Answer:The distances from D to the both sides(AB and AC) of the triangle are 4 ft.
explanation:
In the diagram below, ABC is a triangle in which ∠CAB = 60°
As, AD is the angle bisector of ∠CAB, that means ∠CAD = ∠DAB = 30°
The distance from D to side AC is DE and distance from D to side AB is DF. That means both ∠AED and ∠AFD are right angle.
Given that, the length of AD = 8 ft.
So, in right angle triangle AED.....
Also, in right angle triangle AFD....
So, the distances from D to the both sides(AB and AC) of the triangle are 4 ft.
The distance from point D to the sides of the triangle is 4 feet.
What is an angle bisector?An angle bisector is defined as a line that divides an angle into two equal angles.
Draw the given angle first, then cut it in half, and then draw the angle's bisector.
Given that
In △ABC, m∠CAB = 60°,
AD is the angle bisector of ∠BAC with D ∈ BC
and AD = 8ft.
Angle CAB is 60 degrees, and AD bisects it, so angles CAD and BAD are each 30 degrees.
Let E be the point on AB for which DE is perpendicular to AB.
Then triangle ADE is a 30-60-90 right triangle with hypotenuse 8;
⇒ sin30° = DE/AD
⇒ 1/2 = DE/8
⇒ DE = 4
So the short-leg DE has a length of 4.
But since DE is perpendicular to AB, that is the distance of D from side AB.
So the distance of point D from sides AB and AC is 4.
Thus, the distance from point D to the sides of the triangle is 4 feet.
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Find (1)14x⁴/y ÷ 7x/3y⁴ (2)x²-16/ x+4 ÷ x-4/x+4 (3)
Answer:
I am not sure I am so so so sorry My friend
- During the month of September Hailynn earns $45.00 delivering newspapers. - She earns the same amount for October and November. - However, after that she only earns $39.50 for each month until June during which she earns $45.00 again. -How much money does Hailynn earn from September through June?
Answer:
366.50
Step-by-step explanation:
hope this helps if doesn't help than srry
Answer:
$417Step-by-step explanation:
Sep = Oct = Nov = Jun = $45Dec = Jan= Feb = Mar =Apr = May = $39.50Total:
4*45 + 6*39.50 = $417The value of √ 8 is between which two integers?
a. 2 and 3
b. 3 and 4
c. 7 and 9
d. 49 amd 81
Lines b and a are intersected by line f. At the intersection of lines f and b, the bottom left angle is angle 4 and the bottom right angle is angle 3. At the intersection of lines f and a, the uppercase right angle is angle 1 and the bottom left angle is angle 2. Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f? m∠4 = 110° and m∠3 = 70° m∠1 = 110° and m∠2 = 110° m∠1 = 110° and m∠3 = 70° m∠2 = 110° and m∠3 = 110°
Answer:
m∠1 = 110° and m∠3 = 70°
Step-by-step explanation:
The angles at the intersection of a transversal and parallel lines are supplementary angles.
The true statement is: [tex]\mathbf{\angle 1 = 110^o}[/tex] and [tex]\mathbf{\angle 3= 70}[/tex]
From the complete question, we have:
[tex]\mathbf{\angle 1 = 110^o}[/tex]Angle 1 is supplementary to angle 3This means that:
[tex]\mathbf{\angle 1 + \angle 3= 180^o}[/tex]
Substitute [tex]\mathbf{\angle 1 = 110^o}[/tex]
[tex]\mathbf{110 + \angle 3= 180^o}[/tex]
Subtract 110 from both sides
[tex]\mathbf{\angle 3= 180 - 110}[/tex]
[tex]\mathbf{\angle 3= 70}[/tex]
Hence, the true statement is: [tex]\mathbf{\angle 1 = 110^o}[/tex] and [tex]\mathbf{\angle 3= 70}[/tex]
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Which of the following equations is equal to y= 2x + 3
Answer:
i think its y = 3x + 1
Let p, q, and r be the following propositions:
The water is warm.
People are swimming.
The waves are not big.
Express each of the following sentences using p, q, r, and logical connectives: and, or, not.
A) The water is warm and people are swimming.
B) If people are not swimming, then the water is not warm or the waves are big.
C) If the waves are big and the water is warm, then the people are not swimming.
Answer and Step-by-step explanation:
P= the water is warm.
q = people are swimming.
r = the waves are not big.
