Answer: IT IS CONGRUENT BY ASA POSTULATE.
Step-by-step explanation:
ACCORDING TO THE GIVEN IMAGE
CONSIDER TRIANGLE 1 AS TRIANGLE ABC AND TRIANGLE 2 AS TRIANGLE PQR
IN TRIANGLE ABC AND PQR
ANGLE B = ANGLE C ( 90 DEGREES )
AC = PR ( GIVEN IN FIGURE )
A TRIANGLE HAS SUM OF INTERIOR ANGLES AS 180 DEGREES
IF ANGLE B AND ANGLE Q ARE 90 DEGREES, ANGLE A + ANGLE C = ANGLE P + ANGLE R
WE HAVE ALREADY PROVED THAT AC = PR
If two triangles have one angle equal to one angle, two sides adjoining the equal angles equal, namely, one side adjoining the equal angles, and one opposite the equal angles, and the remaining angles either both less or both not less than a right angle, then the remaining side equals the remaining side and the remaining angles equal the remaining angles.
SO ANGLE A = ANGLE P
THEREFORE BY ASA CONGRUENCY TRIANGLE ABC IS CONGRUENT TO TRIANGLE PQR
HOPE IT HELPS YOU......
(IF I HAVE MADE ANY MISTAKES PLS COMMENT BELOW)
What is the area of the label on a soup can that is 8 inches high and has a diameter of 4 inches? Round to the nearest hundredth. Assume the label wraps around the entire height of the can and does not overlap. SHOW WORK..
Answer:
Area of label = 100 inch² (Approx.)
Step-by-step explanation:
Given:
Height of label = 8 inches
Diameter of label = 4 inches
Find:
Area of label
Computation:
Design of label = Rectangle
So,
Width of label = 2πr
Width of label = 2(3.14)(4/2)
Width of label = 2(3.14)(2)
Width of label = 12.56 inches
Area of label = Height of label x Width of label
Area of label = 12.56 x 8
Area of label = 100.48
Area of label = 100 inch² (Approx.)
Daniel paid interest of 1,020 in 5years at12%per annum on a loan. Hw much did he borrow
Consider the following 8 numbers, where one labelled
x
is unknown.
12, 46, 31,
x
, 49, 24, 41, 14
Given that the range of the numbers is 63,
work out 2 values of
x
.
Put the data set in order:
12, 14, 24, 31, 41, 46, 49
In order to find a value of x using the range, x has to be on either end of the data set. Meaning:
x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
Since the range is the highest value minus the lower value, you can set two equations for x:
x - 12 = 63
x = 75
49 - x = 63
x = -14
Thus, x = 75, -14
Two values of x are -14 & 75
What is range of numbers ?The difference between highest and lowest numbers of the set of numbers is called the range of numbers.
What are the values of x ?The given values are 12, 46, 31, 49, 24, 41, 14
Arranging all the values in ascending order we get,
12, 14, 24, 31, 41, 46, 49
If x will be included, then x is in the 1st position or in the last position.
Then the values are x, 12, 14, 24, 31, 41, 46, 49 or 12, 14, 24, 31, 41, 46, 49, x
The range of the number is 63
So, we get two equations from it.
1 ) 49-x = 63
2 ) x-12 = 63
Solving eq. (1) we get, x = 49-63 = -14
Solving eq. (2) we get, x = 63+12 = 75
So the values of x are -14 & 75
Learn more about range of number here :
https://brainly.com/question/10081172
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Please help me with this question please and thank you ❤️
Answer:
x = -1
Step-by-step explanation:
3x - 1/9 (27) = 18
3x - 3
Divide both sides be 3
x = -1
Answer:
x = 7
Step-by-step explanation:
to solve this equation we are given the value of y which 27. just substitute 27 for y in the equation :
3x - 1/9(27) = 18
3x - 3 = 18
3x = 21
x= 7
what is the value of the expression below? (8^5/3)^1/5
Answer:
8^1/3
Step-by-step explanation:
(8^5/3)^1/5
8^5/3×1/5
8^5/15
8^1/3
Answer:
Step-by-step explanation:
Exponent Rule: [tex](a^{m})^{n}=a^{m*n}[/tex]
[tex](8^{\frac{5}{3}})^{\frac{1}{5}}= 8^{\frac{5}{3}}*{\frac{1}{5}}\\\\\\=8^{\frac{1}{3}}\\\\= \sqrt[3]{8} \\\\= \sqrt[3]{2*2*2}\\\\= 2[/tex]
1/2a=11
a=? P.S I am not in high school I am in 4TH GRADE!!!
