The percent discount on the new phone is 15%.
Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.
To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.
Discount = Original Price - Sale Price
Discount = $46 - $39.10
Discount = $6.90
Percent Discount = (Discount / Original Price) x 100
Percent Discount = ($6.90 / $46) x 100
Percent Discount = 15%
Therefore, the percent discount is 15%.
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What is the slope of the linear regression prediction equation if a person with 12 years of schooling
On solving the provided question, we can say that the e slope of the linear regression prediction equation if a person with 12 years of schooling is 1.
what is linear regression?When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.
the e slope of the linear regression prediction equation if a person with 12 years of schooling
a. 1(correct)
b. 12
c. 13
d. 1,500
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Does 3 3 have a solution?
Given equation 3 = 3 is an identity, so it has infinite solutions.
Consider the given mathematical equation 3 = 3
We need to check whether the given mathematical equation has solution or not.
We know that a statement 3 = 3 's true no matter what.
We can observe that for given statement 3 = 3, there's no variable in sight.
This means, 3 = 3 must has infinite solutions.
We know that an equation which is always true, no matter what values we substituted is called as an identity.
This equation is an identity, all real numbers are solutions.
Therefore, the equation 3 = 3 have infinitely many solutions.
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Please answer ill give 40 points
To rewrite the inequalities in slope-intercept form, the student would first need to solve for y.
2x + 3y > 6 can be rewritten as 3y > -2x + 6 and then solving for y by dividing both sides by 3, the student can have y > (-2/3)x + 2
x-4y > 8 can be rewritten as -4y > -x + 8, and then solving for y by dividing both sides by -4 , the student can have y < (1/4)x - 2
To graph the inequalities, the student would plot the y-intercepts of the equations, which are (0,2) and (0,-2) and then use the slope to find a second point to plot, and then graph the line. Then, based on the inequality symbol the student should shade the appropriate side of the line. If the inequality is greater than > or less than < then they shade one side, otherwise if the inequality is less than or equal to >= or greater than or equal to <= they shade both sides.
It's also important to remember that the slope intercept form is y=mx+b where m is the slope, and b is the y-intercept, if the student already has the equation in this form, they only need to plot the y-intercept point and use the slope to get a second point.
29. Jamie spent $56 for blue blouse. A red blouse cost two-thirds of this price. What was the cost of the red blouse? PLEASE HELP ME WITH THIS QUESTION MY MATH TEACHER WILL BE VERY UPSET PLEASEEE!!!
Habib cut out a rectangle that ha a perimeter of 60 inche and a length of 16 inche. They cut out another rectangle that i the ame length and twice a wide
The required perimeter of the new rectangle is 66 inches.
What is a rectangle?A quadrilateral with all of its angles equal, or right angles, is a rectangle.
In addition to having all equal angles, a square also has all equal sides.
Therefore, a particular case of a square is a rectangle.
To put it another way, a rectangle can also be a square (when all sides to are equal).
Because every square is a quadrilateral with all four angles at right angles, every square is also a rectangle.
To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.
So, a perimeter equals 2(l+b).
50 is the circumference and 17 is the length here.
Suppose the breadth is x.
50 = 2(17+x)
50 = (2*17)+(2*x)
50 = 34 + 2x
50 - 34 = 2x
16 = 2x
16/2 = x
8 = x
The first triangle's width is eight inches.
We know that the length of the other rectangle is 17.
And that the width is two times that of the first triangle.
Length = 17, width = 2*8 = 16, etc.
For the border:
p = 2(l+b)
p = 2(17+16)
p = (2*17)+(2*16)
p = 34+32
p = 66
Therefore, the required perimeter of the new rectangle is 66 inches.
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Complete question:
Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches. He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle?
Find the numbers. A room is 12 feet longer than it is wide. Half the perimeter of the rectangular floor is 72 feet. Find the length and the width. Use elimination or substitution to solve this problem.
Answer: The width of the room is 36 feet and the length of the room is 48 feet.
Step-by-step explanation:
To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.
Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:
l = w + 12
We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (length + width)
Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:
144 = 2 * (w + 12 + w)
Combining like terms and solving for w, we get:
w = 36
Substituting this value back into the equation for the length of the room, we get:
l = 36 + 12 = 48
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.
To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.
For example, we could solve the equation l = w + 12 for w to get:
w = l - 12
Substituting this expression for w into the equation for the perimeter, we get:
144 = 2 * (l - 12 + l)
Combining like terms and solving for l, we get:
l = 48
Substituting this value back into the equation for the width of the room, we get:
w = 48 - 12 = 36
Therefore, the width of the room is 36 feet and the length of the room is 48 feet.
How did you compute sums ofdollar amounts that were not whole numbers? For example, how did you compute the sum of$5. 89 and$1. 45? Use this example to explain your strategy.
How did you compute products ofdollar amounts that were not whole numbers? For example, how did you compute the cost of4 pounds of beef at $5. 89 per pound? Use this example to explain your strategy
To compute the sum of dollar amounts that are not whole numbers and to compute products of dollar amounts that are not whole numbers you can use the standard arithmetic operation and place decimal point correctly.
To compute the sum of dollar amounts that are not whole numbers, such as $5.89 and $1.45, you can use the standard arithmetic operations of addition, just like you would with whole numbers.
$5.89 + $1.45 = $7.34
When adding or subtracting decimal numbers, you align the decimal points and perform the operation column by column, just like you would with whole numbers.
To compute products of dollar amounts that are not whole numbers, such as 4 pounds of beef at $5.89 per pound, you can use the standard arithmetic operation of multiplication.
4 × $5.89 = $23.56
When multiplying decimal numbers, you multiply as you would with whole numbers and place the decimal point in the product to the right of the last digit in the product that corresponds to the number of decimal places in the original factors.
In both examples, it is important to pay attention to the placement of the decimal point and to use proper arithmetic operations. In general, it is important to consider the decimal places when working with decimal numbers and ensure that the final result is rounded to the appropriate number of decimal places, if necessary.
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The vertices of DEF are D(-2, 5), E(5, 1), F(-4, -5). Find the coordinates of the orthocenter of DEF
Using a graph, the orthocenter for this triangle has a coordinate at (x, y) are (-0.46, 0.2)
What is an OrthocenterThe intersection of a triangle's three elevations is called the orthocenter. It is the intersection of the three lines that run perpendicular to the triangle's three sides. Due to its several intriguing characteristics, the orthocenter is a crucial place in the study of triangles..
In this problem, we need to use a graphing calculator and plot each of the coordinates and then find the orthocenter which is an equidistant position from all the coordinates.
In this particular problem, the orthocenter for this triangle is (-0.46, 0.2)
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In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76°, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot. °, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot
The length of OP to the nearest tenth of a foot is 16.9 ft
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
ΔOPQ is right triangle
Tan (p) = opposite/adjacent = OQ/PQ
Tan (76) = OQ/4.1
4.010 = OQ/4.1
OQ = 4.010 * 4.1 = 16.441
OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116
=> OP = √ 287.116 = 16.944
OP≅ 16.9 ft
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[Please help me on this- I will give you brainlist!!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
The degree of polynomial is 2 and leading coefficient is 3.
What are polynomial?A polynomial is a mathematical expression made up of one or more terms. The phrases "poly" and "nominal," for example, are whence the name "polynomial" arose. The words "poly" and "nominal" both signify many. A polynomial is an algebraic expression with two or more algebraic terms, to put it simply. It has exponents, operators, coefficients, coefficients, variables, and constants.
Given polynomials 9, 3x², 8x
standard form of polynomial; The value of the largest exponent in a polynomial is known as its degree. However, it differs between a polynomial with just one variable and one with multiple variables. The degree of a polynomial for a single variable is equal to the variable's highest power in the polynomial.
the standard form is 3x², 8x, 9
degree of polynomial is 2.
and leading coefficient is the constant term followed by the variables with highest power,
LC = 3.
Hence degree = 2 and leading coefficient = 3.
