Answers
Answer:
x = 24
Step-by-step explanation:
ABCD is a parallelogram.
Angle B and Angle C are adjacent (successive) angles.
Adjacent angles of a parallelogram are supplementary.
Therefore,
[tex](5x) \degree + (2x + 12) \degree = 180 \degree \\ \\ (5x + 2x + 12) \degree = 180 \degree \\ \\ (7x+ 12) \degree = 180 \degree \\ \\7x+ 12 = 180 \\ \\7x = 180 - 12 \\ \\ 7x = 168 \\ \\ x = \frac{168}{7} \\ \\ x = 24[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ x \ is \ 24^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle C \ is \ 60^{\circ}}}[/tex]
[tex]\boxed{\pink{\sf\leadsto Value \ of \ \angle D \ is \ 120^{\circ}}}[/tex]
Step-by-step explanation:A parallelogram is given to us . in which m ∠ B = 5x and m ∠C = 2x + 12 ° . And we need to find x .
Figure :-
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\thicklines\put(0,0){\line(1,0){5}} \put(5,0){\line(1,2){2}}\put(7,4){\line( - 1,0){5}}\put(2,4){\line( - 1, - 2){2}}\put(0,-0.4){$\bf A$}\put(5,-0.4){$\bf b$}\put(6.5,4.3){$\bf c$}\put(2,4.3){$\bf d$}\qbezier(4.4,0)( 4.5, 0.8)(5.22,0.54)\put(4,0.4){$\bf 5x$}\put(4.7,3.3){$\bf 2x + 12$}\end{picture}[/tex]
Q. no. 1 ) Find the value of x.
Here we can clearly see that ∠DCB and ∠ABC are co - interior angles . And we know that the sum of co interior angles is 180° .
[tex]\tt:\implies \angle DCB + \angle ABC = 180^{\circ} \\\\\tt:\implies (2x + 12)^{\circ} + 5x^{\circ}=180^{\circ} \\\\\tt:\implies 7x = (180 - 12 )^{\circ} \\\\\tt:\implies 7x = 168^{\circ} \\\\\tt:\implies x =\dfrac{168^{\circ}}{7} \\\\\underline{\boxed{\red{\tt\longmapsto x = 24^{\circ}}}}[/tex]
Hence the value of x is 24° .[tex]\rule{200}2[/tex]
Q. no. 2 ) Determine the measure of < C .
Here we can see that <C = 2x + 12 ° . So ,
[tex]\tt:\implies \angle C = 2x + 12^{\circ} \\\\\tt:\implies \angle C = 2\times 24^{\circ} + 12^{\circ} \\\\\tt:\implies \angle C = 48^{\circ} + 12^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle C = 60^{\circ}}}}[/tex]
Hence the value of <C is 60° .[tex]\rule{200}2[/tex]
Q. no. 3 ) Determine the measure of < D .How you determined the answer .
Here we can clearly see that ∠D and ∠C are co - interior angles . And we know that the sum of co interior angles is 180° .
[tex]\tt:\implies \angle C + \angle D = 180^{\circ} \\\\\tt:\implies 60^{\circ} + \angle D = 180^{\circ}\\\\\tt:\implies \angle D = 180^{\circ} - 60^{\circ} \\\\\underline{\boxed{\red{\tt\longmapsto \angle D = 120^{\circ}}}}[/tex]
Hence the value of <D is 120° .Related Questions
Solve the following: 5(2x+1)=50
Answers
Answer:
x = 9/2
Step-by-step explanation:
Answer:
x = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
Given
5(2x + 1) = 50 ( divide both sides by 5 )
2x + 1 = 10 ( subtract 1 from both sides )
2x = 9 ( divide both sides by 2 )
x = [tex]\frac{9}{2}[/tex]
15. A soccer ball kicked into the air reaches 15 feet in 3 second and falls to 4 points
3 feet after 5 seconds. What is the rate of change between the 3rd second
and the 5th second? Hint: your ordered pairs should be (times in seconds,
height in feet). Your answer should be in feet/s. *
Answers
Answer:
2.6 ft/s
Step-by-step explanation:
Given that a soccer ball kicked into the air reaches 15 feet in 3 second. The first rate or speed will be:
Rate 1 = 15/3 = 5 feet/s
and falls to 3 feet after 5 seconds. Also, the second rate or second speed will be:
Rate 2 = ( 15 - 3 ) / 5
Rate 2 = 12 / 5
Rate 2 = 2.4 ft/ s
What is the rate of change between the 3rd second and the 5th second? That is, the change in speed. Which can be expressed as:
The rate of change = 5 - 2.4
The rate of change = 2.6 ft/s
The data show the number of viewers for television stars with certain salaries. Find the regression equation, letting salary be the independent (x) variable. Find the best predicted number of viewers for a television star with a salary of $33 million. Is the result close to the actual number of viewers, 3.03.0 million? Use a significance level of 0.05.
