A letter to a student who will be taking this math class next year to give them some advice about this class has been written below.
(Sender's address)
20/01/2023
Dearest,
I was happy to see your letter, and I hope this letter finds you in the best of health. I have wanted to go on a trip with you for a long time but I guess that would happen later since you have to start attending classes soon.
I have a list of things to keep in mind when you start your classes. I was always too scared of mathematics, and I know you are too, but I have always wanted to tell you how fruitful it is to learn a subject that will help you in every field you want to go in. Let me know what you think about it after you finish reading this letter. I know it is no secret that maths is a difficult subject but you can master it if you keep what I am going to tell you in mind. Practice your concepts daily. Keep brushing up on whatever your teacher teaches you. Remember the formulas and you will know how to answer any question. I know for sure that it is going to be worth it too.
I will make sure that I meet you next weekend so that we can meet before you begin the classes. If you try hard, you can make this work. See you soon.
Love,
(Sender's name)
Learn more about letter writing on
https://brainly.com/question/24297273?referrer=searchResults
#SPJ4
1. A TV has a width of 45 inches and a height of 30
inches. What is the length of the diagonal of the TV?
A TV has a width of 45 inches and a height of 30inches the length of the diagonal of the TV is 54.08inches.
What is Rectangle?
A rectangle is a quadrilateral with four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
Make a diagonal and a rectangle. Two parallel triangles appear. Pay attention to one of the triangles.
We have a right triangle with a = 45 and b = 30
we have to find the c = ?
Let's find b using the Pythagorean Theorem;
a^2 + b^2 = c^2
45^2 + 30^2 = c^2
2025 + 900 = c^2
2925 = c^2
c = 54.08 inches
Therefore,the diagonal of the TV is 54.08inches.
Learn more about Rectangle click here:
https://brainly.com/question/23008020
#SPJ1
Annette is standing with a tree directly between her and a building. She stands so that, in her eyes, the
top of the tree appears to "touch" the top of the building. If the distance between her and the tree is
30 ft, the distance between the tree and the building is 15 ft, and the tree is 20 ft tall, how tall is the
building? (You may ignore her height.)
The height of the building is 30 feet.
How to find the height of the building?Annette is standing with a tree directly between her and a building. She stands so that, in her eyes, the top of the tree appears to "touch" the top of the building.
The distance between her and the tree is 30 ft, the distance between the tree and the building is 15 ft, and the tree is 20 ft tall.
Therefore, the height of the building can be calculated as follows:
The situation forms two right angle triangle.
Therefore, using similar triangle ratio,
20 / 30 = x / 45
where
x = height of the buildingHence,
45 × 20 = 30x
900 = 30x
x = 900 / 30
x = 30
Therefore,
height of the building = 30 ft
learn more on right triangle here: https://brainly.com/question/11380308
#SPJ1
Using the vertex (5, 17) and a point (11, -109), write your equation in Vertex Form.
Answer:
y=-3.5(x−5)^2+17
Step-by-step explanation:
Let's assume that since this equation has a vertex that it is a parabola with the form y = ax^2 + bx + c.
Let's rewrite it in vertex form as:
y=a(x−h)^2+k
where h and k are the horizontal (h) and vertical (k) coordinates of the vertex.
The vertex of (5,17) gives us both h (5) and k (17), Substituting these values gives us:
y=a(x−5)^2+17
To find a, use the one given point the parabola intersects (11,-109) and solve for a:
y=a(x−5)^2+17
-109=a((11)−5)^2+17
-109=a(6)^2+17
-109-17=a(36)
36a = -126
a = -3.5
This leads us to:
y=-3.5(x−5)^2+17
See the attached graph.
What is the value of the expression below when y=3 y=3?
3 y^2 - 4 y + 8 3 y 2 − 4 y + 8
Answer:
When y = 3, we can substitute 3 for y in the expression 3 y^2 - 4 y + 8
3(3^2) - 4(3) + 8
= 3(9) - 12 + 8
= 27 - 12 + 8
= 15
Therefore, the value of the expression 3 y^2 - 4 y + 8 when y = 3 is 15.
