The function f(x) is represented by the graph attached below. The domain of the graph is given by [-5,5] or {x | -5 ≤ x ≤ 5 ,x ∈ R} .
A function's domain in mathematics is the set of potential inputs that it can take. It can also be written as b, where f is the function.
Formally speaking, X is the domain of f given a function. It is important to note that, in terms of contemporary mathematics, a function's domain is a part of its definition rather than a property.
The function f can be graphed in the Cartesian coordinate system in the uncommon case where X and Y are both subsets of. In this instance, the function's graph, which is projected onto the graph's x-axis, serves as a representation of the domain.
A real function, f, may not be defined for all possible values of the variable if it is specified in a formula. The natural domain, also known as the domain de definition of f, is the set of real numbers to which the formula in this case can be evaluated to either a real number. It is common to refer to a partial function as just a function and its natural domain as just a domain.
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What are the examples of ASA congruence?
Example 1: For Δ ABC, show that AB = AC and Δ ABC is isosceles if the bisector AD of ∠ A is perpendicular to side BC. Also, this condition satisfies the properties of the isosceles triangles.
thus, Δ ABC is an isosceles triangle.
Example 2: Prove that △ACF≅△AEB, if ∠C=∠E and AC=AE.
Please help! Need this by tonight thanks! Question 7 Click on picture
Answer:
Oh god, I don't really know much about this, but I am going to assume that the 25 represents the mn so maybe you have to put 25mn + 6600 on the first box?
Step-by-step explanation:
I just looked up how to do this. I think the form has to be a C=mn+b format. For the third box, I think you need to solve 54100=25mn+6600. On the second box I think you just need to solve C(3600)=25(3600)+6600. idrk
How do you isolate the variable by dividing each side by factors that don't contain the variable?
We isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
According to the question,
We have the following information:
Isolating a variable by dividing each side of the equation in which one side does not contain any variable.
Now, in this case, it is clearly stated that the first step to isolate the variable from the equation is to perform division.
Now, this can be done as follows in the given equation:
2x = 14
Now, the variable x can be isolated by dividing both sides of the equation by 2:
x = 14/2
x = 7
Hence, we isolate the variable in an equation by dividing both sides of the equation in which one side does not contain any variable.
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−8×(−10+(−7))
Evaluate the following expression.
Answer:
136
Step-by-step explanation:
solve the inside of the parentheses and you get -17, then multiply by -8
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A person standing close to the edge on top of a 40-foot building throws a ball vertically upward. The quadratic function h = − 16t^2 + 72t + 40 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? _____________ feet
b) How many seconds does it take until the ball hits the ground? _____________ seconds
Answer:
a) 121 feet ; b) 5 seconds
Step-by-step explanation:
maximum height = y coordinare of vertex
x coordinate = -72/2 * -16
-72/-32 = 9/4 = 2.25
y coordinate =
-16(2.25)^2 + 72(2.25) + 40
-81 + 162 + 40
-81 + 202 = 121 feet
The ball hits the ground when y = 0
-16t^2 + 72t + 40 = 0
-2t^2 + 9t + 5 = 0
discriminant = 81 -4 (-2 * 5) = 81 -4(-10) = 81 + 40 = 121
We are searching only positive value
t = (-9 -11)/-4 = -20/-4 = 5 seconds
By rounding each number to the nearest 10, estimate the value of 197 ÷ 10.3
Answer:
20
Step-by-step explanation:
197 rounded to the nearest 10 is 200.
10.3 rounded to the nearest 10 is 10.
So, 200 ÷ 10 = 20
Answer:
20
Step-by-step explanation:
We are rounding to the nearest 10.
197≈200
10.3≈10
After you have rounded the numbers, The equation simplifies a whole bunch.
200/10=20
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Answer: Horizontal Translation
Step-by-step explanation:
In, a city had a population of 310,000 people. Each year since 2007, the population has grown by 4.8%.
Let t be the number of years since. Let y be the city's population.
Write an exponential function showing the relationship between t and y.
