Answer:
A.10
Step-by-step explanation:
An exponent is a number or letter written above and to the right of a mathematical expression called the base.
x is the base and n is the exponent or power. Definition: If x is a positive number and n is its exponent, then xn means x is multiplied by itself n times.
i need some help on this please
Using the intersecting chord theorem, we can calculate the value of x as: 12
How to solve the Intersecting chord theorem?The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.
Applying the intersecting chord theorem to the two chords of the circle, we can say that:
3x = (9 * 4)
3x = 36
x = 36/3
x = 12
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Can someone please answer and provide an explanation for these problems?
The distance between each pair of points include the following:
44. 2.8 units.
45. 5.8 units.
46. 12.0 units.
47. 16.6 units.
48. 7.1 units.
49. 4.5 units.
How to determine the distance between two end points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Question 44.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(3 - 1)² + (2 - 4)²]
Distance = √[(2)² + (-2)²]
Distance = √8
Distance = 2.8 units.
Question 45.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-2 + 7)² + (0 - 3)²]
Distance = √[(5)² + (-3)²]
Distance = √34
Distance = 5.8 units.
Question 46.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-6 - 2)² + (-2 - 7)²]
Distance = √[(-8)² + (-9)²]
Distance = √145
Distance = 12.0 units.
Question 47.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(1 - 8)² + (-8 - 7)²]
Distance = √[(-7)² + (-15)²]
Distance = √274
Distance = 16.6 units.
Question 48.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(-5 - 2)² + (-4 + 5)²]
Distance = √[(-7)² + (1)²]
Distance = √50
Distance = 7.1 units.
Question 49.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 - 3)² + (5 - 1)²]
Distance = √[(2)² + (4)²]
Distance = √20
Distance = 4.5 units.
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The rear window of Alex's van is shaped like a trapezoid with an upper base
measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.
An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as
shown in the diagram below.
36 in.
21 in.
150 degrees
18 in.
48 in.
a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.
b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.
c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.
d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.
a) The area of the entire trapezoidal rear window = 882 sq.in.
b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12
c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.
d) The percent of the area of the entire rear window is cleared by the wiper = 48.09%
We know that the formula for the area of trapezoid,
A = ((a + b) / 2) × h
Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in
Using above formula, the area of the entire trapezoidal rear window would be,
A = ((36 + 48) / 2) × 21
A = 882 sq.in.
Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.
We know that the measure of entire circle = 360°
So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,
150° / 360° = 5/12
Now we need to find the area of the part of the rear window that is cleared by the wiper.
We know that the formula for the area of sector of a circle is:
A = (θ/360) × πr²
Here, the central angle θ = 150° and radius r = 18 in.
A = (θ/360) × πr²
A = (150/360) × π × 18²
A = 424.12 sq. in.
Now we need to find the percent of the area of the entire rear window is cleared by the wiper.
P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100
P = (424.12 / 882) × 100
P = 48.09%
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the graph of a quadratic function has a y intercept at (0,3) and its vertex at (4,8 1/3) what are its x intercepts in order from least to greatest
can you also explain the steps?
The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).
Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]
Use the y-intercept to find the value of "a".
The y-intercept is (0,3), so when x=0, y=3.
Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].
Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.
To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]
To find the x-intercepts, set y = 0 and solve for x.
The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].
Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]
Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,
we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]
Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]
Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.
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The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
What percentage of adults eat between 5.6 and 8 ounces of chicken in one sitting?
2.5%
34%
47.5%
95%
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.
In the normal distribution,
The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.
This means that the mean of this distribution is 8.
The standard deviation cannot be a negative value,
So in this problem, it is 1.2,
Which means that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
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Susie paid 2/5 of the price of her movie ticket. Her parents paid the remaining portion of the movie ticket price. What decimal is equivalent to the fraction of the price of the movie ticket Susie paid?
17 points!!
Thanks to the other user
To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):
2 ÷ 5 = 0.4
Therefore, the decimal equivalent to 2/5 is 0.4.
