Yes, the triangles are congruent if AB ≅ DE.
Criteria for the Congruency of two Triangles
If two triangles share the same sides and angles, they are said to be congruent triangles.
Triangles are tested for congruence using the following 4 criteria:
1) Angle-side-angle(ASA): Two angles and a side of a triangle are congruent if they are equal to two angles and the corresponding side of another triangle.
2) Side-side-side(SSS): Two triangles make congruent triangles if all three sides of one triangle are equal to three sides of another.
3) Side angle side(SAS): A triangle is congruent if its two sides and any included angles are equivalent to those of another triangle's two sides and corresponding angle.
4) Hypotenuse - leg(HL): If a triangle's hypotenuse and one of its legs are equal, then the triangle's hypotenuse and leg are also equal.
Checking for Congruency in the Given Triangles
ΔDEF and ABC have a equal angles, ∠F=∠B, as well as a pair of equal sides, DF = AC.
Thus, in order to satisfy the SAS criterion of congruent triangles, AB = DE
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Answer:
(D) no, because the hypotenuses must have different lengths
Step-by-step explanation:
Find the equation of the line through point (8,−9) ( 8 , − 9 ) and perpendicular to 3+8=4 3 x + 8 y = 4 .
The equation of the line will be 3y + 8x = 165.
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that:-
Find the equation of the line through point (8,−9) ( 8, − 9 ) and perpendicular to 3 x + 8 y = 4.The given equation of the line is:-
3 x + 8 y = 4.
The slope of this line will be:-
3 x + 8 y = 4.
8y = -3x + 4
y = -3 /8x + ( 1 / 2)
y = mx + c
m = -3 / 8
Since the line is perpendicular to the other line 3x +8y = 4 so the slope will be inverse and negative for the line.
So the slope of the line will be -8 / 3
The equation of the line passing through the point will be given as:-
y - y 1 = m ( x- x1)
y - (-9) = ( -8 / 3) ( x - 8)
Y + 9 = ( -8 / 3 ) ( x -8 )
3 y = -8x + 165
3y + 8x = 165
Therefore the equation of the line will be 3y + 8x = 165.
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Question 1 of 25
Which estimate at a 95% confidence level most likely comes from a small
sample?
It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level.
A proportional confidence interval is provided by
[tex]\pi \pm z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where π is the sample proportion, z is the critical value and n is the sample size.
The margin of error is represented by
[tex]z \sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
As a result, smaller sample sizes result in wider margins of error. Option A has the greater margin of error in this scenario, so it most likely employed the smallest sample size.
Therefore we can conclude It is possible that a small sample size contributed to the 82% (±24%) estimate at a 95% confidence level. Option A is correct.
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The figure below is a right rectangular prism.
X
W
४
M
N
x
Y
N
O
12
2x
T
Which expression represents the volume of the prism?
01x³
O
O
(+)
0 (x)
Answer:
1/2x^3
Step-by-step explanation:
The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).
Just plug the numbers (or in this case variables) into the formula:
v = x times x times 1/2x
v = 1/2 times x^3
v = 1/2x^3
Volume
LBH1/2x(x)(x)1/2(x)³Option A
Here are the dimensions of some rectangles. Which rectangle has an area of 12 square units and a perimeter of 14 units?
a length of 1 unit and a width of 12 units
a length of 6 units and a width of 1 unit
a length of 6 units and a width of 2 units
a length of 3 units and a width of 4 units
Considering the formulas for the area and the perimeter of the rectangle, the one with the desired measures is given as follows:
a length of 3 units and a width of 4 units.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that:
A = lw.P = 2(l + w).For a rectangle with a length of 3 units and a width of 4 units, we have that:
A = 3 x 4 = 12 square units.P = 2(3 + 7) = 14 units.Hence it is the correct option.
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Can somebody please help answer this word problem using grass method? And showing how u get the answer thanks!!!
WILL MARK BRAINLIEST FOR WHOEVER ANSWERS THIS !!! :DD
Answer:3/20
Step-by-step explanation:
Fraction of total area mowed = (3/5) + (1/4) = 17/20
Therefore fraction of total area left = 1 - (17/20) = (20/20) - (17/20) = 3/20
Which two points on the number line represent numbers that can be combined to make zero?
