Vertical angles or contrary angles are the statement that Terra's proof is still absent. The angles formed opposite to each other when two lines cross each other are equal.
The missing word in Terra's proof is described as :Terra describes the parallelogram nature of the diagram. Because they are vertical or opposite angles, these angles are equal.
The angles formed opposite to each other when two lines cross each other are equal. As a result, we have discovered that either vertical angles or opposite angles make up Terra's proof.
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Lock 4 (screen will be blank until you crack the code for lock #3) Awe-sum! You have reached the last lock. Use your equation solving skills to find the value of each variable. Use the values you calculate to help you move along in the puzzle and find all of the missing variables. When you have found all of the variables Imove to the next screen.
Problems:
4a +2= -10
a(2+ b) = -12
-5c+b= 22
7(c+d) = 14
d-c-e= 17
Answers:
a=
b=
c=
d=
e=
The values of the variables are:
a = -3
b = 2
c = -4
d = 6
e = -7
Given, the expressions are:
4a + 2 = -10
4a = -10-2
4a = -12
a = -3
substitute a value in the next expression.
a(2+b) = -12
-3(2+b) = -12
-6-3b = -12
-3b = -12+6
-3b = -6
b=6/3
b = 2
now substitute b value in the next expression.
-5c+b= 22
-5c+2 = 22
-5c = 22-2
-5c = 20
c = -20/5
c = -4
substitute c value in the next expression.
7(c+d) = 14
7(-4+d) = 14
-28+7d = 14
7d = 14+28
7d = 42
d=42/7
d=6
In the last expression substitute c and d values to find e.
d-c-e= 17
6-(-4)-e = 17
6+4-e = 17
10-e = 17
-e = 17-10
-e = 7
e = -7
hence we get the values of all the variables.
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someone pls help me w this. I rlly need this!! thank uu!
"write the equation of a line that is parallel to y=2x-3 and passes through the point (1, 6)"
What is the percentage efficiency of a motor that does 60J of work from 240J of electrical energy?
Answer:
25% is the correct answer
The slope of the graph
Answer:
5 x + 4 y = 4 b
Step-by-step explanation:
You haven't specified what form you need. Here is the Standard form, but you can also calculate the Slope intercept form points and the Point-Slope form.
Find the equation of the line in standard form with the properties:
slope: m = -5/4
At least two parameters must be provided to determine a line equation:
Since the line is incompletely determined, compute the equation assuming an arbitrary y-intercept b
Substitute the slope m = -5/4 into the slope-intercept equation y = m x + b:
y = -(5 x)/4 + b
Add (5 x)/4 to both sides:
(5 x)/4 + y = b
Multiply both sides by 4:
4 ((5 x)/4 + y) = 4 b
Distribute: 4 ((5 x)/4 + y) = 5 x + 4 y:
Answer: 5 x + 4 y = 4 b
6. A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle
(-1,3), (2, -1),(-1,-1)
(6, 0), (6, 7), (0,7)
(-1,-1), (-6, -13), (-9,-9)
(-3,-4), (3,-4), (3,4)
Answer:
Question:
A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A.) (-1,3),(2,-1),(-1,-1)
B.) (6,0),(6,7)(0,7)
C.) (-1,-1),(-6,-13),(-9,-9)
D.) (-3,-4),(3,-4),(3,4)
Triangle and Coordinate Geometry
As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.
So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always
180
∘
.
If a triangle
A
B
C
has the sides
a
,
b
,
and
c
, then
The perimeter of the triangle:
P
=
a
+
b
+
c
In coordinate geometry, the distance between two points:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Answer and Explanation:
Given:
The perimeter of the triangle is
24
units.
There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.
Firstly we chose the option
D
:
The vertices of the triangle are:
P
(
−
3
,
−
4
)
,
Q
(
3
,
−
4
)
,
and
R
(
3
,
4
)
Using the distance formula:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
So
P
Q
=
√
(
3
+
3
)
2
+
(
−
4
+
4
)
2
=
√
6
2
+
0
=
6
u
n
i
t
And
Q
R
=
√
(
3
−
3
)
2
+
(
4
+
4
)
2
=
√
0
+
8
2
=
8
u
n
i
t
And
P
R
=
√
(
3
+
3
)
2
+
(
4
+
4
)
2
=
√
6
2
+
8
2
=
√
36
+
64
=
√
100
=
10
u
n
i
t
So
The perimeter of the triangle
P
Q
R
is:
Perimeter
=
P
Q
+
Q
R
+
P
R
=
6
+
8
+
10
=
24
u
n
i
t
s
Step-by-step explanation:
Find m
A
2x
C
(3x - 10)
D
E
B
Answer:
∠ABC = 40
∠CBC = 50
Step-by-step explanation:
∠ABC + ∠CBD = 90
2x + (3x - 10) = 90
2x + 3x - 10 = 90
5x = 100
x = 20
∠ABC = 2x = 2(20) = 40
∠CBC = 3x - 10 = 3(20) - 10 = 50
4|2x + 5|-7≤9
How would you solve this?