(Mines) Simple Equation2/5 which is know as 2 ÷ 5 is 0.4TipWhenever you see a fraction like 2/5 just divide and it will turn into decimal.
elle can buy 2 quarts of milk for 3$ or 1 gallon of milk for 3$ which is the better deal
Answer:
Elle should buy 1 gallon of milk for $3.
Step-by-step explanation:
In one gallon of milk, there are four quarts. So we can multiply the number of gallons by four to convert it to quarts.
(1 gallon)x(4 quarts) = 4 quarts in one gallon
4 quarts is greater than 2 quarts so 1 gallon for $3 is a better deal than 2 quarts for $3.
The grid shown below is in the shapr of a rectangle. What is the area innsquare units, of the shaded part of the rectangle? It have 48
Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains option D. 48 square units.
To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.
If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,
which is Area = length × width. The result will give us the area of the shaded part in square units.
The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option D
The Question was Incomplete, Find the full content below :
The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
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find the numerical value of the log expression
Answer:
Step-by-step explanation:
The numerical value of the given log expression is -73.
From definitions of logarithms, we know that :
[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]
[tex]log(a^n) = n*log(a)[/tex]
Therefore,
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]
substituting the given values
[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]
we get the value of the given expression
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]
[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]
Therefore the numerical value of the given log expression is -73.
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2x+6 what would be its value if X=-3 *
Answer:0
Step-by-step explanation:
so if x = -3 that means u take -3 * 2 and u get -6 because a negative * A positive is negative so -6 + 6 is 0
Answer:
0
Step-by-step explanation:
Just substitute x=-3
2x+6 =
2(-3) + 6 =
-6 + 6 = 0
50 Points! Multiple choice geometry question. Photo attached. Thank you!
In a rectangle, the value of x is,
⇒ x = 5
We have to given that;
ABCD is a rectangle.
And, AC = 5x + 2
BD = x + 22
Since, We know that;
Diagonal of a rectangle are equal in length.
Hence, We get;
AC = BD
(5x + 2) = (x + 22)
5x - x = 22 - 2
4x = 20
x = 20/4
x = 5
Thus, the value of x is,
⇒ x = 5
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The following transactions were completed by the company:
The company completed consulting work for a client and immediately collected $5,600 cash.
The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
The company paid an assistant $1,450 cash as wages for the period.
The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
The company paid $720 cash for this period's cleaning services.
In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.
Transaction Analysis:
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
This transaction increases both cash and revenue. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$5,600
Revenue: +$5,600
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
This transaction does not impact any account initially. Revenue will increase when payment is received.
Accounts Affected:
Accounts Receivable: +$4,100
Revenue: +$0
c. The company paid an assistant $1,450 cash as wages for the period.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$1,450
Expenses: +$1,450
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.
Accounts Affected:
Cash: +$2,050
Accounts Receivable: -$2,050
e. The company paid $720 cash for this period's cleaning services.
This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.
Accounts Affected:
Cash: -$720
Expenses: +$720
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Complete Question
The following transactions were completed by the company
a. The company completed consulting work for a client and immediately collected $5,600 cash earned.
b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
c. The company paid an assistant $1,450 cash as wages for the period.
d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b
e. The company paid $720 cash for this period's cleaning services Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)
What is the slope of this line?
A line passing through the points (negative 4, negative 3) & (0, 1).
© 2017 StrongMind. Created using GeoGebra.
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]
Given m ∥ n, find the value of x.
The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
What are angles formed by a pair of parallel lines cut by a transversal line?When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.
(2x - 13) + 123 = 180° {supplementary angles}
2x - 13 + 123 = 180°
2x + 110 = 180
2x = 180 - 110 {collect like terms}
2x = 70
x = 70/2 {divide through by 2}
x = 35
Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3
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task1 part b evaluate
The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
We have to given that,
Expression to solve,
⇒ ∫ (0 to 10) (x + 1) dx
Now, We can simplify as,
⇒ ∫ (0 to 10) (x + 1) dx
⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx
⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀
⇒ 1/2 (10² - 0) + (10 - 0)
⇒ 1/2 × 100 + 10
⇒ 50 + 10
⇒ 60
Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,
⇒ 60
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I have been doing this for 4 hours and still can’t figure these out
The equation of the line is y = x/7 - 1/7
What is equation of a line?The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of a line can be expressed as;
y-y1 = m(x -x1)
where m is the slope
The slope = 1/7
x1 = 8 and y1 = 1
Therefore;
y -1 = 1/7( x -8)
7(y-1) = x-8
7y -7 = x-8
collecting like terms
7y = x - 8+7
7y = x -1
y = x/7 -1/7
The intercept is -1/7 and the slope is 1/7
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Use ≈ 3.14 and round your answer
to the nearest hundredth.