B and D
A and B
C and D
A and C
A middle school took all of its 6th grade students on a field trip to see a play. The
students filled 341 seats, which was 55% of the total number of seats in the theater.
How many total seats were in the theater?
only a genius can solve it !!
[tex] \frac{ \cos(A) }{1 - \sin(A) } + \frac{ \sin(A) }{1 - \cos(A) } + 1 = \frac{ \sin(A) \cos(A) }{(1 - \sin(A)(1 - \cos(A)} [/tex]
[tex]\text{L.H.S}\\\\=\dfrac{\cos A}{1-\sin A} + \dfrac{\sin A}{1-\cos A} +1\\\\\\=\dfrac{\cos A(1-\cos A) + \sin A(1-\sin A) + (1-\sin A)(1 - \cos A)}{(1-\sin A)(1 -\cos A)}\\\\\\=\dfrac{\cos A - \cos^2 A + \sin A - \sin^2 A + 1 - \cos A - \sin A + \sin A \cos A}{(1 -\sin A)(1 - \cos A)}\\\\\\=\dfrac{-(\sin^2 A + \cos^2A) +1 + \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\dfrac{-1 + 1 + \sin A \cos A }{(1 - \sin A)((1 - \cos A)}\\\\\\=\dfrac{0+ \sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\[/tex]
[tex]=\dfrac{\sin A \cos A}{(1 - \sin A)(1 - \cos A)}\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
A right rectangular pyramid is sliced parallel to the base, as shown. (100 POINTS)
What is the area of the resulting two-dimensional cross-section?
2 m²
3 m²
9 m²
12 m²
That shaded region area we need
length=2mBreadth=1mArea
Length×Breadth2(1)2m²analyze the following budget,with an income of $600,to determine how much can be spent on food for the month
Answer:
C: 80
Step-by-step explanation:
Take 600, and subtract it by the values of 200, 95, 65, and 160.
You get $80 left.
Hope this helps!
If a_1=9a
1
=9 and a_n=-3a_{n-1}a
n
=−3a
n−1
then find the value of a_5a
5
.
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The value of a₅ is -729.
What is geometrical series?A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
Given the value of a₁=9 and the value of [tex]a_n=-3a_{(n-1)}[/tex]. Therefore, the value of a₅ can be written as,
a₂ = -3(a₁) = -3(9) = -27
a₃ = -3(a₂) = -3(-27) = 81
a₄ = -3(a₃) = -3(81) = -243
a₅ = -3(a₄) = -3(-243) = -729
Hence, the value of a₅ is -729.
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Another way to write g(h(x)) is
(gOh)(x)
(hog)(x)
Answer:
A. Another way to write g(h(x)) is (g×h)(x)
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
On. map with a scale of 1:75 000 the distance between a hotel and the airport is 3 cm
What is the actual distance I'm km?
a. 2.25
b. 2.5
c. 22.5
d. 25 km
please help
Answer:
a. 2.25 km
Step-by-step explanation:
the scale on a map means how many units in the mapp corresponds to how many units in reality.
in this case
1 cm on the map = 75000 cm in reality =
= 75000/100 m = 750 m =
= 750/1000 km = 0.75 km
3 cm = 3×1 cm = 3 × 0.75 km = 2.25 km
y’all help find the area and perimeter
Answer:
área is 15 perimeter is B
What is the average rate of change for this exponential function for the
interval from X.= 0 to x = 2?
Answer:
1.5
Step-by-step explanation:
The average rate of change is 1.5
when x=0 , the value of y =1
when x=2 the value of y = 4
average rate of change formula = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
a= 0 , f(a)=1
b=2, f(b)= 4
4 - 1 / 2 - 0 = 3/2 = 1.5
two dice are thrown what is the probability of two odd number
Answer:
6/12 or 1/2 or 50% or 0.5
Step-by-step explanation:
You have two 6-sided dice, and there are 3 odd numbers on each.
So, you put 6 on top, (the total number of odd outcomes) and 12 on the bottom. (12 total outcomes for both dice.) This simplifies to 1/2 or 50% or .5.
