Answer:
both have a domain and range of all real numbers
Step-by-step explanation:
a triangle has vertices at (-1,5), (4,2), and (0,0). What is the perimeter of the triangle
The perimeter of the triangle is 15.4 units.
Step-by-step explanation:
The triangle has vertices at (-1,5), (4,2), and (0,0).
To find the perimeter of the triangle, you need to find the distance of the three points which is the length of the three sides of the triangle.
Let us consider the points as A (-1,5) and B (4,2) and C (0,0).
The distance formula is given by :
⇒ [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
Distance of AB :
A (-1,5) ⇒ (x1,y1)
B (4,2) ⇒ (x2,y2)
⇒ [tex]\sqrt{(4+1)^{2}+(2-5)^{2} }[/tex]
⇒ [tex]\sqrt{5^{2}+-3^{2} }[/tex]
⇒ [tex]\sqrt{25+9}[/tex]
⇒ [tex]\sqrt{34}[/tex]
⇒ 5.8
∴ The length of the side AB of the triangle is 5.8 units.
Distance of BC :
B (4,2) ⇒ (x1,y1)
C (0,0) ⇒ (x2,y2)
⇒ [tex]\sqrt{(0-4)^{2}+(0-2)^{2} }[/tex]
⇒ [tex]\sqrt{16+4 }[/tex]
⇒ [tex]\sqrt{20}[/tex]
⇒ 4.5
∴ The length of the side BC of the triangle is 4.5 units.
Distance of CA :
C (0,0) ⇒ (x1,y1)
A (-1,5) ⇒ (x2,y2)
⇒ [tex]\sqrt{(-1-0)^{2}+(5-0)^{2} }[/tex]
⇒ [tex]\sqrt{1+25}[/tex]
⇒ [tex]\sqrt{26}[/tex]
⇒ 5.1
∴ The length of the side CA of the triangle is 5.1 units.
Now, the perimeter of the triangle is given by :
Perimeter = Sum of the lengths of all three sides of the triangle.
⇒ 5.8 + 4.5 + 5.1
⇒ 15.4 units.
∴ The perimeter of the triangle is 15.4 units.
4) The hospital and the fire department are 46 meters apart. From a window in the hospital,
the angle of elevation to the top of the fire department is 730. From the same window, the
angle of depression to the ground at the base of the fire department is 640. Find the height
of the fire department to the nearest tenth.
The height of the fire department is 244.72 m
Step-by-step explanation:
A)
Angle of elevation = 73°
The distance between the two buildings = 46 m
tan 73° = b/46
tan 73° = 3.27
tan 73° = b/46
3.27 = b/46
b = 3.27 x 46
b = 150.42 m
B)
Angel of depression= 64°
The distance between the two buildings = 46 m
tan 64° = a/46
tan 64° = 2.05
tan 64° a/46
2.05 = a/46
a = 2.05 x 46
a = 94.3 m
The total height of the fire department building = a + b
= 94.3 + 150.42
= 244.72 m
The height of the fire department is 244.72 m
Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.
Answer:
So when two lines intersect, it creates 4 angles. The angles that lie opposite to each other are congruent
If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.
Step-by-step explanation:
if Anna has one donut and her friend Priya gives her a dozen more how much does she have all together.
What do we do if the slope is a whole number ?
Answer: you convert it to a fraction
Step-by-step explanation: lets say the slope was 7 and you wanted to canovert it to a decimal
then you would make the denominator 1
so 7/1 which is equal to 7
hope this helps mark me brainliest if it helped
Rectangle QRST is shown. Angle QRT is congruent to angle STR, and angle STR is complementary to angle QTR. A rectangle has corner points Q, T, S, R from top left going clockwise. A line cuts through the rectangle from R to T. Which statement is true about angles QRT and QTR? They are congruent. They are complementary. They are supplementary. They are right angles.
Answer:
They are complementary.
Step-by-step explanation:
I made a small visual (mainly so I could visualize it but I figured it might help you too).
Since QRT is congruent to STR, QTR and SRT are also congruent.
Therefore, since STR is complementary to QTR, and STR is congruent to QRT, QTR must be complementary to QRT due to the transitive property.
The angles QRT and QTR are complementary (sum up to 90°)
What is an angle?An angle is formed from the intersection of two lines. Types of angles are acute, obtuse and right angled.
In triangle QRT:
∠QRT + ∠QTR + ∠TQR = 180° (angle in a triangle)
90 + ∠QRT + ∠QTR = 180
∠QRT + ∠QTR = 90°
The angles QRT and QTR are complementary (sum up to 90°)
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A six-sided number cube is labeled with the numbers 1-6, one number on each face. Each number is used exactly once. How
many possible outcomes exist when the cube is rolled two times?
