Q1. In the given figure, ABCD is a parallelogram. Complete each statement along with the definition or property used.
(i) AD = ……….. (ii) DC = ……….. (iii) ∠DCB = ………..
(iv) ∠ADC = ……….. (v) ∠DAB = ……….. (vi) OC = ………..
(vii) OB = ……….. (viii) m∠DAB + m∠CDA = ………..
Answers
Step-by-step explanation:
i. AD = BC= 6cm (each two opposite sides are equal in length in parallelogram)
ii.DC=AB=9cm (each two opposite sides are equal in length in parallelogram)
iii.DCB=60 ,, bec DC and AB are parallel so their interior angles are supplementary their sum equals 180°
so DCB = 180-120=60°
iv.ADC=ABC = 120° because each two opposite angles are equal in measure in parallelogram
v. DAB=DCB =60° because each two opposite angles are equal in measure in parallelogram
vi. OC=AO =7cm because the diagonals of parallelogram bisect each other
vii. OB=DO=5cm because the diagonals of parallelogram bisect each other
viii . DAB=60° ,, CDA= 120 °
DAB+CDA =180°
or you could simply say that because DC and AB are parallel their interior angles are supplementary their sum is 180°
Related Questions
Express √75 in basic form
Answers
Answer:
[tex]5 \sqrt{3} [/tex]
Step-by-step explanation:
Frist find which perfect square goes into 75. In this case its 25 * 3. You then find out what is the square root of 25. Which is 5. you put that number outside the radical and the other number inside the radical. resulting in 5 square roots of 3.
Answer: Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
Exact Form:
5√3
Decimal Form:
8.66025403…
Help please with this maths
Answers
Answer:
9 cm
Step-by-step explanation:
You want the radius of the sphere that has a surface area of 324π cm².
AreaThe area of a sphere is given by the formula ...
A = 4πr²
Filling in the given values, we can solve for r:
324π = 4πr²
81 = r² . . . . . . . . . divide by 4π
9 = r . . . . . . . . . . . take the square root
The radius of the sphere is 9 cm.
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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,
but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15
miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles
is the airport from his home?
(A) 140 (B) 175 (C) 210 (D) 245 (E) 280
Answers
If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.
How to find the distance?Let d represent the distance that is needed to travel 1 hour
1 hour late decreased to 0.5 hours early = 1.5
Hence,
d/50 + 1.5 = d/35
Simplify
7d + 525 =10d
Collect like terms
525 = 10d - 7d
525 = 3d
Divide both side by 3d
d = 525/3
d = 175
Total number of miles :
Total number of miles = 175 + 35
Total number of miles = 210
Therefore we can conclude that the correct option is C.
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0.2(x+50)-6=0.4(3x+20)
Answers
Answer:
2
Step-by-step explanation:
0.2(x+50)-6=0.4(3x+20) multiply both sides by 10 to clear the decimals
2(x + 50) = 4(3x + 20) distribute across the terms in the parentheses
2x + 100 = 12x + 80 subtract 80, 2x from both sides
20 = 10x divide both sides by 10
x=2
how many solutions does y = 5x - 8 and y = 9x - 8 have
Answers
The equation y = 5x - 8 and y = 9x - 8 have one solution at
(0, -8)
How to find the solution of the equationThe equation is solved simultaneously by elimination method as follows
y = 5x - 8
y = 9x - 8
subtraction the equations
0 = -4x - 0
-4x = 0
x = 0
substituting x = 0 into y = 5x - 8
y = 5x - 8
y = 5 * 0 - 8
y =0 - 8
y = -8
The solution of the equation is at the point (0, -8)
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Rewrite the following equation in standard form.
y = 3x + 9
Answers
3x-y=-9
Step-by-step explanation:
Answer: 3x - y = - 9
Step-by-step explanation:
Re-write the equation in the following form:
3x + 9 = y
Take the y to LHS:
3x + 9 - y = 0
Now, take the 9 to the RHS:
3x - y = -9. This is your answer.
A recent report indicated that 90 percent of adults in a certain region actively try to include vegetables in their diet. A simulation was conducted that consisted of so trials with a population parameter of 0.9. Each trial consisted of a sample size of 10. The number of successes out of 10 was recorded, where success represented an adult trying to include vegetables in the diet. Five possible simulation results are shown. Which simulation is the best match to the one described? + 0 1 + 3 N + 4 5 6 7 8 9 10 • : 6 0 1 + 2 w+ 4 5 6. + 8 9 7 10 0 10 20 30 40 50 60 70 80 90 100 D 0 10 20 30 40 50 60 70 80 90 100 0 1 2 + +0 다. 4 D+ + ••• 00+ 6 10
Answers
The dot plot in option E is correct.