The exponential function showing the relationship between t and y is y = 310000(1.048)⁺
How to determine the exponential function?From the question, we have the following parameters that can be used in our computation:
Initial population = 310000
Rate of growth = 4.8%
These parameters can be represeted as
a = 310000 and r = 4.8%
An exponential function is represented as
y = a(1 + r)⁺
Substitute the known values in the above equation, so, we have the following representation
y = 310000 (1 + 4.8%)⁺
Evaluate
y = 310000(1.048)⁺
Hence, the function is y = 310000(1.048)⁺
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Which graph represents the solution set of the system of inequalities?
y ≤ 2x + 1
y>-21-3
Answer:
see below
Step-by-step explanation:
1. Notice that your inequalities have ≤ and >. So one of the lines on the graph must be dotted, eliminating the bottom two choices.
2. The lines on both of the top choices are graphed identically, so now it's all about shading. The best way to determine correct shading is by testing a point to see if it makes a true statement in BOTH inequalities.
a) Choose a point in the shaded region of the first option (I highly recommend (0,0)!!). Replace x and y in each inequality with the x and y from the point, and evaluate:
0 ≤ 2(0) + 1? ⇒ 0 ≤ 1 TRUE
0 > -2(0) - 3 ⇒ 0 > -3 TRUE
b) Since that point made both true statements, the first option is correct. If EITHER statement had been false, you would need to try a point in the shaded region of the second option. I recommend any where x=0 or y=0.
5x-1=3x+5 an equation
Answer:
[tex]x = 3[/tex]
Step-by-step explanation:
[tex]5x-1=3x+5[/tex]
Get the x's on one side.
Add 1:
[tex]5x-1=3x+5\\\box \ \ +1) \ \ (\ \ \ \ +1)[/tex]
[tex]5x=3x+6[/tex]
Subtract 3x from both sides.
[tex]\ \ \ 5x=\ \: 3x+6\\\underline{-3x} \ \ \ \ \underline{-3x}\\[/tex]
[tex]2x = 6[/tex]
Finally, divide both sides by 2.
[tex]2x / 2 = 6/2[/tex]
[tex]x = 3[/tex]
HURRY PLS!!
Kevin took $45 with him to spend on snack for himself and his friends at the movie theater. The price for each bucket of popcorn was $4. The price of each drink was half the price of a bucket of popcorn.
A. Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of buckets of popcorn and the other axis to represent the number of drinks.
Explain your graph.
B. Graph the absolute value function.
C. (a) Graph a linear function of your choice. On the same graph, graph a linear function transformed 2 units up and 3 units down.
(b) What was the equation of your linear function in slope-intercept form?
(c) What was the equation of the transformed function in slope-intercept form?
The equation of Kevin's scenario is 4x + 2y = 45
The absolute equation is y = 2|x - 3| + 5The equation of the linear function in slope-intercept form is y = 2x + 3The equation of the transformed function in slope-intercept form is y = 2x - 1How to determine Kevin's equationFrom the question, we have the following parameters
Amount = $45Bucket of popcorn = $4Bucket of each drink= Half the bucket of popcorn = $2Represent the buckets of popcorn with x and the number of drinks with y
So, we have the following equation
4x + 2y = total amount
This gives
4x + 2y = 45
See attachment for the graph
The graph of an absolute functionAn absolute function is represented as
y = a|x - h| + k
Where the vertex is (h, k)
So, we make use of the following function
y = 2|x - 3| + 5
See attachment 2 for the graph
The graph of a linear functionHere, we are to make use of any equation
A linear equation is represented as
y = mx + b
Where
slope = m
y-intercept = b
So, we make use of
m = 2 and b = 3
This gives
y = 2x + 3
When transformed 2 units up and 3 units down, the resulting equation is
y = 2x + 2 - 3
Evaluate
y = 2x - 1
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The braking distance y in feet that it takes a car to stop on wet, level pavement can be estimated by y=1/25x^2 , where x is the speed of the car in miles per hour. Find the speed associated with the braking distance of 196 feet.
in essence, find "x" when y = 196
[tex]y = \cfrac{1}{25}x^2\qquad \stackrel{\textit{when y = 196}}{196=\cfrac{1}{25}x^2}\implies (196)(25)=x^2 \\\\\\ \sqrt{(196)(25)}=x\implies {\Large \begin{array}{llll} \stackrel{\frac{m}{h}}{70}=x \end{array}}[/tex]
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
Two triangles are said to be congruent if their all corresponding sides are equal and all corresponding angles are equal in measure.
For the given question,
We know that the sum of all angles of a triangle is 180°.
