As far as we are aware, a straight angle is defined as 180 degrees then the bi-conditional assertion is true.
What is meant by bi-conditional assertion?It combines the conditions "if two line segments are congruent then they are of equal length" and "if two line segments are of equal length then they are congruent." Only when both conditionals are true does a biconditional hold. The symbol "or" is used to denote bi-conditionals.
A statement with two conditions is one that has the form "p if and only if q." In other words, if p, then q and if q, then p. "P iff q" or "p q" are other ways to express the biconditional "p if and only if q."
Since we have given that
1) If and only if the angle's measurement is 90 degrees, it is a right angle : True.
As is common knowledge, one angle in a right-angled triangle must be 90 degrees.
2) If and only if an angle is obtuse, it measures 120 degrees : True
Obtuse angle is a term used to describe angles that are more than 90° but less than 180°.
And 90°<120°<180°
3) Only if the angle is a straight angle does it measure 180 degrees : True
As far as we are aware, a straight angle is defined as 180 degrees.
As a result, every bi-conditional assertion is true.
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ABC is an isosceles triangle with BA = BC
D lies on AC
ABD is an isosceles triangle with AB = AD
Angle ABD = 72°
Show that triangle BCD is isosceles.
You must give a reason for each stage of your working.
PLEASE HELP.. WHAT IS THE REASON??????
A property of an isosceles triangle, which is the base angles of the are equal, can be used to show that ΔBCD us an isosceles triangle.
What is isosceles triangle?There are two equal edges and two equivalent angles in an isosceles triangle. The Greek words iso (identical) and Skelos are the source of the name (leg). Equilateral triangles are those in which all of the sides are equal, whereas scalene triangles are those in which none of the sides are equal.
The characteristics of an isosceles triangle are as follows:
The two sides are similar to one another.The base of such an isosceles triangle signifies the third edge of the triangle, and that is unequal to the other two sides.In accord with one another are the two angles that face equal sides.Let assume,
∠DAB = ∠A,
∠DCB = ∠C,
∠ABC = ∠B
The steps to show that ΔABD is an isosceles triangle are as follows;
∠ABD = 72° = ∠ADB :- Base angles of the isosceles triangle ΔABD
∠A + ∠ABD + ∠ADB = 180° (angle summation property)
∠A = 180° - (∠ABD + ∠ADB) = 180° - (72° + 72°) = 36°
∠A = ∠C :- Base angles of the isosceles triangle ΔBDC
∠ADB = ∠C + ∠DBC :- Exterior angle of a triangle theorem
72° = ∠C + ∠DBC
∠BDC = 72° + ∠A
∠DBC + ∠BDC + ∠C = 180° (angle summation property)
∠DBC = 180° - (∠BDC + ∠C) = 180° - (72° + 36° + 36°) = 36°
∠DBC = 36° = ∠C
In ΔBCD, ∠DBC = ∠C
ΔBCD is an isosceles triangle :- definition of an isosceles triangle
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1) y varies inversely with x and y = 40 when x = 5. Find x when y is equal to: a. 50 b. 4
2) y varies inversely with x^2 and y = 10 when x = 15. Find x when y is equal to: a. 22.5 b. 90
Answer:
I have this same question what school do u go to?
Step-by-step explanation:
In the figure below, m/LJK = 37° and m≤KLJ = 69º. What is m/JKH?
A. 90⁰
B. 16°
C. 36°
D. 6°
∠LJK = 37° and ∠KLJ = 69º. So, ∠JKH = 16°. This can be solved by using the concept of triangle.
Correct option: B
What about angles?When two beams or straight lines intersect at one of their ends, an angle is created. The vertices of such an angles is the location where two points come together. The word angle is taken from the Latin word angulus, which means "corner."
Depending on the measurement, there are many angles in geometry. Basic angles are identified by their names: acute, obtuse, right, straight, reflex, and complete rotation.
ΔJKL consist of 3 angles: ∠LJK, ∠KLJ and ∠JKL
We are given the measures of ∠LJK and ∠KLJ
In order to find ∠JKH we must find the missing angle in the triangle
Remember that angles in a triangle add up to equal 180
If we are given two angles we can find the missing angle by subtracting the measures of the known angles from 180
so ∠JKL = 180° - 37° - 69°
180° - 37° - 69° = 74°
Hence, ∠JKL = 74°
Now to find ∠JKH:
Angles ∠K, ∠JKH and ∠JKL appear to be formed on a straight line
Angles formed on a straight line add up to equal to 180°
So, ∠K + ∠JKH + ∠JKL = 180°
∠K is a right angle, indicated by the little square.