What is sample size?
Choosing the number of observations or replicates to include in a statistical sample is the process of determining sample size. Any empirical study whose objective is to draw conclusions about a population from a sample must take the sample size into consideration.
Finding your sample size in five steps
Clarify the term "population size" or "people"
Specify your error margin.
Decide how confident you are.
Calculate the expected variance.
Decide on the sample size.
As long as it doesn't go over 1,000, 10% of the population serves as a good maximum sample size.
The dot plot in option E is correct.
Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.
On X axis, we take no. of successes out of 10.
Hence it having 0 to 10 numbering.
Hence, the dot plot in option E is correct.
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Determine whether the geometric series is convergent or divergent. 10 – 8 + 6.4 – 5.12 +... A. convergent B. divergent If it is convergent, find its sum. (If the quantity diverges, leave this blank.) _____
Answers
The given series is convergent and the sum S∞ is 5.555
Think about 10 - 8 - 6.4 - 5.12
If the common ratio of the series is between -1 and 1, then a geometric progression will be convergent.
the average ratio,
r = -8/10
⇒ r = -0.8
This equals 1 - 0.8 - 1.
The presented series is hence convergent.
Sum of series = S∞ = a/(1 - r)
Here, first term(a) = 10,
common ratio(r) = -0.8,
S∞ = a/(1 - r)
⇒ S∞ = 10/(1 - (-0.8))
⇒ S∞ = 10/(1 + 0.8)
⇒ S∞ = 10/1.8
⇒ S∞ = 5.555
Therefore, the given series is convergent and the sum S∞ is 5.555
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Adine is parallel to y = 5x + 9 and
intersects the point (-2, -3). What is the
equation of this parallel line?
Answers
The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).
What is a parallel line?Parallel lines are coplanar, infinite straight lines in geometry that don't cross at any point. Planes in the same three-dimensional space that never cross each other are said to be parallel.
Curves that are parallel to one another and maintain a set minimum distance do not touch or intersect. A line and a plane that do not share a point are also referred to as being parallel in three-dimensional Euclidean space. But skew lines are used to describe two noncoplanar lines.
We know that slope of parallel line are same. Thus, slope is 5 in y = 5x + 9
Now we need to put the values in y intercept form to find out the equation
y - y1 = m(x - x1)
y - (-3) = m(x - (-2))
y + 3 = 5(x + 2)
y = 5x + 10 - 3
y = 5x + 7
Thus, The equation of the line parallel to y = 5x + 9 which intersects the point (-2, -3).
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The population of a city in 2010 is 50,000, and it grows by 5% each year after.
a. Write a function of f which models the population of the city' years after 2010.
b. What is the population of the city in 2017?
c. What will the population of the city be in 2020? What about in 2030?
d. By what factor does the population grow between 2010 and 2020? What about between 2020 and 2030?
Answers
a. A function that models the population of the city's years after 2010 is:
f(x) = 50,000 * (1 + 0.05)^(x-2010)
where x is the number of years after 2010.
b. The population of the city in 2017 (7 years after 2010) is:
f(2017) = 50,000 * (1 + 0.05)^7
= 65,128
c. The population of the city in 2020 (10 years after 2010) is:
f(2020) = 50,000 * (1 + 0.05)^10
= 76,923.1
The population of the city in 2030 (20 years after 2010) is:
f(2030) = 50,000 * (1 + 0.05)^20
= 129,382
d. The population in 2020 is 76,923.1, and the population in 2010 is 50,000, so the population grows by:
= 76,923.1 / 50,000
= 1.53846
The population in 2030 is 129,382, and the population in 2020 is 76,923.1, so the population grows by:
= 129,382 / 76,923.1
= 1.6859
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Find the unit rate of the constant of proportionality for the following: $9.80 for 5 pounds.
Showing your work would be appreciated, so if you could, that’d be great. But it’s not needed, if you don’t want to. :)
Thank you in advance to anyone who answers!
Answers
The unit rate of constant means that for every 1 pound, the output is 1.96 dollar.
