Answer: (Only for homework, no tests, please!)
Step-by-step explanation:
Hello! An easy way to help you solve this is to use graph paper. Make a coordinate grid using a ruler to help you form the trapezoid and plot the points at the proper coordinates. It should look something like this but with a line going through BC and AD. Draw the midpoint of line segments AD and BC by measuring their lengths with a ruler and divide the length in half to plot the points. Connect the midpoints with a ruler to form the midsegment. Hope this helps you with your homework!
72/10 is equal to which decimal?
Answer:
7.2 because 72 / 10 = 7.2
hope this helps!!!
3 IS A
√
RATIONAL
NUMBER? PLEASE
EXPLAIN
CLEARLY WHY IT
EITHER IS OR
ISN'T.
Answer:
The square root of 3 is an irrational number
Step-by-step explanation:
A rational number is defined as a number that can be expressed as the division of two integers, i.e. p/q. where q is not zero.
√3 = 1.7320508075688772...and keeps getting longer. √3 is an irrational number because the decimal point does not end or repeat.
What is the gradient of y =- 3x 1?.
So, the gradient of y = -3x^1 is -3.
The gradient of a function y = f(x) with respect to x is the derivative of the function with respect to x, denoted by dy/dx or f'(x).
In the case of y = -3x^1, the gradient is -3.
It is a constant function, thus, the slope is always the same and equal to the coefficient of the x term, which in this case is -3.
The gradient of a function tells us the rate of change of the function with respect to x. In other words, it tells us how steep the function is at any given point. A positive gradient means that the function is increasing, while a negative gradient means that the function is decreasing.
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A new roller coaster just opened at Friday Fun Park. When Lisa got in line, a sign said the wait from that point would be 45 minutes. The actual wait was only 35 minutes. What is the percent error for the park sign's estimate? If necessary, round your answer to the nearest tenth of a percent.
Answer:
28.6%
Step-by-step explanation:
10 minute difference, 10 is 28.6% of 35.
Help Me Please :<
In Which Of These Situations Do The Quantities Combine To Make 0?
The situation in which the quantities combine to make 0 is "On Monday, Huang withdraws $30 from a bank account. On Friday, she deposits $30 into the account".
In which case the quantities combine to make 0?For two quantities two make 0, it is necessary to add two numbers with the same value but different sign (positive or negative). Here is an example:
+15-15 = 0For example if you buy 10 apples but use 10 apples to make a pie.
Based on this, the correct situation is "On Monday, Huang withdraws $30 from a bank account..." as -30 + 30 = 0.
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4x+2y≥14 what is the y intercept?
The y-intercept of the line 4x + 2y ≥ 14 is y ≥ 7.
How to find y-intercept?The y-intercept is the point where the graph intersects the y-axis. In other words, the y-intercept of a line is the value of y when x equals to zero.
In simpler term, the y-intercept of a function is the point(s) where the graph of the function crosses the y-axis.
Therefore, let's find the y-intercept of the inequality.
4x + 2y ≥ 14
let's substitute x as 0.
Therefore,
4x + 2y ≥ 14
4(0) + 2y ≥ 14
2y ≥ 14
divide both sides by 2
2y / 2 ≥ 14 / 2
Hence,
y ≥ 7
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U partly varies directly as S and partly inversely as the square root of M. When U=86.75, S=16, M=25 and when U=124.6, S=24, M=36. Find the equation connecting U,S and M. Find the value of 19 when U=110.5 and S=32
The equation connecting U,S and M is K = U√M/S
The value of M when U=110.5 and S=32 is 4.32
How to determine the valueFrom the information given, we have that U partly varies directly as S and partly inversely as the square root of M.
This is represented mathematically as;
U ∝S/√M
To determine the constant of the variation, we have;
U = KS√M
Now, make 'K' the subject of formula;
K = U√M/S
Substitute the values
K = 124.6 √25/86.75
Find the square root
K = 7. 18
To determine the value of M, we have;
KS/U = √M
substitute the values
√M = 7.18(32)/110. 5
√M = 2. 08
find the square of both sides
M = 4. 32
Hence, the value is 4.32
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A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
better same worse
Republican 38 104 44
Democrat 12 87 137
none 21 90 118
Express each of your answers as a percent rounded to the nearest tenth (for example, 12.3%).
