The angle measures of each vertex of the garden are 53.13 degrees.
In Parallelogram ABCD, diagonals AC and BD intersect at point A = √7.
What is angle?Angle is a geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360°.
1. To determine the angle measures of each vertex of the garden, we must first calculate the angles formed by each side. For example, the angle formed by sides AB and BC can be found by using the inverse tangent function. The equation would be
arctan(BC/AB) = arctan (4/3) = 53.13 degrees.
The angles for the other sides can be calculated in the same way. We can then use the sum of angles theorem to calculate the angles at each vertex. Since the garden is an irregular shape, the angles at each vertex will be different.
2. In Parallelogram ABCD, diagonals AC and BD intersect at point A. To calculate , we can use the distance formula.
The equation would be = √((x2 – x1)2 + (y2 – y1)2).
For the coordinates given, we would have
= √((2 – 5)2 + (5 – 1)2)
= √(-9 + 16)
= √7.
Answer 3: To determine whether quadrilateral ABCD is a rectangle, rhombus, or square, we must first calculate the slope.
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Geometry help needed!
The answer is 38 degrees because the angle of HZJ is 38, its a reflection
Answer:
m<FZG= 38
Step-by-step explanation:
<JZG is a straight line equivalent to 180 degrees. Because m<HZJ is 38 degrees, m<HZG is 142 degrees because 180-38=142. Looking now at line HF, equivalent to 180 degrees, we know that m<HZG is 142 degrees. To solve for m<FZG, we use the equation 142+x=180. 180-142=x; x=38. You can also use the vertical angle theorem to solve for m<FZG.
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Daryl Mattingly bought a rental property in Lake Arrowhead for $185,900. After a $40,000 down payment, he mortgaged the rest. His annual expenses totaled $19,850 and he rented the condo for $3,875 per month for 6 months. Determine a) the annual net income and b) the annual yield.
The annual net income and annual yield are $3400 and 2.335 respectively
What is the annual net incomea) To find the annual net income, we need to subtract the annual expenses from the annual rental income. The annual rental income can be calculated as follows:
$3,875 * 6 months = $23,250
The annual net income would be:
$23,250 - $19,850 = $3,400
b) The annual yield can be calculated as the annual net income divided by the total cost of the property, including the down payment:
$3,400 / ($185,900 - $40,000) = 0.023 or 2.33%
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I’m circle Y, what is m
In circle Y, the measure of m∠SZT is equal to: B. 94°.
What is a chord of circle?In Mathematics, a chord of circle can be defined as a line segment that typically join any two (2) points of a circle.
Generally speaking, the inscribed angle of a circle is equal to half of the central angle of a circle. Mathematically, this is given by this mathematical expression:
m∠STR = 1/2(SYR)
m∠STR = 1/2(50)
m∠STR = 50°.
m∠TSU = 1/2(TYU)
m∠TSU = 1/2(72)
m∠TSU = 36°.
For m∠SZT, we have the following:
m∠SZT = 180° - (m∠STR + m∠TSU)
m∠SZT = 180° - (50 + 36)
m∠SZT = 180° - 84°
m∠SZT = 94°
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Lynn works as a bus driver.
She is paid £10.80 per hour for the first 38 hours she works each week.
She is paid 25% more per hour for each extra hour she works.
One week, Lynn was paid £491.40
In total, how many hours did she work that week?
You must show your working.
Answer:
44h
Step-by-step explanation:
money earned per extra hour worked=100+25/100×10.80=13.50
amount earned if working for 38 hours=10.80×38=410.40
remaining money=491.40-410.40=81
number of extra hours worked=81÷13.50=6
total hours worked=38+6=44h
find three consective integers if the sum of the first two is 51 more than the third integer
The three consecutive integers are 52, 53, 54, if the sum of the first two is 51 more than the third integer.
Consecutive Integer:
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.), or a negative integer with a minus sign (−1, −2, −3, etc.). A negative number is the additive reciprocal of the corresponding positive number. In math language, the set of integers is often written as bold Z.
