In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm, find the value of (x − y).
Answers
The value of (x-y) is 9 cm for the given triangle ABC.
According to the question,
We have the following information:
In triangle ABC, if AC = 17 cm, CB = 10 cm, AD = x cm, DB = y cm and AB = 21 cm.
So, we have:
x+y = 21 cm
y = (21-x) cm
Using Pythagoras theorem in right-angled triangle ADC and CDB:
[tex]AC^{2} = AD^{2} +CD^{2}[/tex] and [tex]BC^{2} = BD^{2}+CD^{2}[/tex]
Now, we have the equal values of [tex]CD^{2}[/tex]:
[tex]17^{2} -x^{2} = 10^{2} -y^{2}[/tex]
289 -[tex]x^{2}[/tex] = 100 - [tex](21-x)^{2}[/tex]
289 - [tex]x^{2}[/tex] = 100 - (441+[tex]x^{2}[/tex]-42x)
289-[tex]x^{2}[/tex] = 100 - 441-[tex]x^{2}[/tex] + 42x
289 = 100 -441+42x
42x-331 = 289
42x = 289+331
42x = 630
x = 630/42
x = 15 cm
y = 21-x
y = 21-15
y = 6 cm
Now, x-y = 15-6
x-y = 9 cm
Hence, the value of (x-y) is 9 cm.
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Related Questions
7 1/3 × 2 2/11 3/5 × 6 2/34 1/5 × 1 1/14
Answers
It is easier to perform the operations if you convert the mixed fractions into improper fractions.
For point 1. Make the mixed fractions improper first
[tex]7\frac{1}{3}=\frac{3\cdot7+1}{3}=\frac{21+1}{3}=\frac{22}{3}[/tex][tex]2\frac{2}{11}=\frac{11\cdot2+2}{11}=\frac{22+2}{11}=\frac{24}{11}[/tex]Now, the multiplication of fractions is done like this
[tex]\frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]Then, you have
[tex]7\frac{1}{3}\cdot2\frac{2}{11}=\frac{22}{3}\cdot\frac{24}{11}=\frac{528}{33}=16[/tex]For point 2.
[tex]6\frac{2}{3}=\frac{3\cdot6+2}{3}=\frac{18+2}{3}=\frac{20}{3}[/tex]Now multiplying the improper fractions you have
[tex]\frac{3}{5}\cdot6\frac{2}{3}=\frac{3}{5}\cdot\frac{20}{3}=\frac{60}{15}=4[/tex]Finally for point 3.
[tex]4\frac{1}{5}=\frac{5\cdot4+1}{5}=\frac{20+1}{5}=\frac{21}{5}[/tex][tex]1\frac{1}{14}=\frac{14\cdot1+1}{14}=\frac{14+1}{14}=\frac{15}{14}[/tex]Now multiplying the improper fractions you have
[tex]\begin{gathered} 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{21}{5}\cdot\frac{15}{14}=\frac{315}{70}=\frac{35\cdot9}{35\cdot2}=\frac{9}{2} \\ 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{9}{2} \end{gathered}[/tex]HELP PLEASEEEEE!!!!!!
Answers
The one rational number between -0.45 and -0.46 is -0.455.
What is defined as the term rational number?Rational are numbers which can be specified in the form p/q, in which p and q are integers and q≠. The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the denominator and numerator of such a fraction have been whole numbers (denominator 0), whereas the numerator and the denominator of rational numbers are integers.For the given question.
The two rational number are given as;
-0.45 and -0.46.
To find the on rational number lying between the two given rational number is to take the average of both numbers.
= (-0.45 + (-0.46))/2
= -0.91/2
= -0.455
Thus, the one rational number between -0.45 and -0.46 is -0.455.
