Please help! I need help on the whole worksheet
In this figure ∠7 and ∠3 are alternate interior angles . Alternate interior angles in two parallel lines with a transversal will always be equal . Since ∠7 is congruent to ∠3 , we can say that line m and line n are parallel lines .
Therefore :-
The lines are parallel because the alternate interior angles in them are congruent .
Solution (2) :-Given :-
m∠3 = ( 15x + 22 )°
Then , m∠3 will be equal to :-
x = 8
= 15 × 8 + 22
= 120 + 22
m∠3 = 142°
m∠1 = ( 19x - 10 )°
= 19 × 8 - 10
= 152 - 10
m∠1 = 142°
angle 1 and angle 3 are corresponding angles , which means their value will be equal if they are present on two parallel lines with a transversal . As their values are equal we can say that line m and line n are parallel .
Therefore :-
Yes , the lines are parallel because the corresponding angles in them are equal .
Solution (3) :-∠7 and ∠6 are interior angles on the same side of transversal , which means their angle su, will be equal to 180° . But since their values are equal these two lines are not parallel .
Therefore :-
∠7 and ∠6 are interior angles on the same side of transversal , so their sum will be equal to 180° . But since that is not the case in the lines shown above , those lines are not parallel lines .
Solution (4) :-Given :-
m∠2 = ( 5x + 3 )°
x = 14
= 5 × 14 + 3
= 60 + 3
= 63°
m∠3 = ( 8x - 5 )°
= 8 × 14 - 5
= 112 - 5
= 107°
We know that the sum of angle 2 and angle 3 will be equal to 180° if they are on two parallel lines as they are interior angles on the same side of transversal .
As :-
∠2 + ∠3 ≠ 180°
63° + 107° is not equal to 180° ,
Therefore :-
These lines are not parallel as the sum of their interior angles on the same side of transversal is not equal to 180°.
Solution (5) :-Given :-
m∠8 = ( 6x - 1 )°
x = 9
= 6 × 9 - 1
= 54 - 1
= 53°
m∠4 = ( 5x + 3 )°
= 5 × 9 + 3
= 45 + 3
= 48°
angle 8 and angle 2 are vertically opposite angles , which means m∠8 = m∠2 .
m∠2 = 53°
As ∠2 and ∠4 are corresponding angles their value will be equal , if they are on parallel lines .
Since angle 2 , angle 8 and angle 4 are not equal these lines are not parallel lines .
Therefore :-
The lines are not parallel as their corresponding angles are not equal .
Solution (6) :-Angle 5 and angle 7 are corresponding angles they will be congruent when on parallel lines .
As , m∠5 ≅ m∠7 these lines are parallel .
Therefore :-
These lines are parallel lines as their corresponding angles are equal .
Solution (7) :-Angle 1 and angle 7 are vertically opposite angles , which means their angle measure will be equal . As angle 7 and angle 5 are corresponding angles their angle measure will also be equal .
Since m∠5 ≅ m∠7 , these lines are parallel .
Therefore :-
These lines are parallel lines as their corresponding angles are equal .
Solution (8) :-Here , the value of x is the same .
Which means :-
m∠2 = x + 15° is greater than m∠6 = x + 10°
Angle 2 and angle 6 are alternate interior angles , their values should be equal . But since their values are not equal , the lines on which they reside are not parallel .
Therefore :-
These lines are not parallel as their alternate interior angles are not equal .
Solution (9) :-It is given that angle 1 and angle 3 are supplementary angles . It is also clear that angle 1 and angle 2 are a linear pair , which means their angle sum will be equal to 180° . Also , angle 3 and angle 2 should be equal since they are the supplement of the same angle . Angle 2 and angle 3 are also corresponding angles . Since corresponding angles in two lines with a transversal will be equal and in these two lines the corresponding angles are equal , these lines are parallel lines.
Therefore , JK // HI as their corresponding angles are equal .
Factor 2x^2-x-10. Rewrite the trinomial with the x term expanded using 2 factors.Then group the first 2 and last 2 terms together and find the Gcf of each
Trinomial (2x- ___) + (4x-10)
Gcf __ (2x-5) + __ (2x-5)
Answer:
Trinomial: (2x² – 5x) + (4x – 10)
GCF: x (2x – 5) + 2 (2x – 5)
Step-by-step explanation:
2x² – x – 10
The equation above can be factorised as follow:
2x² – x – 10
Multiply the first term (i.e 2x²) and the last term (i.e –10) together.
