The algebraic properties used in the steps are the distribution property, the associative property, the identity property, and the distribution property
How to justify each step by identifying the property used?The first step in the equation is given as:
t + 5(t + 1) = t + (5t + 5)
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = t + (5t + 5) is the distribution property
Next, we have:
t + 5(t + 1) = (t + 5t) + 5
The associative property states that
a + (b + c) = (a + b) + c
So, the property used in t + 5(t + 1) = (t + 5t) + 5 is the associative property
Next, we have:
t + 5(t + 1) = (1t + 5t) + 5
The identity property states that
a * 1 = a
So, the property used in t + 5(t + 1) = (1t + 5t) + 5 is the identity property
Next, we have:
t + 5(t + 1) = (1 + 5)t + 5
The distribution property states that
a(b + c) = ab + ac
So, the property used in t + 5(t + 1) = (1 + 5)t + 5 is the distribution property
Lastly, we have the solution
(6t + 5)
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What is the value of -7 + a, if the value of a is -3?
Answer:
[tex] \sf \large \: - 10[/tex]
Step-by-step explanation:
−7+a
Evaluate for a=−3
−7+−3
=−10
Answer:
-10 given a = -3
Step-by-step explanation:
-7 + -3 = -10
Hope this helps! :)
The product of two consecutive positive integers is 110. Find the value of the lesser
integer.
Rewrite x4y2 − 6x3y3 using a common factor.
1: x2y2(x2 − 6xy)
2: x2y(xy − 6xy2)
3: 6xy(x3y − x2y)
4: 6xy2(x2 − x2y)
The value of expression by using common factor is x³y² (x - 6y).
Here,
The expression is,
x⁴y² - 6x³y³
We have to solve by using common factor.
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Now,
The expression is,
x⁴y² - 6x³y³
By using common factor we solve as,
x⁴y² - 6x³y³ = x*x*x*x*y*y - 6*x*x*x*y*y*
= x³y² (x - 6y)
Hence, The value of expression by using common factor is x³y² (x - 6y).
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2 Shape 1 and Shape 2 are congruent pentagons.
Shape 1
Shape 2
Shape 2 is congruent to Shape 1 because -
A.
Shape 2 is a translation of Shape 1.
B. Shape 2 is a reflection of Shape 1.
C. Shape 2 is a rotation of Shape 1.
D. Shape 2 and Shape 1 are both pentagons.
Option B) is correct that is shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
We know that two figures or objects are congruent if they have the same shape and size or they are the mirror image of each other.
Translation : It simply means moving. Every point should be moved in same distance and in same direction
Rotation : It means turning around a center.
Reflection : In this, the image is of the same size as the pre-image.
So according to the given figure we can see that the shape is not translated or rotated from a center but is reflected as shape 1 is the image of shape 2.
Hence shape 2 is congruent to shape 1 because shape 2 is reflection of shape 1.
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tracy bought a new flat-screen television. one side of the television screen is 49 inches and the other side is 27 inches..
The new flat screen television that Tracy bought has a diagonal length of 56 inch
With the information given we can calculate the diagonal length of the television using the Pythagorean theorem equation.
The formula and the procedure that we have to use is:
h2= a2 + b2
Where:
h= hypotenusea= minor sideb = major sideInformation about the problem:
h = ?b = 49 inchesa = 27 inchesApplying the Pythagorean theorem and finding the variable, we get:
h² = a² + b²
h² = (27 inch)² + (49 inch)²
h² = 729 inch² + 2401 inch²
h² = 3130 inch²
h = [tex]\sqrt{}[/tex]3130 inch²
h = 55.95 inch rounding up we get 56 inch
What is the Pythagorean theorem?It is a mathematical equation that relates the three sides of a right angled triangle (major side, minor side and hypotenuse) and states that the sum of the squared sides equals the squared hypotenuse. Its general equation is:
h² = a² + b²
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Carol is baking cookies and needs 2/1/4 cups of flower 2/3 cups with sugar 1/4cups of brown sugar and 1/16 cups of baking soda use the information to answer the following question
Answers
3/8
2/3
2
2/2/3
The quotient when we divide the amount of white sugar by the brown sugar will be 2 2/3
How to calculate the value?From the information, it was stated that Carol is baking cookies and needs 2/1/4 cups of flower 2/3 cups with sugar 1/4cups of brown sugar and 1/16 cups of baking soda.