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Save and Exit
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Mark this and return
Answer:
30 possible outcomes
Step-by-step explanation:
The total number of outcomes is found by multiplying the number of possiblities of each number cube together (6*6) which is 36. You now need to remove the double, which there are six of them. So subtract 6 from 36 to get 30.
if i multiply a number by 3 and then subtract 4, the result is the same as adding 6 to twice the number. Find this number
Final answer:
By setting up and solving the equation 3x - 4 = 2x + 6, we find that the number in question is 10. This process involves aligning the equation to solve for the variable x, representing the number we seek.
Explanation:
If we multiply a number by 3 and then subtract 4, the result is the same as adding 6 to twice the number. To find this number, we can set up an equation based on the given conditions.
Let's let the number be x. According to the first condition, multiplying x by 3 and then subtracting 4 can be represented as 3x - 4. According to the second condition, adding 6 to twice the number can be represented as 2x + 6.
The two expressions are equal, so our equation is 3x - 4 = 2x + 6.
Subtract 2x from both sides: x - 4 = 6.
Add 4 to both sides: x = 10.
Therefore, the number we are looking for is 10.
The diagram shows a regular pentagon with side length 5. Expiuleue
area of this pentagon by following these steps.
✓ 1. Press Continue to partition the pentagon into five congruent
triangles.
✓ 2. Press Continue to draw an apothem with length a.
3. Based on the variables on the diagram, how can the area of the
shaded triangle be determined?
Area =
Answer: (1.) 1/2sa
(2.) 5
(3.) Perimeter
Step-by-step explanation: just completed
solve the following: 2x-7/4=x+3/3
Answer:
[tex]x=16\frac{1}{2}=16.5[/tex]
Step-by-step explanation:
[tex]\frac{2x-7}{4}=\frac{x+3}{3}\\ \\3(2x-7)=4(x+3)\\\\6x-21=4x+12\\\\6x-4x=12+21\\\\2x=33\\\\x=33/2\\\\x=16\frac{1}{2}[/tex]
Which pyramid has a volume of 64 cubic inches?
A. Neither
B. 1
C. Both
D. 2
answer this question on the following page below
The coordinate plane shows dig sites for archaeological research. Each unit on the grid represents 1 square foot. What is the distance from Site A to Site C?
Answer:
25
Step-by-step explanation:
The distance between the two points A and C is 25 units.
What is coordinate geometry?A coordinate plane is a 2D plane created by the junction of the x-axis and y-axis, two perpendicular lines. A coordinate system in geometry is a way to use one or more integers or coordinates to determine the positions of the points.
Given points are (5, 20) and (25,5). The distance between the points will be calculated as below:-
D = √ [ ( y₂ - y₁ )² + ( x₂ - x₁ )² ]
D = √ [ ( 25 - 5 )² + ( 20 - 5)² ]
D = √ ( 400 + 225 )
D = 25 units
Therefore, the distance between points A and C is 25 units.
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The graph of y = x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
A) y=-2^3
B) y=-6x^3
C) y=2x^3
D) y=6x^3
Answer:
b
Step-by-step explanation:
Option B is correct. Equation B represents the transformed function. The following equation is observed from the graphs.
What is a function, exactly?It's a unique kind of connection with a predetermined domain and range, and every value in the domain is associated to exactly one value in the range, according to the function.
The given equation is,y=x³
The equation B represents the transformed function.
Hence, option B is correct.
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What is the value log5 25?
Answer:
2
Step-by-step explanation:
You can think of logarithms as a rewritten exponent.
So exponents are in the form of a^b=c
Logarithms are [tex]log_a c=b[/tex]
Here, we have [tex]log_{5} 25[/tex]
Basically we have to figure out 5 to the power of what is 25.
So our answer is 2.
5^2=25
The value of log5 25 is 2, as 5 to the power of 2 equals 25.
The value of log₅ 25 is determined by asking the question: 'to what power do we need to raise 5 to get 25"
Since 5 squared is 25 (5² = 25).
The power of 5 is 2.
