Answer:
x = 2
Step-by-step explanation:
2x + 15 = 27 - 4x
add 4x to both sides:
2x + 15 + 4x = 27 -4x + 4x
that is 6x + 15 = 27
subtract 15 from both sides:
6x + 15 - 15 = 27 - 15
that is 6x = 12
divide both sides by 6:
x = 2
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{2x + 15 = 27 - 4x }[/tex]
[tex]\mathtt{2x + 15 = -4x + 27}[/tex]
[tex]\large\text{ADD 4x to BOTH SIDES}[/tex]
[tex]\mathtt{2x + 15 - 4x = -4x + 27 + 4x}[/tex]
[tex]\large\text{SIMPLIFY it}[/tex]
[tex]\mathtt{2x + 4x + 15 = 27}[/tex]
[tex]\mathtt{6x + 15 = 27}[/tex]
[tex]\large\text{SUBTRACT 15 to BOTH SIDES}[/tex]
[tex]\mathtt{6x + 15 - 15 = 27 - 15}[/tex]
[tex]\large\text{SIMPLIFY it}[/tex]
[tex]\mathtt{6x = 27 - 15}[/tex]
[tex]\mathtt{6x = 12}[/tex]
[tex]\large\text{DIVIDE 6 to BOTH SIDES}[/tex]
[tex]\mathtt{\dfrac{6x}{6} = \dfrac{12}{6}}[/tex]
[tex]\mathtt{x= \dfrac{12}{6}}[/tex]
[tex]\mathtt{x= 2}[/tex]
[tex]\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{x = 2}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What are the steps in substitution method?
The substitution method is a process used to solve a system of equations. It involves replacing one variable with the expression of the other variable in one equation, and then solving for the remaining variable.
The steps in substitution methodWrite the system of equations in the form Ax + By = C.Choose one of the equations and solve for one of the variables.Substitute the solved variable into the other equation.Solve the new equation.Substitute the solved variable into either equation and solve for the other variable.Check your answer by substituting both values into the original equations.Learn more about Substitution: https://brainly.com/question/22340165
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How do you find the area of a triangle rectangle?
The area of a triangle rectangle can be calculated using the formula A = 1/2 * b * h, where b is the base of the triangle and h is the height.
To calculate the area of a triangle rectangle, first measure the length of the base and the height of the triangle. To calculate the area, first we need to measure the base and the height of the triangle rectangle.Then, multiply the two values together and divide the result by two. For example, if the base of the triangle measures 10 cm and the height measures 8 cm, then the area of the triangle rectangle is 10 cm x 8 cm = 80 cm2, and the area of the triangle rectangle is 80 cm2/2 = 40 cm2.
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How do you find the roots of a polynomial equation of degree 3?
We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial.
what are polynomials?A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.
We must factorize the provided polynomial equation in order to obtain a linear and quadratic equation before we can discover the roots of the three-degree polynomial. The zeros of the three-degree polynomial are then easily ascertainable.
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A pediatric dentist office has a toy chest with 7 puzzles, 4 squishy balls, 5 pairs of play sunglasses, and 9 fidget spinners. If a child is allowed to pick two prizes, without looking and without replacement, then what is the probability that the child will select a pair of sunglasses both times?
The probability that the child will select a pair of sunglasses both times is; 1/25
What is the probability of selection?We are given the contents of the toy chest as;
7 puzzles
4 squishy balls
5 pairs of play sunglasses
9 fidget spinners
Total toy chest = 7 + 4 + 5 + 9
= 25
Probability of first choice being sunglasses = 5/25 = 1/5
Probability of second choice being sunglasses = 5/25 = 1/5
P(two choices being sunglasses) = 1/5 * 1/5 = 1/25
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How do you dilate a triangle with a scale factor of 2 3?
The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.The dilation o a triangle with a scale factor of 2 3 represents a contraction.
How to Dilate a triangle with a scale factor ?