Consecutive integers are integers that follow each other in a regular counting pattern. When listing consecutive integers in a sequence, the difference between them is always fixed because there are no skipped digits between them. Consecutive integers are integers that follow each other in ascending order. The Sequential Integer Formula helps to find these integers for a given number or to determine whether a series of integers are consecutive.
According to the Question:
Let the three consecutive integers are
x , x+1, x+2
Since we have given that:
The sum of the first two is 51 more than the third,
Now,
(x + x + 1) - (x+2) = 51
⇒ 2x +1 -x - 2 = 51
⇒ x - 1 = 51
⇒ x = 52
So, the three consecutive integers are
52, 52+1, 52+2
Therefore,
52,53,54.
Hence, the integers are 52,53,54.
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A spinner has 10 equal sized sections labeled 1 through 10. In 40 spins, the spinner lands 3 times in section 5. How does this compare to the number of times the pointer is expected to land in section 5?
a. Find the experimental probability that teh pointer lands in section 5. / which equals %
b. Find the theoretical probability that the pointer lands in section 5. / which equals %
c. How does the actual number of times the pointer landed in section 5 compare to the expected number?
(less often or more often) then expected
a) The experimental probability that the pointer lands in section 5 is 7.5%
b) The theoretical probability that the pointer lands in section 5 is 10%.
c) The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.
a. Experimental probability:
The experimental probability is found by dividing the number of times the spinner lands in section 5 by the total number of spins.
In this case, the spinner landed in section 5 3 times in 40 spins, so the experimental probability is:
Experimental probability = 3/40 = 0.075 or 7.5%
b. Theoretical probability:
The theoretical probability is the expected probability based on the assumption that the spinner is fair and each section has an equal chance of being selected.
With 10 equal sections, the theoretical probability that the spinner lands in section 5 is:
Theoretical probability = 1/10 = 0.1 or 10%
c. Comparison between actual and expected:
The actual number of times the spinner landed in section 5, 3, is compared to the expected number of times, 4 (based on the theoretical probability of 10% and 40 spins).
The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.
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Right triangle TMR is a scalene triangle with the right triangle at M. Which equation is true? Please show work.
For a right triangle TMR the equation that is true is -
Option 3: sin T = cos R
What is a right-angled triangle?
Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.
In a right triangle, the sine of an acute angle is defined as the length of the opposite side divided by the length of the hypotenuse, and the cosine of an acute angle is defined as the length of the adjacent side divided by the length of the hypotenuse.
In triangle TMR, the right angle is at M, which means that T and R are acute angles.
Using the definitions of sine and cosine, determine which equation is true -
1. sin M = cos T
The angle M is the right angle, which means that its sine is 1 and its cosine is 0.
Therefore, this equation is false.
sin R = cos R
2. The sine and cosine of the same angle cannot be equal, except in the case of a 45° angle where both sine and cosine are equal to 1/√2.
Therefore, this equation is false.
3. sin T = cos R
The angle T is the acute angle opposite the side TR, and the angle R is the acute angle adjacent to the side TR.
Therefore, this equation is true.
4. sin T = cos M
The angle M is the right angle, which means that its cosine is 0.
Therefore, this equation is false.
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cross section math
i need help assap
Answer:
Step-by-step explanation: is half cut up so therefore the shape thats cut is a trapeziod
the graph of contains the point . what point must be on the graph of each of the functions below? enter points as including the parentheses.
Based on the provided information, the graph of y = v(3x) - 4 must contain the point (-4, -8) and (b) the graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).
As the graph of y = v(x) contains the point (−12, −7), point that must be on the graph of each of the functions below are:
(a) y = v(3x) - 4
3x = -12
x = (-12)/3= -4
y = -4 – 4 = -8
The graph of y = v(3x) - 4 must contain the point (-4, -8).
(b) y = 1/4 v(x) + 9
x = -12
y = 1/4 (-12) + 9 = 6
The graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).
