ^^^ (25 points)