The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the centre of dilatation. The scale factor and the centre of dilation are used to determine the dilation transformation.
The image stretches if the scaling factor is greater than 1.The image contracts if the scale factor is between 0 and 1.The original image and the resulting image are consistent if the scale factor is 1.Finding the dilation's centre point is the first step in determining the scale factor. Next, we measure the distances between the centre point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.
Since each angle is congruent, every segment is proportional, the slope of every segment is preserved, and the perimeter of the preimage and image have the same scale factor, we may use dilation scale factors to compress or enlarge a figure to the size we desire.
Dilate a triangle with a scale factor
Assume that the coordinate plane's centre of dilation is at (0, 0) at the origin. Every coordinate point of the original triangle is multiplied by the scale factor 2/3 if the scale factor is 2/3. multiplying by half after a scale factor of two.
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What is the quotient of the following division problem? x + 2 x + 1 x2 + 3x + 2 0.
The quotient of the division problem is (x + 1)/(x +2). The result is obtained by determining the factors of the two quadratic equations.
How to find the factors of a quadratic equation?The quadratic equation can be expressed as
ax² + bx + c = 0
Where c is a constant.
To find the factors of a quadratic equation, follow these steps!
Find the two numbers that the product is equal to ac and the sum is equal to b.Use them as the common factors and simplify.Find the quotient of (x² + 2x + 1)/(x² + 3x + 2) = 0!
For quadratic equation x² + 2x + 1:
a = 1, b = 2, c = 1.ac = 1The two numbers are 1 and 1 → 1+1 = 2 and 1×1 = 1.The common factors: (x + 1)(x + 1)
For quadratic equation x² + 3x + 2:
a = 1, b = 3, c = 2.ac = 2The two numbers are 2 and 1 → 2+1 = 3 and 2×1 = 2.The common factors: (x + 2)(x + 1)
The quotient of the quadratic equations is
(x² + 2x + 1)/(x² + 3x + 2) = 0
(x + 1)(x + 1)/(x + 2)(x + 1) = 0
(x + 1)/(x + 2) = 0
Hence, the quotient of the quadratic equations is (x + 1)/(x + 2) = 0.
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The pentagonal prism below has a base area of 34 units² and a volume of 180.2 units³
. Find its height.
height of pentagonal prism is h unit.
What is pentagonal prism?
The prism is one that has two pentagonal bases from which one acts as bottom and the other acts as top. The pentagonal prism has five rectangular sides. This prism has 10 vertices and 15 edges. It is also said five-sided polygon prism.
What is the height of prism as stated above?given, area of pentagonal prism = 34 square unit
volume of pentagonal prism = 180.2 cubic unit
we know the formula for the area of the pentagonal prism.
Total surface area = 5ab + 5hb
Volume of pentagonal prism = 5/2 a b h
where, a =apothem length
b = base length
h = height of the prism
according to the given statement, 34 = 5 a b + 5 h b
180.2 = 5/2 a b h
from the above two equation, we get, the height of prism = h unit.
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I can't find #13 please help
The ratio of the measures of the three angles in a triangle is 14:5:11. Find the measures of the angles.
The smallest angle =
The medium angle =
The largest angle =
Answer:
See below
Step-by-step explanation:
All of the interior angles of a triangle sum to 180 °
Smallest is 5 out of (14 + 5 + 11) = 5/30 ths of 180° = 30°
Middle is 11/30 ths = 66°
Largest is 14/30 ths = 84°
Answer:
30° , 66° , 84°
Step-by-step explanation:
sum the parts of the ratio, 14 + 5 + 11 = 30 parts
divide the sum of the angles in a triangle 180° by 30 to find the value of one part of the ratio.
180° ÷ 30 = 6° ← value of 1 part of the ratio , then
smallest angle = 5 × 6° = 30°
medium angle = 11 × 6° = 66°
largest angle = 14 × 6° = 84°
Students in Mr.Chow's class each contributed money for a gift to a visiting speaker. Each student contributed the same amount, and each gave Mr.Chow the exact same four coins: If $16.81 was collected in all, how many pennies were collected?
