Answers
The interest is compounded four times per year, or once every quarter.Rate is quarterly compounded, hence the periodic rate is 1.64%.
What is Quarterly Compounding?The interest is compounded four times per year, or once every quarter. Quarterly compounding is the method of calculating the interest earned on a fixed deposit or investment on a quarterly basis, based on the principal sum plus the interest earned for prior periods.
You can rapidly determine how long it will take for an investment to double given its interest rate by using the Rule of 72.
It operates by:
/ Interest rate = 72
Rate is quarterly compounded, hence the periodic rate is
= 6.56%/4
= 1.64%
Time to double equals 72/1.64
equals 43.9 quarters
As measured in years:
= 43.9/4
= 11 years
To learn more about Quarterly Compounding refer
https://brainly.com/question/20392017
#SPJ1
Related Questions
Explain whether there is enough information given in the figure to prove that the triangles are congruent using SSS or SAS
Answers
The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle,
prove that the triangles are congruent using SSS or SAS?
If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.
To learn more about triangles refers to:
https://brainly.com/question/1058720
#SPJ1
.
What is the slope 0 /- 2?
Answers
The slope 0/(-2) means, the line is coincident or parallel to the x-axis
We know that the slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate.
The slope of the line describes the steepness of a line.
Also, if a line makes an angle θ with the positive direction of the x-axis, then the slope of the line will be tangent of angle θ
m = tan θ
Here we have been given a slope 0/(-2)
As we know 0/(-2) = 0
So, the slope is 0.
Let m = 0
From definition of slope of line,
m = tan θ
0 = tan θ
θ = arctan(0)
θ = (nπ) where n = 0, 1, 2, . . .
This means, the slope 0/(-2) means for every two units of horizontal distance crosses there is no change of vertical distance.
Learn more about the slope here:
brainly.com/question/16180119
#SPJ4
FIND THE SLOPE BETWEEN THE FOLLOWING POINTS!!!
15 POINTS
Answers
The slope between the points (-6, 6) and (-6, -1) is -infinity.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect with the change in the independent variable.
Therefore, the slope is define as rise over run.
Hence let's find the slope between the points (-6, 6) and (-6, -1)
Therefore,
slope = y₂ - y₁ / x₂ - x₁
x₁ = -6
x₂ = -6
y₁ = 6
y₂ = -1
Therefore,
slope = -1 - 6 / -6 + 6
slope = -7 / 0
slope = - infinity
learn more on slope here:https://brainly.com/question/15166299
#SPJ1
What is the factored form of a quadratic function?
Answers
The factored form of a quadratic function is (x + a)(x+ b).
In math the term quadratic function is defined as a polynomial function of degree 2.
Here we have to find the process to convert the quadratic equation into the factored form.
As per the definition of quadratic equation, we all know that the standard form of the quadratic equation s written as,
=> y = ax² + bx + c
As we all know that factorization of quadratic equations can be done using different methods such as splitting the middle term or by using the quadratic formula or by completing the squares, etc.
Here we spilt the middle term then the expression is written as,
=> (x + a) (x + b)
To know more about function here
https://brainly.com/question/28193995
#SPJ4
The sides of a triangle are 55, 69, and 73. Use the Pythagorean Theorem to determine
if the triangle is right, acute, or obtuse.
Answers
If the sum of the squares on a triangle's two shorter sides is more than the square on its longest side, the triangle is said to be acute.
How do you know if a triangle is acute or obtuse?A triangle is said to be acute if the sum of its two shorter sides' squares is larger than its longest side's square. The triangle is obtuse, though, if the squares added together of its two shorter sides are less than those added together of its longest side.
The Pythagorean Theorem's antithesis states that if the square of the length of a triangle's longest side equals the sum of the squares of its other two sides, then the triangle is a right triangle.
With the aid of Pythagoras' theorem, it is possible to establish whether a triangle has a right angle. A straight angle is present in a triangle if the squares of the two shorter sides equal the square of the hypotenuse.