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A ratio is a comparison of two quantities. For example, the ratio of cows to pigs on a farm could be 1 to 3. For every 1 cow, there are 3 pigs. The ratio of chocolate chips to raisins in a cookie could be 5 to 9. For every 5 chocolate chips in the cookie, there are 9 raisins. Do you notice a repeating phrase in these examples? “For every” is key ratio language. It tells you how much of one quantity exists in comparison to the other quantity. A ratio consists of just the numbers, not the units. If someone asked the ratio of chocolate chips to raisins in the cookie example, you’d say 5 to 9.
Which of these could you represent with a ratio?
The solution is given by the equation A = how many diet sodas there are in the fridge compared to how many regular sodas
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the equation will be
The ratio of cows to pigs on a farm could be 1 to 3
So , the proportion is 1 : 3
Now , The ratio of chocolate chips to raisins in a cookie could be 5 to 9
So , the proportion is 5 : 9
Now , the number of diet sodas there are in the fridge compared to number of regular sodas is also a proportion
Hence , the proportion is number of diet sodas to number of regular sodas
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What are two angles on a line called?
Answer:
supplementary angles
Step-by-step explanation:
140 + 40 = 180.
  PLS PLS HELP ASAP!!! ILL GIVE BRAINIEST AND 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS. Explain why it’s the missing side or angle.
Answer:
Mark angles C and F as congruent.
Step-by-step explanation:
Angle-Angle-Side (AAS) Congruence Theorem
If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
The given triangles have one corresponding angle and one corresponding side marked as congruent.
To satisfy AAS congruency, another pair of corresponding angles need to be marked as congruent.
As an included side is the side between two angles, we cannot mark angles A and P as congruent, as this would not satisfy AAS congruency since sides AB and PD would be the included sides.
Therefore, to make triangle ABC congruent to triangle PDF by AAS, mark angles C and F as congruent.
Pls help quickly. Calculate the bearing of Y from
Z.
N
X
135°
z+
105°
Z
Y
Not draw
The bearing of point Y from point Z is 30 degrees.
What is the bearing of a point?
The bearing of a point is the angle measured in degrees clockwise from a reference direction (usually north). To find the bearing of point Y from point Z, we need to determine the angle between the line connecting point Z to point Y and the reference direction.
we know that the bearing of point X from point Z is 135 degrees, and the bearing of point X from point Y is 105 degrees.
we can use the following mathematical relationship to find the bearing of point Y from point Z:
Bearing of Y from Z = (Bearing of X from Z) - (Bearing of X from Y)
Substituting the values we know:
Bearing of Y from Z = 135 - 105 = 30 degrees
Hence, the bearing of point Y from point Z is 30 degrees.
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Solve 84=3u^2, where u is a real number.Round your answer to the nearest hundredth.
3u^2-84 = 0 then u=5.29 is the nearest hundredth
What are real numbers?The union of both rational and irrational numbers is known as a real number. They are represented by the letter "R" and can be either positive or negative.
This category includes all natural integers, decimals, and fractions.
In the number system, real numbers are only the fusion of rational and irrational numbers.
These numbers can generally be used for all arithmetic operations and can also be expressed on a number line.
Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolize complex numbers. Examples of actual numbers include 23, -12, 6.99, 5/2, and so forth.
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find the volume of this triangular prism.
The volume of the triangular prism is 120 cm cube.
How to find the volume of a triangular prism?A triangular prism is a three-sided prism. The volume of a triangular prism can be represented as follows:
volume of a triangular prism = 1 / 2 bhl
where
b = base of the triangular faceh = height of the triangular facel = height of the triangular prismTherefore,
b = 10 cm
h = 12 cm
l = 6 cm
Therefore,
volume of a triangular prism = 1 / 2 × 10 × 12 × 6
volume of a triangular prism = 1 / 2 × 120 × 6
volume of a triangular prism = 60 × 6
volume of a triangular prism = 120 cm³
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A whale descends from the surface of the water at a rate of 22 feet per minute.
What is the position of the whale relative to the surface after diving for 3
minutes?
Answer:
66
Step-by-step explanation:
22 per minute
? Per 3 minutes
22 x 3 = 66
Answer: The position of the whale relative to the surface of the water can be determined by multiplying the rate at which it descends (22 feet per minute) by the amount of time it has been descending (3 minutes).
