Answer: Choice D, -5x^3 + 8
A binomial consists of two terms being added or subtracted. The two terms are -5x^3 and 8. The term -5x^3 has a leading coefficient -5 and exponent 3. The largest exponent determines the degree of the polynomial. The 8 is constant as there are no variables attached or multiplying with it.
It takes three painters 4 hours to paint 1 classroom.How many hour does it talk 1 painter to paint to classrooms?
It takes 1 painter 24 hours to paint two class rooms
Step-by-step explanation:
When some worker do a job together, then
The number of worker is varies inversely with the time to finish the job, because 2 workers take time less than 1 worker to finish the same jobWhen y varies inversely with x, then x y = k, where k is constantIf 5 workers finish a job in 2 hours, then 10 workers finish the same job is 1 hour because 5 × 2 = 10 × 1∵ It takes three painters 4 hours to paint 1 classroom
∵ It takes 1 painter x hours to paint 1 class room
- Equate 3 × 4 by 1 × x because they will do the same job
∴ 3 × 4 = 1 × x
∴ 12 = x
∴ It takes 1 painter 12 hours to paint 1 class room
We need to find it takes 1 painter to paint two class room
∵ The painter will paint 2 class rooms
∵ He takes 12 hours to paint 1 class room
- Multiply his time in one class room by 2
∵ 12 × 2 = 24
∴ It takes 1 painter 24 hours to paint 2 class rooms
It takes 1 painter 24 hours to paint two class rooms
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Domain and Range Mapping Diagrams
Determine whether each diagram depicts a function or not.
Function
VOON
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
4. If the expression 25y^2- 70y+d is a perfect square, where d is a constant, find the
value of d.
Answer:
d = 49
Step-by-step explanation:
Given that the expression is a perfect square of the form
(ay - b)² = a²y² - 2aby + b²
Then comparing like terms
a²y² = 25y², that is
a² = 25 ⇒ a = 5
and -2aby = - 70y, thus
2ab = 70, that is
2(5)b = 70
10b = 70 ⇒ b = 7
b² = 7² = 49
Hence
25y² - 70y + d = (5y - 7)² = 25y² - 70y + 49
Thus d = 49
what is triangular number
Answer:
Theory
Step-by-step explanation:
A triangular number or triangle number counts objects arranged in an equilateral triangle. The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers , starting at the 0th triangular number, is 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...
(–x^2y^3m)^5 write the monomial in standard form
Answer:
-m^5*x^10*y^15
Step-by-step explanation:
remember alphabetical order
The standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is (–x²y³m)⁵. The standard form of the number will be written as,
E = (–x²y³m)⁵
Solve the exponents and simplify.
E = -m⁵x¹⁰y¹⁵
Therefore, the standard form of the monomial equation (–x²y³m)⁵ is -m⁵x¹⁰y¹⁵.
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Is the expression 3(x+1 1/2)-3 equivalent to 3x+1 1/2
Answer:
No
Step-by-step explanation:
3(x+11/2)-3 = 3x + 33/2 -3 = 3x + (33-6)2 = 3x + 27/2
The expression 3(x+1 1/2)-3 is equivalent to 3x+1 1/2 once the distributive property is applied and the constants are combined.
The expression 3(x+1 1/2)-3 is not equivalent to 3x+1 1/2. To determine the equivalency, we need to apply the distributive property to the expression on the left-hand side. The distributive property states that we can multiply the outside term by each term inside the parentheses. Thus, the expression 3(x+1 1/2) becomes 3x + 4 1/2. When we subsequently subtract 3 from 4 1/2, we get 1 1/2, which results in the final expression of 3x + 1 1/2. This confirms the expressions are equivalent.
The ratio of quarters to dimes in a coin collection is 5:3. You add the same number of new quarters as dimes
to the collection. Is the ratio of quarters to dimes still 5 : 3
The ratio of quarters to dimes is not still 5 : 3
Solution:
Given that ratio of quarters to dimes in a coin collection is 5:3 .
You add same number of new quarters as dimes to the collection .