Answer:
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
inequalities of the type | x | ≤ a , have solutions of the form
- a ≤ x ≤ a , then
4 | 2x + 5 | - 7 ≤ 9 ( add 7 to both sides )
4 | 2x + 5 | ≤ 16 ( divide both sides by 4 )
| 2x + 5 | ≤ 4 , so
- 4 ≤ 2x + 5 ≤ 4 ( subtract 5 from each interval )
- 9 ≤ 2x ≤ - 1 ( divide each interval by 2 )
- [tex]\frac{9}{2}[/tex] ≤ x ≤ - [tex]\frac{1}{2}[/tex]
if asked to evaluate the following expression (5x+25) for x=3,5,-5,0 how many different substitutions will you make?
we did 4 different substitutions to evaluate the expression in 4 different values of x.
when x = 3 we get 40when x = 5 we get 50when x = -5 we get 0when x = 0 we get 25.How to evaluate an expression?
Here we have a linear expression that depends on the variable x, and can be written as:
(5x + 25)
And we want to evaluate this in some different values of x. This just means that we need to replace the value of x by different numbers.
First, let's use x = 3
This will give:
(5*3 + 25) = 15 + 25 = 40
Then we use x = 5
(5*5 + 25) = 25 + 25 = 50
Then we use x = -5
(5*-5 + 25) = -25 + 25 =0
Finally, we evaluate in x = 0.
(5*0 + 25) = 0 + 25 = 25
So we did 4 different substitutions to evaluate the expression in 4 different values of x.
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how many time does 13 go into 26
Answer:
2
Step-by-step explanation:
13+13=26
Answer:
Twice
Step-by-step explanation:
13+13=26
Which liner function represents the line given by the point-slope equation y + 7 = -2/3(x + 6)?
the linear function that represents the given line is:
y = f(x) = (-2/3)*x - 11
Which linear function represents the given line?
Here we have a line given by a point-slope equation:
y + 7 = (-2/3)*(x + 6)
And we would want to get a function of the form y = f(x). So the first thing we need to do is isolate y in one side of the above equation. If we subtract 7 in both sides we will get:
y = (-2/3)*(x + 6) - 7
Expanding that:
y = (-2/3)*x + (-2/3)*6 - 7
y = -(2/3)*x - 4 - 7
y = (-2/3)*x - 11
Then the linear function that represents the given line is:
y = f(x) = (-2/3)*x - 11
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a janitor had 3/5 of a spray bottle of a cleaning solution . he used 1/9 of the soloution in a day. how much of the bottle did he use?
The Janitor used 8/15 of the bottle
How to calculate the amount of the solution of the bottle used ?
The Janitor has 3/5 of a spray bottle solution
He uses 1/9 of the solution in a day
The amount of solution used can be calculated as follows
3/5 × 1/9
= 3/45
= 1/15
The initial amount in the bottle is
3/5 - 1/15
= 8/15
Hence the amount of solution he has used is 8/15
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4. A regular pentagon has side lengths given below. Find the length of one side.
4q+1 = 11-q
r+s
s+t-1
3r
a) 9
b) 4
c) 3
d) 2
Answer:
d)2
Step-by-step explanation:
you would group-like terms and so
4q+q=11-1
5q=10(you would let q stand on it own)
so you divide through by 5
5q/5=10/5
q=2
Sue's science class is competing to see who can build the tallest tower. Each group of students gets 10 newspapers and 2 meters of tape. Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimeters of tape. How many meters of tape do they have left?
The amount of tape left in metres is 0.75 metres.
How to find the length of the tape left in metres?Each group of students gets 10 newspapers and 2 meters of tape.
This means the total length of tape for each group of student is as follows:
length of tape for each group = 2 metres
Sue's group decides to roll up each of their newspapers. Then, they tape each roll with 125 millimetres of tape.
Each roll of the 10 newspaper was taped with 125 mm tape.
Hence,
total taping = 125 × 10
total taping = 1250 mm
Let's convert from millimetres to metres.
