Find m∠ABD and m∠CBD given m∠ABC = 111∘
The Equations are (-10x+58)∘ and (6x+41∘)
Write and Solve an equation
Answer:
x=-3
<ABD=88
<CBD=23
Step-by-step explanation:
We know that <ABC is made up of 2 angles: <ABD and <CBD.
We also know that the m<ABC is 111.
Therefore, <ABD and <CBD added together must equal 111.
<ABD+ <CBD =111
We know that <ABD is -10x+58 and <CBD is 6x+41, so we can substitute these in.
-10x+58+6x+41=111
Combine like terms
(-10x+6x)+(58+41)=111
-4x+99=111
Now we need to solve for x. First, move all the constants to the same side. Subtract 99 from both sides, since 99 is being added to -4x.
-4x+99-99=111-99
-4x=12
Next, divide both sides by -4, since -4 and x are being multiplied.
-4x/-4=12/-4
x=-3
Now we know x, and can substitute it in to find the angle measures.
<ABD
-10x+58
-10(-3)+58
30+58
88
<CBD
6x+41
6(-3)+41
-18+41
23
[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]
Given:
m∠ABC = 111∘
m∠ABD = (-10x+58)∘
m∠CBD = (6x+41)∘
First, find the value of x by creating an equation
Thus:
[tex]m\angle ABD + m \angle CBD = m \angle ABC[/tex] (angle addition postulate)
Substitute
[tex](-10x+58) + (6x+41) = 111[/tex]
Solve for x
[tex]-10x+58 + 6x+41 = 111[/tex]]
Add like terms
[tex]-10x+58 + 6x+41 = 111\\-4x + 99 = 111\\-4x = 111 - 99\\-4x = 12\\[/tex]
Divide both sides by -4
[tex]x = -3[/tex]
Find m∠ABD and m∠CBD by plugging in the value of x
[tex]m\angle ABD = -10x + 58 \\m\angle ABD = -10(-3) + 58 \\m\angle ABD = 88^{\circ}[/tex]
[tex]m \angle CBD = 6x + 41\\m \angle CBD = 6(-3) + 41\\m \angle CBD = 23^{\circ}\\[/tex]
Therefore:
[tex]m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}[/tex]
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Choose the function whose graph is given below.
Y = csc x
Y= tan x
Y= sec x
Y = cot x
The given graph shown in the image is of function y = cotx. Option D is correct.
Given that,
To determine the function whose curve is plotted in the graph.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.
Here,
Since the given graph is of cots because only cotx tends to infinity whenever x tends nπ where n is an integer on the number line.
Thus, the given graph shown in the image is y = cotx. Option D is correct.
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Factor this expression.
4x-12
O A. 4(x-4)
OB. 4(x-6)
O C. 4(x-3)
O D. 4(x-8)
Answer:
C. 4(x-3)
Step-by-step explanation:
Suppose the equation h =− 16t2 + 35t models the altitude a football will reach t seconds after it is kicked. Is it possible for the football to reach 16 ft in the air? Justify your answer.
Answer:
The ball will be able to reach the 16 ft.
Step-by-step explanation:
In order to calculate if the ball will be able to reach that height, we must make "h" equal to 16, if there's a real positive solution, then the ball will be able to reach it.
16 = -16t² + 35t
16t² - 35t + 16 = 0
t = [-(-35) +- sqrt((-35)² - 4*16*16)]/(2*16)
t = [35 +- sqrt(1225 - 1024)]/32
t = [35 +- sqrt(201)]/32
t = (35 +- 14.177)/32
t1 = 0.65071875
t2 = 1.5367
The ball will reach that height at 0.65 s and 1.53 s.
what is the area of this triangle?
Answer:
I believe the answer is 24
Answer:
The area of the triangle is 24 units2
Step-by-step explanation:
To find an area of a triangle you simply have to multiply a and b which are the legs of a triangle, in this case it would be 6 and 8, after doing that you divide the result by 2. So A= 6x8/2 ---> A=48/2 -----> A=24
1. Show work and find the value of the circumference of the circle with a 12 cm radius.
Answer:
75.36
Step-by-step explanation:
3.14(pi) x 24(diameter) = 75.36(circumference)
factorise 15x- 10x^3
Answer:
5x (3-2x^2)
Step-by-step explanation:
so all you have to do is 15x-10x=5x right?, then all you have to do is 15/5=3. 10x/5x=2x. then subtract 1 from the exponents. then you get the answer. okay Im sure about the fist part and the divison but not the exponents, I did use a calculator to check it though.
The factorize equation is, [tex]\rm 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0[/tex].