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Suppose that the 99% confidence interval for the true average number of canteen operating hours is [6, 9]. Which conclusion is correct if the average number of operating hours for canteens in the region is 8 hours? a. The average number of canteen operating hours in this city is not significantly different from that of the region since 8 is not contained in the interval. b. The average number canteen operating hours in this city is not significantly different from that of the region since 8 is contained in the interval. c. The average number of canteen operating hours in this city is significantly different from that of the region since 8 is contained in the interval. d. The average number of canteen operating hours in this city is significantly different from that of the region since 8 is not contained in the interval.
Answers
Given: Suppose that the 99% confidence interval for the true average number of canteen operating hours is [6, 9].
To Determine: Which conclusion is correct if the average number of operating hours for canteens in the region is 8 hours
Solution
Given the confidence interval of [6,9]. This means that
A confidence interval indicates where the population parameter is likely to reside. For example, a 99% confidence interval of the mean [6 9] suggests you can be 99% confident that the population mean is between 6 and 9
If the average number of operating hours for canteens in the region is 8 hours, then we can conclude that
The average number canteen operating hours in this city is not significantly different from that of the region since 8 is contained in the interval, OPTION B
Elisa has 24 black and white photographs and 72 photographs that are in color. She is arranging the photographs in an album and wants to contain the same combination of color and black and white photographs. What is the greatest number of pages elisa can fill with photographs
Answers
72/24 = 3
72+24 = 96
96/3 = 32
Just a guess!
given two circles (all circles are similar) , with circumferences of 30cm and 12cm each, find the ratio of their areas. state answer as fraction.
Answers
The circumference of a circle is given by the following formula
[tex]C=2\pi r[/tex]where r represents the radius.
The ratio between two circumferences is equal to the ratio of the radius.
[tex]\frac{C_1}{C_2}=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}[/tex]The area of a circle is given by the following formula
[tex]A=\pi r^2[/tex]Then, the ratio between two circle areas is equal to the square of the ratio of the radius, which is the square of the ratio between the circumferences.
[tex]\frac{A_1}{A_2}=\frac{\pi r_1^2}{\pi r_2^2}=(\frac{r_1}{r_2})^2=(\frac{C_1}{C_2})^2[/tex]Then, applying this relation in our problem, the ratio between the areas is:
[tex]\frac{A_1}{A_2}=(\frac{30}{12})^2=\frac{25}{4}[/tex]The ratio between the areas is 25/4.
If three angles of a triangle are 2x°, 6x° and x°, find the size of largest angle.
Answers
Answer:
so the answer is 6x°which is equals to 120°
Step-by-step explanation:
2x°+6x°+x°=180(The sum of the interior angle of the triangle is 180°)
9x°=180°
9x°÷9=180°÷9
x=20°
2x°is equals to 2×20°=40°
6x° is equals to 6×20°=120°
x° is equals to x×20°=20°
Together, Katya and Mimi have 480 pennies in their piggy banks. After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left. How many pennies did they lose altogether?
Answers
The number of pennies they lose altogether is 288 pennies.
How to find the number of pennies they lost together?Together, Katya and Mimi have 480 pennies in their piggy banks.
Therefore, there total amount of pennies is 480.
After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.
Therefore,
let
x = number of pennies Katya have
y = number of pennies Mimi have
Hence,
x + y = 480
x = 480
Katya pennies left = x - 1 / 2x = 1 / 2x
Mimi pennies left = y - 2 / 3 y = 1 / 3 y
1 / 2 x = 1 / 3 y
2y = 3x
y = 3 / 2 x
Substitute the value in equation(i)
x + 3 / 2 x = 480
2.5x = 480
x = 480 / 2.5
x = 192
Therefore,
192 + y = 480
y = 480 - 192
y = 288
The number of pennies they loose can be calculated as follows;
Katya losses = 1 / 2 × 192 = 96Mimi losses = 2 / 3 × 288 = 192Therefore, they lost 96 + 192 = 288 pennies altogether.
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15÷6%=
A. 1004
B. 100
C. 24
D. 24
Answers
Can someone help me with this?
Answers
x to the zeroth power - 3x +5
Hi there, I need help with this question. Thank you in advance!
Answers
For the data given, we have 24 entries in all.
