Answers
1) [tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex] bisect each other (given)
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)
3) [tex]\overline{BE} \cong \overline{ED}[/tex] (a bisector splits a segment into two congruent parts)
4) [tex]\angle BEA \cong \angle CED[/tex] (vertical angles are congruent)
5) [tex]\triangle BEA \cong \triangle DEC[/tex] (SAS)
6) [tex]\angle EBA \cong \angle EDC[/tex] (CPCTC)
7) [tex]\overline{AB} \parallel \overline{CD}[/tex] (converse of alternate interior angles theorem)
8) [tex]\angle DEA \cong \angle BEC[/tex] (vertical angles are congruent)
9) [tex]\triangle AED \cong \triangle BEC[/tex] (SAS)
10) [tex]\angle BCE \cong \angle EAD[/tex] (CPCTC)
11) [tex]\overline{BC} \parallel \overline{AD}[/tex] (converse of alternate interior angles theorem)
Related Questions
Please help!!!!! I’ve been stuck for like hours
Answers
[tex]10^2 + b^2=15^2\\\\100+b^2=225\\\\b^2=125\\\\b =\sqrt{125}\\\\b \approx \boxed{11.2}[/tex]
Maya invests $3,000 into a brokerage account
which earns 10% per year. In 15 years, how
much will Maya's investment be worth if
interest is compounded monthly? Round to the
nearest dollar.
Answers
Answer: $13361.76
Step-by-step explanation:
Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)
A = 3000(1+0.1/12)^12*15
A = 3000(1.0083)^180
A = 3000(4.4275)
A = 13361.76
Hope this helps!
After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly. The relationship between the elapsed time, t in seconds, and the number of bacteria, Bsecond(t) in the petri dish is modeled by the following function:
Answers
Using the given exponential function, we have that:
Every minute, the number of bacteria decays by a factor of 0.98.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the function is, for the amounts each second:
[tex]Bs(t) = 6000\left(\frac{15}{16}\right)^{t}[/tex]
The initial amount is of 6000 bacteria. After 60 seconds = 1 minute, the amount will be of:
[tex]Bs(60) = 6000\left(\frac{15}{16}\right)^{60} = 125[/tex]
The decay factor after 1 minute is:
(6000 - 125)/6000 = 98% = 0.98.
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What is the solution of
2x + 7 ≥ or 8 - x/3 ≤ 5
Answers
Answer: Second option from the top
Step-by-step explanation:
First, we will simplify the given inequalities.
2x + 7 ≥ 1
2x ≥ -6
x ≥ -3
-
8 - [tex]\frac{x}{3}[/tex] ≤ 5
- [tex]\frac{x}{3}[/tex] ≤ 5
- [tex]\frac{x}{3}[/tex] ≤ -3
x ≥ 9
Now, we will graph them. See attached.
If measure of AC= 50 degrees, then…
1) How many degrees measures the central angle O?
2) How many degrees measures the inscribed angle B?
Answers
1) Because [tex]\angle AOC[/tex] is a central angle, the answer is 50 degrees.
2) By the inscribed angle theorem, the answer is 25 degrees.
The inverse of F(x) is a function.
-5
OA. True
OB. False
Answers
The inverse of any function F(x) is also a function.
A function is an abecedarian notion in mathematics and computer programming. In both contexts, a function is a regulation or relationship that maps input values to corresponding output values. It takes one or more input values, performs a set of operations or calculations, and produces a single output value.
There are many types of functions such as trigonometric function, logarithmic function, exponential function, and so on.
If a function f(x) gives output y then its inverse will be [tex]f^{-1}(y)[/tex] and will return x as output.
So, the statement is true.
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A(N) _______________ questions require respondents to select one or more response options from a set of predetermined choices. Group of answer choices
Answers
Closed-end
You can answer "yes" or "no" to the completed question. Or, the number of answers is limited (eg A, B, C, or all of the above). Closed-end questions are often suitable for voting, as response rates are high when users don't have to type too much.
Closed-end questions are defined as question types that require respondents to choose from a specific set of predefined answers. B. Between "yes/no" or fixed multiple-choice questions. In a typical scenario, closed-end questions are used to collect quantitative data from respondents.
An indefinite definition represents a situation or question with a predetermined number of results. An example of a closed ending is the question "Do you need help?" This usually has only four answers-yes, no, maybe, or not.
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if there are 22 successful outcomes in a sample with a size of 50, what is the sample proportion?
Answers
Explication…
The sum of two numbers is 8 and sum of their reciprocal is 8/15. Find the numbers.