Answer:
Basically since y = 3 we just have to remove the 'y' from the equation and replace it with the number 3. (Also pretty sure you wrote the equation twice)
Original Equation:
3 y^2 - 4 y + 8
Modified Equation:
→ 3 (3²) - 4(3) + 8
→ 3 (9) - 12 + 8
→ 27 - 12 + 8
→ 15 (answer)
Equation with 'y' included:
→ y (y²) - 4 (y) + 8
→ y (9) - 12 + 8
→ 27 - 12 + 8
→ 15 (answer)
If you help you get a cookie :)
What operation is happening between this coefficient and variable?
4y
Responses
A DivisionDivision
B AdditionAddition
C MultiplicationMultiplication
D Subtraction
Answer: the answer is A SO WERE IS MY COOKIE :(
Step-by-step explanation:
All the information is in the picture help please
That X, w, and Z w are related we demonstrate that these are identical.
What is congruence of angle?This makes a right triangle with segment y V as the opposite side, and we once more know that X Y and segment y Z are perpendicular. The reason why these Arkan wrote them this time is because, in my mind, they are nooses of similar triangles on the triangles, X, y v um, and our other triangle will be a Z y V. Finally, we wish to demonstrate the congruence of angle visi w with angle v X w, which will be right here. So, it's a little difficult to establish this one in this instance. However, in essence, because we have previously established that X, w, and Z w are related we demonstrate that these are identical. Additionally, we demonstrated that the Zeevi Arkin Group and XVI, which border on the last side, will both inform us that our angles are same. Therefore, given that we have previously established certain elements,
To learn more about congruence refer to:
https://brainly.com/question/11949261
#SPJ1
If the domain of f(x) is -3 ≤ x ≤ 9 and the range of f(x) is 2 ≤ y ≤ 15, then which of the following
statements is correct about the domain and range of 9 (x) = f(x-2) - 8?
"The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.
What is the Domain and Range of the function?
The domain of a function is the set of all input values (x-values) for which the function is defined. It is the set of all values of x for which the function is defined.
The range of a function is the set of all output values (y-values) that the function can produce. It is the set of all possible values that the function can take on.
The domain of a function is the set of all input values (x-values) for which the function is defined. The range of a function is the set of all output values (y-values) that the function can produce.
When we shift a function horizontally, the domain remains unchanged, but the range will change. In the case of a shift of -2, the domain of f(x) is still -3≤x≤9
For 9(x) = f(x-2) - 8, it means that we are taking the output of f(x-2) and subtracting 8 from it. So, the range of 9(x) will be (2-8) ≤ y ≤ (15-8) = -6 ≤ y ≤ 7.
In summary,
The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9
The range of 9(x) = f(x-2) - 8 is -6 ≤ y ≤ 7
Hence, statement "The domain of 9(x) = f(x-2) - 8 is -3 ≤ x ≤ 9 and the range is -6 ≤ y ≤ 7" is correct.
To learn more about Domain and Range, Visit
https://brainly.com/question/10197594
#SPJ1
Alexia used three reams of paper in her first semester of school. Each ream has the same number of sheets. She used another 40 sheets after that. Write an expression to represents the number of sheets Alexia used
An expression to represent the number of sheets Alexia used is y = 3x + 40.
In math, expressions are mathematical statements with a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
The mathematical operators can be any of addition, subtraction, multiplication, or division. For example, p + q is an expression where p and q are terms having an addition operator in between.
There are two types of expressions, numerical expressions - which contain only numbers, and algebraic expressions- which contain both numbers and variables.
let
x = the number of sheets per ream
y = the total number of sheets
Alexia used three reams of paper, so the total number of sheets per ream will be 3x since each ream has the same number of sheets.
After that, she used another 40 sheets. Therefore the expression will become as
y = 3x + 40 represents the total number of sheets Alexia used.
To know more about expression, here
https://brainly.com/question/13947055
#SPJ4
Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5% and he left a 20% tip after the tax was added.
