Answer: To prove that AB is parallel to DC, we can use the following steps:
Draw a diagram of the cyclic quadrilateral ABCD with the point E where sides AD and BC are produced to meet.
Since ABCD is a cyclic quadrilateral, all its interior angles add up to 360 degrees. Therefore, angle A + angle B + angle C + angle D = 360 degrees.
Since AE = BE, we can say that angles A and B are equal (by corresponding angles). Similarly, angles C and D are also equal.
Since angles A and B are equal and angles C and D are also equal, we can say that angle A + angle B = angle C + angle D.
Substituting this into our equation from step 2, we get: angle A + angle B + angle C + angle D = angle A + angle B + angle A + angle B.
Simplifying, we get: 360 = 2(angle A + angle B). This means that angle A + angle B = 180.
Since angle A + angle B = 180, we can say that angle A = angle B and angle C = angle D.
Now we can use the fact that corresponding angles are equal, then angle A = angle C and angle B = angle D.
We know that opposite angles of a parallelogram are equal, so we have proved that AB is parallel to DC.
It's important to note that this proof uses the fact that quadrilateral ABCD is cyclic, which means that the sum of its angles is equal to 360 degrees. It also uses the fact that opposite angles are equal in a parallelogram, and corresponding angles are equal when two lines are parallel.
Step-by-step explanation:
I will give Branley
A rectangular flag is 80 centimeters by 92 centimeters. What are the dimensions of a scale drawing of the flag using the scale 1:4?
20 cm by 23 cm
320 cm by 360 cm
8 cm by 9.2 cm
1.15 cm by 4.35 cm
The dimensions for the scale drawing of the flag is 20 cm by 23 cm
What is scale?A scale is a set of levels or numbers which are used in a particular system of measuring things or are used when comparing things.
Given that, A rectangular flag is 80 centimeters by 92 centimeters. we need to find dimensions of a scale drawing of the flag using the scale 1:4,
Therefore,
80 / 92 = 20 / 23
Hence, the dimensions for the scale drawing of the flag is 20 cm by 23 cm
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Answer:
20cm by 23cm
Step-by-step explanation:
What is the differentiation of log 7 x?.
The derivative of log₇(x) is 1/(xln(7))
To find the derivative of log₇(x), we can use the chain rule and the properties of logarithms.
The chain rule states that if we have a composite function, such as y = f(g(x)), then the derivative of y with respect to x is given by
dy/dx = dy/dg * dg/dx.
In this case, y = log_7(x) and g(x) = x, so
dy/dx = d/dx (log_7(x))
As by logarithmic property log₇x = ln(x)/ ln(7)
dy/dx = d/dx (ln(x)/ln(7))
To find the derivative of ln(x), we can use the property that the derivative of ln(x) is 1/x. This is because the natural logarithm function is the inverse of the exponential function eˣ, and the derivative of eˣ is eˣ. Therefore, the derivative of ln(x) is the reciprocal of x, or 1/x.
The differentiation of log₇(x) is given by:
d/dx (log₇(x)) = (1/x) * (d/dx (x)) * (1/ln(7))
= (1/x) * 1 * (1/ln(7))
= 1/(x ln(7))
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How to solve systems of linear equation in two variables by substitution?.
Solving systems of linear equations in two variables by substitution involves isolating one of the variables and substituting its value into the other equation.
This can be done by adding or subtracting the same term from both sides of one equation and then using that result to substitute into the other equation.
For example, consider the system of equations below:
2x + 3y = 8
3x + 2y = 7
Start by solving for x in the first equation by subtracting 3y from both sides:
2x + 3y = 8
2x = 8 - 3y
x = (8 - 3y)/2
Now substitute this expression for x in the second equation:
3(8 - 3y)/2 + 2y = 7
24 - 9y + 2y = 7
11y = 17
y = 17/11
Finally, solve for x, add y = 17/11 to the first equation as follows:
2x + 3(17/11) = 8
2x + 51/11 = 8
2x = 8 - 51/11
x = (8 - 51/11)/2
x = 21/22
The solution is x=21/22 and y=17/11.
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The royals softball team played 75 games and won 55 games what percent of the games did they louse round to the nearest tenth
The percent of the games that was lost is 26.7%.
What is the percentage of games that were lost?Percentage is the ratio of two numbers expressed as a number out of 100. The sign that is used to represent percentage is %.
Percentage of the games lost = (number of games lost / total number of games) x 100
Number of games lost = total number of games - number of games won
75 - 55 = 20
Percentage of the games lost = (20 / 75) x 100 = 26.7%
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HELP PLEASE ASAP!!! PRECAL!!
The average rate of change from x = 1 to x = 5 is given as follows:
-1.25.
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The numeric values for the function graphed are given as follows:
f(1) = 7.5.f(5) = 2.5.Hence the change in the output is given as follows:
2.5 - 7.5 = -5.
The change in the input is given as follows:
5 - 1 = 4.
Hence the average rate of change is given as follows:
-5/4 = -1.25.
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What is an example of a perfect trinomial?.
Examples of perfect trinomials are-
x 2 + y 2 + XY,
A trinomial that can be expressed as the square of a binomial is referred to as a perfect square trinomial. Remember that the square of the first term, twice the product of the first two terms, and the court of the final time are the results of squaring a binomial. The perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the condition b 2 = 4ac has the form ax 2 + bx + c, it is said to be a perfect square. The outcome variables are (x + r) and (x + s). For instance, to factor x2 + 7x + 10, you need to find two numbers whose sums are 7 (the middle term's coefficient), and 10.To learn more about polynomials here
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Drag each tile to the correct box.
Match each type of insurance to its description.
life insurance
property and casualty insurance
health insurance
disability insurance
Description
provides for the replacement of earned income
lost because of a person's inability to work
covers damages to property
provides benefits to a policyholder's beneficiary
(or beneficiaries) when the policyholder dies
pays for medical treatment in the event of an
illness
Type of Insurance
This type of insurance is designed to provide financial protection for the policyholder's loved ones in the event of their death.
Explain about types of Insurance:Life insurance: provides benefits to a policyholder's beneficiary (or beneficiaries) when the policyholder dies.Property and casualty insurance: covers damages to property. This type of insurance provides protection for the policyholder's property, such as a home or car, from losses due to accidents, theft, or natural disasters.It also covers the policyholder's liability in the event that they are found responsible for damages to someone else's property.Health insurance: pays for medical treatment in the event of an illness. Disability insurance: provides for the replacement of earned income lost because of a person's inability to work. It can also cover preventive care and certain preventive treatments.To learn more about insurance refer to:
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An oven is being preheated . The temperature starts at 75F and increases at a constant rate for 8 minutes until it reaches the desired temperature , 350F . it remains the same temperature for 27 minutes . then the temperature decreases at a constant rate for 5 minutes until it reaches 175 , where it remains steady to keep the food warm , sketch a graph to represent the situation .
Answer:
The required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.
Step-by-step explanation:
Given that,
An oven is turned on and set to reach the desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes.
What are functions?
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
At time m = 1 min, temperature T = 134 °F
At time m = 5 min. temperature T = 450 °F
Slope of the equation M = 450 - 134 / 5 - 1
= 216 / 4
= 54
Linat relationship can be given as,
T - 134 = 54 (m - 1)
T = 54m -54 + 134
T = 54m + 80
Thus, the required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.
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PLS HELPPP (algebra 2)
Given f(x)=4(2)^x
a. find f(4)
b. write your answer as a logarithmic expression
a) The numeric value at x = 4 is given as follows: f(4) = 64.
b) The logarithmic expression is given as follows: x = log2(16).
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 4(2)^x.
At x = 4, the numeric value is found replacing the lone instance of x by 4, hence:
f(4) = 4(2)^4 = 64.
For the logarithmic expression, we obtain the inverse function, hence:
64 = 4(2)^x.
2^x = 16
x = log2(16).
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What are the coordinates of the vertex for f/x )= 3x 2 6x 3?.
The coordinates of the vertex for f(x) = 3x²+6x+3 are (-1, 0).
For any equation of the type y=ax²+bx+c, the vertex is given by (h, k)
Where, h = -b/2a and k = (4ac - b²)/4a.
Given, the equation is y = 3x²+ 6x+3
Here, a = 3, b = 6 and c = 3
So, h = -6/2(3)
h = -6/6
h = -1
4ac = 4(3)(3)
4ac = 36
So, k = [36 - (6)2]/4(3)
k = (36 - 36)/12
k = 0
Therefore, the coordinates of the vertex are (h,k) = (-1, 0).