Answers
x = 8 - y
And,
1/x + 1/y = 8/15
y + x/xy = 8/15
8/xy = 8/15
xy = 15
( 8 - y)y = 15
8y - y^2 = 15
y^2 - 8y + 15 = 0
y^2 - 3y - 5y + 15 = 0
y(y - 3) - 5( y - 3) = 0
(y - 3) (y - 5) = 0
y = 3 & x = 5
Thus, the two numbers are 3 and 5.
Answer:
The 2 numbers are 3 and 5.
Step-by-step explanation:
x + y = 8
1/x + 1/y = 8/15
From first equation y = 8 - x so
1/x + 1 / (8-x) = 8/15
Multiply through by the LCM 15x(8-x):-
15(8 - x) + 15x = 8x(8-x)
120 - 15x + 15x = 64x - 8x^2
8x^2 - 64x + 120 = 0
x^2 - 8x + 15 = 0
(x - 3)(x - 5) = 0
x = 3 or 5
so y = 8-3 = 5 or 3.
A pencil cost $1.20 and a pen cost $2.90. Jasmiah bought an equal number of such pencils and pens. She spent $32.30 more on the pens than on the pencils. How many pencils and pens did she buy altogether?
Answers
Answer:
38
Step-by-step explanation:
Let x be the number of pencils bought.
Let y be the number of pens bought.
Given information from the question:
x = y - equation 1
2.9y - 1.2x = 32.30 - equation 2
From here we can use the substitution method in solving simultaneous equations to find x and y. We will substitute equation 1 into equation 2.
2.9y - 1.2y = 32.30
1.7y = 32.30
y = [tex]\frac{32.3}{1.7} \\= 19[/tex]
Now since we know number of pens = number of pencils,
x = 19
Total Pencils and Pens bought = x + y = 19 + 19 = 38
Answer:
19
Step-by-step explanation:
hope it helps.good day.
Kelly offers to pay for 9 of her friends to play laser tag, but 2 of them don't want to play.
if laser tag costs $4 per person, how much will Kelly spend on her friends /
Answers
Answer:
$28Step-by-step explanation:
If she offers to 9, but 2 reject, that means she paid for 7 friends.
If each friend costs $4, multiply 4 by 7.
The answer is $28
Hope this helps! (:
Solve for p and k. For 50 POINTS!!
Answers
Answer:
P = 55°
K = 27°
Step-by-step explanation:
55° + 98° + c = 180°
153° + c = 180°
c = 27°
since C is opposite K, K = 27°
Since 55° is opposite P, P = 55°
We can check this by adding up the values of P, K, and 98
27°+55°+98° = 180°
Jorge worked 6 hours of overtime this week but has decided to take time off instead of overtime pay. How many hours will Jorge receive in time off from work
Answers
Jorge will receive 9 hours in time off from work.
How many hours will Jorge get to take time off?
It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.
Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.
As a result, the time off he receives from work = [tex]1\frac{1}{2} (6)[/tex] hours
[tex]=\frac{3}{2}(6) = 9 hours[/tex]
Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.
What is Fair Labor Standards Act?
The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.
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Please help soon! I have a trig question...
Answers
The value of x will be 33 units approximately. Thus, option A is correct.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We need to find the value of x
so first
Tan 60 = Perpendicular / 11√6
Perpendicular = 1.732 (11√6)
Perpendicular = 46.66
Then,
Sin 45 = Perpendicular / x
Sin 45 = 46.66/ x
x = 33.00
So, the value of x will be 33 units approximately.
Thus, option A is correct.
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Which of the following is the equation for the graph shown
Answers
Answer:
I don't see a list of equations. See the attached image for an equation that works well.
Step-by-step explanation:
A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer to all of them, Tysm!
Answers
#1
No
#2
We can see f(1) has 3 values so it's not a function as it's failed in vertical line test
#3
f(10) has two values -2 and 11
So not a function
#4
As per definition of function
every domain has an unique rangeSo it's not a function
and the other answer that you didnt see is ( 2+3×2+5+6+7+9 units ) .
pls give me the answer .. and ty <3 .
Answers
There is a rule for finding perimetre of all polygons that perimetre is the sum of all the side's lengths ; according to this rule add the length of the sides of this polygon and you'll get the answer , the answer is the choice that you've written ( 2+3×2+5+6+7+9 ) or ( 2+3+3+5+6+7+9 ) both are correct because 3+3 is same as 3×2
perimetre is 2+3×2+5+6+7+9 = 35 units
HOPE IT HELPS
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What are some steps you can take to protect yourself from predatory lenders?
