Answers
Answer:
The correct option is;
ASA
Step-by-step explanation:
The given information are;
1. ∠A ≅ ∠D, 1. Given
2. [tex]\overline{CD}\left | \right |\overline{AB}[/tex], 2. Given
3. [tex]\overline{CB}\cong \overline{BC}[/tex], 3. refl. prop.
4. ∠ABC ≅ ∠ DCB, 4. Alt int. ∠s are ≅
5. ΔABC ≅ ΔDCB, 5. Angle Side Angle ASA rule of congruency
The conditions for two triangles to be congruent includes;
1. All sides equal or SSS rule
2. Side Angle Side or SAS rule
3. Angle Side Angle or ASA rule
4. Angle Angle Side or AAS rule
5. Right angle Hypotenuse Side or RHS also known as Hypotenuse Leg, HL rule
Related Questions
How many gallons of a 20% salt solution must be mixed with 4 gallons of a 30% salt solution to make a 25% salt solution?
Answers
Answer:
4 gallons
Step-by-step explanation:
Say that g = the number of gallons of a 20% salt solution,
The first thing we want to do here is to convert each " percentage " into decimal form, to make things a bit simpler here.
( [tex]20(percent) = 0.20[/tex]
( [tex]30( percent ) = 0.30[/tex]
( [tex]25( percent ) = 0.25[/tex]
Before this mixture takes place, the 20% salt solution is associated with g, the number of gallons of a 20% salt solution. Respectively the 30% salt solution is associated with 4 gallons. After mixing the two ( g and 4 ) the 25% salt solution should be associated with g + 4. We can therefore conclude the following equation -
0.20( g )+0.30( 4 ) = 0.25( g + 4 )
And now, let us solve for " g, "
0.2g + 1.2 = 0.25g + 1
- 0.2g = - 0.2g
_________________
1.2 = 0.05g + 1
- 1 = - 1
_________________
0.2 = 0.05g,
g = 4 gallons of a 20% salt solution
Solve: 1.2n+1=1-n
HELP PLS ASAP WILL GIVE BRAINLIEST IF CORRECT
Answers
Answer:
Hello!
~~~~~~~~~~~~~~~~~
1.2n+1=1-n
=
n = 0
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you!
Ronnie can paint 8 rocks in 5 minutes. How long will it take him to paint 54 rocks
Answers
54 rocks / 8 rocks = 6.75
6.75 x 5 minutes = 33.75 minutes
Answer:
33 minutes and 45 seconds.
Step-by-step explanation:
We can easily set up a proportion...
He can paint 8 rocks in 5 minutes. He can paint 54 rocks in x minutes.
[tex]\frac{8}{5} =\frac{54}{x}[/tex]
8 * x = 54 * 5
8x = 270
4x = 135
x = 33.75
So, it will take Ronnie 33 minutes and 45 seconds to paint 54 rocks.
Hope this helps!
Solve (x-5)^2 =3.
Help me pls
Answers
Answer:
The correct answer is C.
Step-by-step explanation:
I solved by finding for X. Hope this helps!
Answer:
option c is correct.
hope it will help u...
What is an equation of the line that is perpendicular to y + 1 = -3(x - 5) and passes through the point (4, -6)?
Answers
Answer:
Option A.
Step-by-step explanation:
y + 1 = -3x + 15
y = -3x + 14
A line perpendicular would have a slope of 1/3.
y = 1/3x + c
-6 = 1/3 * 4 + c
4/3 + c = -6
c = -18/3 - 4/3
c = -22/3
So, we have y = 1/3x - 22/3.
y + 6 = 1/3(x - 4)
y + 6 = 1/3x - 4/3
y = 1/3x - 4/3 - 18/3
y = 1/3x - 22/3
So, the correct answer is Option A.
Hope this helps!