To learn more about Pythagorean Theorem's refer to:
https://brainly.com/question/343682
#SPJ1
Consider the quadratic equation $ax^2 + bx + c = 0$ with $a, b, c$ integers from $-4$ to $4$ and $a not equal to 0$.
The solutions to this equation are in the form [tex]\frac{P+=\sqrt{D}}{Q}[/tex] where $D$ is square free.
Determine the largest possible value of $D$.
Answers
The largest possible value of D is 6.4.
What is the largest possible value of D?
The largest possible value of D is calculated by applying the following formula as shown below.
The largest possible value of D is obtained when the situation occurs;
b will be positive or negative a is positive and c is negativea is negative and c is positivelet b = 3
a = 4
c = - 2
D = √ ( b² - 4ac )
D = √ ( 3² - ( 4 x 4 x - 2 )
D = √ ( 9 + 32 )
D = √ ( 41 )
D = 6.4
Learn more about discriminant here: https://brainly.com/question/2507588
#SPJ1
Adjacent angles (select ALL that apply)
1.have a common angle.
2. have a common side.
3. have a common vertex.
4. are equal.
Answers
The properties of adjacent angles are
2. have a common side.3. have a common vertex.When are angles said to be adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be adjacent angles.
The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
Angles are said to be adjacent when they lie side by side to each other.
hence we can conclude that adjacent angles have a common vertex and side
Learn more about adjacent angles at:
https://brainly.com/question/28394984
#SPJ1
Answer:
2. have a common side.
3. have a common vertex.
Step-by-step explanation:
The cost of 5 sixty minute cassette tapes and 9 ninety minute tapes is $71.40. The cost of 8 sixty minute tapes and 7 ninety minute tapes is $74.65. Find the cost of each type of tape.
Answers
The cost of a sixty minute tape is $11.40 and the cost of a ninety minute tape is $1.60.
What is the step by step explanation?This is a system of equations problem. We can start by setting up the equations using the information given. Let x be the cost of a sixty minute tape and y be the cost of a ninety minute tape.From the first piece of information:5 x + 9 y = 71.40From the second piece of information:8 x + 7 y = 74.65To solve for x and y, we can use the method of substitution, where we solve one equation for one variable and substitute that expression into the other equation.5 x + 9 y = 71.408 x + 7 y = 74.65Solve the first equation for x:x = (71.40 - 9 y)/5Substitute this expression into the second equation:8((71.40 - 9 y)/5) + 7 y = 74.65Solving for y:y = $1.60Now we can substitute this value of y into the first equation to find the value of x:5 x + 9(1.60) = 71.405 x = 71.40 - 14.405 x = 57x = $11.40So, the cost of a sixty minute tape is $11.40 and the cost of a ninety minute tape is $1.60.To learn more about systems of equation refer:
brainly.com/question/13729904
#SPJ1
the diagonal of a particular square is 5 inches. the diameter of a particular circle is also 5 inches. by how many square inches is the area of the circle greater than the area of the square? express your answer as a decimal to the nearest tenth.
Answers
7.13 square inches is the area of the circle greater than the area of the square
area of a circle is pir^2 = pi*2.5^2
side of the square by Pythagoras
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
5^2 = 2x^2
x^2 = 12.5 = area of the square
area of circle = pi * 6.25 = 19.63
difference in areas = 19.63 - 12.5 = 7.13 sq ins
Know more about area of a circle
https://brainly.com/question/14068861
#SPJ4
Please answer fast I will mark brainliest
Answers
Answer: bro what question is it
A system of equestions is given for the following scenario Solve using substitution and fill in the blanks Brittany wants to buy a charm braceletSpringdale Fine Jewelry charges $11 per charm, plus 42 for the braceletChu Jewelers, in contrast charges per charm and 84 for the braceletBrittany wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shopHow many charms would that be? What would the total cost of the bracelet be? Springdale Fine Jewelry y = 11c + 42 Chu Jewells y = 8c + 84
Answers
Answer:
Step-by-step explanation:
is this college
Sam is driving to Dallas. Suppose that the distance to his destination (In miles) is a linear function of his total driving time (in minutes). Sam has 69 miles to his
destination after 42 minutes of driving, and he has 54.6 miles to his destination after 60 minutes of driving. How many miles will he have to his destination after
68 minutes of driving?
