Answer:
29n - 39/2.
Step-by-step explanation:
To simplify the expression 8(3n-2) + 1/2 (10n-7), we can start by using the distributive property of multiplication over addition to simplify the terms inside the parentheses:
8(3n-2) + 1/2 (10n-7) = (83n - 82) + (1/2 * 10n - 1/2 * 7)
This gives us:
24n - 16 + 5n - 7/2
Next, we can combine like terms:
24n + 5n - 16 - 7/2 = 29n - 16 - 7/2
Finally, we can simplify the expression by finding a common denominator for -16 and -7/2:
29n - 16 - 7/2 = 29n - 32/2 - 7/2 = 29n - 39/2
Therefore, 8(3n-2) + 1/2 (10n-7) simplifies to 29n - 39/2.
Which of the
following points
would be a solution
to this system of
linear inequalities?
y≤-3x-2
y> x-2
(-4,1)
(2, 2)
Neither of the given points is a solution to the system of linear inequalities.
What does solution to the system of linear inequalities mean ?
A system of linear inequalities is a set of two or more linear inequalities with the same variables. This system consists of two linear inequalities, each involving the variables x and y, and each inequality uses one of the inequality symbols.
The solution to a system of linear inequalities is the set of values for the variables that satisfy all the inequalities in the system simultaneously. This solution can be represented graphically as the region of the coordinate plane that satisfies all the inequalities in the system.
Check the given points whether they are solutions to the system of linear inequalities or not :
Substitute the x and y values of each point into both inequalities and check if they are true.
(a) (-4,1) :
y ≤ -3x - 2
1 ≤ -3(-4) - 2
1 ≤ 10
This is false, so (-4,1) is a not solution to the first inequality.
y > x - 2
1 > -4 - 2
1 > -6
This is true, so (-4,1) is a solution to the second inequality.
Since (-4,1) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.
(b) (2,2):
y ≤ -3x - 2
2 ≤ -3(2) - 2
2 ≤ -8
This is false, so (2,2) is not a solution to the first inequality.
y > x - 2
2 > 2 - 2
2 > 0
This is true, so (2,2) is a solution to the second inequality.
Since (2,2) is a solution to only one of the inequalities and not both, it is not a solution to the system of linear inequalities.
Therefore, neither of the given points is a solution to the system of linear inequalities.
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Effect of Price on Supply of Eggs Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation.
625p2 − x2 =100
If 37000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of 7¢/carton/week, at what rate is the supply changing? (Round your answer to the nearest whole number.) (Hint: To find the value of p when x = 37, solve the supply equation for p when x = 37.)
The supply of the supply of eggs is changing at 10.7¢ per carton per week
How to determine the rate at which the supply changing?The equation of the function is given as
625p^2 - x^2 = 100
When the supply is 37000, we have
x = 37
So, the equation becomes
625p^2 - 37^2 = 100
Evaluate
625p^2 - 1369 = 100
This gives
625p^2 = 1469
Divide by 625
p^2 = 2.3504
Take the square roots of both sides
x = 1.53
The supply rate is then calculated as
Rate = 7¢ * 1.53
Evaluate
Rate = 10.7¢
Hence, the supply is changing at 10.7¢ per carton per week
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Mr. Perez ask Monica to measure the dimensions of the aquarium to see whether it could fit on the table S applied Michael measured the aquarium's left hand with angle at 96CM and 60CM respectively what is the area of the base of the aquarium
Therefore, the area of the base of the aquarium is 5760 square centimeters.
What is area?Area is a measure of the amount of space inside a two-dimensional (2D) shape or figure. It is usually measured in square units, such as square meters (m²) or square centimeters (cm²). The area of a shape is calculated by multiplying the length of one side or dimension of the shape by the length of another side or dimension. The resulting value represents the total number of square units that are contained within the shape. Area is an important concept in mathematics and is used in various fields, such as geometry, physics, and engineering. It helps in measuring and comparing the sizes of shapes and figures, and in determining how much material is needed to cover or fill a certain area.
Here,
The area of the base can be calculated using the dimensions of the aquarium.
Let's assume that the aquarium has a rectangular base with length L, width W, and height H. Then, the area of the base of the aquarium can be calculated as:
Area of base = Length x Width = L x W
If Monica measured the length and width of the base, we can use those measurements to calculate the area of the base. If not, we'll need to make additional assumptions or measurements.
