Answer:
[tex]\angle ABC=(46)^{\circ}[/tex]
Step-by-step explanation:
Given: BD bisects [tex]\angle ABC[/tex]
[tex]\angle ABD=(4x-5)^{\circ}\\\angle DBC=(3x+2)^{\circ}[/tex]
To find: [tex]\angle ABC[/tex]
Solution:
A bisector of an angle divides it into angles of equal measures.
As BD bisects [tex]\angle ABC[/tex], [tex]\angle ABD=\angle DBC[/tex]
Put [tex]\angle ABD=(4x-5)^{\circ}\,,\,\angle DBC=(3x+2)^{\circ}[/tex]
[tex]\angle ABD=\angle DBC\\(4x-5)^{\circ}=(3x+2)^{\circ}\\4x-3x=2+5\\x=7^{\circ}[/tex]
So,
[tex]\angle ABD=(4x-5)^{\circ}=(4(7)-5)^{\circ}=(28-5)^{\circ}=(23)^{\circ}\\\angle DBC=(3x+2)^{\circ}=(3(7)+2)^{\circ}=(21+2)^{\circ}=(23)^{\circ}[/tex]
[tex]\angle ABC=\angle ABD+\angle DBC\\=(23)^{\circ}+(23)^{\circ}\\=(46)^{\circ}[/tex]
A bisector divides lines, angles and shapes into equal segments
The measure of angle ABC is 46 degrees
The given parameters are:
m∠ABD = (4x−5)∘ m∠DBC = (3x+2)∘Given that line BD is the bisector of angle ABC, it means that:
[tex]\angle ABD = \angle DBC[/tex]
and
[tex]\angle ABC = 2\times \angle ABD[/tex]
So, we have:
[tex]4x - 5 = 3x +2[/tex]
Collect like terms
[tex]4x - 3x = 5 +2[/tex]
Evaluate like terms
[tex]x = 7[/tex]
Recall that
[tex]\angle ABC = 2\times \angle ABD[/tex]
So, we have:
[tex]\angle ABC = 2 \times (4x - 5)[/tex]
Substitute 7 for x
[tex]\angle ABC = 2 \times (4\times 7 - 5)[/tex]
[tex]\angle ABC = 2 \times (28 - 5)[/tex]
[tex]\angle ABC = 2 \times 23[/tex]
[tex]\angle ABC = 46[/tex]
Hence, the measure of angle ABC is 46 degrees
Read more about bisectors at:
https://brainly.com/question/5371386
Ella has $50,000 is a saving account. The savings collect interest at an 8% annual rate that compounds every year. How much money will be in Ellas account after 5 years?
Answer:
210000$
Step-by-step explanation:
1st we find the SI which will be P*R*T/100=50000*8*5/100
=32000
32000 will be added per year
32000*5=160000 for 5 years
160000+50000=210000$
how to simplify y- 3/3 +12
Answer:
11+y
Step-by-step explanation:
3/3 evaluates to 1
Y-3/3 evaluates to y-1
So the answer is y-1
(4,3.5,5,5.5,4,2)
What is the mean of City A?
a.)4
b.)5
c.)8
d.)12
Answer: 4
Order the Numbers
Before: 4,3.5,5,5.5,4,2
After: 2,3.5,4,4,5,5.5
Add
2+3.5+4+4+5+5.5=24
Divide
24÷6=4
Which of the following is a rational number?
Square root of 36, 0.93993..., square root of 85, or 3.4563728...
Answer:
It would be the square root of 36.
Step-by-step explanation:
in your sock drawer, you have 12 blue socks and 12 yellow socks. It is dark in the morning when you were getting dressed, and you can’t see the color of the socks. What is the probability of randomly picking a yellow sock?
A.) 1/23
B.) 1/2
C.) 1/12
D.) 1/11
E.) 1/24
Answer:
1/2
Step-by-step explanation:
There are 12+12 = 24 socks in the drawer
P(yellow) = number of yellow socks/ total socks
= 12/24
=1/2
Given the function
Calculate the following values
Answer: 1. F(-1)= 8(-1)-8
2. F(0)= 8(0)-8
3 F(2)= 8(2)-16
Step-by-step explanation:
i think i got some wrong i haven't these math [problem in a long time
Help me I’m begging you please
Answer:
Air pressure = [tex]4.6\frac{\text{lb}}{\text{in}^{2} }[/tex]
Step-by-step explanation:
Relationship between air pressure and altitude can be modeled by,
P = 14.7e[tex]14.7e^{-0.00004h}[/tex]
Where P = Air pressure
and h = altitude above the sea level
Air pressure on Mount Everest having altitude = 29028 feet abve the sea level will be,
P = [tex]14.7e^{-0.00004\times 29028}[/tex]
= [tex]14.7\times e^{-1.16112}[/tex]
= 4.603
≈ 4.6 [tex]\frac{\text{lb}}{\text{in}^{2} }[/tex]
Therefore, air pressure on Mount Everest = 4.6 [tex]\frac{\text{lb}}{\text{in}^{2} }[/tex]
Two numbers are in the ratio 7:5 . When 10 is subtracted from each term , the ratio becomes 3:2 .Find the numbers.
