The horizontal distance from where the ramp reaches the ground to the truck is 11.9 feet.
Scott is using a 12-foot ramp to help load furniture into the back of a moving truck.
If the back of the truck is 3.5 feet from the ground,
Round to the nearest tenth.
The horizontal distance is 11.9 feet.
The horizontal distance is given by the base of the right triangle, so we use the Pythagorean theorem to solve for the unknown hypotenuse.
c² = a² + b²
where c = 12 feet (hypotenuse),
a = unknown (horizontal distance), and
b = 3.5 feet (height).
We get:
12² = a² + 3.5²
a² = 12² - 3.5²
a² = 138.25
a = √138.25
a = 11.76 feet
≈ 11.9 feet (rounded to the nearest tenth)
The correct answer is 11.9 feet.
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Square each binomials and place them into perfect square trinomial form, then subtract the trinomial
1 (x + 3) 2 - (x - 4) 2
2 (7b2 - 7) 2 - (2b2 - 11) 2
3 (5ab2 + 3) 2 - (6ab2 - 7) 2
The results of subtractions between perfect square trinomials are listed below:
(x + 3)² - (x - 4)² = 14 · x - 7 (7 · b² - 7)² - (2 · b² - 11)² = 45 · b⁴ - 54 · b² - 72 (5 · a · b² + 3)² - (6 · a · b² - 7)² = - 9 · a² · b⁴ + 114 · a · b² - 40How to simplify subtractions of perfect square trinomials
In this problem we have three cases of subtractions between two perfect square trinomials that must be simplified. According to algebra, perfect square trinomials can be expanded by means of the following definition:
(a + b)² = a² + 2 · a · b + b²
Where a, b are real constants.
The procedure is summarized below:
Expand the perfect square trinomials.Add and subtract similar terms.Arrange the resulting polynomial in standard position.Case 1
(x + 3)² - (x - 4)²
(x² + 6 · x + 9) - (x² - 8 · x + 16)
x² + 6 · x + 9 - x² + 8 · x - 16
14 · x - 7
Case 2
(7 · b² - 7)² - (2 · b² - 11)²
(49 · b⁴ - 98 · b² + 49) - (4 · b⁴ - 44 · b² + 121)
49 · b⁴ - 98 · b² + 49 - 4 · b⁴ + 44 · b² - 121
45 · b⁴ - 54 · b² - 72
Case 3
(5 · a · b² + 3)² - (6 · a · b² - 7)²
(25 · a² · b⁴ + 30 · a · b² + 9) - (36 · a² · b⁴ - 84 · a · b² + 49)
25 · a² · b⁴ + 30 · a · b² + 9 - 36 · a² · b⁴ + 84 · a · b² - 49
- 9 · a² · b⁴ + 114 · a · b² - 40
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Write an equation in standard form with an x-intercept of 5 and a y-intercept of -4
An equation in standard form with an x-intercept of 5 and a y-intercept of -4 is,
⇒ 5x + 4y = 20
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The x - intercept = 4 ,
So, ( 4,0) is a point on the line.
And, The y - intercept = 5,
So, ( 0, 5) is a point on the line.
Now, Slope of the line passing through the point (4, 0) and (0, 5) is,
⇒ m = (5 - 0) / (0 - 4)
⇒ m = - 5/4
So, The slope intercept form of an equation is,
⇒ y = mx + b
Where, m = slope and b = y- intercept.
Hence, We get;
⇒ y = - 5/4x + 5
We know that;
An equation in standard form is,
⇒ Ax + By = C
So, We get;
⇒ y = - 5/4x + 5
⇒ 4y = - 5x + 20
⇒ 5x + 4y = 20
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Solving Equations
solve for the variable in each of the following equations. Write your final solution as an equation
please tell me the answer to each 4
The solution for given equations are: z = 4, b = -12, w = 5, c = -11
What is mean by equations? How can be solve variables?An equation is a mathematical statement that expresses the equality of two expressions.
Variables are symbols or letters used to represent unknown values in equations.
To solve for a variable, one must first isolate the variable by performing the same operations on both sides of the equation until the variable is alone on one side of the equation.
For example, if the equation is 2x + 4 = 10, the first step would be subtracting 4 from both sides of the equation to get 2x = 6. The next step would be to divide both sides of the equation by 2 to get x = 3. This is how one would solve for the variable in this equation.