Note: The question is incomplete. The complete question probably is: The graph of y=v(x) contains the point (−12,−7). What point must be on the graph of each of the functions below? Enter points as (a,b) including the parentheses. (a) The graph of y = v(3x) - 4 must contain the point _ (b) The graph of y = 1/4 v(x) + 9 must contain the point _ .
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The area of the base of the nonagonal prism below is 40 square
meters. Its volume is 320 cubic meters. What is the height of the
prism?
The height of the prism with base area of 40 square meters and volume of 320 cubic meters is 8 meters
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The volume of the prism is the amount of space that the solid figure occupies.
The volume of prism = area of base * height
The area of the base of the nonagonal prism below is 40 square meters. Its volume is 320 cubic meters. Hence:
The volume of prism = area of base * height
Substituting:
320 m³ = 40 m² * height
height = 8 m
The height of the prism is 8 meters
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The probability of rain on any particular day is 0. 2. However, the probability of rain on a day after a rainy day is 0. 85, whereas the probability of rain on a day after a non-rainy day is 0. 1.
a) On two consecutive days, find the probability of having:
i. Two rainy days
ii. Exactly one rainy day
iii. At least one dry day
b) On three consecutive days, find the probability of having:
i. Three rainy days
ii. Exactly one dry day
iii. At most two rainy days
a) i. the probability of two rainy days is 0.2 * 0.85 = 0.17.
ii. The total probability of having exactly one rainy day is the sum of these two probabilities is 0.18.
iii. probability of having At least one dry day is 0.83.
b)i. The probability of having Three rainy days is 0.1447.
ii. The probability of having Exactly one dry day is 0.1881
iii. The probability of having At most two rainy days is 0.35
a) On two consecutive days, the probability of having:
i. Two rainy days: The probability of two rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of two rainy days is 0.2 * 0.85 = 0.17.
ii. Exactly one rainy day: There are two ways to have exactly one rainy day in two consecutive days: either the first day is rainy and the second day is dry, or the first day is dry and the second day is rainy. The total probability of having exactly one rainy day is the sum of these two probabilities, which can be calculated as:
P(rainy day first) * P(dry day second) + P(dry day first) * P(rainy day second) = 0.2 * 0.9 + 0.8 * 0.1 = 0.18
iii. At least one dry day: To find the probability of at least one dry day, we can subtract the probability of two rainy days from 1, since the only possibility in which there is no dry day is if both days are rainy:
1 - P(two rainy days) = 1 - 0.17 = 0.83
b) On three consecutive days, the probability of having:
i. Three rainy days: The probability of three rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of three rainy days is 0.2 * 0.85 * 0.85 = 0.1447.
ii. Exactly one dry day: To have exactly one dry day in three consecutive days, we need two rainy days followed by a dry day, or a rainy day followed by two dry days, or two dry days followed by a rainy day. The total probability of having exactly one dry day can be calculated as:
P(rainy day first, rainy day second, dry day third) + P(rainy day first, dry day second, dry day third) + P(dry day first, rainy day second, rainy day third)
= 0.2 * 0.85 * 0.9 + 0.2 * 0.9 * 0.9 + 0.8 * 0.1 * 0.1 = 0.1881
iii. At most two rainy days: To find the probability of at most two rainy days, we need to add up the probabilities of two rainy days and one rainy day.
P(at most two rainy days) = P(two rainy days) + P(one rainy day) = 0.17 + 0.18 = 0.35
So, the probability of having at most two rainy days in three consecutive days is 0.35.
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What is the solution to 56x−13>113 ?
Responses
x>2518
x is greater than 25 eighteenths
x<2518
x is less than 25 eighteenths
x>2
x is greater than 2
x<2
Answer:
x > 2
Step-by-step explanation:
To solve the inequality 56x - 13 > 113, you can start by isolating the variable on one side of the inequality. Subtract 113 from both sides:
56x - 113 > 0
Next, add 113 to both sides:
56x > 113
Finally, divide both sides by 56:
x > 2
So the solution is x > 2, meaning that x can be any value greater than 2.