Answer:
a: 1/22
Step-by-step explanation:
cross multiply 1/2a=11
which will give 22a=1
divide both sides by 22
to give a=1/22
Last night, the temperature fell from 0°F to -13 1/5 in 4 2/5 hours What was the average temperature change per hour? the problem: -13 1/5 divided by 4 2/5
The temperature drop per hour can be represented by ___?
Answer:
What was the average temperature change per hour -3 degrees per hour
Step-by-step explanation:
Take the temperature drop and divide by the time
-13 1/5 ÷ 4 2/5
Change to improper fractions
-(13 *5+1)/5 ÷ (4*5+2)/5
-66/5 ÷22/5
Copy dot flip
-66/5 * 5/22
Rewrite
-66/22 * 5/5
-3 degrees per hour
Since we are looking for a drop
3 degrees per hour
evaluate
[tex] {( - 7)}^{ \frac{5}{3} } \times {( \frac{1}{56} )}^{ \frac{5}{3} } [/tex]
please explain
[tex]\frac{-1}{32}[/tex] is a required answer.
Answer:
Solution given:
[tex] {( - 7)}^{ \frac{5}{3} } \times {( \frac{1}{56} )}^{ \frac{5}{3} } [/tex]
take power common
[tex](\frac{-7*1}{56})^{\frac{5}{3}}[/tex]
Reduce the fraction
[tex](\frac{-1}{8})^{\frac{5}{3}}[/tex]
make the1 and 8 in terms power 3
[tex](\frac{-1³}{2³})^{\frac{5}{3}}[/tex]
take the common power
[tex](\frac{-1}{2})^{3*\frac{5}{3}}[/tex]
Reduce power
[tex](\frac{-1}{2})^{5}[/tex]
now
distribute power
[tex]\frac{-1^{5}}{2^{5}}[/tex]
[tex]\frac{-1}{32}[/tex]
how can you find the slope of a line and use it to
solve problems?
Answer:
Step-by-step explanation:
1) Mark two points on the line in the graph.
2) Determine the rise and run. Rise ---> difference in y-coordinates. (y2-y1)
Run -----> difference in x-coordinates (x2 - x1)
3) Plugin the values in the below mentioned formula.
[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
1.If slope = 0, then the line is parallel to x-axis.
2. If slope is undefined, then the line is parallel to y-axis.
3. If slope is +ve, then the line slant upwards and if slope = -ve, then the line slant downwards.
Which expression is equivalent to 6(3n-4)?
1)9n-10
2)18n-24
3)18n-4
4) 3n-24
Answer:
[tex]18n - 24[/tex]
Step-by-step explanation:
[tex]6(3n - 4) = 18n - 24[/tex]
Answer:
18n-24
Step-by-step explanation:
6(3n-4)
Open the brackets .......
(6×3n)-(6×4)
=18n_24
can yaweeeeeeeee hlp
Answer:
( 25 x 100 )
option 1 is the answer
Step-by-step explanation:
Remaining options are not correct since they don't have 100 as a factor.
Line ab and cd (if presented in the picture) are straight lines. Find x (the pictures are not scaled)
Answer:
[tex]x + 2x + 34 + 20 = 180 [/tex]
Answer:
x=42
Step-by-step explanation:
Statement Reason
1. m∠AOB = 180° — Def. of straight ∠
2. m∠AOE + m∠EOF + m∠FOB = m∠
AOB —- Parts − whole Postulate
3. x + 2x+34° + 20° = 180° —- Substitution
4. x = 42°. —- Algebra
This is statement and reason! (no problem rsm people)
What is a counterexample to this claim? Dividing a number by 2 always results in a smaller number.
Given:
Dividing a number by 2 always results in a smaller number.
To find:
The counterexample to the given claim.
Solution:
If 0 is divided by is divided by any non-zero real number [tex]a[/tex], then
[tex]\dfrac{0}{a}=0[/tex]
Let us consider the unknown number be 0. Then dividing a number by 2, we get
[tex]\dfrac{0}{2}=0[/tex]
Here, the result is not a smaller number because [tex]0=0[/tex].
Therefore, the counterexample to the given claim is "Dividing 0 by 2".
Answer:
-1
Step-by-step explanation:
What is the slope of the line shown below?