They are :
75, 36, 80, 49, 24, 61, 34, 39, 30, 76, 44, 44, 40, 35, 21, 89, 34, 70, 79, 65, 66, 53, 99, 11
(1) Minimum refers to the lowest data in the table. we can see out of all the data in the table, the lowest is 11. Therefore,
Min = 11
(2) Maximum refers to the highest data in the table.
The highest is 99.
Therefore,
Max = 99
(3) Range is defined as highest data minus lowest data
Range = 99 - 11
Range = 88
(4) Mean:
[tex]\begin{gathered} \text{ Mean =}\frac{\text{ sum of the data}}{total\text{ count}} \\ \operatorname{mean}\text{ = }\frac{75+36+80+49+24+61+34+39+30+76+44+44+40+35+21+89+34+70+79+65+66+53+99+11}{24} \\ \\ \text{Mean = }\frac{1254}{24} \\ =52.25 \end{gathered}[/tex]Therefore,
Mean = 52.25
(5) Standard deviation:
The steps to calculate the standard deviation in shown in the picture below.
The standard deviation = 22.8386..
To 2 decimal places, we have 22.84
Therefore,
Standard deviation = 22.84
Use the diagram to calculate the measure of angle 5
Answers
Answer:
m∠5=22 °
Explanation:
In the diagram:
• Angles 4 and 90 degrees, are ,vertical angles,.
,• Angles 2 and 68 degrees, are ,vertical angles,.
Since the measure of vertical angles is equal:
[tex]\begin{gathered} m\angle4=90\degree \\ m\angle2=68\degree \end{gathered}[/tex]In the triangle:
[tex]m\angle2+m\angle4+m\angle5=180\degree\text{ (sum of angles }in\text{ a triangle)}[/tex]Substitute the measures of angle 2 and 4 obtained earlier:
[tex]\begin{gathered} 90\degree+68\degree+m\angle5=180\degree \\ 158\degree+m\angle5=180\degree \\ Subtract\text{ }158\degree\text{ from both sides of the equation.} \\ m\angle5=180\degree-158\degree \\ m\angle5=22\degree \end{gathered}[/tex]The measure of angle 5 is 22 degrees.
Lines a and b intersect do that the measure angle 1 is 85°. If angle 2 is complement to angle 1, what's the measure for angle 2?
Answers
if the angles are complementary, then the sum of the angles is 90°
[tex]\begin{gathered} 85+m\angle2=90 \\ m\angle2=90-85=5 \end{gathered}[/tex]so the measure of the angle 2 is 5°
Justin and poor friends are going to a movie each person buys a movie ticket that costs one 50 less than the square of $3 of the friends bought a bag of popcorn and a small soda that cost $2.25 more than the score of $2 right expression that can be used to find the total amount that Justin is trying to at the movies
Answers
Answer:
4(3² - 1.5) + 3(2² + 2.25)
Explanation:
First, they buy 4 tickets that cost $1.50 less than the square of $3. So, we can express that as follows:
4 x (3² - 1.5)
Then, they buy 3 bags of popcorn and a small soda that cost $2.25 more than the square of $2, so the expression for this is:
3 x (2² + 2.25)
Therefore, the numerical expression that can be used to find the total amount is the sum of the expression above:
4 x (3² - 1.5) + 3 x (2² + 2.25)
4(3² - 1.5) + 3(2² + 2.25)
So, the answer is:
4(3² - 1.5) + 3(2² + 2.25)
Please see attached picture of problem I need help with.