The quotient when we divide the amount of white sugar by the brown sugar will be:
= 2/3 ÷ 1/4
= 2/3 × 4/1
= 2 2/3
Therefore, the quotient is 2 2/3.
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Carol is baking cookies and needs 2 1/4 cups of flour 2/3 cup of white sugar 1/4 cup of brown sugar and 1/16 cup of baking soda use this information to answer the following questions
divide the amount of white sugar by the amount of brown sugar. what is the quotient? (must be a fraction)
Find the product of 18.6 and 3
Answer: 55.8 Hope this helps, please consider making me Brainliest.
Step-by-step explanation:
18.6 * 3 = (18 * 3) + (0.6 * 3) =
54 + 1.8 =
55.8
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Answer:55.6
Step-by-step explanation:
55.6
80,000 as a scientific notation?
Find the missing fraction.
5|2
13
adoncia makes a scale drawing of the front of the lincoln memorial she uses a scale of 15 ft in the monument to 1 in In the drawing the front of the monument is about 80ft high and 200ft long will adoncia drawing fit on an 8 1/2 in by 11 in sheet of paper
No, the Adoncia drawing will not fit on the drawing sheet.
Given adoncia is drawing to scale, she uses a 15-foot scale in the 1-inch monument. And in the drawing, the front of the monument is about 80 feet high and 200 feet long.
The given parameters are;
The scale of the drawing in the front of the monument is 15 ft = 1 in.
Actual size of the monument;
Height = 80 feet
Length = 200 feet.
So we have;
Required size of paper height = 80/15 = 16/3 = 5.33 in.
Required size of paper length = 200/15 = 40/3 = 13.33 in.
The size of the paper is 11 in. about the size of a standard 8.5-inch sheet of letterhead. equals 11 in.
Design length, 13.33" > Paper length > 11".
Therefore, when Adoncia draws a scale drawing of the front of the linco and she uses the 15ft scale in the 1in monument, the drawing does not fit on the paper.
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The average rain in Annette, Alaska, in September is 0.31 inch per day. How much rain falls over the course of an average September? (September has 30 days)
Answer:
9.3
Step-by-step explanation:
If it rains 0.31 in per day and there is 30 days in September that means you need to MULTIPLY0.31
× 0.30
-----------------
0.30
9.30
-----------
9.6
Alisa drove from her house to the beach at a speed of 55 miles per hour. If it took her 1.8 hours to get to the beach, about how many miles away from the beach is Alisa's house?
Alisa's house is about 99 miles from the beach
What is speed?Speed is the distance travelled per unit. Mathematically, it can be expressed as:
Speed = distance / time
With above formula, we can determine the distance of Alisa's house from the beach. Details below
How to determine the distanceThe following data were obtained from the question:
Speed = 55 miles per hourTime = 1.8 hoursDistance =?The distance of Alisa's house from the beach can be obtained as followed:
Speed = distance / time
Cross multiply
Distance = speed × time
Distance = 55 × 1.8
Distance = 99 miles
Thus, Alisa's house is about 99 miles from the beach
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The distance between the beach and Alisa's house is 99 miles.
About how many miles away from the beach is Alisa's house?Here we need to use the general relation:
Distance = Speed*Time.
Here we know that Alisa's speed is 55 miles per hour, and she drives for 1.8 hours, then we can replace:
Speed = 55 mi/h
Time = 1.8 hours
Replacing that in the distance relation we will get:
D = (55 mi/h)*(1.8 h)= 99 mi
The distance between the beach and Alisa's house is 99 miles.
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find the error javier claimed that all cubic functions are odd. is he correct? if not, provide a counterexample.
Answer:
The cubic function f(x) = x3 is symmetric about the origin (it is an odd function). Here are some types of functions that are odd: Lines Through The Origin – any line with a zero y intercept (b = 0) and a nonzero slope (m not zero) will have equation f(x) = mx.
Step-by-step explanation:
Answer: No
f(x) = x³ + 2x − 5
Step-by-step explanation:
No
f(x) = x³ + 2x − 5
The volleyball team had to play quite a bit last week. they practiced .5 hours on monday, 1.3 hours on tuesday, 2.2 hours on wednesday and .8 hour on thursday. if they wanted to practice a total of 6 hours last week, how many hours did they end up practicing on friday?
The volleyball team ended up practicing for 1.2 hours on Friday.
The total number of hours the volleyball team practiced on Monday, Tuesday, Wednesday, and Thursday can be determined by adding the values given in the statement.
