What is the missing reason in the proof? Given: ∠ABC is a right angle, ∠D B C is a straight angle Prove: ∠ABC ≅ ∠A B D A horizontal line has points D, B, C. A line extends vertically from point B to point A. Angle A B C is a right angle. definition of angle bisector segment addition property definition of congruent angles transitive property
Answer:
Definition of Congruent angles.
Step-by-step explanation:
Given
See attachment
Required
Complete the proof at step 8
At step 8, we have:
[tex]\angle ABC \cong \angle ABD[/tex]
When the sign [tex]\cong[/tex] is used, it means congruence
In other words;
ABC and ABD are congruent
Hence, the missing statement at step 8 is: Definition of Congruent angles.
Answer:
ABC and ABD are congruent
Step-by-step explanation:
EFGH is an isosceles trapezoid and EFGI is a parallelogram. If m∠IEF = 36°, then m∠HGI = ° (Blank 1).
The base angles of an isosceles trapezoid are equal; For EFGI to be a parallelogram, the measure of [tex]\angle HGI[/tex] is: 108 degrees
Given that:
[tex]\angle IEF = 36^o[/tex]
IEF and GHI are the base angles of the trapezoid.
So:
[tex]\angle GHI = \angle IEF = 36^o[/tex]
Also:
[tex]\triangle GHI[/tex] is an isosceles triangle.
This means that:
[tex]\angle GHI = \angle HIG = 36^o[/tex] --- base angles of an isosceles triangle
So:
[tex]\angle GHI + \angle HIG + \angle HGI = 180[/tex] --- sum of angles in a triangle
Substitute known values
[tex]36 + 36+ \angle HGI = 180[/tex]
[tex]72 + \angle HGI = 180[/tex]
Collect like terms
[tex]\angle HGI = 180-72[/tex]
[tex]\angle HGI = 108[/tex]
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The triangle below is isosceles. Find the length of side x in simplest radical form with
a rational denominator.
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V10
Answer: 2=
=
Submit Answer
Answer:
x=2*sqrt(5)
Step-by-step explanation:
Since the triangle is isosceles, the other side of the triangle is sqrt(10) too. By using Pythagoras theorem, we have 10+10=x^2, x=2*sqrt(5).
please help me!!
how many times does 10% go into 34,950,101?
Answer:
10
Step-by-step explanation:
If you multiply 10% of 34,950,101 by 10, you will get the value of 34,950,101.
16 + 28 = ___ ´ (4 + 7).
Answer:
Solution given:
16+28=44
(4+7)=11
Answer:
The solution is 4
Step-by-step explanation:
Step 1: Find the correct answer
I'm not really sure what you are asking but I will give it a shot.
16 + 28 = ___ (4 + 7)
44 = ___ (11)
44 / 11 = ___ (11) / 11
4 = ___
Answer: The solution is 4
Write the ratio of detective headphones to total headphones in the sample. Then write the ratio as a decimal and as a percent
The question given is incomplete as the information about the headphones isn't given.
However, we can solve the problem by using hypothetical values.
Answer:
Kindly check explanation
Step-by-step explanation:
Given
Write the ratio of detective headphones to total headphones in the sample. Then write the ratio as a decimal and as a percent.
Let :
The number of defective headphones = 10
The total number of headphones on the sample = 50
To express as a ratio :
Defective headphones : total headphones
10 : 50 = 1 : 5
To express as a percentage ;
1 / 5 * 100% = 20%
Please hurry I will mark you brainliest
What is the slope of the line with an x-intercept of 4 and a y-intercept of -3?
the answer to this question is the slope is 43
Answer:
Therefore, the slope is 3/4
Step-by-step explanation:
An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)
Likewise, an
y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)
Now we have two points(4,0) (0,-3)
To find the slope given two points, we use the formula
rise÷run , or y2−y1÷x2−x1 .
Plug in the given points into the formula
-3-0/0-4
-3/-4
3/4
Therefore, the slope is 3/4
Hope this helps!