The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
Given that,
Equation; [tex]\rm 15x - 10x^3[/tex]
We have to determine,
Factorize the equation and factor of the equation.
According to the question,
To factorize the equation and determine the factor of the equation following all the steps given below.
Equation; [tex]\rm 15x - 10x^3[/tex]
Step1; Taking the term 5x common from the equation,[tex]\rm = 15x - 10x^3 = 0 \\\\= 5x (3-2x^2) = 0[/tex]
Step2; Simplify the equation,[tex]\rm = 5x (3-2x^2) = 0\\\\ = 5x (\sqrt{3} - \sqrt{2x}) (\sqrt{3}+\sqrt{2x}) = 0[/tex]
Step3; The roots of the equation are,[tex]\rm = 5x (\sqrt{3} - \sqrt{2}x) (\sqrt{3}+\sqrt{2}x}) = 0\\\\ The \ roots \ of \ the \ equation \ are;\\\\5x = 0, \ x = \dfrac{0}{5}, \ x =0\\\\\\[/tex]
[tex]\sqrt{3} - \sqrt{2x} = 0, \sqrt{2}x = \sqrt{3}, \ x = \dfrac{\sqrt{3} }{\sqrt{2} }\\\\ \sqrt{3} +\sqrt{2x} = 0, \sqrt{2}x = -\sqrt{3}, \ x =- \dfrac{\sqrt{3} }{\sqrt{2} }[/tex]
Hence, The roots of the equation are [tex]0 , \ \dfrac{\sqrt{3}}{\sqrt{2} }, \dfrac{-\sqrt{3}}{\sqrt{2} }[/tex].
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Find the value of the variable. If the answer is not a whole number, round to the nearest tenth.
The image is of a circle with two secant segments which intersect outside the circle. Inside and outside length of first one are marked as x and 5 respectively. Inside and outside length of second one are marked as 10 and 4 respectively.
A. 9
B. 8
C. 6.2
D. 22.5
Answer:
C
Step-by-step explanation:
Two secants drawn to a circle from a common external point, then
The product of the external part and the entire part of one secant is equal to the product of the external part and the entire part of the other secant, that is
5(5 + x) = 4(4 + 10) = 4 × 14 = 56
25 + 5x = 56 ( subtract 25 from both sides )
5x = 31 ( divide both sides by 5 )
x = 6.2 → C
If you take out a loan that costs $561 60 over eight years at an interest rate of 9% how much was the loan for?
Answer:
The loan was $28184.81
Step-by-step explanation:
Let the loan amount be x
Rate of interest on Loan = 9%
Time = 8 years
Amount of loan over 8 years = $56160
Formula : [tex]A=P(1+r)^t[/tex]
Where A = Amount =56160
P = Principal = x
r = rate of interest = 9% = 0.09
t = time = 8 years
Substitute the values in the formula :
So,[tex]56160=x(1+0.09)^8[/tex]
[tex]\frac{56160}{(1+0.09)^8}=x[/tex]
$28184.81=x
Hence The loan was $28184.81
Order the steps to solve the equation
log(x2 - 15) = log(2x) form 1 to 5.
x² - 2x - 15=0
Potential solutions are -3 and 5
IIIII
x² - 15 = 2x
x - 5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0
Answer:
Attention for the conditions:
[tex]x^{2} -15>0\\2x>0\\so\\x>0[/tex]
Step-by-step explanation:
we have
[tex]log(x^{2}-15)= log(2x)\\\\x^{2} -15 = 2x\\\\x^{2} -5x+ 3x-15=0\\ (x^{2}-5x)+(3x-15)=0\\ x(x-5)+3(x-5)=0\\(x-5)(x+3)=0\\x-5=0, x=5 \\\\x+3=0, x= -3[/tex]
So the solutions are 5 because x>0
Each side of a triangle is a different length. One side is 6, one side is greater than 6, and one side is less than 6. The perimeter of the triangle could not be
a) 13
b) 18
c) 22
d)24
Answer:
i think the correct answer is c sorry if im wrong
Answer:
The perimeter of the triangle could not be 24 - which is our solution.
Step-by-step explanation:
The first approach to this problem that comes to my mind, is to find the most " restricting " triangles possible. By that I mean the largest length of the side greater than 6 and the side less than 6.
The length of the side greater than 6 has to be less than 12 - considering it has to stretch the sum 6 + 6 - by the Triangle Inequality Theorem. Therefore, the most restricting triangle possible to the 1st decimal place should be the following -
{ 6, 5.9, 11.8 } ... the catch here is that this triangle does not need to be composed of lengths being whole numbers. If that was true the most " restricting " triangle would have lengths { 6, 5, 10 } throwing you off track as it's perimeter is 21.