The equations of four lines are given. Identfy which lines are parallel. Line 1: y = -9x + 6 Line 2: x + (1/3)y = -6 Line 3: y = -3x - 8 Line 4: y + 7 = (-1/9)(x + 4)
Answers
Answer:
line 2 and line 3
Step-by-step explanation:
line1=y=-9x+6. gradient 1= -9
line2=x+⅓y=-6
⅓y=-6-x. gradient2= -3
y=-18-3x
line3=y=-3x-8. gradient3= -3
line4=y+7=-1/9x-4/9
y=-1/9x-4/9-7. gradient4= -1/9
y=-1/9x-7⁴/9
parallel lines have the same gradient
Determine if the coordinate (6, 8) lies on the circle x^2 + y^2 = 100.
Answers
Answer:
x² + y² = 100
6² + 8² = 100
36 + 64 = 100
100 = 100
Because this is a true statement, the answer is yes, it does lie on the circle.
solve the following: x+5=11 x-6=8 3+x=7 12=x+5
Answers
Answer:
1) x = 6
2) x = 14
3) x = 4
4) x = 7
Step-by-step explanation:
1) x+5=11
x = 11-5
x =6
2) x-6=8
x = 8+6
x = 14
3) 3+x=7
x = 7-3
x = 4
4) 12=x+5
12-5 = x
7 = x
please help ASAP: Factorise the following:
Answers
Answer:
hope u will understand it....
Answer:
Hello!
___________________
A)Factor x^2 - 12x + 32 using the AC method. ( x - 8 ) ( x - 4)
B) Factor x^2 - 14x + 48 using the AC method. ( x - 8) ( x - 6)
C) Factor x^2 - 3x + 2 using the AC method. ( x - 2) ( x - 1)
Step-by-step explanation: Always factor by x^2 while using the AC method.
Hope this helped you! :D
I need help with this:What is the value of y? Enter your answer in the box. y =
Answers
Answer:
y=5 degrees
Step-by-step explanation:
It is an isosceles triangle so that means that there are two angles that equal 75, so that means the third side with 4y + 10 is equal to 30 degrees.
4y+10=30
4y=20
y=5 degrees
what is the domain represented by the graph
Answers
Answer:
All real numbers.
Step-by-step explanation:
Since the graph is a linear function, and the line doesn't have any holes or asymptotes, the graph can input any x-value and output any y-value. Therefore, our domain is all real numbers (any x-value can work).
Answer: All real numbers
Step-by-step explanation:
It is a infinite line, therefore all x values and all y values can be put in and will read a value :)
11) Forty percent of the homes constructed in the Quail Creek area include a security system. Three homes are selected at random: 1. What is the probability all three of the selected homes have a security system? 2. What is the probability none of the three selected homes have a security system? 3. Did you assume the events to be dependent or independent?
Answers
Answer:
1) Pr(all three) = 0.064
2) Pr(none) = 0.216
3) Independent event
Step-by-step explanation:
Let Probability of homes constructed in the Quail Creek area with a security system = Pr (security)
Where Pr = probability
This is a binomial distribution problem. There ate only two outcomes in this distribution: a success and a failure
Where p = success, q = failure
For n trials,
Pr(X = x) = n!/[(n-x)!x!] × p^x × q^(n-x)
Pr (security) = 40% = 0.4
p = 0.4
q = 1-p = 1-0.4 = 0.6
Numbers selected at random = n = 3
See attachment for more details on the workings.
1) Probability all three of the selected homes have a security system = Pr(all three)
Pr(all three) = 1× (0.4)³ (0.6)^0 = 0.4³
= 0.4×0.4×0.4
Pr(all three) = 0.064
2) Probability none of the three selected homes have a security system
= Pr(none)
Pr(none) = 1 × (0.4)^0 × (0.6)³
= 0.6³ = 0.6×0.6×0.6
Pr(none) = 0.216
3) The events were assumed to be independent as the selection of one house doesn't affect the outcome of the selection of another.