Assuming we have the length and width of the base, we can calculate the area as follows:
Area of base = Length x Width
Area of base = 96 cm x 60 cm
Area of base = 5760 cm²
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to find the sum of two fractions with the same denominator you just have to add the
A. numerators
B. medians
C. differences
D. denominators
hi
im pretty sure the answer is
a. numerators
hope this helps
good luck;)
Answer:
A
Step-by-step explanation:
You have to add the numerator and keep the denominators the same! :)
Determine if the triangle pictured below is a right triangle.
(30 points)
Answer: Yes
Step-by-step explanation: Even though the sides might be different because there is little detail in this illustration, you actually have to predict, and if it looks as straight up as it is here, it counts as right. (Also, if you have a tool like a protractor, you could use that to measure it.)
Work out 15:
6
Give your answer as an integer or as a
fraction in its lowest terms.
PLEASE HELP
Answer:
[tex] \frac{25}{2} [/tex]
Step-by-step explanation:
Given 15 ÷6/5
[tex]15 \div \frac{6}{5} \\ = > 15 \times \frac{5}{6} \\ = > 5 \times \frac{5}{2} \\ = > \frac{25}{2} \\ therefore \: the \: answer \: is \: \frac{25}{2} \\ this \: is \: because \: it \: cannot \: be \: broken \: down \: into \: lowest \: term \: again[/tex]
PLEASE HELPP
If BE = 10x - 12 and EF = 2x, Find AC
The length of AC is 12.
What are Arithmetic operations?Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.
Given is a line.
A, B, C, D, E and F are equally spaced on the line.
Given that, EF = 2x
This means that distance between each of the point is 2x.
AB = 2x, BC = 2x, CD = 2x, and DE = 2x
Given BE = 10x - 12
BE = BC + CD + DE
= 2x + 2x + 2x
= 6x
So, 10x - 12 = 6x
10x - 6x = 12
4x = 12
x = 3
Now, we have to find AC.
AC = AB + BC
= 2x + 2x
= 4x
= 4 × 3
= 12
Hence AC is 12.
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Use implicit differentiation to find an equation of the tangent line to the curve
sin(x+y)=4x−4y at the point (π,π)
Answer:
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Step-by-step explanation:
o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:
Differentiate both sides of the equation with respect to x:
cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx
Simplify by grouping the terms with dy/dx on one side and the rest on the other side:
cos(x+y) * (1 + dy/dx) + 4dy/dx = 4
Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):
cos(2π) * (1 + dy/dx) + 4dy/dx = 4
Simplify:
-5dy/dx = 4 - cos(2π)
dy/dx = -4/5
Use the point-slope form of the equation of a line to write the equation of the tangent line:
y - π = (-4/5)(x - π)
Simplify:
y = (-4/5)x + (8/5) + π
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $47.96 and costs an additional $0.19 per mile driven. The second plan has an initial fee of $53.96 and costs an additional $0.15 per mile driven. How many miles would Debra need to drive for the two plans to cost the same?
By answering the above question, we may state that Debra would thus function need to travel 150 miles for the price of the two plans to be the same.
what is function?Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.
The starting charge and the cost per mile would be added together for the first plan's total cost:
Costs for plan 1 total 47.96 plus 0.19x.
The first charge and the cost per mile would be added together for the second plan's total cost:
Plan 2's overall cost is 53.96 plus 0.15x.
Set the two total cost expressions equal to one another and solve for x to get how many miles Debra would need to go for the two plans to be the same in price:
47.96 + 0.19x = 53.96 + 0.15x
0.04x = 6
x = 150
Debra would thus need to travel 150 miles for the price of the two plans to be the same.
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explain what we mean by marginal cost
Answer: Marginal cost is the added cost to produce an additional good or the increase in production costs generated by the production of additional product units
Step-by-step explanation: It is calculated by taking the total change in the cost of producing more goods and dividing that by the change in the number of goods produced.
Answer:
So it's basically the cost added by producing one extra unit of a product or service. I hoped this helped and if you need a better explanation let me know!
Help me please I need help i dont know the answer!
The value of x that makes the equation true is 2.25.
What are model representations of equation?A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modelling is the process of creating a mathematical model. Both applied mathematics and the natural sciences employ mathematical models. The area of operations research is largely concerned with using mathematical models to resolve issues in commercial or military operations.
Using the figure we see that, for the left model we have:
3 (-x) = -3x.
Also, we have 10(1) = 10
Thus the left model has the equation:
-3x + 10
For the right model we have:
5x - 8
Equate the two models:
-3x + 10 = 5x - 8
18 = 8x
x = 2.25
Hence, the value of x that makes the equation true is 2.25.
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Angel 270 and radius 12
Therefore, the length of the arc intercepted by the central angle is 56.52 cm (rounded to two decimal places).
