The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
What are similar triangles?
It is important to note the following;
"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."
The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."
SSS similarity postulates that; "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."
SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."
SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."
For given question,
We have been given triangles ABD and CBD.
B is the midpoint of line AC
⇒ AB = BC
For triangles ABD and CBD,
side AB = side CB; since, B is the midpoint of line AC
side BD = side BD ; they have common sides
side AD = side CD = 15 units each
So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.
Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A
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Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Given:
f(x) = ln(x)
n = 4
c = 3
nth Taylor polynomial for the function, centered at c
The Taylor series for f(x) = ln x centered at 5 is:
[tex]P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+ \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}[/tex]
Since, c = 5 so,
[tex]P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+ \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}[/tex]
Now
f(5) = ln 5
f'(x) = 1/x ⇒ f'(5) = 1/5
f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25
f'''(x) = 2/x³ ⇒ f'''(5) = 2/5³ = 2/125
f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625
So Taylor polynomial for n = 4 is:
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
Hence,
The nth taylor polynomial for the given function is
P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴
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a=3. b=2
5ab+4b+10a
help please?
Answer:
68
Step By Step Explanation:
Evaluate for a=3,b=2
(5)(3)(2)+(4)(2)+(10)(3)
(5)(3)(2)+(4)(2)+(10)(3)
=68
Answer:
The solution is 68
Step-by-step explanation:
a = 3 and b = 2
5ab+4b+10a
= 5(3)(2)+4(2)+10(3)
= 5(6)+8+30
= 30+8+30
= 38+30
= 68
Help!!! Brainliest to 1 or 2 answer!!
Answer:
35-17=3y
Step-by-step explanation:
3y+17=35
-17 -17
3y=35-17
A monkey has a strict banana eating
schedule. On a sunny day it eats 20
bananas and on a rainy day it eats 12
bananas. In 8 consecutive days it eats
112 bananas. Question: how many
sunny days are there in these 8 days?
A photo below is being enlarged you a 24 negative by 30 inches current what is the scale factor being used to enlarge it
If a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.
Scale factorGiven:
Enlarged size=24 negative by 30 inches
Original size=4 in, 5 in
Using this formula
Let k represent the (ratio) scale factor being used to enlarge it
Scale factor/Enlarged size/Original size
Let plug in the formula
K=24/4
K=6
K=30/5
K=6
Therefore if a photo below is being enlarged you a 24 negative by 30 inches current. The scale factor being used to enlarge it is: 6.
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Use completing the square to solve for x in the equation (x 7) (x minus 9) = 25.
The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
To find the values of x:
Given equation: [tex](x+7)(x-9)=25[/tex]
Then: [tex]x(x-9)+7(x-9)=25[/tex]
Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]
[tex]x^{2} -9x+7x-63=25[/tex]
Combine like terms:
[tex]x^{2} -2x-63=25[/tex]
Subtract 25 from both sides and obtain:
[tex]x^{2} -2x-88=0[/tex]
Using completing square form:
Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:
[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]
Add 89 to both sides we have:
[tex](x-1)^{2} =89[/tex]
Taking square roots on both sides, obtain:
[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]
Add 1 to both sides we have:
[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]
Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].
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The complete question is given below:
Use completing the square to solve (x + 7)(x – 9) = 25 for x.
if the perimeter of an equilateral triangle is 24cm, find the length of it's side
Answer:
it's side length equals to 8.
Step-by-step explanation:
Hello!An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a "regular" triangle.
Perimeter: 3 x side of equilateral triangle
[tex]24 = 3 \times each \: sides[/tex]
divide both sides by 3
[tex]one \: of \: its \: side = 8[/tex]
Thus, as all the three sides equals to 8.
Hope it helps!
What is the domain of the exponential function shown in the graph?
A.x > -1
B.x ≤ -1
C. x < 0
D. -∞ < x < ∞
The domain of the exponential function shown in the graph is -oo < x < oo
How to determine the domain of the exponential function shown in the graph?The function on the graph is an exponential function.