According to question:-
A. 3(7z-6)=-(-18z+6)
21z - 18 = 18z - 6
3z = 12
z = 4
B. -8b+2(-5b-2)=212
-8b - 10b - 4 = 212
-18b - 4 = 212
b = -12
C. 4/5w+5 = 1/5w+8
4/5w-1/5w = 8-5
3/5w = 3
w = 5
D. (-c-8)-(7c-6)= 18c+284
-c-8-7c+6 = 18c + 284
18c + 8c = -2-284
26c = -286
c = -11
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Two ships are sailing parallel to each other. the path of one ship is represented on a coordinate plane as the line y = –13x 4. the second ship’s path passes through the point (3, 5). select another point that the path of the second ship passes through.
The second ship's route also goes through another site, which is (0, 44)
What is Slope?
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope.
In the coordinate plane, it describes the slope of the line.
Finding the slope between two separate points and calculating the slope of a line are related tasks.
In general, we require the values of any two separate coordinates on a line in order to determine its slope.
According to our question-
Parallel lines have equal slopes.
Therefore,
m₁ = m₂
The equation for one ship's trajectory is
y = - 13x + 4
utilizing the slope-intercept model
y = mx + b
m = -13
slope = -13
The second vessel sails by the points (3, 5). The second argument could be
located below. Remember that they share a slope.
Therefore,
y = -13x + b
using (3, 5) b, the following is obtained:
5 = -13(3) + b
5 = -39 + b
5 + 39 = b
b = 44
The second ship's equation will be as follows:
y = -13x + 44
y = -13(0) + 44
y = 44
The key could be (0, 44)
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Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
The triangle can be constructed from sides of triangle measuring 3.5 cm 9.2 cm and 5.3 cm due to side rule of triangle.
The possibility to construct the triangle will be found out through the sum of any two sides of triangle. If the sum is greater than the remaining side of the triangle, the construction is possible. Let us assume the side a, b and c of triangle to be 3.5, 9.2 and 5.3 cm.
Now, using the side-side-side rule of triangle -
Side a + side b > side c
3.5 + 9.2 > 5.3
Add the values
12.7 > 5.3
Side b + side c > side a
9.2 + 5.3 > 3.5
Add the values
14.5 > 3.5
side c + side a > side b
5.3 + 3.5 > 9.2
Add the values
8.8 not greater than 9.2
Based on the results, the construction of triangle from mentioned sides is possible according to length rule of the triangle.
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The temperature in Coldspot is 4 Fand is increasing 2.5 Fper hour The temperature in Frostberg is 30 and is decreasing 4 Fper hour a, How long will it be until the temperatures are the same? What will the temperature be then?
Answer:
Step-by-step explanation:
Which question can be answered by finding 4
You have 4 pounds of fruit and use pound. How much fruit is remaining?
How much is of 4 pounds of fruit?
CLEAR
You are buying pound containers of fruit at the store. How many containers do you need to buy to have 4 pounds of truit? Please hely
The question that can be answered by finding 4 1/2 ÷ 1/4 is this:
C. You are buying 1/4 pound containers of fruits at the store. How many containers do you need to buy to have 4 1/2 pounds of fruit?
What expression does the question represent?The expression that is best represented by the question is statement C. Here, we are told to find how many containers we need to buy 4 1/2 pounds of fruit.
Let's assign the figure x to the number of containers we are to find. So,
1/4x = 4 1/2
Divide both sides by 1/4 to find x
x = 4 1/2 ÷ 1/4
Option C is the right answer.
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which number is a factor of the prime factorization of 60?
Answer:
Step-by-step explanation:
So, the prime factorisation of 60 is 2 × 2 × 3 × 5 or it can be written as 22 × 3 × 5. where 2, 3 and 5 are prime numbers.
What should be added to 2x2 xy 2y2 to obtain 3x2 5xy?
To obtain 3x² + 5xy from 2x² + 2xy², you would need to add the polynomial x² + 5xy to the original expression.
In order to add two polynomials together, the terms must have the same degree and variable. In this case, we see that 2x^2 and 2xy^2 have different degrees and variables. So, we need to find a polynomial that when added to 2x² + 2xy² will give us 3x² + 5xy.
To do this, we can start by looking at the x² term in 3x² + 5xy. We can see that we need to add x² to our original polynomial. Next, we can look at the xy term in 3x² + 5xy. We can see that we need to add 5xy to our original polynomial.
So by adding x² + 5xy to 2x² + 2xy², we get the desired polynomial of 3x² + 5xy.
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The complete question is:
What should be added to 2x² + 2xy² to obtain 3x² + 5xy.
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What is a 3 action sequence?
A 3 action sequence is a set of three actions that are related and follow one another in a logical order.
