The expression equivalent to (25x - 10y) is (5(20x - 10y)) thus option D, is correct.
To determine the equivalent expression, we can use the distributive property, which states that (a(b + c) = ab + ac). In this case, option D,(5(20x - 10y)), applies the distributive property by multiplying 5 to both terms within the parentheses. The result is [tex]\(5 \times 20x - 5 \times 10y\)[/tex], which simplifies to (100x - 50y). Therefore, option D is equivalent to (25x - 10y).
Understanding the distributive property is fundamental in algebraic simplification. When applying the distributive property to option D, each term inside the parentheses is multiplied by 5, resulting in the expression (100x - 50y). This matches the given expression (25x - 10y), confirming that option D is the correct equivalent expression.
Recognizing and using algebraic properties, such as the distributive property, is crucial for simplifying expressions and identifying equivalent forms. In this case, option D accurately represents the given expression in a different but equivalent form, providing a valuable tool for algebraic manipulation and problem-solving in mathematics.
Final answer:
The expression that is equivalent to 25x – 10y is 5(5x – 2y), where 5 is factored out as the greatest common factor.
(Option A)
Explanation:
The expression equivalent to 25x – 10y can be found by factoring the greatest common factor out of each term. Looking at 25x and -10y, the largest number that divides both 25 and 10 is 5. Factoring a 5 out of each term, we get 5(5x – 2y). Hence, the equivalent expression is 5(5x – 2y).
So, the answer to the question is:
A. 5(5x – 2y)The factored expression, 5(5x – 2y), is the result of extracting the greatest common factor from 25x – 10y. This simplified form is equivalent to the original expression and confirms that option A, 5(5x – 2y), is the correct answer.
What are the leading coefficient, constant term and degree, if any, of the algebraic expression (x - 1)(x^2+1)
a. leading coefficient: 1; constant term: -1; degree: 3 b. leading coefficient: -1; constant term: 1; degree: 3
c. leading coefficient: 1; constant term: 1; degree: -3. d. none, expression is not a polynomial
Answer:
See below in bold.
Step-by-step explanation:
(x - 1)(x^2 + 1)
= x(x^2 + 1) - 1(x^2 + 1)
= x^3 + x - x^2 - 1
= x^3 - x^2 - x - 1.
Leading coefficient = 1.
Constant term = -1.
Degree = 3. (because of the x^3).
If the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that the expression is,
(x - 1)(x² + 1)
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
=(x - 1)(x²+ 1)
= x(x² + 1) - 1(x² + 1)
= x³ + x - x² - 1
= x³ - x² - x - 1.
From the expression the obtained result is,
Leading coefficient = 1
Constant term: -1
Degree: 3
Thus, if the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.
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Which of the points is NOT one of the vertices (s,t) of the shaded region of the set of inequalities shown below?
Please help
Answer:
Option D
Step-by-step explanation:
Given: set of inequalities
To find: Points which do not satisfy all the inequalities
Solution:
For point [tex](15,0)[/tex]:
[tex]15\leq 30-3(0)=30\\15\geq 15-0=15\\15\leq 25-0=25\\15\geq 0\\0\geq 0[/tex]
So, (15, 0) satisfies all the inequalities
For point [tex](7.5,7.5)[/tex]:
[tex]7.5\leq 30-3(7.5)=30-22.5=7.5\\7.5\geq 15-7.5=7.5\\7.5\leq 25-7.5=17.5\\7.5\geq 0\\7.5\geq 0[/tex]
So, (7.5, 7.5) satisfies all the inequalities
For point (22.5,2.5):
[tex]22.5\leq 30-3(2.5)=30-7.5=22.5\\22.5\geq 15-2.5=12.5\\22.5\leq 25-2.5=22.5\\22.5\geq 0\\2.5\geq 0\\[/tex]
So, (22.5,2.5) satisfies all the inequalities
For point (7.5 ,0):
Put s = 7.5 and t = 0 in [tex]s\geq 15-t[/tex]
[tex]7.5\geq 15-0=15[/tex] which is false
So, [tex](s,t)\neq (7.5,0)[/tex]
Answer:
D.