Answers
Answer:
y = 5.064 - 0.010x
Here, in this question x = 33
y = 4.734 million views
In this question data is missing and I filled it out and calculated the questions accordingly. Please refer to the attachment for the data calculated.
Step-by-step explanation:
First of all, this question is incomplete. It lacks the data needed to calculate the required things.
So, I figured out the question and I will try my best to solve the question at hand.
I have calculated the some data sheet in excel. Please refer to the attachment for that data.
let a be the salaries
b be the viewers
[tex]S_{aa}[/tex] = ∑[tex]a^{2}[/tex] - [tex]\frac{ Summtion a^{2} }{n}[/tex]
[tex]S_{aa}[/tex] = 7522.8571
[tex]S_{bb}[/tex] = ∑[tex]b^{2}[/tex] - [tex]\frac{ Summtion b^{2} }{n}[/tex]
[tex]S_{bb}[/tex] = 47.1943
[tex]S_{ab}[/tex] = ∑[tex]ab^{}[/tex] - [tex]\frac{ Summtion a x Summation b^{} }{n}[/tex]
[tex]S_{ab}[/tex] = -76.8286
Now the slope of the required regression equation is:
Slope = [tex]S_{ab}[/tex]/[tex]S_{aa}[/tex] = -76.8286/7522.8571 = -0.010
And the intercept of the required regression equation:
intercept = [tex]\frac{1}{n}[/tex] x (∑b - slope x ∑a) = 5.064
So, the regression equation will be:
y = intercept + slope x
y = 5.064 - 0.010x
Here, in this question x = 33
y = 5.064 - 0.010 (33)
y = 4.734 million views
What is 40% of 500? Please help!!
Answers
Answer:
40/100 times 500=200
Step-by-step explanation:
somebody can give me a redeem code pls
Answers
Answer:
Lol for what
Step-by-step explanation:
Chris has 115$ to spend at a shopping mall . If he decides to spend $42 on clothing and $37 on food how much money will he have left
Answers
Answer:
$36 left
Step-by-step explanation:
42+37=79
115-79=36
I need the answer right now please help me
Answers
Answer:
P+Q+R+S+T=540. then substitute x for result in p
Step-by-step explanation:
i would work it out but im lazy sorry
In a pentagon, there are 540 degrees
First, find x.
Set up the equation
132 + (4x+2) + 128 + (5x -11) + (4x - 10) = 540
Combine like terms
260 +13x -19 = 540
241 + 13x = 540
solve
13x = 299
x = 23
Now plug x in to angle p (4x + 2)
4(23) + 2
92 + 2 = 94
Therefore angle P = 94 degrees
Estimate the cost of painting the inner
wall of a well, if the depth of the well is
14 ft and the diameter is 8 ft. The cost of
painting 2.5 sq. ft is 20.
Answers
Answer:
2816 rupees
Step-by-step explanation:
here , depth = 14 ft
diameter = 8 feet
so , radius = 4 ft
We will paint it in its C.S.A.
C.S.A. of a cylindrical well
= 2πrh
= 2×(22/7)× 4 × 14
= 352 ft²
so,
cost = rate per unit area × area
= (20/2.5)×352
= 8×352
= 2816
so,the cost of the painting will be 2816 rupees
f(x)=x−5 translated 2 units down
Answers
explanation: the function is already being translated down 5, so subtracting 2 more units leaves you with this new equation
Figure ABCD is a parallelogram. use what you know about the properties a parallelograms to solve for x and find the measures of
Answers
Answer:
Step-by-step explanation:
opposite angles are congruent
find the measures of the numbered angles in the rhombus, will give brainliest ! pls show how you solved it :)))
Answers
Answer:
∠1 = 72°
∠2 = 54°
∠3 = 54°
∠4 = 72°
Step-by-step explanation:
In the isosceles triangle in which ∠4 is the top vertex angle and ∠3 & 54° are it's base angles. As it is an isosceles triangle , ∠3 = 54°
Using angle sum property of a triangle ,
∠4 + ∠3 + 54° = 180°
⇒ ∠4 + 54°+ 54° = 180°
⇒ ∠4 = 180° - 108° = 72°
Diagonals of a rhombus bisect the vertex angles of a rhombus. So,
∠2 = ∠3 = 54°
Also , opposite vertex angles of a rhombus are equal, So , ∠1 = ∠4 = 72°
The steps shown can be used to prove that the medians of a triangle meet at a point.