Answers
Step 1
List the elements of D
[tex]D=\lbrace2,.........\rbrace[/tex]List the elements of E
[tex]E=\lbrace........,8\rbrace[/tex]Find
[tex]D\cap E[/tex][tex]D\cap E=(1,8]--(\text{what is common\rparen}[/tex]Find
[tex]D\cup E[/tex][tex]\begin{gathered} D\cup E=(1,\infty)\cup(-\infty,8]--(Listing\text{ all elements in D and E\rparen} \\ D\cup E=(-\infty,\infty) \end{gathered}[/tex]Answers;
[tex]\begin{gathered} \begin{equation*} D\cap E=(1,8] \end{equation*} \\ \begin{equation*} D\cup E=(-\infty,\infty) \end{equation*} \end{gathered}[/tex]During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)
Answers
Answer:
11 percent
Step-by-step explanation:
No idea to explain
48.001 to the hundredths
Answers
Since we want to express 48.001 to the hundredths, let's look at the places of the digits after the decimal point:
Therefore, 48.001 to the hundredths is 48.00
Find the sum of integers from 33 to 47:
33+34+...+46
+47
Answers
The sum of integers from 33 to 47 is 600.
What are integers?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers. The Z symbol is a common way for mathematicians to refer to an integer set.An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.So, the sum of integers:
33 - 47Simply perform addition as follows:
33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 + 41 + 42 + 43 + 44 + 45 + 46 + 47= 600Therefore, the sum of integers from 33 to 47 is 600.
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Given Z VYX is bisected by YW, mZ VYX =(6r-18), and m2 VYW = 36. What is the value of r? A. 15 B. 30 C. 36 D. 72
Answers
A) 15
1) Let's sketch that
According to the Bisector Theorem, the bisected line equally divides the angle. So we can write:
∠VYW≅∠WYX
And:
6r-18 = 36+36
6r -18 = 72
6r= 90
r= 15
Reflected over the x-axis , horizontal shrink of 1/2, translated 7 down.
Answers
Given:
Reflected over the x-axis, horizontal shrink of 1/2, translated 7 down.
The parent function is y=|x|.
[tex]\begin{gathered} \text{reflected over x-axis=-f(x)} \\ \text{horizontal shrink=f(}\frac{x}{b}\text{)} \\ \text{translation to the down=f(x)-d} \end{gathered}[/tex]The function becomes,
[tex]y=-|2x|-7[/tex]Answer:
[tex]y=-|2x|-7[/tex]You purchase a TV set that is originally valued at $1090. You receive a 45% discount on the purchase of a promo. Your sales tax rate is 7%. What is the total cost of the merchandise?
Answers
Answer:
The answer would be $641.47 I believe.
Step-by-step explanation:
3
y + yz + z + y use y = -2, and z = 6
Answers
Step by step
3y + yz + z + y
Use y= -2 and z = 6
Substitute values for y and z
3(-2) + (-2*6) + 6 + (-2)
Multiply first per PEMDAS rule
-6 + (-12) + 6 + (-2)
Add and subtract
= -14
Find the smallest distinct positive numbers that provide a counterexample to show the statement is false.The sum of any two different odd numbers plus any even number is odd.
Answers
The sum of two even or odd numbers ALWAYS gives an even number.
We'll run a test with 1,2 and 3.
Odd numbers: 1, 3
Even number: 2
Adding the odd numbers, we get 1 +3 = 4.
Adding it to the even number, we get 4 +2 = 1 + 3 + 2 =6
The general form of an odd number = 2n + 1
The general form of an even number = 2n
Adding 2 odd numbers give 2(2n + 1) = 4n + 2
Adding to an even number; 4n + 2 + 2n
Giving 6n + 2
Any number of the form above is an even number
The statement is thus false.
Brookner's Grocery Store sells bars of chocolate in cartons. There are 39 bars of
chocolates in each box. There are 25 boxes in each carton. Last weekend
Brookner's Grocery sold 48 cartons of chocolates. How many bars of chocolate did
the Brookner's Grocery sell last weekend? Explain your thinking.
Answers
1,200 boxes of chocolate
1,200 x 39 = 46,800 bars of chocolate.
Answer is 46,800.
Step - By - Step Explanation:
Multiply the cartons sold with how many boxes are in each carton to find how many boxes was sold.