Therefore, log₅ 25 = 2
Pedro uses a coordinate system to map the locations of some tourist locations in a large city. Each grid unit represents 1 mile. Pedro wants to walk from the historic village to the science center. Then he will walk from the science center to the muesem. If he walks at speed of 2 7/10 miles per hour, how long will it take him. PLEASE ANSWER FAST
Answer:
5 hours
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
Given that:
Each grid unit represents 1 mile Pedro's routes are: historic village => the science center => the museum Speed of 2 7/10 = [tex]\frac{27}{10}[/tex] miles per hourand the given coordinates are:
historic village (-4 1/2, 5 1/4) = (-4.5, 5.25)
science center (-4 1/2, -1 3/4) = (-4.5, -1.75)
the museum (2, -1 3/4) = (2, -1.75)
=> The distance from historic village to the science center :
=[tex]\sqrt{(-4.5 -(-4.5))^{2} + (-1.75 - 5.25)^{2} }[/tex] = 7
=> The distance from the science center to the museum:
= [tex]\sqrt{(2 -(-4.5))^{2} + (-1.75 - (-1.75))^{2} }[/tex] = 6.5
=> the total distance he travel is: 7 + 6.5 = 13.5 miles
The hours he traveled is: 13.5 miles / [tex]\frac{27}{10}[/tex] miles per hour
= 5 hours
A pair of pants costs twice as much as a shirt. The total cost of 1 pair of pants and 1
shirt is $18. If s represents the cost of 1 shirt, which equation could you use to find the
cost of 1 shirt?
Answer:
The equation, or more accurately, the system of equations we can use is:
x + y = 18
2x = y
Step-by-step explanation:
Consider that the cost of the shirt was x.
Consider the cost of the pants to be y.
Then, you can say that 2x = y since twice the cost of the shirt would give you the cost of the pants which are represented by y.
The next piece of information can be used to form the equation x + y = 18 since the cost of a pair of pants and a shirt are, in total, $18.
We can use a system of equations to answer this.
2x = y
x + y = 18
Since y = 2x, use substitution.
x + 2x = 18
3x = 18 (Divide both sides by 3)
x = 6
x represents the cost of the shirt and thus, the shirt costs $6.
The equation, or more accurately, the system of equations we can use is:
x + y = 18
2x = y
Answer:
2s+1s = 18
3s = 18
Since the question asks for the equation
Step-by-step explanation:
Let s = cost of 1 shirt
Pants cost twice the price of 1 shirt
p = 2s
We are buying 1 pair of pants and 1 shirt for 18 dollars
2s+1s = 18
Combining like terms
3s = 18
Either equation can be used to solve
We can divide by 3 to solve for the cost of 1 shirt
3s/3 = 18/3
s = 6
What is the slope of the line on the graph below?
On a coordinate plane, a line goes through points (0, negative 5), (3, negative 4), and (6, negative 3).
Answer:
i think the answer is 1/3 but i'm not positive
Step-by-step explanation:
The slope of a linear line which is passing through the lines (0,-5), (3, -4) , (6,3) is 1/3. The slope of a straight line is the ratio of y values of two points to the difference in x values of the two points.
What is slope ?In mathematics, slope of a line describes the steepness or inclination and the direction of the line. Slope of a line is calculated based on the characteristic of the line.
For straight line passing through some points, the x and y coordinates are related by the following expression:
y = mx +c
Where c is the intercept m be the slope.
For a line passing through two points, the slope m is :
m = y2 - y1 / (x2- x1)
Consider the line passing through the points (0, -5) and (3, -4). The slope m = -4 - (-5) / (3 - 0) = 1/3
Similarly if we consider the points (3, -4) and (6, -3) we get the same slope 1/3.
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What is the measure of QS?
84°
The measurement of arc QS is 168 degree.
Now, Let the center of the given circle is O .
And central angle is double of the angle subtended by the arc.
So central angle is twice of 84 degree.
Hence, the measure of QS is,
= 2 x 84
= 168 degree
So, the central angle is of measurement 168 degree.
Therefore, The measurement of arc QS is 168 degree.
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somebody pls answer this for me i will give you the brainliest
The total area of the parallelogram is 20 square inches
Calculating the area of the parallelogramFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
The total area of the parallelogram is calculated using
Area = Base * Height
Measuring the side lengths of the parallelogram, we have
Base = 4 inches
Height = 5 inches
Using the area formula , we have the following:
Area = 4 inches * 5 inches
Evaluate
Area = 20 square inches
Hence. the total area of the figure is 20 square inches
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Hey y’all please help me with this
Answer:
-12
Step-by-step explanation:
I try to think of it as how many steps would I need to get to zero
-12 would take 12 steps to get to 0
7 would take 7 steps to get to 0
-9 would take 9 steps to get to 0
1 would take 1 step to get to 0
-12 would take the most steps to get to 0 so it is the farthest from 0 on the number line
An observer at the top of a skyscraper sees a car on the road below. The angle of depression to the car is 29°. If the car is about 62 m from the skyscraper when it is seen, how tall is the skyscraper?
The height of the skyscraper is 34.4m
Step-by-step explanation:
Let the height of the skyscraper be 'h'
Distance between the skyscraper and the car = 62 m
Angle of depression = 29°
Angle = 61°
tan 61° = 62/h
1.80 = 62/h
h = 62/1.80
h = 34.4m
The height of the skyscraper is 34.4m
Which value of x makes the following equation true?