Therefore,
1 mm = 0.001 m
1250 mm = ?
cross multiply
amount of taping done by Sue's group = 1.25 m
Therefore,
amount of meters of tape left = 2 - 1.25 = 0.75 metres
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Bob fenced in his backyard. the perimeter of the yard is 22 feet, and the length of his yard is 5 feet. use the perimeter formula to find the width of the rectangular yard in inches: p = 2l 2w. (1 foot = 12 inches)
The width of yard in inches is 72 inches.
We are given the perimeter and length of yard. We are also given the perimeter of the rectangle, which is as follows -
P = 2l 2w
Rewriting this formula in simplified form, by taking 2 common from both the values -
P = 2×(l + w), where P refers to perimeter, l refers to length and w refers to width.
Now, keep the values in formula to find the width of rectangle -
22 = 2 × (5 + w)
Shifting 2 to other side of equation and performing division
5 + w = 22÷2
5 + w = 11
Shifting 5 to other side of equation and performing subtraction to find the value of width
w = 11 - 5
w = 6 feet
Now, we need the width in inches. We are given -
1 foot = 12 inches
So, 6 feet = 12 × 6
6 feet = 72 inches
Hence, the width of rectangular yard is 72 inches.
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Answer:
72in
Step-by-step explanation:
perform the indicated operation and simplify the result leave yuour answer in factored form 4x/x2 - 1
The simplified result is :
[tex]4x/x^{2}[/tex] - 1
= 4/x -1
4-x / x.
Factored form, the product of a constant and two linear terms: or. The parameters and are the roots of the function (the x-intercepts of the graph). Converting a quadratic function to factored form is called factoring.
An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex.
In algebra, simplifying and factoring expressions are opposite processes. Simplifying an expression often means removing a pair of parentheses; factoring an expression often means applying them.
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94.
Scale: 1 in. = 3 ft
The diagram above shows a plan for a community garden. The plan is drawn on a grid made up of 1-inch squares. About how many square yards will be used to grow herbs?
Answer:
About 9 sq yd
Step-by-step explanation:
First, you know that 3ft. = 1 yd. That means each square is 1 sq yd. The length of the herb garden is 6 squares, while the width is about 1.5 squares. If you multiply those two to find the area, then you get about 9 square yards.
If a first integer is represented by the variable x, then which of the following would be the next four consecutive odd integers?
Choose the correct answer below.
A. x+1, x+2, x+3, x+4
B. x+2, x+4, x+6, x+8
Points: 0 of 1
C. x, x+2, x+4, x+6
OD. x+1, x+3, x+ 5, x+7
the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
We are given that:
The first integer is represented by the variable x.
We need to find the next four consecutive odd integers.
We know that the difference between the two consecutive odd integers will always be 2.
So, this means, we can always get the next odd integers by adding 2 to the previous one.
So, we get that:
x + 2
x + 2 + 2 = x + 4
x + 4 + 2 = x + 6
x + 6 + 2 = x + 8
Therefore, we get that, the next four consecutive odd integers will be given by the option (B) x + 2, x + 4, x + 6 and x + 8.
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The graph below shows the distance a helicopter traveled over time. Find the rate of change from 1 hour to 2 hours.
The rate of change from 1 hour to 2 hours will be 125 miles per hour. Option C is correct.
What is linear equation?
A relationship between two or more parameters that, shown on a graph, produces a linear model. The degree of the variable will be one.
Given that;
Two points on the graph are (1, 125) and (2, 250).
Now, The slope of the line is calculated as;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Hence, Slope of the line passes through the points (1, 125) and (2, 250).
m = (250 - 125) / (2 - 1)
m = 125
So, The rate of change from 1 hour to 2 hours will be 125 miles per hour.
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.
Nickels: Someone offers to double the amount of money you have every
day for 1 month (30 days). You have 1 nickel. On the first day, you will
have 2 nickels worth $.10. On the second day, you will have 4 nickels
worth $.20. How much money will you have on the 30th day?
Answer: you will have $53,687,091.2 dollars once you reach the thirty-day milestone.
Step-by-step explanation:
Multiply 0.05 by 2 thirty times to get your answer.
0.05 * 2^30
0.05 * 1,073,741,824 = $53,687,091.2 or 10,737,418.24 nickels.
a major disadvantage of correlations is that they cannot make a(n) blank statement. multiple choice question.
A major disadvantage of correlations is that they cannot make a cause-and-effect statement.
What are correlations?Correlations are statistical measures that describe the size and direction of a relationship between variables.
Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.