{ 6, 5.9, 11.8 } adds to a sum of 23.7, eliminating answer choice c. Therefore, we can conclude that the perimeter of the triangle can't be 24. In fact this is only to the first decimal place, you could be more specific and go to the 100th decimal place even. Either way, the perimeter of the triangle has to be less than 24.
Find the volume of this triangular prism
Answer:
4608 ft2
To find the volume of a prism, you have to multiply the area*base*height.
So in this case you have (8*8)*8*9.
That results in, 64*8*9.
You multiply them and get 4608 ft2.
Have a nice day!
At Ken's boutique, 33 customers wore a size small, and 51 customers wore a different size.
What is the probability that a randomly selected customer wore a size small?
Write your answer as a fraction or whole number.
Answer:
11/28
Step-by-step explanation:
1. Add up all of the customers to get the sample size.
33 + 51 = 84
2. Since we are finding the chance of it being a size small, 33 will be out numerator.
3. Create the final fraction, (33/84)
4. Simplify (11/28)
Hope this helps! Comment if you have any questions. :)
Answer:
11/28
Step-by-step explanation:
First, you add 33 and 51 to get a total of 84 customers. Then you put the number of selections you want (33) as the numerator to 84, to get 33/84. Finally you simplify and get the probability of selecting a customer at random. Answer= 11/28 is your probability
Jenny has bought 24 pounds of dog food. She feeds her dog 3/8 pounds for each meal. For how many meals will the food last?
Answer:
64 meals
Step-by-step explanation:
24 ÷ 3/8
= 24 x 8/3
= 192/3
= 64 meals
A garden measuring 16 meters by 8 meters is going to have a walkway constructed all around the perimeter, increasing the total area to 240 square meters. What will be the width of the pathway?
Answer:
The width of the pathway is:
7 meters.Step-by-step explanation:
To identify the width of the pathway, you must remember the area formula of a rectangle:
Area of a rectangle = length * width.From which the width can be cleared:
Width of a rectangle = area / length.We know that the length of the terrain was not modified since the pathway is in the perimeter of the rectangle (16 m) and that the new area is 240 m^2, so we only have to replace the cleared formula:
Width of a rectangle = 240 m^2 / 16 m = 15 m.The new width is equal to 15 meters, but since the question is not the total width but the width of the pathway, the width of the previously provided land must be subtracted from the value obtained.
Pathway width = Total width - Garden width. Pathway width = 15m - 8m = 7 meters.Jack ran 13.5 miles in 1.5 hours. What was his speed in miles per minute?
Answer:
9
Step-by-step explanation:
13.5 / 1.5 = 9
Answer:
[tex] \boxed{Speed = 0.15 \: miles \: per \: minute} [/tex]
Given:
Distance travelled = 13.5 miles
Time taken = 1.5 hours = 1.5 × 60 = 90 minutes
Step-by-step explanation:
[tex]Speed = \frac{Distance \: travelled}{Time \: taken} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{13.5}{90} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 0.15 \: miles \: per \: minute[/tex]
3~ Please help. What is m∠BED?
Enter your answer as a number, like this: 42
Answer:
34
Step-by-step explanation:
There is the same opposite arch for both angles so they should be equal.
Hope this is helpful!
Solve the inequality for X.
-3x - 3 <-63
es
A)
x > 20
B)
x > 22
9.
x < 20
D)
x < 22
------------------------------------------------
-3x - 3 <-63
Add 3 to both sides:
-3x-3+3 < -63+ 3
Simplify:
-3x < -60
Multiply both sides by -1:
(reverse the inequality)
(-3x)(-1) > (-60)(-1)
Simplify:
3x > 60
Divide both sides by 3:
3x/3 > 60/3
Simplify:'
x > 20
Your Answer Is x > 20
plz mark me as brainliest if this helped :)
1. Use substitution to create a one-variable linear equation: -3= 4x - 5.
2. Solve to determine the value of the unknown variable.
3. Write the solution to the system of equations as an ordered pair.
The solution to the system is (
-3).
Intro
3 of 15
Answer:
x = 1/2
Step-by-step explanation:
-3= 4x - 5 becomes 5 - 3 = 4x when 5 is added to both sides. Then:
2 = 4x, and x = 2/4, or x = 1/2.
The solution of the linear equation -3= 4x - 5 is x = 1/2.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An equation: -3 = 4x - 5.