Logical connectives are:
Not p = ¬p
P or q = p ∨ q
P and q = p ∧ q
If p, then q = p → q
P if and only if
q = p ↔ q
By using p, q, r and logic connectives and or not, we have:
1-water is warm and people are swimming.
= p ∧ q
2- If people are not swimming then water is not warm or waves are big.
= ¬q → ¬p v ¬r
3- if waves are big, water is warm then people are not swimming
= ¬r ∧ p → ¬q
PLEASEE HELP FASTT Water flowed out of a tank at a steady rate. A total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. Which expression determines the quantity of water leaving the tank per hour?
StartFraction 17 over 4 EndFraction divided by StartFraction 36 over 2 EndFraction
StartFraction 36 over 2 EndFraction divided by StartFraction 17 over 4 EndFraction
StartFraction 17 over 4 EndFraction divided by StartFraction 37 over 2 EndFraction
StartFraction 37 over 2 EndFraction divided by StartFraction 17 over 4 EndFraction
Answer:
The answer would be D, 37/2 divided by 17/4
Explanation:
I did the test.
Answer: The answer would be D, 37/2 divided by 17/4
Step-by-step explanation:
Yes I admit I did copy and paste the answer above I did this because other people would copy it and would not give credit. Credit Goes to raydenhallstar
Jack had 3.5870 units of rice. How many units of rice did he have to
the nearest hundredth?
label optional
i need help right away
Answer:
3.59
Step-by-step explanation:
3 is a whole number, 5 is in the tenths place, 8 is in the hundreths place, and 7 is in the thousandths place. Eventhough 8 is in the tenths place, we have to apply a certain rule to get the exact answer. if the number in the next place (the thousandths place so 7) is greater than 5, add 1 to the tenths place number, but if the number is less than 5, leave it as it is. The 8 will round to 9 because 7 is greater than 5.
What is the solution to the equation 1/4x+2=-5/8x-5
O X=-8
O x=-7
O X= 7
O X=8
Answer:
x = -8
Step-by-step explanation:
1/4x+2=-5/8x-5
Add 5/8 x to each side
1/4x + 5/8 x+2=-5/8x + 5/8x-5
1/4x + 5/8x +2 = -5
Subtract 2 from each side
1/4x + 5/8x +2-2 = -5-2
1/4x + 5/8x = -7
Get a common denominator of 8
1/4 *2/2 x + 5/8x = -7
2/8x + 5/8x = -7
7/8x = -7
Multiply each side by 8/7
8/7 * 7/8x = -7*8/7
x = -8
The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is y hat = -959.00 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.)
Answer:
y hat = 2114.20 + 18.96x
Step-by-step explanation:
Given the least square regression model equation:
y hat = -959.00 + 8.60x
weld diameter x ; shear strength y (in pounds)
1 lb = 0.4536 kg
To express shear strength y in kilogram:
y is multiplied by 0.4536
(y hat × 0.4536) = -959.00 + 8.60x
Divide both sides by 0.4536
(y hat × 0.4536) / 0.4536= (-959.00 + 8.60x) / 0.4536
y hat = 2114.1975 + 18.959435x
y hat = 2114.20 + 18.96x
The equation of the least-squares line when y is expressed in kilograms is y = 2114.20 + 18.96x.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more two variables.
The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern.
The least-squares line is [tex]\rm y = -959.00 + 8.60x[/tex]. Because [tex]\rm 1\ lb = 0.4536 \ kg[/tex] the strength observations can be re-expressed in kilograms through multiplication by this conversion factor:
New [tex]\rm y = 0.4536 (old \ y)[/tex].
y is multiplied by 0.4536, then we have
[tex]\rm y \times 0.4536 = -959.00 + 8.60x[/tex]
Then divide both sides by 0.4536, then we have
[tex]\rm y = \dfrac{-959.00 + 8.60x}{0.4536}\\\\\\\rm y =2114.20+ 18.96 x[/tex]
More about the linear system link is given below.
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Five friends share three pizzas that cost $12.75 each. How much does each friend pay?
Answer:
each friend paid $7.65
Step-by-step explanation:
(3*12.75)/5
38.25/5
7.65
Answer:
2.25
Step-by-step explanation:
Simplify the radical start root 18a^9 end root
Answer: D, 3a^4 sqrt 2a
Step-by-step explanation:
I just did it on edgenuity :)
Can someone please help, ty!!
