When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.
The two triangles are congruent if we can demonstrate that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.
Triangles are considered congruent by SAS if their two sides match those of the other triangle's corresponding two sides, and if their included angles are parallel in both triangles.
Hence we get the required answer.
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What would the answer be? I tried 4 and -4 and a lot more.
Answer:
-2
Step-by-step explanation:
a is -3
d is -1
you subtract the two
-3 - (-1)
when you have two negatives they cancel each other out and become positive
-3 + 1
-3 + 1 = -2
that is your answer
tic is an isosceles triangle with a vertex angle i if the measure of i90
Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.
An Isosceles triangle has a vertex angle and two equal base angles.
Given that triangle TIC is an isosceles triangle:
angle I is the vertex angle = 90 degrees
angle T is a base angle
angle C is also a base angle
Thus:
angle C and angle T are congruent or equal to each other.
Therefore,
Angle T = (180 - 90)/2
⇒ Angle T = 90/2
⇒ Angle T = 45 degrees.
applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.
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Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula 1 w, where I represents
the length, and w represents the width. The floor of the shed will have measurements of either / = 9 and w =
= 7 or/= 8 and
w = 8. What is the area of the larger floor?
O63
O 64
O 56
O 72
The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).
To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.
If w = 7 and l = 9
A = l × w = 8 × 6 = 48
If w = 8 and l = 8
A = l × w = 8 × 8 = 64
So, the second case would obtain a larger area.
Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.
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What are the 4 types of properties?
There are four basic properties of numbers: commutative, associative, distributive, and identity.
1.Commutative Property
a. Addition
. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.
3 + 5 = 8 or 5 + 3 = 8
b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.
3 x 5 = 15 or 5 x 3 = 15
2.Associative Property
a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.
6 + (4 + 3) = 13 or (6 + 4) + 3 = 13
b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.
6 x (4 x 3) = 72 or (6 x 4) x 3 = 72
3.Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number.
5 x (7 + 2) = 45 or 5 x 7 + 5 x 2 = 45
4.Identity Property
a. Addition. The sum of any number and zero is that number.
12 + 0 = 12
b. Multiplication, The product of any number and one is that number.
18 x 1 = 18
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A college student has budgeted $25 a month for phone services. If the telephone
company charges $17 a month for basic service and $0.05 a minute for each long
distance call, how many minutes can be spent on long distance calls each month?
(Define a variable, create an equation, solve using algebra, and answer in a sentence.)
Answer:
160 minutes can be spent on long distance calls each month.
Step-by-step explanation:
first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.
let's write that into an equation to solve for (a) which will be number of minutes.
17 + a(0.05) = 25
solving:
17 + a(0.05) = 25
carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.
a(0.05) = 25 - 17
a(0.05) = 8
carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.
[tex]a = \frac{8}{0.05} [/tex]
a = 160
therefore 160 minutes can be spent on long distance calls each month.
You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes
What information is needed to show that △ ABC ≅ △ DEF by SAS congruence?
In order to show that △ ABC ≅ △ DEF by SAS congruence, we need the sides of triangles ABC and DEF with the angle between the respective sides.
What do we understand by congruency of a triangle?Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides and all three of their corresponding angles have the same measurements. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. "" is the congruence symbol. When two figures are comparable to one another in terms of their size and shape, this is what mathematicians mean by congruence. In essence, there are four congruence principles that demonstrate if two triangles are congruent. However, locating all six dimensions is essential. As a result, the congruence of triangles can be assessed using just three of the six variables.
Congruency Requirements:
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle-Side)
RHS (Right angle-Hypotenuse-Side)
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Evaluate the expression for j = –5, k = 2, and m = 3.
jk2 − m = ?
Answer: -23
Step-by-step explanation:
[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]
A rectangular yard measuring 40 ft by 70 ft is bordered (and surrounded) by a fence. Inside, a walk that is 4 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of the path is 456 square feet
How to determine the areaThe formula for determining area of a rectangle is given as;
A = lw
Where;
l is the length of the rectanglew is the width of the rectangleNow, substitute the values into the formula, we have;
Area of the rectangle = 40 × 70
Area of the rectangle = 2800 square feet (1)
Bordered fence with a 4 ft path so dimensions 44 ft by 74 ft
Area of rectangular garden with Path = 44 × 74
= 3256 square feet (2)
Area of the walk = (2) - (1) = 3256 - 2800 = 456 square feet
Hence, the value is 456 square feet
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Round 0.799 to the nearest hundredth
Answer:
0.80
Step-by-step explanation:
The hundredth is 2 digits after the decimal.
Rounding 0.799, we want 0.xx
Look at the third digit, 9, meaning we round up.
However, since the second digit after the decimal is also a 9, we can make that a 0 by adding 1 to the first digit after the decimal.
We get 0.80
A rectangular piece of paper with length 25 cm and width 12 cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
The area of the rectangular paper left after two semi circles are cut out of it is 186.96 cm².