If Mr. Rankin put $120 on the table, how much change did he receive?
If Mr. Rankin put $120 on the table, the change he would receive $8.82
What is Percentage ?
Percentage can be defined as the product ratio of given value, total value and hundred.
Mr. Rankin took his family out to dinner last night and their subtotal was $88.24. The sales tax was 5% and he left a 20% tip after the tax was added.
If Mr. Rankin put $120 on the table, the change he would receive
tax = 5/100 * 88.24
tax = 4.412
tip = 20/100 * 88.24
tip = 17.648
Total amount = 88.24 +4.412+17.648
= 111.18
So, If Mr. Rankin put $120 on the table, the change he would receive
= 120 -111.18 = 8.82
Therefore, If Mr. Rankin put $120 on the table, the change he would receive $8.82
To learn more about Percentage from the given link.
https://brainly.com/question/21865143
#SPJ1
a track star runs two races on a certain day. the probability that she wins the first race is 0.7, the probability that she wins the second race is 0.6, and the probability that she wins both races is 0.5. what is the probability that: note: define your events, and write the probability statement before you calculate an answer. you can show your work using equations or venn diagrams.
The probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1
Let A be the event that the track star wins the first race, B be the event that the track star wins the second race.
The probability that the track star wins at least one race is: P(A U B) = P(A) + P(B) - P(A ∩ B)
The probability that the track star wins the first race but not the second race: P(A ∩ B') = P(A) - P(A ∩ B)
The probability that the track star wins the second race but not the first race: P(A' ∩ B) = P(B) - P(A ∩ B)
Given:
P(A) = 0.7
P(B) = 0.6
P(A ∩ B) = 0.5
P(A U B) = 0.7 + 0.6 - 0.5 = 0.8
P(A ∩ B') = 0.7 - 0.5 = 0.2
P(A' ∩ B) = 0.6 - 0.5 = 0.1
So the probability that the track star wins at least one race is 0.8, the probability that she wins the first race but not the second is 0.2, and the probability that she wins the second race but not the first is 0.1.
To learn more about probability visit: brainly.com/question/30034780
#SPJ4
Consider the two equations below. Explain completely the similarities and differences in how you would solve each equation. Be clear and complete.
The first equation, 3^x = 12, is an exponential equation. To solve for x, we would take the logarithm of both sides with base 3:
x = log3(12)
The second equation, x^3 = 12, is a polynomial equation of degree 3. To solve for x, we would take the cube root of both sides:
x = ∛12
How does the equation compare?The similarity between these two equations is that both are equations with one variable and are looking for the value of that variable.
The main difference between these two equations is the type of function they represent. The first equation is an exponential function, represented by 3^x, while the second equation is a polynomial function, represented by x^3.
As a result, the methods used to solve these equations are also different. The first equation is solved by taking the logarithm of both sides and the second equation is solved by taking the cube root of both sides.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ1
Pablo draws rectangle p he says that the area is greater than 50 square units what could the missing side length be
Any pair of positive numbers x and y that satisfy the inequality x * y > 50 will be the sides of rectangle.
If the area of rectangle P is greater than 50 square units, then the product of its length and width must be greater than 50. Let the length of the rectangle be x and the width be y. Then, we have:
x * y > 50
Since the missing side length is unknown, we cannot solve for a specific value. But we can say that any pair of positive numbers x and y that satisfy the inequality will represent a rectangle with an area greater than 50 square units.
To learn more about inequality here:
https://brainly.com/question/19003099
#SPJ4
where do i put the line pls help i’ll give brainly
Answer:
5,7
Step-by-step explanation:
HURRY PLEASE!!!!!
Which statements about the factors of the terms in the expression 20 a + 15 a b + 24 b are true? Select three options.
Group of answer choices
a) The GCF of the expression is 1
b) The factors common to 20a and 24b are 1, 2, and 4.
c) The GCF of the expression is ab.
d) The factors common to 20a and 15ab are 1, 5, a, and b.
e) The factors common to 20a and 15ab are 1, 5, and a.