What percent of survey respondents identified themselves as affiliated with neither party?
____%
What percent of survey respondents thought the economy was about the same?
____%
What percent of those affiliated with neither party thought the economy was about the same?
____%
Among survey respondents who thought the economy was about the same, what percent were affiliated with neither party?
____%
The percentages for this problem are given as follows:
Neither: 35.2%.Economy about the same: 43.2%.Economy about the same, neither: 39.3%.Neither, economy about the same: 32%.How to obtain the percentages?The percentages are obtained applying proportions, as a percentage is the division of the number of desired outcomes by the number of total outcomes, and then multiplied by 100%.
651 adults were surveyed, of which 21 + 90 + 118 = 229 were affiliated with neither party, hence the percentage is of:
229/651 x 100% = 35.2%.
104 + 87 + 90 = 281 said that the economy was about the same, hence the percentage is of:
281/651 = 43.2%.
90 people out of the 229 that were unaffiliated felt that the economy was the same, hence:
90/229 x 100% = 39.3%.
Of the 104 + 87 + 90 = 281 people that thought that the economy is about the same, 90 were affiliated with neither part, hence:
90/281 = 32%.
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3, -26, -1, -5, 4, 1, 3 Question 1 options: Either the Mean of the Median The Median Only The Mode Only
A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
How to explain the measure of deviation?MEAN =Sum of observations/Total number of observations.
MEDIAN= If n is odd, then the following formula is used: Value of (n+1/2th observation. If n is even, then the following formulae is used: {Value of (n/2) th observation + (n/2 +1)th observation/2}
MODE= Most number of times occurring value in the data
Note that your information wasn't properly written and a overview was given.
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4. If a and b are the acute angles of a right triangle and sec a = 3/2, find the six trig function of b
sin b=
cos b=
tan b=
ctn b =
sec b =
csc b=
Sin b=4/5 cos b=3/5 tan b=4/3 ctn b=3/4 sec b=5/3 csc b=5/4
What is trigonometric functions?The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecanIn mathematics, the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many othersTrigonometry is the study of relationships between angles, lengths, and heights of triangles. It includes ratios, functions, identities, and formulas to solve problems based on it, especially for right-angled triangletrigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).To learn more about trigonometric functions refers to:
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Jayden i making frozen dog treat for hi puppy Spot. He mixe 1 quart of yogurt, 10 fluid ounce of peanut butter, and 6 fluid ounce of honey. Then, he freeze the mixture in ice cube tray. Each tray hold 16 fluid ounce of treat. How many tray of dog treat doe Jayden make?
Jayden makes 3 trays of dog treats for his puppy Spot
What is unit conversion?It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.
To solve this problem, we have to do the conversion of units with the given information:
Information about the problem:
Yogurt = 1 quartPeanut butter = 10 ouncesHoney = 6 ouncesTray capacity = 16 ounces/ trayNo. trays = ?1 quart is equal to 32 ouncesBy converting the unit from quart to ounce, we have:
1 quart * (32 ounce / 1 quart) = 32 ounce
Calculating the total of ingredients Jayden mixed we have:
Total ounces = Yogurt + peanut butter + honey
Total ounces = 32 ounces + 10 ounces + 6 ounces
Total ounces = 48 ounces
Calculating the number of tray that Jayden can make we have:
No. trays = Total ounces / tray capacity
No. trays = 48 ounces / 16 ounces/ tray
No. trays = 3 trays
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When P x )= x³ 3x² 4x 32 is divided by x 2 The remainder is?.
When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.
In the given question, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then we have to find the remainder.
The given equation is
P(x) = [tex]x^3-3x^2+4x+32[/tex]
We have to divide this equation by x+2.
To find the remainder we firstly equate x + 2 equal to zero to find the value of x.
x + 2 = 0
Subtract 2 on both side, we get
x = -2
Now we put x value in the given equation to find the remainder.