Therefore,
the total number of hours the team practiced on Monday, Tuesday, Wednesday, and Thursday=0.5 hours+1.3hours+2.2hours+0.8hours= 4.8 hours
Total number of hours the team practiced last week = 6 hours
The number of hours they practiced on Friday can be calculated by subtraction of the total number of hours of the week from the total number of hours on Monday, Tuesday, Wednesday, and Thursday.
Hence, the number of hours the team practiced on Friday = 6 - 4.8= 1.2 hours.
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can someone please help me? i’ve been struggling with factoring for a little bit now.
Factor.
81-22
Answer:59
Step-by-step explanation:
81-22=59
answer is 59 because 59 is a prime number
help pls i don’t know this
guys help please. Enter the value for x that makes the equation 5x-2+3+-7 HELP
Step-by-step explanation:
5x-2+3-7
0=5x-9+3
0=5x-6
6=5x
x=6/5
rita, john, and kareem sent a total of 92 text messages during the weekend. kareem sent 4 times as many messages as rita. john sent 10 fewer messages than rita. how many messages did they each send?
Rita, John, and Kareem sent 17, 7, and 68 messages, respectively.
Use algebraic expressions to solve this problem.
Let x, y, and z be the number of messages sent by Rita, John, and Kareem, respectively.
If Rita, John, and Kareem sent a total of 92 text messages during the weekend, then:
x + y + z = 92
If Kareem sent 4 times as many messages as Rita, then:
z = 4 * x
z = 4x
If John sent 10 fewer messages than Rita, then:
y = x - 10
Evaluating z = 4x and y = x - 10 to the first equation:
x + y + z = 92
x + (x - 10) + 4x = 92
x + x - 10 + 4x = 92
6x = 92 + 10
6x = 102
x = 17
Recall that y = x - 10:
y = 17 - 10
y = 7
And z = 4x:
z = 4(17)
z = 68
If x, y, and z are the number of messages sent by Rita, John, and Kareem, respectively, then Rita, John, and Kareem sent 17, 7, and 68 messages, respectively.
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Over a period of 12 hours the temperature dropped 36 F. What was the average change in temperature in one hour?
An electrically neutral atom of beryllium has four protons. Which statement is true? There are four protons in the nucleus. There is a charge of −4 on an atom of beryllium. There are four neutrons in the nucleus. There is a charge of +4 on an atom of beryllium.
The right answer is that there are four electrons.
What is an atomic number?The charge number of an atomic nucleus is the chemical element's atomic number, also known as the nuclear charge number.
For conventional nuclei, this is comparable to the proton number, or the number of protons found in the nucleus of each atom of that element.
Equal numbers of protons and electrons make up a neutral atom. This figure establishes the atom's atomic number.
The fourth element on the periodic table is beryllium.
Number of protons in Be-atom = 4
Number of electrons in Be-atom = 4
Therefore, it is true that there are four electrons.
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-8w > -6/5 What is the answer
Answer:
51
Step-by-step explanation:
Can anyone find the value of x and y from the given figure?:
Answer:
little tricky question but i managed to do it..
Alang has a points card for a movie theater.
He receives 55 rewards points just for signing up.
• He earns 3.5 points for each visit to the movie theater.
• He needs 83 points for a free movie ticket.
How many visits must Alang make to earn a free movie ticket?
The number of visits that Alang makes to earn a free movie ticket will be 8.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Alang has a rewards card at a cinema.
The mere act of joining up earns him 55 reward points.
Every time he enters a movie theater, he receives 3.5 points.
To receive a free movie ticket, he needs 83 points.
Let x be the number of visits. Then the equation is given as,
3.5x + 55 = 83
Simplify the equation, then the value of x will be
3.5x = 83 - 55
3.5x = 28
x = 28 / 3.5
x = 8
The number of visits that Alang makes to earn a free movie ticket will be 8.
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Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
the distance a falling object travels towards the earth is directly proportional to the square of the time that it falls. if an orange falls 16 feet in 4 seconds, how far will it fall in 8 seconds ?
The orange will fall 64 feet in 8 seconds.
Distance:
Distance is defined as how much ground an object has covered despite its starting or ending point.
Given,
The distance a falling object travels towards the earth is directly proportional to the square of the time that it falls.
And an orange falls 16 feet in 4 seconds.
Here we need to find the how far it will fall in 8 seconds.
Based on the given details,
We know the that distance is,
D = kt²
where
k is the constant of proportionality.
To find the value of k we have to apply the given values on the equation.
=> 16 = k x (4)²
=> 16 = k x 16
=> k = 16/16
=> k = 1.
