if the measure of angle 1 is (3x-4)° and the meadure of angle 2 is (4x+10)° what is the measure of angle 2 in degrees?
Answers
=>
7x + 6 = 90
=>
7x = 84 => x = 84/7 = 12
<2 = 4x + 10 = 4*12 + 10 = 48 + 10 = 58
The answer is: 58
Answer:
The measure of ∠ 2 in 58° .
Step-by-step explanation:
As given
if the measure of ∠ 1 is (3x-4)° and the measure of ∠ 2 is (4x+10)° .
As shown in the picture given in the question
90° + ∠1 + ∠2 = 180°
(By linear pair property)
Put the value of ∠1 and ∠2 in the above
90° + (3x -4)° + (4x+10)°= 180°
90 + 3x -4 + 4x + 10 = 180
7x + 6 = 180 - 90
7x + 6 = 90
7x = 90 -6
7x = 84
[tex]x = \frac{84}{7}[/tex]
x = 12
Put the value of x in the (4x+10)° .
∠2 = (4 × 12 + 10)°
∠2 = 58°
Therefore the measure of ∠ 2 in 58° .
Related Questions
To make lemonade, you used one gallon of water, four quarts of lemon juice, and 32 ounces of honey. How much lemonade did you make?
Answers
We have 4 quarts of lemon and it is 1 gallon ( and we also have 1 gallon of water ). Also we have 32 ounces of honey, which is 1 quart more.
4 quart + 4 quart + 1 quart = 9 quarts = 2 gallons 1 quart
Answer:
There is 9 quarts or 2 gallons and 1 quart of lemonade.
Find the measure of an angle whose supplement is 9 times the measure of its complement
Answers
180 - x = 9(90-x)
180-x = 810 - 9x
8x = 630
x = 78.75 degrees
The equation is 180 - x = 9 (90 - x).Then the measure of the angle will be 78.75 degrees.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
Let 'x' be the angle. Then the equation is given as,
180 - x = 9 (90 - x)
180 - x = 810 - 9x
8x = 630
x = 78.75 degrees
The measure of the angle will be 78.75 degrees.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ5
PLEASE HELP!!!
How can one thirdx − 2 = one fourthx + 11 be set up as a system of equations?
3y − x = −6
4y − x = 44
3y + x = −6
4y + x = 44
3y − 3x = −6
4y − 4x = 44
3y + 3x = −6
4y + 4x = 44
Answers
3y=x-6
3y-x=-6
y=1/4x+11
4y=x+44
4y-x=44
Answer: Hello!
we have that:
one third x − 2 = one fourth x + 11
this means:
(1/3)x - 2 = (1/4)x + 11
if this are equal numbers, we can write it as:
(1/3)x - 2 = y = (1/4)x + 11
now we have the system of equations:
(1/3)x - 2 = y
(1/4)x + 11 = y
if we "simplify" the rational therm in each equation, we get:
3*(1/3)x - 3*2 = 3y
x - 6 = 3y
and
4*(1/4)x + 4*11 = 4y
x + 44 = 4y
Then our system of equations is:
x - 6 = 3y
x + 44 = 4y
Now we can subtract x in each side of both equations:
-6 = 3y - x
44 = 4y - x
Then the right option is the first one.
3y - x = -6
4y - x = 44
which of the following fractions will convert to repeating decimals?
a. 1/3
b. 1/6
c. 1/4
d. 3/8
e. 1/5
Answers
a. 1/3 = 0.33333333
b. 1/6 = 0.16666666
c. 1/4 = 0.25
d. 3/8 = 0.375
e. 1/5 = 0.2
A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volume the same?
Answers
The square pyramid has a volume of
5x5xheight/3
what would be the measure of angle DGF, if segment DG is a bisector of angle G
30 degrees.60 degrees.90 degrees.None of the choices are correct.
Answers
a bisector, means, it "cuts in two equal halves".
Find the value of x in the equation √ x + 5 = √ x + 45.
Answers
A chocolate bar measures 40 mm wide, 80 mm long, and 5 and 1 over 2 mm high. Will’s Wrapping Company is making a wrapper to cover the chocolate bar. Use the correct net and determine how much paper will be needed to make the wrapper
Answers
The surface area of the rectangular prism is calculated through the equation,
SA = 2LW + 2WH + 2LH
Substituting the known values,
SA = (2)(80 mm)(40 mm) + 2(40 mm)(5.5 mm) + 2(80 mm)(5.5 mm)
SA = 6400 mm² + 440 mm² + 880 mm²
SA = 7720 mm²
Thus, the least area needed to completely cover or wrap the chocolate bar is 7720 mm².
Answer:
Will’s Wrapping Company needs 7,720 mm of paper to wrap the chocolate bar.