Position = Rate x Time
Position = 22 feet/minute x 3 minutes = 66 feet
So, after diving for 3 minutes, the position of the whale relative to the surface of the water is 66 feet.
It means the whale descended for 66 feet from the surface level of the water.
Please keep in mind that this information is assuming a linear motion, without taking into account any other factors that could affect the whale's descent such as currents or obstacles in the water.
Step-by-step explanation:
Classify each transformation by its properties.
The classification of the transformations based on the properties are presented as follows;
[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]
What are the different transformation effects?The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.
Rigid transformations includes; Reflections, rotations, and translations
Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations
Non rigid transformations includes; Dilation with a scale factor
Transformations that does not preserve the angle measure includes; Shear transformation
A translation and a dilation transformation does not preserve the lengths of the original figure.
The classification of the transformations based on their properties are therefore presented as follows;
[tex]{}[/tex] Preserves lengths Does not preserve lengths
Preserves Reflection [tex]{}[/tex] Translation followed by dilation
angle measure Rotation [tex]{}[/tex] with k > 1
[tex]{}[/tex] Dilation with k > 1
Does not
Preserve angle
measure
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.You have an "equality sign" that connects 1kg of NaCl to 27 ml of a solvent, how many ml are associated with 9100 grams?
Two tiny parallel horizontal lines serve as the "equality sign" connecting 1 kilogramme of NaCl to 27 ml of a solvent.
What does ≡ mean in math?is a synonym for exactly. This is comparable to equals but not quite the same. To avoid confusion, always use the symbol =, which stands for about equal to or virtually equal to. This symbol indicates two sides of a connection that are not precise enough to be mathematically manipulated.≅ (mathematics) equivalent to around. quotes (geometry) similar to. The computer science term "it is defined as" is denoted by the meta symbol::=, which is not a mathematical expression , everywhere.x ≔ y or x ≡ y indicates that x is understood to be another name for y (however it should be noted that can also denote other things, such as congruence). P :⇔ Q denotes the logical equivalence of P to Q. Congruent or, more generally, an arbitrary equivalence relation is denoted in some circumstances by the triple bar or equal sign with three lines.To learn more about equality sign refer to :
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Thomas wants to buy a new baseball bat. The one he likes costs $130, but it is on sale for $104. What is the percent of the discount Tomas will get if he buys the bat
On solving the provided question we can say that the percentage discount will be equal to 20%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
Tomas wants to buy a new baseball bat. T
he one he likes costs $130, but it is on sale for $104.
The discount percentage will be calculated as:-
( $130 - $104) = $26
( 26 / 130) x 100 = ( 2600 / 130 ) = 20%
the discount will be equal to 20%.
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The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear.
Time (min), x Distance (m), y
5 1,930
10 1,380
15 830
20 280
The equation of the function in the form y=mx+b is y = 110x-2020
Adaptation of function speed
A line's equation is written as mx + b = y, where m denotes the rate of change or slope.
The intercept is B.
utilizing the coordinates
Calculate the slope.
m = 550/5
m = 110
The intercept for
280 + 110(20) + b
280 = 2200 + b
b = 180 - 2200
b = -2020
The equation for the function of the type y=mx+b is hence y = 110x-2020.
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The complete question would be:
The table shows the distance Penelope is from the park as she walks to soccer practice. Assume the relationship between the two quantities is linear. Find and interpret the rate of change and initial value. Then write the equation of the function in the form y=mx+b
Indicated angles :
6. Find the measures of the indicated angles. Give reasons for your answers
Answer:
k\
Step-by-step explanation:
j
Can someone help on this?
Answer:
x=0 and y=36
Step-by-step explanation:
30 + 6 equals 36 but it is negative so you would add 30 to negative thirty to get to zero and go into the positive numbers. So if you add 6 more you would have positive 6. so it it 36 y is 36
Question is attached. Show workings. Question 11
65 POINTS TO WHO EVER ANSWERS CORRECT
Kim and her friends watched the server making smoothies. The table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Which statement is correct based on the data?