What is arc?In geometry, an arc is a part of a circle. Specifically, it is a portion of the circumference of a circle. An arc can be defined by two endpoints and all the points on the circle's circumference between those endpoints. Arcs are commonly measured in degrees, just like angles. A full circle has 360 degrees, so a semicircle has 180 degrees, and so on. The length of an arc depends on the size of the circle and the size of the central angle that intercepts it. Arcs are important in many applications of geometry, such as in navigation, architecture, and engineering. They are also used in trigonometry and calculus to study functions that involve circular or periodic behavior.
Here,
We can use the formula for the length of an arc of a circle to find the length of the arc intercepted by a central angle. The formula is:
Length of arc = (Central angle / 360) x (2 x π x radius)
where π (pi) is a mathematical constant approximately equal to 3.14.
In this case, the central angle measures 270 degrees and the radius of the circle is 12 cm. We can substitute these values into the formula to get:
Length of arc = (270 / 360) x (2 x π x 12)
Length of arc = (3/4) x (2 x 3.14 x 12)
Length of arc = 0.75 x 75.36
Length of arc = 56.52 cm
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Complete question:
A central angle measures 270 degrees . If the radius of the circle is 12 cm , what is the length of the arc intercepted by the central angle ?
A rectangle ABCD has coordinates A(1, 2), B(7, 5) and C(1, 5) for three of its vertices. The rectangle is dilated by a scale factor of 3 with the center of dilation at the origin. The new rectangle that is formed is A’B’C’D’. What are the coordinates of D’ ?
Answer:
I think is D'C becausse everything goes back words
The average cost to build a 4 , 000 sq ft fast-food restaurant in Miami is about $ 952 , 000 . Find the average cost per square foot to build a fast-food restaurant.
Average cost per square foot to build a fast-food restaurant is $238 .
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers.
Given,
Area of the restaurant = 4000 sqft
Total average cost to build the restaurant
= $952000
Average cost of per sqft
= 952000/4000
= $238
Hence, $238 is the average cost per square foot to build a fast-food restaurant.
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Patrick bought 4 bags of beans. There are b beans in each bag. Write an expression that shows how many beans Patrick bought.
how do you figure this out????????????
Patrick bought 4 times the number of beans in each bag.
What is expressions ?
An expression is a combination of one or more numbers, variables, and operations. It can contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be evaluated to obtain a numerical result or simplified by combining like terms or using mathematical rules.
To find an expression that shows how many beans Patrick bought, you can multiply the number of bags by the number of beans in each bag.
So, if Patrick bought 4 bags of beans, and there are b beans in each bag, then the expression would be:
4b
This means that Patrick bought 4 times the number of beans in each bag.
Therefore, Patrick bought 4 times the number of beans in each bag.
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the dot plot shows the number of wins for 16 baseball teams which statement about the data is true
Based on the dot plot, it appears that the data is spread relatively evenly across the teams, with no one team dominating the others by a wide margin.
What is data in math?Data is the raw information that can be collected and analyzed to provide insights. It is the foundation of decision-making and can be used to identify trends, patterns, and relationships. Data can come from many different sources, including surveys, databases, and software applications. Data can be qualitative or quantitative, static or dynamic, structured or unstructured, and can be used to inform decisions, inform policy, and inform research. Data can also be used to make predictions, monitor performance, and improve efficiency.
This suggests that the competition between the teams is relatively balanced, and that no team is significantly outperforming the others in terms of number of wins. This could indicate that the teams are of about equal skill level, or that the schedule for each team is balanced enough that no team has an advantage over the others.
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What does a right triangle equal
Answer:
180 degree
Step-by-step explanation:
The right triangle equals 180 degree. All three angles must add up to 180.
Answer:
180°
Step-by-step explanation:
right triangles equal 180°
which part of diagram shows the quantity x?
The diagram shows the quantity x is 13.
What is tape diagram?A tape diagram, also known as a bar model or a strip diagram, is a visual representation of a problem or situation that helps students to organize and solve mathematical problems. It involves drawing a rectangular strip or bar to represent a quantity or a value, and then dividing or labeling the strip to represent different parts of the problem.
The full completed question is related to an equation as shown in the below diagram (Check it).
Given equation is x+4 = 17
Draw a tape diagram to represent the equation.Which part of the diagram shows the quantity of x ?If we select part 'a' the diagram is shown in the below diagram, see it.
For part 'b' the quantity x can be represent by:
x+4 = 17
x = 17 - 4
x = 13
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Now that you have the height of the cone, how can you solve for the slant heights
Height = 21 mm
Volume = 8792 mm
Radius 20mm
The slant height [tex]l = 29 \: mm[/tex].