Answer:
Denote the two numbers: a and b
Two numbers are in the ratio 7:5
=> a/b = 7/5
=> a = (7/5) x b (1)
When 10 is subtracted from each term , the ratio becomes 3:2
=> (a - 10)/(b - 10) = 3/2
=> 2 x (a - 10) = 3 x ( b - 10)
=> 3 x b - 2 x a = 10
From (1) => 3 x b - 2 x (7/5) x b = 10
=> (1/5) x b = 10
=> b = 50
=> a = (7/5) x b = (7/5) x 50 = 70
Hope this helps!
:)
What is the solution to the system of equations below?
y=-3x+8 and x = -6
Answer:
( - 6 , 26 )
Step-by-step explanation:
You can solve this in a number of ways, you can graph it, you can substitute the value of x into the first equation, or you can do it the elimination method.
So lets just do the substitution method because i can't do the others on here, i can't write :/.
so substitute x = -6 into the equation y = -3x + 8
y = -3(-6) + 8
y = 18 + 8
y = 26
now you know what (X) equals to and what (Y) equals to so its,
(-6,26)
A car travels 100 meters in 5 seconds. What is the speed of the car in miles per hour?
speed = distance over time; 1 mile = 1609 meters
Answer: 5,000 you'll welcome
Step-by-step explanation:
To mail a letter first class, the us postal service charges $0.34 for the first ounce and $0.21 for each additional ounce. What will be the weight of a letter costing 5.76?
Answer:
25.599
I think
Step-by-step explanation:
if its right can u please give me the brainilest
For a right triangle, what happens to the value of sine as the angle increases?
Answer:
In a right triangle, as the angle increases, the value of the sine increases.
Step-by-step explanation:
Think of the unit circle, a circle with radius 1 unit centered at the origin which is the point with coordinates (0, 0). Draw a radius of the circle from the center, to point (1, 0) on the positive x-axis. The angle formed by this radius and the positive x-axis is 0 degrees. This is an angle in standard position. The endpoint of the radius on the circle has a y-coordinate. The y-coordinate is the sine of the angle. As you choose points on the circle going up from the positive x-axis, the angle formed by the radius connected to the point on the circle and the positive x-axis increases in measure until it coincides with the positive y-axis, where it has a measure of 90 degrees. The sine of the angle is always the y-coordinate of the point on the circle. As the angle increases from 0 to 90 degrees, the y-coordinate increases from 0 to 1. The acute angles of a right triangle can have measures of only between 0 and 90 degrees.
Answer: In a right triangle, as the angle increases, the value of the sine increases.
Steven rolled a 1-6 number cube four times. What is the proballity that Steven rolled an odd number on all four rolls of
the die? (leave your answer as a reduced fraction)
Answer: 0.0625
Step-by-step explanation:
From the question, Steven rolled a 1-6 number cube four times. This means the 1-6 number cube has numbers 1, 2, 3, 4, 5 and 6. There are 3 odd numbers which are 1, 3 and 5. If the 1-6 number cube is rolled once, the probability will be:
3/6 = 1/2
Since Steven rolled the 1-6 number cube four times, the probability of getting an odd number on all four rolls of the die will be:
= 1/2 × 1/2 × 1/2 × 1/2
= 1/16
= 0.0625
Find the slope of a line parallel to each given line
Answer:
x intercept = 1
y intercept = - 5
slope = -5
Step-by-step explanation:
m = y2 - y1 / x2 - x1
m = (-5 - 0)/ (1 - 0)
m = -5
Kylie sent a chain letter to her friends, asking them to forward the letter to more friends. The relationship between the elapsed time t tt, in hours, since Kylie sent the letter, and the number of people, P ( t ) P(t)P, left parenthesis, t, right parenthesis, who receive the email is modeled by the following function: P(t)=(1.09)6t+25.5 Complete the following sentence about the hourly percent change in the number of people who receive the email. Round your answer to the nearest percent.
Answer:
68%
Step-by-step explanation:
I just did it on Khan Academy!