Answer:
So in total, 1681 pennies were collected.
Step-by-step explanation:
divide the total amount collected, $16.81, by the value of a penny, which is $0.01.
16.81 / 0.01 = 1681 pennies.
So in total, 1681 pennies were collected.
Jon drank 2/3 liter of water on Monday before jogging. He drank 5/7 liter of water after hi jog. How much water did Jon drink altogether? Write your anwer a a Mixed number
Answer:
1 8/21.
Step-by-step explanation:
Total number of water Jon drink altogether
2/3 + 5/7
=LCM 21
=2/3 + 5/7
=14 + 15
21
=29/21
Mixed fraction
=1 8/21.
Is 25 a prime number?
No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.
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a businessman bought x bags of maize at a cost of shs.960 per bag. he spend she 15 per bag on transport. he later sold the maize39 per tine making a profit of shs.515 per bag. (a) calculate the number of tins in one bag. (b) if the business man made total of sha 29,640. how many bags had he sol? (c) the businessman later used the total sales to buy more maize at shs.926.25 per bag he sold half of the bags to the maize millers the rate of shs.1,390 per bag and retailed the remaining at his stall to consumers at shs.39 per tin. which option would earn more profit and by how much? (2mk) (d) express the difference as a percentage of the sales to the consumers.
a) To calculate the number of tins in one bag, we can use the information given in the problem: "he later sold the maize39 per tine"
So we can assume that one bag of maize is divided into tins and the price per tin is 39 shs.
b) To find out how many bags the businessman sold, we can use the information that he made a total of 29,640 shs in profit.
We know from the problem that the profit per bag is 515 shs, so to find out how many bags he sold we can divide the total profit by the profit per bag: 29,640 shs / 515 shs/bag = 57.5 bags
c) To find out how much profit the businessman made by selling half of the bags to the maize millers, we can use the information that he bought the bags at 926.25 shs and sold them at 1,390 shs.
We know that he sold half of the total number of bags, so we can divide the total number of bags by 2: 57.5 bags / 2 = 28.75 bags
To find out the total profit he made, we can multiply the number of bags sold by the profit per bag: 28.75 bags * (1,390 shs - 926.25 shs) = 22,447.5 shs
d) To express the difference as a percentage of the sales to the consumers, we can use the information that the businessman sold the bags to the maize millers at 1,390 shs and to the consumers at 39 shs.
To find the difference, we can subtract the price he sold the bags to the consumers from the price he sold the bags to the maize millers: 1,390 shs - 39 shs = 1351 shs
To find the percentage of the difference, we can divide the difference by the price he sold the bags to the consumers and multiply by 100: (1351 shs / 39 shs) * 100 = 34,641.03%
Find the measure of angle TSB.
The measure of angle TSB is m ∠TSB = 40°.
What is inscribed angle?
In terms of geometry, an inscribed angle is the angle created when two chords intersect within a circle. It can also be described as the angle formed by two specified points on a circle at a given point on the circle. Two chords of the circle sharing an endpoint are equivalently used to define an inscribed angle.
Given:
The measure of arc BR = 100°.
We have to find the measure of angle TSB.
Since the measure of half of the arc is 180°.
⇒ TR = 180°
TS + BR = 180°
TS + 100° = 180°
TS = 180° - 100°
TS = 80°
The measure of arc TS is 80°.
Since,
TS = 2 m ∠TSB
⇒ m ∠TSB = 1/2TS
m ∠TSB = 1/2(80°)
m ∠TSB = 40°.
Hence, the measure of angle TSB is m ∠TSB = 40°.