You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded quarterly
Which investment as the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
the investment with simple? or compound?
interest earns $___ more in interest.
(Round to the nearest cant as needed.)
Answers
Answer:
Step-by-step explanation:
the simple interest formula= principal* interest rate*time
simple interest : 100000*%2*2 years
simple interest= 4000 dollars
compound quarterly : A=principal(1+r/4)^t
since it is quarterly and have 4 quarters in a year, and 8 in two years.
compound quarterly: 100000(1+0.03/4)^8=106159.88
it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.
the difference between the interest: 6159.88-4000=2159.88
One length of a rectangular garden lies along a patio wall. However, the rest of the garden is enclosed by 32 feet of fencing. If the length of the garden is twice its width, what is the area of the garden?
Answers
Answer:
128 square feet
Step-by-step explanation:
Let the perimeter of the rectangular garden be expressed as 2(L+W)
L = length of the garden
W = width of the garden
If the length of the garden is twice its width then L = 2W; W = L/2
P = 2(L+L/2)
Since the perimeter is L + 32 (One length of a rectangular garden that lies along a patio wall and the rest of the garden is enclosed by 32 feet of fencing.)
Substituting in the formula above:
32+L = 2(L+L/2)
32+L = 2L+L
32 = 2L
L = 16 feet
Since L = 2W
W = L/2 = 16/2
Width = 8 feet
Area of the garden = Length × Width
Area of the garden = 16×8
Area of the garden = 128 square feet
The area of the rectangular garden is equal to 128 square feet.
Let the length of the rectangular garden be L.Let the width of the rectangular garden be W.Given the following data:
Perimeter = 32 + L feet.Translating the word problem into an algebraic equation, we have;
The length of the garden is twice its width:
[tex]L=2W[/tex] = [tex]W=\frac{L}{2}[/tex]
The formula for perimeter of a rectangle.Mathematically, the perimeter of a rectangle is given by the formula;
[tex]P=2(L+W)[/tex]
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Substituting the parameters into the formula, we have;
[tex]32+L=2(L+\frac{L}{2})\\\\32+L=2L+L\\\\32+L=3L\\\\3L-L=32\\\\2L=32\\\\L=\frac{32}{2}[/tex]
Length, L = 16 feet.
For the width:
[tex]W=\frac{L}{2}\\\\W=\frac{16}{2}[/tex]
Width, W = 8 feet.
Now, we can calculate the area of the rectangular garden:
[tex]Area = LW\\\\Area = 16 \times 8[/tex]
Area = 128 square feet.
Read more on area of a rectangle here: https://brainly.com/question/25292087
Please answer this - i'm so desperate!
Answers
The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. What are the dimensions of Sally’s garden
Answers
Answer:
Width=8
Length=28
Step-by-step explanation:
Width=x
Length=3x+4
perimeter is 2 lengths and 2 widths
2x + 2(3x+4)=72
2x+6x+8=72
8x=72-8
8x=64
x=8, so the width is 8
the length Is 3(8)+4 = 28
2 Points
Find the solution(s) to the system of equations. Select all that apply.
y = x2 - 2x-3
y = 2x - 3
O A. (0,-3)
B. (-1,0)
C. (3,0)
D. (4,5)
Answers
Answer:
A (0,-3) and D(4,5)
Step-by-step explanation:
Given system of equations
y = x2 - 2x-3
y = 2x - 3
Solution to these will be value of x for which value of y in both equation will same.
In graph, solution will point at which curve of both equation intersect each other
To solve this we will equate the two equations
[tex]x^2 - 2x-3 = 2x-3\\ =>x^2 - 2x-3 -2x + 3 = 0\\=> x^2 - 2x - 2x -3 + 3 = 0\\\=> x^2 - 4x = 0\\=>x(x-4) = 0\\Thus\\x = 0 \ or \ x-4 = 0\\x = 0 \ or \ x = 4[/tex]
Thus, value of x is 0 and 4
we will put this value in given set of equation.
y = 2x- 3
taking x = 0
y = 2*0 -3 = 0-3 = -3
one solution is (0,-3)
taking x = 4
y = 2*4 - 3 = 8-3 = 5
Another solution is (4,5).