What is a rectangle?A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).The opposite sides of a rectangle are equal and parallel.
To caluculate the area of the paper that remains, we use the formula below.
Formula:
Ar = lb-π(b/2)²............ Equation 1Where:
Ar = Area of the paper that remainl = Length of the rectangular paperb = width of the rectangular paperr = Radius of the semi circleFrom the question,
Given:
l = 25 cmb = 12 cmr = 12/2 = 6 cmπ = 3.14Substitute these values into equation 1
Ar = (25×12)-(3.14×6²)Ar = 300-113.04Ar = 186.96 cm²Hence, the area of the paper left is 186.96 cm².
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When a transversal cuts parallel lines, how can one angle measurement be used to determine all of the other measurements?
Answer: If two parallel lines are cut by a transversal, then corresponding angles are congruent.
Step-by-step explanation:
When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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What is a paragraph proof of Theorem 3 8?
We prooved the paragraph proof of Theorem 3.8 that if two lines are perpendicular to the same line, then they are parallel to each other.
In the given question we have to explain the a paragraph proof of Theorem 3.8.
Let the lines that cross line a be m and n. Let m be parallel to a. As a result, the intersection of m and a produces four 90° angles.
Let n be parallel to a. This indicates that each of the four angles created by the intersection of n and an is 90 degrees.
The same-side internal angles (between lines m and n) are also congruent because all of the angles are congruent. The lines are parallel if two internal angles on the same side are congruent.
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The right question is:
Write a paragraph proof of theorem 3-8: in a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
What are the types of inverse?
The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions
If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.
A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.
The various types of inverse function are:
Inverse Trigonometric Functions : The inverse trigonometric functions are also known as arc function as they produce the length of the arc.Inverse Hyperbolic Function : Just like inverse trigonometric functions, the inverse hyperbolic functions are the inverses of the hyperbolic functions. There are mainly 6 inverse hyperbolic functions exist which include sinh⁻¹ , cosh⁻¹, tanh⁻¹, csch⁻¹, coth⁻¹, and sech⁻¹Inverse Logarithmic Functions and Inverse Exponential Function : The natural log functions are inverse of the exponential functions.To know more about The inverse of function here
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Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
The number of nickels and the number of dimes that Joseph has are 12 and 5 respectively.
What is a linear equation?An equation of degree one is known as a linear equation.
A linear equation of two variables can be represented by ax + by = c.
Let the no. of nickels be N and no. of dimes be D.
∴ N + D = 17...(i) and 0.05N + 0.1D = 1.45...(ii)
Multiplying (ii) by 100 we get 5N + 10D = 145...(iii)
Now multiply (i) by 5 we get 5N + 5D = 85...(iv)
Now subtracting (iv) from (iii) we get,
5D = 60.
D = 12 hence N = 5.
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Explain how you can use compatible numbers to estimate the quotient of
925÷29.
HELPP PLEASEE ITS 50 POINTS TYY
Answer:
We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.
Step-by-step explanation:
An airplane is flying 700 feet above ground. From the plane to the base of the control tower, the angle of depression is 47◦ . How far away is ground directly underneath the plane to the control tower? Round your answer to the nearest tenth.
Using trigonometric ratio the distance to the control tower is 750.7ft
Trigonometric RatioIn trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.
The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.
Using trigonometric ratio, the distance is
tan θ = opposite / adjacent
tan 47 = x / 700
x = 700 tan 47
x = 750.7 ft
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Determine whether the relation is a function
Explain why or why not.
1. (9, -1) (4,2) (5,3) (8, -1) (3, 0)
The relation:
(9, -1) (4,2) (5,3) (8, -1) (3, 0)
Is a function, because each element of the domain appears only once.
Is the relation a function?A relation maps elements from a set, called the domain, into elements from another set, called the range.
Such that the element x being mapped into the element y is written as:
(x, y).
A relation is a function only if each element in the domain is mapped into only one element of the range.
Here we have the relation:
{ (9, -1) (4,2) (5,3) (8, -1) (3, 0)}
We can see that no element of the domain appears twice, so yes, this is a function.
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What is a prime multiple?
The multiples of a number are numbers found by multiplying the original number by any whole number. Prime multiples are number which multiply each other and form a prime
What are Prime Numbers ?
A prime number is a number that is only divisible by 1 and itself. So, prime numbers have only two factors, 1 and the number itself.
This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.
Numbers that have more than 2 factors are known as composite numbers.
For example :
The factors of 3 are 1 and 3.
Therefore, the prime multiples of 3 are 1 and 3.
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One integer is 2 times another. If the product of the two integers is 32, then find the integers
Answer:
The integers could be 8 and 4, just checked with a calculator
How do you find the degree of a polynomial in precalculus?
Answer:
add up the exponents of each term and select the highest sum.
Mark needs to cut a board to use for a project. The board is 12 feet long. He first has to cut off 24 feet from one end of the board. He
then cuts the remaining section of board into 4 equal pieces.