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cos 2x + 3 = 4 can some one help me with finding all solutions
Answer:
x=0 or x=pi / x=πn
Step-by-step explanation:
cos2x + 3 = 4
subtract 3 from both sides
cos2x = 1
take the inverse cos/arccos of both sides
arccos(cos2x) = arccos(1)
2x=0 or 2x=2pi
divide both sides by 2
x=0 or x=pi
beyond (0,2pi) for every possible answer you should do x=(pi)n since any multiple of pi gives you the same answer
Do the lengths 5 12 and 13 form a right triangle?
Answer:no
Step-by-step explanation:
1. Which polygon or polygons are regular? (2 points)
Answer: 1st, 2nd, and 3rd
Step-by-step explanation: the last one isn't because not all of the sides are the same length
A paint store sells 4 pt of paint for $19.use a model to write a rate for this situation. What does this mean? Show your work
A model for the rate situation is written as
4x = $19
This means that a unit of paint is sold for $4.75 hence 4 units will be $19
What is unit price?The cost per unit of an item is represented by the unit price.
To determine the unit price of an item, we divide the price of a specific number of units by the number of units.
How to write a model for the rate situationIf a paint store sells 4 pt of paint for $19. the rate of the paint is solved for as follows
let a unit be x
4 = 19
1 = x
cross multiplying
4x = 19 * 1
x = 19 / 4
x = 4.75
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6.
In George's classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students
A. 1:3
B. 3:1
C. 1:4
D. 4:1
On solving the provided question, we can say that there are 6 girls for every 2 boys, ratio = 3:1
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
there are 6 girls for every 2 boys.
ratio will be
6/2 = 3/1
ratio = 3:1
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A magician asks a volunteer to think of two different positive integers without telling her what they are. She then asks him to calculate x, the sum of the larger number with the square of the smaller, and y, the difference between the numbers. The volunteer tells her that x = 9 and y = 3. Find the original numbers.
Answer:
the original numbers are 5 and 2
Step-by-step explanation:
fistly it says inorder to find x one has to add the larger number to the square of the smaller number. So in this case start off with smaller guesses of positive integers as it is simpler that way.
the first guesses that would end up giving you 9 as an answer is 5 and 2
5+(2×2)=9So now that the integers chosen fit in when calculating x we have to check if it also checks out in calculating y.
For y the difference between the 2 integers have to give an answer of 3. after calculations it the numbers comply to the statement for y;
5-2=3hence the answers are 5 and 2
If a car lot 3600 in depreciation in the firt year. What i the original cot of thi car?
The original cost of the car would be the total depreciation plus the cost of the car after one year. So, the original cost of the car would be 3600 + (the cost of the car after one year).
1. Calculate the total depreciation for the year: 3600
2. Add the total depreciation to the cost of the car after one year: 3600 + (cost of the car after one year)
3. The answer is the original cost of the car: (3600 + (cost of the car after one year))
The original cost of the car would be the total depreciation plus the cost of the car after one year. So, the original cost of the car would be 3600 + (the cost of the car after one year).
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PLEASE HELP !!!!!!!! Joanne is copying angle BAC with technology. An angle is created from points B, A, and C. A circle with a center of A has a radius of AB and intersects with rays AB and AC. Another ray is created from points D and E. A circle has been created from point D that is congruent to circle A. Which of the following describes her next step? Draw a circle with a center F and a radius equal to BG. Draw the point of intersection between circle D and ray DE. Draw ray DE away from angle BAC. Draw the points of intersection between circle D and circle A.
He should do all the steps that are mentioned in the question to make sure the new angle is congruent to angle BAC and has the same properties.
What is the construction of a circle?
Circle constructions are used in many fields such as geometry, engineering, and architecture to create precise circles. It's a fundamental concept in mathematics, and it's important to understand how to construct circles to apply these concepts in different fields.
His next step would be to draw a circle with a center F and a radius equal to BG.
By creating a circle with a center F and a radius equal to BG, He is creating a congruent circle to the original circle A with the center A, and radius AB.
The point of intersection between circle D and ray DE would also be an important step as it would give the location of the new angle. The point of intersection between circle D and circle A would also be an important step as it would confirm that the two circles are congruent.