What is proportionality?Proportionality is a relationship between two variables in which their ratio is always equal to a constant value. In mathematical terms, it can be expressed as y = kx, where y and x are the two variables, and k is the constant of proportionality.
What is rate?A rate is a measure of how one quantity changes in relation to another quantity. It is usually expressed as a ratio and has units of measurement, such as miles per hour, dollars per pound, etc. A unit rate is a rate in which the second quantity is one unit of measurement.
The unit rate of the constant of proportionality is found by dividing the change in y (output) by the change in x (input).
In this case:
$9.8/5$ = $1.96$, so the unit rate of the constant of proportionality is 1.96 pounds/dollar.
It means that for every 1 pound, the output is 1.96 dollar.
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Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories. Determine the number of calories per cup of popcorn and per ounce of soda
Answers
The number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let the number of calories per cup of popcorn be x and the number of calories per ounce of soda be y.
Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories.
3x+6y=162 ------(I)
Carmel has 1 cup of popcorn and 11 oz of soda for a total of 162 calories.
x+11y=182
x=182-11y------(II)
Substitute equation (II) in equation (I), we have
3(182-11y)+6y=162
546-33y+6y=162
546-162-27y=0
384-27y=0
384=27y
y=384/27
y=14
Substitute y=14 in equation (II), we get
x=182-11(14)
x=28
Therefore, the number of calories per cup of popcorn is 28 oz and the number of calories per ounce of soda is 14 oz.
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"Your question is incomplete, probably the complete question/missing part is:"
Roselle has 3 cups of popcorn and 6 oz of soda for a total of 162 calories. Carmel has 1 cup of popcorn and 11 oz of soda for a total of 182 calories. Determine the number of calories per cup of popcorn and per ounce of soda
The length of ome material i 8. 3m correct to 1 decimal place. Write the error interval for the length ,x, of the material
Answers
The error interval for the length ,x, of the material is [8.25, 8.35)
We know that error interval is nothing but the limits of accuracy when a number has been rounded.
It is the range of possible values that a number could have been before a number was rounded.
Here, The length L of a some material is 8.3 meters.
The length of the material has been rounded to 8.3 to one decimal place.
The number below 8.3 is 8.2 and the number above is 8.4
Consider a half way between 8.2 and 8.3 for the lower bound and half way between 8.3 and 8.4 for the upper bound.
This means, the length of the material must have been between 8.25 meters and 8.35 meters to round to 8.3 meters to one decimal place.
Therefore, the required error interval would be 8.25 ≤ x < 8.35
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URGENT!! 60 POINTS!!!!! Based on the linear table of ordered pairs, what is the y intercept?
Answers
Answer:
The y-intercept is (0, 8)-----------------------------------
According the the table the slope is:
m = (12 - 4)/(1 - (-1)) = 8/2 = 4Use slope-intercept form:
y = mx + b, where b is the y-interceptAnd substitute one of the ordered pairs, to find the value of b:
4 = 4(-1) + b4 = - 4 + bb = 4 + 4b = 8The y-intercept is (0, 8).
graphing piece wise functions
Answers
Answer:
thats by step overr.ic. yttt. .
Mr.Coy receives a 80 bill for his meal. He leaves 14.30 as a tip. What percent did he leave
Answers
Answer:
around 18%
Step-by-step explanation:
14.30/80=0.17875
0.17875*100=17.875
18%
Answer:
Step-by-step explanation:
the answer is [tex]\frac{14.30}{80}[/tex]=17.875%
NEED HELP ASAP - Algebra 2
Every complex number has the form a+bi with a and b as real numbers. Is it possible to create a complex number in which b=0? If so, create two examples to show your hypothesis is true. If not, explain why it is not possible.
Your response must be at least 50 words.
Answers
No, It is not possible to have a complex number in the form of a + bi when b = 0.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Complex number.
It is in the form of a + ib.
Where a and b are real numbers.
Now,
If b = 0 then we can not have a complex number.
Example:
a + bi
a = 1 and b = 0
1 + 0i = 1 which is not a complex number.
In order to have a complex number a can be any real number and 0 but b can not be a zero.
Thus,
It is not possible to have a complex number in the form of a + bi when
b = 0.
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What are the 6 parent functions?
Answers
These are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
A parent function is the simplest form that a function can be. Its basic shape is not in any way altered. In mathematics, you see certain graphs over and over again. For that reason, these original, common functions are called parent graphs, and they include graphs of quadratic functions, square roots, absolute values, cubics, and cube roots.