Answer: A, B, E
Step-by-step explanation:
For A:
None of the factors have one same factor they can be divided by besides 1.
For B:
Both 20a and 24b can be divisible by 1,2,4.
For E:
Both 20a and 15ab are divisible by 1,5 and a.
The line inside this circle is its
A)
radius
B)
center
C)
diameter
D)
circumference
The line inside the circle depicted in the figure is radius.
A circle is defined as the round shape lacking corners and line. However, it does comprise of all the points in a plane. The center of the circle is the middle point which is equidistant from the outer surface of the circle. The outer surface or boundary of circle is called circumference.
A line joining the centre of the circle with circumference is called radius and the same is exhibited in the adjoining figure. A line that passes through the centre of the circle and touches the circumference at two ends is called diameter. Diameter is double in size to the radius.
Learn more about radius -
https://brainly.com/question/24375372
#SPJ4
The complete question is attached in the figure.
Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters. Use estimation to complete the statements below about Adya's soup.
the remaining soup at Adya's place is 24/114 liters As per the given ratio.
What is the ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, Adya makes 9/38 liters of soup for a party. The guests eat 3/57 liters.
Since the total soup was 9/38 liters
Thus,
Remaining soup at Adya = 9/38 -3/57
LCM of 38 and 57 are 114
Remaining soup at Adya = 27/114 - 6/114
Remaining soup at Adya = 27/114 liters
Therefore, the remaining soup at Adya's place is 24/114 liters.
Learn more about ratios here:
https://brainly.com/question/13419413
#SPJ1
A three-column table is given. Part A C D Part 14 28 63 Whole 50 B 90 What is the value of B in the table? 64 50 40 12
Using the constant of proportionality the value for B in the table is obtained as option C: B = 40.
What is a COP?
The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
The table contains three columns A, C, D.
The first row contains all the part values - 14, 28, 63
The second row contains all the whole values - 20, B, 90
It is necessary to calculate the constant of proportionality.
In this case, for A, we have 14 part and 20 whole, the constant will be -
COP = Whole / Part
COP = 20 / 14
COP = 1.42857
In this case, for C, we have 63 part and 90 whole, the constant will be -
COP = Whole / Part
COP = 90 / 63
COP = 1.42857
Since, the constant of proportionality is same for A and C, it will be same for B also.
In this case, for B, we have 28 part and B whole, the constant will be -
COP = Whole / Part
1.42857 = B / 28
B = 1.42857 × 28
B = 40
Therefore, the value for B is obtained as 40.
To learn more about constant of proportionality from the given link
https://brainly.com/question/27598477
#SPJ1
A three-column table is given. Part A C D Part 14 28 63 Whole 20 B 90 What is the value of B in the table? 64 50 40 12
Which of the following is the product of the rational expressions shown below?
[tex]\frac{3x^{2} }{x^{2} +x-6}[/tex] is the product of the rational expressions.
What are rational expressions?
Two polynomials' ratio is shown through rational expressions. It denotes a polynomial in the denominator as well as the numerator. It is an algebraic expression that contains an unknown variable and is similar to a fraction in that it is a ratio.
We are given [tex]\frac{3x^{2} }{x^{2} +x-6}[/tex]
This means that the expression has to be multiplied by the number 1 for obtaining the product of the rational expression.
We know that when anything is multiplied by the number 1, we get the number itself.
Hence, [tex]\frac{3x^{2} }{x^{2} +x-6}[/tex] is the product of the rational expressions.
Learn more about rational expression from the given link
https://brainly.com/question/30291585
#SPJ1
Multiply.
(x² - 5x) (2x²+x-3)
O A. 2x+9x3 - 8x² + 15x
OB. 2x4-9x3-8x² + 15x
OC. 4x+9x3-8x² + 15x
OD. 2-9x3-9x² - 15x
The resultant of the given expression (x² - 5x) (2x²+x-3) is 2x^4 - 7x^3 -8 x^2 + 15x .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression,
(x² - 5x) (2x²+x-3)
= x^2 ( 2x^2+x-3) - 5x(2x^2 + x - 3)
= 2x^4 + x^3 - 3x^2 - 5x * 2x^2 + x*-5x - 3 * -5x
= 2x^4 + x^3 -3x^2 - 10 x^3 - 5x^2 + 15x
= 2x^4 + x^3 - 10x^3 -3x^2 - 5x^2 + 15x
= 2x^4 - 7x^3 -8 x^2 + 15x .