Answer:
[tex]x > \dfrac{9}{4} \\\\[/tex]
or
x > 2.25
This does not fit any of the provided answer choices. Either the inequality is copied wrong or the answer choices are copied wrong
Step-by-step explanation:
The inequality is 56x - 13 > 113
Add 13 to both sides:
56x - 13 + 13 = 113 + 13
56x > 126
Divide by 56 both sides
[tex]\dfrac{56x}{56} > \dfrac{126}{56}[/tex]
Reducing the above fraction to lowest by dividing numerator and denominator by 14 to get:
[tex]x > \dfrac{126 \div 14}{56\div 14}\\\\x > \dfrac{9}{4}[/tex]
None of your answer choices fit. So not sure whether the inequality given is incorrectly copied/pasted or the answer choices are.
The closest this comes to is x > 2 but the inequality will not be satisfied for any value of x between 2(excluded) and 2.25(included)
Find the equation of the line parallel to -3x+2y=4 and passing through (-1,1)
The equation of the line parallel to the given line is 3x - 2y + 5 = 0.
What is the equation of a line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation.
A straight line's equation is y=mx+c, where m denotes the gradient and c, commonly known as the y-intercept, is the height at which the line crosses the y-axis.
The given line is -3x+2y = 4
Then, [tex]y = \frac{3}{2}x + 2[/tex]
Slope [tex](m_1) = \frac{3}{2}[/tex] and [tex]c_1[/tex] = 2
Now, the slope of the parallel line [tex]m_2[/tex] = [tex]m_1[/tex] = 3/2
and passes through a point (-1,1)
Then,
the equation of the parallel line is
[tex]or, y-y_1=m(x-x_1) \\\\or, y-1=\frac{3}{2}(x+1) \\\\ or, 2y-2=3x+3\\\\or, 3x-2y+5=0[/tex]
Hence, the required equation of the line is 3x - 2y + 5 = 0.
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What is the circumference if the radius is 8?
Also explain please.
Answer:
16π
Step-by-step explanation:
π is the ratio between the circumference and the diameter. 2x8xπ = 16π
Answer: 16π, or 50.2655
Step-by-step explanation:
Circumference is calculated using πd, where d is the diameter. Since d = 2r, where r is the radius, this can be rewritten as circumference = π2r. Plugging our radius, 8, into the equation gives us π(2)(8), which simplifies to 16π, or 50.2655.
Help me please
Please help me i need help with this
Answer:
Please send a clearer image so I can answer question 1 and 3
Step-by-step explanation:
2: "One of the parallel lines can be translated so that it lands on the other line. After that, you would notice that the angles of the two lines have exactly the same measurement. Therefore, the interior and exterior angles of two parallel lines cut by transversal are equal."
5: The angles congruent to <8 are <6, <4, and <2
6: The value of m<6 = 70°
7: The equation to find <8 = 180 - <1
The measure m<8 = 85°
8: The value of x must be equal to 34
Use sets to solve the problem.
Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen,
100 support both Moore and Allen, and 250 support only Moore. How many residents support Moore?
The number of residents that support more are 350
What is set?Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
The number of residents that support more will be number of residents that support Moore only plus the number of residents that support both Moore and Allen
therefore ;
the number of residents that support Moore =
250+100 = 350 residents
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The center of a clock is at (0,0) in a coordinate system, and the minute hand is 10 inches long. Find the approximate coordinates of the tip of the minute hand at:
12:05 p.m.
12:45 p.m.
12:55 p.m.
Answer: At 12:00 p.m., the minute hand points straight up at (0,10).
At 12:05 p.m., the minute hand has rotated 30 degrees clockwise. The tip of the minute hand would be approximately:
x = 10 * cos(30) = 8.66
y = 10 * sin(30) = 5
So, the coordinates would be approximately (8.66, 5).
At 12:45 p.m., the minute hand has rotated 180 degrees. The tip of the minute hand would be approximately:
x = 10 * cos(180) = -10
y = 10 * sin(180) = 0
So, the coordinates would be approximately (-10, 0).