There are 7 teachers going to a 5 day math conference if registration is $225 for each teacher how much do the teachers pay
Answer:
1,575 dollars
Step-by-step explanation:
7 multiple 225 is 1,575
Compute the largest n for which 2^n is a divisor of 80!
Answer:
The largest n for which [tex]2^{n}[/tex] is a divison of 80 is 4.
Step-by-step explanation:
Numbers can be composited, that is, a product of prime numbers, or primer numbers themselves. A entire number is a divisor of another entire number if result is an entire number.
As first step we need to decompose 80 as a product of prime numbers, whose procedure is presented below:
1) [tex]80[/tex] Given
2) [tex]40\times 2[/tex] Definition of multiplication.
3) [tex]20\times 2\times 2[/tex] Definition of multiplication.
4) [tex]10\times 2\times 2\times 2[/tex] Definition of multiplication.
5) [tex]5\times 2\times 2\times 2\times 2[/tex] Definition of multiplication.
6) [tex]5\times 2^{4}[/tex] Definition of power/Result.
In a nutshell, the largest n for which [tex]2^{n}[/tex] is a divison of 80 is 4.
carlita made 2 kinds of lemonade for her friends to enjoy at a fall celebration. After the celebration, she had 6.8 liters of pink lemonade left over and 10.2 liters of yellow lemonade left. About how many more liters of yellow lemonade were leftover to the nearest liter
Answer:
17 liters of pink lemonade
Rays PQ and PR are perpendicular. What is the value of X?
A)40
B)70
C)80
D)110
Answer: 2.70
Step-by-step explanation 20+70=90
Write an equation of the line, in point-slope form, that passes through points (3, –10) and (–5, –2).
A. y – 10 = x – 3
B. y + 10 = –(x – 3)
C. y + 10 = 2(x – 3)
D. y – 10 = one half(x – 3)
Answer:
b. y+10=-(x-3)
Step-by-step explanation:
please help me asap
Answer:
1/125
-5.06 is less than -5.6
-1 3/4 is less than 3/4
2 3/4 is less than 2 4/6
Sorry my handwriting is so bad!!
consider the equations 3x+2=14and2+3x=14. do they have the same solution? why or why not?
Answer:
yes
Step-by-step explanation:
Yes, because x=4 so 3x=12 so 12+2=14
chance paid $15.52 for stamps so he could mail thank you notes for wedding gifts. the number of $0.05 stamps was 26 more than twice the number of $0.39 stamps. How many $0.39 stamps, and $0.05 stamps were purchased?
Answer:
I'm pretty sure the number of stamps purchase is about 132 stamps
Pilar wanted to use estimation to solve a decimal addition problem. She correctly used estimation to rewrite the problem as 12+3+5+6. What could her original problem have been?
A. 12.38+4.45+4.14+6.7
B. 12.5+3.05+5.23+0.6
C. 11.5011+3.6+5.17+5.7
D. 11.75+ 3.299+5.31+6.27
Answer:
D
Step-by-step explanation:
In answer D all of the numbers round to the numbers in the equation if you use the rule where numbers 5 and greater round-up while4 and below round down.
11.75 rounds up to 12
3.299 rounds down to 3
5.31 rounds down to 5
6.27 rounds down to 6
Answer:
Its D
Step-by-step explanation:
Im doing edge 2021 peeps this is the Adding and Subtracting Decimals quiz :)
I have a question attached pls help
Answer:
10.35oz
Step-by-step explanation:
Cuz if you do the math 16 times 14 equals 224 and 15.5 times 10 equals 155 so if you minus 155 from 224 then you have 69 square inches which you multiply by 0.15 which thus gets you the answer 10.35
For which function is 3 NOT an element of the range?
Answer:
B: y = -(-x)^2
Step-by-step explanation:
The y value will always be negative and therefor it can never be 3
The solution is Option B.
The function with equation y = - ( -x )² will not have a range of 3 because the function always returns a negative value
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the equation be y = -2x + 4
when x = 1/2
y = -2 ( 1/2 ) + 4
y = -1 + 4
y = 3
So , the value of y = 3
b)
Let the equation be y = - ( - x )²
For all the values of x , the value of y will be negative
So , the value of y ≠ 3
c)
Let the equation be y = x⁵
when x = 3^ (1/5)
y = ( 3^ (1/5) )⁵
y = 3
So , the value of y = 3
d)
Let the equation be y = 3
The value of y = 3
Hence , the equation y = - ( - x )² will not have a range of 3
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A recent college graduate is planning to take the first three actuarial examinations in the coming summer. She will take the first actuarial exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam is .9. If she passes the first exam, then the conditional probability that she passes the second one is .8, and if she passes both the first and the second exams, then the conditional probability that she passes the third exam is .7.
