Answers
Answer:
∠DBC = 155°
Step-by-step explanation:
Assuming that ABC is a straight line.
Angles on a straight line sum to 180°.
⇒ (2x² + 3x - 2) + ∠DBC = 180°
⇒ ∠DBC = 180° - (2x² + 3x - 2)
The sum of the interior angles of a triangle is 180°:
⇒ (x² + 1) + (4x + 3) + ∠DBC = 180°
⇒ ∠DBC = 180° - (x² + 1) - (4x + 3)
Therefore, we can equate the equations and solve for x:
⇒ ∠DBC = ∠DBC
⇒ 180 - (2x² + 3x - 2) = 180 - (x² + 1) - (4x + 3)
⇒ 180 - 180 = (2x² + 3x - 2) - (x² + 1) - (4x + 3)
⇒ (2x² + 3x - 2) - (x² + 1) - (4x + 3) = 0
⇒ 2x² + 3x - 2 - x² - 1 - 4x - 3 = 0
⇒ x² - x - 6 = 0
⇒ x² + 2x - 3x - 6 = 0
⇒ x(x + 2) - 3(x + 2) = 0
⇒ (x + 2)(x - 3) = 0
Therefore, x = -2, x = 3
As angles are positive, x = 3 only
Substituting found value of x into the angle expressions:
⇒ ∠BDC = x² + 1 = (3)² + 1 = 10°
⇒ ∠DCB = 4x + 3 = 4(3) + 3 = 15°
The sum of the interior angles of a triangle is 180°:
⇒ ∠DBC + ∠BDC + ∠DCB = 180°
⇒ ∠DBC = 180° - ∠BDC - ∠DCB
⇒ ∠DBC = 180° - 10° - 15°
⇒ ∠DBC = 155°
Sum of two interiors=exterior
x²+1+4x+3=2x²+3x-2x²+4x+4=2x²+3x-22x+6=x²x²-x+6=0(x-3)(x+2)=0Take it positive
x=3Now
2x²+3x-22(3)²+3(3)-22(9)+9-218+725Now
<DBC=180-25=155°
Related Questions
what statement best describes the relationship between the side lengths and angle measures of teo triangles
Answers
Answer:
Figure RST is congruent to figure R’S’T’.
Step-by-step explanation:
how do you find the volume for a dome, pyramid, and a cylinder.
Answers
to find the volume of a cylinder you would do pi x radius^2 x height
i’m sorry but i’m not too sure about the dome but i know them two!
What is the interquartile range of this data 0, 5, 10, 15, 20,
Answers
Answer:
15
Step-by-step explanation:
The range from Q1 to Q3 is the interquartile range (IQR).
The interquartile range is the difference between the third and first quartiles.
The third quartile is 17.5.
The first quartile is 2.5.
The interquartile range = 17.5 - 2.5 = 15.
A series of transformations on quadrilateral Y
resulted in quadrilateral Z. The angle measures of
quadrilateral Y are congruent to those of
quadrilateral Z. The side lengths of quadrilateral
Z are twice as long as those of quadrilateral Y.
Which transformation on quadrilateral Y must be
included to result in quadrilateral Z?
Answers
Answer:
reflections Couse it keeps repeating y and z bit not sure
Step-by-step explanation:
I am sorry if it is the wrong answer
Find the Value of X.
Solve for X
Answers
Answer: x=21
Step-by-step explanation:
50-90=40
40=2x-2
2*21=42
42-2=40
x=21
Help please calculus
Answers
Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.
The box has a fixed volume of 252 cm³, so
xyz = 252
The surface area of the box is
2xy + 2xz + 2yz
and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by
C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)
or, omitting units and simplifying,
C (x, y, z) = 7xy + 6 (x + y) z
In the volume constraint, solve for any one variable; I'll do z.
z = 252/(xy)
Substitute this into the cost function:
C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)
Since this is now a function of 2 variables, I'll rewrite this as
C* (x, y) = 7xy + 1512 (1/y + 1/x)
Compute the partial derivatives of C and find the critical points:
∂C/∂x = 7y - 1512/x² = 0 ⇒ x² y = 216
∂C/∂y = 7x - 1512/y² = 0 ⇒ x y² = 216
It follows that
x² y = x y² ⇒ x = y
Just like before, we can think about C* as yet another function but only of 1 variable,
C** (x) = 7x² + 3024/x
Now find the critical points of C** :
dC**/dx = 14x - 3024/x² = 0 ⇒ x = 6
All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.
Jaws purchases 15 packages of baseball cards each package contains six cards how many total cards are in the six packages
Answers
Answer:
90
Step-by-step explanation:
There are 15 packa of 6 cards in each pack. You could either do it the long way and count it out on paper or just times 15x6 and it equals 90.
1. Marlene is going on a camping trip with a group of friends. She brings 3 boxes of granola bars,
plus 3 extra bars. Robyn bring 2 boxes of granola bars and Wendy brings one box. They have a
total of 57 granola bars. If each box contains the same number of bars, how many bars are in
each box?
Answers
Answer:
13.5
Step-by-step explanation:
total boxes of granola is = 3 + 2 + 1
= 6 boxes
6 boxes = 57 bars
1 box = 57 / 6
1 box = 9.5 + 3
= 13.5 (ANS)
i hope my ans is correct if not i apologise.
Marlene brought 3 boxes AND 3 extra bars so you would have to subtract those from the total before dividing.
57-3=54
54/6=9
Jane has a pre-paid cell phone with NextFell. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 450 minutes and the cost was $139.50. In July she used 870 minutes and the cost was $244.50. A) Express the monthly cost C as a function of x , the number of minutes of calling time she used.
Answers
Minutes=450
X=450:139.50$
In June C=$244.50
Minutes=870
X=minute:C
A right triangle is shown. What is the value of x? Round to the nearest tenth.
Answers
Step-by-step explanation:
B²=a²+c²
12²=4.2²+c²
144=16.4+c²
144-16.4=c²
127.6=c²
√127.6=√c²
11.3=c
I'm not sure how to find a Wrighteasyrement so how do I find it.
Answers
Response
I'm assuming that by 'wrighteasyrement' you meant weight measurement? If you need a conversion tool you can just look up ___ to ___ on (g-search engine). If you need the initial one, use a scale??? or a formular, you can also look those up, sorry, i'm not really sure what you're asking.
if two angles in a triangle are 50 and 40, it must be a/an___________________triangle.
Answers
Answer:
right triangle
Step-by-step explanation:
Hey there!
A triangle has to have three vertices that add up to 180 degrees
The angle measurments 50 and 40 are already given and added up, they equal 90 degrees
Now out of 180 degrees, 90 degrees is already shown
What you need to do now is try to find how much more degrees you need to get 180 degrees
As you know 180-90=90
So this means that the missing angle is 90 degrees
Now that we know this, we can find out what type of triangle this is
Since the triangle has an angle that is equal to 90 degrees, or it has a right angle, the triangle can be called a right triangle
A right triangle is a triangle that has an angle that is equal to 90 degrees
So this triangle is a right triangle
Is 1/8 x 20 greater than or less than 20? Please explain!
Answers
Answer:
1/8x20 is less than 20
Step-by-step explanation:
Since we know that 1x20 is equal to 20, and 1/8 is 8 times smaller than 1, we know that 1/8x20 is 20 divided by 8 which is smaller than 20
If y=x+4 then what is (x-y)^3
Answers
Answer:
64
Step-by-step explanation:
y = x + 4
y - x = 4
4^3 = 64
Doug would like to construct a fence
along his property borders. The scale
on his property map is 1 inch to 3 feet.
If the perimeter of his property on the
map is 10 inches, how many feet of
fencing will he need?
[?] feet
Answers
He would need 30 feet of fencing.
The room is a cube with edge length 11 feet including the ceiling in the floor how much surface area must be painted
Answers
Surface area is the area of all the faces added together.
If the area of one face is 11x11=121
Because it is a cube and it has six faces with the same surface area we do 121x6=726 to give us the total surface area.
Giving brainliest to who will help!
Answers
Answer:
A C F G H J ARE THE FIGURES WHERE AB IS AN ALTITUDE
Which of the following is the graph of y = negative (x minus 2) cubed minus 5?
Answers
Step-by-step explanation:
(x-2)^3 = x^3-6x^2+12x-8
-(x^3-6x^2+12x-8)=
-x^3+6x^2-12x+8
-x^3+6x^2-12x+8 -5=
y=-x^3+6x^2-12x+3
I attached the picture
Answer:
NOT D graph 4
Step-by-step explanation:
Please Help!!! . . . . .
Answers
So first do stuff in parenthesis.
Then do divide because thats next on the list and it happens earlier than the multiply one.
So, A
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus
Answers
Answer: diameter
Step-by-step explanation:
Answer:
diameter
Step-by-step explanation:
The diameter connects two points on the edge of a circle through it's centre.
Select the correct answer
Answers
Answer:
B.
Step-by-step explanation:
it's B because if you put it as a mixed number it would be 21/2 ÷ 9/4 and then the rest is easy
Answer:
B
Step-by-step explanation:
4 2/3
In a school, there are 6 floors and on each floor there are 8 classrooms. In each classrooms there are 40 students. How many total students are there in a school?
Answers
What are two ways the debt-to-gdp ratio can increase?
Answers
Answer:
GDP decreases and Debt increases
Step-by-step explanation:
Write the equation
for this line in
slope-intercept form.
y = ?/?x+ ?
Answers
Answer:
y = 2/3x - 1 (or y = 2/3x + -1 to fit the graphic)
Step-by-step explanation:
Slope intercept form is written as (y = mx + b) where m is slope and b is the y intercept.
First you need to find the slope, m. We'll use the two points (-3, -3) and (3, 1)
m = (y2 - y1) / (x2 - x1)
m = (1 - (-3)) / (3 - (-3))
m = 4/6
m = 2/3
Next we need the y intercept, b. On the graph we can see that is -1 but we can also find it substituting the known slope and one point on the line for our values to solve for b. We'll use (3, 1) as the point.
y = mx + b
1 = 2/3 * 3 + b
simplify 2/3 * 3
1 = 2 + b
subtract 2 from both sides
-1 = b
Now we have all the values we need to plug into our slope intercept equation (m = 2/3, b = -1)
y = mx + b
y = 2/3x - 1
[tex]\sf{y=\displaystyle\frac{2}{3} x-1[/tex]
Solution:We are given two points: (3, 1) and (-3, -3).We can use these points to find the slope of the line:m=[tex]\displaystyle\frac{y2-y1}{x2-x1}[/tex][tex]\displaystyle\frac{-3-1}{-3-3} =\frac{-4}{-6} =\frac{2}{3} \longleftarrow\sf{slope}[/tex]Now, we need to identify the line's y-intercept.The y-intercept is the point where the graph touches the y-axis.Since the graph touches the y-axis at (0, -1) the y-intercept is equivalent to (0, -1) or -1.Hope it helps.
Do comment if you have any query.
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices - a, b, c, d, e-
and only one correct answer. What is the probability that he answered neither of the problems correctly?
Do not round your answer.
0
X
?
Answers
Answer: The student answerd the problems wrong because he guessed instead of taking his time to correctly get the right answer.
Step-by-step explanation:
1. Find the sum.
Use tiles to find 29 + 28.
Answers
Answer:
57?
Step-by-step explanation:
calculate the shaded area
Answers
Answer:
42 cm²
Step-by-step explanation:
the length of the shaded area is the length of the white rectangle, that is
length = 7 cm
the width of the blue area is the length of the white rectangle subtract twice the width of the white rectangle, that is
width = 7 - (2 × 0.5) = 7 - 1 = 6 cm
shaded area = length × width = 7 × 6 = 42 cm²
someone pls help will give brainliest to the first to answer
Answers
Answer:
Help with what, I may be able to help. :)
Choose the x- and y- intercepts for the graph of –3x + 6y = –30.
Answers
Answer:
Some vocabulary we should know:
mx = slope while b is the y-intercept.
-3x = x
6y = y
BRAINLIEST is APPRECIATED. This is based on speculation! Good luck in your future studies.
- daintysword
Students were surveyed about their preference between dogs and cats. The following two-way table displays
data for the sample of students who responded to the survey.
Approximately what percent of students in the sample prefer cats?
Round your answer to the nearest percent.
48
Preference
Male
Female
TOTAL
Prefers dogs
36
20
56
Prefers cats
10
26
36
No preference
2
6
8.
TOTAL
48
52
100
Not quite!
Try again. Get help or skip for now
Show Calculator
Answers
explained 36/100= 36%