The triangle with sides 56 , 55 and 43 is acute triangle
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the base of the triangle is BC
The measure of BC = 43
The height of the triangle is AB
The measure of AB = 55
The hypotenuse of the triangle is AC
The measure of AC = 56
Now , if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
On simplifying the equation , we get
BC² + AB² > AC²
Substituting the values in the equation , we get
43² + 55² > 56²
1849 + 3025 > 3136
4874 > 3136
Hence , it is an acute triangle
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The floor of the cargo space in max truck is in the shape of a rectangle. If the floor of the cargo space of the truck is 4' x 8', what is the maximum area of a cargo space in Mac truck
The maximum area of the cargo space in a Mac truck is 32 sq ft.
What is Area of Rectangle?
The area of a rectangle can be calculated by multiplying its length and width.
[tex]Area \ of\ Rectangle = length * breadth[/tex]
The maximum area of the cargo space in a Mac truck can be calculated by finding the area of a rectangle. To find the area of a rectangle, you multiply the length by the width.
In this case, the length of the floor of the cargo space is 4' and the width is 8', so:
Area = 4' x 8' = 32 sq ft
So, the maximum area of the cargo space in a Mac truck is 32 sq ft.
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1. Solve this system by substitution.
(y = 3x + 27
y = 4x + 18
2. Solve this system by elimination
(-2x - 4y = -4
2x - 5y = 40
4. Solve this system by substitution
-6x + y = 18
-3x+6y= -24
5. Solve this system by elimination
9x + 21y = 15
-10x + 21y = -61
Answer:
1. x = 9
2. (10, -4)
4. (-4, -6)
5. (4, -1)
Step-by-step explanation:
1. Since we know that y = 3x + 27, we can substitute that into y = 4x + 18.
3x + 27 = 4x + 18
9 = x
x = 9
Continue the processes of setting both equations of a system to a specific value, and then substituting it into the other equation.
What is the formula for the nth partial sum of the series?.
The formula for the nth partial sum of the series is Sn=a1(1−rn)1−r.
The initial term a1 and the common ratio r can be used to determine the nth partial sum of a geometric sequence is given by Sn equals to a1(1−rn)1−r, where a1 denotes the first term in the partial sum and a the nth (final) term.
One of a number of sums of items in a particular sequence, starting with the first sum, which is the first element, going on to the second sum, which is the first element plus the second element, and so forth. This is the concept of partial sum.
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Given the Square JKLM, if the area of JKLM i 64 q in. , what i the length of the diagonal KM?
The length of the diagonal KM is 8√(2) inches.
The area of a square is given by the formula: area = side^2.
So, if the area of square JKLM is 64 square inches, then we know that:
64 = side^2
To find the diagonal KM, we can use the Pythagorean Theorem. The diagonal KM is the hypotenuse of a right triangle where the legs are the side of the square.
So the formula is KM = √(side^2 + side^2)
Substituting in the known area of the square, we have:
KM = √(64 + 64)
KM = √(128)
KM = 8√(2)
Therefore, the length of the diagonal KM is 8√(2) inches.
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KM = √(side^2 + side^2)
Substituting in the known area of the square, we have:
KM = √(64 + 64)
KM = √(128)
KM = 8√(2)
Write a poitive or negative integer that repreent the ituation. You walk up 83 tair
83 is a positive integer that represents the situation.
An integer is a whole number, meaning it does not include any fractional or decimal component. It can be positive, negative, or zero. Integers are numbers that can be written without a fractional or decimal component.
The number of stairs walked up is a positive value, because it is a quantity that increases, and in mathematics, positive numbers represent an increase in value. In this case, walking up 83 stairs is an increase in elevation, and so it is represented by a positive number.
Therefore, the situation can be written as a positive integer which is 83.
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A comedy club earns $1088 from an opening night performance and $1183 from a second performance
The solution is $95.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
A comedy club earns $1088 from an opening night performance
and $1183 from a second performance
so, earns more =$(1183-1088)
=$95
Hence, the solution is $95.
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1. The simple interest owed on a loan of $4000 after 3 years is $240. What percent
represents the annual interest rate on the loan? Please, Please show your work and
write your answer here
The annual interest rate on the loan is 0.02 or 2%.