I hope this helps! ;)
Answer:
68% in addition to
Step-by-step explanation:
Khan Academy
The length of a rectangle is $3x+10$ feet and its width is $x+12$ feet. If the perimeter of the rectangle is 76 feet, how many square feet are in the area of the rectangle?
Answer:
352ft²Step-by-step explanation:
Given the length of a rectangle = 3x+10
Width of the rectangle = x+12
Perimeter of the rectangle = 76ft
For us to get the area of the rectangle we need to get the value of its length and width.
Given the perimeter of a rectangle P = 2(L+W) where;
L is the length and W is the width, on substitution
76 = 2(3x+10+x+12)
76 = 2(4x+22)
76 = 8x+44
8x = 76-44
8x = 32
x = 32/8
x = 4
Substituting x = 4 into the function of the length and width we have;
Length = 3(4)+10
Length = 22feet
Width = 4+12
width = 16feet
Area of the rectangle = Length * Width
Area of the rectangle = 22feet * 16feet
Area of the rectangle = 352ft²
Please help with this!!
Answer:
200
Step-by-step explanation:
As you can see the line marks and meets up with 200 as it marks with 60
What is the perimeter of the figure?
Answer: 48
Step-by-step explanation: Tienes q sumar lo que suman todos los lados.
15×2=30
9×2=18
30+18=48
Joshua has 30 trading cards. He adds 20 cards to his collection each week.
Mackenzie has 45 trading cards and adds 20 cards to her collection each week.
How many cards will each person have after 6 weeks?
Answer:
Joshua will have 150 cards.
Mackenzie will have 165 cards.
PLZ HELP 20 PTS
Match each value to the correct entry in matrix AB.
Answer:
Step-by-step explanation:
The matrix AB is:
[tex]AB=\left[\begin{array}{ccc}50&44&-43\\31&16&7\\37&119&-94\end{array}\right][/tex]
-----------------------------------
This question is solved using multiplication of matrices.
To do this, we multiply the lines of the first matrix by the columns of the second.
-----------------------------------
In this question:
The first matrix is:
[tex]A =\left[\begin{array}{ccc}5&7&2\\4&-1&3\\6&8&-5\end{array}\right][/tex]
The second matrix is:
[tex]B = \left[\begin{array}{ccc}6&11&-4\\2&1&-5\\3&-9&6\end{array}\right][/tex]
------------------------------------
First line:
The first element is the multiplication of the first line of A by the first column of B. So: [tex]AB_{1,1} = 5\times6 + 7\times2 + 2\times3 = 50[/tex]The second element is the multiplication of the first line of A by the second column of B. So:[tex]AB_{1,2} = 5\times11 + 7\times1 + 2\times -9 = 44[/tex]The third element is the multiplication of the first line of A by the third column of B. So:[tex]AB_{1,3} = 5\times -4 + 7\times-5 + 2\times6 = -43[/tex]------------------------------------
Second line:
Second line of A by each column of B, so:
[tex]A_{2,1} = 4\times6 - 1\times 2 + 3\times3 = 31[/tex]
[tex]A_{2,2} = 4\times11 - 1\times 1 + 3\times (-9) = 16[/tex]
[tex]A_{2,3} = 4\times(-4) - 1\times (-5) + 3\times 6 = 7[/tex]
------------------------------------
Third line:
Third line of A by each column of B, so:
[tex]A_{3,1} = 6\times6 + 8\times 2 - 5\times3 = 37[/tex]
[tex]A_{3,2} = 6\times11 + 8\times 1 - 5\times (-9) = 119[/tex]
[tex]A_{3,3} = 6\times(-4) + 8\times (-5) - 5\times 6 = -94[/tex]
------------------------------------
Thus, the matrix is:
[tex]AB=\left[\begin{array}{ccc}50&44&-43\\31&16&7\\37&119&-94\end{array}\right][/tex]
A similar question is found at https://brainly.com/question/12088021
Point A is at (3, 4) and point M is at (5.5,0).
Point M is the midpoint of point A and point B.
What are the coordinates of point B?
Answer:
the real answer is (8,-4)
Step-by-step explanation:
If the midpoint of the AB is (5.5, 0) then the coordinate of the B will be given as (8, -4).
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.
Point A is at (3, 4) and point M is at (5.5,0).
Point M is the midpoint of points A and B.