At 12:55 p.m., the minute hand has rotated 330 degrees clockwise. The tip of the minute hand would be approximately:
x = 10 * cos(330) = -5.77
y = 10 * sin(330) = -8.66
So, the coordinates would be approximately (-5.77, -8.66).
Step-by-step explanation:
a recipe calls for of a cup of milk for 12 cookies. how many cups of milk are needed to make 108 cookies?
In a linear equation, 9 cups of milk are needed to make 108 cookies .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
1 cup of milk makes 12 cookies.
If you wanted to make twice as many cookies (24), then you would need 2 cups.
If you wanted to make three times as many cookies (36), then you would need 3 cups.
1 cup / 12 cookies = X cups / 108 cookies
1/12 = X/108
X = 9
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a pin can contain 3 numerical digits. however, no digit can be repeated. how many pins are possible?
There are 720 possible pins, as no digit can be repeated. This is calculated by taking 3! (3 factorial) which is 3x2x1, which equals 6, and then multiplying it by 10, as there are 10 digits, 0-9.
A pin can contain 3 numerical digit and no digit can be repeated. To calculate the amount of pins possible, we use 3! (3 factorial), which is 3x2x1, equaling 6. Then, we multiply this by 10, as there are 10 digits, 0-9. Therefore, 6x10 = 720. In order to calculate 3! (3 factorial) we start by multiplying 3x2x1. This is because each digit has to be multiplied by the number of digits before it, as no digit can be repeated. The first digit has no digits before it, so it stays as 3. The second digit has one digit before it, so it is multiplied by 2. The third digit has two digits before it, so it is multiplied by 1. Therefore, 3x2x1 = 6. Then, we multiply 6 by 10, as there are 10 digits, 0-9. 6x10 = 720, which means there are 720 possible pins with no digit being repeated.
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Satvik plans to take piano lessons. He has two payment options : He can pay $3 per lesson plus $18 per month or he can pay $60 for the a month of unlimited lessons. For what number of lessons is it cheaper for Satvik to pay $60 for the month? Write and solve the inequality that represents the situation.
The inequality that represents the situation when the number of lessons would mean that it is cheaper for Satvik to pay $60 for the month is x ≥ 15.
What is inequality?Inequality is a mathematical statement that two mathematical expressions are unequal.
Inequality is represented as either:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).Payment Plans:
Plan A = $18 + $3 per lesson
Plan B = $60
Let each lesson = x
Solving Equations:18 + 3x = 60
3x = 42
x = 14
x ≥ 15
Thus, if the number of lessons is greater than or equal to 15, it is cheaper for Satvik to pay under Payment Option B.
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Given sin x= 3/5 and sin y= 2/3 , where x and y are both in first quadrant ' Evaluate sin(x + y)
With the values sin x= 3/5 and sin y= 2/3 , where x and y are both in first quadrant, then after calculation sin(x + y) = (3 * √(7/9)) / 5 + 1/2.
To evaluate sin(x + y), we can use the identity sin(a + b) = sin a cos b + cos a sin b.
Given that sin x = 3/5 and sin y = 2/3, we have:
sin(x + y) = sin x cos y + cos x sin y
= (3/5) * √(1 - (2/3)^2) + (√(1 - (3/5)^2)) * (2/3)
= (3/5) * √(7/9) + (4/5) * (2/3)
= (3 * √(7/9)) / 5 + (8/15)
= (3 * √(7/9)) / 5 + (8/15)
= (3 * √(7/9)) / 5 + (16/30)
= (3 * √(7/9)) / 5 + (1/2)
= (3 * √(7/9)) / 5 + 1/2
So, sin(x + y) = (3 * √(7/9)) / 5 + 1/2.