The equation
P(x) = [tex]x^3-3x^2+4x+32[/tex]
Put x = -2
P(x) = [tex](-2)^3-3(-2)^2+4(-2)+32[/tex]
Simplify
P(x) = -8 - 3×4 + (-8) + 32
P(x) = -8 - 12 - 8 + 32
P(x) = 4
Hence, when P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2 then the remainder is 4.
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The complete question is:
When P(x) = [tex]x^3-3x^2+4x+32[/tex] is divided by x + 2. The remainder is?
If cosine of x degrees equals three-fifths, what is the value of b?
triangle LMN in which angle M measures 90 degrees, angle L measures x degrees, LN measures 20 units, and LM measures 3b units
b = 4
b = 5
b = 6
b = 7
If cos x = 3/5 then the value of b = 4
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin(tetha) = opp/hyp
cos ( tetha) = adj/hyp
tan ( tetha) = opp/ adj
In the triangle adj = 3b and hyp = 20
cos x = 3b/20
cos x = 3/5
therefore 3/5 = 3b/20
multiply both sides by 20
3/5×20 = 3b/20 × 20
3b = 12
divide both sides by 3
b= 12/3 = 4
therefore the value of b is 4
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Answer:A: b = 4
Step-by-step explanation:
Which values are within the range of the piecewise-defined function?
The values within the range of the piecewise-defined function are
y = -6, y = -4, y = 1 and y = 3.
What is a piecewise function?A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.
Given f(x) = 2x + 3, if x < -3
f(x) = x, if x = -3
f(x) = -x - 2, if x > -3
the function will be at x ≤ -3 and x ≥ -3
We now wish to determine which values fall within this function's range. Keep in mind that the set of possible outputs from a function constitutes its range.
The range of the first part of the function f(x) = 2*x + 2 has an upper bound at x = -3
f(-3) = 2*-3 + 2 = -6 + 2 = -4
Then the range of the first part is (-∞, -4)
Notice that the actual value -4 belongs to the range because x is smaller than and equal to -3.
The range of the second part has a lower bound for x = -3, the lower bound is:
f(-3) = -(-3) - 2 = 1
Then the range of this part is (1, ∞)
Then the range of the piecewise function is:
(-∞, -4) U (1, ∞)
and including -4 and 1
y = -6, y = -4
y = 1, y = 1
Hence values in the range are y = -6, y = -4, y = 1, and y = 3.
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(Continuouly Compounded Interet LC)
A cutomer ue a tore credit card to purchae a boat for $10,500. The tore credit card offer an annual interet rate, compounded continuouly, of 18. 99% with no payment due for the firt two year. If no payment are made for the two year, what will be the balance on the card, rounded to the nearet penny?
a ) $12,679. 59
b ) $12,695. 85
c ) $15,311. 62
d ) $15,350. 92
The balance on the card, rounded to the nearest penny $15350.92..
The correct option is D.
Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.
Formula of continuous compound interest rate;
P(t) = P₀[tex]e^{rt}[/tex]
where P₀ is the principal amount, r is the interest rate and t is the time period.
A customer uses a store credit card to purchase a boat for $10,500.
The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.
That means,
P₀ = $10500, r = 18.99 and t = 2.
So,
P(t) = P₀[tex]e^{rt}[/tex]
Substituting the values,
P(t) = (10500)
P(t) = (10500)(1.46199)
P(t) = 15350.917
P(t) = $15350.92
Therefore, the final amount is $15350.92.
The balance on the card, rounded to the nearest penny $15350.92.
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a) Fill in the gap to make the statement true: Even numbers are numbers that are divisible by b) 2 is the only even prime number. Write a sentence to explain why this is true.
a. Even numbers are numbers that are divisible by 2
b. prime number is the number that has two factors by 1 and itself, all even numbers are divisible by 2 hence any other even number aside 2 will be divisible by 1, 2 and itself and this does not define a prime number any more
What is prime number?A prime number is a positive integer greater than 1 that is only divisible by 1 and itself. In other words, a prime number has exactly two positive integer divisors: 1 and itself.
For example, the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, and so on. The number 2 is the only even prime number, and all the other prime numbers are odd.
Prime numbers are important in mathematics because they play a crucial role in various fields such as number theory, cryptography, and coding theory. They are also used as basic building blocks for constructing larger composite numbers.