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Expert need please follow the directions below and answer accurately it will be greatly appreciated. Thank you
Answer:
a. [tex]62^{\frac{1}{3}} = \sqrt[3]{62}[/tex]
b. [tex]220^{\frac{1}{2} = \sqrt{220}[/tex]
a. [tex]\sqrt[3]{240} = 240^{\frac{1}{3}}[/tex]
b. [tex]\sqrt{5} = 5^{\frac{1}{2}}[/tex]
Step-by-step explanation:
a test is worth 100 points each problem is worth either 2 points or 5 points the number of 5 point problems is22 less than the number of 2 point problems how many problems of each type are on the test
The test had 30 number of problem worth 2 points and 8 number of problem worth 5 points
What is an equation?An equation consists of numbers and variables linked together by mathematical operations to form an expression.
Let x represent the number of 2 points and y represent the number of 5 points.
The number of 5 point problems is 22 less than the number of 2 point, hence:
y = x - 22
x - y = 22 (1)
Also, the test is worth 100 points, hence:
2x + 5y = 100 (2)
From both equations:
x = 30, y = 8
30 number of problem worth 2 points and 8 number of problem worth 5 points
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solve:16^x+64=5*4^x-1
Y = [tex]4^{x}[/tex] + 64 = 5y - 1, x = (5y - 65)/16, and x = (20*[tex]4^{x}[/tex] - 260). Take the logarithm of both sides, apply the laws of logarithms, and solve for x.
What is logarithm?A logarithm is a mathematical function for expressing the relationship between two integers. It is the exponent to which a base number must be increased in order to equal a particular number. The base-10 logarithm of 100, for example, is 2, because 10 to the power of 2 equals 100.
Let y = [tex]4^{x}[/tex]
[tex]16^{x}[/tex] + 64 = 5y - 1
[tex]16^{x}[/tex] = 5y - 65
Dividing both sides by 16
x = (5y - 65)/16
x = (5*[tex]4^{x}[/tex] - 65)/16
Substituting y = [tex]4^{x}[/tex]
x = (5*([tex]4^{x}[/tex]) - 65)/16
Simplifying,
x = (5*[tex]4^{x}[/tex] - 65)/16
x = (20*[tex]4^{x}[/tex] - 260)/16
Divide both sides by 20
x = ([tex]4^{x}[/tex] - 13)/2
Take the logarithm of both sides:
log(x) = log([tex]4^{x}[/tex] - 13)/2
Apply the laws of logarithms:
log(x) = x*log(4) - log(13)/2
Solve for x:
x = (log(13)/2)/log(4) - log(x)/log(4)
x = (log(13)/2 - log(x))/log(4)
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Find The coordinate of the interection of the diagonal of a parallelogram with the vertical WXYZ
The coordinate of the intersection is (k, m*k + b).
A parallelogram is a four-sided shape with opposite sides that are parallel. The diagonal of a parallelogram cuts the shape into two congruent triangles. The coordinates of the intersection of the diagonal of a parallelogram with the vertical line of the parallelogram can be found by solving the equation of the line that forms the diagonal and the equation of the vertical line.
If the diagonal of the parallelogram is given by the equation y = mx + b, where m is the slope of the diagonal and b is the y-intercept, and the vertical line is given by the equation x = k, where k is the x-coordinate of the vertical line.
To find the x-coordinate of the intersection point, we can substitute x = k into the equation of the diagonal:
x = k
Then, we can substitute this value of x into the equation of the diagonal:
y = mx + b
This will give us the y-coordinate of the intersection point.
So, the coordinate of the intersection is (k, m*k + b)
Note: You need the equation of the diagonal and the equation of the vertical line to find the intersection point.
Therefore, The coordinate of the intersection is (k, m*k + b).
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x = k
Then, we can substitute this value of x into the equation of the diagonal:
y = mx + b
This will give us the y-coordinate of the intersection point.
So, the coordinate of the intersection is (k, m*k + b)
You need the equation of the diagonal and the equation of the vertical line to find the intersection point.
Therefore, The coordinate of the intersection is (k, m*k + b).
The father of maria is x years old. Which expression best represents maria's age if she is 13 of her father's age?.