It is a technique used to break down complex tasks into smaller, more manageable steps. For example, if you want to cook a meal, a 3 action sequence could be: (1) gather ingredients, (2) prepare ingredients, and (3) cook meal. Each of these three steps is related and follows the one before it.
The 3 action sequence is a great tool for breaking down complicated tasks into more manageable parts. It can help you stay on track and keep focus when working on a task. It can also be used to create a timeline for completing a task, or to create a checklist of items that need to be completed.
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Is 4 6 and 2 3 equivalent?
So we can write 4/6 as equivalent to 2/3
What is Equivalent ?Equal is not the same as equivalent. While comparable indicates similar but not the same, equal means the same in all respects. For instance, 1 + 1 is comparable to 2, even if 2 is supposed to be equal to 2.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 1/2, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.
So , 4/6 can be written as 2*2/3*2 = 2/3
So we can write 4/6 as equivalent to 2/3
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The spring musical cost $600 for costumes and $450 for the stage materials.
If the spring musical cost $600 for costumes and $450 for the stage materials. the number of tickets is 56 tickets.
How to find the number of tickets?Total ticket = $600 + $450
Total ticket = $1050
Now let find the number of tickets that they have to sell to profit.
Number of tickets = $1,050 - $375 / $12
Number of tickets = $675/$12
Number of tickets = 56 tickets
Therefore the number of tickets is 56 tickets.
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The complete question is:
The spring musical cost $600 for costumes and $450 for the stage materials.
Students raised $375 from advertisements in the program. Tickets cost $12 each.
How many tickets do they have to sell to profit?
i need my question and i dont feel like watching all of these ads to get the answer
Answer:
ok whats the question
Step-by-step explanation:
The sum of two numbers is 10 and the difference of those two
numbers is 18. (Usef to represent the first number and s to represent
the second number.)
how do I find out if a table is linear or non linear
Answer:
In the case of the classification problem, the simplest way to find out whether the data is linear or non-linear (linearly separable or not) is to draw 2-dimensional scatter plots representing different classes. Here is a picture that represents the linearly and non-linearly separable dataset and how one can use scatter plots to visualize them.
Step-by-step explanation:
match each system of equations with the number of solutions the system has
solutions are :
one solution
no solution
infinitely many solutions
(6x -7) +(-4x - 8) simplified
Answer:
2x−15
Step-by-step explanation:
6x−7−4x−8
=6x+−7+−4x+−8
Combine Like Terms:
=6x+−7+−4x+−8
=(6x+−4x)+(−7+−8)
=2x+−15
Suppose the x and y vary inversely and x=1 when y=3. wrote a function that models that models the inverse variation. graph the function and find when x=5
The value of y= 1.6667 when x= 5.
The graph is attached below.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
x= 1 when y=3, if x and y vary inversely.
Then, x = k/y
where is proportionality constant
So, k = x y
k = 3
Using Proportion
x/ y = k
5/y= 3
y= 5/3
y= 1.6667
Hence, y= 1.6667 when x= 5.
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What are the types of substitutions?
Answer:
"Substitution comes in three flavors: nominal, verbal, or clausal, depending on the item being substituted.
Step-by-step explanation:
Hope it helps!
Number of Houses Sold
The graph below shows the number of houses sold over x days. What is the average rate of change from day 2 to day
10?
y
(2,8)
(0,0)
2
House Sales
(6.6)
f(x)
(12,4)
(10,2)
4
6 8 10
Number of Days
12
INING
X
02:39:25
The average rate of change from day 2 to day 10 is given as follows:
-0.75 houses sold per day.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The points of interest are given as follows:
(2,8) and (10,2).
The change in the output is of:
2 - 8 = -6.
The change in the input is of:
10 - 2 = 8.
Hence the average rate of change is obtained as follows:
r = -6/8
r = -3/4
r = -0.75 houses sold per day.
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What is the intersection of plane TUY and plane VUY?
The intersection of plane TUYX and plane VUYZ is found as UY.
Define the term intersection of plane?In geometry, a plane is a flat plate that, from all angles, extends to infinity. Non-parallel planes that intersect together in line are known as intersecting planes. A line is formed by the connection of two planes. The planes are parallel if they do not intersect. Due to the endless nature of planes, they cannot connect at a single place.For the stated question-
According to the supplied figure, TUYX is one side of both the rectangular prism while UVYZ is its opposite side.
One edge, which is represented by the line segment UY, has both sides intersecting perpendicularly.
It is depicted in the figure.
Thus, UY is the line that intersects as a result.
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The correct question is attached.