2x² × (–10) = –20x²
Find two factors of –20x² such that when we add them together, it will result to the 2nd term in the equation (i.e –x).
The factors are 4x and –5x.
Next, replace –x in the equation above with 4x and –5x. This is illustrated below:
2x² – x – 10
2x² – 5x + 4x – 10
Next, factorise
2x² – 5x + 4x – 10
Trinomial: (2x² – 5x) + (4x – 10)
GCF: x (2x – 5) + 2 (2x – 5)
easy to read
Practice Problems
1.4.-62
Answer:
1.4-62=-60.6
Step-by-step explanation:
Ask me if you need any other help!
Dave is making lemonade. For each 8 cups of water, he uses 3 cups of lemon juice and 2 cups of sugar. If w the number of cups of water, l is the number of cups of lemon juice, and s is the number of cups of sugar, which equations are correct?
A. l = 3/8 (w)
B. l = 3s
C. w= 4s
D. l = 2/3 (s)
Answer: A and C are correct.
Step-by-step explanation:
Look at the proportions. For 8 cups of water there are 3 cups of lemon juice. So L 3/8(w)
For 8 cups of water there are 2 cups of sugar. 8 is 4 times 2. So the amount of water is 4 times the amount of sugar. W= 4s
Doughnuts are sold in bags and cartons.
A bag hold 4 doughnuts and a carton holds 10 doughnuts
Tom buys B bags and C cartons of doughnuts.
He buys a total of T doughnuts.
Write down a formula for T in terms of B and C
Answer:
t = b4+c10
Step-by-step explanation
4 times however how many bags
10 times however how many cartons
Solve -16x = -80.
-5
5
-96
-64
Will mark as brainliest
[tex] - 16x = - 80[/tex]
Divided sides by -16
[tex] \frac{ - 16}{ - 16}x = \frac{ - 80}{ - 16} \\ [/tex]
[tex]x = 5[/tex]
And we're done...♥️♥️♥️♥️♥️
Select the equation that is the inverse of the given function.
f (x) =( x minus 3 Over 5)
Answer:
x+3/5
Step-by-step explanation:
f(x)=x-3/5
y=f(x) let
y=x-3/5
put x at y and y at x
then,
x=y-3/5
y=x+3/5
f(x) inverse is x+3/5
6x+8=x-2 what is the answer to this
Answer:
x= -2
Step-by-step explanation:
6x+8=x-2
6x-x= -2-8
5x= -10
x= -10/5
x= -2
A 3. What is the midpoint M given S(-8,-6) and T(4, 12)?
0 (-2,3)
O (7,8)
0 (-6, -9)
0 (-1,-4)
Answer:
The answer is ( - 2 , 3)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
S(-8,-6) and T(4, 12)
We have
[tex]M = ( \frac{ - 8 + 4}{2} \: , \: \frac{ - 6 + 12}{2} ) \\ = ( - \frac{4}{2} \: , \: \frac{6}{2} )[/tex]
We have the final answer as
( - 2 , 3)Hope this helps you
What is a uniform circular motion?
a. Uniform circular motion is when an obiect accelerates on a
circular path at a constantly increasing velocity
b. Uniform circular motion is when an object travels on a
circular path at a variable acceleration
c. Uniform circular motion is when an object travels on a
circular path at a constant speed
d. Uniform circular motion is when an object travels on a
circular path at a variable speed (answer this quickly pls)
Answer:
C. Uniform circular motion is when a object travels on a circular path at a constant speed.
How much is the interest on my loan?
I borrowed $400 to buy an MP3 player. I got a two-year loan,
and the lender is charging 8% Simple annual interest. How
much money will I have to pay back?
Time
Interest Principal
$ ?
$400
Rate
0.08
2
/= Prt
1 = 400 x 0.08 x 2
Interest
I
1.00
You will have to pay back a total of $464 over the course of the two-year loan, which includes the $400 principal plus $64 in interest.
What is Simple Interest ?
Simple interest can be defined as the ratio of product of principal amount , rate , time and hundred.
The interest on your loan can be calculated using the formula:
Interest = Principal x Rate x Time
In this case, the principal is $400, the rate is 8% (or 0.08 as a decimal), and the time is 2 years.