For ΔABC,
∠A + ∠B + ∠C = 180°
42° + 53° + ∠C = 180°
95° + ∠C = 180
∠C = 85°
For ΔABC and ΔRQM,
∠A = ∠R
∠C = ∠Q
AB = RM
So, by the AAS postulate, ΔABC and ΔRQM are congruent triangles.
For ΔRQM,
∠R + ∠Q + ∠M = 180°
42° + 85° + ∠M = 180°
∠M = 53°
For ΔABC and ΔRQM,
∠A = ∠R
∠B = ∠M
AB = RM
So, by the ASA postulate, ΔABC and ΔRQM are congruent triangles.
Therefore, ΔABC and ΔRQM are congruent triangles. They are congruent by either ASA or AAS.
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The complete question is -
Are the triangles congruent Why or why not triangle congruence ASA and AAS?
A baseball player has 746 plate appearances in his first year, 727 plate appearances
in his second year, and 512 plate appearances in his third year. How many plate
has the player had in three years?
appearances
O 2,075
O 1,975
O 1,885
O 1,985
The player has a total plate of 1985 plate appearances (optionD)
What is addition?Addition is a way of combining things and counting them together as one large group. Addition is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum. For example if there a 5oranges, 6 bananas and 9 pineapple Ina basket. The total fruit in the basket is 5+6+9= 20 fruits
The baseball player has 746 plate appearances in his first year and 727 plate appearances in the second year and 512 in his third year.
The total plate appearances = 746+727+512=1985 plate appearances
Therefore the plate appearance the player had in three years is 1985 plate appearances.
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2. Claire is painting some windows that are all the same size. She used gallon of paint to paint 2 windows. How many gallons of paint are needed to paint 1 window?
Answer:3
Step-by-step explanation:
since 7 is a number and b is to u should just put 3 windows cause u need to add them all up i think, not sure but just do that, why not,
What is an equation of the line that passes through the points (-6,6) and (-3,1)?
Answer:
y=-[tex]\frac{5}{3}[/tex]x-4
Step-by-step explanation:
find the slope m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-6}{-3+6}[/tex]
m=-[tex]\frac{5}{3}[/tex]
Use the slope and one of the points to solve for the y-intercept
y1=mx1+b
6=-[tex]\frac{5}{3}[/tex](-6)+b
6=10+b
b=6-10
b=-4
plug the values for m and b into y=mx+b
y=-[tex]\frac{5}{3}[/tex]x-4
Answer:
y= -1.6x+12Step-by-step explanation:First find the slope.
m=y2-y1 / x2-x1
m= 1-6
-3-(-6)
m=-5
-3+6
m=-5
3
m= -1.6
y-y1=m(x-x1)
y-6= -1.6(x-(-6))
y-6= -1.6x+6
y=-1.6x+12Find the domain of the function.
f(x)= 3 x−2
Answer:
All real numbers
Step-by-step explanation:
What is the length of the radius of a circle given the equation x² y² 8?
The length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.
What is a circle?All points in a plane that are at a specific distance from a specific point, the center, form a circle.
In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
In the center of a circle, equal chords subtend equal angles.
The chord is divided in half by the radius drawn perpendicular to it.
So, the length of the radius of the circle is:
The formula for the circle's general equation is: (x - h)² + (y - k)² = r²
Where, the center is (h, k) and the radius is represented by r.
The equation we have: x² + y² = 8
Then, r² = 8
Taking square root as follows:
r = √8
r = √2*2*2
r = 2√2
Therefore, the length of the radius of the given circle with the equation x² + y² = 8 is 2√2 units.
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Correct question:
What is the radius of the circle whose equation is x² + y² = 8?
what is the solution a b to this system of linear equations 3a6b45 2a 2b 12
Solution of the system of linear equation 3a + 6b = 45 , 2a -2b = -12 is equal to a = 1 and b =7.
As given in the question,
System of linear equation are:
3a + 6b = 45 __( 1 )
2a - 2b = -12 __(2 )
Solution of the linear equation by elimination method is given by:
Multiply ( 2 ) by 3 and add it to (1) we get,
3a + 6b = 45
6a - 6b = -36
9a = 9
⇒ a = 1
Substitute the value of a = 1 in (1) we get,
3( 1 ) + 6b = 45
⇒ 6b = 42
⇒ b = 7
Therefore, the solution of the system of linear equation is a = 1 and
b =7.