Multiply the amount of boxes they sold with how much bars is in each box to find the solution.
use the figure to the right to find the value of PT
Answers
the figure show, the length between P and T and the length between T and Q, are equal.
so we can say PT=TQ
PT= 3x+2 and TQ=5x-6
so we can replace:
3x+2=5x-6
now we solve
2+6=5x-3x
8=2x
8/2=x=4
and finally, to find PT we replace x by 4
PT=3*4+2=14
So the answer is: PT=14
Question 5 of 8
What is the largest proper fraction less than 1 that can be made by using these
numbers only once: 1, 3, 6, 11 and 12?
Answers
The largest proper fraction that can be formed is 16/17
What is a fraction?
A fraction (from the Latin fractus, "broken") is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction has a numerator above a line (or before a slash like 12) and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.
The largest proper fraction that can be formed is
= 1+3+12/11+6 = 16/17
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Solve the equation 2x^3 – 5x² + x + 2 = 0 given that 2 is a zero of f (x) = 2x^3 – 5x^2 + x +2.
Answers
Hence, 2 is a zero of f(x). That is x - 2 is a factor of f(x).
So we can find
[tex]\frac{2x^3-5x^2+x+2}{x-2}[/tex][tex]\Rightarrow\frac{2x^3-5x^2+x+2}{x-2}=2x^2-x-1[/tex][tex]\text{Next we solve }2x^2-x-1=0[/tex][tex]\begin{gathered} \Rightarrow2x^2-x-1=0 \\ 2x^2+x-2x-1=0 \\ x(2x+1)-1(2x+1)=0 \\ \Rightarrow(x-1)(2x+1)=0 \\ \Rightarrow x-1=0\text{ or 2x+1=0} \\ \Rightarrow x=1\text{ or 2x=-1} \\ x=1\text{ or x =-}\frac{1}{2} \end{gathered}[/tex]Hence,
[tex]x=2,1,\text{ or -}\frac{1}{2}[/tex]What is the volume of this aquarium??in.in?in5 in.20 in.14 in.12 in.10 in
Answers
ANSWER :
2040 in^3
EXPLANATION :
From the problem, we have an aquarium.
If we divide the solid into two parts, we will have two rectangular prisms :
The big prism is 10 in by 12 in by 14 in.
The small prism is 5 in by 12 in by (20 - 14 = 6) 6 in
The volume formula of a prism is :
[tex]V=lwh[/tex]The volume of the solid is the sum of the volumes of two prisms.
That will be :
[tex]\begin{gathered} V=10(12)(14)+5(12)(6) \\ V=2040in^3 \end{gathered}[/tex](4xy³y⁴)(5x²y) expand and simplify
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
(4xy³y⁴)(5x²y)
Step 02:
[tex](4xy^3y^4)(5x^2y)=(4xy^7)(5x^2y)=20x^3y^8^{}[/tex]This is the solution.
[tex]20x^3y^8^{}[/tex]Suppose that an individual has a body fat percentage of 19.2% and weighs 153 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answers
Step 1
The given body fat percentage = 19.2%
The given body weight = 153 pounds
Required: To find how many pounds of his weight is made up of fat.
Step 2
Find out what 19.2% of his weight is
[tex]\begin{gathered} \frac{100}{19.2}=\frac{153}{x} \\ \text{where x represents the value of 19.2\% of his weight in pounds} \end{gathered}[/tex][tex]\begin{gathered} 100x=\text{ 153}\times19.2 \\ \frac{100x}{100}=\frac{2937.6}{100} \\ x=29.376\text{ pounds} \\ x\approx\text{ 29.4 pounds to the nearest tenth} \end{gathered}[/tex]Hence, the pounds of his weight made up of fat to the nearest tenth = 29.4 pounds
if cd = 23.19 and BD=176.8 find BC.Round your answer to the nearest tenth
Answers
we have the following:
[tex]BC=BD-CD[/tex]replacing:
[tex]\begin{gathered} BC=176.8-23.19 \\ BC=153.61 \end{gathered}[/tex]Therefore, the answer is 153.61 units