Alex is applying for positions at two different electronic stores in neighboring towns. The first job offer is a $200 weekly salary plus 5% commission on sales. The second job offer is a $75 weekly salary plus 10% commission.
The amount of sales at which Company A's offer is the same as Company B's is $600
How to calculate the amount?The given parameters that will help us to understand the question are
Company A:
Base = $200
Commission = 10% of sales = .1*S
A = .1S + 200
Company B:
Base = 400
Commission = .05*S
B = .05S + 400
We're looking for the point where they're equal.
200 + .1S = 400 + .05S
Multiply by 100 to get rid of decimals
20000 + 10S = 40000 + 5S
Subtract 20000 from both sides
10S = 20000 + 5S
Subtract 5S from both sides
5S = 20000
Divide both sides by 5
S = 4000
So, at $4000 sales, the two jobs pay the same.
You have to always check your work. This can be done by plugging the values into the basic equations and determining if they check. Or we can graph the two lines and see where they cross.
Company A:
200 + .1(4000) = 200 + 400 = 600
Company B:
400 + .05(4000) = 400 + 200 = 600
Conclusively Alex (A) offers $600 as same as Company B
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Complete question:
A salesperson has two job offers. Company A offers a weekly salary of $200 plus commission of 10% of sales. Company B offers a weekly salary of $400 plus commission of 5% of sales. What is the amount of sales at which Company A's offer is the same as Company B's?
From Belmont, how much farther is it to Riverside than to Yardley? Use paths shown below
On solving the provided question, we can say that by addition, the distance between Belmont and Yardley is by adding all distances in between them = 9.75+8324 = 17.99 mils
what is addition?The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.
by addition,
the distance between Belmont and Yardley is
by adding all distances in between them = 9.75+8324 = 17.99 mils
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Please answer ill give extra points and brainiest please im begging you, answer both questions please all i need is the answer and a small explanation
(Ignore what i wrote on the paper btw)
The school biology club member want to buy matching shirts to wear on a field trip they needed to determine from which of two stores to purchase the shirts these tables show the total cost including set up fee for purchasing different numbers of the shirt
If you want to buy fewer than 25 shirts, then prefer Shirts By Sam shop. If you want to buy more than 25 shirts, then prefer Might T Shirt shop.
What is an equation?
A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.
Given that:
Shirts By Sam
The cost of 10 shirts is $127.5
The cost of 15 shirts is $168.75.
Assume the equation that represents total cost is y = ax+b
Putting x= 10 and y=127.5 in y = ax+b:
127.5 = 10a+b.....(i)
Putting x= 15 and y=168.75 in y = ax+b:
168.75 = 15a+b.....(ii)
Use elimination method to solve equation (i) and (ii).
Subtract equation (i) from (ii)
15a+b = 168.75
10a+b = 127.5
____________
5a = 41.25
a = 8.25
Putting a=8.25 in equation (i)
127.5 = 10×8.25+b
b = 40
The equation is y = 8.25x+40.
Might T Shirt
The cost of 8 shirts is $137
The cost of 12 shirts is $163
Assume the equation that represents total cost is y = ax+b
Putting x= 8 and y=137 in y = ax+b:
137 = 8a+b.....(iii)
Putting x= 12 and y=163 in y = ax+b:
163 = 12a+b.....(iv)
Use elimination method to solve equations (iii) and (iv).
Subtract equation (iv) from (iii)
8a+b = 137
12a+b = 163
____________
4a = 26
a = 6.5
Putting a=6.5 in equation (iii)
137= 8×6.5+b
b = 85
The equation is y =6.5x+85.
The solution of the system of equations:
y = 8.25x+40 .....(vi)
y =6.5x+85 ......(vii)
Use substitution method to solve equations (vi) and (vii).
Subtract equations:
8.25x+40 - 6.5x-85=0
1.75x - 45 =0
x = 45/1.75
x = 25.71
Putting x = 26 in equations (vi) and (vii)
y = 8.25×26+40 = 254.5
y = 6.5×26+85 = 254
Putting x = 24 in equations (vi) and (vii)
y = 8.25×24+40 = 238
y = 6.5×24+85 = 241
Thus if you buy more than 25 shirts, then prefer Might T Shirt shop.
if you buy fewer than 25 shirts, then prefer Shirts By Sam.
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Use the figures to complete the statements proving the converse of the Pythagorean theorem.
Drag and drop a phrase, value, or equation into the box to correctly complete the proof.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To prove the converse of the Pythagorean theorem, we can define a right triangle, Response area, with sides a, b, and x. Then, we will show that if △ABC is a triangle with sides a, b, and c where a² + b² = c², then it is congruent to △DEF and therefore a right triangle.