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A square floor is covered by a number of whole rectangular tiles of sides 54 cm by 30 cm such that a uniform margin of width 6 cm is left on a round the floor. calculate the least possible area of the floor giving me answer in square metres.
Answer: 7.9524 m^
Step-by-step explanation:
The square with the least area can only be formed when we take LCM of the dimensions of the rectangular tile I.e. 54 CM × 30 CM
LCM = 270
This means that a square of length 270 CM will be formed when we take least no. of tiles.
Also given in question, 6cm is left around the square that means 12cm is added on every side to make the floor with minimum area = 282 × 282 cm^2
minimum area = 79524 cm^
in m^2 = 79524/10000 = 7.9524 m^
What are m<1 and m<2?
1. <1 is an exterior angle of the triangle. What are the measures of its remote interior angles?
2. Add the measures of the remote interior angles you identified in Exercise 1 to find m<1.
3. Complete the equation.
M<1+m<2=
4. Use your answer to Exercise 2 and the equation in Exercise 3 to find M<2
5. What are m<1 and m<2?
(photo attached)
please answer i’ll give brainliest
The remote interior angles of ∠1 are 34° and the right angle. The amount of m∠2 is 56°.
∠1 is an exterior angle because it is located outside the triangle. It has 2 remote interior angles. Remote interior angles are the angles with no shared vertex with the exterior angle. In this case, the remote interior angle of ∠1 is angle 34° and the right angle.
m∠1 can be measured by adding the remote interior angles:
m∠1 = 34° + 90°
m∠1 = 124°
Since m∠1 share a vertex with m∠2, then the total of both angles should be equal to 180° (a straight line). Hence:
m∠1 + m∠2 = 180°
Using the value of m∠1 known above, we can find the value of m∠2:
m∠1 + m∠2 = 180°
124° + m∠2 = 180°
m∠2 = 56°
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How doe the location of the negative make value of 5. 3 x 10^-4 different from -5. 3 x 10^4
Location of the negative make value different from each other that is 5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])
According to this rule, if the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.
The negative exponent rule is given as:
5. 3 x 10^-4
= 5.3/10^4 (1)
-5. 3 x 10^4
-(5.3 * [tex]10^{4}[/tex]) (2)
from equation 1 and 2 these two equations are different from each other.
location of the negative make value different from each other that is 5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])
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Cameron want to download ome movie that cot $14. 50 and want an ebook that cot $22. 50. He ha $66 write and olve an equation that can be ued to find the number of movie he can download
Cameron can download 4 movies with his $66. He can solve an equation of 14.50x + 22.50y = 66 and x + y = 4
14.50x + 22.50y = 66
14.50x = 66 - 22.50y
14.50x = 43.50
x = 3 (43.50/14.50)
x + y = 4
3 + y = 4
y = 1
Cameron wants to download some movies and an ebook with his $66. To figure out how many movies he can download, he needs to solve an equation. The equation is 14.50x + 22.50y = 66, where x is the number of movies and y is the number of ebooks. By solving for x, he can figure out how many movies he can get, which is 3 (43.50/14.50). To find the number of ebooks, he can solve for y in the equation x + y = 4, which is 1. Therefore, Cameron can download 4 movies with his $66.
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The table shows the depths of four plants. Order the numbers form least to greatest
Answer:
sea grass red algae green seaweed mangrove or -20 3/4, -15 1/2, -14 3/4, -1/4
Step-by-step explanation:
negatives switch around the rules of positive so the one with the number tat is bigger when not negative is the lowest when negative
3.8 liters= how many mL
If x and y vary directly and y is 44 when x is 11, find y when x is 9.
The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, x and y vary directly and y is 44 when x is 11.
Let, y ∝ x.
y = kx.
44 = 11k.
k = 44/11.
k = 4.
Now x = 9.
y = 4×9.
y = 36.
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What is co-prime numbers for Class 6?.
Co-prime numbers are those numbers that have only one common factor, namely 1.