Find the number of permutations of the first 8 letters of the alphabet taking 4 letters at a time.
Answers
8P4
using the calculator this will give us:
8P4=1,680
This tells us that there are more than 1,680 different ways that the leteers will be selected.
HELP
If f(x)=-6x+12, then f^-1(x)=?
Answers
Zeus Industries bought a computer for $2011. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 5 years?
Answers
Value after 1 year:
24/100*2011
=$482.64
2011-482.64
=$1528.36
or
76/100*2011
=$1528.26
Value after 2nd year:
76/100*1528.36
=$1,161.55
Value after 3rd year:
76/100*1,161.55
=$882.78
Value after 4th year:
76/100*882.78
=$670.91
Value after 5th year:
76/100*670.91
=$509.89
hence the value after five years will be: $509.90
The perimeter of a rectangle is 42 m. the length of the rectangle is 3 m more than twice the width. find the dimensions of the rectangle.
Answers
42/2 = 21
21 = w +2w+3
21 = 3w +3
18 =3w
w = 18/3 = 6
width is 6
length = 6x2=12+3 = 15
6+6+15+15 = 42
width = 6 m
length = 15 m
Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After nine hours, the velocity of the cyclist is 4 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 10 hours? (5 points)
Answers
Define the function v(t) for velocity in km/h, and t in hours.
Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
m = 14/4 = 3.5, and the y-intercept is
b = 0.
Therefore
v(t) = 3.5t, for 0 ≤ t ≤ 4
Fromt=4 to t=9, changes from 14 to 4.
Let v(t) = mt + b
The slope is
m = (4 - 14)/(9 - 4) = -2
Therefore
v = -2t + b
When t=4, v=14, therefore
14 = -2*4 + b = -8 + b
22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.
Answer:
The equation for the velocity is
v(t) = 3.5t, 0 ≤ t ≤ 4
= -2t + 22, 4 < t ≤ 9
Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h
A polygon with 12 sides is called a/an
Answers
In geometry, a dodecagon or 12-gon is any twelve-sided polygon.
hope this helps!
What is the solution set of the following equation? 3x2 - 6x = 0
Answers
Use the information in the figure. If m∠F = 76°, find m∠E
Answers
Answer:
m∠E=52°.
Step-by-step explanation:
The given triangle has two sides equal. In isosceles triangle two sides are equal and base angles are equal.m∠E=m∠D.
Let m∠D=m∠E= x
The sum of angles in any triangle is 180°.
Or,
x+x+76= 180
Addling like terms :
2x+76=180
Subtracting 76 both sides,
2x=104.
Dividing by 2:
x=52.
m∠E= 52°.
0.43 is 10 times as mush as what
Answers
The number that is 10 times less than 0.43 is 0.043, found by dividing 0.43 by 10.
To find the number that 0.43 is 10 times as much as, we need to divide 0.43 by 10. This is the same as multiplying by 10 raised to the power of -1, which is a division by 10.The operation looks like this:
0.43*10^{-1} = 0.043.
Therefore, 0.43 is 10 times as much as 0.043
Which of the following is an identity? A. sin2x sec2x + 1 = tan2x csc2x B. sin2x - cos2x = 1 C. (cscx + cotx)2 = 1 D. csc2x + cot2x = 1
Edit: no one answered but I figured out that the right answer is A
Answers
sin²(x) + cos²(x) = 1
tan²(x) + 1 = sec²(x)
1 + cot²(x) = csc²(x)
We can start by checking each option to see which one would give us any of the 'Pythagorean' identities as its simplest form
Option A:
sin²(x) sec²(x) + 1 = tan²(x) csc²(x)
Rewriting sec²(x) as 1/cos²(x)
Rewriting tan²(x) as sin²(x)/cos²(x)
Rewriting csc²(x) as 1/sin²(x)
We have
[tex]sin^{2}(x)[ \frac{1}{ cos^{2}(x) }]+1=[ \frac{ sin^{2}( x)}{ cos^{2} (x)}][ \frac{1}{ sin^{2}(x) } ][/tex]
[tex] [\frac{ sin^{2}(x) }{ cos^{2}(x) } ]+1= \frac{1}{ cos^{2}(x) } [/tex]
[tex] tan^{2}(x)+1= sec^{2}(x) [/tex]
Option B:
sin²(x) - cos²(x) = 1
This expression is already in the simplest form, cannot be simplified further
Option C:
[ csc(x) + cot(x) ]² = 1
Rewriting csc(x) as 1/sin(x)
Rewriting cot(x) as cos(x)/sin(x)
We have
[tex][ \frac{1}{sin(x)}+ \frac{cos(x)}{sin(x)}] ^{2} =1[/tex]
[tex] \frac{1}{sin^2(x)}+2( \frac{1}{sin(x)})( \frac{cos(x)}{sin(x)})+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex][tex]csc^2(x)+2csc^2(x)cos(x)+cot^2(x)=1[/tex]
Option D:
csc²(x) + cot²(x) = 1
Rewriting csc²(x) as 1/sin²(x) and cot²(x) as cos²(x)/sin²(x)
[tex] \frac{1}{sin^2(x)}+ \frac{cos^2(x)}{sin^2(x)}=1 [/tex]
[tex] \frac{1+cos^2(x)}{sin^2(x)} =1[/tex]
[tex]1+cos^2(x)=sin^2(x)[/tex]
[tex]1=sin^2(x)-cos^2(x)[/tex]
from our working out we can see that option A simplified into one of 'Pythagorean' identities, hence the correct answer
Answer: A is the correct answer.