The expression that best represents maria's age if she is 13 of her father's age is y = x/3
Given that,
The age of Maria's father is x.
To find: Which equation best describes Maria's age if she is 13 years older than her father?
Father of Maria is x years old. We have to find the expression best represents Maria's age.
Let age of Maria = y years
If Maria is 1/3 of her father's age then we can write the expression as below.
Age of Maria y = x/3.
Therefore answer is " y = x/3 "
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D is the midpoint of AC, AE CF, AB IDE and BC L DF.
Prove AB=BC
Out of 130 students interviewed it was observed that 30 read both comics and novels,10 read neither comics nor novels and twice as many students read comics as novels. How many students read [1] comics [2] novels [3] only 1 book
There are 60 pupils who don't read novels but read comic books, since there are twice as many students who do.
How to find the calculation?When two algebraic expressions have at least one unknown or variable, they are equal.
If they are novels and comic books:
novels
yes no
comics
yes 30 2x
no x 10
Since there are no other alternatives, the matrix's total number of digits must be 130.
30 + 2x + x + 10 = 130
Since x = 30 and 3x + 40 = 130,
The percentage of students that don't read comic books is x.
There are 60 pupils who don't read novels but read comic books, since there are twice as many students who do.
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Is molar mass equal to Avogadro's number?.
Yes, The molar mass of a substance is defined as the mass of 1 mol of that substance, expressed in grams per mole, and is equal to the mass of 6.022 × 10²³(Avogadro's number) atoms, molecules, or formula units of that substance.
The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)
So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A
atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.
We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).
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15n2 - 7n - 2
Algebra. Factoring Trinomials.
Please help.
Factor the following trinomials. Helpful Hint: Use the Sum/Product and Factoring
by Grouping method for trinomials with a leading coefficient other than one.
Check your answers using the FOIL method
Answer:
(5n + 1)(3n - 2)
Step-by-step explanation:
Find what number multiplies into -7 and adds into -2, including the coefficient in 15n^2
Find the area of these shaded regions (10-12)
The area of the shaded region is h² +6h, 3x²- 3x and r².
What is Area?•The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. Draw a square on a piece of paper using a pencil. A 2-D figure, that is. The term "Area" refers to the area that a shape occupies on paper.
•The surface area of a specific 2-D shape is measured as the number of unit squares needed to cover its whole surface area.
•Area measurements are frequently expressed in square cm², square feet, square inches, square meters, etc. Draw unit squares with sides of 1 centimeter to determine the area of the square figures shown below. In order to measure the shape, we shall use the unit cm² or square centimeters.
1st figure
area of shaded region = outer rectangle - inner rectangle
= 3h(h+2) - 2h(h)
= 3h² +6h- 2h²
= h² +6h
area of shaded region = outer rectangle - inner rectangle
= 3x²- 3x
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If a block is drawn from the box as shown above 200 times with replacement, predict the number of times the block drawn will have
the vowel A.
The letter E would be drawn roughly 40 times, but probably not exactly 20 times.
What does probably mean?The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
P(A) = f / N determines probability, which quantifies the possibility of an event happening. Probability and odds are connected, but probability is necessary for odds to exist.
Statistical formula
P(A) stands for the likelihood that event A will occur.
f = Number of possible outcomes of an event (frequency)
N stands for the total number of outcomes.
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Please help me fast thank you
Answer:
x=32°.
Step-by-step explanation:
Exterior angle add up to 360°
85°+71°+2x°+3x°+44°=360°
=2x°+3x°+200°=360°
=5x°=360°-200°
=5x°=160°
=5x/5=160/5
x =32°.
Steven has a rope that is 6 ft long. He cuts it into 9 pieces, as shown in the model.
The model shows that there are 9 pieces that are each 2/3 ft long.
Which division equation represents the situation?
Answer: 6 divided by 2/3 = 9
Step-by-step explanation:
For division always take the first number in the word problem so in this question the answer would be 6 then you take the 2/3 and divide it by 6. So it would be 6 divided by 2/3. then you take the 9 from the word problem and do 6 divided by 2/3 equals 9. So in this question the answer would be option 2 or could also be called option B. And if this is it that means the answer is, 6 divided by 2/3 = 9.