Triangle A B C is shown on an x and y-axis. Lines are drawn from each point to the opposite side and intersect at point G. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), and point E is at (a, b).
1. Define segments BD and CE as medians of triangle ABC.
2. Write linear equations for Line B D and Line C E.
3. Use a system of linear equations to solve for the coordinates of intersection point G.
4. Write the equation of Line A G.
5. Write an expression for the midpoint of BC, point F.
6. ?
Write a linear equation for each side of the triangle.
Write an expression for the midpoint of AC and BC.
Show that A F is congruent to BD and CE.
Show that A F is the median of BC.
Answers
Answer:
D
Step-by-step explanation:
EDGE
Answer: Show that A F is the median of BC.
Step-by-step explanation:
What are the coordinates of the point on the directed line segment from (-8, 5)(−8,5) to (4, -3)(4,−3) that partitions the segment into a ratio of 5 to 3?
Answers
Answer:
(2, -7/2)
Step-by-step explanation:
According to the midpoint theorem;
M(X, Y) = [(ax1+bx2/a+b), ay1+by2/a+b ]
(x1, y1) and (x2, y2) are the coordinates
a:b is the given ratio
Given the following
Coordinate of the line segment (-8, 5) and (4, -3)
Ratio: 5:3
Get the X coordinate;
X = ax1 + bx2 / a+b
X = 5(-8) + 3(4)/5+3
X = -40+12/8
X = -28/8
X = -7/2
Get the Y coordinate
Y = ay1 + by2 / a+b
Y = 5(5) + 3(-3)/5+3
Y = 25-9/8
Y = 16/8
Y = 2
Hence the required coordinate is (2, -7/2)
Describe how the graph of y= x^2 can be transformed to the graph of the given equation.
y = x^2 - 12 (5 points)
a) Shift the graph of y = x2 left 12 units.
b) Shift the graph of y = x2 down 12 units.
c) Shift the graph of y = x2 right 12 units.
d) Shift the graph of y = x2 up 12 units.
Answers
Answer:
b
Step-by-step explanation:
Given y = x² then y = x² + c is a vertical translation of y = x²
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here c = - 12 < 0
Thus y = x² - 12 is the graph of y = x² shifted 12 units down → b
Answer:
b) Shift the graph of y = x2 down 12 units.
Step-by-step explanation:
Graphs
The graph of the function
[tex]y=x^2[/tex]
can be found by giving the variable x some values and calculating the values of y as follows:
For x=-2, [tex]y=(-2)^2=4[/tex]. Point (-2,4)
For x=-1, [tex]y=(-1)^2=1[/tex]. Point (-1,1)
For x=0, [tex]y=(0)^2=0[/tex]. Point (0,0)
For x=1, [tex]y=(1)^2=1[/tex]. Point (1,1)
For x=2, [tex]y=(2)^2=4[/tex]. Point (2,4)
The graph of
[tex]y=x^2-12[/tex]
Can be similarly found:
For x=-2, [tex]y=(-2)^2-12=-8[/tex]. Point (-2,-8)
For x=-1, [tex]y=(-1)^2-12=-11[/tex]. Point (-1,-11)
For x=0, [tex]y=(0)^2-12=-12[/tex]. Point (0,-12)
For x=1, [tex]y=(1)^2-12=-11[/tex]. Point (1,-11)
For x=2, [tex]y=(2)^2-12=-8[/tex]. Point (2,-8)
The graphs are shown in the attached image. It can be clearly seen that the second graph (in blue) is shifted down 12 units with respect to the red graph. Answer:
b) Shift the graph of y = x2 down 12 units.
What is the solution to the following inequality?
-16<14-5x
Answers
-30 < -5x
6 > x
help please I beg you I need to return it tomorrow
Answers
Answer:
it will be 3x+1. it means 3 multiplied by my number plus 1
Answer: Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. For example: Distributive
Multiplication distributes over addition. That is:
∀
How are operations on functions like operations on real numbers?
please help!!!! 20 points
Answers
Step-by-step explanation:
I am explain you in image
find the zeros (roots) of the following equations.
f(x) = 2x^5-9x^4+12x^3-12x+10x-3=0
I need to find five roots
Answers
9514 1404 393
Answer:
x ∈ {1/2, 1, 3, i, -i}
Step-by-step explanation:
We assume your function is supposed to be ...
f(x) = 2x^5 -9x^4 +12x^3 -12x^2 +10x -3=0
I find it convenient to use a graphing calculator to find the real roots of higher-degree polynomials. The attached shows the real roots are ...
x = 1/2, 1, 3
Factoring those out leaves the quadratic factor ...
x^2 +1 = 0
That one has roots ±i.