Simplifying,
by using substitution,
4x - 2 = 0
This is a one variable linear equation. Where x is a variable.
In order to solve the equation:
Simplifying,
4x = 2
x = 1/2
Therefore, the solution of the equation is 1/2.
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How many pops of kernel come in a bag of popcorn?
Please choose one of the following answers below
70
120
200
100,000
Answer:
100,000
Step-by-step explanation:
I don't think they're give you 70 or 100,000 kernels so either 120 or 200. But if I had to choose one, it'd be 120 kernels.
Matt has $900 in a checking account, has $15,000 in investments, owns an
$8000 car, and owns a $30,000 house. What is the total value of his large
assets?
A. 53,900
B.23,000
C. 15,900
D. 38,000
The total value of his large assets is $53,900.
What are Assets?Assets are defined as the possessions that a person or the company holds which has a value which affects positively for the person or the company.
Given that,
Amount in a checking account = $900
Amount as investments = $15,000
Amount for the car = $8000
Amount for the house = $30,000
Total value for the assets = $900 + $15,000 + $8000 + $30,000
= $53,900
Hence the total value of the asset is $53,900.
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Which best describes the scale factor for each dilation?
Answer: 1= between 0 and 1. 2= greater than 1. 3= equal to 1
Step-by-step explanation: I just did the warm up
Answer:
Dilation 1 has a scale factor
✔ between 0 and 1
.
Dilation 2 has a scale factor
✔ greater than 1
.
Dilation 3 has a scale factor
✔ equal to 1
.
Step-by-step explanation:
I Point
Which of the following shows the polynomial below written in descending order?
4x^3 + 3x^7 - 9x + x^12
The polynomial in descending order would be:
x^12 + 3x^7 + 4x^3-9x.
It all has to do with their degrees (exponents).
I don't know what the answer choices are because you didn't post them, but that is the answer.
I hope this helps.
Which of the following is true about the bird population? Please!!!
Answer:
D
Step-by-step explanation:
if something is multiplied by 1.025 it is increasing by 2.5 percent
Answer:
D , 2.5%
Step-by-step explanation:
1.025 - x = 1; x = .025; as a percent = .025 * 100 = 2.5%.
Of all 25 marbles in a bag, 3 of the marbles are white. What is the probability that a white marble will be randomly selected from the bag without looking? Write your answer as a percent.
Step-by-step explanation:
Total marbles = 25
Probability of white marble = 3/ 25 = 0.12
At the candy store the sell a 3 -pack of large chocolate bars for $6.45 and a 4 -pack of large chocolate bars for $8.20. Use Unit Rate to find out which pack is a single bar the cheapest.
Answer:
the cheapest is 8.20/4 bars
Step-by-step explanation:
we have to compare the price of one bar in both situations
1 bar= 6.45/3 compare with 1 bar=8.20/4
2.15 >2.05
the cheapest is 8.20/4 bars
Question 3 Please help. What is the measure of JLK⌢?
Answer:
Answer is option
Options are related to find the angle of JLK
Step-by-step explanation:
[tex]we \: know \: that \: the \: angle \\ \: in \: a \: circle \:i s \: 360 \: degrees. \\ angle \: of \: JLK = 360 - (given \: angle) \\ \: \: \: \: = 360 - 154 \\ \: \: \: \: = 206 \: degrees[/tex]
Here the given angle is 154 degrees.
Hence the answer is option b) 206 degrees .
HAVE A NICE DAY !
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
If you have a cube with a side length of ¼, how many cubes can fit into your rectangular prism? Explain.
Answer:
Step-by-step explanation:
No of cubes that can fit into rectangular prism = Volume of rectangular prism
Volume of cube
Find the volume of rectangular prism and divide that by the volume of cube
What is P(Foreign Language | Sport)?
Answer:
23/33 x 10/33 = 21/100
Probability of A and B (independent events): p(A and B) = p(A) * p(B).
P(Foreign language | Sport) would mean P for probability
We use P in questions
and P in answer format.
We Know that F Union S F Union Sport = All in A + B and both = 47
The probability in both means you need to subtract the middle values as they are in both and repeated. It also becomes a special
Union. The union of two or more sets is the set that contains all the elements of each of the sets; an element is in the union if it belongs to at least one of the sets. The symbol for union is ∪ , and is associated with the word “or”, because A∪B A ∪ B is the set of all elements that are in A or B (or both.)
Two number cubes each have sides that are labeled 1 to 6. Jude rolls the 2 number cubes. What is the probability that the sum of the numbers on
cubes will equal 4?
Answer: 3
This is the answer if you think its wrong i don't know its correct i got it right