What is the annual interest rate?To find the annual interest rate on the loan, we need to use the formula for simple interest:
I = Prt
where:
I is the interest,
P is the principal (the amount of the loan),
r is the annual interest rate (expressed as a decimal),
t is the time in years
We know the following information:
I = $240
P = $4000
t = 3
We can use this information to set up the equation and solve for r:
240 = 4000 * r * 3
240 = 12000r
r = 240/12000
r = 0.02
Therefore, the annual interest rate on the loan is 0.02 or 2%.
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write the trinomial as a square of a binomial or as an expression opposite to a square of a binomial
24ab-16a^2-9b^2
Answer: The given trinomial, 24ab-16a^2-9b^2, can be written as an expression opposite to a square of a binomial.
To do this, we first factor out the greatest common factor of -4a, which gives us:
-4a(6b-4a-9b^2)
We can then factor -9b^2 as -(3b)^2, and group the remaining terms together:
-4a((3b-2a)^2-4a^2)
So the trinomial can be written as -4a( (3b-2a)^2 - 4a^2 ) which is an expression opposite to a square of a binomial (3b-2a)^2.
Step-by-step explanation:
What is the range of this radical function f(x) =4squareroot x-6
Answer: Unless there is a vertical shift the range for ALL radical functions will remain [0,infinity)
Step-by-step explanation:
Which expression is equivalent to 24+56
Answer:
24+56 is equivalent to 80.
What is the largest integer value that makes this inequality true?
4x-8<-2x+1
Answer:
Step-by-step explanation:
the answer would be 10
Five cups of flour are divided equally into 4 bowls. How much flour is in each bowl?
Answer: D, 1 1/4 cups of flour and 5/4.
Step-by-step explanation:
There are four bowls, so subtract four from 5, and you have 1. Divide the remaining 1 by 4, and you have 1/4. So, 1 1/4 cups per bowl. A simpler way would be to divide 5 by 4, as you would end up with 1.25, which equals 1 1/4.
Answer: 5/4 cups of flower
5 ÷ 4= 1.25
1.25 in fraction form is 5/4, so the answer would be a.
What is the modulus of the complex number 4 +3i?.
The modulus of the complex number is:
|z| = 5
Now, According to the question:
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
The modulus of complex number z=a+bi is:
[tex]|z| = \sqrt{(a+bi)(a-bi)}[/tex]
[tex]|z| = \sqrt{a^2+b^2}[/tex]
The given complex number is :
4 + 3i.
a = 4 and b = 3
The modulus of the complex number will be:
[tex]|z|=\sqrt{4^2+3^2}[/tex]
[tex]|z|=\sqrt{16+9}\\\\|z|=\sqrt{25}[/tex]
|z| = 5
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A car sales associate receives a monthly salary of $1,700 a month plus $140 for every car he sells. How many cars must he sell to earn at least $4,500?
Answer:
20 cars
Step-by-step explanation:
He wants 4500
He makes 1700 salary
4500-1700=2800
Now you need to divide the remaining 2800 needed by the 140 he gets per car he sells
2800÷140=20
So he needs to sell 20 cars
Contruct a quadrilateral ABCD given that AB=2. 4cm,BC=4. 3cm,CD=3. 1cm,AD=2cm and diagonal BD=3. 9cm
We can draw a quadrilateral ABCD with sides AB, BC, CD, and AD having lengths of 2.4 cm, 4.3 cm, 3.1 cm and 2 cm respectively. The diagonal BD has a length of 3.9 cm.
Step 1: Draw a line segment AB with length 2.4 cm.
Step 2: Draw a line segment BC with length 4.3 cm.
Step 3: Draw a line segment CD with length 3.1 cm.
Step 4: Draw a line segment AD with length 2 cm.
Step 5: Draw the diagonal BD with length 3.9 cm.
Step 6: Connect the endpoints of the line segments AB, BC, CD, and AD to form a quadrilateral ABCD.