Though , the problem is solved we will see it this value satisfies other equation or not better understanding
y = x^2 - 2x-3
taking x = 0
y = 0^2 - 2*0-3 = -3
one solution (0,-3)
taking x = 4
y = 4^2 - 2*4-3 = 16-8 -3 = 8-3 = 5
other solution (4,5)
thus, we see both equation gives same set of solution.
Claim: Most adults would erase all of their personal information online if they could.
A software firm survey of 453 randomly selected adults showed that 60% of them would erase all of their personal information online if they could. Find the value of the test statistic. (Round to two decimal places as needed.)
Answers
Answer:
271.80
Step-by-step explanation:
453 ⇒ 100% x(the missing value) ⇒ 60%using the proprtionality we get
x =[tex]\frac{453*60}{100}[/tex] x = 271.80Can someone please help me I really need help please help me thank you
Answers
Answer:
Negative 1/300
Step-by-step explanation:
I took the qiuz
Eight more than four times a certain number is
equal to 12 less than eight times the number. What
is the number?
Answers
Answer: 5
Step-by-step explanation:
4x+8=8x-12
20=4x
5=x
Answer:
5.
Step-by-step explanation:
Let's say that the mysterious number is x.
8 more than 4 times x equals 12 less than 8 times x.
8 + 4x = 8x - 12
8x - 12 = 4x + 8
8x - 4x = 8 + 12
4x = 20
x = 5
Hope this helps!
what is the rate of change between (1,15) (3,45)?
Answers
Answer:
15
Step-by-step explanation:
Rate of change or slope or gradient of a line passes two points (x1, y1) and (x2, y2) could be calculated by:
(y2 - y1)/(x2 - x1)
=> Rate of change of the line passing (1,15) and (3,45):
(45 - 15)/(3 - 1) = 30/2 = 15
MATH HELP ASAP PLSSSS
Answers
Answer:
(30,0)
Step-by-step explanation:
y=0
-2/5 *x +12=0
2x/5=12
2x=12*5
2x=60
x=60/2
x=30
Hey there! :)
Answer:
(30, 0).
Step-by-step explanation:
Solve for the x-intercept, or zero of the equation by setting the equation equal to 0:
y = -2/5x + 12 becomes:
0 = -2/5x + 12
Subtract both sides by 12:
-12 = -2/5x
Divide both sides by -2/5:
-12 (-5/2) = -2/5x (-5/2)
30 = x.
Therefore, the x-intercept is at (30, 0).
Jessica and Barry squeezed oranges for juice. Jessica squeezed 23 5 cups of juice. Barry made 1 4 cup less than Jessica. Barry estimated that Jessica squeezed about 21 2 cups of juice. Which is the best estimate for the amount of juice Barry made? 2 1/4 cups How much juice did Barry actually make? 2 and three-fifths minus one-fourth = StartFraction 13 over 5 EndFraction minus one-fourth = StartFraction 52 over 20 EndFraction minus StartFraction 5 over 20 EndFraction
Answers
Answer:
1. 2 1/4 cups
2. 2 7/20 cups
Answer:
2 1/4 and 2 7/20
Step-by-step explanation:
What is the equation of a horizontal line that passes
through the point (-4, -5)?
Answers
Answer: y=-5
Step-by-step explanation:
A horizontal line appears on the graph if it goes through the y-axis. Knowing this, the coordinate tells us that the y-coordinate is -5. This tells us that the equation of the line is y=-5.
A student wants to estimate the mean score of all college students for a particular exam. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible scores range from 300 to 2200. Use technology and the estimated standard deviation to determine the sample size corresponding to a 90% confidence level and a margin of error of 100 points. What isn't quite right with this exercise? The range. rule of thumb.estimate for the standard deviation. nothing.