The Lewis family and the Martin family each used their sprinklers last summer. The water output rate for the Lewis family's sprinkler was 30L per hour. The water output rate for the Martin family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total water output of 1350L. How long was each sprinkler used
Answer:
Martin family: 20 hours
Lewis family: 35 hours
Step-by-step explanation:
Let's say that the Lewis family sprinklers were out for L hours and the Martin family's sprinklers were out for M hours. We know that for each hour that the Lewis family sprinkler was on, 30L of water was put out. We can thus write the Lewis family sprinkler water output as 30L per each hour of L = 30 * L. Similarly, the Martin family sprinkler water output = 15 * M .
We know that the total hours for the sprinklers is 55, so L + M = 55. The total water output for the sprinklers is the sum of the sprinkler outputs, so 30 * L + 15 * M = 1350
L + M = 55
30 * L + 15 * M = 1350
One way to solve this would be to solve for L in the first equation and substitute that into the second
subtract M from both sides in the second equation
55 - M = L
30 * (55-M) + 15 * M = 1350
30 * 55 - 30 * M + 15 * M = 1350
1650 - 15M = 1350
subtract 1650 from both sides to isolate the M and its coefficient
-15M = -300
divide both sides by -15 to isolate M
M = 20
L = 55-20 = 35
upon receiving your first salary, you deposited 3000 taka monthly in a fund for your future for 18 years. the fund earns 6% interest rate compounded monthly. after 18 years, you want it to make payments at the end of every quarter for five year 4.5% compounded quarterly, what is the amount of each annuity payment to you?
The Annuity payment will be "65,209.35 Taka". A further solution is provided below.
Given:
Monthly payment,
= 3000 Taka
Interest rate,
= 6% (compounded monthly)
Time,
= 18 years
The Future value will be:
→ [tex]FV = PMT\times \frac{((1+r)^{nt}-1)}{r}[/tex]
By putting the values, we get
[tex]=3000\times \frac{((1+\frac{6}{12\times 100} )^{12\times 18}-1)}{\frac{6}{12\times 100} }[/tex]
[tex]=3000\times \frac{((1+\frac{6}{1200} )^{216}-1)}{\frac{6}{1200} }[/tex]
[tex]=1,162,059.58 \ Taka[/tex]
hence,
The Annuity payment will be:
→ [tex]P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-4\times 5}}[/tex]
[tex]=P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-20}}[/tex]
By substituting all the values, we get
[tex]=65,209.35 \ Taka[/tex]
Thus the correct answer is "65,209.35 Taka".
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hi, please solve these three questions for me, i have to shoe solving steps.
question 3
Step-by-step explanation:
i only able to show you the step of question 3..so sorry
find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
A. {(6, 5)}
B. {(5, 6)}
C. {(13/5, 6/5)}
D. {(6/5, 13/5)}
Step-by-step explanation:
+ Both equations
You will get : 5x=13 ; x=13/5
and put x to the first equation
2*13/5-y=4
y=6/5
(13/5;6/5)
Answer is C
I don't understand this one
Answer:
9/8 = n
Step-by-step explanation:
9 = 8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
A scientist started with a sample of 8 cells. The sample increased as shown in the table.
Assume that the pattern in the table continues. Which equation can be solved for t, the time in hours when the number of cells will reach 100,000?
A
8⋅t4=100,000
B
8⋅4t=100,000
C
4⋅t8=100,000
D
4⋅8t=100,000
Answer:
100000 = 8 (4) ^t
Step-by-step explanation:
We are multiplying by 4 each time
y = a (4)^t
The initial amount is 8
y = 8 (4)^t
We want to get to 100000
100000 = 8 (4) ^t
Answer:
B
8 ⋅ 4^t = 100,000
Step-by-step explanation:
Can i please get this answered
Answer:
0 is the answer . The explanation is in the attachment .
The sum of two numbers is 83 if one of the number is 7 more than the other find the two numbers?
Answer:
48.5 and 34.5
Step-by-step explanation:
83 divided by 2 and then subtract 7
Answer:
45 and 38 equal 83 and 45 is 7 more than 38
A storeowner orders 25 calculators that cost $38 each. The storeowner can sell each calculator for $42. The storeowner sold 22 calculators to customers. He had to return 3 calculators that were never sold and pay a $2 charge for each returned calculator (although the initial cost is refunded). What is the storeowner's profit?
Answer:
Step-by-step explanation:
25*-30= -$750
Second: He sells 22 of those calculators for $35 each, so he is making money.
22*35= $770
Third: With the remaining three calculators, he must pay $2 each for returned calculators, so he is losing money again.