So, plugging in the numbers:
Interest = $400 x 0.08 x 2 = $64
Therefore, the total amount you will have to pay back is the sum of the principal and the interest, which is:
Total = Principal + Interest
= $400 + $64 = $464
Hence, You will have to pay back a total of $464 over the course of the two-year loan, which includes the $400 principal plus $64 in interest.
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. Line A is represented by the equation y=1/4x+5
(a) Write in slope-intercept form the equation of a line that is parallel to Line A and passes through the point, (8, 2) − . Show your work.
(b) Write in slope-intercept form the equation of a line that is perpendicular to Line A and passes through the point, (4, 1) . Show your work.
Answer:
(a) y = 1/4x - 4
(b) y = -4x + 17
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
m - slope
b - y-intercept
(a)
Parallel lines have the same slope but different y-intercepts.
m = 1/4x
y = 1/4x + b
-2 = 1/4(8) + b
-2 = 2 + b
b = -4
y = 1/4x - 4
(b)
Perpendicular lines have the negative reciprocal slope.
m = -4
y = -4x + b
1 = -4(4) + b
1 = -16 + b
b = 17
y = -4x + 17
Solve and show your work or explain.
[tex]x-\sqrt{2x-5}=5[/tex]
Answer:
[tex]x= 6+ \sqrt {6}[/tex]
Step-by-step explanation:
[tex]-\sqrt {2x-5}+x=5\\-\sqrt {2x-5}=-x+5\\\\\frac {-\sqrt {2x-5}}{-1} = \frac {-x+5}{-1}\\\\\sqrt {2x-5}=x-5\\2x-5=(x-5)^2\\2x-5=x^2-10x+25\\2x-5-(x^2-10x+25)=x^2-10x+25-(x^2-10x+25)\\-x^2+12x-30=0\\\\x=\frac {-12(+/-)\sqrt {12^2-4(-1)(-30)}}{2(-1)}\\\\x=6+\sqrt {6}[/tex]
A rectangle has a length that is 3 more than twice the width. Its perimeter is 96 inches.
Which equation models this?
Answer:
8x=96 inch
Step-by-step explanation:
How its in the draw you have this situation then the equation that model is the next one:
2*(3X) + 2*X = 96 inch
6X + 2X = 96 inch
8X=96 inch
We must multiply due that there is two sides that measure the same.
The equation which models this situation is,
⇒ 96 = 2 ((3 + 2x) + x)
or ⇒ 96 = 2 (3 + 3x)
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
A rectangle has a length that is 3 more than twice the width.
And, Its perimeter is 96 inches.
Let the width of rectangle = x
So, The length of rectangle = 3 + 2x
Now, We know that;
⇒ Perimeter of rectangle = 2 (Length + Width)
Substitute all the values, we get;
⇒ Perimeter of rectangle = 2 (Length + Width)
⇒ 96 = 2 ((3 + 2x) + x)
⇒ 96 = 2 (3 + 3x)
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Write an inequality
I can work at most 30 hours per week
Answer:
[tex] h \le 30 [/tex]
Step-by-step explanation:
Let h = number of hours of work.
At most 30 hours means 30 hours or less.
[tex] h \le 30 [/tex]
7 is a solution to the equation 3n + 9 = 33.
true or false
Answer:
false
Step-by-step explanation:
3(7) = 21+9 = 30
Answer:
False
Step-by-step explanation:
Hope This Helps!!!
Adrian is a songwriter who collects royalties on his songs whenever they are played in a commercial or movie. Adrian will earn $40 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie. Adrian earned a total of $1010 in royalties on 14 commercials and movies. How many commercials and movies did Adrian's songs play on?
Answer:
Adrian's songs played on 9 commercials and 5 movies.
Step-by-step explanation:
Let x denotes number of commercials and y denotes number of movies.
Total number of commercials and movies = 14
So,
[tex]x+y=14\\x=14-y\,\,\,\,...(i)[/tex]
Adrian will earn $40 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie
Total amount earned = $1010
[tex]40x+130y=1010\,\,\,...(ii)[/tex]
Put [tex]x=14-y[/tex] in (ii)
[tex]40(14-y)+130y=1010\\560-40y+130y=1010\\90y=1010-560\\90y=450\\y=\frac{450}{90}=5[/tex]
Put [tex]y=5[/tex] in [tex]x=14-y[/tex]
[tex]x=14-5=9[/tex]
Therefore, Adrian's songs played on 9 commercials and 5 movies.