ОА. - 17
(5, 1)
X
O B. -4
-5
5
(-3,-1)
O c. 4
-5
O D.
1
4
Answer:
C
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, - 1) and (x₂, y₂ ) = (5, 1) ← 2 points on the line
m = [tex]\frac{5-(-3)}{1-(-1)}[/tex] = [tex]\frac{5+3}{1+1}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → C
1.If a number is chosen at random from the integers 5 to 25 inclusive , find the probability that the number is a multiple of 5 or 3.
2.Good Limes =10
Good Apples = 8
Bad Limes = 6
Bad Apples 6
The information above shows the number of limes and apples of the same size in a bag . If two of the fruits are picked at random , one at a time without replacement .Find the probability that :
I. Both are good limes
II.Both are good fruits
III. One is a good apple and the other a bad lime
I'll do problem 1 to get you started.
set A = multiples of 3 between 5 and 25 = {6, 9, 12, 15, 18, 21, 24}
there are 7 items in set A, so we can say n(A) = 7
set B = multiples of 5 between 5 and 25 = {5,10,15,20,25}
Here we have n(B) = 5
set C = multiples of 3 and 5, between 5 and 25 = {15}
n(C) = 1 which we can rewrite as n(A and B) = 1.
-----------------------------------------
To summarize so far,
n(A) = 7n(B) = 5n(A and B) = 1From those three facts, then we can say,
n(A or B) = n(A) + n(B) - n(A and B)
n(A or B) = 7 + 5 - 1
n(A or B) = 11
There are 11 values between 5 and 25 that are multiples of 5, multiples of 3, or both.
Those 11 values are: {5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25}
This is out of 25-5+1 = 21 values overall which are in the set {5,6,7,...,24,25}
So we have 11 values we want out of 21 overall, which leads to the probability 11/21
Final Answer: 11/21
Answer:
Solution given:
total outcomes between 5 to25 inclusive
n[T]=25-5+1=21
multiple of 5n[5]=5,10,15,20,25=5
multiple of 3n[3]=6,9,12,15,18,21,24=7
now
probability of getting multiple of 5p[5]=5/21
and
probability of getting multiple of 3 p[3]=7/21=1/3
again
the probability that the number is a multiple of 5 or 3 P[5or 3]=p[5]+p[3]=5/21+1/3=4/7
the probability that the number is a multiple of 5 or 3 is 4/7.2:
.Good Limes n[GL] =10
Good Apples n[GA]= 8
Bad Limes n[BL] = 6
Bad Apples n[BA]= 6
total fruits n[T]=10+8+6+6=30
no of good apple n[G]=10+8=18
no of bad apple n[B]=6+6=12
again
I. Both are good limes
=[tex]\frac{n[GL]}{n[T]}×\frac{n[GL]-1}{n[T]-1}[/tex]
=10/30*9/29=3/29
II.Both are good fruits
=[tex]\frac{n[BL]}{n[T]}×\frac{n[BL]-1}{n[T]-1}[/tex]
=6/30*5/29=1/29
III. One is a good apple and the other a bad lime
=n[G]/n[T] *n[B]/(n[T]-1)
=18/30*12/29=36/145
Given quadrilateral ABCD, where the diagonals AC and BD intersect at point E. AE⎯⎯⎯⎯⎯⎯⎯≅EC⎯⎯⎯⎯⎯⎯⎯⎯AE¯≅EC¯ and BE⎯⎯⎯⎯⎯⎯⎯≅DE⎯⎯⎯⎯⎯⎯⎯⎯BE¯≅DE¯. Can you prove can you prove that the figure is a parallelogram? Explain.
Given:
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
To prove:
The figure is a parallelogram.
Solution:
We know that if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
In a quadrilateral ABCD, diagonals AC and BD intersect at point E.
[tex]AE\cong EC[/tex]
[tex]BE\cong DE[/tex]
Since the diagonals AC and BD of a quadrilateral ABCD bisect each other, therefore the quadrilateral ABCD is a parallelogram.
Hence proved.
What is the function rule for the line?
Answer:
y =2/3x -2
Step-by-step explanation:
The y intercept is -2
The slope is
m = (y2-y1)/ (x2-x1)
Using the points (0,-2) and (3,0)
m = ( 0 - -2)/(3 -0)
= (0+2)/(3-0)
= 2/3
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y =2/3x -2
It cost David $16.75 to fill his 5-gallon gas can.