3*-2= -6
Add all the costs and sales together, and you get 770-750-6= $14 profit
However, the problem does not say if he gets his money back for the 3 returned calculators. In that case if he did, you would add the cost of each of those calculators to his profit. 30*3= 90
$90+$14= $104 profit
here u go
Simplify
1)a³b⁴/ ab³
2)2 (x³ )²
3)3x*2x³ y²
Answer:
1) a³b⁴/ ab³ = a²b
2)2 (x³ )² = 2x^6
3)3x*2x³ y² = 6x⁴y²
The Vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).Find the length of each diagonal.Show me with the steps Please!
Answer:
13 and 17 units
Step-by-step explanation:
explaination is in pic.
The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.
What is the length between two points in a plane?The length between two given points (x₁, y₁) and (x₂, y₂) will be:
√[(x₂ - x₁)² + (y₂ - y₁)²] units
Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).
Therefore, the diagonals of the quadrilateral will be AC and BD.
The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).
Now, the length of the diagonal AC will be:
= √[(-8 - 4)² + (2 - (- 3))²] units
= √[(- 12)² + (5)²] units
= √[144 + 25] units
= √(169) units
= 13 units (length can't be negative)
Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).
Now, the length of the diagonal BD will be:
= √[(-1 - 7)² + (- 5 - 10)²] units
= √[(- 8)² + (- 15)²] units
= √[64 + 225] units
= √(289) units
= 17 units (length can't be negative)
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Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?
Answer:
C(x)=40x+14, 6 days
Step-by-step explanation:
C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.
C(x)=254=40x+14, 40x=240, x=6
ABCD is a rectangle. AB = 3x+5, AC = 7x-9, BC = 2y+5, BD = 2x+62. Solve for x. (Round your answer to one decimal place, if necessary.)
Answer:
x=14.2
Step-by-step explanation:
AC = BD
The diagonals of a rectangle are equal
7x-9 = 2x+62
Subtract 2x from each side
7x-9-2x = 2x+62-2x
5x-9 = 62
Add 9 to each side
5x-9+9 = 62+9
5x= 71
Divide by 5
5x/5 = 71/5
x=14.2
Na
C
9
Which rule describes the transformation?
Parallelogram ABCD is rotated to create image
A'B'C'D'.
SEE
0 (x, y) - (y, -x)
O (x, y) + (-y, x)
O (x, y) + (-X, -y)
(x, y) - (x,-y)
5
VX
4
R
D
2
1
C
-5.-5.4.-3.-2.-
23
4
SIB
Х
2
D
A
C
B
no
Answer:
(x, y) → (y, -x)
Step-by-step explanation:
The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)
The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)
The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;
(x, y) → (y, -x)
The resulting transformation used will be (x, y) -> (y, -x)
Transformation of coordinatesTransformation are rules applied to an object to change its orientation
For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage
The coordinate of A is (2, 5) while that of A' is (5, -2).
From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.
Hence the resulting transformation used will be (x, y) -> (y, -x)
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find the surface area of the cylinder and round to the nearest tenth
Answer: A = 833.66 in^2
Step-by-step explanation:
Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2
Height of the cylinder = 12 in
Circumference of the base = (2)(pi)(r) = 44in
Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2
of (3, -2) reflected across the line x = 1 is?
Answer: (-1, -2)
===========================================================
Explanation:
Plot (3,-2) on the xy grid. Then draw a vertical line through 1 on the x axis.
Note that the horizontal distance from the point to the line is exactly 2 units. We move 2 units to the left to go from (3,-2) to (1,-2). Then we move another 2 units to the left to arrive at the final destination of (-1, -2)
In short, (3,-2) reflects over the vertical line x = 1 to get to (-1, -2)
See the diagram below.
A furniture store is having a sale on sofas and you're going to buy one. The advertisers know that buyers get to the store and that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement. Let X be the cost of the sofa. What is the average cost of a sofa if the advertised sofa is $250 and the more expensive sofa is $450
Answer:
$290
Step-by-step explanation:
We are told that 1 out of 5 buyers change to a more expensive sofa than the one in the sale advertisement.
Now we are told that the advertised sofa is $250 and the more expensive sofa is $450.