Right angles have a measure of 90° so ∠K = 90°
We have also calculated the measure of ∠JKH = ( 74° )
That being said we plug in the given values into the equation created earlier and solve for ∠mJKH
We would have 90° + ∠JKH + 74° = 180°
For calculation ∠JKH:
90° + 74° = 164°
now we have 164° + ∠JKH = 180°
or, ∠JKH = 16°
Hence the answer is B
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The complete question is as follows:
In the array below, in how many different ways can we start with the letter $A$ and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
[asy]
usepackage("amsmath");
usepackage("amssymb");
unitsize(0.6 cm);
label("$\text{A}$", (0.5,3.5));
label("$\text{R}$", (1.5,3.5));
label("$\text{C}$", (2.5,3.5));
label("$\text{H}$", (3.5,3.5));
label("$\text{R}$", (0.5,2.5));
label("$\text{R}$", (1.5,2.5));
label("$\text{C}$", (2.5,2.5));
label("$\text{H}$", (3.5,2.5));
label("$\text{C}$", (0.5,1.5));
label("$\text{C}$", (1.5,1.5));
label("$\text{C}$", (2.5,1.5));
label("$\text{H}$", (3.5,1.5));
label("$\text{H}$", (0.5,0.5));
label("$\text{H}$", (1.5,0.5));
label("$\text{H}$", (2.5,0.5));
label("$\text{H}$", (3.5,0.5));
[/asy]
Based on the information, it can be inferred that the number of possibilities to write arch is 37
How to find the number of possibilities that there are to write the word ARCH?To find the number of possibilities there are to write the word arch we must analyze the graph. Once we identify the position of each letter we must carry out the following procedure.
Find how many possible combinations each letter has to form the word. In this case, to begin with, we only have 3 options to connect A with R. However, each R has at least 3 options to connect with the letter C, the R in the center has 5 possibilities to connect with the letter C.
On the other hand, each letter C has at least 4 possibilities of connecting with the letter H, and the middle C has 7 possibilities of connecting with the letter H.
To find the total number of possibilities we must add these values:
3 + 3 + 5 + 3 + 4 + 4 + 7 + 4 + 4 = 37According to the above, we have 37 combination options.
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escribir la fracción como un decimal
16/25
Answer:
0.64
Step-by-step explanation:
16/25 = 0.64
Can you factorise 8x + 12 please
Answer: 4(x + 3)
Step-by-step explanation:
8x + 12
= 4(2x + 3)
Answer: look below :))
Step-by-step explanation: Yes, 8x + 12 can be factored as follows:
8x + 12 = 4x + 6 + 4x + 6
= (4x + 6) + (4x + 6)
= 2(2x + 3) + 2(2x + 3)
= 2(2x + 3) + 2(2x + 3)
= 4(2x + 3)
So the factored form of 8x + 12 is 4(2x + 3).
GEOMETRY
The following proof was written to prove that triangle BCD is congruent to triangle DAB. The proof is incomplete. Complete the missing pieces.
Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Side DB is congruent to side BD because they are the same segment.
Angle A is congruent to angle c because they are both right angles.
By the ______ theorem, angle ADB is congruent to angle ____
By angle- side triangle congruence theorem, triangle BCD is congruent to triangle DAB.
Angle A is congruent to angle c because they are both right angles. By the angle sum theorem, angle ADB is congruent to angle CBD.
What are congruent triangles?A triangle is a closed polygon with three-line segments that intersect at each of its three angles. When the sides and angles of two triangles match, the triangles are said to be congruent. Thus, two triangles can be placed side by side and angle by angle on top of one another.
Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Side DB is congruent to side BD because they are the same segment.
Angle A is congruent to angle c because they are both right angles.
By the angle sum theorem, angle ADB is congruent to angle CBD.
By angle- side triangle congruence theorem, triangle BCD is congruent to triangle DAB.
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What is the quotient of
7.584
×
1
0
6
7.584×10
6
and
7.9
×
1
0
2
7.9×10
2
expressed in scientific notation?
0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²
What is Division?A division is a process of splitting a specific amount into equal parts.
We need to find the quotient of
7.584×10⁶ and 7.9×10²
Dividend is the number that is to be divided by the divisor.
Divisor is the number by which the dividend is to be divided is called the divisor.