Step-by-step explanation:
-2x + 3y = -5
2x + 4y = 26
Answer:
[tex]x=7[/tex]
[tex]y=3[/tex]
Step-by-step explanation:
Considering the system of equations:
[tex]$\left \{ {{-2x + 3y = -5} \atop {2x + 4y = 26}} \right. $[/tex]
[tex]$\left \{ {{ 3y = -5} \atop {4y = 26}} \right. $[/tex]
[tex]7y=21\\y=3[/tex]
[tex]2x + 4(3) = 26\\2x + 12 = 26\\2x=14\\x=7[/tex]
Lily offers embroidery services at her clothing store. She charges $2 for every letter plus a $6 setup fee. Which graph represents the cost of Lily's embroidery services?
Answer:
Ok so the way i see it lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40. If it isn't to much can you give me brainliest? if not a simple thanks will do!!!
~~ Night
Answer: lily would take $2 and $6 and multiply it by the price of the item say someone walks in and buy's a 5 letter's she'd first multiply 2x5 = 10 and then she'd multiply 6x5= 30 add the two 30 + 10 = 40. Brainliest?
a sightseeing bus picks up a group of tourists at a hotel. it then travels 2 blocks north, 2 blocks eats , 1 block south,2 blocks east, and 1 block south. describes where the bus is in relation to the hotel.
(*It would mean a lot if you could answer*)
Answer:
the hotel is four blocks west from the bus; the bus is four blocks east from the hotel.
The bus is 4 blocks east of the hotel.
Since a sightseeing bus picks up a group of tourists at a hotel, and it then travels 2 blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south, to determine where the bus is in relation to the hotel, the following calculation must be carried out:
North and South are antagonistic, the same as East and West 2 N + 2 E - 1S + 2E - 1S 2 N - 2S = 0 2E + 2 E = 4E
Therefore, the bus is 4 blocks east of the hotel.
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Given: y=x^2-4x-12
A.) determine the roots/zero
(By factoring & setting the answer equal to zero)
B.) use h=-b/2a to get vertex
Answer:
see below
Step-by-step explanation:
y=x^2-4x-12
Set equal to 0 to find the zeros
0 =x^2-4x-12
Factor. What 2 numbers multiply to -12 and add to -4
-6*2 = -12
-6+2 = -4
0= (x-6) (x+2)
Using the zero product property
0=x-6 0 = x+2
x=6 x = -2
zeros: -2,6
Vertex
h = -b/2a = - (-4)/ 2(1) = 4/2 = 2
OR Average the roots (-2+6)/2 = 4/2 =2
The y coordinate is found by substituting into the equation
y = (2)^2 -4(2) -12
y = 4-8-12
y =-16
vertex : (2, -16)
Answer:
x = -2, 6
Vertex: (2,-16)
Step-by-step explanation:
x² - 4x - 12
x² - 6x + 2x - 12
x(x - 6) + 2(x - 6)
(x - 6)(x + 2) = 0
x = -2, 6
h = -(-4)/2
h = 4/2
h = 2
k = 2² - 4(2) - 12
k = 4 - 8 - 12
k = -16
Vertex: (2,-16)
Complete the equation 3 x 18 = 3 x ____ x 9
Need answer ASAP
Answer:
2
Step-by-step explanation:
Since the 3's are the same on either side, you need to find a number that, when multiplied by 9, yields 18. The only number that satisfies that is 2, which is the answer. Hope this helps!
What is 1,000,000,000,000 as a power of 10?
Answer:
1,000,000,000 as a power of 10, is: 10^12
Step-by-step Solution:
We can expand 1,000,000,000, and write this number as a multiplication sentence using only the number 10. By doing this, we can count the number of tens needed to be multiplied to get to his answer:
1,000,000,000 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Since 10 is multiplied by itself 12 times, we can therefore say that 10^12 is equal to 1,000,000,000
Answer:
10^12 (10 to the 12th power)
Step-by-step explanation:
10 to the twelth power would basically be 10x10x10x10x10x10x10x10x10x10x10x10
This equals 1,000,000,000,000, which is one trillion.
why is this correct idkidkidkidkidkidk
Answer:
Step-by-step explanation:
because you go with you first answer bc its going to be right
What is the measure of ∠ADC?
Answer:
<ADC = 131
Step-by-step explanation:
< ADC = <ADB + < BDC
The large angle is the sum of the two smaller angles.
<ADC = 89+42
=131
Answer:
131 degrees
Step-by-step explanation:
The reason for, is since <ADC is equal to < ADB + <BDC and that we already know the values of <ADB and <BDC, we can simply do
89 + 42 = 131.