Which equation can be used to determine the the length of each equal piece?
04r-2-12
02-4-12
O2+4=12
O 4x+2¹-12
Next
The equation that best defines the length of the equal piece is 4x+2¹-12
How to determine an equation?We should know that an equation is a mathematical model that shows the equality of two sides of an expression
Based on the given condition 12-24=4*x
Applying multiplicative distribution -12=4x
Rearrange the equation 4x=-12
Calculate the product of the quotient x=-3
Now 24feet divided by -3 =-4
Since it deals with length =4
In conclusion the equation that determines the length of each equal piece is 4x+2¹-12
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A ball is dropped from a height of 10 ft and bounces 83% of its previous height on each bounce. How high off the ground is the ball at the top of the 4th bounce?
Answer:
The height of the 4th bounce would be 4.7458321; rounded would be 4.8.
Step-by-step explanation:
We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:
0.83.
And then setting up this equation:
0.83 x 10 = 8.3
Now, this is for 1 bounce. We have to do this 4 more times:
0.83 x 8.3 = 6.889
3rd time:
0.83 x 6.889 = 5.71787
4th time:
0.83 x 5.71787 = 4.7458321.
Now, we can round this answer to:
4.8
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Slopes of Parallel/Perpendicular Lines (5x - 4y = -24) Show steps please
The slope of the perpendicular line to the equation 5x - 4y = -24, is: 4/5.
How to Find the Slope of Perpendicular Lines?The slope values of two lines which lie perpendicular to each other on a coordinate plane are always negative reciprocals to each other.
Rewrite the equation, 5x - 4y = -24 in slope-intercept form:
5x - 4y = -24
-4y = 5x - 24
Divide both sides by -4
-4y/-4 = 5x/-4 - 24/-4
y = -5/4x + 6
The slope of y = -5/4x + 6 is -5/4. The negative reciprocal of -5/4 is 4/5. Thus, the slope of the line that is perpendicular to the equation of the given line is: 4/5.
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A toy maker is putting multicolored sand in transparent cubes. Each cube measures 10 millimeters on each side. A coworker remarks that, for the cubes to be completely filled, each cube will need no more than 30 cubic millimeters of sand. Is the coworker correct? The coworker is correct. The volume of each cube is 20 cubic millimeters. The coworker is correct. The volume of each cube is 30 cubic millimeters. The coworker is not correct. The volume of each cube is 100 cubic millimeters. The coworker is not correct. The volume of each cube is 400 cubic millimeters. The coworker is not correct. The volume of each cube is 1,000 cubic millimeters.
The true statements are
The co-worker is not correct. The volume of each cube is 1,000 cubic millimetresHow to determine the true statement about the volume?The side length of the transparent cube is given as
Length = 10 millimetres
The volume of the cube is calculated as
Volume = Length³
Substitute the known values in the above equation, so, we have the following representation
Volume =10³
Evaluate
Volume = 1000 cubic millimetres
1000 cubic millimetres and 30 cubic millimetres do not have the same value
So, the co-worker is incorrect.
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How do you find a polynomial?
Answer:
To find a polynomial, you must identify the terms, coefficients, and degrees. The degree of a polynomial is the highest exponent of the variable in the equation. The coefficients of a polynomial are the values that are multiplied by the variables. The terms of a polynomial are the pieces of the equation, including the coefficients and the variables. After identifying the terms, coefficients, and degree of the polynomial, you can write it in standard form.
Step-by-step explanation:
There are 28 students in the classroom. Each student needs 2 pencils for the exam. How many pencils in all are needed for the exam?
Total 56 pencils are needed for the exam.
What is Multiplication?Multiplication is one of the arithmetic operation used to find total numbers of items or things.
Given,
Total students in the classroom = 28
Total number of pencils needed by each student for the exam=2 pencils
Total number of pencils needed for the exam are,
= Total student × Number of pencils needed by each student
= 28 × 2
= 56 pencils
Hence , The total number of pencils needed by the students for the exam would be 56 .
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A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answer: y=x−2 y = x − 2
Step-by-step explanation:
what is the equation of yx3 with the given transformations vertical compression by a factor of 17
The transformed equation of is y = x³ is y =-1/7(x+8)³
Given that :
The equation of y=x^3 and Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis
Applying the given transformations, we have:
To have a vertical compression by a factor of 1/7, we need to multiply the function by 1/7. So, we have:
y=1/7x³
We must add 8 to x in order to have a horizontal shift of 8 units to the left. We thus have:
y=1/7(x+8)³
A reflection over the x-axis would be the final step, we need to multiply the function by −1. So, we have:
y= -1/7(x+8)³
Therefore, the transformed equation is y= -1/7(x+8)³
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Pls help answer fast rapidly is of khan academy:
Answer:
expanded: 7+0.08
standard: 7.08
Step-by-step explanation:
The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.