The disadvantages of correlations include:
There are no causes and effects.Results can find no inference.The strength of the relationship is not explained.There is the possibility of a confounding factor.Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.
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does the ratio 2/5 to 1/3 has a unit rate of 2/15
The statement that the ratio 2/5 to 1/3 has a unit rate of 2/15 is; True
How to find the unit rate?
A unit rate is defined as a rate for one of something. This can be written as a ratio with a denominator of one.
For example, if you ran 50 meters in 10 seconds, you ran an average 5 meters in 1 second. Both of the ratios, 50 meters in 10 seconds and 5 meters in 1 second, are rates, but the 5 meters in 1 second is a unit rate.
We are given the ratio 2/5 to 1/3. Now, this can be expressed as;
(2/5)/(1/3) = 2/5 * 1/3 = 2/15
Thus, this corresponds with the given unit rate of 2/15.
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f(x) = -2x + 10, If f(x)= 40, what is the value of x? (find the input)
Answer:
-15
Step-by-step explanation:
set it up
f(40)=-2x+10
40=-2x+10
subtract ten
30=-2x
divide by -2 to isolate the x
-15=x
Answer:
f(x) = -2x + 10
If f(x)= 40
By using equation,
or, 40=-2x+10
or, 40-10=-2x
or, 30=-2x
or, 30/-2=x
Therefore x=-15
This list gives information about a video collection.
Study the list carefully. Then, use the drop-down menu to complete the statement
below about the list.
It
make sense to add the items on the inventory because these quantities
have meaning for the inventory.
The number 299
Romance:
74
Comedy: 123
Action: 102
Total: 299
CLEAR
be expressed using the same unit.
CHECK
Answer:
oh no I lost the Answer is was 18369
Answer:
Step-by-step explanation:
Find the slope of the line through the
points (16,7) and (−14, 3).
Answer:
2/15
Step-by-step explanation:
Slope: m=(y2-y1)/(x2-x1)
m = (3 - 7)/(-14 - 16) = (-4)/(-30) = 4/30 = 2/15
Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip.
How much did they get altogether?
Answer:
Let Pip get = x
Fiona gets = x + 35
Ratio = 6:1
x+35/x = 6
x + 35 = 6x
5x = 35
x = 7
Total money = x + x + 35 = 14+ 35 = £49
Answer:
£49
Step-by-step explanation:
Fiona gets 35 more than Pip so 6-1 =5 and 5 portions = 35
so 1 portion = 7
7x6 = 42
7x1 =7
7+42 = 49
so they got £49
hope this works :)
there are 50 solidiers in a military camp. food provision for them is for 12 days, how long will their provision last if 10 more soldiers to win the camp (direct and inverse proportion)
Answer:
10 days
Step-by-step explanation:
60/50×12 give u the number of days it will last them
Solve for x in the diagram below
The value of x will be 34°
Given that
(x+12)°+100°+x° are forming linear pair
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.
(x+12)°+100°+x°= 180°
⇒ x+ 12+ 100+x = 180°
⇒ 2x+112 = 180°
⇒ 2x = 180- 112
⇒ 2x = 68
⇒ x= 68/2
⇒ x= 34
For verification we will put value of x
(34+12)°+100°+34°
⇒ 46°+100°+34°
⇒146°+34°
⇒ 180°
So here we can see that by putting value of x we are getting the sum of 180°
Therefore value of x is 34
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Brian is throwing a party. He needs 3/4 of a pound of hamburger meat for each person at the party. If 12 people are coming to the party, how many pounds of hamburger meat will Brian need to buy?
9 pounds of hamburger meat will be needed by Brian.
We are given value for one unit. The calculation is required for more than one units, hence, multiplication will be performed.
As per the given information, amount of hamburger meat required for one person is = 3/4 pound
Amount of hamburger meat required for 12 people = (3/4) × 12
Performing division to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 3 × 3
Performing multiplication to find the amount of hamburger meat required for 12 people
Amount of hamburger meat required for 12 people = 9 pounds
Therefore, Brain needs to buy 9 pounds of hamburger meat.
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Factor completely.
100-9x^2=
please help!!
Answer:
(10 + 3x) (10 - 3x)
Hope this helps!
Chelsea and nine of her friends went out to eat. They decided to split the bill evenly. Each person paid $21.00. What equation would depict this scenario
Answer:
21(10)
Step-by-step explanation:
youll have to do 21 times 10
Answer:
[tex]\frac{210.00}{10}[/tex] = x
Step-by-step explanation:
[tex]\frac{210.00}{10}[/tex] = x
Let x is the number that each person needs to pay.