What is a Cone?A cone is a three-dimensional geometric shape with a smooth transition from a flat, usually circular base to the apex or vertex, which forms an axis to the base's center.
As per the given data:
Height = 21 mm
Volume = 8792 mm
Radius = 20 mm
For slant height of the one ([tex]l[/tex]):
[tex]l = \sqrt{r^2 + h^2}[/tex] {using Pythagoras theorem}
[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]
[tex]l = \sqrt{(20)^2 + (21)^2}[/tex]
[tex]l = \sqrt{400 + 441}[/tex]
[tex]l = 29 \: mm[/tex]
Hence, the slant height [tex]l = 29 \: mm[/tex].
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In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Aaron sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
38 visitors purchased no costume.
239 visitors purchased exactly one costume.
12 visitors purchased more than one costume.
Based on these results, express the probability that the next person will purchase no costume as a decimal to the nearest hundredth.
The probability that the next person will purchase no costume is 0.13.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The total number of visitors to the website in a single day is:
38 + 239 + 12 = 289
Of these visitors, we know that 38 purchased no costume.
Therefore, the probability that the next person to visit the website will also purchase no costume is:
38/289 = 0.13
Hence, the probability that the next person will purchase no costume is approximately 0.13, or 13% to the nearest hundredth.
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What is the area of this complex figure?
178 m²
128 m²
30 m²
20 m²
Answer: 164
Step-by-step explanation: (16 X 8) + (6 X 5)+ (^^triang)+ 164
Is this line proportional or non-proportional
The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. What is the best predicted value for y given x=41? Assume that the variables x and y have a significant correlation.
X= 38 41 45 48 51 53 57 61 65
Y= 116 120 123 131 142 145 148 150 152
The solution is : the predicted blood pressure for a person aged 64 will be : 156.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x ; ax^2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.
here, we have,
Given the data:
Age (X) :
38
41
45
48
51
53
57
61
65
Pressure(Y) :
116
120
123
131
142
145
148
150
152
From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :
The regression equation obtained is :
y = 1.48769X + 60.46103
Using the model, the predicted blood pressure for a person aged 64 will be :
y = 1.48769(64) + 60.46103
y = 95.21216 + 60.46103
y = 155.67319
y = 156 (nearest whole number)
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The best predicted value of y for the given x=41 is 121.45.
What is the correlation coefficient?The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.
Given that,
X= 38 41 45 48 51 53 57 61 65
Y= 116 120 123 131 142 145 148 150 152
∑x= 459
∑y= 1227
∑x²= 24059
∑y²= 168843
∑xy= 63544
Sxx= ∑x²-∑x²/n
= 24059-459²/9
= 650
Sxy = ∑xy-(∑x·∑y)/n
= 63544-(459×1227)/9
= 63544-62577
= 967
Now, slope =967/650= 1.488
Mean of x=459/9 =51
Mean of y=1227/9 = 136.33
Now, intercept is b=136.33-(1.488×51)
= 60.442
Here, the equation of a line is y=1.488x+60.442
When x=41, we get
y=1.488×41+60.442
y= 121.45
Therefore, the best predicted value of y is 121.45.
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Given CB is 7 and angle A is 25, find the value of triangle ABC.
The value of area of triangle ABC is found as 11.42 sq. unit.
Explain about the area of triangle?A triangle is really a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides with three angles in every triangle, and some of them could be the same.A triangle's surface area is equal to the product of its base and height.Area of a triangle = ½ × base × height.
From the given data:
Using trigonometric function.
tan 25 = 7 / AC
AC = 7*tan 25
AC = 3.26
Area of triangle ABC = ½ × 7× 3.26
Area of triangle ABC = 11.42
Thus, the value of area of triangle ABC is found as 11.42 sq. unit.
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Kallie works at a pet store. Part of her job is to add the correct amount of water
conditioner to each fish tank. The list below provides information about the
number of fish tanks and the amount of water conditioner she uses.
• There are 12 fish tanks that need water conditioner.
• Each fish tank is filled with 20 quarts of water.
• For every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner.
What is the total number of teaspoons of water conditioner Kallie will use for all the
water in the 12 fish tanks?
The number of teaspoons that Kallie will use for all the water in the 12 fish tanks is given as follows:
6 teaspoons.
How to obtain the number of teaspoons?The number of teaspoons that Kallie will use for all the water in the 12 fish tanks is obtained applying the proportions in the context of the problem.
Each fish tank is filled with 20 quarts of water, which is equivalent to 20 x 0.25 = 5 gallons of water.
There are 12 fish tanks, hence the total number of gallons that are needed is given as follows:
12 x 5 = 60 gallons.