Answers
56.6 miles will he have to his destination after 68 minutes of driving.
What is linear function?A linear function is a mathematical expression involving variables that, when graphed, creates a straight line. Linear functions are used to model relationships between two variables, such as cost and revenue, price and demand, and distance and time. Linear functions can also be used to solve equations and are especially useful for predicting future outcomes.
The linear function representing Sam's distance to his destination can be expressed as:
Distance to Destination = 69 - (60 - Driving Time)
Therefore, after 68 minutes of driving, Sam will have 56.6 miles to his destination:
Distance to Destination = 69 - (60 - 68)
Distance to Destination = 56.6.
To know more about linear function click-
https://brainly.com/question/2248255
#SPJ1
What are the coordinates of the midpoint of the line segment joining the point A (4,-2) and B (10,-6)?
Answers
Answer: (7, -4)
Step-by-step explanation: To find the midpoint of a line segment, We take the average of the X-coordinates and the Y-coordinates of the two endpoints.
Given points A(4,-2) and B(10,-6), the midpoint can be found using the following steps.
1. Take the average of the X-coordinates: (4+10)/2=7.
2 Take the average of the Y-coordinates: (-2 + -6)/2=-4.
So the midpoint of the line segment joining A and B is (7,-4).
How do you find f (- 1 on a graph?
Answers
To find f(-1) on a graph, you need to locate the point (-1, y) and then read off the value of y.
Begin by locating the point (-1, 0) on the graph. This point is located at the far left side of the x-axis. Then, draw a line from this point to the line representing the function. This line will intersect the line of the function at a point which is the coordinates (-1, y).
Now, read off the value of y at this point. This is the value of f(-1). To double-check your answer, make sure that the coordinates of the point you have located are (-1, y). If they are, then the value of y is the value of f(-1).
For more questions like Graph click the link below:
https://brainly.com/question/74883
#SPJ4
question 1 a clinic surveys a group of male and female patients about their experience with physical therapy. the survey does not include people with disabilities. is the survey data biased?
Answers
Yes, the survey data is biased.
The survey data is biased because the sample group lacks inclusivity.
Bias is a statistical word that means a systematic deviation from the actual value. It is a sampling method that may show some serious problems for the researcher as a less increase cannot reduce in sample size.
In a biased sample, one or more parts of the population are favored over others, whereas in an unbiased sample, each member of the population has an equal chance of being selected. We also saw that a representative sample is a subset of the population that reflects the characteristics of the larger group.
Read more about bias:
https://brainly.com/question/24491228
#SPJ4
Multiply and combine like terms to determine the product of these polynomials. ( 2 x − 3 ) ( 5 x + 6 ) (2x−3)(5x+6)
Answers
The product of these given polynomials will be
(4x^2+9-12x)(25x^2+36+60x)
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial.
Now
Given polynomial (2x−3)(5x+6)(2x−3)(5x+6)
After combining like terms
(2x-3)^2(5x+6)^2
(4x^2+9-12x)(25x^2+36+60x) ( As (a+b)^2 = a^2 + b^2 + 2ab
(a-b)^2 =a^2 + b^2 - 2ab )
To know more about polynomials visit the link
https://brainly.com/question/11536910?referrer=searchResults
#SPJ1
Dani's neighbors paid her to take care of their bird during their vacation. Dani spent $4 of her earnings on an afternoon snack and $16 on a new book. Afterward, she had at least $8 left. Complete the inequality below to represent how much Dani's neighbors paid her.
Answers
Answer: Her neighbors paid her 28 dollars
Step-by-step explanation: if you add 4, 16, and 8 then you get 28
Which is equivalent to RootIndex 3 StartRoot 8 EndRoot Superscript x?