We can construct a quadrilateral ABCD given the given dimensions. To begin, we will draw a line segment AB with a length of 2.4 cm. This will be the first side of our quadrilateral. Next, we will draw a line segment BC with a length of 4.3 cm. This will be the second side of our quadrilateral. After that, we will draw a line segment CD with a length of 3.1 cm. This will be the third side of our quadrilateral. Then, we will draw a line segment AD with a length of 2 cm. This will be the fourth side of our quadrilateral. Finally, we will draw the diagonal BD with a length of 3.9 cm. To complete the quadrilateral, we will connect the endpoints of the line segments AB, BC, CD, and AD. This will form a quadrilateral with the given dimensions. The quadrilateral ABCD will have side lengths of 2.4 cm, 4.3 cm, 3.1 cm, and 2 cm respectively. The diagonal BD will have a length of 3.9 cm. Our quadrilateral ABCD is now constructed and ready to use.
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So if a cashier only has $10 and one bills what are two ways, he could make Mr. Rosso change
Answer:
2 5$ bills
1 10$ bill
5 2$ bills
Step-by-step explanation:
Find the area of a
rectangle with a
diagonal of 11
units and length of
8 units.
The area of something like a rectangle with a length of 8 units and a diagonal of 11 units is 60.396.
What is a diagonal and give an example?A diagonal in mathematics is a line that joins two vertices of a solid or polygon whose vertices seem to be not on the same edge. Generally general, a diagonal is a sloping or slanting line that joins the vertices of a form. Diagonals are lateral shapes with sides, edges, and corners.
According to the given information:Length = 8
Diagonal = 11
A=w l
D = √(w² + l²)
Area = l√(d²- l²)
= 8.√(11² - 8²)
=60.396
the area of a rectangle with a diagonal of 11 units and length of 8 units = 60.396
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ABCD is a cyclic quadilateral in whicj side Ad and BC are produced to meet at E such that AE = BE .Prove that AB// DC
Answer: To prove that AB is parallel to DC, we can use the following steps:
Draw a diagram of the cyclic quadrilateral ABCD with the point E where sides AD and BC are produced to meet.
Since ABCD is a cyclic quadrilateral, all its interior angles add up to 360 degrees. Therefore, angle A + angle B + angle C + angle D = 360 degrees.
Since AE = BE, we can say that angles A and B are equal (by corresponding angles). Similarly, angles C and D are also equal.
Since angles A and B are equal and angles C and D are also equal, we can say that angle A + angle B = angle C + angle D.
Substituting this into our equation from step 2, we get: angle A + angle B + angle C + angle D = angle A + angle B + angle A + angle B.
Simplifying, we get: 360 = 2(angle A + angle B). This means that angle A + angle B = 180.
Since angle A + angle B = 180, we can say that angle A = angle B and angle C = angle D.
Now we can use the fact that corresponding angles are equal, then angle A = angle C and angle B = angle D.
We know that opposite angles of a parallelogram are equal, so we have proved that AB is parallel to DC.
It's important to note that this proof uses the fact that quadrilateral ABCD is cyclic, which means that the sum of its angles is equal to 360 degrees. It also uses the fact that opposite angles are equal in a parallelogram, and corresponding angles are equal when two lines are parallel.
Step-by-step explanation:
What is the area of a triangle whose height is 6 cm and base is 10 cm?.
The area of a triangle whose height is 6 cm and the base is 10 cm is 30 cm².
Area of triangle = 1/2 × b × h
= 1/2 × 10 × 6
= 1/2 × 60
= 30 cm².
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Yall could help a scholar out real quick? xx
Answer: 1 apple = 3 bananas
Step-by-step explanation:
10 bananas = 2 pineapples
which means
5 bananas = 1 pineapple eq_i
1 pineapple = 2 bananas + 1 apple eq_ii
Using eq_i and eq_ii, we conclude
1 apple = 3 bananas ... answer
hope that helps...
Alex went to Seattle for the weekend d with his parents. He went into the Hard Rock Cafe and bought a sweatshirt for 59.99. Sales tax is 7.5% how much did Alex pay the cashier?
Alex paid 64.48
price of sweatshirt which alex bought : 59.99
sales tax : 4.499
total price alex paid is 64.48
calculation of salex tax
price of sweatshirt :59.99.
sales tax :4.499
{59.99 x 7.5% } = 4.49
Alex paid 64.48
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How many solutions does the pair of linear equations y 0 and y =- 7 have?.
The pair of linear equations y = 0 and y = -7 have no solution.
Given the pair of equations is
y = 0
y = -7
We have to find a solution.