Step-by-step explanation:
Just did the question, followed OP's advice since no one answered. Good luck.
Practice writing linear equations in different forms. Line AB goes through the points A (0, –4) and B (6, 2). Which equation represents line AB? y – 4 = 3x y – 2 = 3(x – 6) y + 4 = x y + 6 = x - 2
Answers
slope = (2 - (-4) / (6 - 0) = 6/6 = 1
y = mx + b
slope(m) = 1
(0,-4)..x = 0 and y = 4
sub and find b
4 = 1(0) + b
4 = b
equation is : y = x + 4...or x - y = -4
or y + 4 = 6(x - 0) ...or y - 2 = 6(x - 6)
the answer is c . y + 4 = x
The perimeter of a triangle is 510 ft and the sides are in the ratio of 11:16:24. Find the area of the triangle. Need help, is there a specific formula for this?
Answers
The side lengths are in the ratio 11:16:24, so let them be
11k, 16k, and 24k for some number k.
11k+16k+24k=510
k(11+16+24)=510
51k=510
k=10
so the actual sides are 110, 160 and 240 feet.
2.
There is a famous formula, called Heron's formula, which calculates the area of a triangle, given its sides a, b and c.
we first calculate the half perimeter, which we usually denote by u:
[tex]u= \frac{a+b+c}{2} [/tex]
then the theorem states that the area A is as follows:
[tex]A= \sqrt{u(u-a)(u-b)(u-c)} [/tex]
3.
In our case:
[tex]u= \frac{a+b+c}{2} =\frac{110+160+240}{2} = \frac{510}{2} [/tex]
[tex]u-a= \frac{510}{2} -110= \frac{510-220}{2} = \frac{290}{2} [/tex]
[tex]u-b= \frac{510}{2} -160= \frac{510-320}{2} = \frac{190}{2} [/tex]
[tex]u-a= \frac{510}{2} -240= \frac{510-480}{2} = \frac{30}{2} [/tex]
[tex]A= \sqrt{\frac{510}{2}*\frac{290}{2}* \frac{190}{2} * \frac{30}{2}} =7,258.745[/tex] feet squared
Answer:D 7,258.745 ft squared
Final answer:
To find the area of a triangle with sides in a given ratio, first find the value of x by setting up and solving an equation using the perimeter. Then, multiply each side by x to find the base and height of the triangle. Finally, substitute the base and height into the formula for the area of a triangle.
Explanation:
To find the area of a triangle, we can use the formula: Area = 1/2 × base × height. In this case, we don't know the base and height directly, but we do know that the sides of the triangle are in the ratio of 11:16:24. Let's assume the sides are 11x, 16x, and 24x. The perimeter of the triangle is 510 ft, which means 11x + 16x + 24x = 510. Simplifying this equation, we get 51x = 510. Therefore, x = 10. Now we can find the base and height of the triangle by multiplying the corresponding sides by 10. The base is 11x * 10 = 110 ft and the height is 16x * 10 = 160 ft.
Now we can substitute these values into the formula to calculate the area of the triangle. Area = 1/2 × base × height = 1/2 × 110 ft × 160 ft = 8800 square feet.
10-2v=-5-50
+5 +5
10-3v=-50
+3 +3
10=47
Answers
10-2v=-5-50
add : 5
10 - 2v + 5 = 5 - 5 - 50
15 -2v = -50
add : -15
-15 +15 -2v = -15 -50
-2v =-65
v = 65/2
Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?
