Assume we cut the last piece of the pie into two sections (1 and 2) along ray BD
such that m∠ABD = 2x+3, m∠CBD = 4x+7, and m∠ABC = 40°. Based on this information,
would you ask for section 1 or section 2 (you have to pick one) for dessert? Provide numerical evidence to back up your choice. Explain your reasoning and your methods.
Answers
Answer:
If we want the greatest portion of pie, then you must choose the section with the greatest angle. Therefore, we must choose Section 2. But if we want the smallest portion of pie, then we must choose Section 1.
Step-by-step explanation:
From statement, we know that measure of the angle ABC is equal to the sum of measures of angles ABD (section 1) and DBC (section 2), that is to say:
[tex]m \angle ABC = m\angle ABD + m\angle DBC[/tex] (1)
If we know that [tex]m\angle ABC = 40^{\circ}[/tex], [tex]m\angle ABD = 2\cdot x + 3[/tex] and [tex]m\angle DBC = 4\cdot x + 7[/tex], then the value of [tex]x[/tex] is:
[tex](2\cdot x + 3)+(4\cdot x + 7) = 40^{\circ}[/tex]
[tex]6\cdot x +10^{\circ} = 40^{\circ}[/tex]
[tex]6\cdot x = 30^{\circ}[/tex]
[tex]x = 5[/tex]
Then, we check the angles of each section:
Section 1
[tex]m\angle ABD = 2\cdot x + 3[/tex]
[tex]m\angle ABD = 13^{\circ}[/tex]
Section 2
[tex]m\angle DBC = 4\cdot x + 7[/tex]
[tex]m\angle DBC = 27^{\circ}[/tex]
If we want the greatest portion of pie, then you must choose the section with the greatest angle. Therefore, we must choose Section 2. But if we want the smallest portion of pie, then we must choose Section 1.
Related Questions
easy algebra question below first correct answer gets brainliest if you put a link you will be blocked and reported
Answers
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the concept of areas,
we know that, area of rectangle = length * width,
here, length = x-2 and width = x-1
hence, area = (x-2) (x-1)
==> area = x^2 -x -2x +2
==> Area = x^2 - 3x + 2
hence the Option D.) is correct
In a survey, 250 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 1.
Cards Chosen Number 1 2 3 4 5
Frequency 40 70 80 20 40
The theoretical probability of choosing a card with the number 1 is nothing%. The experimental probability of choosing a card with the number 1 is nothing%. The theoretical probability is ▼ less than equal to greater than the experimental probability.
Answers
Answer:
20%, 16%, greater than
Step-by-step explanation:
1/5*100= 20% 250*20%=50 times 1 is picked up.
Ex. Probability: 40/250*100= 16%
Hopes this makes sense!
Answer: Your welcome!
Step-by-step explanation:
The theoretical probability of choosing a card with the number 1 is 20%. The experimental probability of choosing a card with the number 1 is 16%. The theoretical probability is greater than the experimental probability. This is because the theoretical probability is based on the assumption that each card has an equal chance of being chosen, while the experimental probability is based on the actual results of the survey, which showed that 16% of the people chose a card with the number 1.
PLEASE HELP!! GIVING 20 PTS!!
Answers
Answer:
1. a translation of (-1,3)
2. a reflection across a line through points (0,4) and (3,4)
Use the distributive property to multiply, combine like terms & find the equations
34(x + 5) - 2(x+5)
Answers
Answer:
32+160
Step-by-step explanation:
pls help its the last question
Answers
Answer:
Step-by-step explanation:
9.2 to 9.3 the top right one
A triangular portion of a baseball field is marked as shown below. To the
nearest tenth, what is the length of the side labeled c?
Answers
Answer:
D. 1.6 yd
Step-by-step explanation:
Use the law of sines.
[tex] \dfrac{c}{\sin C} = \dfrac{a}{\sin A} [/tex]
[tex] \dfrac{c}{\sin 28^\circ} = \dfrac{2~yd}{\sin 36^\circ} [/tex]
[tex] c = \dfrac{2~yd \times \sin 28^\circ}{\sin 36^\circ} [/tex]
[tex] c = 1.6~yd [/tex]
CAN SOMEONE PLEASE HELP ME NOW PLEASE HURRY
Answers
Answer:
your answer is C
Step-by-step explanation:
took the test
Hey guy can you pls help me find the area and pls show your working
*links are not allowed*
Answers
Step-by-step explanation and Answer :)
So we can split this shape into a few easier shapes to solve the area!
There are multiple combinations:
rectangle, triangle, and another rectangle
rectangle, trapezium
The second option is faster so lets use that :)
[tex]187m^{2}[/tex]
You should draw a dotted line across the top of the rectangle so now there is a rectangle on the bottom and a trapezium on the top!