Need to check if ratio of quarters to dimes is still 5 : 3
As ratio of dimes and quarters is 5 : 3
lets assume initially number of quarters = 5x and number of dimes = 3x.
Now add same number of new quarters as dimes to the collection
Let add "x" number of quarters and "x" number of dimes
So After adding,
Number of quarters = initially number of quarters + added number of quarters = 5x + x = 6x
Number of dimes = initially number of dimes + added number of dimes
= 3x + x = 4x
New ratio of quarters to dimes is 6x : 4x = 3 : 2
So we have seen here ratio get change when same number of new quarters and dimes is added to the collection
Ratio get change from 5 : 3 when same number of new quarters and dimes is added to the collection and new ratio will depend on number of quarters and dimes added to collection.
3tenths - 3 twentieth
Answer:
0.15
Step-by-step explanation:
Given expression
3 tenths- 3 twentieth
⇒
[tex]=\frac{3}{10} -\frac{3}{20} \\=\frac{6}{20} -\frac{3}{20}\\=\frac{6-3}{20} \\=\frac{3}{20} \\=0.15[/tex]
Therefore value of given expression is 0.15
The length of a rectangle is three times width. If the perimeter of the rectangle is 40cm, find its length and width?
Answer:
width = 5
length = 15
Step-by-step explanation:
width: x
length : 3x
x + 3x + x + 3x = 40
8x = 40
x = 5
width = 5
length = 15
Dora is conducting a performance appraisal for Sue, one of her employees. The company's performance appraisal form asks her to rate Sue's performance on various items like "Submits reports on time with minimal errors" on a scale from 1 to 5.
The correct answer is "behaviorally anchored rating scale."
Further Explanation:
This type of testing is used by employers to rate an employees patterns of behaviors or their performance. This testing is also known as BARS. They use a scale system from either 1-5 or 5-9. This helps to see how the employee or trainee will do in certain situations.
This is commonly used by Human Resource departments, supervisors, or other higher ups in a company. This is used to benefit the company in the long run in case the employee or trainee doesn't work out during the appraisal. This can also be done during a yearly review of a seasoned employee.
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One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Find the two numbers.
One number is 7 less than a second number. Twice the second number is 1 less than 5 times the first. Then the two numbers are 5 and 7
Solution:
Given that one number is 7 less than a second number.
Twice the second number is 1 less than 5 times the first.
Need to determine two numbers.
Let assume first number be represented by variable x and second number be represented by variable y.
As first number is 7 less than a second number, adding 7 to first number will give us second number
=> x + 7 = y ------ (1)
[tex]\begin{array}{l}{\text { Twice of second number }=2 \times \text { second number }=2 \times y=2 y} \\\\ {\text { 5 times the first number }=5 \times \text { first number }=5 \times x=5 x}\end{array}[/tex]
As given that Twice the second number is 1 less than 5 times the first , if we 1 to twice of second number we will get 5 times first number ,
=> 2y + 1 = 5x ------ (2)
On substituting value of y as x + 7 from equation 1 into equation 2 , we get
2(x + 7) + 1 = 5x
=> 2x + 14 + 1 = 5x
=> 2x – 5x = -15
=> -3x = -15
x = 5
Substituting x = 5 in equation (1) to get value of y
=> y = 5 + 7 = 12
Hence first number is 5 and second number is 12
Diana has an end table in the shape of a right triangle. The triangular tabletop is twice as high as it is wide at the base. If the area of the tabletop is 4 square feet (4ft2), what is the width of the base of this triangular tabletop in feet?
Answer:
The width of the base is 2.828 feet
Explanation:
Given the area of the table top is 4 square feet
The triangular table top is twice as high as it is wide at the base
Therefore, we can say that height = base
Area of a right angled triangle is calculated by, Area = ½ * base * height
In this case, height = base
Therefore, area =[tex]\frac{1}{2}\times (base)^2[/tex]
Substituting the values,
4 = [tex]\frac{1}{2}\times (base)^2[/tex]
[tex](base)^2[/tex] = 8
Base = 2√2 = 2 * 1.414 = 2.828 feet
Therefore, the width of the base is 2.828 feet
There are 4, 000 books in the towns library. Of these, 2, 600 are fiction. Write a percent equation that you can use to find the percent of the books that are fiction. Then solve your equation.