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IPSOS (2020) mencionó que, en la última encuesta realizada por Global
Advisor a casi 14 000 personas de 15 países, el 43 % de los encuestados
dijeron estar impacientes por volver a la vida normal. Otro tercio (34 %) se
muestra preocupado por su salud, mientras que el 15 % se siente solo y el
12 % está enojado por las restricciones a su libertad. Al mismo tiempo, sin
embargo, más de la mitad (55 %) se preocupa por los que son vulnerables o
débiles, mientras que poco menos de un tercio (31 %) se siente feliz de pasar
tiempo con su familia. Otro de cada cinco (22 %) se inspira en la forma en
que las personas se están adaptando.
Elaborar una tabla estadistica
Una tabla estadística para resumir los resultados de la encuesta podría ser la siguiente:
Emoción/Sentimiento Porcentaje de Encuestados
Impaciente 43%
Preocupado por salud 34%
Solo 15%
Enojado 12%
Preocupado por vulnerables 55%
Feliz de pasar tiempo con familia 31%
Inspirado por adaptación 22%
Esta tabla muestra los diferentes sentimientos y emociones que los encuestados experimentaron durante la encuesta realizada por Global Advisor.
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
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Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa.
There are 180 grams of cocoa in the resulting mixture.
When the 200 grams of dark chocolate and the 200 grams of milk chocolate are mixed together, the amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate.
First, the amount of cocoa in the dark chocolate is calculated by multiplying the total weight of the dark chocolate by its cocoa percentage:
200 grams(0.60) = 120 grams
Next, the amount of cocoa in the milk chocolate is calculated in the same manner:
200 grams(0.30) = 60 grams
Finally, the total amount of cocoa in the mixture is found by adding the amount of cocoa in each type of chocolate:
120 grams + 60 grams = 180 grams
Therefore, the total amount of cocoa in the resulting mixture is 180 grams.
The problem seems incomplete, it must have been...
"Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa. How many grams of cocoa are in the resulting mixture?"
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Find the perimeter of the area of the rectangle 15 cm and 12 CM
a) perimeter: 54 cm,area:180cm 2 (squared)
b)perimeter:54cm, area:108 cm 2 (squared)
c)perimeter: 42 cm, area 180 cm2 (squared)
d) perimeter: 42 cm, area:108 cm2 (squared)
(a) perimeter:54cm, area:108 cm 2 (squared)
The perimeter of a rectangle with length 15 cm and width 12 cm is 54 cm (2 * (15 + 12) cm).
The area of the rectangle is 180 square cm (15 * 12 cm^2).
Measure the length (l) and the width (w) of the rectangle. In this case, the length is 15 cm and the width is 12 cm.
To find the perimeter, calculate the sum of twice the length and twice the width. This is done by multiplying each measurement by 2 and then adding them together: 2 * l + 2 * w. In this case, the calculation is 2 * 15 + 2 * 12 = 30 + 24 = 54 cm.
To find the area, multiply the length and the width: l * w. In this case, the calculation is 15 * 12 = 180 cm^2.
The perimeter of the rectangle is the sum calculated in step 2. In this case, the perimeter is 54 cm.
The area of the rectangle is the product calculated in step 3. In this case, the area is 180 cm^2.
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A company fee pays a fee to use a song in their advertisement. There are 3 people in the band: the writer gets 4/12 of the fee, the singer gets 1/12 of the fee and the guitarist gets 1/12 of the fee.
What fraction of the fee does the whole band get??
Can u please help me I really need answers by this evening!!!
The whole band gets 1/2 of the fee.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
The writer gets 4/12 of the fee, the singer gets 1/12 of the fee and the guitarist gets 1/12 of the fee, so the total fraction of the fee that the band members get is 4/12 + 1/12 + 1/12 = 6/12.
So, the whole band gets 6/12 or 1/2 of the fee. This means that half of the fee paid by the company goes to the band members, while the other half goes to other costs or expenses.
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Abby is creating a stained glass windowpane that will be 6 inches by 8 inches. To make the
rectangular windowpane, Abby fuses together two triangles of colored glass. What is the
perimeter of one triangle?
In inches
The perimeter of the triangles will be 24 inches.
What is the perimeter of one of the triangles?