The division equation which representant this situation is 6 ÷ 2/3 = 9.
What is an division equation?Division equations are mathematical equations with the division operator in them. Division equations are useful not only in math class, but in everyday life as well. For example, if we wanted to evenly distribute a bag of candies among our friends, we could use division to find our answer. Assume we have 100 candy bars and four friends. Divide 100 by 4 to find out how many candies each person gets. We discover that our answer is 25, which means that each of our friends receives 25 candies.
It's our job to figure out what the division equals. This can be represented by a variable, such as x. As a result, our total division equation will be: 100/4=x. On both sides of the equals sign, we have things.
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How do you graph Y <- 3x 5?.
The equation y=3x+5 depicts a straight line with a slope of -3 and a y-intercept of 5, and it is written in slope intercept form. Replace x with any number and solve for y to find ordered pairings that can be graphed.
How are linear equations graphed?Write the equation in the form y = mx + b to determine the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept (0, b). Plot the y-intercept next. 3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.
How is a function graphed?You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
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Full Question = What kind of line does the linear inequality y=3x+5 represent?
3/4 ( x + 8 ) = 1/2 ( x - 6) what is the solution to this equation?
The solution for this equation is x = -36
3/4 ( x + 8 ) = 1/2 ( x - 6)
(Opening the brackets)
(3x + 24)/4 = ( x - 6)/ 2
By cross multiplication,
2(3x + 24) = 4( x - 6 )
6x + 48 = 4x - 24
(Taking the Variable to one side)
6x - 4x = - 24 - 48
2x = - 72
x= - 72/2
x = -36
Hence, the solution for this equation is x = -36
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Answer:wach the vido
Step-by-step explanation:
Lola ay thee two expreion have the ame value. Expreion A
Expreion B
Left-bracket (StartFraction a Over b EndFraction) Supercript negative 4 Baeline Right-bracket Supercript 0
Left-bracket (StartFraction a Over b EndFraction) Supercript 0 Baeline Right-bracket Supercript negative 4
Which explain whether Lola i correct?
Each phrase has a value, Lola is right. Because each equation has a value of 1, Lola is right.
These two phrases, according to Lola, have the same value.
Equivalent expressions are those that have the same value. In mathematics, equivalent numbers and statements frequently appear. Let's think about a few instances. Since the decimal numbers 0.5 and the fraction 1/2 have the same value, they are comparable numbers.
[a/b -] Expression A Expression B
0 [ a/b 0]-4 Which clarifies if Lola is right.
Because each phrase has a value, Lola is right. Because each equation has a value of 1, Lola is right.
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Complete question
Lola says these two expressions have the same value.
Expression A
Expression B
Left-bracket (StartFraction an Over b EndFraction) Superscript negative 4 Baseline Right-bracket Superscript 0
Left-bracket (StartFraction a Over b EndFraction) Superscript 0 Baseline Right-bracket Superscript negative 4
Which explains whether Lola is correct?
Lola is correct because each expression has a value of 0.
Lola is correct because each expression has a value of 1.
Lola is not correct because the value of expression A is 1 and the value of expression B is (StartFraction b Over a EndFraction) Superscript 4.
Lola is not correct because the value of expression A is (StartFraction b Over a EndFraction) Superscript 4 and the value of expression B is 1.
ZA and ZB are vertical angles. If m
-
then find the value of x.
The value of X of the vertical angles would be = 1.36
What is a vertical angles?The vertical angles are the type of angles that are known to be directly opposite each other which are also equal angles.
The given vertical angles are ZA and ZB.
If m A = (8x – 20)°
m B = (3x – 5)º
The vertical angles are equal, to find X;
mA = mB
8x -20 = 3x - 5
Bring the like terms together;
8x + 3x = 20- 5
11x = 15
X= 15/11
X= 1.36
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Complete question:
ZA and ZB are vertical angles. If m A = (8x – 20)° and m B = (3x – 5)º, then find the value of x.
Which expression is equivalent to the given expression?
√45
A. 5√9
B. 3√5
C. 9√5
D. 5√3
Which of the following reasons states why line
segment TV is congruent to line segment VT?
Vertical Angles
Reflexive Property
Transitive Property
Complementary Property
Answer:
complementary property
Step-by-step explanation:
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Answered By Solution 49