Answers
Answer:
See explanation below
Step-by-step explanation:
range = 2200 - 300 = 1900
To find standard deviation, we have:
standard deviation = range/4 = [tex] \frac{1900}{4} [/tex] = 475
The range rule of thumb estimate for the standard deviation is 475
Given:
Standard deviation,[tex] \sigma[/tex] = 475
Margin of Error, ME = 100
[tex] \alpha [/tex] = 1 - 0.90 = 0.10
Za/2 = Z0.05 = 1.64
Find sample size, n:
n ≥ [tex] [Z_\alpha_/_2 * (\frac{\sigma}{ME})]^2 [/tex]
n ≥ [tex][1.64 * (\frac{475}{100})]^2[/tex]
n ≥ 60.68
≈ 61
Minimun sample size,n = 61
What is the square root of 100000000?
Answers
Answer:
10,000 is the answer to ur question
Answer:
10000
Step-by-step explanation:
√100000000 = 10000
simplify.
I need this answer..
Answers
Ignore the bit crossed out at the bottom
Let f(x)= (2/3)^x
Complete each statement.
A. The domain of f(x) is____.
B. The range of f(x) is_____.
C. The y-intercept of the graph of f(x) is______.
D. The horizontal asymptote of the graph of f(x) is the ( x-axis / y-axis ). (Circle one.)
E. The graph of f(x) is ( increasing / decreasing ) from left to right. (Circle one.)
F. The value of the ( base / coefficient / exponent ) determines whether the graph of an exponential
function is increasing or decreasing from left to right. (Circle one.)
Answers
Answer:
A. All real number
B. Positive Real numbers
C. y intercept is 1
D. x axis
E. Decreasing
F. Base
Step-by-step explanation:
Given:
[tex]f(x) = (\frac{2}{3})^x[/tex]
A.
Domain of a function f(x) is the value of 'x' for which it has a defined value.
Here, f(x) can have any real number to be given to x.
So, domain is all real numbers.
B.
Range of a function f(x) is the value of f(x) when we give some value of x as input.
Here, we can not have negative value of f(x) because x is in the exponent.
So, the range is Positive Real numbers.
C.
y intercept of any function f(x) is the value of f(0).
[tex]f(0)=(\frac{2}{3})^0 = 1[/tex]
So, y intercept is 1.
D. Horizontal asymptote is the the line where value of [tex]x \rightarrow \infty[/tex]
x axis is the answer.
E. The graph is decreasing with increasing value of x(from left to right).
Because the base is less than 1.
F. The value of base determines whether the graph will be decreasing or increasing.
If base > 1, the graph will be increasing will increasing value of exponent (x).
Here the base is less than 1 so decreasing graph.
Please refer to the attached graph for better understanding of the given function.
Pls help me out!! Ill be so happy!! TYSM
Answers
Answer:
Hey there!
The line 4x-3y=-9 can be converted to y=mx+b form.
4x-3y=-9
-3y=-4x-9
3y=4x+9
y=4/3x+3
The slope of a line perpendicular to this line would be -3/4.
The slope of a line parallel to this line would be 4/3.
Hope this helps :)
Kyree had a summer job cutting lawns. He made $32 in June, $45 in July, and $43 in August. In September he spent $17 on school supplies and $26 on clothes. How much money does he have left?
Answers
Answer:
77
Step-by-step explanation:
you add the amount he earn which is 32+45+43 which will give you 120 and than you subtract the amount he spend which are 17 and 26, after that you will get 77 as your answer
Answer:
See below.
Step-by-step explanation:
June: $32
July: $45
August: $43
[tex]32+45+43=120[/tex]
Kyree has $120 in total.
School supplies: $17
Clothes: $26
[tex]26 +17=43[/tex]
[tex]120-43=77[/tex]
Kyree has $77 left.
:)