The resultant of the division is called the quotient.
7.584×10⁶/7.9×10²
0.96×10⁶⁻²
0.96×10⁴
Hence, 0.96×10⁴ is the quotient of 7.584×10⁶ and 7.9×10²
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If -8x + 2y = -10 and 7x + 6y = -3 are true equations what would be the value of 15x + 4y
If -8x + 2y = -10 and 7x + 6y = -3 are true equations what would be the value of 15x + 4y is Cross out the common factor: 7.
Verify your math to ensure that the values on either side of the equals sign are the same in order to create a genuine equation. To create a genuine equation, ensure sure the numbers on both sides of the "=" symbol are equal. For instance, the equation 9 = 9 is real. The equation 5 + 4 = 9 is accurate. The formula 6 + 3 = 9 is accurate.
Multiplying both side of a equation by a coefficient:{3(-8x + 2y) = -10 × 3, 7x + 6y = -3}
apply the distributive property {-24x + 6y = -30, 7x +6y -3}
Subtract the two equations: -24x + 6y - (7x +6y) = -30 - (-3)
Remove parentheses: -24x + 6y - 7x - 6y = -27
Cancel one variable : -24x - 7x = -27
Solve the equation: x = 27/31
Substitute into one of the equations: 7 × 27/31 + 6y = -3
Solve the equation: y = -47/31
The solution of the system is {x = 27/31, y = -47/31}
Substitute { x = 27/31 , y = -47/31 into 15x + 4y :: 15 × 27/31 + 4 × (-47/31)
Determine the sign of multiplication or division: 15 × 27/31 - 4 × 47/31
Write as a single fraction: 15 × 27 /31 - 4 × 47 /31
calculate the product or quotient: 405/31 - 188/31
Write the numerators over common denominators: 405 - 188/31
calculate the sum or difference: 217/31
Cross out the common factor: 7
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Leah meaured a line to be 2. 1 inche long. If the actual length of the line i 2. 2 inche, then what wa the percent error of the meaurement, to the nearet tenth of a percent?
The percent error of the measurement, to the nearest tenth of a percent, is 4.54%
Percent error of the measurement:
Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
In other words, the percent error is the relative error multiplied by 100.
The formula for percent error is:
PE = (|Estimated value-Actual value|/ Actual value) × 100
Here,
T = True or Actual value
E = Estimated value
Estimated length of a line = 2.1 inches
The actual length of the line = 2.2 inches
Error = 2.2-2.1=0.1inches
Percent error of the measurement = 0.1/2.2(100)=4.54.
PE=4.54%
So, the percent error of the measurement, to the nearest tenth of a percent is 4.54%
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6. if f(x) =2x - 6 and g(x)=3x+9, find (f+g)(x)
lan didn't know if his eyes were playing tricks on him or what. When he first looked at all the students from the bleachers at the assembly everyone on the gym floor was in groups of 2 with O left over. Those groups seemed to drift together to form groups of 4, but there were 2 left over. The next time he looked, they appeared to be in groups of 3 with 2 left over again. As he double checked, it seemed the groups of 3 were transformed into groups of 5, and this time there were 4 left over. if there were less than 100 people on the gym floor, how many were there? Show your work and explain your thinking and process of elimination. (Hint:. There. are z possible answers. For full credit you must have both answers.)
So on solving the question Mary Ann saw each of these patterns of people while she was on the hill equation is 3x+2 and answer is 14.
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra.
Mary Ann saw each of these patterns of people while she was on the hill:
1)All in groups of two, no leftover
2) All in groups of four, two left over
3)All in groups of three, two leftover
4)All in groups of five, four leftover.
So the number must give 2 as remainder when divided by 3.
So the number must be 4x+2 . So the number will be 3x+2 Thus from the above information, we can easily say that the number is 3*4+2 = 12+2 = 14
However , we have to check whether 14 matches the last part.
Groups of five in which 4 was leftover.
2 groups of 5 taken out of 14 (2*5) will have 4 as a remainder.
So the right answer is 14.