The percent equation showing the fiction books is y = 0.65x showing that among the 4,000 books in the library, 2,600 are fiction.
An equation is a mathematical representation of the equality of two expressions.
The number of books in the town's library = 4,000
The number of fiction books = 2,600
The number of nonfiction books = 1,400 (4,000 - 2,600)
The percentage of fiction books to the total number of books = 65% (2,600/4,000 x 100)
Let the total number of books in the library = x
Let the number of fiction books = y
Equation:
y = 0.65x
y = 2,600 (0.65 x 4,000)
Express the ratio of the area of the circle to the area of the square
Answer:
π/4
Step-by-step explanation:
The area of the circle is A = π(2x)^2 = 4πx².
The length of one side of the square is 2(2x), or 4x, so the area of the square is A = 16x².
The ratio of the area of the circle to the area of the square is
4πx²
ratio = ------------- and this reduces to ratio = π/4.
16x²
euben's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Reuben $5.70 per pound, and type B coffee costs $4.30 per pound. This month, Reuben made 167 pounds of the blend, for a total cost of $820.30. How many pounds of type A coffee did he use?
Answer:
The quantity of type A coffee is 73 pounds
The quantity of type B coffee is 94 pounds .
Step-by-step explanation:
Given as :
The price of Type A coffee costs = $ 5.70 per pound
The price of Type B coffee costs = $ 4.30 per pound
The total quantity of coffee does Reuben purchases = 167 pounds
The total cost of the coffee for 167 pounds = $ 820.30
Let The quantity for type A coffee = a pounds
And The quantity of type B coffee = b pounds
Now, According to question
a + b = 167 pounds And
$ 5.70 × a + $ 4.30 × b = $ 820.30
Now solving equations
5.70 × ( a + b ) = 5.70 × 167
or, 5.70 a + 5.70 b = 951.9
Now ,
( 5.70 a + 5.70 b ) - ( 5.70 a + 4.30 b ) = 951.9 - 820.30
or, ( 5.70 a - 5.70 a ) + ( 5.70 b - 4.30 b ) = 131.6
Or, 0 + 1.4 b = 131.6
∴ b = [tex]\frac{131.6}{1.4}[/tex]
I.e b = 94 pounds
Put the value of b to get a value
So, a = 167 pounds - b
Or, a = 167 - 94
∴ a = 73 pounds
Hence The quantity of type A coffee is 73 pounds
And The quantity of type B coffee is 94 pounds . Answer
Use the array to solve the problem 8x9
Answer:
72
Step-by-step explanation:
multiply
Answer:
72
Step-by-step explanation:
Seniors at a high school were asked what color car they drive. The results were put in a circle graph. The measure of each central angle is shown. If a senior is chosen at random from this school, find the probability of each response.
What Color Is Your Car?
Car color is not red or blue.
options:
0.51
0.47
0.53
0.49
Answer:
P(The color of the car is red) is 0.32 .
P(The color of the car is white) is 0.34 .
P(The color of the car is silver) is 0.19 .
P(The color of the car is blue) is 0.15 .
P(car color is not red or blue) is 0.53 .
Step-by-step explanation:
We know that total angle subtended at the center by a complete circle is
360° .
According to the question,
P(The color of the car is red)
= [tex]\frac {115.2}{360}[/tex]
= 0.32
P(The color of the car is white)
= [tex]\frac {122.4}{360}[/tex]
= 0.34
P(The color of the car is silver)
= [tex]\frac {68.4}{360}[/tex]
= 0.19
P(The color of the car is blue)
= [tex]\frac {54}{360}[/tex]
= 0.15
So
P(car color is not red or blue)
= 1 - (0.15 + 0.32)
= 0.53
Answer:
0.53 is the correct answer.
Step-by-step explanation:
How do u solve 4(3x-1)=9-x
Answer:
x = 1
Step-by-step explanation:
Well the first step is to apply the distributive property:
4(3x - 1) is equal to (12x - 4). You DISTRIBUTE a '4' to what is inside the parentheses.