[tex]A_{square} = b * h\\A_{square} = 16 * 6\\A_{square} = 96m^{2} \\\\\\A_{trap} = \frac{(a + b)h}{2}\\[/tex]
[tex]A_{trap} = \frac{(10 + 16)7}{2}\\\\A_{trap} = \frac{(182)}{2}\\\\A_{trap} = 91 m^{2}[/tex]
96 + 91 = [tex]187m^{2}[/tex]
Hope this helps!
Please mark as brainliest (Press the crown) :0
6. CHALLENGE How many sides does a
regular polygon have if the measure of
an interior angle is 171°?
Answers
Answer:
40
Step-by-step explanation:
It is given that the measure of interior angle of a polygon is 171∘ . So, the correct answer is “ 40 ”.
Elena notices that when she spends less time on social media the night before a quiz she gets a higher test score. Before one quiz she spent 107 minutes on social media and earned 37 points on a quiz.!before another quiz she spent 73 minutes on social media and scored 41 points. Write a function to model a linear relationship between elenas social media usage in minutes and her quiz scores assuming that the total number of points on each quiz remains a constant?
Answers
Step-by-step explanation:
CCC and I have a very different view on the situation than the one I have been using for me since 6AM when you have been in the same situation for me and my
The equation that represents the total score points will be y = - (4/34)x + 49.58.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\\[/tex]
The two points are (107, 37) and (73, 41).
Let 'x' be the number of minutes and 'y' be the total score. Then the equation is given as,
(y - 41) = [(41 - 37) / (73 - 107)](x - 73)
y - 41 = - (4/34)(x - 73)
y = - (4/34)x + 49.58
The equation that represents the total score points will be y = - (4/34)x + 49.58.
More about the line passing through two points link is given below.
https://brainly.com/question/12740817
#SPJ3
if the vertex of a parabola is (0, -4), what is the axis of symmetry?
Answers
If the vertex of a parabola is (0, -4). The equation of the axis of symmetry for this parabola is x = 0.
How to convert the given equation to vertex form?We first take out the coefficient of x squared, and then inside the bracket, we try to make a perfect square-like situation.
For parabolas, its axis of symmetry always goes through the vertex of the parabola.
In other words, the axis of symmetry is a vertical line that goes through the x-coordinate of the vertex.
Now, if the vertex of a parabola is (0, -4) which is at x = 0, y = -4.
Thus, the vertical line that goes through the coordinate of the vertex would be x = 0
Thus, the equation of the axis of symmetry for this parabola is x = 0.
Learn more about the vertex form of a quadratic equation here:
https://brainly.com/question/9912128
#SPJ2
Which set of ordered pairs is not a direct variation?
{(2,6), (8,12), (14,18)}
{(6,6), (12,12), (18,18)}
{(3,6), (6,12), (9,18)}
{(2,6), (4,12), (6,18)}
Answers
Answer:
The first option is not a direct variation
Step-by-step explanation:
When we talk of a direct variation, as one value increases, the other value increases too
Or as one value decreases, the other value decreases
A direct variation is of the form;
y = kx
k = y/x
where k is the coefficient of variation that must be a constant value all through the set of values
The values we are comparing here are the x and y values
So
let us take a look at the options;
The first option is not a direct variation
For the first option, the rate of increase is not constant;
2/6 = 1/3 , 8/12 = 2/3 , 14/18 = 7/9
for the second;
the ratio is 1 to 1
for the third;
3/6 = 1/2 ; 6/12 = 1/2; 9/18 = 1/2
for the fourth;
2/6 = 1/3, 4/12 = 1/3 , 6/18 = 1/3
Quadrilateral ABCD is inscribed in this circle
What is the measure of angle A?
Answers
Answer:
The four angles of a quadrilateral sum to 360 degrees.
If A and B are right angles then (2x+1) + 148 equal 180 degrees.
Therefore angle A = 32 degrees.
Step-by-step explanation:
does anybody know the answer?
Answers
Answer:
Option B:Step-by-step explanation:
As,
It has shown that line d cuts line b by making 90° so those lines are called perpendicular bisectors
Hence,
Option B is the correct symbol shown for perpendicular bisector of line d to line B.
Round off 631 to the nearest 100
And also round off 8348 to the nearest 100
Answers
Answer:
600
8300
Step-by-step explanation:
Answer:
1) 600
2) 8300
Step-by-step explanation:
Okay so rounding is simple
If the place digits before the digit your rounding to is 1-4 then just everything stays the same. If its 5 or above then you round the number up and put everything else into 0s.
-2x=x^2-6−2x=x 2 −6minus, 2, x, equals, x, squared, minus, 6 1) Rewrite the equation by completing the square.