10 ft
6 ft
square feet
The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
We know that,
In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.
The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.
The surface area of this cylinder = (2π x r)h
We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.
The surface area of this cylinder = (2π x r)h
= (2π x 8)10
= (50.24)10
= 502.4
Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.
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The complete question is attached below:
Make selections to complete the proof.
Given: ∠WXZ≅∠YXZ, ∠XZW≅∠XZY, WX⎯⎯⎯⎯⎯⎯≅YX⎯⎯⎯⎯⎯, WZ⎯⎯⎯⎯⎯⎯≅YZ⎯⎯⎯⎯⎯
Prove: ∆WXZ≅∆YXZ
The required angles are,
∠BAC = 73 degree
∠BCA = 17 degree
∠DCF = 17 degree
∠CDF = 80 degree
∠CFD = 95 degree
Since we can see that,
In triangle ABC
The angle B is right angled
Since we know that,
Sum of interior angles of triangle = 180 degree
Therefore, in triangle ABC
⇒ (9x -8 ) + (2x-1) + 90 = 180
⇒ 11x = 99
⇒ x = 9
Thus,
Angle BAC = 9x - 8
= 9x9 - 8
= 73 degree
Angle BCA = 2x - 1
= 2x9 - 1
= 17 degree
Now in triangle, CDF,
Angle C is alternate angle for both the triangles,
Therefore,
Interior angle C of triangle CDF = angle DCF = 17 degree
Angle CDF = 9y - 1
= 9x9 - 1
= 80 degree
Angle CFD = 11y + 4
= 11x9 - 4
= 95 degree
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What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
The measure in radians for the central angle is approximately 0.7 radians.
To find the measure in radians for the central angle of a circle, we can use the formula:
θ = s / r
where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.
In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.
Plugging these values into the formula, we have:
θ = 5.6 cm / 8 cm
Simplifying the expression:
θ = 0.7
We may use the following formula to get the centre angle of a circle's measurement in radians:
= s / r
s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.
The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.
When these values are plugged into the formula, we get:
θ = 5.6 cm / 8 cm
Condensing the phrase:
θ = 0.7
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Convert the polar representation of this complex number into its standard form. A 4-451 B. -43-4/ C. -8√5 +8/ D. 4-4√3 i
The complex number in standard form is written as:
Z = 1.99 + i*0.201, so the correct option is a
How to write the complex number in standard form?Remember that a complex number can be written in standard form as:
Z = a + b*i
And in polar form the notation is (R, θ):
[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]
Here we have the complex number:
Z = 2(cos(11pi/6) + i*sin(11pi/6))?
So here we just need to solve these expressions, we will get:
Z = 2*(0.995 + i*0.100)
Z = 1.99 + i*0.201
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Complete question:
"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "
Help with number 8 please
The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].
How to solve an exponential expression?The exponential expression can be solved as follows:
Therefore, let's simplify the expression.
To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.
∛8x⁴y⁸ / 125
let's solve them individually,
125 = 5³ = 5 × 5 × 5
8 = 2³ = 2 × 2 × 2
Therefore,
∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]
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Ben records the time it took each person to complete a different event.
He is completing a table with information.
Note that in this case, the missing information which is the shortest time is 27 minutes. this is computed using the knowledge of the range.
What is range?The range of a collection of data in statistics is the difference between the highest and smallest values, calculated by subtracting the sample maximum and minimum. It's measured in the same units as the data.