Drawing ray DE away from angle BAC is also an important step, as it would create a new angle with the same properties as angle BAC.
Hence, He should do all the steps that are mentioned in the question to make sure the new angle is congruent to angle BAC and has the same properties.
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In this triangle below, what is the side adjacent?
By analyzing the question, The side adjacent to angle L is D)JR.
What is adjacent side of triangle?In a triangle, adjacent sides are sides that share a common vertex (or corner) and are next to each other.
What is angle?An angle is the amount of rotation between two lines or planes that share a common point. It is typically measured in degrees or radians.
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Chloe is trying to pick out outfit for the first day of school. she can choose from 4 pairs pair of pants 4 t-shirts, 2 pair of shoes. how many different outfits does chloe have choose from
Answer: 32
Since you have 4 choices of shirts, then 4 choices of shorts, and then 2 choices of shoes, the formula should be set up as 4 x 4 x 2. This gives you 32 outfit options.
Given JKL ~ NPM find jk
no just no because I'm too busy for this stupodnesss and ur in the matrix
Copy and complete this sentence to describe the shaded region: The locus of points inside triangle ABC that are closer to AB / BC / AC than to AB / BC / AC A B 40° 40° C
The locus of points inside triangle [tex]ABC[/tex] that are closer to [tex]AB[/tex] than [tex]BC[/tex].
Subtract (6.25x + 12) - (4.25x "-7)"
Answer: 2x+19
Step-by-step explanation:
Simplify the expression by combining the like terms
How do you check if a value is present in a table?
Use the exists condition to determine whether a record in a MySQL table exists or not. Subquery and the exists condition are both compatible.
what is sequence ?Informally, a sequence in mathematics is a list of items that are in some order (or events). It possesses members, much like a set (also called elements, or terms). The length of the sequence is the quantity of ordered elements (which may be infinite). You should be familiar with the following four main categories of sequences: arithmetic, geometric, quadratic, and special. Lists of numbers connected by a rule are known as number sequences. The subsequent numbers in the series can be calculated if the rule is understood. Each of the numbers in this example differ by 6, thus that is the case. It follows that adding 6 each time is the rule for this sequence.
given
Use the exists condition to determine whether a record in a MySQL table exists or not. Subquery and the exists condition are both compatible. When a row is present in the table, it returns true; otherwise, false is returned. False is represented as 0, whereas true is represented as 1.
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Why is the exponential power 0 to 1?
Answer:The zero exponent is equal to 1 to satisfy a certain case in manipulating bases with exponents. When multiplying or dividing the same base with exponents we add or subtract the exponents: To find the value of (3^3) (3^2) [the short form of (3 X 3 X 3) X (3 X 3) or (27) (9)] we add exponents to get 3^ (3+2) or 3^5 with a value of 243.
Step-by-step explanation:
What are the 6 types of triangle explain with example?
Answer:
There are six types of triangles based on their side lengths:
Equilateral Triangle: A triangle with all sides of equal length. For example, a triangle with sides of 3cm each is an equilateral triangle.
Isosceles Triangle: A triangle with two sides of equal length. For example, a triangle with sides of 2cm, 2cm, and 3cm is an isosceles triangle.
Scalene Triangle: A triangle with no sides of equal length. For example, a triangle with sides of 2cm, 3cm, and 4cm is a scalene triangle.
Acute Triangle: A triangle with all angles measuring less than 90 degrees. For example, a triangle with angles measuring 60, 75, and 45 degrees is an acute triangle.
Right Triangle: A triangle with one angle measuring exactly 90 degrees. For example, a triangle with angles measuring 45, 45, and 90 degrees is a right triangle.
Obtuse Triangle: A triangle with one angle measuring more than 90 degrees. For example, a triangle with angles measuring 90, 45, and 45 degrees is an obtuse triangle.
Step-by-step explanation: