Answer: 1.71, 1 3/4, 16/9, pie
Step-by-step explanation: We convert all the numbers to improper fractions. 1.71 = 171/100. 1 3/4 = 175/100 because 3/4 is 0.75. pi is 3.14... which is larger than all of the other numbers. So, pi is the largest. For 16/9, we can just divide to find the solution. Once you divide, you will notice that the answer is 1.77777777... This means that it is larger than 1.71 and 1.75 so 16/9 is the second largest. 1.71 is smaller than 1.75 so the order is 1.71, 1 3/4, pie, 16/9
If point O represents the origin, PQ = 12 units, and P'Q' = 3 units, find the scale factor. (Note: point O represents the origin, what is the scale factor to dilate a shape on the other side of the origin?)
Answer:
1/4
Step-by-step explanation:
To transform PQR into P'Q'R, dilate the preimage by 1/4, or shrink it by a scale factor of 4 because 3/12 = 1/4
Ekaete collected 12 raffle tickets. Roseline collected twice as many. How many raffle tickets did they collect in all?
Answer:
36
Step-by-step explanation:
12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36
which expression is equivalent to (125^2/ 124^4/3)
The answer is 25.
What is numerator and denominator?The value above the horizontal line is the numerator in a fraction. It represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the vinculum. It indicates the overall total of all of the equal portions.For instance, the fraction bar is the line that separates the numbers 4 and 5, and 45 is a fraction. Here, the numerator is the number above the fraction bar, and the denominator is the number below the fraction bar. The denominator, or the number of pieces out of the whole, is represented by a numerator.Multiplying the numerator times the numerator and denominator. Denominator. The answer should be lowered to a mixed number in the simplest form.The expression is equivalent to [tex]\frac{125^{2} }{125^{\frac{4}{3}} }[/tex] :
[tex]\frac{125^{2} }{125^{\frac{4}{3}} } =125^{2-(\frac{4}{3}) }[/tex]
[tex]=125^{\frac{2}{3} }[/tex]
[tex]125=5x^{3}[/tex]
[tex](5^{3} )^{\frac{2}{3}} =5\frac{6}{3} =5^{2} =25[/tex]
Therefore, The answer is 25.
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Are 14, 6 + 8, and (6 + 8) equivalent expressions? Explain your reasoning.
The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1
Equivalent expression14
6 + 8
= 14
(6 + 8)
= 14
The coefficient of (6 + 8) is 1, so, the expression remains the same.
What is equivalent expression?Equivalent expressions refers to those expressions that work the same even though they look different.
The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.
Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.
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HELP
answer the questions 61 and 62 SHOW UR WORK please i’ll mark brainliest
help me
Answer:
Step-by-step explanation:
Question mode multiple choice question despite the large number of media options today, the average millennial still blank______ for an average of 10 hours every week.
Verify that the intermediate value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x2 7x 1, [0, 9], f(c) = 19 c =
we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
According to the given question.
We have a function.
f(x) = x^2 + 7x + 1
As, we know that "the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M".
Now, we will apply the theorem for the given function f(x).
So,
f(0) = 0^2 +7(0) + 1 = 1
And,
f(9)=9² + 7(9) + 1 = 81 + 63 + 1 = 145
Here, f(0) = 1< 19< 145 = f(9).
So, f is continous since it is a polynomial. Then the IVT applies, and such c exists.
To find, c,
We have to solve the quadratic equation f(c) =19.
This equation is
c² + 7c + 1 = 19.
Rearranging, c²+ 7c - 18=0.
Factor the expression to get
c² + 9c - 2c -18 = 0
⇒ c(c + 9) - 2( c + 9) = 0
⇒ (c - 2)(c + 9) = 0
⇒ c = 2 or -9
c = -9 is not possible beacuse it is not in the interval [0, 9].
So, the value of c is 2.
⇒ f(2) = 2^2 + 7(2) + 1 = 4 + 14 + 1 = 19
Hence, we verified the intermidiate value theorem applies to the function f(x) = x^2 + 7x + 1 . And the value of c is 2.
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What is the greatest possible error if irina measured the length of her window as 3.35 feet? 0.5 0.05 0.005 0.0005
3.35 feet have a maximum inaccuracy of 0.005 feet.
The correct option is C.
What is error analysis?When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.
Given:The window is 3.35 feet long.
Find the biggest error you can
According to the given data:Half of the measuring unit is considered to be the maximum amount of measurement error.
3.35 feet are calculated to the nearest centimeter, or 0.01 feet
Consequently, the largest conceivable error is equal to half of the measurement unit.