So, <ADC is 131 degrees.
:)
Wich fraction is the largest? 8/6 8/4 9/6 5/7 6/9
Answer:
8/4
Step-by-step explanation:
8/4 is equal to 2 and the others equal less than 1 1/2 and 2
Answer:
8/4
Step-by-step explanation:
8/4 is 2
8/6 is 1.333
9/6 is 1.5
5/7 is .7142
6/9 is .666
Which expression has a term with a coefficient greater than 1?
A. M - 5 x3
B. 5/6m + 3
C. 5 + m
D. 5 + 3m
Answer:
D
Step-by-step explanation:
I'm sorry, but I don't know what option A is.
However, we are asked which expression has a coefficient greater than one. A coefficient is a number in front of a variable. D is the only one with a coefficient GREATER than 1, so that is the answer.
You can tell me if I did anything wrong! :)
Enter the trigonometric equation you would use to solve for x in the following right triangle. Do not solve the equation.
Answer:
sin 70= x/8
Step-by-step explanation:
Opposite of 70 degrees is x and the hypotenuse is 8.
Sin is opposite over hypotenuse
Therefore, sin 70=x/8
Will a set of data always have a mode? Explain your answer.
A set of data will not always have a mode.
A mode is defined as the value that appears the most often in a set.
For instance, a set of 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6 would have a mode of 4, as it appears more often than any other number in the set.
However, a set of 1, 2, 3, 4, 5, 6 has no mode as there is no number that appears more than other numbers in the set.
why is it not possible to make a right triangle using lengths of 10 feet, 60 feet, and 65 feet ?
Answer:
the answer is C
Step-by-step explanation:
Please help me I need help with answer
Answer:
+30 + -25
Savings is positive
Buying is negative
Step-by-step explanation:
We save 30 dollars
+30
We buy a game for 25
-25
+30 -25
Savings is positive
Buying is negative
Find the area of the figure shown below and type your result in the empty box.
Answer:
Area =
b1 + b2 ×h
2
=
10 + 10 × 10
2
= 100 feet2
Step-by-step explanation:
Find the exact circumference of a circle with an area equal to 36π sq. in.
1. 12π
2. 18π
3. 324π
Answer:
C = 12 pi
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
36 pi = pi r^2
Divide each side by pi
36 = r^2
Take the square root of each side
sqrt(36) = sqrt (r^2)
6 =r
We can find the circumference
C = 2 * pi *r
C = 2* pi *6
C = 12 pi
Answer:
first option
Step-by-step explanation:
Dominick drew a triangle on a map connecting his house, his school, and his favorite skate park. He used a scale on the map to determine that the height of the triangle that he drew represented 2 miles, and the base of the triangle that he drew represented 6 miles. What is the area of the triangle in square miles?
A triangle has points House, skate park, school. The height of the triangle is 2 miles and the base is 6 miles.
Use the formula for the area of a triangle, A = one-half b h, where A is the area of the triangle, b is the base, and h is the height.
Square miles
A farmer plants corn and soybeans. This model shows the area reserved for each.
A model with 4 rows of 5 squares that represent corn and 4 rows of 3 squares that represent soybeans. Corn is 20 acres and soybeans is 12 acres.
(sorry theirs no picture)
Which expression is equivalent to the sum of the two areas?
4(5)(3)
5(4 + 3)
4(5 + 3)
(4 + 5)(4 + 3)
Answer:
C) 4 (5+3)
Step-by-step explanation:
Iceberg lettuce is grown and shipped to stores for about 50 cents a head, and consumers purchase it for about 120 cents a head. Find the percent increase.
ANSWER FAST PLEASE
Final answer:
The percent increase in the price of iceberg lettuce is 140%.
Explanation:
To find the percent increase, we need to calculate the difference between the price at which iceberg lettuce is grown and shipped and the price at which consumers purchase it, and then divide that difference by the original price and multiply by 100.