Answer :14
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I want to be done already :(
Answer: 4/D
Step-by-step explanation: going through the options one by one.
for the first point, the first statement is true since both lines intersect at (4,5)
for the second point, this is also true because since (4,5) is on both functions, x=4 and y=5 will be a solution for both
for the third point, this is also true since the point of intersection is (4,5), this is the solution for the system
for the fourth point, this is untrue. since we don't know what f and g are and the only solution to the system is (4,5), what works for f may not necessarily work for g. so 4/d is the answer.
ps. you got this :) you'll be done before you know it
Math help rn pls
1. Write the equation for this sequence. Be sure to start your equation with t(n)
2,−4,−10,−16
2. The French club sold rose bouquets and chocolate hearts for Valentine’s Day. The roses sold for $5 and the hearts sold for $3. The number of bouquets sold was 15 more than the number of hearts sold. If the club collected a total of $339, how many hearts sold?
3. What will the price of the tickets be in 6 years? Round to the nearest 100th (two decimal places ). file attached for this one
Answer:
1 n) = -2n^2 + 2
2 Let x be the number of chocolate hearts sold. The number of rose bouquets sold is x + 15. The total cost of the chocolate hearts is 3x and the total cost of the rose bouquets is 5(x + 15). The total cost of both products is 3x + 5(x + 15) = 3x + 5x + 75 = 8x + 75 = $339. Solving this equation for x, we get x = (339 - 75) / 8 = 64. So the number of chocolate hearts sold is 64.
3 The price of the ticket is increasing at a constant rate. This suggests that the price of the ticket is following an arithmetic sequence. The formula for the nth term of an arithmetic sequence is t(n) = a + (n-1)d, where a is the first term, d is the common difference, and n is the number of terms.
Using the given information, we can find the common difference, d = t(2) - t(1) = $60.50 - $55 = $5.50.
Now, to find the price of the ticket after 6 years, we can use the formula t(n) = a + (n-1)d where n = 6, a = $50, and d = $5.50.
So t(6) = $50 + (6-1)$5.50 = $50 + 5$5.50 = $50 + $27.50 = $77.50. So, the price of the ticket in 6 years will be $77.50.
how much volume in one grain of rice
A grain of rice contains about 0.029 milliliters of volume.
A grain of rice is a tiny, ingestible seed that comes from either Oryza sativa (Asian rice) or Oryza glaberrima, two types of grass (African rice). A single grain of rice is round or oval in shape and measures about 3–4 millimeters in length. A grain of rice has a volume of 0.029 milliliters and a mass of approximately 0.05 grams. The type of rice and the method of processing affect the size and form of a single grain of rice. Over half of the world's population relies heavily on rice as a source of nutrition and as a staple food in many different cultures. Sushi, risotto, rice pudding, and many more recipes all use rice as an ingredient.
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The lines shown below are parallel. If the green line has a slope of -1/2, what is the slope of the red line?
The slope of the red line is -1/2
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Here, we have
Two lines are parallel. Two lines are shown by the color green and red line.
As we know if lines are parallel then their slope is equal.
W are given a green line parallel to the red line.
The slope of the green line is -1/2
But The slope of the red line = slope of the green line.
The slope of the red line = -1/2
Hence, The slope of the red line is -1/2.
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In the Cartesian Plane, draw a triangle with vertices (-1 ,7) ,(5,5) ,(-2 ,1). By distance formula, show that the triangle is isosceles.
The triangle with given vertices is not an isosceles triangle.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Let a triangle with vertices be A(-1 ,7), B(5, 5) and C(-2 ,1).
Using the coordinates A(-1, 7) and B(5, 5), we get
AB =√(5-7)²+(5+1)²
AB=√40
AB=2√10 units
Using the coordinates B(5, 5) and C(-2 ,1) we get
BC=√(-2-5)²+(1-5)²
BC=√65 units
Using the coordinates C(-2 ,1) and A(-1 ,7) we get
BC=√(-1+1)²+(7-1)²
BC= 6 units
Therefore, the triangle with given vertices is not an isosceles triangle.
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janelle is a junior counselor at cactusville craft camp. one day, janelle's campers make lanyard keychains out of plastic string. for each keychain, janelle cuts a long piece of string into 4 equal pieces. each piece is 1.5 feet long.which equation can you use to find the length s of the long piece of string before janelle cuts it?
The length of the long piece of string before Janelle cuts it is 6 feet.
We can use the following equation to find the length s of the long piece of string before Janelle cuts it:
s = 4 * 1.5 feet
where 4 is the number of pieces and
1.5 feet is the length of each piece.
Therefore, s = 4 * 1.5 feet = 6 feet.
Multiplication is the process of taking one integer and multiplying it by a certain number of times. Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.