Then the point of B is given as
[tex]\rm (x_1,y_1) = (2x-x_2, 2y-y_2)\\\\(x_1,y_1) = (2\times 5.5 - 3, 2\times 0-4)\\\\(x_1,y_1) = (8, -4)[/tex]
More about the coordinate geometry link is given below.
https://brainly.com/question/1601567
Can you please help me with this question please help and i will give you a Brainiest
Answer:
Cans for food drive
Step-by-step explanation:
Answer:
Cans for food drive
Step-by-step explanation:
The header should encapsulate all aspects of the table.
Cans of food are brought by the teachers to be donated to the food drive. Hence the answer should be cans for food drive.
Cans recycled are out of context as the cans of food are for donation as seen in the table, not for recycling.
Favourite food and favourite teacher cannot be measured by the data provided which is which teacher bringing how many cans of food for donation. Hence, these 2 are not the answer as well.
Type the correct answer in the box
6 inches across
12 inches up and down
A machine part consists of a half sphere and a cylinder, as shown in the figure. The total volume of the part is ____ pie cubic inches.
Answer:
126 pie cubic inches.
Step-by-step explanation:
i dont have one^ but i completed the test with a 100%
What is the hydrogen ion concentration
of orange juice that has a pH of 1?
0.1 mole per liter
0.01 mole per liter
0.0001 mole per liter
0.00001 mole per liter
Answer:
0.1 mole per liter
Step-by-step explanation:
i got it right
CAN SOMEONE PLZ HELP ME
Answer:
the first one
4*10^12
Step-by-step explanation:
Answer:
4000000000
Step-by-step explanation:
(600000000) / (0.00015)
4000000000
4*10^12
Solve using synthetic division.
(x2 + 3) ÷ (x − 1)
Answer:
2x+3 / x = 1
Step-by-step explanation:
Gloria has a $125,000 home financed with a 30-year loan at 6%. If she wished to pay one extra monthly payment each year, how many months will t take her to pay off her mortgage?
Answer:
295 months
Step-by-step explanation:
You want to know the number of months required to pay off a 30-year loan of $125000 at 6% if an extra payment is made each year.
Number of paymentsThe number of payments required will depend on the actual payment schedule, and the way the lender computes interest due.
The attached calculation shows it takes 319 payments. The assumption is that they are evenly spaced at 13 payments per year (one every 4 weeks), and the interest is computed on the interval between payments.
Number of monthsIf 13 payments are made per year, the number of years it takes to pay off the loan will be ...
319/13 = 24 7/13
24 years and 7 months is 295 months.
__
Additional comment
If the first payment is made on Jan 28, and payments are made every 4 weeks, there will be 2 payments in Dec. That is, except for the last month of the year, there will be 1 payment per month.
If regular monthly payments are made, but one of the payments is doubled, the result may be different.
What is 84/100 simplifyed
Answer:
21/25
Step-by-step explanation:
84/100
Divide the top and bottom by 4
84/4 = 21
100/4 = 25
84/100 = 21/25
Answer:
21/25
Step-by-step explanation:
84/100 divided by 2/2=
42/50 divided by 2/2=
21/25
Zhen is an audiobook narrator. The table gives some completed audio lengths and the amount of time Zhen spends researching, recording, and editing the audiobook.
Completed length of audiobook (hours) Working time (hours)
1 6 1/2
3 1/2 22 3/4
7 45 1/2
10 65
What does 6 1/2 mean in this sitiuation?
a. Zhen 6 1/2 hours working for every hour of the completed audiobook.
b. Zhen completes 6 1/2 audiobooks in an hour.
c. Zhen spends 6 1/2 hours working per audiobook.
Answer:
c. Zhen spends 6 1/2 hours working per audiobook.
Step-by-step explanation:
The table below gives some completed audio lengths and the amount of time Zhen spends on the audiobook.
[tex]\left|\begin{array}{c|c}$Completed length of audiobook (hours) &$Working time (hours)\\---------&--------\\1&6\frac{1}{2} \\\\3\frac{1}{2}&22\frac{3}{4}\\\\7&45\frac{1}{2}\\\\10&65\end{array}\right|[/tex]
We observe that from the table, in 6.5 hours, Zhen completes 1 audiobook.
In fact, across the table:
[tex]\dfrac{6\frac{1}{2}}{1}=\dfrac{22\frac{3}{4}}{3\frac{1}{2}}=\dfrac{65}{10}=6\dfrac{1}{2} $ hour per audiobook[/tex]
Therefore, in this situation, 6.5 hours mean that Zhen spends 6.5 hours working per audiobook.
The correct option is C.
What is the area of the shaded region
Answer:
A≈28.27
Step-by-step explanation:
Solved for area
Shape: circle
Radius: 3cm
Formula: A=πr2
Answer: A≈28.27
Hope this helps.