Given m||n, find the value of x.
(8x-27) (7x-4)
Answer:
56ײ-221x+108
Step-by-step explanation:
i need help me please :(
3) x-intercept = -3, y-intercept = 1
Y=-3/1 x -3
Would that be how I set it up in the formula form?
Answer:
y = 1/3x+1
Step-by-step explanation:
Use the intercepts to find the slope
(-3,0) and (0,1)
(1-0) / (0-(-3)) = 1 / 3
Plug it into the equation
y= 1/3x + 1
Peter drives at a speed of 70 miles per hour.
How long will it take to drive 455 miles?
hours
Answer: 6.5 hours
Step-by-step explanation:
You have to find out how long it’ll take, so you divide the total amount by the speed, so 455/70=6.5
Answer:6
Step-by-step explanation:
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C?
A.
(7, -1)
B.
(2, -3)
C.
(2, -1)
D.
(5, -3)
Rese
Answer:
a
Step-by-step explanation:
Answer:
The correct answer for plato is option C
Step-by-step explanation:
C. (2, -1)
state whether the linear equation has one (unique),infinely many,or no solutions
12(x+8)=11x-5
PLZ HELP! DO NOT PUT A SILLY AWSER I WILL REPORT U!
Answer:
One solution
Step-by-step explanation:
12x+96=11x-5
12x-11x= -5-96
x= -101
x only equals one solution, which is -101.
3x2 + 8x - 10
Please someone help ...
QUICK I NEED HELP!!!
Solve the absolute value:
| x + 1| + 3 <4
Answer:
x<0 and x>-2
Step-by-step explanation:
Answer:
x<0 and x>−2
Step-by-step explanation:
Step 1: Add -3 to both sides.
|x+1|+3+−3<4+−3
|x+1|<1
Step 2: Solve Absolute Value.
|x+1|<1
We know x+1<1 and x+1>−1
x+1<1(Condition 1)
x+1−1<1−1(Subtract 1 from both sides)
x<0
x+1>−1(Condition 2)
x+1−1>−1−1(Subtract 1 from both sides)
x>−2
An____ is a number, a variable, or a combination of numbers and variables and operation symbols.
A. Equation
B. Expression
C. Ratio
D. Proportion
Answer:
Expression.
Step-by-step explanation:An expression containing variables, numbers, and operation symbols is called an algebraic expression. is an example of an algebraic expression. Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
What is Expression?An expression is combination of variables, numbers and operators.
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
For example 2x+3y-4
In the given expression x and y are the variables.
plus and minus are the operation symbols.
4 is a number and 2 and 3 are the coefficients of a variable.
If the expression has an equal sign then it becomes the equation.
Hence, an expression is a number, a variable, or a combination of numbers and variables and operation symbols.
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Write an inequality for the graph.
Easy buddy...
[tex]y \geqslant |x - 5| + 1 [/tex]
Just it....
And we're done.
Thanks for watching buddy good luck.
♥️♥️♥️♥️♥️
Eric is swimming along the surface of the sea. He uses positive numbers to represent elevations above the surface of the sea and negative numbers to represent depths under the surface of the sea. Mark is sitting on the deck of a ship above Eric , and Ariel is diving beneath Eric. Who could be at an elevation of -3 m?
Answer:
Ariel will be at an elevation of -3 m.
Step-by-step explanation:
There are three persons Eric, Mark and Ariel.
Location of these persons are,
Mark - Sitting at deck (Above the sea level)
Eric - swimming along the surface (At the sea level)
Ariel - diving beneath Eric (Below the sea level)
Since, all the distances above the sea level are measured with positive notation and below the sea level with negative.
Ariel will be at an elevation of -3 m.
Answer:
Ariel
Step-by-step explanation:
khan says so
(3x-8)(x + 2) = 2x2
1. -9n + 1 = -80
2. 144 = 144 = -12(m + 5)
3. -243 = -9(10 + r)
4. -10 = -10 + 7x
5. 4 - 7m = - 66
6. 2(y – 3) = −12
7. 16 = 2(1 + 7a)
8. 3 + 5r = −47
9. −10x + 6 = −74
With work please :) Please and ty
Answer:
1. n = 9
2. m = - 17
3. r = 17
4. x = 0
5. m = 10
6. y = -3
7. a = 1
8. r = -10
9. x = 8
Step-by-step explanation:
