The measurement of angle DBC is 100°. It can be obtained by the properties of bisector of an angle and algebriac multiplication.
What is angle bisector?
An angle bisector is the ray or line segment that divides the angle into two equal parts.
Since the segment BD bisects angle ABC hence,
∠ABC = ∠ABD+∠DBC ..... (1)
Also, since segment BD bisects angle ABC hence,
∠ABD = ∠DBC
Use this fact in equation (1)
∠ABC = ∠ABD+∠ABD
∠ABC =2 ∠ABD
Now, substitute values and use algebriac multiplication.
7x = 2(3x+25)
7x = 6x+50
7x - 6x= 50
x=50
Now, substitute the value of x in the expression of ∠ABD.
∠ABD = 3x+25
∠ABD = 3(50)+25
∠ABD = 100
Now, since ∠ABD = ∠DBC hence, ∠DBC = 100.
Hence, the measurement of angle DBC is 100°.
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Line l Intersects line m. Find the value of a,b, x. Give reasons
The angles in the intersected lines are as follows:
a = 80 degreesb = 80 degreesx = 92 degreesHow to find angles when lines intersect?When lines intersect angle relationships are formed such as vertically opposite angles, linear angles etc.
Angle a is vertically opposite to angle b.
Vertically opposite angles are congruent.
Therefore,
∠a ≅ ∠b
Hence,
x + 8 = 100(vertically opposite angles)
x = 100 - 8
x = 92
b + x + 8 = 180(sum of angles on a straight line)
b + 92 + 8 = 180
b = 180 - 100
b = 80 degrees.
Hence,
a = 80 degrees
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7(x-1)=3x+2 in a improper fraction
Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good
Step-by-step explanation:
7(x-1)=3x+2
Distribute through the parentheses
7x-7=3x+2
Move the variable to the left-hand side and change its sign
7x-7-3x=2
or Move the constant to the right-hand side and change its sign
7x-7-3x=2
Collect like terms
4x=2+7
And then Add the numbers
4x=9
Divide both sides of the equation by 4
x=9/4
Mixed number is 2 1/4
I need help with this question, I don't understand how we get the x value in the equation.
I'm not trying to cheat, I just need steps to see how we get to the end of it.
y=x-1
y=-x+3
Step-by-step explanation:
the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.
the hudson valley renegades stadium hold a maximum of 4,505 people. During the height of their popularity, they sold out 219 consecutive games. how many tickets were sold during this time?
Answer:
Step-by-step explanation:
4,505 tickets were sold 219 times.
4,505 x 219
The answer is 986,595
simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
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Please Help me With this ASAP (20 Points)
Answer:
200*1-0.95-0.95+0.9025
200*1-1.9+0.9025
200*0.0025
0.5
Which is equivalent to (3^4n)^1/2
The expression which is equivalent to the given expression as in the task content by virtue of the laws of indices is; ( 3 )^2n.
Which expression is equipped to the given expression?It follows from the task content that the expression which is equivalent to the given expression is to be determined.
Since the given expression is;
( 3^4n ) ^(1/2)
However, it follows from the power of power law of indices that the expression above can be written as follows;
( 3 ) ^ (4n × 1/2)
= ( 3 )^2n
Therefore, the required equivalent expression is; ( 3 )^2n.
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recursively define the set of binary strings with more 0s than 1s.
0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.
What do binary strings mean?A series of bytes make up a binary string. A binary string is used to store non-traditional data, including images, as opposed to a character string, which typically holds text data. The quantity of bytes in a binary string determines its length. The CCSID for a binary string is 65535.Binary refers to this system of 1s and 0s. Because of the way they are made, computers only speak in binary. A computer is nothing more than a sizable number of switches. On those curiously engraved boards inside the computer, there are millions of microscopic electronic switches.If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y. A procedure P is defined recursively if its action, P(x), is defined in terms of another action, P(y), where x>y.Explanation:
0>1.
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The graphs of functions f(x) and g(x) = f(x) + k are shown: Graph of line f of x going through ordered pairs 0, 1 and 2, 6. Graph of line g of x going through ordered pairs 0, negative 1 and 2, 4. What is the value of k? a k = 2 b k = −2 c k = 1 d k = −1
Based on the graphs of functions f(x) and g(x) = f(x) + k, the value of k is: B. k = -2.
What is y-intercept?In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).
Since the graph of the line for function f(x) passes through the ordered pairs (0, 1) and (2, 6), its y-intercept is given by:
y = f(0) = 1.
Since the graph of the line for function g(x) passes through the ordered pairs (0, -1) and (2, 4), its y-intercept is given by:
y = g(0) = -1.
From the information provided above, we have the following function:
g(x) = f(x) + k
g(0) = f(0) + k
Making k the subject of formula, we have:
k = g(0) - f(0)
k = -1 - 1
k = -2.
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what is the equation in slope intercept form of the line that passes through the point (-0.5,7) and is parallel to the graph of y=-8x-2 please help
Answer:
y = -8x + 3
Step-by-step explanation:
Pre-SolvingWe are given that a line passes through the point (-0.5,7), and is parallel to y = -8x - 2
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
Parallel lines have the same slopes.