Here, b₁ = 1, c₁ = 0
b₂ = 1, c₂ = -7
So, b₁/b₂ = 1/1 = 1
c₁/c₂ = 0/-7 = 0
So, b₁/b₂ ≠ c₁/c₂
We know that,
Let's assume a pair of linear equations in two variables be a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,
If a₁/a₂ = b₁/b₂ ≠ c₁/c₂, then
i) the given pair of linear equations is inconsistent
ii) the graph will be a pair of parallel lines, so the pair of equations will have no solution.
Therefore, the pair of equations has no solution.
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The drama club is selling tickets to their play to raise money for the
show's expenses. Each student ticket sells for $5.50 and each adult
ticket sells for $9.50. There was a total of $703 in revenue from the
sale of 98 total tickets. Write a system of equations that could be used
to determine the number of student tickets sold and the number of
adult tickets sold. Define the variables that you use to write the system.
Let the number of student tickets be [tex]s[/tex] and the number of adult tickets be [tex]a[/tex].
[tex]\begin{cases} 5.50s+9.50a=703 \\ s+a=98 \end{cases}[/tex]
Anyone know this? Struggling highschool student here
The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.
Calculate the monthly payment?The monthly payment for a 15-year term mortgage with a 15% down payment on a $315,200.00 purchase price for a household with a 711 credit score is $2,408.60.To calculate this, first you must review the Monthly Principal & Interest Factor chart.Since the credit score is 711, this falls into the range of 710-729. For a 15-year term, the interest factor is 7.0.Once you have determined the interest factor, you can then calculate the monthly payment.To do this, you must subtract the 15% down payment of $47,280.00 from the purchase price of $315,200.00, which leaves $267,920.00.Then, you must multiply the $267,920.00 by the interest factor of 7.0 and divide it by 12 to get the monthly payment of $2,408.60.To learn more about The monthly payment refer to:
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20pts for whoever can help me with this
It is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
(a)
(a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)²
LHS,
= a²(c² + d²) + b² (c² + d²)
= a²c² + a²d² + b²c² + b²d²
= a²c² + b²d² + 2abcd + b²c² + a²d² - 2abcd
= (ac + bd)² + (bc - ad)²
= RHS
Thus, it is been proved that (a² + b²)(c² + d²) = (ac + bd)² + (bc - ad)².
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An experiment calls for each student to use 3.50 g of sodium hydroxide. There is only
78.2 g of sodium hydroxide remaining. How many students can complete the experiment?
Answer:
22 students
Step-by-step explanation:
What is the main difference between polynomial and equation?.
A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them. The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).
A polynomial example could be-
[tex]\mathrm{p}(\mathrm{x})=2 x^{3-3(x+y)+7 / 5}[/tex]
A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.
An illustration of an equation is
[tex]3 x-5 y=(7 x+9) / 5[/tex]
In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.
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A polynomial is described as a set of mathematical phrases with numerical coefficients, variables, and operations between them.
The variables' degree must be a non-negative integer (addition, subtraction, multiplication and division).
A polynomial example could be-
p(x) =³
A mathematical notion known as an equation is one in which two quantities are equal and are indicated by the symbol "=" in between.
An illustration of an equation is
In contrast to polynomials, equations have no limits on the coefficients or the powers of the variables.
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Find the area of a rectangle whose length is 6.4 and breadth is 5cm
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSolution is in the attached photo, do note this question tests on finding the area of shapes.
Is the function 2x 3 Surjective?.
The function f(x)=2x-3 is not surjective.
The surjective function is defined with reference to the elements of the range set, such that every element of the range is a co-domain.
A surjective function is a function whose image is equal to its co-domain, and every element y can be mapped from element x so that f(x) = y.
it suffices to give an example of y∈Z such that f(x)=y has no solutions. Just pick y=−2 and derive that
f(x)=−2⟺2x−3=−2⟺2x=1
and it should be quite clear that this has the unique solution x=0.5 over Q so no solutions for Z.
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3/5 divied by what is 3/4
[tex]\it \dfrac{3}{5}:x=\dfrac{3}{4} \Rightarrow x=\dfrac{3}{5}:\dfrac{3}{4}=\dfrac{\not3}{5}\cdot\dfrac{4}{\not3}=\dfrac{4}{5}[/tex]
[tex]\it So,\ \ \dfrac{3}{5}\ divided\ by\ \dfrac{4}{5}\ is\ \dfrac{3}{4}[/tex]