Thus,
Range = Longest time - Shortest time
Since
Mean: 39 minutes
Range: 26 minutes
Longest time: 53 minutes
Shortest time = Longest time - Range
⇒ Shortest time = 53 - 26
= 27 minutes.
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Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. (A reading above 140 is considered to be high blood pressure). Find the percentage of people with blood pressure below 133.
The percentage of people with blood pressure below 133 is 78.81%.
First, we need to calculate the Z-score for the value 133 using the formula:
Z = (X - μ) / σ
where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).
Z = (133 - 121) / 15
Z = 12 / 15
Z = 0.8
Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.
Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.
Therefore, the percentage of people with blood pressure below 133 is 78.81%.
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find the center and radius by completing the square x2+6x+y2-4y=3
Answer:
Center: (-3, 2)
Radius: 4
Step-by-step explanation:
x2 + 6x + y2 - 4y = 3
x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4
(x + 3)² + (y - 2)² = 16
(x + 3)² + (y - 2)² = 4²
Center: (-3, 2)
Radius: 4
Show that the triangles are congruent for the given value in the variable.
5. GH= 3
HI= 3x-9 and x=4
HI= 3(4)-9=
= 12-9
= 3
so, GH = HI
Do the same for GJ and JI.
6. 36=2x
18=x
So, the angles are the same.
4x-11=61
4(18)-11=61
So, the sides are also the same meaning the triangles are congruent.
A ferris wheel has a radius of 10 inches and is 2 inches off the ground. It makes a complete revolution every 10 seconds.
If a rider is directly horizontal to the center of the wheel and moving downward, find an equation that gives his height above the ground as a function of time .
Answer:
y = -10·sin(πt/5) +12
Step-by-step explanation:
You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.
EquationThe general form of the equation will be ...
y = A·sin(2πt/T) + B
where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.
HeightWe assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:
B = 2 + 10 = 12
Scale factorThe scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...
A = 10
PeriodThe period (T) is given as 10 seconds.
Height functionPutting these parameters together gives ...
y = -10·sin(2πt/10) +12
y = -10·sin(πt/5) +12
__
Additional comment
We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.
Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.
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Which statement accurately describes the relationship between JKL and MNP?
The triangles are not similar
Given data ,
Let the first triangle be ΔJKL
Let the second triangle be ΔMNP
Now , the corresponding sides are
JK / JL ≠ NM / MP
where the corresponding sides of similar triangles are not in the same ratio
And , the common angle to both the triangles is ∠J = ∠M
So , ∠J = ∠M and JK / JL ≠ NM / MP
Hence , the triangles are not similar
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make t the subject of the formula k=2(t+3)/t-3
t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.
The given equation is k=2(t+3)/t-3.
We need to isolate t on one side of the equation.
Let's start by cross-multiplying:
k(t - 3) = 2(t + 3)
Expanding the brackets:
kt - 3k = 2t + 6
Now, let's gather all the terms with t on one side and all the constant
terms on the other side:
kt - 2t = 6 + 3k
Factoring out t on the left side:
t(k - 2) = 6 + 3k
Finally, we can solve for t by dividing both sides of the equation by (k - 2):
t = (6 + 3k)/(k - 2)
Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).
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a triangle is shown below, find the m
The value of angle L is 61°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;
A+B = C
Similarly,
angle L and angle E are the interior angles and 113 is the exterior angle, therefore;
113 = L + 52
L = 113 -52
L = 61°
Therefore angle L is 61°
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(X-7)(x-7) multiply the binomials
The product of given two binomials which are (x-7)(x-7) is equal to x² - 14x + 49.
To multiply the binomials (x-7)(x-7), we use the distributive property of multiplication, which states that:
(a + b)(c + d) = ac + ad + bc + bd
Using this property, we can expand the expression as follows:
(x-7)(x-7) = x(x-7) - 7(x-7)
= x² - 7x - 7x + 49
= x² - 14x + 49
The distributive property of multiplication is a mathematical rule that states that when a number is multiplied by the sum of two or more numbers, it is equivalent to multiplying the number by each of the addends and then adding the products.
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