And btw, to make it easier, you can make 9 - x so that x is first. For example, (-x + 9). They're both the same thing, just written differently.
Your new equation is 12x - 4 = -x + 9. You want to now solve the equation.
Add the (-x) to both sides. It cancels out on the right side and you add it to 12x on the left side.
[If there's no number in front of a variable, you can always just put 1 in order to make it easier]
12x + 1x = 13x. Your new equation is 13x - 4 = 9. This should look very familiar. You simply add 4 to both sides. 9 + 4 = 13
Finally, 13x = 13. Divide 13 ÷ 13 to get 1.
x = 1
You rotate a triangle 90° counterclockwise about the origin. Then you translate its image 1 unit left and 2 units down. The vertices of the final image are (-5,0),(-2,2) and (-2,-1) . What are the vertices of the original triangle?
Answer:
The coordinates of the original triangle are (2,4). (4,1) and (1,1)
Step-by-step explanation:
About the origin, I have to rotate a triangle 90° counterclockwise. Then I translate its image 1 unit left and 2 units down.
The vertices of the final image are (-5,0), (-2,2), and (-2,-1).
We need to get the vertices of the original triangle.
So, start from a triangle with vertices (-5,0), (-2,2), and (-2,-1) and do the reverse to get the original triangle.
So, we will translate the image triangle by 1 unit right and 2 units up and we will get the triangle with vertices (-5 + 1, 0 + 2), (- 2 + 1, 2 + 2) and (- 2 +1, - 1 + 2) ≡ (-4,2), (-1, 4) and (-1,1).
Now, we have to rotate this intermediate triangle by 90° clockwise.
Therefore, the coordinates of the original triangle are (2,4). (4,1) and (1,1) (Answer)
{Since, for 90° rotation the coordinates of all the vertices will interchange their location (i.e. x-value to y-value and y-value to x-value) and a negative sign will be added to the y-coordinate of the interchanged coordinates}
10/3 = 5y how do I find y
Answer: y= 2/3
Step-by-step explanation:
Divide 10 by 5 and you get the 2 so you keep the denominator and it makes 2/3
If on a scale drawing 75 feet are represented by 45 inches, then a scale of 1/5 inch represents how many feet?
Answer:
1/3 or 0.33 feet
Step-by-step explanation:
This question can be easily answered by using simple proportions.
If 75 feet are represented by 45 inches on a scale, then the scaling factor from feet to inches is 45/75, or from inches to feet is 75/45
If we have 1/5 inch and want feet, just multiply by 75/45 to get
1/5*75/45=1/3=0.33 feet
Answer:
1/3 feet
Step-by-step explanation:
We are given that
On a scale drawing
45 inches represented =75 feet
We have to find a scale of 1/5 inch how many feet represents.
To find the value in feet represented by a scale of 1/5 inch we will use unitary method.
Using unitary method
45 inches represents =75 feet
1 inch represents =[tex]\frac{75}{45}[/tex] feet
1/5 inch represents =[tex]\frac{75}{45}\times \frac{1}{5}[/tex] feet
1/5 inch represents=[tex]\frac{1}{3}[/tex] feet
Hence, a scale of 1/5 inch represents 1/3 feet
The drawing below has four lines . How many lines does it have
Answer: I think you answered your own question
Step-by-step explanation:
Think of something in your home or community that could be described as a proportional relationship. List at least three examples.
Answer in 3 complete sentences.
Answer:
The 3 examples are given below.
Step-by-step explanation:
1. While decorating my home the amount of paint required ([tex]A_{m}[/tex]) for the wall is proportional to the area of the wall (A),
or [tex]A_{m}[/tex] ∝ A .
2. The no. of tiles required(T) to fill the floor of a house is proportional to the area of the floor(F) provided area of each tile(t) is constant here,
or T ∝ F when t is constant
3.The tuition fee (M) taken by my sister's school for her studies is proportional to the no. of months(H) she is in that school,
or M ∝ H
Final answer:
Examples of proportional relationships include electricity bills proportionate to usage, water in a tank related to tap flow time, and pay from a job based on the number of performed tasks.