The domain is the set of x values the function can take
From the graph, we have the following x values
This means that the domain of x in the graph is -oo < x < oo
Hence, the domain of the exponential function shown in the graph is -oo < x < oo
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Divide. Write the quotient in lowest terms.
4 2/3 / 7
The quotient in lowest term exists 2/3.
What is an improper fraction?An improper fraction exists as a fraction whose numerator exists equivalent to, larger than, or of equivalent or higher degree than the denominator.
Given the quotient: [tex]$4\frac{2}{3} \div 7[/tex]
Write [tex]$\frac{2}{3}[/tex] in improper fraction
[tex]$4\frac{2}{3}= \frac{14}{3}[/tex]
Dividing throughout by 7 on both sides of the equation, we get
[tex]$4\frac{2}{3} \div 7 = \frac{14}{3}\div 7[/tex]
Change the division sign to multiplication by taking the reciprocal of 7
[tex]$\frac{14}{3}\div 7 = \frac{14}{3} \times \frac{1}{7}[/tex]
Simplifying the above equation, we get
[tex]$\frac{14}{3}\div 7 = \frac{2}{3}[/tex]
Therefore, the quotient in lowest term exists 2/3.
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MULTIPLY (x^2-5x)(2x^2+x-3)
[tex]\bf{ (x^2-5x)(2x^2+x-3)}[/tex]
[tex]\bf{Distribute \ the \ sum \ group. }[/tex]
[tex]\boldsymbol{\sf{x^{2} (2x^{2} +x-3)-5x(2x^{2} +x-3) }}[/tex][tex]\bf{Expand \ the \ distribution \ of \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -5x(2x^{2} +x-3) }}[/tex][tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -(10x^{3}+5x^{2} -15x) }}[/tex][tex]\bf{Remove \ parentheses. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+x^{3}-3x^{2} -10x^{3}+5x^{2} -15x }}[/tex][tex]\bf{Collect \ like \ terms. }[/tex]
[tex]\boldsymbol{\sf{2x^{4}+(x^{3}-10x^{3})+(-3x^{2} -5x^{2} )+15x }}[/tex][tex]\bf{Simplify}[/tex]
[tex]\boxed{\boldsymbol{\sf{2x^{4}-9x^{3}-8x^{2} +15x }}}[/tex]3. If the geometric mean of a and 25 is 20,
find the value of a.
Answer:
Value of a is 16.
Step-by-step explanation:
Solution Given:
we know that
Geometric mean=[tex]\sqrt{a*b}[/tex]
By using this formula
20=[tex]\sqrt{a*25}[/tex]
20=5[tex]\sqrt{a}[/tex]
dividing both side by 5, we get
20/5=5/5* [tex]\sqrt{a}[/tex]
4=[tex]\sqrt{a}[/tex]
squaring both side
4²=a
:. a=16
sketch graphs of the following on the same plane using different colours y=2x-3;y=-3;x=-3;2x+3y-6=0
The graph of the four linear equations is the one we can see below, such that:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.How to graph the linear equations?
Here we have the set of linear equations:
y = 2x - 3y = -3x = -32x + 2y - 6 = 0We want to graph these 4 lines on the same coordinate axis.
The line:
y = -3
Is an horizontal line at y = -3
The line:
x = -3
Is a vertical line at x = -3.
And the other two are common linear equations that are graphed in the usual way, then the graph of all the linear equations is the one you can see below.
Where:
Blue line is y = -3Green line is x = -3Orange line is y = 2x - 3Purple line is 2x + 3y - 6 = 0.If you want to learn more about linear equations:
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At a furniture manufacturer, worker a can assemble a shelving unit in 5 hours. worker b can assemble the same shelving unit in 3 hours. which equation can be used to find t, the time in hours it takes for worker a and worker b to assemble a shelving unit together? rate (shelving units per hour) time (hours) fraction completed worker a one-fifth t worker b one-third t 5 t 3 t = 1 one-fifth t minus one-third t = 1 one-fifth t one-third t = 1 5 t minus 3 5 = 1
If they work together, they need 15/8 hours to assemble one shelving unit.
