the rule for the tile pattern is y=10x-18, figure 12 will be...?
By substituting '12' into the given linear equation 'y = 10x - 18', we find that figure 12 in this tile pattern would be 102.
Explanation:The given pattern follows the linear equation y = 10x - 18. To find the value of figure 12, smaller 'x' with '12' in the equation: y = 10 * 12 - 18 = 102. Therefore, figure 12 in this tile pattern would be 102.
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Write the complex number in the form a + bi. 6(cos 330° + i sin 330°)
Answer:
The complex number 6(cos 330° + i sin 330°) in the form of a+bi is:
3√3-3 i
Step-by-step explanation:
6(cos 330° + i sin 330°)
= 6(cos(360°-30°)+ i sin(360°-30°))
=6(cos30°- i sin30°) (since, 360°-30° lies in fourth quadrant and cos is positive there and sin is negative)
=[tex]6(\dfrac{\sqrt{3}}{2}-i\dfrac{1}{2})[/tex]
Distributing 6, we get
=3√3-3 i
Hence, the complex number 6(cos 330° + i sin 330°) in the form of a+bi is:
3√3-3 i
solve -5x-42>-2-(x+4)
In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect?
*SHOW WORK*
Answer:
There will be 150 defective cars among the set of 10,000 cars
Step-by-step explanation:
For every 200 cars 3 are defective
Let X numbers of car be defective out of 10000 cars
There is a proportional relationship between the two
Thus,
[tex]\frac{3}{200} = \frac{X}{10,000} \\X = \frac{(10,000)(3)}{(200)} = 50 * 3\\= 150[/tex]
1. If m<1 = 43, what is m<4?
A. 53
B. 43
C. 37
D. 27
2. If m<1 = 50, what is m<5?
A. 50
B. 40
C. 35
D. 25
3 use the figure. Assume that lines JL and MP are parallel.
Name a pair of corresponding angles.
A. <1 and <6
B. <2 and <6
C. <3 and <5
D. <4 and <5
By using what we know about intersecting lines, we will see that the correct options are:
1) B2) A3) BHow to get the measures?
In an intersection of two lines, if two angles are adjacent, then their measures must add to 180°. And if the angles are not adjacent, then the angles have the same measure.
a) 1 and 4 are not adjacent, so these angles have the same measure.
so if m<1 = 43, then m<4 = 43
The correct option is B.
b) 1 and 5 are equivalent (where we assume that JL and MP are parallel, so all the angles formed in the two intersections are equal).
Then if m<1 = 50, m<5 = 50.
So the correct option is A.
c) The corresponding angles occupy equivalent positions.
For example:
2 and 6 are corresponding.3 and 7 are corresponding4 and 8 are corresponding.etc.
The correct option is B.
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To date, this year, Company XYZ has sold 450 units. They sell units at an average rate of 15 per week. The company wants to sell more than 750 units this year. Which of the following inequalities could be used to solve for x, the number of weeks necessary to reach the company's year-end goal?
Final answer:
To reach the goal of selling more than 750 units this year, it will take more than 50 weeks.
Explanation:
To determine the number of weeks necessary to reach the company's year-end goal of selling more than 750 units, we can set up an inequality using the average rate of sales per week. Let x represent the number of weeks needed to reach the goal. The total number of units sold in x weeks can be calculated by multiplying the average rate of sales per week (15) by the number of weeks (x). So, the inequality would be: 15x > 750. To solve for x, divide both sides of the inequality by 15: x > 50. Therefore, it would take more than 50 weeks to reach the company's goal.
Final answer:
The inequality to solve for x, the number of necessary weeks, is 450 + 15x > 750.
Explanation:
To determine for x, the number of weeks necessary for Company XYZ to reach their goal of selling more than 750 units this year, we need to set up an inequality.
They have already sold 450 units and sell units at an average rate of 15 per week.
The company's target is more than 750 units.
Therefore, we can represent this scenario with the following inequality:
450 + 15x > 750
Here's how to solve for x:
Subtract 450 from both sides of the inequality to isolate the term with x on one side:15x > 750 - 45015x > 300Divide both sides of the inequality by 15 to solve for x:x > 300 / 15x > 20Therefore, Company XYZ will need to sell for more than 20 additional weeks to exceed their goal of 750 units.
A washer and a dryer cost $600 combined. the cost of the washer is three times the cost of the dryer. what is the cost of the dryer? answer
A picture framer has a board 10 1/12 feet long. The framer notices that 2 3/8 feet of the board is scratched and cannot be used. The rest of the board will be used to make small picture frames. Each picture frame needs 1 2/3 feet of the board. At most, how many complete picture frames can be made?
Final answer:
The framer can make at most 4 complete picture frames from the usable length of the board, after deducting the scratched section, and each frame using 1 2/3 feet of the board.
Explanation:
The picture framer has a board that is 10 1/12 feet long. However, part of this board is unusable due to scratches, and that section is 2 3/8 feet. Therefore, the usable length of the board is 10 1/12 feet - 2 3/8 feet. Each picture frame requires 1 2/3 feet of this board. To find out how many complete picture frames can be made, we need to divide the usable length of the board by the length required for each frame.
First, convert the mixed numbers to improper fractions:
Total length of the board: 121/12 feet
Scratched section: 19/8 feet
Frame length: 5/3 feet
After subtracting the scratched section from the total length, we have:
(121/12) - (19/8) = (968/96) - (228/96) = 740/96 feet
Now we divide the usable length by the frame length:
(740/96 feet) / (5/3 feet) = (740/96) * (3/5) = 740/160 = 4.625
Since we cannot have a partial frame, the framer can make at most 4 complete picture frames.
Insert commas in the following numbers. a. 13886 b. 365 c. 719463 d. 40047209 e. 2145739180 f. 1783457
What point in the feasible region maximizes P for the objective function P = 2x + 3y? Constraints
2x+y≤15
x+3y≤20
x≥0,
y≥0 A. (0, 15) B. (5, 5) C. (8, 7) D. (2, 6)
Final answer:
To find the point that maximizes P for the objective function P = 2x + 3y, calculate P at each vertex of the feasible region created by the constraints. Point A (0, 15) yields the highest value of P, which is 45. Therefore, point A (0, 15) is the correct answer.
Explanation:
To determine which point in the feasible region maximizes P for the objective function P = 2x + 3y, consider the given constraints: 2x + y ≤ 15, x + 3y ≤ 20, x ≥0, y ≥0. To find the maximum value of P, we need to check the value of P at all vertices of the feasible region formed by the constraints. In such linear programming problems, the maximum or minimum value of the objective function occurs at one of the vertices of the feasible region.
Let's test the given points against the objective function:
A. (0, 15) yields P = 2(0) + 3(15) = 45
B. (5, 5) yields P = 2(5) + 3(5) = 25
C. (8, 7) yields P = 2(8) + 3(7) = 37
D. (2, 6) yields P = 2(2) + 3(6) = 22
Comparing these values, we see that point A (0, 15) gives us the highest value of P, which is 45. Hence, the correct answer to the question is point A (0, 15).
A pack of cinnamon-scented pencils sells for $9.00. What is the sales tax rate if the total cost of the pencils is $9.45?
if the given square is one side of a cube the volume of the cube will be the cube of the side length of the square write and evaluate an exponential expression for the volume of the cube.
P.S. the side length of said square is 8cm
Is a flame test qualitative or quantitative test for the identity of an unknown explain?
Which of the following is the correct action to take when simplifying the expression A. add the exponents B. subtract the exponents C. multiply the exponents D. divide the exponents
Final answer:
To simplify an expression involving division of exponential terms with the same base, subtract the exponents of those terms. Numerical coefficients are divided normally while applying the subtraction rule to the exponents.
Explanation:
When simplifying the expression that involves division of exponentials, the correct action is to subtract the exponents. This rule applies when the bases of the exponential terms are the same. For example, when dividing [tex]a^m[/tex] by [tex]a^n[/tex], you would calculate a^(m-n). If we have numerical coefficients in front of the terms, we divide those normally, then apply the rule for exponents. An example is 4.5 × [tex]10^9[/tex] / [tex]10^6[/tex] = 4.5 × [tex]10^(9-6)[/tex] = 4.5 × [tex]10^3[/tex].
Which product is the factored form of the polynomial?
(–x2 – 5)(3x2 + 2)
(x2 – 2)(3x2 + 5)
(x2 + 5)(3x2 – 2)
(3x2 – 5)(x2 + 2)
How would you graph this parabola? it's just confusing because of the fractions ...
To graph the parabola [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], plot the vertex at (2, -4), note the axis of symmetry at x = 2, and create a downward-opening parabolic shape on a coordinate plane.
To graph the parabola given by the function [tex]f(x) = -1/3x^2 + 4/3x - 16/3[/tex], follow these steps:
1. Identify the vertex: The vertex of a parabola in the form of [tex]y = ax^2 + bx + c[/tex] is given by (-b/2a, f(-b/2a)). In this case, a = -1/3 and b = 4/3. Calculate the x-coordinate of the vertex using -b/2a:
x-coordinate of the vertex = -b / (2a) = -(4/3) / (2 * (-1/3)) = 2.
Now, find the corresponding y-coordinate by plugging the x-coordinate back into the function:
[tex]f(2) = (-1/3)(2)^2 + (4/3)(2) - 16/3 = (-4/3) + (8/3) - 16/3 = -12/3 = -4.[/tex]
So, the vertex is at (2, -4).
2. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex. In this case, it's the vertical line x = 2.
3. Calculate additional points: To create a more accurate graph, you can choose additional x-values and calculate their corresponding y-values. For instance, you can select x-values to the left and right of the vertex.
- For x = 0:
[tex]f(0) = (-1/3)(0)^2 + (4/3)(0) - 16/3 = -16/3.[/tex]
- For x = 4:
[tex]f(4) = (-1/3)(4)^2 + (4/3)(4) - 16/3 = -64/3 + 16/3 - 16/3 = -64/3.[/tex]
4. Plot the points: Plot the vertex (2, -4) and the additional points you calculated on a coordinate plane.
5. Draw the parabola: Connect the points smoothly to form the parabolic shape. Since the leading coefficient (-1/3) is negative, the parabola opens downward.
6. Label the axis of symmetry: Label the vertical line x = 2 as the axis of symmetry.
Your graph of the parabola f(x) = -1/3x^2 + 4/3x - 16/3 should resemble a downward-opening parabola with the vertex at (2, -4) and the axis of symmetry at x = 2.
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I NEED HELP QUICK, PLEASE!
Find f(-10). f(x) = 7x - 5
f(x) = 7x-5
find f(-10)
replace x with -10
so you have 7(-10)-5
7*-10=-70 - 5 = -75
so f(-10) = -75
f(x) = 7x-5
find f(-10)
replace x with -10
so you have 7(-10)-5
7*-10=-70 - 5 = -75
so f(-10) = -75
What is the value of the expression 4x+y2y−x when x = 2 and y = 4?
If 15 percent of the sixth graders have blonde hair, and there are 120 sixth graders, how many of them have blonde hair?
Beau has a 30-mile commute for work each day. He drives at least an additional 225 miles every month. He needs an inequality to relate his monthly mileage, y, to the number of days he commutes, x. Which answer choice correctly describes this scenario?
A His monthly mileage is greater than the difference between 30 times the number of days and 200.
B His monthly mileage is less than the difference between 30 times the number of days and 200.
C His monthly mileage is greater than or equal to the sum of 30 times the number of days and 200.
D His monthly mileage is less than or equal to the sum of 30 times the number of days and 200.
Jeff's average math grade is 92.8. Sarah's average math grade is 67.9.
How much higher is Jay's average math grade than Sarah's?
A) 24.9
B) 25.1
C) 25.9
D) 34.9
From this year to ten years later the number of people employed as physician assistants in the country is expected to increase by 47% the number of people employed as physician assistants today is 55000 find the predicted number of physician assistants after ten years
Ther are 120 crayons and 30 pieces of paper to give to students. what is the largest number of students to have in class so each student gets equal number of crayons and equal number of paper?
The diameter of each wheel of a bicycle is 28 inches28 inches. if you are traveling at a speed of 30 miles per hour30 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning
Are the below pairs of lines parallel, perpendicular, or neither?
9x+12y = 8 and 6x+8y = −1
Parallel
Perpendicular
Neither
The snow fox can run at a rate of 8.5 feet per second. Write and solve an equation to find the time it takes the snow fox to travel 120ft. Please show your work.
divide distance by speed
equation: time = distance / speed
120/8.5 = 14.117 seconds
You are carving a block of ice for a banquet. It measures 1 ½ feet long, 1 ½ feet wide and 1 ½ feet thick. Ice weighs 57 pounds per cubic foot. What is the weight of the ice block?
volume = l x w x h
1.5 x 1.5 x 1.5 = 3.375 cubic feet
3.375 * 57 = 192.375 pounds
Which of the following is the inverse of the statement if you lift weights then you will be strong
Answer:
Inverse statement : "If you don't lift weights, then you will not be strong".
Step-by-step explanation:
If a statement is defined as
p → q : If p is true, then q is true.
then the inverse of the given statement is
¬ p → ¬ q : If p is not true, then q is not true.
The given statement is "If you lift weights then you will be strong".
We need to find the inverse of the given statement.
Here,
p = you lift weights
q = you will be strong
The inverse of the given statement is "If you not lift weights, then you will not be strong".
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A(t) denote the area to paint A (measured in square meters) as a function of time t (measured in hours). What is the Functions formula? A(t)=?
8*3 = 24 + 28 = 52 total square feet
he is painting at 8 sq m per hour
so A(t) = -8t +52
Answer:
[tex]A(t)=-8t+52[/tex]
Step-by-step explanation:
Let
A(t)------> the area to paint
t------> the time in hours
Step 1
Find the total area of the room
[tex]A=8*3+28=52\ m^{2}[/tex]
Step 2
Find the linear equation that represent the situation
[tex]A(t)=-8t+52[/tex]
Classify each of the triangles as acute, obtuse, or rights?
Triangle JKL is obtuse triangle.
Triangle XYZ is acute triangle.
What is an obtuse trianglesAn obtuse triangle is a type of geometric figure with three sides and three angles. In an obtuse triangle, one of the angles measures more than 90 degrees (∠A, ∠B, or ∠C > 90°). The other two angles are acute angles, measuring less than 90 degrees each. Consequently, the sum of the angles in an obtuse triangle is greater than 180 degrees.
what is the acute triangle
An acute triangle is a type of geometric shape defined by its angles. It consists of three sides and three angles, all of which are acute angles, meaning each angle measures less than 90 degrees (∠A, ∠B, and ∠C < 90°)
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