Explanation:
Proportional relationships involve constants of proportionality which indicate a direct or inverse relationship between two quantities. For example, in a household setting, the electricity bill is directly proportional to the amount of electrical usage; the higher the usage, the higher the bill. Similarly, the amount of water in a tank can be seen as directly proportional to the time the tap runs if the flow rate is constant. Additionally, the pay for a college work-study job, such as making calls for donations, can be directly proportional to the number of calls made; if you're paid $2.50 per call, doubling the number of calls doubles your pay.
This is 6 grade homework please help me
Answer:
what is the problem?
Step-by-step explanation:
Answer:
What work do you need help with tag a photo or write it out.
The perimeter of a basketball court is 90 meters and the length is 6 meters longer than twice the width. What are the length and width?
The length of basketball court is 32 meters and width is 13 meters.
Step-by-step explanation:
Perimeter = 90 meters
Let w be the width
Length = l = 2w + 6
As basketball court are in rectangular shapes, therefore,
Perimeter = 2(length+width)
[tex]90=2(2w+6+w)\\90=2(3w+6)\\90=6w+12\\90-12=6w\\6w=78[/tex]
Dividing both sides by 6;
[tex]\frac{6w}{6}=\frac{78}{6}\\w=13\ meters[/tex]
Length = 2w+6
[tex]l=2(13)+6\\l=26+6\\l=32\ meters[/tex]
The length of basketball court is 32 meters and width is 13 meters.
Keywords: perimeter, rectangles
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q.15ab with step pls
Answer:
(a) The cost of 1 model house A = $24
(b) YES, with $200 Victor can purchase 3 A model & 4 B model houses.
Step-by-step explanation:
Let us assume the cost of model house B = $ m
So, the cost of model house A =$ ( m - 6)
So, the price of 5 A model house = 5 x ( Rate of 1 model house A)
= 5(m-6)
And, the price of 3 B model house = 3 x ( Rate of 1 model house B)
= 3 x (m) = 3 m
So, the cost of 3 B house + 5 A house = 5(m-6) + 3 m
⇒5(m-6) + 3 m = $210
or, 5 m - 30 + 3 m = 210
or, 8 m = 240
or, m = 30
So, the cost of 1 B house = m = $30
And the cost of 1 house A = (m -6) = (30 - 6) = $24
Now, The cost of 3 A model + 4 B model
= 3( 24) + 4(30) = 72 + 120 = 192
So, The cost of 3 A model + 4 B model = $192 and $192 < $200
Hence, YES, with $200 Victor can purchase 3 A model + 4 B model houses.
Four times a number,y,increased by eight
I'm assuming your teacher wants you to translate the given sentence into an algebraic expression.
y = some unknown number
4y = 4*y = four times a number y
4y+8 = four times a number, y, increased by 8
Answer: 4y+8Solve for u.
3u+4u = 56
Answer:
8
Step-by-step explanation:
3u+4u=7u
7u=56
u=8 because you divide
Answer:
U=8
Step-by-step explanation:
3u+4u=56
7u=56
u=8
There are 1/35 of the students in the school that are allergic to seafood. there are 1/15 of the students in school that are allegic to peanuts? Are there more students allergic to seafood or peanuts?
More people are allergic to peanuts because the smaller the denominator, the bigger the fraction.
Tours of the art museum are offered every 1/3 hr from 10:00 A.M. until closing at 4:00 P.M. How many tours are offered each day?
Answer: 3 Each hour × (difference in 10 am and 4 pm= 5) = 15.
Step-by-step explanation:
Answer:
18 tours are offered
Step-by-step explanation:
So 1/3 of a hour is 20 mins, so every 20 mins a tour is offered so we know 1 hour equals to 3 tours offered so
10:00 to 11:00 is 3, 11:00 to 12:00 is 3, 12:00 to 1:00 is 3, 1:00 to 2:00 is 3, 2:00 to 3:00 is 3, 3:00 to 4:00 is 3.
6 hours times 3 equals, 18 tours are offered