1. The ratio of smoothie size to mangos used for Kim is 1:8, and the ratio of smoothie size to mangos used for Bri is 3:24.
2. The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
3. The ratio of smoothie size to mangos used for Angela is higher than the ratio of smoothie size to mangos used for Kim.
4. The ratio of smoothie size to mangos used for Bri is 64:3, and the ratio of smoothie size to mangos used for Angela is 64:4.
The correct statement based on the data is,
⇒ The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
Option 2 is true.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
Given that;
The given table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.
Mangos Used Smoothie Size
Kim 1 8 oz
Bri 3 24 oz
Angela 4 32 oz
Now, By definition of ratio, we get;
The ratio of smoothie size to mangos used for Bri is,
⇒ 24 : 3
⇒ 8 : 1
And, The ratio of smoothie size to mangos used for Angela is,
⇒ 32 : 4
⇒ 8 : 1
Thus, The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.
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is dilated from the origin to create segment A prime B prime at A' (0, 6) and B' (6, 9). What scale factor was segment AB dilated by
The scale factor of segment AB was 1.94.
What is scale factor?Scale factor is a number by which a given set of measurements is multiplied in order to increase or decrease the size of the measurements. It can be used to enlarge or reduce the size of an object, image, or diagram. It is a useful tool in many areas of mathematics, including geometry, engineering, and computer graphics.
The scale factor for segment AB can be found by taking the ratio of the lengths of the two segments. To calculate this, use the distance formula to find the length of segment AB and A'B' and set them equal to each other.
The distance formula is: d = √[(x2-x1)^2 + (y2-y1)^2]
The coordinates of A and B are (0, 0) and (6, 9), respectively. The coordinates of A' and B' are (0, 6) and (6, 9), respectively.
For segment AB, the distance formula becomes: d = √[(6-0)^2 + (9-0)^2], which simplifies to d = √[36 + 81], which simplifies to d = √117.
For segment A'B', the distance formula becomes: d = √[(6-0)^2 + (9-6)^2], which simplifies to d = √[36 + 9], which simplifies to d = √45.
The scale factor is then found by taking the ratio of the two distances, √117/√45, which simplifies to √117/3, or approximately 1.94. Therefore, the scale factor of segment AB was 1.94.
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Jesse wanted a stamp collection his grandfather gave him 48 stamps to start it then his parents gave him 23 stamps and his aunt gave him 17 stamps how many stamps does Jesse have in his collection
Answer:88
Step-by-step explanation:
(a) Write down the value of xº
Given that 2-3 x 2⁹ = 2n
(b) find the value of n
From the equation (2-3 x 2⁹ = 2n), the value of n is -767.
What is the equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.
The word equation and its cognates in various languages may have slightly different meanings. In mathematics, an equation is a formula that uses the equals sign to denote the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Given data :
2-3 x 2⁹ = 2n
= 2n = 2 - 3 .
= 3 . = 1536
= 2n = 2 - 1536
= 2n = -1534
Divide both sides by 2
= 2n/2
= -1534/2
n = -767
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Solve the equation −14 - 1 4 (x – 26) = –200 for x.
Hello there!
Answer:
x = 39 2/7
Step-by-step explanation:
-14 - 14(x - 26) = -200
- 14 + 14 - 14(x - 26) = -200 + 14
-14(x - 26) = -186
-14(x - 26)/(-14) = -186/(-14)
x - 26 = 93/7
x - 26 + 26 = 93/7 + 26
x = 275/7
x = 39 2/7
Solve for x. each figure is a parallelogram
it's 40 points for the 4
3.) x = 15.25 or 15 1/4 ( not sure if you'll need to round your answer )
4.) x =6
5.) x = 10
6.) x = 9
Explanation:
1.) write your equation down 8x + 9 = 131
2.) Subtract +9 from 131. you'll get 122
3.) divide 8x and 122.
4.) Then there's your answer 15.25
you'll do the same thing throughout each equation. write down your equation but with the 22x and 23x you're going to subtract 22x from 23x. and you'll get 1x then continue on the same way as with the last equation.