Hence, The resultant of the given expression (x² - 5x) (2x²+x-3) is 2x^4 - 7x^3 -8 x^2 + 15x .
To learn more about Algebraic expression from the given link.
brainly.com/question/953809
#SPJ1
rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} \sqrt{3} \sqrt{7}}$, and write your answer in the form\[ \frac{a\sqrt{2} b\sqrt{3} c\sqrt{7} d\sqrt{e}}{f}, \]where everything is in simplest radical form and the fraction is in lowest terms, and $f$ is positive. what is $a b c d e f$?
The sum of a+b+c+d+e+f=57.
Apparently, you want to simplify: [tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7} }[/tex]
so the denominator is rational. It looks like the form you want is:
[tex]\frac{A\sqrt{2}+B\sqrt{3} +C\sqrt{7} +D\sqrt{E} }{F}[/tex]
And you want to know the sum A+B+C+D+E+F.
We can start by multiplying the numerator and denominator by a conjugate of the denominator. Then we can multiply the numerator and denominator by a conjugate of the resulting denominator.
[tex]\frac{1}{\sqrt{2} +\sqrt{3} +\sqrt{7}} .\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{\sqrt{2} +\sqrt{3} -\sqrt{7}} =\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6-2} } \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}}{2\sqrt{6} -2} .\frac{\sqrt{6}+1 }{\sqrt{6} +1} =\frac{(1+\sqrt{6} )(\sqrt{2} +\sqrt{3} -\sqrt{7})}{10} \\\\\\=\frac{\sqrt{2} +\sqrt{3} -\sqrt{7}+2\sqrt{3}+3\sqrt{2} -\sqrt{42} }{10} =\frac{4\sqrt{2} +3\sqrt{3} -\sqrt{7} -\sqrt{42} }{10}[/tex]
Comparing this to the desired form we have:
A = 4, B = 3, C = -1, D = -1, E = 42, F = 10
Then the sum is : A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57
The sum of interest is 57.
To know more about radical form:
https://brainly.com/question/24236997
#SPJ4
Translate each verbal description into an algebraic expression. Simplify the expression when you can. 120% of 5x
120% can be expressed as a decimal by dividing it by 100: 120 / 100 = 1.2 So, 120% of 5x can be expressed as: 1.2 * 5x = 6x The expression simplifies to 6x.
What is algebraic expression?Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient. An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).These expressions are represented with the help of unknown variables, constants and coefficients. The combination of these three (as terms) is said to be an expression.
To learn more about Algebraic expressions refer to:
brainly.com/question/2164351
#SPJ1
Two circle of radii 8cm with centre p and q are given the chord AB of circle with centre P and the chord CD of the circle with centre Q are equal if angle PAB=40 then find angle CQD
The angle PAB is given as 40 degrees so we can use the sine rule to calculate the lengths of the chords is CQD = 17.7 degrees.
The sine rule states that the ratio of the length of a side of a triangle to the sine of its opposite angle is equal to the ratio of any other side to the sine of its opposite angle.
Let us denote the length of chord AB by x and the length of chord CD by y.
Therefore x/sin 40 = y/sin (180-40)
=> x/0.766 = y/0.939
=> x = 0.766*0.939 = 0.723
y = 0.939*0.766 = 0.723
Since AB=CD, x=y=0.723.
We can now use the cosine rule to calculate the angle CQD.
The cosine rule states that the square of the length of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides times the cosine of the included angle.
Therefore CQ^2 = 8^2 + 8^2 - 2(8^2)cosCQD
=> CQ^2 = 64 - 64cosCQD
=> 64 - 64cosCQD = 0.723^2
=> 64 - 64cosCQD = 0.521
=> 64cosCQD = 63.479
=> cosCQD = 63.479/64
=> cosCQD = 0.988
Therefore CQD = cos^-1(0.988)
=> CQD = 17.7 degrees.