So, the full complement of roots is ...
x ∈ {1/2, 1, 3, i, -i}
_____
Descartes' rule of signs tells you the real roots are all positive. The rational root theorem tells you that rational roots are in the set {1/2, 1, 3/2, 3}. The sum of coefficients is 0, telling you that x=1 is a real root.
Factoring that from the polynomial leaves the 4th-degree factor ...
2x^4 −7x^3 +5x^2 −7x +3 . . . . . division shown in 2nd attachment
For x=1, this has a negative value (-4), so you know there is a root between f(0) =3 and f(1) = -4. The only rational choice is 1/2.
Similarly, factoring that from the polynomial (along with a factor of 2) leaves the cubic ...
x^3 -3x^2 +x -3 . . . . . division shown in 3rd attachment
This is clearly factorable by grouping to (x -3)(x^2 +1), so we have our third real root and the quadratic that yields the complex roots.
PLEASE HELP ASAP
What is the solution to the system of equations graphed below?
y = 3x + 2
y = -2x - 3
Answers
Answer: x = -1; y = -1
y = 3x + 2
y = -2x - 3
⇔ y = 3x + 2
3x + 2 = -2x - 3
⇔ y = 3x + 2
5x = -5
⇔ y = 3x + 2
x = -1
⇔ y = -1
x = -1
Step-by-step explanation:
Answer plz I will correct answer as brainliest
Answers
y=180-50
=130 degrees (angles in a straight line equal to 180)
z=180-130-30 (angle sum of a triangle equal to 180)
z=20 degrees
A building is 50 ft high. At a distance away from the
building, a person notices that the angle of elevation
with the ground to the top of the building is 41°.
How far is the person from the base of the building?
Answers
PLZ HELP!!! I HAVE ONLY 15 MINUTE LEFT BEFORE CLASS IS OVER!!!!
Answers
Answer:
268
Step-by-step explanation:
I hope this helped!
I would appreciate it if you gave me a Thanks and a brainliest (:
Will give Brainliest!! This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of proportionality? Number of Teachers A line graph titled Number of Teachers has number of students on the x-axis, and number of teachers on the y-axis. For every 60 students, there are 4 teachers; 120, 8. StartFraction 1 over 25 EndFraction StartFraction 1 over 20 EndFraction StartFraction 1 over 15 EndFraction StartFraction 1 over 10 Will Give brainliest!
Answers
Answer:
C
Step-by-step explanation:
Answer:
C) 1/15
Step-by-step explanation:
Write 34/38 in lowest terms
Answers
The lowest term of 34/38 is 17/19.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
34/38
= 17/19
Thus,
17/19 is the lowest term.
Learn more about fractions here:
https://brainly.com/question/24370499
#SPJ2
4. Which statement is true?
A. The value of the 7 in 17,265 is 20 times the value of the 7 in 26,173.
B. The value of the 7 in 17,265 is 10 times the value of the 7 in 26,173.
C. The value of the 7 in 17,265 is 100 times the value of the 7 in 26,173.
D. The value of the 7 in 17,265 is to times the value of the 7 in 26,173.
Answers
Which graph models the equation - 3x + 4y = 8?
Answers
A restaurant sells cheeseburgers to chicken sandwiches in a ratio of 7:2. If the restaurant sells 12 chicken sandwiches one day, how many cheeseburgers does it sell
Answers
Answer:
Food problems are fun :D
Step-by-step explanation:
[tex]\frac{7}{2}[/tex] = [tex]\frac{cheeseburgers}{chicken}[/tex]
chicken =12 sooo..
[tex]\frac{7}{2}[/tex] = [tex]\frac{x}{12}[/tex]
and solve for x.... that is... get x by itself... "isolate x"
12 * [tex]\frac{7}{2}[/tex] = x
6 * 7 = x
42 = x
the restaurant sold 42 cheeseburgers :P
Can someone help me with this?
Answers
Answer:
3. a) 37 b) 48 c) 48 d) 24
Step-by-step explanation:
Help me pleaseeeeeeeeeeeee
Answers
Answer:
i think the first one
Step-by-step explanation:
Answer:
A. 2x2y +7xy2
Step-by-step explanation:
I will mark branliest!
Answers
Answer:
C
Step-by-step explanation:
If he collects 25 cans everyday,
and you use -s- for the number of days.
Multiply to get the total amount of cans.