So, in 8 seconds it will fall at
=> D = 1 x (8)²
=> D = 1 x 64
=> D = 64 feet.
Therefore, the orange will fall at 64 feet in 8 seconds.
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shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. the area of the enlarged photo is 256 square inches. in the equation (x 10)2
The dimensions of the original photo are 6 x 6.
What is an area?A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
The formula for a square's area, A = s², is the side length raised to the power of two. The 256 in2 section of the larger image was made available to us. Additionally, it was mentioned that the length of the expanded image is equal to the original image's length plus ten inches.
We can therefore create an equation to solve for x, which stands for the length of the original snapshot, based on the aforementioned statements.
A = s²
where s = ( x + 10 )
A = ( x+10 )² = 256
Solving for x,
x = 6 in.
The dimensions of the original photo are 6 x 6.
The complete question is given below:-
Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. The area of the enlarged photo is 256 square inches. In the equation (x + 10)2 = 256, x represents the side measure of the original square photo. What were the dimensions of the original photo?
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Multiply (4x^2 +8)^2
Answer:
5/2 or 2.5
Step-by-step explanation
Five over two or two and 5 tenths
Write an compound inequality for the following graph.
The compound inequality for the graph is -5 ≤ x ≤ -1
How to write a compound inequality for the following graph?On the graph, we have the following endpoints
Endpoint 1 = -5 (closed circle)Endpoint 2 = -1 (closed circle)Also, the region between endpoints is shaded.
This means that the endpoint is a union inequality
So, we have the compound inequality to be
Endpoint 1 ≤ x ≤ Endpoint 2
This gives
-5 ≤ x ≤ -1
Hence, the compound inequality for the graph is -5 ≤ x ≤ -1
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A. A person goes from a sauna at 1208F to an outside temperature of -208F. What is the change in temperature
The change in temperature should be 1208 - (-208).
Rewrite 20 − 4x^3 using a common factor.
4x(5 − x^2)
4(5 − 4x^3)
2x(10 − 2x^2)
2(10 − 2x^3)
Answer:
4x(5 − x^2)
Step-by-step explanation:
20 − 4x^3
= 4x(5 − x^2)
The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
What is Mathematical expression?
The combination of numbers and variables by using sign addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression is;
⇒ 20 - 4x³
Now, Take common factor as;
⇒ 20 - 4x³ = 2 × 10 - 2 × 2x³
= 2 (10 - 2x³)
Thus, The equivalent expression after taking a common factor is,
⇒ 2 (10 - 2x³)
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2 l2x+7l = 16
Please help me with this ASAP
Answer:
x = 1/2 and
x = -15/2
Step-by-step explanation:
First, get the absolute value alone on one side if the equation.
2 |2x + 7 | = 16
Divide both sides by 2.
| 2x + 7 | = 8
Once the absolute value sign is by itself, you will separate the equation into two separate equations.
2x+7=8 and 2x+7=-8
Solve these two equations separately and get two solutions.
2x + 7 = 8
Subtract 7.
2x = 1
Divide by 2.
x = 1/2 Here is one solution.
2x + 7 = -8
Subtract 7.
2x = -15
Divide by 2.
x = -15/2 Here is a second solution.
Answer:
x = - [tex]\frac{15}{2}[/tex] , x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
2 | 2x + 7 | = 16 ( divide both sides by 2 )
| 2x + 7 | = 8
the absolute value function always gives a positive result, but the expression inside can be positive or negative , that is
2x + 7 = 8 ( subtract 7 from both sides )
2x = 1 ( divide both sides by 2 )
x = [tex]\frac{1}{2}[/tex]
or
- (2x + 7) = 8
- 2x - 7 = 8 ( add 7 to both sides )
- 2x = 15 ( divide both sides by - 2 )
x = - [tex]\frac{15}{2}[/tex]
As a check
substitute these values into the left side and if equal to the right side then they are a solution
x = [tex]\frac{1}{2}[/tex]
2 | 2([tex]\frac{1}{2}[/tex] ) + 7 | = 2 | 1 + 7 | = 2 | 8 | = 16 = right side
x = - [tex]\frac{15}{2}[/tex]
2 | 2(- [tex]\frac{15}{2}[/tex] ) + 7 | = 2 | - 15 + 7 | = 2 | - 8 | = 2 | 8 | = 16 = right side
then x = - [tex]\frac{15}{2}[/tex] and x = [tex]\frac{1}{2}[/tex] are the solutions