What does work mean in math?
In summary, work is done when a force acts upon an object to cause a displacement. Three quantities must be known in order to calculate the amount of work. Those three quantities are force, displacement and the angle between the force and the displacement.According to tittle, we know worker A can assemble a shelving unit in 5 hours , which means worker A can finish 1/5 of work in 1 hour . And worker B can finish 1/3 of work in 1 hour.
If A & B work together , they will spend the same time t to assemble only one shelving .
That means, 1/5t + 1/3 t = 1 (equation)
1/5 t is worker A's workload during time t , 1/3 t is worker B workload.
So, 1/5 t + 1/3t = 1 is the answer
⇒ 5t + 3t = 15
⇒ t = 15/8 hours
If they work together, they need 15/8 hours to assemble one shelving unit.
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Answer:
Letter C is the correct answer or 1/5 t + 1/3t = 1
23-2(17+3^3)
Sjshjshdjsjshs
Answer:
-65
Step-by-step explanation:
23-2(17+3^3)
23-2(17+27)
23-2(44)
23-88
=-65
Please please please help
Answer:r=14°
Step-by-step explanation:
(5r-5)°+ (8r+3)°=180
(Sum of angles on a straight line =180°)
Collect like terms
5r+8r-5+3=180
13r-2=180
13r=180+2
13r=182
r=182/13
r=14°
If the vertex of a parabola is at the point (-2, 5), then the equation for the axis of symmetry for the parabola is x = -2. True or false?
Answer:
true
Step-by-step explanation:
thats really it i believe its true
What is the last digit of the product of all the numbers between 11 and 29?
we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
What is the last digit of the product of all the numbers between 11 and 29?
Here we want to find the last digit of the product between all the whole numbers larger than 11 and smaller than 29.
Then we have the product:
P = 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28
Now, notice that there is a 20 there.
Any number times 20 will end with a zero, then:
P = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)
Only with that, we can conclude that the last digit of the product of all the numbers between 11 and 29 is 0.
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10 points!!!!!!!!!!!!!!!!!!!!!
Answer:
23
Step-by-step explanation:
5 1/2 divided by 1 3/8
Answer:
4
Step-by-step explanation:
1. Convert from mixed number to fraction
[tex]5\frac{1}{2} =\frac{5(2)+1}{2} =\frac{11}{2}[/tex]
[tex]1\frac{3}{8}=\frac{(1)(8)+3}{8} =\frac{11}{8}[/tex]
2. Divide fractions
[tex]\frac{\frac{11}{2} }{\frac{11}{8} } =\frac{(11)(8)}{(11)(2)} =\frac{8}{2} =4[/tex]
Hope this helps
Use the polynomial [tex]4x^{5} -3x^{2} + x[/tex]
a. How many terms are in this polynomial? _____
b. What is the degree of this polynomial? _____
c. What is the contrast? _____
what is the volume of a triangular pyramid that is 12 feet tall and has a base area of 5 square feet
The volume of the triangular prism as described is; 20 cubic foot.
What is the volume of the triangular pyramid?A triangular pyramid refers to pyramid which has a triangular base
It follows from the formula for calculating the volume of a triangular prism that;
Volume = (1/3) × base area × height.
Consequently,
volume of the prism = (1/3) ×5 × 12
Volume = 20 cubic foot
Therefore, volume of the triangular prism as described is; 20 cubic foot.
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(x+3)^0 Rewrite the equation with positive exponents and simplify. x≠-3.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\huge\textbf{Simplifying:}[/tex]
[tex]\mathsf{(x + 3)^0}[/tex]
[tex]\text{Anything raised to the 0 power it automatically equal to 1.}[/tex]
[tex]\huge\text{So, this mean that your answer should be: \boxed{\mathsf 1}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find lim f(x) if f(x)
x->5
=
{
-x² -1, x #5
-3, x=5
Given
[tex]f(x) = \begin{cases} -x^2 - 1 & \text{if }x \neq 5 \\ -3 & \text{if }x=5 \end{cases}[/tex]
we have
[tex]\displaystyle \lim_{x\to5} f(x) = \lim_{x\to5} (-x^2-1) = -5^2-1 = \boxed{-26}[/tex]
since we are approaching [tex]x=5[/tex], so effectively [tex]x\neq 5[/tex] and we use the definition of [tex]f(x)[/tex] under that condition.
area of an isosceles triangle is 60 square cm. If the measure of its equal sides is 13 square cm then find the base sides.