Answers
The expression [tex]\sqrt[3]{8^{x} }[/tex] is equivalent to, [tex]8^{x/3}[/tex], So Option C is correct
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression, [tex]\sqrt[3]{8^{x} }[/tex]
equivalent expression = ?
⇒ [tex]\sqrt[3]{8^{x} }[/tex]
⇒ [tex]\sqrt[3][/tex]cube root can be written as 1/3 power of 8
So, expression will convert like this,
⇒ [tex]8^{x/3}[/tex]
Hence, the equivalent expression is [tex]8^{x/3}[/tex]
To know more about Expressions check:
brainly.com/question/16804733
#SPJ1
What is another name for the addition method to solve a system of equations in two variables?
Answers
The elimination method is another name for the addition method to solve a system of equations in two variables.
What is The elimination method?
The elimination approach involves removing one of the variables from the system of linear equations by adding or subtracting, as well as multiplying or dividing the variable coefficients.
What are some instances of elimination methods?
Utilizing the addition property of equality, the elimination approach is used to solve systems of linear equations. Each side of an equation can be increased by the same amount.
You can therefore add x + y to the left side of the first equation and add 8 to the right side of the equation if your system is x - 6 = 6 and x + y = 8.
Learn more about The elimination method
brainly.com/question/30287548
#SPJ4
At Andy's Market, the price of a box of brand-name cereal is 1.5 1.51, point, 5 times the price of a box of generic cereal. If the price of a box of brand-name cereal is $ 3.60 $3.60dollar sign, 3, point, 60, which of the following can be used to determine � xx, the price of a box of generic cereal in dollars? Choose 1 answer: Choose 1 answer: (Choice A) A � 1.5 = 3.6 1.5 x =3.6start fraction, x, divided by, 1, point, 5, end fraction, equals, 3, point, 6 (Choice B) B 1.5 � = 3.6 1.5x=3.61, point, 5, x, equals, 3, point, 6 (Choice C) C 3.6 � = 1.5 3.6x=1.53, point, 6, x, equals, 1, point, 5 (Choice D) D � + 1.5 = 3.6 x+1.5=3.6
Answers
C 3.6 = 1.5 3.6x=1.53, point, 6, x, equals, 1, point,5.
What is equation?An equation is a mathematical statement that states that two expressions are equal. It is composed of two expressions, one on each side of an equals sign, and can be used to solve for unknown values. Equations can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They are used to solve a wide variety of mathematical problems.
The equation to solve for the price of a box of generic cereal is 3.6/1.5 = x, where x is the price of the box of generic cereal. By dividing 3.6 by 1.5, the price of a box of generic cereal is determined to be $2.40.
To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1
5m3 + 3m² – 2m
5m3 + 3m? – 2m
8m3 - 4m2 + 3m
What is the perimeter of the triangle?
Help ASAP!!!!!
Answers
The perimeter of the triangle is given by an expression 18m³ + 2m² - m
Consider the following diagram.
In this question we have been given a triangle.
The sides of the triangles are represented by a mathematical expressions
(5m³ + 3m² - 2m), (8m³ - 4m² + 3m) and (5m³ + 3m² - 2m)
From given expression we can observe that, there are two sides with expression 5m³ + 3m² - 2m.
This means, the triangle must be an isosceles triangle.
We know that the formula for the perimeter of isosceles triangle.
P = 2a + b
where, a = side and b = base of isosceles triangle
Using above formula the perimeter of given triangle would be,
P = 2(5m³ + 3m² - 2m) + (8m³ - 4m² + 3m)
P = (10m³ + 6m² - 4m) + (8m³ - 4m² + 3m)
P = (10 + 8)m³ + (6 - 4)m² + (-4 + 3)m .....(combine like terms)
P = 18m³ + 2m² - m
Learn more about an expression here:
https://brainly.com/question/30091997
#SPJ4
Refer to the figure to complete the following problem.
Given: A RST is circumscribed about circle A. What is the measure of angle S?