(a) What is the probability that she passes all three exams?
(b) Given that she did not pass all three exams, what is the conditional probability that she failed the second exam?
Answer:
(a) 0.7
(b) [tex]\frac 13[/tex]
Step-by-step explanation:
Let [tex]E_1, E_2,[/tex] and [tex]E_3[/tex] be the events of passing the 1st, 2nd, and 3rd exam individually.
Given that [tex]P(E_1)=0.9\;\cdots(i)[/tex]
where [tex]P(E_1)[/tex] denotes the probability of passing the 1st exam.
Condition for passing the second exam is, at first, the candidate must have to pass the 1st exam.
So, [tex]P\left(\frac{E_2}{E_1}\right)=0.8\;\cdots(ii)[/tex]
where [tex]P(E_2/E_1)[/tex] denotes the probability of passing the 2nd exam when she already passed the 1st exam (given, 0.8).
Similarly, as the conditional probability of passing the 3rd exam is 0.7, and the condition for this is, at first, she must have to pass the 1st and 2nd exam. i.e,
[tex]P\left(\frac{E_2}{P(E_2/E_1)}\right)=0.7\;\cdots(iii)[/tex]
(a) For passing all the exams, the condition is, at first, she has to pass the 1st and 2nd exam, then she has to pass the 3rd exam too. The probability for this conditional has been given as 0.7.
So, the probability that she passes all three exams is 0.7.
(b) Given that she didn't pass all three exams that means she either failed in 1st exam or she passed the 1st and failed in 2nd exam or she passed both 1st and 2nd but failed in the 3rd exam.
Let F be the event that she didn't pass all three exams. So,
[tex]P(F)=(1-P(E_1))+\left(1-\frac{P(E_2)}{P(E_1)}\right)+\left(1-\frac{P(E_2)}{P(E_2/E_1)}}\right)[/tex]
[tex]\Rightarrow P(F)=(1-0.9)+(1-0.8)+(1-0.7)=0.6[/tex]
Lef [tex]F_2[/tex] be the event that she failed the 2nd exam, so
[tex]P(F_2)=1-\frac{P(E_2)}{P(E_1)}[/tex]
[tex]\Rightarrow P(F_2)=1-0.8=0.2[/tex]
So, the conditional probability that she failed the 2nd exam is
[tex]P\left(\frac{F_2}{F}\right)=\frac{P(F_2)}{P(F)}[/tex]
[tex]\Rightarrow P\left(\frc{F_2}{F}\right)=\frac{0.2}{0.6}=\frac{1}{3}=0.33[/tex]
Write the equation of a line perpendicular to and = 2 x – 5 that passes through the point (2,-5).
Answer: y = -x/2 -4
Step-by-step explanation:
I hope you mean perpendicular to y= 2x - 5 and that passes through (2, -5)
Take the reciprocal of the original slope. Reverse the slope to negative. Substitute the values of the given coordinates for x and y in the base equation y =-x/2 and solve for "b" the new y-intercept.
-5 = - (2)/2 +b
-5 = -1 +b
-5+1 = b
-4 = b
you can paint 4 boxes in 30 minutes. at this rate, how many boxes can you paint in 5 hours?
3 − 4( + 1) = 2 − 1
Answer:
2
Step-by-step explanation:
-4(+1)= -4
3-4= -1
-1=2-1
-1=1
1+1=2
CAN SOMEONE HELP ME PLEASE (ASAP)
Answer:
what do you need help with
Step-by-step explanation:
Consider the figure below.
Find the value of x.
Answer:
x = 5
Step-by-step explanation:
When two straight lines intersect, four angles are formed. The angles that are directly opposite of each other are equal. Since the angles are equal set the values equal to each other and solve for x.
5x - 5 = 2x + 10
5x - 5 - 2x = 2x + 10 - 2x
3x - 5 = 10
3x - 5 + 5 = 10 + 5
3x = 15
3x/3 = 15/3
x = 5