= .01/2
= .005
Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.
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Rick runs 5 miles which burns approximately 500 calories. how many miles would rick have to run to burn one pound of adipose tissue?
35miles Rick have to run to burn one pound of adipose tissue.
According to the given question.
Rick runs 5miles to burn 500 calories.
⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.
As we know that
1 pound = 3,500 calories.
So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles
Hence, 35miles Rick have to run to burn one pound of adipose tissue.
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Describe what a line with zero rate of change looks like.
Answer:
Step-by-step explanation:
rate of change = change in y/ change in x
The rate of change is 0 if the change in y = 0
0 = 0 / change in x
The graph is a horizontal line since the y values do not change.
15 POINTS
Data Analysis and Probability
Constructing a box-and-whisker plot
The box and whisker plot for the data-set is given at the end of the question.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.For this problem, we have that:
The smallest value is of 50, hence the left dot has to be at 50 in your graph.The highest value is of 77, hence the right dot has to be at 50 in your graph.The data-set has an even cardinality, of 17, hence the median is the 9th element, which is of 65, which means that the middle vertical line should be at 65.The first quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements, which are 55 and 57, hence the first quartile is of 56, which means that the left vertical line should be at 56.The third quartile is the median of the first eight elements, hence the mean of the 4th and 5th elements of the second half, which are both 71, hence the third quartile is of 71, which means that the right vertical line should be at 71.The graph at the end gives a vertical version of the box plot.
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Kelley writes the expression n 2 to model the phrase "xander studied two more hours than nandini." which best explains the accuracy of kelley’s expression? it is accurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n or n 2 are correct translations. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more" is " ," and nandini’s study time is unknown or "n," so 2 n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is ">," and nandini’s study time is unknown or "n," so 2 greater-than n is the correct translation. it is inaccurate. in the phrase "two more hours than nandini," "two" is "2," "more than" is "<," and nandini’s study time is unknown or "n," so 2 less-than n is the correct translation.
It is accurate. In the phrase “two more hours than Nandini,” n + 2 are correct translations. Then the correct option is A.
What is Algebra?Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols.
As an example, Kelley models the sentence "Xander studied two more hours than Nandini" using the equation n + 2.
Consequently, the following will describe Kelley's expression's accuracy the best:
It is precise. Since "two" is translated as "2," "more" as "+," and "Nandini's study time is unknown or "n," 2 + n or n + 2 are the appropriate translations for the sentence "two more hours than Nandini."
So, option A is the best choice.
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I understand that the question you are looking for is :
Kelley writes the expression n + 2 to model the phrase “Xander studied two more hours than Nandini.” Which best explains the accuracy of Kelley’s expression?
It is accurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n or n + 2 are correct translations.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more” is “+,” and Nandini’s study time is unknown or “n,” so 2 + n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “>,” and Nandini’s study time is unknown or “n,” so 2 greater-than n is the correct translation.
It is inaccurate. In the phrase “two more hours than Nandini,” “two” is “2,” “more than” is “<,” and Nandini’s study time is unknown or “n,” so 2 less-than n is the correct translation.
(50 POINTS PLEASE HELP!!!)
!!!THE QUESTION THAT I NEED TO BE ANSWERED IS THE PICTURE ATTACHED!!! BELOW IS JUST THE REQUIREMENTS AND EXAMPLE!!!
He has hired you as their new production manager. Your job is to look at four different figures and determine which would best suit the needs of the company for packaging the candy. You will choose one of the four options shown below. The candy is animal gummies. The package must hold between 80 and 100 cubic inches (roughly 5-7 cups of space). The cost of the plastic for the packaging is $0.004 per square inch. When finding cost you would multiply the Total Surface Area by $0.004.
For example:
Total Surface Area = 86 sq. in
Cost per sq in = $0.004
86 * .004 = .344 when rounded to nearest penny = $0.34
Your project should include the volume, total surface area, and materials cost for each figure given below, including the formulas you used and each step of your work. Be sure to find all measures for each figure, even if the figure does not meet the restraints that the company has given. Make sure to use the formulas given in your lessons, round your volume and area to the nearest hundredth, and round your cost to the nearest penny.
The figure in the question is a box with dimensions of 6 in. by 2 in. by 9 in., which gives;
Surface area of the packaging = 168 in.²Package volume = 108 in.³Cost of packaging = $0.672Which method can be used to provide the packaging estimates for the company?The dimensions of the box in the given figure are;
Length, L = 9 in.
Width, W = 2 in.
Height, H = 6 in.