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select the correct answer from each drop-down menu consider the given equation 3x+2y=8 the equation y=______x+____ represents the line parallel to the given equation and passed through the point (-2,5)
equation 3x+2y=8 the equation y= -3/2, x+2 represents the line parallel to the given equation and passed through the point (-2,5)
How do equations work?The concept of an equation in algebra is a quantitative statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
(formula of the line ) y= mx+c
y= -3/2+8/2
y= -3/2+4 ( m= -3/2)
this is given equation of the line
and its parallel line is
y-5/x+2 = -3/2
2y- 10 = -3x-6
3x+2y =4
2y = -3x+4
y = -3/2x+2
y = -3/2
x =2
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After the GCFs are factored out, what is the common binomial factor for x2 + 3x + 5x + 15?
The common binomial factor for the given expression is[tex]$x+3$[/tex].
What is binomial factor?Polynomial factors known as binomial factors contain two terms only. Because binomials are simple to solve and the roots of the binomial factors are the same as the roots of the polynomial, binomial factors are intriguing. The first step in locating a polynomial's roots is to factor it.Consider factoring by grouping if your set of four words lacks a GCF. Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each individual binomial. 3. Factor the common binomial out.We are given the expression[tex]$x^2+3 x+5 x+15$.[/tex]
We wish to find the common binomial factor for the given expression. So, we have:
Solution:
Factoring by grouping, we have:
[tex]x^2+3 x+5 x+15 & =x(x+3)+5(x+3) \\[/tex]
[tex]& =(x+3)(x+5)[/tex]
Therefore, we can see that the common binomial factor for the given expression is[tex]$x+3$[/tex].
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Please help me with this i don't know how to set up a graph. Thank you!
Answer:
Why do you need to set up a graph for this equation?
Step-by-step explanation:
A bank says you can double your money in 10
10
years if you put $1,000
$
1
,
000
in a simple interest account. What annual interest rate does the bank pay?
Divide the principal by the time, interest rate, and time period to calculate simple interest.Annual interest rate is 0.02.
What rate of interest does the bank charge annually?
Divide the principal by the time, interest rate, and time period to calculate simple interest.The equation is expressed as "Simple Interest = Principal x Interest Rate x Time."It is easiest to calculate interest using this equation.
I, or the interest earned or charged on a loan, can be calculated using the straightforward interest formula.
I = Prt, where P is the principal, r is the yearly interest rate stated in decimal form, and t is the loan term expressed in years, gives the amount of interest.
It is necessary to transform the rate r from percentage to decimal form.
Then, 2,000 = 1,000 * r * 10 ;
Finally, r = 2 ÷ 10 = 20 ÷ 100 = 0.02
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use polar coordinates to find the volume of the given solid. under the cone z = x2 y2 and above the disk x2 y2 ≤ 36
The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
The volume of the solid can be found by integrating the equation:
V = ∫∫∫r2sin(θ)dzdθdr
where r is the radius and θ is the angle of the polar coordinates.
The limits of integration are as follows:
r = 0 to 6
θ = 0 to 2π
z = 0 to x2y2
The integral is then:
V = ∫0 to 2π∫0 to 6∫0 to r2sin(θ)dr dθ
V = ∫0 to 2π∫0 to 6 r3sin(θ)θdr
V = ∫0 to 2π [r4sin(θ)]0 to 6 dθ
V = ∫0 to 2π 644sin(θ)dθ
V = 7056π
The volume of the solid under the cone z = x2y2 and above the disk x2y2 ≤ 36 is 7056π. This was found by using polar coordinates and integrating the equation V = ∫∫∫r2sin(θ)dzdθdr with the limits of integration r = 0 to 6, θ = 0 to 2π, and z = 0 to x2y2.
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Graph the function y=|x|-3
Enter the correct answer in the box.
A delivery company uses cars, cargo vans, and semitrailers. The company uses its cargo vans to deliver packages to locations at a 75-mile radius from the warehouse. If the distance to the delivery location is 8 miles or less from the delivery boundary, a cargo van will still be used. The company uses the other vehicles for any distance outside this range.
Write an inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse.
The inequality to represent the instances when a vehicle other than a cargo van is used, where x is the distance of a location from the warehouse is given as follows:
x ≤ 8.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.Distances of 8 miles or less are of at most 8 miles, hence the inequality is defined as follows:
x ≤ 8.
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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2012, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1171.
Regression equation:
Final answer:
The linear regression model is expressed as y = -25.31x + 1017.075.