1. Write two different rates.
2. What is the best unit rate to use?
3. If David decided to fill up his car that has a 22-gallon gas tank, would $73 be enough to cover it? If so, how much does he have leftover? If not, how much is he short?
Answer: I divided 16.75 by 5
Step-by-step explanation:
For every 1 gallon hes using 3.35
So 22 x 3.35 is 73.70 so hell need 70 cent more
hey are In 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per pound. How 0 35. much did the oranges appreciate (percent of increase)?
SHOW YOUR WORK.
Answer:
Solution given:
in 1990
cost of orange[C.P]=$0.56
in 2003
cost of orange[S.P]=$0.86
now
increased price[profit]=S.P-C.P=$0.86-$0.56=$0.3
Now
increased percent [profit%]=?
we have
profit%=profit/c.p*100%
=0.3/0.56*100=53.57℅
Therefore
the oranges appreciated by 53.57%
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
Given:-are In 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per poundFind:-percentage of increasing Solution:-we have, 1990 oranges cost $0.56 per pound. In 2003 they cost $0.86 per pound.
so,
C.P of 1990=0.56$c.p of 2003=0.86$[tex]\sf{increase_{(profit)}=0.86-0.56=0.3 }[/tex]
we know that,
[tex]\bold{ profit\%=\dfrac{profit}{C.P}×100 }[/tex]
According to the question,
[tex]\sf{percentage_{(profit)}=\dfrac{0.3}{0.56}×100 }[/tex] [tex]\sf{percentage_{(profit)}=\dfrac{5357}{100} }[/tex] [tex]\sf{percentage_{(profit)}=53.57\% }[/tex]14 less than 8 times a number is 3 more than 4 times the number. What is the number?
Answer:
x = 17/4
Step-by-step explanation:
Let x = the number
8x-14 = 4x+3
Subtract 4x from each side
8x -14-4x = 4x+3-4x
4x-14 = 3
Add 14 to each side
4x-14+14 = 3+14
4x = 17
Divide by 4
4x/4 = 17/4
x = 17/4
Enter an equation in point-slope form for the line.
Slope is 4 and (-2,-1) is on the line.
The equation of the line in point slope form is:
Answer:
[tex]y+1=4(x+2)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and (x₁,y₁) is the given point
[tex]y-y_1=m(x-x_1)[/tex]
Plug in the slope and the point
[tex]y-(-1)=4(x-(-2))\\y+1=4(x+2)[/tex]
I hope this helps!
Manuel bought a set of tracks for $35 and 8 individual train cars,
which were priced the same. If the total cost was $155, what was the
price for each train car?
Please help
Answer:
155÷8= 19,375
The unit price of each wagon can be obtained by dividing (155 by 8)
luck in your tasks.
The 555 points plotted below are on the graph of y=\log_b{x}y=log
b
xy, equals, log, start base, b, end base, x.
Based only on these 555 points, plot the 555 corresponding points that must be on the graph of y=b^{x}y=b
x
y, equals, b, start superscript, x, end superscript by clicking on the graph.
Answer:
See attachment for graph
Step-by-step explanation:
See comment for correct question
Given
[tex]y = \log_bx[/tex]
Required
The corresponding points on [tex]y =b^x[/tex]
On the graph, we have:
[tex](x_1,y_1) \to (1,0)[/tex]
[tex](x_2,y_2) \to (2,1)[/tex]
[tex](x_3,y_3) \to (4,2)[/tex]
[tex](x_4,y_4) \to (8,3)[/tex]
[tex](x_5,y_5) \to (16,4)[/tex]
First, we solve for b in [tex]y = \log_bx[/tex]
Using laws of logarithm, the equivalent of the above is:
[tex]x = b^y[/tex]
[tex](x_2,y_2) \to (2,1)[/tex] implies that:
[tex]2 = b^1[/tex]
[tex]2 = b[/tex]
Rewrite as:
[tex]b =2[/tex]
So, the equation [tex]y =b^x[/tex] becomes:
[tex]y = 2^x[/tex]
Using the same values of x, we have:
[tex](x_1,y_1) = (1,2)[/tex]
[tex](x_2,y_2) = (2,4)[/tex]
[tex](x_3,y_3) = (4,16)[/tex]
[tex](x_4,y_4) = (8,256)[/tex]
[tex](x_5,y_5) = (16,65536)[/tex]
See attachment for graph
The points (1,2), (2,4), and (4,16) are plotted on the graph attached below and this can be determined by using the given data.