Eschool
geometry v19, cindy mcdermott ( 4872/ s) -
question 14 multiple choice worth 1 points)
(04.03 mc)
a segment with endpoints a (3, 4) and c (5, 11) is partitioned by a point b such that ab and bc form a 2:3 ratio. find b.
o (3.8, 6.8)
o (3.9, 4.8)
o (4.2, 5.6)
o (4.3, 5.9)
question 15(multiple choice worth 1 points)
The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let b = (x, y) represent the location of the point B, hence:
x = (2 / (2 + 3))(5 - 3) + 3 = 3.8
y = (2 / (2 + 3))(11 - 4) + 4 = 6.8
The location of point B that partitions A(3, 4) and C(5, 11) in the ratio 2:3 is (3.8, 6.8).
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which one is the correct graph
Graph f(x) = -1/2x
Click on the graph until the graph of f(x) = -1/2x appears
Answer:
The third graph
Step-by-step explanation:
The third graph depicts the function f(x) = -1/2x because for every 1 unit decrease along the y-axis, you travel 2 units on the x-axis.
Also, the two points on the third graph can satisfy the equation.
Point 1: (-2,1)
f(-2) = (-1/2)(-2)
f(-2) = 1
Point 2: (0,0)
f(0) = (-1/2)(0)
f(0) = 0
hii guys please answer this question
if two -1 and 2 are two zeroes of the polynomial 2x3- x2 - 5x - 2, find its third zero
Answer:
-1/2
Step-by-step explanation:
Zeros of a polynomial function are its x-intercepts, the values of x that make the polynomial zero. Each zero x=p corresponds to a linear factor (x-p) of the polynomial.
Monic polynomialA monic polynomial is one that has a leading coefficient of 1. For a monic polynomial of degree n, the coefficient of the term of degree n-1 is the opposite of the sum of all of the zeros. The constant term of any odd-degree monic polynomial is the opposite of the product of the zeros.
The given polynomial can be made monic by dividing by its leading coefficient:
(2x^3 -x^2 -5x -2)/2 = x^3 -(1/2)x^2 -(5/2)x -1
Sum of zerosThe given polynomial has degree 3, so we're interested in the coefficient of the x^2 term. That coefficient is -1/2, so the sum of zeros will be ...
sum of zeros = -(-1/2) = 1/2
If z represents the third zero, then we have the sum ...
1/2 = -1 +2 +z
z = -1/2 . . . . . . subtract 1 from both sides
The third zero is -1/2.
Product of zerosThe given polynomial is of odd degree, so the product of the zeros is the opposite of the constant.
(-1)(2)(z) = -(-1)
z = 1/(-2) = -1/2 . . . . . divide by the coefficient of z
The third zero is -1/2.
GraphOf course, a graph will show all of the (real) zeros. The attached graph from a graphing calculator shows the third zero is -1/2.
Here are the first five terms of a number sequence .
10 16 22 28 34
The nth term of a sequence T is given by n squared-3
There are numbers that are terms in both the sequence S and the sequence T.
Find one of these numbers.
Answer:
t=4+6n
Step-by-step explanation:
a = 10
d=6
in general
tn = a + (n-1)*d
tn = 10 + (n-1)*6
tn = 10 + 6n - 6
tn = 4 + 6n
So if n = 5 then
t5= 4+6*5
t5= 4 + 30
t5 = 34 which agrees with your givens.
What is the slope of the line with the equation y-3=-1/2(x-2)?
Answer: [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]y -3 = -\frac{1}{2}(x-2)[/tex]
Write as slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
[tex]y-3=-\frac{1}{2}x + 1[/tex]
[tex]y = -\frac{1}{2}x+4[/tex]
Therefore, the slope is [tex]-\frac{1}{2}[/tex].
A function is a rule thats assigns each value of the independent variable to exactly ____ value of he dependent variable.
Free response:
A function assigns the values. A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The given statement can be completed as given below.
A function is a rule that assigns each value of the independent variable to exactly each value of the dependent variable.
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¿Es necesario que los triángulos congruentes tengan el mismo tamaño?