Learn more about length of chord here:
https://brainly.com/question/29200017
#SPJ4
The 5th graders are going to paint miniature self portraits in art class. Each student has a canvas that is 5. 3 cm wide and 8. 5 cm tall.
The art teacher has 6 bottles of white paint for the background. Each bottle covers 220. 8 square cm of canvas.
There are 30 students in the class.
Does he have enough paint for all the canvases? If not, how much more does he need?
There is not enough paint for all the canvases. 26.7 cm² of more white paint is required.
Area of each canvas = Length × width
Area of each canvas = 5.3 × 8.5
Performing multiplication
Area of each canvas = 45.05 cm²
Total area of canvas in the class = 45.05 × 30
Performing multiplication
Total area of canvas in the class = 1351.5 cm²
Available amount of white paint = 6 × 220.8
Performing multiplication
Available amount of white paint = 1324.8 cm²
The available amount is less than canvas area in the class.
Amount of paint required = 1351.5 - 1324.8
Performing subtraction
Amount of paint required = 26.7 cm²
Thus, 26.7 cm² of white paint is required.
Learn more about multiplication -
https://brainly.com/question/10873737
#SPJ4
find an appropriate scale to use to graph the algebraic tule y= 3x — 11. Consider input values from -5 to 5.
To graph the algebraic rule y = 3x - 11, we need to consider input values from -5 to 5 and also choose appropriate scaling for the x and y axes.
How to use scale?A common way to choose a scale is to use 1 or 2 increments on the x and y axes. This makes it easy to draw points and read charts easily.
The x-axis goes from -5 to 5, so you can scale from -5 -4 -3 -2 -1 0 1 2 3 4 5.
For the y-axis, I need to find the minimum and maximum values of y given the input x values.
Substituting the x value into the formula y = 3x - 11 gives the y value.
y = 3(-5) - 11 = -16
y = 3(5) - 11 = 14
So for the y axis you can take -20 -15 -10 -5 0 5 10 15 20
So a good scale for the x-axis is -5 to 5 in increments of 1, and -20 to 20 in increments of 5 for the y-axis. Graphing the equation y = 3x - 11 using these scales makes the graph easier to read and understand.
To know more about graph visit:
https://brainly.com/question/17267403
#SPJ1
GIVING 50 POINTS!
The right triangle below has legs of length a=7 and b=10. The hypotenuse has length c.
(look at the image)
Part 1: compute the total combined area of the four triangles.
Part 2: Compute the area of the large (outer) square.
Part 3: Using your answers from parts 1 and 2, find the area of the small inner square.
Part 4: We are given the side lengths a=7 and b=10. Compute a²+b².
Part 5: use <, >, or = to complete the statement below.
Part 1
The area of one triangle is [tex](1/2)(7)(10)=35[/tex]. Multiplying this by 4 yields [tex]\boxed{140}[/tex].
Part 2
[tex](10+7)^2=\boxed{289}[/tex]
Part 3
[tex]289-140=\boxed{149}[/tex]
Part 4
[tex]10^2+7^2=\boxed{149}[/tex]
Part 5
The statement is missing.
1) The total combined area of the four triangles is: 140; 2) The area of the outer square is c² = c * c; 3) The area of the small inner square is: c² - 70; 4) The sum of the squares of the two legs of a right triangle is: 149.
How to solve the area problem?Part 1:
The area of each triangle is (a * b) / 2, so the total combined area of the four triangles is 4 * (a * b) / 2 = 2 * 7 * 10 / 2 = 70.
Part 2:
The side length of the outer square is c, the hypotenuse, so the area of the outer square is c² = c * c.
Part 3:
The area of the small inner square is the area of the outer square minus the total combined area of the four triangles, so it is c² - 2 * 7 * 10 / 2 = c² - 70.