Given :
Logarithmic Function -- [tex]\rm y = log_b(x)[/tex] --- (1)
The following steps can be used in order to determine the corresponding points that must be on the graph [tex]\rm x = b^y[/tex]:
Step 1 - Now, substitute the value of x and y that is (2,1) in the expression [tex]\rm x = b^y[/tex].
[tex]\rm 2 = b^1[/tex]
b = 2
Step 2 - Now, substitute the value of b in the equation [tex]\rm y=b^x[/tex].
[tex]\rm y = 2^x[/tex] --- (2)
Step 3 - At (x = 1) the above expression becomes:
y = 2
Step 4 - At (x = 2) the expression (2) becomes:
y = 4
Step 5 - At (x = 4) the expression (2) becomes:
y = 16
The graph of [tex]\rm y = 2^x[/tex] is attached below.
For more information, refer to the link given below:
https://brainly.com/question/14375099
What are the x-intercepts of the parabola?
A: (4.5, 0) and (5, 0)
B: (0, 4.5) and (0, 5)
C: (0, 5) and (0, 4)
D: (5, 0) and (4, 0)
Answer:
D: (5, 0) and (4, 0)
Step-by-step explanation:
The x-intercepts of a parabola are the points where the parabola intersect the x-axis (horizontal axis). Therefore, the y-value of the x-intercepts are always 0. Since coordinates are written (x, y), we can immediately eliminate answers B and C.
Next, we look at the x-coordinates of where the parabola intersects the x-axis. We can see clearly that the parabola crosses the x-axis at [tex]x=4[/tex] and [tex]x=5[/tex]. Therefore, the x-intercepts of the given parabola are (4, 0) and (5, 0).
1. The diagram shows a triangle OAB and point M is a point on AB. Rajah menunjukkan segi tiga OAB dan titik M ialah satu titik pada AB. A 5 5a M 0 B ub Given OA= 5a , OB = 4b and 2 AM =3MB, find vector Diberi OA=5a, OB = 4b dan 2 AM =3MB, cari vektor (a) AB [4b – 5a (b) OM 12 2a +
we have to find the value of the x°=<GHC
In the triangle BDH,
<D=31°
<B=47°
we know that,
Sum of three angle of a triangle is 180°
According to the question,
<D+<B+<BHD=180°
31°+47°+<BHD=180°
78°+<BHD=180°
<BHD=180°-78°
<BHD=102°
But,
<GHC and <BHD forms a straight line
so,
<GHC+<BHD=180°
102°+x=180°
x=180°-102°
x=78°
Therefore,
The value of x is 78°
Which graph represents the function f(x) = √x+3 – 1?
Answer:
look at the png below
Step-by-step explanation:
simplify 6÷[5{6÷(5-2)}]
answer correctly i will give brainliest.
Answer:
hope this helppppp youuu
Ayuda
Which of the following represents the isolate the variable "r" from the following formula?
V = K * q / r
Answer:
r = K * q / V
Step-by-step explanation:
V = K * q / r
Use the data in the table to complete the sentence.
х
-2
-1
0
1
y
7
6
5
4
The function has an average rate of change of ______.
Answer:
-1
Step-by-step explanation:
Increasing the x-value by one results in the y-value decreasing by 1. Therefore, the average rate of change is -1.
Answer: -1
Step-by-step explanation: ;)
Segment addition and midpoints.
======================================================
Explanation:
AC = 13 and BC = 8
Those two facts must mean AB = AC-BC = 13 - 8 = 5.
Similarly, CD = BD - BC = 12 - 8 = 4
So,
AD = AB + BC + CD
AD = 5 + 8 + 4
AD = 17
------------
Another way to approach this problem would be to say
AD = AC + BD - BC
AD = 13 + 12 - 8
AD = 17
This works because when we add up AC with BD, we're double counting the portion from B to C. So this is why we subtract off BC to correct for this overcounting so to speak.
Answer:
Segment AD is 17.
Step-by-step explanation:
We know AC is 13, BC is 8, and BD is 12. We need the lengths of AB and CD.
To get AB's length, subtract BC's length from AC's length. We should get 5 for the length of AB (13 - 8 = 5).
To get CD's length, subtract BD's length from BC's length. We should get 4 for the length of CD. (12 - 8 = 4)
Now to add AB, BC, and CD. Add 5, 8, and 4 to get 17. (13 + 4 = 17)
The length of Segment AD is 17.