Therefore, we can start by finding the slope of y = -8x - 2.
It is also written in slope-intercept form. -8 is where m (slope) should be; therefore, the slope of the line is -8.
SolvingWe can plug in -8 for m in y=mx+b.
y = -8x + b
Now we need to find b.
As the equation passes through the point (-0.5,7), we can use its values to help solve for b.
Substitute -0.5 as x and 7 as y.
7 = -8(-0.5) + b
Multiply
7 = 4 + b
Subtract 4 from both sides
3 = b
Substitute 3 as b in the equation.
y = -8x + 3
Topic: parallel and perpendicular lines
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Examine the table, which represents the number of guests visiting a museum during a period of time.
If the relationship between hours and guests is proportional, what is the value of h?
Enter your answer as a number, like this: 42
Answer:
7
Step-by-step explanation:
649-531=118
We know that there are 118 more guests per hour.
Divide 826 by 118 to get 7.
Answer: 7
Step-by-step explanation:
The first line of the table is 2 and 236 if you divide 236 by 2 you get 118
Then after that you times it by any number after 5.5 until you get 826.
solve the system of equations using any method
3x-3= y
6x-5y=12
(please i need help im begging you)
Answer:
(1/3, - 2)-------------------------------
Given system3x - 3 = y6x - 5y = 12Solve by substitution6x - 5(3x - 3) = 126x - 15x + 15 = 12- 9x = 12 - 15- 9x = - 3x = - 3 / - 9x = 1/3Find y:
y = 3 * 1/3 - 3y = 1 - 3y = - 2help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
Select the values that make the inequality h<3h<3 true. (Numbers written in order from least to greatest going across.) -5 -2 0 2 2.9 2.99 2.999 3 3.001 3.01 3.1 4 6 8 11
The values that make the inequality, h < 3h < 3, true are the values of h in the range 0 < h < 1. The values -5, -2, 0, 2, 2.9, 2.99, 2.999, 3, 3.001, 3.01, 3.1, 4, 6, 8, 11, are larger or smaller than the values make the inequality true.
What is an inequality in mathematics?An is a comparison between two expressions, using non equal expressions, such as ≥, >, ≠, <, or ≤ symbols.
The specified inequality is; h < 3·h < 3
When h < 3·h, we get;
h is a positive number larger than 0, such that we get;
When h < 0, 3·h < h
Therefore; h > 0
The inequality, 3·h < 3, indicates;
3·h < 3
h < 3/3 = 1
h < 1
Which indicates that we get;
0 < h < 1
Therefore, non of the values make the inequality, h < 3·h < 3
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PLEASE HELP ME
What is the y-intercept of this line?
I keep getting confused someone please help me and explain it better to me
Answer:
2
Step-by-step explanation:
The y-intercept is the point at which the graph crosses the y-axis.
(I have marked it in blue on the attached graph).
From inspection of the given graph, the line crosses the y-axis at point (0, 2). So the y-intercept is 2.
5) Simplify the expression and identify any restrictions on x.
Answer:
attached in the file
Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
I need help with 9 10 and 11
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
33. Let M2x2 be the vector space of all 2x 2 matrices, and define T : M2x2 → Mo by T(A) A + AT, where a. Show that T is a linear transformation. b. Let B be any element of M2 c. Show that the range of T is the set of B in M2x2 with the d. Describe the kemel of T such that BT B. Find an A in M2xz such that T(A) B property that B B
a) T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂). So, T is a linear transformation.
b) T(A)=B, if B be any element of M₂
c) Range of T=={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
What is meant by matrix?A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns that is used to represent a mathematical object or an attribute of such an item.
A square matrix's determinant is a number connected with the matrix that is crucial for studying a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and a square matrix's eigenvalues are the roots of a polynomial determinant.
Define T: [tex]M_{ 2*2}[/tex] ⇒ [tex]M_{ 2*2}[/tex] by T(A)=A+[tex]A^{T}[/tex]
a) Let T is a linear transformation
Consider K₁A₁+K₂A₂ ∈ [tex]M_{ 2*2}[/tex]
T( K₁A₁+K₂A₂)= K₁A₁+K₂A₂+( K₁A₁+K₂A₂)[tex]( K₁A₁+K₂A₂)^{T}[/tex]
= K₁T(A₁)+K₂T(A₂)
T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂)
Therefore, T is a linear transformation.
b) Let B∈ [tex]M_{ 2*2}[/tex] such that [tex]B^{T}[/tex]=B
Therefore, B is a symmetric matrix.
Let A=(1/2)B∈ [tex]M_{ 2*2}[/tex]
T(A)=A+[tex]A^{T}[/tex]
=(1/2)B+[tex](1/2B)^{T}[/tex]
T(A)=B
A=(1/2)B such that T(A)=B
c) Range of T is the set of B in [tex]M_{ 2*2}[/tex], [tex]B^{T}[/tex]=B
T( [tex]M_{ 2*2}[/tex])={B∈ [tex]M_{ 2*2}[/tex]/ [tex]B^{T}[/tex]=B}
d) Kernel of T={A∈ [tex]M_{ 2*2}[/tex]/T(A)=0)
={A∈ [tex]M_{ 2*2}[/tex]/A+[tex]A^{T}[/tex]=0}
={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
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Three points Assuming M22 is the vector space containing all 22 matrices, T: M22 M22 is defined as T(A) = A + AT.