I don't understand your question
Sorry!!! :)
let pheta be an acute angle. if cos2pheta+cos^2pheta=1, then cospheta=
2/3
1
√6/3
√2/3
The required value of value of cospheta = √2/3, here correct option is d) √2/3.
The given equation is a Trignomatric Equation,
cos2pheta+cos^2pheta = 1
These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
cos2pheta + cos^2pheta = 1
Now we know that,
[tex]cos2x[/tex] = [tex]cos^2x -1[/tex]
so, substituting cos2pheta = 2cos^2pheta - 1
2cos^2pheta-1 + cos^2peta = 1
3cos^2peta = 2
cos^2pheta = 2/3
cospheta = √2/3
Thus, the required value for the cospheta = √2/3.
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Is this pattern a net for the three-dimensional figure?
no
yes
Answer:
no
Step-by-step explanation:
the bet displays 3 hexagonal bases when in the figure there is only 2 bases.
Answer:
No.
Step-by-step explanation:
Examples of three-dimensional figures are: Cuboid, Cube, Cylinder, Sphere, Pyramid, and a Cone.
Richard has a debt of $45. Express it in the form of absolute value.
The absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
As we know,
The absolute value of a negative account balance is equal to the amount of debt. A balance of $0 on an account means there is no debt. Credit is shown by a positive account balance.
Richard has a debt of $45.
The negative of 45 value represents the debt.
-$45 = debt
Absolute value = |-45| = 45
Thus, the absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
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Please help, I have been trying for a while :(
question on photo
Answer:
[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
Step-by-step explanation:
multiply the numerator/denominator of the first fraction by (x - 4)
multiply the numerator/denominator of the second fraction by (x + 2)
this ensures that the fractions have a common denominator
[tex]\frac{4}{x+2}[/tex] - [tex]\frac{3}{x-4}[/tex]
= [tex]\frac{4(x-4)}{(x+2)(x-4)}[/tex] - [tex]\frac{3(x+2)}{(x+2)(x-4)}[/tex] ← subtract numerators leaving the common denominator
= [tex]\frac{4x-16-3x-6}{(x+2)(x-4)}[/tex]
=[tex]\frac{x-22}{(x+2)(x-4)}[/tex]
4. If u = {1,2,3,....10) A = { odd numbers up to 9} B = {numbers less than 7). Write out the members of the following sets: (i) AUB (ii) An B (ii) A(prime) U B
Answer:
i. {1,2,3,4,5,6,7,9}
ii. {1,3,5}
iii. {1,2,3,4,5,6,8,10}
Step-by-step explanation:
U= {1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,7,9}
B= {1,2,3,4,5,6}
A U B = {1,2,3,4,5,6,7,9}
A n B = { 1,3,5}
A (prime) U B =
A(prime)= {2,4,6,8,10}
Therefore A(prime)= {1,2,3,4,5,6,8,10}
I’ve been stuck in this for almost 20 minutes
help :/
Answer:
pi/2 units to the left
Step-by-step explanation:
the formula is y = cos(x-b) so when b is negative, the formula will show a plus sign because minus negative is adding. this means the graph is shifted -pi/2 to the right which is really pi/2 to the left
help me with a maths question thanks a lot!!
Answer:
Side b is approximately 4.00064cm or since the question asked for the answer to be up to one decimal point, your answer should be 4 cm
Step-by-step explanation:
First of all, this triangle isn't a right triangle. This can be proven if we assume that the triangle is a right triangle. If it is a right triangle, since, one of its angle is 30 degrees, we can find the last unknown angle to = 60 degrees. Therefore, using the side ratios of a 30-60-90 triangle, and since side b is the smallest side (because it has the smallest angle facing it), its length is one half the length of the hypotenuse, therefore making its length 4. However, the 30-60-90 ration also states that, in this case, side b * sqrt(3) should be equal to the side tha measure 7cm, which is clearly not true. Therefore, proving that this triangle isn't a rigt tirangle.
So now, let's get to solving the question. Since we found out that this isn't a right triangle, we have to use the law of cosines which states
a^2 = b^2 + c^2 - 2bc*cos(A) where A is the angle facing side a
If we do this, it comes to the solution that a is approximately 4.00064cm.
Therefore, side b measures to 4.00064cm.