For instance, when you see a u-shaped graph that is inverted and vertically stretched, you should still recognize that it is a parabola which has undergone different transformations.
We can take a few examples to understand this concept further.
For a quadratic equation, the parent graph is [tex]f(x) = x^{2}[/tex], which is a parabola.For a cubic equation, the parent graph is [tex]f(x) = x^{3}[/tex].Now, there are 6 parent functions:
IdentityAbsolute ValueSquare RootQuadraticCubicReciprocalHence, these are the 6 parent functions: Identity, Absolute Value, Square Root, Quadratic, Cubic, Reciprocal.
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Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, use the drop-down menu below to write an inequality representing ss, the number of sets of glasses Julia should buy.
Answers
The inequality representing s, the number of sets of glasses Julia should buy is 286 + 6s ≥ 316.
How to illustrate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since Julia needs to order some new supplies for the restaurant where she works. The restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on sale contains 6 glasses, the number of sets will be:
286 + 6s ≥ 316
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please help: find m∠LHF
Answers
Answer:
17
Step-by-step explanation:
5y - 8 = 9y - 28
-8 = 4y - 28
4y = 20
y = 5
9(5) - 28
45 - 28
17
Last week, Alex took 90 selfies and Vic took 75 selfies. Today,
they each decided that some of these selfies were not very good
and deleted them. Alex deleted three times as many selfies
as Vic. Now, Alex has half as many selfies as Vic. How many
selfies did Alex delete?
Answers
Answer:
Alex deleted 37.5 selfies
Step-by-step explanation:
Let X be the number of selfies that Vic deleted.
Alex deleted 3X selfies.
After deleting selfies, Alex has 90-3X selfies left.
Vic has 75-X selfies left.
Since Alex has half as many selfies as Vic, we can set up the equation: 90-3X = (75-X)/2
Multiplying through the parentheses on the right side, we get: 90-3X = 75-X/2
Combining like terms, we get: 2X = 15
Dividing both sides by 2, we get: X = 7.5
Since X represents the number of selfies that Vic deleted, Vic deleted 7.5 selfies.
Since Alex deleted 3 times as many selfies as Vic, Alex deleted 37.5 = <<37.5=22.5>>22.5 selfies.
The number of selfies deleted by Alex is 51.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that Alex took 90 selfies and Vic took 75 selfies. Today, they each decided that some of these selfies were not very good and deleted them. Alex deleted three times as many selfies as Vic. Now, Alex has half as many selfies as Vic.
Let Vic deleted x selfies and number of selfies deleted by Alex is 3x,
Therefore,
Since, Alex has half as many selfies as Vic, we can set up the equation: 90-3x = (75-x)/2
180 - 6x = 75 - x
5x = 105
x = 17
3x = 51
Hence, the number of selfies deleted by Alex is 51.
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23x² + 6x + 7 please help
Answers
Answer:
the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
Step-by-step explanation:
The expression 23x² + 6x + 7 is in the form of a quadratic equation. A quadratic equation is an equation in the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. In this case, the coefficients of the x², x, and the constant term are a = 23, b = 6, c = 7.
One way to factor a quadratic equation is by using the factoring by grouping method, where we group the terms in pairs and factor out the greatest common factor (GCF) from each group.
Here is one way to factor this equation:
23x² + 6x + 7 = (23x² + 6x) + 7
= (23x² + 6x) + 7
= (23x² + 6x + 6x) + 7
= (23x² + 12x) + 7
= (23x(x) + 3x(4)) + 7
= (23x(x+4) + 7)
= (x+4)(23x + 7)
So the expression can be factored into (x+4)(23x + 7) and it is a product of two binomials.
It's important to note that the above expression factors into a product of two binomials and not two factors of 23x² + 6x + 7
You can also use Quadratic formula to solve the above expression if this method seems confusing.
The line of best fit for a data set is y=1. 1x+3. 4. Find the residual for each of the coordinate pairs, (x,y).
D. (1. 5,5. 05)
Answers
The residual values are -0.1, 3.8, 0.32, and 0 respectively for the given coordinate pairs.
A residual is a difference between the observed value (y) and the predicted value (y-hat) for a given x value. To find the residual for each coordinate pair (x,y), we need to substitute the x value into the equation for the line of best fit and calculate the difference between that value and the observed y value.