T is a linear transformation, therefore demonstrate it.
b) Assume that B is any element from M22 where BT = B. In M22, look for an A such that T(A) = B.
c) Explain the T kernel.
a) Verifying that T preserves sums and multiplication by scalars—which implies that T(0) = 0 in particular—is sufficient to determine if T is linear.
Additions: T(A+B) = A+B+A+B T = A+B+A T +B
T = (A + A T ) + (B + B T ) = T(A) + T (B).
Scalar multiplication
T(c · A) = (c · A)
T = c · A
T = c · T(A) (A).
b) Calculate A = 1 2B. Since AT = 1 2BT = 1 2B, T(A) = A + A.
T = \s1 \s2 \sB + \s1 \s2 \sB = B.
c) If 0 0 0 0 = A + A, then and only if A = a b c d, A is in the kernel of T.
If and only if 2a = b + c = 2d = 0, i.e., a = d = 0 and c = b, then T = a b c d + a c b d = 2a b + c b + c 2d. Therefore, the set ker(T) = 0 b b 0 : b R is the kernel of T.
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If you vertically stretch the exponential function f(x) = 2x by a factor of 4, what is the equation of the new function?
The equation of the new function is g(x) = 4(2ˣ)
How to determine the equation of the new function?The exponential equation is given as
f(x) = 2ˣ
Then, we have the transformation to be:
Vertically stretch by a scale factor of 4
The scale factor can be represented as k
So, we have
k = 4
The rule of vertical stretch by a scale factor of k is represented a
g(x) = kf(x)
So, we have
g(x) = 4 * 2ˣ
This gives
g(x) = 4(2ˣ)
Hence, the equation is g(x) = 4(2ˣ)
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Michael swam 2,000 yards on each of eighteen days.
The scatterplot above shows his swim time for and
corresponding heart rate after each swim. The line of
best fit for the data is also shown. For the swim that
took 34 minutes, Michael's actual heart rate was
about how many beats per minutes less than the rate
predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4
Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B
What is a scatterplot?A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.
On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.
From the graph the actual heart rate=150
but calculated heart rate from best fit line=148
Difference between actual and calculated=150−148=2
Option B is correct.
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Marco has 2 peices of rope that are each 8 yards long.how many feet of rope does m arco have
Answer:
48 feet
Step-by-step explanation:
Marco has 2 pieces of rope that are each 8 yards long.
2 x 8 = 16 yards.
Marco has a total of 16 yards of rope.
Note that for converting yard to feet, that: 1 yard = 3 feet.
Marco, in this case, has 16 yards. Multiply 16 yards with 3 feet to obtain your answer:
16 yards x (3 feet/1 yard) = 48 feet/16 yards.
Marco has 48 feet worth of rope.
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Which equation represents the partial sum of the geometric series? 125 + 25 + 5 + 1.
The correct option which represents sum expressed in sigma notation is A.
What is sigma notation?
A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.
The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.
The geometric series.
Main body:
∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.
Now, Calculate the partial sum of the geometric series as;
The geometric series = ∑ 125 (1/5)ⁿ⁻¹
Substitute n = 1, 2, 3, 4, we get;
= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹
= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³
= 125 + 25 + 125/25 + 125/125
= 125 + 25 + 5 + 1
Thus, The partial sum of the geometric series is;
⇒ 125 + 25 + 5 + 1
Option A is true.
The correct question is in the figure.
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. If g = -4 and h = -5 find the value of
a) 4gh
b) g²h
c) 5h - g²
Answer:
a) 80
b) -80
c) -41
Step-by-step explanation:
For g = -4 and h = -5, you want the values of ...
4ghg²h5h -g²To evaluate these expressions, put the value of the variable where the variable is, and do the arithmetic. A calculator can help.
a) 4gh= 4(-4)(-5) = 80
b) g²h= (-4)²(-5) = -80
c) 5h -g²= 5(-5) -(-4)² = -25 -16 = -41
pls help right now I need help
giving brainliest
this is reading btw
Answer:
The answer is A
Step-by-step explanation: I'm so smart
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
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help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Can someone please help me
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]n^{4}[/tex]
This is already simplified.
[tex]\frac{1}{n^{-5}}[/tex]
This is already simplified.
[tex]n^6 . n^{-8}[/tex]
= [tex]n^{6 - 8}[/tex]
= [tex]n^{-2}[/tex]
[tex]n^7 . p^8[/tex]
= [tex]n^{7 + 8}[/tex]
= [tex]n^{15}[/tex]
[tex]\frac{1}{n^3}[/tex]
This is already in simplified form.
Thus,
The expressions that are simplified are:
[tex]n^{4}[/tex]
[tex]\frac{1}{n^{-5}}[/tex]
[tex]\frac{1}{n^3}[/tex]
Options A, B, and E are the correct answer.
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Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
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