For every 10 gallons of water, Kallie uses 1 teaspoon of water conditioner, hence the number of teaspoons is given as follows:
60/10 = 6 teaspoons.
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If a system has no solution, what do you know about the lines being graphed?
PART B:
If a system has 1 solution, what do you know about the lines being graphed?
PART C:
If a system has infinitely many solutions, what do you know about the lines being graphed?
If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint.
If a system has 1 sοlutiοn, it means that the lines being graphed intersect at a single pοint.
If a system has infinitely sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther.
What is Linear Equatiοn in Twο Variables?A linear equatiοn in 2 variables is an algebraic expressiοn that represents a straight line οn a 2D cοοrdinate plane.
It can be written in the fοrm οf y = mx + b, where m is the slοpe οf the line, b is the y-intercept, and x and y are the twο variables.
PART A:
If a system has nο sοlutiοn, it means that the lines being graphed are parallel and dο nοt intersect at any pοint. This implies that there are nο values οf the variables that can satisfy bοth equatiοns simultaneοusly.
PART B:
If a system has one sοlutiοn, it means that the lines being graphed intersect at a single pοint. This implies that there is οnly οne unique sοlutiοn that satisfies bοth equatiοns simultaneοusly.
PART C:
If a system has infinitely many sοlutiοns, it means that the lines being graphed are cοincident, i.e., they lie οn tοp οf each οther. This implies that there are an infinite number οf values οf the variables that can satisfy bοth equatiοns simultaneοusly since every pοint οn the shared line is a valid sοlutiοn tο the system.
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a package of 8 count AA batteries costs $6.16, a package of 20 count AA batteries costs $15.20
Answer:
What is the unit price of each battery in each package?
To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.
For the package of 8 count AA batteries:
Total cost: $6.16
Number of batteries: 8
Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery
For the package of 20 count AA batteries:
Total cost: $15.20
Number of batteries: 20
Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery
Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.
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Step-by-step explanation:
To find the unit price of each battery in each package, we need to divide the total cost of each package by the number of batteries in each package.
For the package of 8 count AA batteries:
Total cost: $6.16
Number of batteries: 8
Unit price = Total cost / Number of batteries = $6.16 / 8 = $0.77 per battery
For the package of 20 count AA batteries:
Total cost: $15.20
Number of batteries: 20
Unit price = Total cost / Number of batteries = $15.20 / 20 = $0.76 per battery
Therefore, the unit price of each battery in the package of 8 count AA batteries is $0.77, and the unit price of each battery in the package of 20 count AA batteries is $0.76.
Using arithmetic operation, the statement that is true is -
A: The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.
D: The 8-count pack of AA batteries has a lower unit price of S0.77 per battery
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
To find the unit price per battery, we divide the cost of each package by the number of batteries in the package.
For the 8-count pack -
Use the arithmetic operation of division.
Unit price per battery = $6.16 / 8 batteries = $0.77 per battery
For the 20-count pack -
Use the arithmetic operation of division.
Unit price per battery = $15.60 / 20 batteries = $0.78 per battery
Therefore, the statements A and D are correct.
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Image! (URGENT)
(Please give answer to combine like terms part too if its not correct)
Answer:
3y²+6y-2y²+3y
collect like terms
3y²-2y²+6y+3y
5y²+9y
find the value of x. 6cm 4cm x = ? cm angle measures and segment lengths
The length of segment in the given circle x is 5 cm.
What is circleA circle is formed by all points in a plane that are at a particular distance from the centre. The radius of a circle is the separation between any point on the circle and its center.
Intersecting Secant-Tangent TheoremThe product of the measures of the secant segment and its external secant segment equals the square of the measure of the tangent segment if a tangent segment from a location outside the circle, secant segments are drawn.
In the circle shown, if
AB=6cm
AC=4cm and
CD=x?
According to tangent-secant relation:AC×AD=[tex]AB^{2}[/tex]
4(4+x)=[tex]6^{2}[/tex]
4+x=36/4
x=5
Hence, The length of segment in the given circle x is 5cm.
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If the surface area of a shape is 314 and a 5 by 5 cube is taken out of the shape what is the surface area now?
The surface area of the shape when a cube is taken out of it would be = 164.
How to calculate tye surface area of the shape?The surface area is defined as the area that is being occupied by outer surface of a shape of object.
The surface area of a given shape = 314
An area of a cube shape is taken out of it with sides = 5×5
The area of a cube = 6(a²)
where a = 5
area of the cube = 6(5²)
= 6×25 = 150
Therefore, the surface area of the shape after area of cube such as = 150 has been removed from it ;
= 314-150
= 164.
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