0.5 arc XQ minus arc XPQ
0.5 (arc XPQ- arc XQ)
angle R + angle T
Answers
the measured angle S is 1/2((Arc XPQ-Arc XQ)).
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angles of the triangle = 180
The circle is within the triangle,
The arc XPQ is the total, arc XQ
So the measured angle S is 1/2((Arc XPQ-Arc XQ)).
0.5 (Arc XPQ-Arc XQ)
Hence the measured angle S is 1/2((Arc XPQ-Arc XQ)).
Learn more about triangle, by the following link
brainly.com/question/17335144
#SPJ1
A garment shop announces a flat 50% discount on every purchase of items for their customers. Draw that graph for the relation between the market price and the discount.
Hence find (1) the marked price when a customer gets a discount of Rs3250(from graph)
(2)the discount when the market price is rs2500
Answers
The marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The relation between the market price and the discount is
y=0.5x
Which is the required relationship between the Marked Price and the Discount.
We have to find the marked price when a customer gets a discount of 3250
As discount is 3250
In the graph is represent the point F ( 3250, 0)
If we draw a line parallel to Y axis and passing through the point F( 3250, 0) then it intersects the line y = 2x at B( 3250 , 6500)
Accordingly we get the point A ( 3250, 6500)
Hence the Marked Price = 6500
Manually it can be checked
As discount is 3250
x = 3250
So y = 2 × 3250 = 6500
(2) We have to find the discount when the marked price is 2500
As marked price is 2500
In graph it represent the point C( 0, 2500)
If we draw a line parallel to X axis and passing through the point C( 0, 2500) then it intersects the line y = 2x at B( 1250 , 2500)
Accordingly we get the point B( 1250 , 2500)
Hence the discount = 1250
Manually it can be checked
As marked price is 2500
y = 2500
So x = 2500 ÷ 2 = 1250
Hence, the marked price when a customer gets a discount of 3250 (from graph) and the discount when the marked price is 2500
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Pls help this one question is worth 25 points !!!
3. (05. 04 MC)Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches. The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches. Part A: Using the formula for circumference, solve for the value of pi for each circle. Part B: Use the formula for area and solve for the value of pi for each circle. Part C: What observation can you make about the value of pi for circles A and B?
Answers
Part A: The value of π for circle A using the circumference is 3.14 and the value of π for circle B using the circumference is 3.14.
Part B: The value of π for circle A using the area is 3.14 and the value of π for circle B using the area is 3.14.
Part C: You can notice that pi's value remains constant in both circles, proving that it is a constant.
Circle A has a diameter of 7 inches, a circumference of 21. 98 inches, and an area of 38. 465 square inches.
The diameter of circle B is 6 inches, the circumference is 18. 84 inches, and the area is 28. 26 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle.
Circumference formula of circle = 2πr
The diameter of circle A d = 7 inches
The radius of circle A r = 7/2 inches
The circumference of circle of A = 21. 98 inches
Now putting the values in the formula
2π×[tex]\frac{7}{2}[/tex] = 21. 98 inches
7π = 21. 98 inches
Divide by 7 on both side, we get
π = 3.14
The value of π for circle A is 3.14.
The diameter of circle B d = 6 inches
The radius of circle B r = 6/2 inches = 3 inches
The circumference of circle of B = 18.84 inches
Now putting the values in the formula
2π×3= 18.84 inches
6π = 18.84 inches
Divide by 6 on both side, we get
π = 3.14
The value of π for circle B is 3.14.
Part B: Use the formula for area and solve for the value of pi for each circle.
The area of circle = [tex]\pi r^2[/tex]
The radius of circle A r = 7/2 inches = 3.5 inches
The area of circle A = 38.465 square inches
Now putting the value
[tex]\pi (3.5)^2[/tex] = 38.465
π × 12.25 = 38.465
Divide by 12.25 on both side, we get
π = 3.14
The value of π for circle A is 3.14.