The base side of the isosceles triangle in discuss as described in the task content is; 10cm.
What is the length of the base side of the isosceles triangle?According to the task content, the area of the isosceles triangle is 60 square cm.
Since, the length of its longest sides is 13 cm and since it follows from convention that the bisection of an isosceles triangle results in the formation of two right-triangles.
Consequently, it follows from Pythagoras triples that the height of each right triangle is 12 and its base is; 5.
Consequently, the base of the whole isosceles triangle is; 2 × 5 = 10cm.
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Which of the following values would complete the ordered pair if the point is on the graph of f(x) = -3x + 2?
(-1, )
0-1
05
01
0-5
The y-coordinate that completes the point exists 5.
What is an ordered pair?An ordered pair (x, y) denotes the x-and-y coordinates of a general point, where x exists the input value of a function and y exists the output value of a function.
The output value exists y = f(x) and must be found using the rule (function) to the given input value.
In this case the rule exists f(x) = - 3x + 2, and the input value, x, exists - 1 (the first value of the ordered pair).
This exists the mathematical procedure:
x = - 1
f(x) = f (-1)
Then substitute the value x = -1 then
f(-1) = -3 (-1) + 2 = 3 + 2 = 5.
Therefore, the correct answer is option b) 5.
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pls help will mark this brainlest
Answer: D
Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.
Answer:
Line D
Step-by-step explanation:
Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.
Larry took 21 minutes to do 7 math problems. Mary took 19 minutes to do 8 math problems. Which student
did more problems per minute
find the discriminant of the following quadratic equation
x^-5x+3=0
The discriminant of the given quadratic equation as in the task content can be evaluated by means of the formula; D = b²-4ac and it's value is; 13.
What is the discriminant of the quadratic equation as given in the task content?According to the task content, it follows that the quadratic equation whose discriminant is to be determined is; x²-5x+3=0.
By comparison with the standard form equation of a quadratic graph which goes thus; ax²+bx +c = 0, in which case, the determinant is given by the expression; b² - 4ac.
We can consequently evaluate the determinant of the quadratic equation in discuss as follows;
Determinant = b² -4ac = (-5)² - (4×1×3) = 25 - 12
Hence, the determinant in this case is; 13.
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A cell phone carrier introduced a new strategy to increase their number of subscribers. The function below represents the increase in number of subscribers, where f(t) represents the number of subscribers and represents the time in months
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An exponential function is in the form:
y = abˣ
Where a is the initial value of y and b is the multiplication factor.
Let f(t) represents the number of subscribers and t represents the time in months. Hence:
[tex]f(t) = 250(1.4)^t[/tex]
a = 250, b = 1.4
The cell phone carrier had 250 subscribers before the strategy was introduced. After the new strategy is introduced, the number of staffs increased by a factor of 1.4.
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Answer: 250, 1 month, and 1.4
A company found that an experienced surveyor can survey a roadbed in 7 hours. An apprentice surveyor needs 8 hours
to survey the same stretch of road. If the two work together, find how long it takes them to complete the job.
***
The number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
Rate of workHours it takes the experienced surveyor = 7 hoursSurveyors rate of work = 1/7Hours it takes the apprentice = 8 hoursApprentice rate of work = 1/8If the two work together;
Time taken for both to complete the task = Surveyors rate of work + Apprentice rate of work
= 1/8 + 1/7
= (7+8) / 56
= 15/56 hours
Therefore, the number of hours it will take both the surveyor and apprentice to complete the same job is 15/56 hours.
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