Answers
Answer:
How To Protect Against Predatory Lending
1) Consider alternatives to borrowing
2) Borrow federal first
3) Check your credit before applying for private loans
4) Shop around when looking for a loan
Explanation:
Definition: "Imposing unfair and abusive loan terms on borrowers." - FDIC
Write a piecewise-defined step function f(x) that has the following characteristics:
f(x) has more than one x intercept.
The domain of f(x) is the real numbers.
The range of f(x) consists of four unique integers.
Answers
Here use general math mind
F(x) has more than one x inetercept .
We shall take one quadratic function in which will give 2 intercepts(Real)Domain is for real numbers
Four unique numbers?
Add 4 constants for 4 unique definations and that shouldn't fall under quadratic regionLets see
[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}[/tex]
Has 2 x interceptsFor -2
y=(0)²=0(-2,0)For 0 it's (0,0)
And for extra ,it's discontinuous on x=0
2. Given the equation of a line, y = 1/5x, the slope is:
Answers
Answer:
1/5
Step-by-step explanation:
The slope-intercept form looks like [tex]y=mx+b[/tex] where b is the y-intercept and m is the slope. m is the slope because if you increase x by 1, the value y increases by m, and if you increase x by 1 again, the y-value will increase by the value of m, because it's being multiplied. b is the y-intercept since the y-intercept is when x=0 so mx will become m(0) which is just 0 leaving b by it self. In this case you have y=1/5x so if you were to start with 0 as x the value of y is 0. Now increase it by 1 so x becomes 1, the value of y becomes 1/5x, now increase it by 1 again so x becomes 2, the value of y is 2/5x, so as you can see the function is just increasing by 1/5 so that's the slope, so essentially whatever the coefficient of x is (the number in front of the variable x), is the slope
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{Slope = 1/5}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{y = 1/5x}[/tex]
Find: [tex]\textsf{The slope of the line}[/tex]
Solution: In order to determine the slope of the line we need to see how the slope-intercept form compares to this expressions. The slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. In this case we have no y-intercept therefore we do not have a b. However, our slope is equal to 1/5 as it fits perfectly with the form that was provided.
How can the basic fact help find 3,000 divided by 5?? I need help
Answers
Answer:
3000/5 = 600
Step-by-step explanation:
Every multiplication fact is equivalent to two (2) division facts:
a·b = c ⇒ c/a = b and c/b = a
Multiplication or division by 10 involves moving the decimal point one place to the right or left (respectively).
Recasting the problemThe division ...
[tex]\dfrac{3000}{5}[/tex]
is fully equivalent to ...
[tex]\dfrac{30}{5}\times 100[/tex]
Using the basic factWe assume your "basic fact" is 5×6 = 30. In accordance with the above equivalence to division problems, this tells you ...
[tex]\dfrac{30}{5}=6\\\\\dfrac{30}{5}\times100 = 6\times100\\\\\dfrac{3000}{5}=600[/tex]
What are domain and range of these two and how step by step please?
Answers
Answer:
Step-by-step explanation:
[tex]\sf f(x) = \dfrac{1}{Sin \ x}[/tex]
f(x) does not contain values where sin x = 0. Sin x is 0 at integral multiples of π.
Domain = R - nπ , n is integers.
The range of Sin x is [-1 , 1] and in this range we cannot find 1/sin x .
Range = (-∞, -1] U [1,∞)
[tex]\sf f(x) =\dfrac{1}{Cos x}[/tex]
f(x) does not contain values where Cos x = 0 . Cos x is 0 at integral of multiples of (π/2)
[tex]\sf Domiain =R -\dfrac{(2n+1)\pi }{2}[/tex]
The range of Cos x is [-1,1] and in this range we cannot find 1/Cos x.
Range = (-∞, -1] U [1,∞)
Given: S is the midpoint of QR, QR¯⊥PS¯ and ∠RSP and ∠QSP are right angles.
Prove: PR≅PQ
Answers
ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.
What is the CPCTC Theorem?If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.
Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)
∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)
SP ≅ SP based on the reflexive property (one pair of congruent sides)
Therefore, ΔRSP ≅ ΔQSP by SAS.
Conclusively, PR ≅ PQ by CPCTC theorem.
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Please assist me with this question
Answers
Answer:
? = 45
Step-by-step explanation:
the inner and outer triangles are similar ( AA postulate )
Then the ratios of corresponding sides are in proportion, that is
[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex] , that is
[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )
[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )
7(105 + ? ) = 1050 ← distribute parenthesis on left side
735 + 7? = 1050 ( subtract 735 from both sides )
7? = 315 ( divide both sides by 7 )
? = 45
what does 160=7x+6 equal to?