By the Pythagorean theorem, because △DEF is a right triangle, a² + b² = x².
If a² + b² = x² and a² + b² = c² , then c² = x². Further, since sides of triangles are positive, then we can conclude that c = x. Thus, the two triangles have congruent sides and are congruent.
If △ABC is congruent to a right triangle, then it must also be a right triangle.
Two right triangles with points labeled in capital letters and sides labeled in lower case letters.
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in familiar algebraic notation, a2 + b2, are equal to the squares on the legs.
Who was Pythagoras' inventor?Greek philosopher Pythagoras made significant contributions to mathematics, astronomy, and music theory. Although the Babylonians were aware of the theorem 1000 years prior to Pythagoras, he may have been the first to demonstrate it.
What is Pythagoras' fundamental tenet?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides, according to a theory put forth by Pythagoras.
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What is quotient formula?
A quotient is a number created when two numbers are divided. The formula for this is Quotient = Dividend ÷ Divisor.
The division is the process of dividing one number by any other number to produce a different number. Consequently, the dividend is the number that is divided in this instance. A number's divisor is the one that divides the given number. The quotient is the number that we get as a result.
Then, the quotient formula is given by Quotient = Dividend ÷ Divisor. For example, 50÷5=10. Here, 50 is the dividend, 5 is the divisor, 10 is the quotient, and 0 is the remainder.
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Angle B= 27, a=28ft, b=18ft solve for measurement(s) of angle c
Answer: In a triangle, the sum of the angles is 180 degrees. Therefore, if we know two of the angles, we can use this property to find the measure of the third angle.
In this case, we are given angle B = 27 degrees and we want to find the measure of angle C. We can use the following equation to find angle C:
Angle B + Angle C + Angle A = 180
27 + Angle C + 90 = 180
Angle C = 180 - 27 - 90
Angle C = 63 degrees
Additionally, we can use the Law of Cosines to find the measure of angle C.
c² = a² + b² - 2ab * cos(C)
c² = 28² + 18² - 2 * 28 * 18 * cos(C)
c² = 784 + 324 - 1008 * cos(C)
c = √(1108 - 1008*cos(C))
We know that cos(C) = (a² + b² - c²) / 2ab
cos(C) = (784 + 324 - c²) / (22818)
We can substitute the value of c² that we obtained from the first equation and find cos(C) and thus angle C.
So the measure of angle C is 63 degrees.
Step-by-step explanation:
Bong's savings in February was P9,500 and his savings in May was
P7,300. What was the percentage decrease in Bong's savings? Solution:
Answer: 23.16%
Step-by-step explanation: 7300/9500 can be simplified to 73/95 which gives us 76.84%. subtract that from 100 and you get 23.16
Meg i making a lit of rule for diviion fill in the blank with the correct anwer to make Meg rule true
If a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero.
As the name suggests, divisibility tests or division rules in Maths help one to check whether a number is divisible by another number without the actual method of division.
Finding the product of two or more corresponding integers is done mathematically through the action of multiplication. It is frequently represented by the letters "x" or "*." In order to discover the result of multiplication, a multiplicand, also known as the multiplicand, is multiplied by a multiplier, also known as the multiplier. The result of the two integers, for instance, is 56 if the multiplicand and multiplier are both 8. A multiplication process always yields a greater number as the outcome than either of the initial factors. Multiply is also used to describe the process of adding a number to itself a certain number of times, as in "7 multiplied by 3 equals 21."
How to solve?
For instance, if the multiplication error is 8 x 7 = 56, then the matching division error 56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.
This connection is true for every multiplication and division problem as long as the numbers are utilised consistently in both operations.
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What value of x will make the triangles similar by the sss similarity theorem brainly.
The value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem states that if three corresponding sides of two triangles are proportional, then the two triangles are similar. This applies to all triangles, regardless of their size or shape.
To use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Once you have this information, you can use the theorem to determine if the two triangles are similar.
It's important to note that to use the SSS similarity theorem, you must know the length of at least three corresponding sides of the two triangles. Without this information, it's not possible to determine if the two triangles are similar.
Therefore the value of x is not given in the question, and it's not possible to determine the value of x that will make the triangles similar by the SSS similarity theorem.
The SSS similarity theorem only states that the two triangles are similar, it doesn't tell anything about the angles of the triangles.
To learn more about SSS similarity theorem, use the link:
brainly.com/question/24167205
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