Let's start by finding the difference:
Difference = Consumer price - Production price
Difference = 120 cents - 50 cents = 70 cents
Now, let's calculate the percent increase:
Percent Increase = (Difference / Production price) * 100
Percent Increase = (70 cents / 50 cents) * 100 = 140%
-9
- 12 square root of 3
Answer:
b = 9
Step-by-step explanation:
A= 30° a = 3[tex]\sqrt{3x}[/tex]
B = b =
C = 90° c =
find B first
90 + 30 = 120
180 - 120 = 60
B = 60°
Now, let's find b
use the Law of Sines
[tex]\frac{sin A}{a} = \frac{sin B}{b} \\\frac{sin 30}{3\sqrt{3} } = \frac{sin 60}{b}\\b = \frac{3\sqrt{3} sin 60 }{sin 30}\\b = 9[/tex]
3. Liam has a rectangular back
yard. He measured one side of the
yard and found it to be 85 feet and its
diagonal to be 117 feet. Determine, to
the nearest tenth of a foot, the length
of the other side of his back yard
Answer:
Length of the other side of the backyard is 80.4 feet.
Step-by-step explanation:
Let the dimensions of the Liam's rectangular backyard = 85 feet × a feet
Diagonal of the rectangle, AD = 117 feet
When we apply Pythagoras theorem in ΔABD,
AD² = AB² + BD²
(117)² = (85)² + BD²
a² = 13689 - 7225
a = √6464
= 80.399 feet
a ≈ 80.4 feet
Therefore, length of the other side of the backyard is 80.4 feet.
hiya! any help is appreciated!
solve the equation x-8=3x
Answer:
x = -4
Step-by-step explanation:
x - 8 = 3x
First, subtract x from both sides:
x - 8 = 3x
-x - x
________
-8 = 2x
Then, divide both sides by 2:
-8 = 2x
-4 = x
Which elevation is lowest?
-80 m
220 m
-120 m
45 m
Answer:
I think its -120m
Step-by-step explanation:
Coz negatives are less than positives
In a clothing store, 75% of the customers buy a shirt, 20% of the customers buy a pair of pants, and 15% of the customers by both the shirt and a pair of pants. If a customer is chosen at random what is the probability that he or she buys a shirt or a pair of pants?
Answer:
80%
Step-by-step explanation:
75% + 20% - 15% = 80%
The probability is 80%
The probability that he or she buys a shirt or a pair of pants is 80%.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that in a clothing store, 75% of the customers buy a shirt, 20% of the customers buy a pair of pants, and 15% of the customers buy both the shirt and a pair of pants.
The percentage of customers who buy only shirt = 75% - 15% = 60%
The percentage of customers who buy only pant= 20% - 15% = 5%
The percentage of customers who buy both = 15%
Now, the probability that he or she buys a shirt or a pair of pants is,
Probability = 60% + 5% + 15% = 80%
Hence, the probability that he or she buys a shirt or a pair of pants is 80%.
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Mr. Falcone’s pizza shop offers three sizes of pizza. The large pizza has a diameter 12 inches. What is the area of the large pizza in terms of pi ?
Answer:
37.68
Step-by-step explanation:
12 times 3.14
hope this helps
Answer:
113.04
Step-by-step explanation:
The diameter is 12 which means the radius is 6
The formula to find the area of a circle is A=π r²
r²=36
π=3.14
3.14×36=113.04
So your answer is 113.04
If angle B measures 120 degrees, find
the Q
A.30 degrees
B.60 degrees
C.120 degrees
D.90degrees
Answer:
C. 120°
Step-by-step explanation:
There are two paralell lines, one is part of Angle B, and the other of Angle Q. Then there is a diagonal line, coming at the same angle from B all the way to Q, because the other two lines are paralell. It basically means if you were to slide the flat line which is connected to Q up the diagonal line, it would fit perfectly with it's parallel. So the two angles; Angle B and Angle Q; are the exact same.
Hope this helped! Good luck with future math problems :)
Answer:
The answer for this question is 120 degrees
Step-by-step explanation:
The triangle shown below has an area of 25 units squared. What is the missing height?
Answer:
height = 5
Step-by-step explanation:
If area = (1/2)bh, the equation would be 25 = (1/2)10h.
The first step I'd do is multiply both sides by 2 to get rid of the (1/2). So, now the equation is 50 = 10h.
Divide both sides by 10, and you get h = 5! :D
Answer:
x=5 unitsStep-by-step explanation:
Given:
A= 25
b=10
Find the height:-
[tex]\sf A=0.5\:bh[/tex]
[tex]\sf 25=0.5(10)h[/tex]
[tex]\sf 25=5h[/tex]
[tex]\sf 5h=25[/tex]
[tex]\sf \cfrac{5h}{5}=\cfrac{25}{5}[/tex]
[tex]\sf h=5[/tex]
Hope it helps!