Coprimes are pair of numbers that have no common factor other than 1. There should be at least two numbers to form a set of coprimes. Such numbers have only 1 as their highest common factor, for example (4 and 7), (5, 7, 9) are co-prime numbers. It should be noted that concurrent primes need not always be primes. If the only common factor of two numbers a and b is 1, then a and b are coprimes. In this case, (a, b) is considered a prime pair. Minor primes are also referred to as relatively primes. To determine whether any two numbers are co-prime, we first find their greatest common factor (GCF). If their GCF is 1, we can say they are co-prime. Consider the two numbers 5 and 9. The factors of 5 are 1 and 5. The factors of 9 are 1, 3, and 9. The factor that is common to both 5 and 9 is 1. The GCF of (5, 9) = 1. Thus, (5 , 9) is a co-prime pair.
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The perimeter of a rectangular field i 274 yard. If the width of the field i 63 yard, what i it length?
The length of the rectangle is 74 yard.
What is perimeter of rectangle?The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is
P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.
The perimeter of rectangle is given by 2 ( l + b)
where l is length of rectangle and b is width of the rectangle
given that perimeter of rectangle is 274
so 2 (l+b)= 274
=> l+b= 137 ---(i)
so l = 137 -b
=> l = 137 - 63
=> 74
so the lenth of rectangle is 74 yard.
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What is the slope intercept form of the following equation − 6x − 2y − 18?.
The slope intercept form of the following equation 6x - 2y = 18 is y = 3x - 9
We knwo that the slope intercept form of equation of line is y = mx + b, where m is the slope and b is the y-intercept.
Consider given equation,
6x - 2y = 18
6x - 2y - 6x = 18 - 6x .......(Subtract 6x from each side)
- 2y = 18 - 6x
- 2y × (-1) = (18 - 6x) × (-1) ......(Multiply each side by -1)
2y = -18 + 6x
2y/2 = (-18 + 6x)/2 ..........(Divide each side by 2)
y = -18/2 + 6x/2
y = -9 + 3x
y = 3x - 9
This equation is in the form y = mx + b
Here, slope m = 3 and the y-intercept b = -9
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The complete question is:
What is the slope intercept form of the following equation 6x - 2y = 18?
A wheel of radius 14 in. is rotating 0.5 rad/sec. What is the angular speed in RPM (revolutions per minute)? What is the linear speed in in/sec?
Round to three decimal places.
Answer:
The linear speed (V) is equal to 7 in/s.
The angular speed in rpm is equal to 4.77 rpm.
The angular speed in deg/s is equal to 28.65 deg/s.
Step-by-step explanation:
What is a perfect square trinomial formula?.
The general form of a perfect square trinomial is (x + y)², where x and y are the roots of the trinomial. It can also be written as x² + 2xy + y² or x² + (2xy)x + y².
The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.
It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.
Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.
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What is the extended ratio relating the side lengths of a 30 60 90 triangle?.
Answer:
Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).
State the postulate or theorem that can be used to prove the triangles congruent.If you cannot prove the triangles congruent, write not enough information.
To prove the congruence between two triangles there are several postulates, that can be applied depending on the congruent parts of the triangles.
What are the postulates?The postulates are:
SAS (Side-Angle-Side): This postulate states that if two triangles have two corresponding sides congruent and one corresponding angle congruent, we can conclude that those triangles are completely congruent.
ASA (Angle-Side-Angle): This postulate states that if two triangles have two corresponding angles congruent and one corresponding side congruent, then those triangles are congruent.
SSS (Side-Side-Side): This postulate states that if two triangles have all three corresponding sides congruent, then triangles are congruent.
AAS (Angle-Angle-Side): If two pairs of corresponding angles are congruent and one pair of corresponding sides is congruent, then both triangle are congruent each other.
HL (Hypothenuse-Leg): this postulate is applied when we have right angles. It states that two right triangles are congruent if they have one pair of corresponding leg congruent, and the hypothenuses are also congruent. We could conclude that those right triangles are congruent.
From these postulate, we can demonstrate the congruence between two triangles. Then, from that congruence, we deduct the congruence between each corresponding parts of those triangles. For example, if we demonstrate the congruence by AAS, we deduct that the third angle is also congruent, and the other two sides are also congruent.
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