Thus;
P(x) for expensive sofa = 1/5
P(x) for sofa in sale advertisement = 4/5
Thus, expected value is;
E(X) = (1/5)450 + (4/5)250
E(x) = 90 + 200
E(x) = $290
Answer:
The average cost of a sofa = [tex]\$290[/tex]Step-by-step explanation:
Cost of advertised sofa = [tex]\$250[/tex]
Cost of more expensive sofa = [tex]\$450[/tex]
So, the average cost of sofa,
[tex]E(x) = (450*\frac{1}{5})+ (250*\frac{4}{5})\\\\E(x) = 90 + 200\\\\E(x) = 290[/tex]
Hence,
The average cost of a sofa = [tex]\$290[/tex]
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What is the Answer to: 120 Times 2/3
Answer:
80
Step-by-step explanation:
You could multiply by 2 and then divide by 3
120*2 = 240
240/3 = 80
Or you could divide by 3 and then multiply by 2
120/3 = 40
40*2 = 80
Answer:
80Step-by-step explanation:
120 × 2/3= 120/1 × 2/3= 240/3= 80[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants his
hourly salary to be at least $35.
The inequality that relates the number of hours to the weekly sales is:
[tex]450 + 0.20x \ge 35y[/tex]
The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales
We make use of the following representation:
[tex]x \to[/tex] weekly sales from cars.
[tex]y \to[/tex] hours worked in a week
His weekly salary is then calculated as:
Salary (S) = Earnings per week + Commission * Sales from car
So, we have:
[tex]S = 450 + 20\% * x[/tex]
Express percentage as decimal
[tex]S = 450 + 0.20* x[/tex]
[tex]S = 450 + 0.20x[/tex]
Assume he works for y hours in a week.
His hourly rate is:
[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours
[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]
For this rate to be at least [tex]\$35[/tex], the following condition must be true
[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35
So, we have:
[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]
Multiply both sides by y
[tex]450 + 0.20x \ge 35y[/tex]
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3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
b) Given that y = 1/2 determine the value of k.
Answer:
(a): x is 3 and ky is -1
(b): k is -2
Step-by-step explanation:
Let: 3x + ky = 8 be equation (a)
x - 2 ky = 5 be equation (b)
Then multiply equation (a) by 2:
→ 6x + 2ky = 16, let it be equation (c)
Then equation (c) + equation (b):
[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]
Then ky :
[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]
[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]
Simultaneous equations are used to represent a system of related equations.
The value of k when [tex]y = \frac 12[/tex] is -2
Given that:
[tex]3x + ky = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]y = \frac 12[/tex]
Substitute [tex]y = \frac 12[/tex] in both equations
[tex]3x + ky = 8[/tex]
[tex]3x + k \times \frac 12 = 8[/tex]
[tex]3x + \frac k2 = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]x - 2k \times \frac 12 = 5[/tex]
[tex]x - k = 5[/tex]
Make x the subject in [tex]x - k = 5[/tex]
[tex]x = 5 + k[/tex]
Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]
[tex]3(5 + k) + \frac k2 = 8[/tex]
Open bracket
[tex]15 + 3k + \frac k2 = 8[/tex]
Multiply through by 2
[tex]30 + 6k + k = 16[/tex]
[tex]30 + 7k = 16[/tex]
Collect like terms
[tex]7k = 16 - 30[/tex]
[tex]7k = - 14[/tex]
Divide both sides by 7
[tex]k = -2[/tex]
Hence, the value of constant k is -2.
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After getting RM24 from his mother, Samuel had 3 times as much as he had previously. How much did he have previously?
Answer:
Samuel had RM8 previously
Step-by-step explanation:
24÷3=8
Please help me with this I need it
9514 1404 393
Answer:
2/3
Step-by-step explanation:
Let x represent the fraction of Cheryl's income she spent in September. Then 1-x is the fraction she saved.
In October, her spending increased by 0.2x, and her savings decreased by 0.4(1 -x). Since Cheryl spends or saves all of her income, these two change amounts must be equal:
0.2x = 0.4(1 -x)
x = 2(1 -x) . . . . . . multiply by 5 to clear fractions
x = 2 -2x . . . . . . eliminate parentheses
3x = 2 . . . . . . . . add 2x
x = 2/3 . . . . . . divide by 3
Cheryl spent 2/3 of her income in September.