Answers
Answer:
x=22
Step-by-step explanation:
7x+6=160.
Lets start by moving 6 over to the other side. We can do this by subtracting 6 from both sides of the equation.
7x+6-6=160-6
7x=154
Now, let's isolate x by getting rid of the 7. The 7 is being multiplied with x, so to get rid of it we have to divide both sides by 7.
7x/7 = 154/7
x=22
Look Below :
Step-by-step explanation:
160 - 6 = 7x
154 = 7x
Or
7x = 154
x = 22
32 less than 3/7 of a number is 11/35 of that number. Find the number.
Answers
Step by step
We know 32 less than is subtraction -32
We know 3/7 of a number is 3/7x
We know “is” is equal =
We know 11/35 of a number is 11/35x
So
3/7x - 32= 11/35x
Now solve by first by combining like terms
Change the denominator of 3/7 to match the other fraction so we can combine. 7x5=35 so we do the same to the numerator, 3x5.
3. 15
____. _____
7. 35
3/7x -32 = 11/35x
15/35x - 32 = 11/35x
Subtract 15/35x from both sides to combine like terms
-32 = -4/35x
Now divide both sides by -4/35 to solve for x
To divide a fraction flip it and multiply
( -35/4 )(-32)
X= 280
You can check your work by substituting your number for x into your equation
3/7 (280) -32 = 11/35 (280)
120 - 32 = 88
88 = 88
Answer:
Step-by-step explanation:
Let "a number" be x.
"3/7 of a number" means (3/7)x
"32 less" means - 32
Thus, "32 less than 3/7 of a number" means (3/7)x -32
"is 11/35 of that number" means = (11/35)x
Put these together and we get:
(3/7)x -32 = (11/35)x
(3/7)x - (11/35)x = 32 Rearrang to get the x on one side
We need to change "(3/7)x - (11/35)" so that the two terms have a common denominator.
If we multiply the first term by (5/5) [which is equal to 1], we get:
(5/5)(3/7)x or
(15/35)x
We can now write:
(15/35)x - (11/35)x = 32
(4/35)x = 32
Multiply both sides by (35/4)
(35/4)(4/35)x = (35/4)(32)
x = (35)(8)
x = 280
Points S, U, and T are the midpoints of the sides of TrianglePQR.
Triangle S U T is inside of triangle P Q R. Points S, U, and T are the midpoints of triangle P Q R.
Which statements are correct? Check all that apply.
One-halfQP = UT
One-halfTS = RQ
SU = PR
SU ∥ RP
UT ⊥ RP
Answers
Option A and D. The statements that are correct here are
1/2 QP = UTSU ║ RPHow to arrive at the statements about the midpointsIf the two points UT and QP are parallel, then UT is going to be the half of QP. This would be due to a scale factor of 1/2.
Then at a midpoint T is that of PR. SU is parallel to RP. SU is half of RP due to as scale factor of 1/2.
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Answer: A and D E2020
Step-by-step explanation:
E2020 geometry B!! :)
PLEASE HELPPP ASAPP
I WILL MAKE YOU BRAINLIEST
Answers
The transformation that's illustrated in the diagram is translation.
What is transformation?It should be noted that transformation simply means the manipulation of that moves a shape from a space to another.
In this case, the transformation that's illustrated in the diagram is translation. This is the sliding of try shape across certain number of spaces.
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construct a right angle triangle abc where m b is equal to 90 degree BC is equal to 4.5 cm and ac is equal to 7 cm
Answers
The triangle will be computed based on the information illustrated below.
How to compute the triangle?The steps needed for the construction will be:
Draw a segment XY.
Locate B, C on XY such that BC = 4.5cm.
Construct a line segment such that B = 90°.
With C as center and radius 7cm, draw a arc cutting BD at A.
Then, the required triangle ABC will be gotten.
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Points U, M, And D are collinear with U between U and D.
Given:
UM=5x+30
MD=3x+80
UD=10x+20
What is x
Answers
The value of x from the given equation is 5/3
How to determine the valueSince the three points are collinear to U, they are on a straight line which equals 0
Then we have,
UM + UD = MD
5x+30 + 10x+20 = 3x+80
Collect like terms
5x + 10x + 50 = 3x + 80
15x - 3x = 80 - 50
12x = 30
x = 30/12 = 15/6 = 5/3
Thus, the value of x from the given equation is 5/3
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