The answer is D.243.33
(I looked up the question and couldnt find it so i thought i'd post it for anyone who needed it)
Answers
Predicted spent of gas next month = $50 * 1.08
Predicted spent of gases for the four months:
$50 * 1.08
$50 * 1.08^2
$50 * 1.08^3
$50 * 1.08^4
Total spent for the four months: $50 (1.08 + 1.08^2 + 1.08^3 + 1.08^4) = $50 * (4.8666) = $243.33, which is the option D. 243.33
lady runs 20 miles in 4 hours. write an equation representing the direct relationship between distance and time
Answers
20=40t
divide by 20
t=2
d=10
In a 45-45-90 triangle, the length if the hypotenuse is 11. Find the length of one of the legs
Answers
Answer:
[tex] \frac{11\sqrt{2}}{2}[/tex]
Step-by-step explanation:
In a 45-45-90 triangle, the length if the hypotenuse is 11
WE use the common ratio of 45-45-90 degree triangle
common ration is x: x: x sqrt(2)
x sqrt(2) is the length of the hypotenuse
[tex]x\sqrt{2} = 11[/tex]
Divide by sqrt(2) on both sides
[tex]x= \frac{11}{\sqrt{2}}[/tex]
To rationalize the denominator, multiply by sqrt(2) at the top and bottom
sqrt(2) * sqrt(2) = 2
[tex]x= \frac{11\sqrt{2}}{2}[/tex]
Find the midpoint of the segment below
Answers
If we are given 2 points A(a, b) and B(c, d),
the midpoint M, of segment AB has coordinates:
[tex]M_A_B=( \frac{a+c}{2} , \frac{b+d}{2} )[/tex]
2.
We are given the points A(2, 3) and B(10, 3)
the midpoint of AB, is given by the above formula:
[tex]M_A_B=( \frac{2+10}{2} , \frac{3+3}{3} )=(6, 3)[/tex]
3.
Remark, since the segment is horizontal, that is the y-coordinate of both points is 3, the y coordinate of the midpoint will also be 3.
While the x coordinate is still found by [tex]\frac{2+10}{2}[/tex]
Answer: (6, 3)
Please HELP
1-) Solve the equation using the Properties of Equality.
11 − c = −17
2-)Solve the equation using the Properties of Equality.
1/2y + 1/5=1/2
Answers
11-c = -17
First, we need to isolate the term with the variable. We can simply do that by subtracting 11 from both sides as follows:
11-11-c = -17-11
-c = -28
Then, we will multiply both sides by -1 to get the positive value of c as follows:
-c x -1 = -28 x -1
c = 28
Problem 2:
1/2 y + 1/5 = 1/2
First, we need to isolate the term with the variable by subtracting 1/5 from both sides as follows:
1/2 y = 1/2 - 1/5 = 3/10
Then, we will get rid of the coefficient in the term with variable by dividong both sides with 1/2, this will give the following output:
y = 3/5
Ac=3x+6 and CD=2x+14 what is the value of x
Answers
And since the problem gave us two equations to use we will substitute them into the previous statement.
3x + 6 = 2x + 14
We now simplify with algebra and I will show every step.
3x + 6 = 2x + 14
-2x = -2x
x + 6 = +14
-6 = -6
x = 8
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
We have been given that [tex]AC=3x+6[/tex] and [tex]CD=2x+14[/tex].
To solve for x, we are assuming that C is the midpoint of segment AD and we will equate both expressions as:
[tex]3x+6=2x+14[/tex]
[tex]3x-2x+6=2x-2x+14[/tex]
[tex]x+6=14[/tex]
[tex]x+6-6=14-6[/tex]
[tex]x=8[/tex]
Therefore, the value of x is 8.
The sum of three interior angles of a convex Pentagon is 420°.if the remaining angles are equal how much does each angle measure?
Answers
Sum of angles = (n-1)x180°, where n is the number of sides. For the pentagone n = 5, then Sum of angles of a PENTAGONE = (5-1)x180° = 720°.
Already the sum of 3 angles is 420°, the measure of the 2 remaining one is
720° - 420° = 300°. Since the remaining angles are equal, hence each one will have a measure of 300°/2 = 150°
Each one of the remaining angles measures 60°.
How much does each angle measure?
We know that the sum of the interior angles of a closed figure of n sides is given by:
(n - 2)*180°.
A pentagon has 5 sides, so we use n = 5 and we get:
(5 - 2)*180° = 540°
Now we know that 3 angles add up to 420°.
Then the other two angles must add up to:
540° - 420° = 120°
And those two angles are equal, then each one measures:
120°/2 = 60°.
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
A card is chosen at random from a standard deck of 52 playing cards. What is the probability that the chosen card is a jack or a queen?
Answers
200 gallon tank fills at 3 gallons/minute and loses 2 gallons/minute how long does it take to fill up
Answers
it fills at 3 gallons per minute, but loses 2 gallons per minute
3-2 =1, so it fills at 1 gallon per minute
200 gallons at 1 gallon per minute = 200 minutes,
200/60 = 3 hours and 20 minutes