What is linear regression?The best-fit line is given by:
y = bx + a
The slope is as follows:
b = Σ(x - X) ( y - Y)/Σ(x - X)²
After determining the slope using the means for x and y, the coefficient an is calculated.
The means are provided by:
X = (0 + 1 + 2 + 3 + 4 + 5)/ 6 = 2.5
Y= (904 + 924 + 938 + 957 + 977 + 1023)/6
= 953.83
The figures are as follows:
Σ(x - X) = (0 - 2.5) +(1 - 2.5) + ---------+ (5 - 2.5)
Σ( y - Y) = ( 904 - 953.83) + (924 - 953.83) + ---------- + ( 1023 - 953.83)
Making use of a calculator:
Σ(x - X) ( y - Y) = -443
Σ(x - X)² = 17.5
As a result, the slope is:
b = -443/17.5
= -25.31
y = -25.31x + a
Using the means to locate a:
953.83 = -25.31 x 2.5 + a
a = 1017.075
As a result, the linear regression model is:
y = -25.31x + 1017.075
After 2012, the number of cases would reach 1171 in x years, and x is found when y = 1171. Thus:
1171 = -25.31x + 1017.075
1171 - 1017.075 = -25.31x
x = 6
2012 + 6 = 2018
The number of reported cases is expected to reach 1171 by 2018.
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special right triangle
The value of a is 12 and b is 10.39, for the given special right triangle.
What is the special right triangle?A special right triangle is a right triangle with a regular feature that facilitates calculations on the triangle or for which straightforward formulas are available. Angles in a right triangle, for instance, could form straightforward relationships like 45°-45°-90°. Right triangle that is "angle-based" is what this is. When the side lengths of a right triangle form ratios of whole numbers, like 3:4:5, or of other unusual numbers, like the golden ratio, the triangle is said to be "side-based." Without using more complex techniques, one can quickly calculate different lengths in geometric problems by understanding the relationships between the angles or side ratios of these special right triangles.
The opposite sides of a 30-60-90 special right triangle are always in the ratio of 1:√3: 2.
so opposite of 30deg here is 6
as When opposite side 30deg is 6 then opposite side 90deg is 2(6)
a = 2(6)
a = 12
Now we have base = 6 and hypotenuse = 12
Use Pythagoras theorem
b [tex]= \sqrt{12^2 - 6^2}[/tex]
b = 10.39
Thus, The value of a is 12 and b is 10.39, for the given special right triangle.
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an account earns simple intrest find the interest earned and the balance of the account 200 at 3 % for 5 years
The interest earned and the balance of the account 200 at 3 % for 5 years is 30.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that an account earns simple intrest
We have to find the interest earned
the balance of the account 200 at 3 % for 5 years
I=PRT
P is the principal amount
t is the time
r is the rate of interest
I=200×0.03×5
I=30
Hence, the interest earned and the balance of the account 200 at 3 % for 5 years is 30.
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Please Help me with numbers 1 2 and 3!!!! I dont know!!!
Step-by-step explanation:
it says it in the headline : the cube root function.
1.
it goes through (0, 0) and (1, 1) and (-1, -1).
so,
f(x) = cubic root(x)
domain = (-infinity, +infinity)
range = (-infinity, +infinity)
x-intercept = 0
y-intercept = 0
2.
the function is y = cubic root(x + 2)
compared to
y = cubic root(x)
the domain is x >= -2
wrong !
this is not a square root. for the square root that domain would be correct (there are no real number square roots for negative values). but cubic roots are possible also for negative values. this function has the same domain and range as the basic y = cubic root(x) : (-infinity, +infinity).
the function is a vertical translation of g(x) = cubic root(x).
wrong !
vertical means up/down.
but it is a horizontal (left/right) translation of that g(x). by 2 units to the left, actually.
3.
for 1 <= x <= 4 we have already the average rate of change :
about 0.197
for 4 <= x <= 7 we get
(f(7) - f(4))/(7 - 4) ≈ (1.91 - 1.59)/3 ≈ 0.109
so, the interval [1, 4] has a greater average of change.
which is also clear when looking at the graph : the function increases stronger for the lower x-values than for the larger x-values.
This afternoon Dan left school, rode the bus 1/4 of a mile, and then walked 1/8 of a mile to get home. How much farther did Dan ride than walk?
Answer:
0.125 miles
Explanation:
1/4 of a mile is 440 yards and 1/8 of a mile is 220. 440-220=220.