The radius of circle B r = 3 inches
The area of circle B = 28.26 square inches
Now putting the value
[tex]\pi (3)^2[/tex] = 28.26
π × 9 = 28.26
Divide by 9 on both side, we get
π = 3.14
The value of π for circle B is 3.14.
Part C: We have to explain what observation you can make about the value of pi for circles A and B.
You can notice that pi's value remains constant in both circles, proving that it is a constant.
To learn more about circumference and area of circle link is here
brainly.com/question/16125353
#SPJ4
solve each equation
20x-3/15=8
Answers
Answer:
20x-3/15=8
We move all terms to the left:
20x-3/15-(8)=0
determiningTheFunctionDomain
20x-8-3/15=0
We multiply all the terms by the denominator
20x*15-3-8*15=0
We add all the numbers together, and all the variables
20x*15-123=0
Wy multiply elements
300x-123=0
We move all terms containing x to the left, all other terms to the right
300x=123
x=123/300
x=41/100
Answer:
x = 0.41
Step-by-step explanation:
20x-3/15=8
20x - 1/5 = 8
20x - 1/5 = 40/5
20x = 41/5
20x = 8.2
x = 0.41
What does a production possibilities diagram represent?
Answers
Answer: The production possibilities is a graph that shows all of the different combinations of output that can be produced given current resources and technology. Sometimes called the production possibilities frontier, the PPC illustrates scarcity and tradeoffs.
Your weekly net income is $380. Your total budgeted monthly expenses $1. 550,00. Do you have a surplus or deficit balance at the end of the month?
Answers
We will have a Deficit balance of $30 at the end of the month.
"Unilateral transfer" is the term used to describe the balance of payments deficit's most obvious cause. For instance, Americans who contribute money to another country in the form of foreign aid do not receive anything in return (economically speaking). Few economists would argue that foreign aid-related balance of payment deficits are a "bad thing."
Weekly net income = $380
Monthly net income = $380 * 4 weeks = $1520.
Monthly expenses = $1550
Balance = Monthly income - monthly expenses = $-30.
The negative sign shows a deficit of $30 monthly
Therefore, We will have a Deficit balance of $30 at the end of the month.
To learn more about Deficit, visit the link below:
brainly.com/question/2290367
#SPJ4
michael is examining a data set and trying to determine which category he can transform into a dummy variable. of the four variables, employee number, pay rate, hire date, and sex, which is the best fit to use a dummy variable?
Answers
Of the four variables, employee number, pay rate, hire date, and sex, the "Sex" variable is the best fit to use as a dummy variable.
The variable "Sex" is the best fit to use as a dummy variable. A dummy variable is used to represent a categorical variable with a numerical value, such as 0 or 1. In this case, "Sex" is a categorical variable with two categories (male and female) and can be transformed into a dummy variable with values 0 or 1 to represent the categories. The other variables, Employee Number, Pay Rate, and Hire Date, are not categorical variables and would not be appropriate to use as dummy variables.
Read more about variables:
brainly.com/question/15158734
#SPJ4
How do you solve a 30 60 90 triangle given only the hypotenuse?
Answers
Yes, it is possible to solve 30 60 90 triangles if only a hypotenuse is given. The 30, 60, and 90 are special right triangles.
30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse
In this type of triangle, the hypotenuse is double of height.
Let's assume the hypotenuse given = [tex]x[/tex]
therefore, height = [tex]\frac{x}{2}[/tex]
and the base is [tex]\sqrt{3}[/tex] times the height
so, base = [tex]\frac{x}{2}\sqrt{3}[/tex]
Points to be noted:
the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.
Learn more about 30 60 90 triangles here:
https://brainly.com/question/11751274
#SPJ4
What is the equation, in point-slope form, of the line passing through the point (5,-3) with a slope of 1/7?
O y+3= 1/7(x-5)
O y-3= 1/7(x+5)
O y-3= 7(x+5)
O y+ 3 = 7(x - 5)
Answers
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{1}{7}}(x-\stackrel{x_1}{5}) \implies y +3= \cfrac{1}{7} (x -5)[/tex]