The equation for the line of best fit is y = 1.1x + 3.4
The residual for each coordinate pair (x,y) is given by -
Residual = Yactual - y
A. (5, 8.8) ; Yactual = 8.8
Residual = 8.8 - (1.1(5) + 3.4) = - 0.1
B. (2.5, 9.95) Yactual = 9.95
Residual = 9.95 - (1.1(2.5) + 3.4) = 3.8
C. (0, 3.72) Yactual = 3.72
Residual = 3.72 - (1.1(0) + 3.4) = 0.32
D. (1.5,5.05) Yactual =
Residual = 5.05 - (1.1(1.5) + 3.4) = 0
It's worth noting that residuals are used to measure how well the line of best fit represents the data set. The residuals should be as close to zero as possible, indicating that the line of best fit is a good representation of the data set.
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The complete question is -
The line of best fit for a data set is y=1.1x+3.4. Find the residual for each of the coordinate pairs, (x,y).
A. (5, 8.8)
B. (2.5, 9.95)
C. (0, 3.72)
D. (1.5,5.05)
isabella is setting up a cheese board for a neighborhood Super Bowl viewing party. the top of the cheese board is shaped like a triangle. the base of the triangle is 24 inches long, and its heigh is 20 inches. what is the area of the top of the cheese board
Answers
To find the area of a triangle, you can use the formula:
area = (base * height) / 2
In this case, the base of the triangle is 24 inches and the height is 20 inches, so plugging these values into the formula gives:
area = (24 * 20) / 2
area = 240 / 2
area = 120 square inches
So the area of the top of the cheese board is 120 square inches.
I GIVE THANKS AND MARK BRAINLIEST
WHAT ARE THE CORRECT ANSWER(S)?
Answers
On solving the provided question, we can say that - the slope of the following will be slope, m = [tex]4-6/4-2 = -2/2 = -1[/tex]
what is slope?A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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On solving the provided question, we can say that - the slope of the following will be slope, m = -1
what is slope?
A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).
here,
(x1,x2) = (6,4)
(y1,y2) = (2,4)
slope, m = 4-6/4-2 = -2/2 = -1
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Andrew buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of the cot per pound. True or Fale: Two pound of apple cot more than $3. 50
Answers
It is false that the cost of two pounds of apple cast is more than $ 3.50.
Finding the cost of a given quantity:Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.
Given that
Andrew buy 8 pounds of apples for $ 12.00
Let 'x' be the cost of 1 pound of apples
By the given data,
=> 8x = $ 12
=> x = 12/8
=> x = 1.5
The cost of 1 pound of apples = $ 1.5
Cost of 2 pounds apples = 2 × 1.5 = 3
Therefore,
It is false that the cost of two pounds of apple cast is more than $ 3.50.
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gcf of 15 and 18 and -45
Answers
Answer: 3
Step-by-step explanation:
Factor of 15: ±1, ±3, ±5, ±15
Factor of 18: ±1, ±2, ±3, ±6, ±9, ±18
Factor of -45: ±1, ±3, ±5, ±9, ±45
=> GCF of 15, 18, -45 is 3
Graph the line y=-2x-1
Answers
Answer:2024
Step-by-step explanation:
Whats 3x+1? for in high school its really hard to solve none of my friend cant do it
Answers
As per the zeros of the function, the value of the function 3x + 1 is x = -1/3.
Zeros of the function in math is defined as the values of the variable of the function such that the function equals 0.
Here we have given the function 3x + 1.
Now, we have to equate the function with zero, in order to solve it, then we get,
=> 3x + 1 = 0
Now, we have to subtract 1 on both sider to individualize the x value then we get the rewritten expression as,
=> 3x = -1
Now, we have to divide each side by 3, then we get the value of x as,
=> x = -1/3
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Keith ordered a hamburger for $2.25, a medium raspberry ice tea for $1.25, and a small sundae for $0.99. He also ordered French fries. All of these items totaled $6.24. What was the cost of the French fries?
Answers
The fries costs $1.49
What is addition?Addition in math is a process of combining two or more numbers.
Given that, Keith ordered a hamburger for $2.25, a medium raspberry ice tea for $1.25, and a small sundae for $1.25. He also ordered French fries. All of these items totalled $6.24.
Let the price of fries be x,
Therefore,
$2.25 + $1.25 + $1.25 + x = $6.24
$4.75 + x = $6.24
x = $6.24 - $4.75
x = $1.49
Hence, the fries costs $1.49
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