With two triangles she forms a rectangle of 6in by 8 in.
Then the triangles will have legs with these dimensions, and the last side (the hypotenuse) has a length equal to the diagonal of the rectangle:
diagonal = √( (6in)² + (8in)²) = 10in
Then the perimeter of te triangle is:
P = 10in + 8in + 6in = 24in
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2. What is the product of -2x^3+x and x^3-3x-4 ?
(a) Show your work.
(b) Is the product of 2x^3+x-5 and x^3-3x-4 equal to the product of x^3-3x-4 and -2x^3+x-5 ? Explain your answer.
(a) To find the product of -2x^3+x and x^3-3x-4, we can use the distributive property of multiplication:
(-2x^3 + x)(x^3 - 3x - 4)
= -2x^3(x^3) - 2x^3(-3x) - 2x^3(4) + x(x^3) - x(-3x) - x(4)
= -2x^6 + 6x^4 - x
= -2x^6 + 6x^4 - x
Therefore, the product of -2x^3+x and x^3-3x-4 is -2x^6 + 6x^4 - x.
(b) No, the product of 2x^3+x-5 and x^3-3x-4 is not equal to the product of x^3-3x-4 and -2x^3+x-5. This is because the order of the factors in a multiplication expression affects the outcome. When we expand both products using the distributive property, we get different expressions:
(2x^3 + x - 5)(x^3 - 3x - 4) = 2x^6 - 5x^3 - 3x^2 - 17x + 20
(x^3 - 3x - 4)(-2x^3 + x - 5) = -2x^6 + 11x^4 + 13x^3 - 3x^2 - x + 20
So the expanded expressions are not equal. Therefore, the two products are not equal.
Find the x intercept and the y intercept of each line. Express the answers as ordered pairs
Y=5x-10
The x-intercept and the y-intercept of each line include the following ordered pairs:
x-intercept = (2, 0).
y-intercept = (0, -10).
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).
What is y-intercept?In Mathematics, the y-intercept is sometimes referred to as an initial value and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
In this exercise, we would use an online graphing calculator to plot the linear function in order to determine the x-intercepts and y-intercepts as shown in the image attached below.
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what is the probability that the first son of a woman whose mother's brother has lesch-nyhan syndrome will be affected?
If a woman's uncle has Lesch-Nyhan syndrome and her father carries the mutation, the probability of her first son being affected is 50%.
Lesch-Nyhan syndrome is an X-linked recessive genetic disorder, which means it is caused by a mutation on the X chromosome and is passed down through families primarily from affected fathers to their daughters. The probability that a son of a woman with an affected uncle (mother's brother) will be affected depends on the genetic status of the woman's father and the mother's X chromosome that she inherited from her mother.
If the woman's father does not carry the mutation, she will not carry the mutation herself and cannot pass it on to her children. In this case, the probability of her first son being affected is 0%.
If the woman's father carries the mutation, she has a 50% chance of inheriting the mutated X chromosome from her father and a 50% chance of inheriting a normal X chromosome from her mother. In this case, if the woman is a carrier of the mutation, her first son has a 50% chance of inheriting the mutation from her and being affected.
It's important to note that this is a simplified answer and that more complex genetic testing and counseling may be necessary to determine the specific risk in a particular family.
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a square that is 10in. on a side is placed inside a rectangle that has a width of 13in. and a length of 19in. what is the area of the region inside the rectangle that surrounds the square?
The area of the region inside the rectangle that surrounds the square is 147 square in.
The side of square is 10 in
Area of square is = side x side
A = 10 x 10
A = 100 square in.
Therefore, Area of square is 100
The length of rectangle is 19 in and width of rectangle is 13in
area of rectangle = l x w
A = 19 x 13
A = 247 square in.
Area of rectangle is 247 square in.
To calculate area of the region inside the rectangle that surrounds the square,
= A[rectangle] - A[square]
= 247 - 100
= 147 square in.
Therefore, The area of the region inside the rectangle that surrounds the square is 147 square in.
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