Answers
Answer:
(x+1)² = 7
Step-by-step explanation:
Given the expression
-2x = x² - 6
Rewrite
x² - 6 + 2x = 0
x²+2x-6 = 0
Add 6 to both sides
x²+2x-6+6 = 0+6
x²+2x = 6
Add square of half of coefficient of x to both sides
Coefficient of x = 2
Half of Coefficient of x = 2/2 = 1
Square of half of Coefficient of x = 1² = 1
Add 1 to both sides
x²+2x + 1= 6 + 1
Factorize the LHS
x²+x+x + 1 = 7
x(x+1)+1(x+1) = 7
(x+1)(x+1) = 7
(x+1)² = 7
hence the equation rewritten by completing the square method is
(x+1)² = 7
Identify if the question is
statistical or non statistical.
"Do leopards weigh
more than cheetahs?"
non statistical or statistical
Answers
Answer:
statistical!!
Step-by-step explanation:
There is a line that includes the point (4, – 10) and has a slope of 8. What is its equation in point-slope form?
Answers
y=8x+c
-10=8(4)+c
-10=32+c
-42=c
y=8x-42
4 3/8 divded by 3 1/3
Answers
as fraction 21/16
decimal form- 1.3125
Mixed number- 1 5/16
There are 95 seats on a train. 76 of the seats are empty. What percentage of the seats on the train are empty?
Answers
Answer
80%.............
Step-by-step explanation:
76/90 is .8 which is 80%
if AB= 2x + 3 and BC= x + 7, find CD explain it too pls
Answers
2x+3=x+7
x=4
So AB = 2(4)+3=11
CD is congruent (similar) to AB, so CD =11
the answer should be 11
Which angles are congruent?? (Look at the picture)
Answers
Answer:
A. DEF=EDF
Step-by-step explanation:
A map of the Orchid Hill Neighborhood is shown. The population of Orchid Hill Neighborhood is 360 people. The length of each block is the same and the length of 20 blocks is 1 mile.
Answers
The question is incomplete. The complete question is :
A map of the Orchid Hill Neighborhood is shown. The population of Orchid Hill Neighborhood is 360 people. The length of each block is the same and the length of 20 blocks is 1 mile.
a). What is the area in square miles of Orchard Hill?
b). What is the population density of the Orchard Hill Neighborhood, given as a number of people per square mile?
Solution :
It is given that :
The total population of Orchid Hill Neighborhood is = 360
The length of 20 blocks = 1 mile
So, 20 blocks = 1 mile
∴ [tex]$1 \text{ block} = \frac{1}{20} \text{ mile} $[/tex]
= 0.05 mile
So the length of the neighborhood is = 4 x 0.05
= 0.20 mile
The width of the neighborhood is = 3 x 0.05
= 0.15 mile
a). Therefore, the area of the Orchid Hill Neighborhood in square miles is
A = length x width
= 0.20 x 0.15
= 0.03 square miles
b). Population density is defined as the number of people living in an unit area.
i.e. [tex]$\frac{360}{0.03}$[/tex]
= 12,000 people per square mile
2c + -2 = -6
what isthe answer
Answers
-(-2) -(-2)
————————
2c = -4
————
2
C = -2
how many pickles grow on a tree a year
Answers
Answer:
50-65 days
Step-by-step explanation:
50-65 days
Pickling cucumbers should be ready to harvest between 50-65 days from planting and can be picked over the course of a several weeks. Growing pickling cucumber plants is just like growing other types of cucumber. They prefer a soil pH of 5.5, well-drained soil, and lots of nitrogen.
please helpppppp asap (triangle inequality theorem) show the work
Answers
Answer:
a - yes
b - no
Step-by-step explanation:
triangle inequality theorem - the sum of any 2 sides of a triangle must be greater than the measure of the third side
For a
5 + 4 must be greater than 7 for the set to be measures of the sides in a triangle
5 + 4 = 9
9 is greater than 7 therefore 4,5, and 7 can be measures of the sides in a triangle
For b
3 + 2 must be greater than 6 in order for the set to be measures of the sides in a triangle
3 + 2 = 5
5 is less than 6 therefore 2,3 and 6 can not be measures of the sides in a triangle
5/6 + 7/9
help me pls
Answers
Decimal form:1.61
Mixed number form: 1 11/18
Pls help me asapppp.
Answers
Answer:
m a t h
Step-by-step explanation:
i am in middle school so i dont know
how to write 0.00007 in scientific notation
Answers
Answer:
As 7.0 is the same as seven, 0.00007 written in scientific notation is seven multiplied by 10 to the power of negative five.
Step-by-step explanation:
Answer:7x10 ^-5
Step-by-step explanation:
It costs $35 to join a gym. The monthly fee is $25. Write and graph an equation in two variables that represents the total cost of a gym membership. Let m represent the number of months and c represent the total cost of the gym membership.
An equation in two variables that represents the total cost of a gym membership is c=
.
Answers
Answer:
c= 35+25m
Step-by-step explanation:
The $35 is a one time payment and the 25 dollars is each month!
Hope this helps!