The surface area, A, of a box is found using the following formula;
A = 2•L•W + 2•L•H + 2•H•W
Therefore;
A = 2×9×2 + 2×9×6 + 2×2×6 = 168
The surface area of the figure, A = 168 in.²The volume of a box, V, is calculated as follows;
V = L•W•HFor the given figure, therefore;
V = 9 × 2 × 6 = 108
The volume of the given figure, V = 108 in.³Cost of packaging per square inch, c = $0.004
Cost to package the figure, C, is therefore;
C = c × AWhich gives;
C = $0.004/in.² × 168 in.² = $0.672
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Using a calculator, the line of best fit for the function is given by:
y = 51.7x - 5.7.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator. For this problem, a linear regression is used because the data only increases.
From the given table, the points are:
(1, 68), (2,97), (3, 134), (4, 176), (5, 241), (6,335).
Inserting these points on the calculator, the line of best fit for the function is given by:
y = 51.7x - 5.7.
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Select the correct answer.
What is the approximate measure of exterior angle B in the polygon?
Answer:
C
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 4 exterior angles and equate to 360
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is
31x + 12 = 360 ( subtract 12 from both sides )
31x = 148 ( divide both sides by 31 )
x ≈ 11.23 ( to 2 dec. places )
then exterior angle at B is
9x + 3 = 9(11.23) + 3 ≈ 104° → C
The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A polygon is given in the picture with angle measures.
As we know,
The sum of the exterior angles of a polygon = 360°
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360
31x + 12 = 360
31x = 148
x ≈ 11.23
= 9x + 3 = 9(11.23) + 3
≈ 104°
Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
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Factor the cubic polynomial 6x3 – 11x2 – 12x 5. use the rational root theorem and synthetic division
The factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is:
6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
For given question,
We have been given the cubic polynomial 6x³ - 11x² - 12x + 5
We need to factorize given cubic polynomial.
By the rational roots theorem, any rational zero of f(x) is expressible in the form ± [tex]\frac{p}{q}[/tex] for integers p, q with p a divisor of the constant term 5 and q a divisor of the coefficient 6 of the leading term.
Factors of p = 5: 1, 5
Factors of q = 6: 1, 2, 3, 6
That means that the only possible rational zeros are:
±{ [tex]\frac{1}{1} ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,\frac{5}{1} ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
= ±{ [tex]1 ,\frac{1}{2} ,\frac{1}{3} ,\frac{1}{6} ,5 ,\frac{5}{2} ,\frac{5}{3} ,\frac{5}{6}[/tex] }
We need to find the exact zeros of given cubic polynomial.
For x = 1,
6(1)³ - 11(1)² - 12(1) + 5 = -12
This means, x = 1 is not a zero of given cubic polynomial.
For x = -1,
6(-1)³ - 11(-1)² - 12(-1) + 5 = 0
This means, x = -1 is a zero of given cubic polynomial and (x + 1) is a factor.
To factorize given cubic polynomial we use synthetic division.
The synthetic division (6x³ - 11x² - 12x + 5) ÷ (x + 1) is as shown in following image.
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(6x² - 17x + 5)
The factors of above quadratic polynomial 6x² - 17x + 5 are:
⇒ 6x² - 17x + 5 = (x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
So, the factors of given cubic polynomial are:
⇒ 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
Therefore, the factorization of given cubic polynomial 6x³ - 11x² - 12x + 5 is: 6x³ - 11x² - 12x + 5 = (x + 1)(x - [tex]\frac{5}{2}[/tex])(x - [tex]\frac{1}{3}[/tex])
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X
3.
What is the value of x to the nearest tenth?
6
24
Answer:
C. 13.4=======================
Connect the center with one end of the chord, this gives us a right triangle with hypotenuse of x, one leg of 6 and another leg of 24/2 = 12.
Use Pythagorean to find the value of x:
x² = 6² + 12²x² = 36 + 144x² = 180x = √180x = 13.4 (rounded)Correct choice is C.
Answer:
x = 13.4
Step-by-step explanation:
Definitions
Radius: a straight line from the center of the circle to its circumference.
Chord: a straight line joining two points on the circle.
Perpendicular: at a right angle (90°).
Isosceles triangle: a triangle with 2 sides of equal length and 2 congruent base angles.
From inspection of the given diagram:
radius = xchord = 24 unitssegment of the radius perpendicular to the chord = 6 unitsIf lines are drawn from the center of the circle to the endpoints of the chord, an isosceles triangle is created with base of 24 units and height of 6 units.