3(x - 4) - 12 = 2(x - 6) + 5
Answer:
x = 17
Step-by-step explanation:
3(x - 4) - 12 = 2(x - 6) + 5
3x - 12 - 12 = 2x - 12 + 5
3x - 24 = 2x - 7
3x - 2x = -7 + 24
x = 17
Answer:
x=17
Step-by-step explanation:
3(x - 4) - 12 = 2(x - 6) + 5
Distribute
3x -12 -12 =2x-12 +5
Combine like terms
3x-24 = 2x -7
Subtract 2x from each side
3x-2x -24 =2x-2x-7
x-24 = -7
Add 24 from each side
x-24+24 = -7+24
x = 17
what is 7 + 7 + 7 +7 +7 = ???
Answer:
35
Step-by-step explanation:
There are 5 sevens. All you have to do is multiply 7 and 5 and you will get 35.
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The difference of 3 times a number and 15 is no less than the square of the number.
Select the inequality that represents this relationship.
P
Answer:
d
Step-by-step explanation:
35% off $85.98. I'm having trouble with this.
Answer:
$55.89
Step-by-step explanation:
To figure out the discounted price, you multiply the original price (85.98) by the percentage, (35% = .35) Then subtract that number, (30.093) from the original price to find the discounted price.
Answer:
$24.56
Step-by-step explanation:
85.98 / 35 = 2.456
2.456 x 10 = 24.56
In circle C major arc ADB is represented by 4x + 50
a) type the equation needed to solve for x
B) what is the value of x in the diagram
Please help!
Answer:
x = 50
Step-by-step explanation:
[tex] m\angle ACB = m\overset {\frown} {AB} \\
\therefore m\angle ACB = 110°\\
\therefore m (reflex\angle ACB) = 360°- 110°\\
\therefore m (reflex\angle ACB) = 250°\\
Now \\
m\overset {\frown} {ADB}= m (reflex\angle ACB) \\
\therefore (4x + 50)°= 250°\\
\purple {\boxed {\bold {\therefore 4x + 50= 250}}} \\
(which\: is \: required\: equation) \\
\therefore 4x = 250-50\\
\therefore 4x = 200\\
\therefore x = \frac{200}{4}\\
\huge \red {\boxed {\therefore x = 50}} \\[/tex]
A) The equation needed to solve for x is [tex]4x + 50 = 250[/tex]. B) The value of x in the diagram is 50.
To solve the problem, we need to understand the relationships between the different parts of the circle and the given information.
Given:
[tex]\( \text{Measure of major arc ADB} = 4x + 50 \)[/tex]
[tex]\( \text{Measure of minor arc AB} = 110^\circ \)[/tex]
The total degrees in a circle = [tex]\( 360^\circ \)[/tex]
A) Type the equation needed to solve for x:
Since the sum of the measures of the minor arc AB and the major arc ADB must equal [tex]\( 360^\circ \)[/tex]:
[tex]\[\text{Measure of minor arc AB} + \text{Measure of major arc ADB} = 360^\circ\][/tex]
[tex]\[110^\circ + (4x + 50) = 360^\circ\][/tex]
[tex]4x + 50 = 250[/tex]
B) Solve for x:
First, set up the equation:
[tex]\[110 + 4x + 50 = 360\][/tex]
Combine the constant terms on the left side:
[tex]\[160 + 4x = 360\][/tex]
[tex]\[4x = 200\][/tex]
Divide both sides by 4:
[tex]\[x = 50\][/tex]
The complete question is:
In circle C major arc ADB is represented by 4x + 50.
A) Type the equation needed to solve for x.
B) What is the value of x in the diagram?
*2.6-(5.85)
Evaluate It
Answer: -3.25
Step-by-step explanation:
2.6-(5.85)
remove parentheses
2.6-5.85
answer: -3.25
Evaluate the expression when x=-6.
x² + 5x-5
Answer:
1
Step-by-step explanation:
x² + 5x-5
Let x = -6
(-6)^2 + 5(-6) -5
36 -30 -5
6-5
1
To evaluate the expression x² + 5x - 5 for x=-6, substitute -6 into the expression and follow the order of operations to obtain a result of 1.
Substitute -6 for x in the expression, which gives us (-6)² + 5(-6) - 5.Calculate the square of -6, which is 36.Multiply 5 by -6, which is -30.Add these results and subtract 5: 36 - 30 - 5 = 1.Therefore, the value of the expression when x = -6 is 1.
Which sentence illustrates the Inverse Property for Multiplication?
A. 6 + (-6) = 0
B. 1/6 x 6 = 1
C. 1 x 6 = 6
D. 1 x 6 = 6 x 1
Answer:
the answer is .143728353
Step-by-step explanation:
answer