Part 4:
The formula for the sum of the squares of the two legs of a right triangle is a² + b² = c², so a² + b² = 7² + 10² = 49 + 100 = 149.
Part 5:
c > a and c > b, so c > 7 and c > 10. Therefore, c must be the largest of the three values: a, b, and c.
To know more about Triangle visit:
https://brainly.com/question/28752684
#SPJ1
What is the equation of the line that passes through the point (-3,4) and has a slope of 2/3?
Answer:
y = 2/3x + 6
Step-by-step explanation:
for this problem, we need to find the value of b (the y-intercept). to do so, all we have to do is plug in the x and y values of the given ordered pair into the x and y values of the function. this will give us:
[tex]4=\frac{2}{3}(-3)+b[/tex]
solve for b and we get 6.
so, our slope-intercept equation is [tex]y=\frac{2}{3}x +6[/tex] .
hope this helped, good luck!
At the movies, John was sent to the lobby to buy refreshments for his friends. Some wanted popcorn which sold for 50 cents a bag and others wanted caramel corn which was 75 cents a bag. If John bought 9 bags and spent $5.00, how many of each kind of bag did he buy?
If John bought 9 bags and spent $5.00, using simultaneous equations, the number of each kind of bag he bought is 7 bags of popcorn and 2 bags of caramel corn.
What are simultaneous equations?Simultaneous equations are two or more equations solved simultaneously or concurrently.
When two or more equations are solved at the same time, they are described as simultaneous equations or a system of equations.
The cost of popcorn per bag = $0.50
The cost of caramel corn per bag = $0.75
The total number of bags bought = 9
The total cost of the 9 bags = $5
Let the number of bags of popcorn = p and the number of caramel corn = c
Equations:0.5p + 0.75c = 5 ... Equation 1
p + c = 9 ... Equation 2
Multiply Equation 2 by 0.5:
0.5p + 0.5c = 4.5 ... Equation 3
Subtract Equation 3 from Equation 1:
0.5p + 0.75c = 5
-
0.5p + 0.5c = 4.5
0.25c = 0.5
c = 2
p = 9 - 2
= 7
Learn more about simultaneous equations at https://brainly.com/question/148035
#SPJ1
Helpppp
could somebody help me with the following question?
Answer: y = -4x -2
Step-by-step explanation:
For a linear equation, we can use this formula:
y - y_1 = m(x - x_1)
We have the slope and the coordinates, so we can just plug everything in:
y - 14 = -4( x + 4)
y - 14 = -4x -16
y = -4x -2
Suppose Nigel has a bag of colored wristbands,
and he chooses one without looking. The bag
contains a total of
25 wristbands and 6 of
the wristbands are blue.
What is the probability that he will choose a blue wristband
The probability that he will choose a blue wristband is 6/25.
Probability is a method to know how likely something is going to happen. Whenever we're uncertain about the outcome of an event, we can talk about the probabilities of certain outcomes. The analysis of events overseen by probability is called statistics.
Total number of wristbands = 25
Number of blue colour wristbands = 6
As we know, the formula of experimental probability is
Probability of an Event P(E) = Total Number of times an event occurs/Total number of trials.
Number of blue colour wristbands = 6
Total number of wristbands = 25
∴ Probability of an Event P(Blue) = 6/25
To know more about experimental probability, here
https://brainly.com/question/3733849
#SPJ4
Simplify
The following expression.
6 1/1 ÷ 6 91/10
A. 18
B. 1/126
C. 216
D. 1/18
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Explain about the Expression?A term may be a number, a variable, the product of two or more variables, a number and a variable, or any combination of these. A single term or a collection of phrases can be used to create an algebraic expression. For instance, 4x and y are the two terms in the formula 4x + y.
Expressions that use numbers to perform operations. An example of a numerical expression is 2(3 + 8). At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic expression is 2(x + 8y).
The following elements can be used to determine the algebraic expressions: a single variable or a group of related variables.
= 6/6 /546/60
=1 / 9.1
=0.109
To learn more about Expression refer to:
https://brainly.com/question/1859113
#SPJ1