The isosceles triangle is made up of two right triangles with base of 12 units and height of 6 units. The radii are the hypotenuse of these right triangles. Therefore, to calculate the radius of the circle (x), use Pythagoras Theorem.
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right trianglec is the hypotenuse (longest side) of the right triangleTherefore:
[tex]\sf \implies 6^2+12^2=x^2[/tex]
[tex]\implies \sf x^2=36+144[/tex]
[tex]\implies \sf x^2=180[/tex]
[tex]\implies \sf \sqrt{x^2}=\sqrt{180}[/tex]
[tex]\implies \sf x=\pm 6\sqrt{5}[/tex]
As length is positive:
[tex]\implies \sf x = 6\sqrt{5}=13.4\:units\:(nearest\:tenth)[/tex]
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A graph titled Population of Old Town has Time (years after 2000) on the x-axis, and number of people on the y-axis. A line goes through points (4, 7,000) and (6, 6,500). What is the slope for this scenario? -500 -250
The slope of the scenario is calculated as: -250.
How to Find the Slope Value?Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).
Given the points:
(4, 7,000) = (x1, y1)
(6, 6,500) = (x2, y2)
Plug in the values
Slope (m) = (6,500 - 7,000) / (6 - 4)
Slope (m) = (-500) / (2)
Slope (m) = -250
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Which of the following shows the simplified function of csc x sin(pi/2 -x)?
Answer:
cot x
Step-by-step explanation:
using the identities
csc x = [tex]\frac{1}{sinx}[/tex]
sin([tex]\frac{\pi }{2}[/tex] - x) = cos x
then
csc x × sin ([tex]\frac{\pi }{2}[/tex] - x)
= [tex]\frac{1}{sinx}[/tex] × cosx
= [tex]\frac{cosx}{sinx}[/tex]
= cot x
pls help!
using the numbers 1-9 fill in the boxes so that it meets the criteria. use each number only once per red box and once per blue box
The way to solve this is to try to get the vales that would best fill the empty spaces in the diagram. This has been done below
a. log6⁰, log 2 . 1, log 8/3
b. log 1 .4 , 1 , log 4. 6
c. log 9/2, log 3. 5 , log 5⁷
How to find the logarithm of a numberTo do this, you have to decide on that specific number whose logarithm you are trying to determine. Next you have to find the base of that number.
The logarithm of the number is the power that it would have to be raised for us to obtain a different number.
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HELP ILL BRAINLIST WHO EVER HELPS
PICTURE BELOW
Applying the SAS congruence theorem and the definition of angle bisector, the complete proof is shown in the image attached below.
What is the SAS Theorem?The SAS theorem (side-angle-side theorem) state that two triangles are congruent to each other if they have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.
What is an Angle Bisector?A line segment that divides an angle into two equal parts is referred to as an angle bisector.
From the proof given, we know that;
m∠DEK = 2(m∠DEF)
m∠DEK = 2(44) = 88°
With the given information and using the reflexive property, we know that triangles DEF and KEF have two pairs of congruent sides that are corresponding to each other and a pair of congruent angles that are corresponding to each other.
Therefore, ΔDEF ≅ ΔKEF based on the SAS congruence theorem. Because they are congruent triangles, DF = KF based on the CPCTC theorem.
Then, KF = 1/2(DK) = 1/2(16) = 8.
The complete proof is show in the image attached below.
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Select the reason that best supports statement 2 in the given proof.
Answer:
Transitive property
The reason that best supports statement 2 in the given proof is division property of equality. Therefore, the correct answer is option D.
Given that, 3(m∠A)=90° and m∠B=m∠A.
We need to prove m∠B=30°.
According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0.
Here,
Statement: Reason:
1. 3(m∠A)=90° 1. Given
2. m∠A=30° 2. Division property of equality
3. m∠B=m∠A 3. Reflexive property
4. m∠B=30° 4. Transitive Property
Therefore, the correct answer is option D.
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divide the polynomials:
x^2-3x+9/x-2
The value of dividing x^2-3x+9 by x-2 is x + 3
Ways of dividing polynomialsThere are several ways to divide polynomial functions; some of these ways include
By factorizationBy long divisionBy synthetic divisionBy using technology such as graphHow to divide the polynomials?The expression for the polynomial division is given as:
x^2-3x+9/x-2
To divide polynomial functions, we make use of the division by factorization method
Start by expanding the numerator of the polynomial division
x^2-3x+9/x-2 = x^2 + 3x - 6x + 9/x-2
Factorize the equation
x^2-3x+9/x-2 = x(x + 3) - 2(x + 3)/x - 2
Factor out x + 3 from the numerator
x^2-3x+9/x-2 = (x- 2)(x + 3)/x - 2
Cancel out the common factors
x^2-3x+9/x-2 = x + 3
Hence, the value of dividing x^2-3x+9 by x-2 is x + 3
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In the figure below, AD is the perpendicular bisector of CB. Based on this information, which other statement can be proven to be
true?