The complete question is :
What is the solution (a, b) to this system of linear equations?
3a+6b = 45 , 2a-2b = -12
a. (-27, 6)
b. (-1, 7)
c. (1, 7)
d. (27, -6)
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if the probability of selecting the number is 3/10, the what could the question be?
The question can be:
"From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?"
The answer is that the probability is 3/2, as expected.
What could the question be?We want to find a question about probability, such that the answer is 3/10.
So we will have a set of 10 numbers, and 3 of them make a given event true, the probability of selecting one of these 3 numbers out of the whole set is:
P = 3/10
So, for example:
From the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
What is the probability of randomly selecting a multiple of 3?
There are 3 multiples of 3 on that set of 10 numbers, then the probability is P = 3/10.
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a rectange has the area of 60 in2. what can its dimentions be? copy and fill in the chart. length 1,2,10,30,120,3,_,5,_ width 60,_,_,_,_,_,5,_,100
PLS HELP FAST
The length and width of the rectangle can be 30 and 2 inches, 1 inches and 60 inches and 12 inches and 5 inches.
How to find the area of a rectangle?A rectangle is a quadrilateral with opposite sides equal to each other. Opposite sides of a rectangle is equal to each other.
A rectangle has the area of 60 in².
The dimension of the rectangle can be as follows:
area of a rectangle = lw
where
l = lengthw = widthTherefore,
60 = 30 × 2
60 = 1 × 60
60 = 12 × 5
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It snowed 40% more this year than it did last year. If it snowed 45 inches last year, how much did it snow this year?
Answer:
.4 times 45
That means it snowed 63 inches
Step-by-step explanation:
Answer:
-5 johu tella no for the best
Step-by-step explanation:
one sfeoo by and the offer and the nd.
Graph the line for y-6=-4(x+2) on the coordinate plane.
Answer:
x
Step-by-step explanation:
x
Answer:
Step-by-step explanation:
the answer is 8
A mathematical statement that ________ two quantities using <, >, =
Answer:
compares
Step-by-step explanation:
HELP ME QUICK PLEASE!!!!!
Which inequality is a true statement?
Select each correct answer.
-3>-1
-3 ≥ -1
-3=-1
-3≤-1
-3 <-1
Answer:
-3 <-1
-3 is less than -1.
write -1/2x + 4 = 10 in slope intercept form
Answer: y=-1/2x+4
Step-by-step explanation:
What is the double of 8 in math?
Using doubles plus one fact the sum of 8 + 8 + 1is equal to 17 it is done by simply adding 1 to the given number.
Doubles plus one fact is used to add numbers which are next to each other.
Doubles plus one fact is simply done by doubling the number and adding one to it.
The sum of 8 + 8 can be determined by using doubles plus one fact as:
Simply add 1 in 8 + 8 + 1 to get the result required.
8 + 8 + 1 = 17
Therefore by using doubles plus one fact the sum of 8 + 8 + 1 is equal to 17.
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Please help asap!!!!!!
A line is parallel to the line y = -x + 5 and passes through the point (4. - 1). Which of the following is an equation of the
line?
Answer:
y = -x + 3; could also be y + 1 = -(x - 4) or y = -(x - 4) - 1 or x + y = 3
Step-by-step explanation:
No options given, so I hope this helps.
1. Identify any of the equations that have the same slope as your given equation (-1). If there's only one, stop here.
2. Find the y-intercept by replacing (x,y)=(4,-1) in the equation y = -x + b and solve for b: -1 = -(4) + b ==> 3 = b
3. Replace b in the equation y = -x + b with 3.
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house. One- half of the comission goes to the broker, and one- half of the remainder to another salesperson. Stevenson receives the rest. Find the amount she receives.
Danielle Stevenson receives $2600.
What is a total amount?
A total is the sum of several numbers or the number of items in a group, as determined by addition or counting.
Here, we have
Danielle Stevenson receives a commission of 6.5% for selling a $160,000 house.
One-half of the commission goes to the broker and one-half of the remainder to another salesperson.
We have to find out how much amount she receives.
Danielle has a 6.5% × $160,000 = $10400
Then, Danielle half of $10400 to the broker so she remains $10400 × 1/2 = $5200
Now,
Danielle one-half of the $5200 to another salesperson. so she gets $5200 × 1/2 = $2600
Hence, Danielle Stevenson receives $2600.
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