OA AB AC
OB. AB CB
OCAC CB
OD AD CB
A
C
D
B
Answer:
463833
expand
Medium
Solution
verified
Verified by Toppr
In △ABD and △ACD, we have
DB=DC ∣ Given
∠ADB=∠ADC ∣ since AD⊥BC
AD=AD ∣ Common
∴ by SAS criterion of congruence, we have.
△ABD≅△ACD
⇒AB=AC ∣ Since corresponding parts of congruent triangles are equal
Hence, △ ABC is isosceles.
Answer:
A.
Step-by-step explanation:
With the given information, triangles ABD and ACD can be proved congruent, and by CPCTC, segments AB and AC are congruent.
Please help me solve this problem with work
Answer:
m∠B ≈ 51.5°
Step-by-step explanation:
A triangle solver can find this answer simply by entering the data. If you do this "by hand," you need to first find length BC using the Law of Cosines. Then angle B can be found using the Law of Sines.
Length BCThe Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
a² = 21² +13² -2(21)(13)cos(91°) ≈ 619.529
a ≈ 24.8903
Angle BThe Law of Sines tells us ...
sin(B)/b = sin(A)/a
B = arcsin(sin(A)×b/a) = arcsin(sin(91°)×21/24.8903)
B ≈ 57.519°
The measure of angle B is about 57.5°.
What is [tex]\frac{a+3}{8}[/tex] x [tex]\frac{2}{a}[/tex]
Answer: [tex]\frac{2a+6}{8a}[/tex]
Step-by-step explanation:
[tex]\frac{2(a+3)}{8a}=\frac{2a+6}{8a}[/tex]
A circle with center O. Two tangents to the circle from the point C meet the circle at points A, and B. Two lines O B, and O C forms an exterior angle of 250 degrees. Two lines B D, and A D are drawn from a point D on the circle.
In this figure, m∠BDA =
° and m∠BCA =
°.
Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
First of all, we would determine angle BOA:
∠BOA + ∠BOA = 360° (Angles at a point)
∠BOA + 250° = 360°
∠BOA = 360° - 250°
∠BOA = 110°
Next, we would determine angle BDA:
2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)
2 × m∠BDA = 110°
m∠BDA = 110°/2
m∠BDA = 55°.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle BCA will be given by this formula:
m∠BCA = ½ × (m<AO - m<BO)
Substituting the given parameters into the formula, we have;
m∠BCA = ½ × (250 - 110)
m∠BCA = ½ × 140
m∠BCA = 70°.
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Answer:
70
Step-by-step explanation:
what is the value of x= and y=
Answer:
x = 18
y = 18
Step-by-step explanation:
We are given a right triangle (notice the 90 degree angle), with one of the angles being 45°.
We also know that the hypotenuse (the side opposite of the 90° angle) is 18√2.
We want to find the value of x and y.
First, let's figure out what the value of the other angle is.
The angles in a triangle all add up to 180 degrees.
Let's call the value of the angle we don't know s.
s + 45 + 90 = 180
Add 45 and 90 together.
s + 135 = 180
Subtract 135 from both sides.
s = 45
So the value of the other angle is 45 degrees.
When a right triangle is a 45-45-90 triangle (the numbers referring to the measures of the degrees), there is actually something special about it; if the legs (the sides that make up the 90 degree angle) have the value a (they would both be congruent because a 45-45-90 triangle is isosceles), then the hypotenuse will be a√2.
Keeping this in mind, let's solve for a.
Set 18√2 equal to a√2.
18√2=a√2
Divide both sides by √2.
18 = a
The value of a, aka the legs is a.
Both x and y would be equal to a in this case.
Therefore, x = 18, and y = 18.
Evaluate 5(14 – 23) + 8 ÷ 2. (1 point) 26 34 44 56
Answer:
-41
Step-by-step explanation:
5(14-23)+8 ÷ 2
=5(-9)+4
=-45+4
=-41
The solution of the given expression 5(14-23)+8 ÷ 2 is -41.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Example; 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
WE have given an expression as;
5(14-23)+8 ÷ 2
Solve the bracket then division;
=5(-9) + 4
=-45+4
=-41
Therefore, the solution of the given expression is -41.
Learn more about simplification;
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i do not know how to get what they are asking me too
