Answer:
Explanation:
Given the function, g(x) below:
[tex]g(x)=2(3^x)[/tex]We evaluate g(x) for x=1,2 and 3:
[tex]\begin{gathered} g(1)=2(3^1)=6 \\ g(2)=2(3^2)=18 \\ g(3)=2(3^3)=54 \end{gathered}[/tex]We see that whenever x increases by 1, the value of g(x) triples.
Triangle XYZ is shown on the coordinate grid. The coordinates of each vertex of the triangle are integers.
What is the slope of XZ ?
The slope of line segment XZ in triangle XYZ is: -1/3.
What is the Slope of a Line Segment?Given a line segment on a coordinate plane, we can find the slope of the line by using two points on the line to find the ratio of change in y / change in x = (y2 - y1)/(x2 - x1).
The coordinates of the two points of line segment XZ in triangle XYZ are:
X(1, 5) = (x1, y1)Z(7, 3) = (x2, y2)Plug the values into the formula used for finding the slope of a line:
Slope of line segment XZ = change in y / change in x = (5 - 3)/(1 - 7)
Slope of line segment XZ = 2/-6
Slope of line segment XZ = -1/3
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The Sugar Sweet Company delivers sugar to its customers. Let C be the total cost to transport the sugar (in dollars). Let S be the amount of sugar transported (in tons). The company can transport up to 30 tons of sugar. Suppose that =C+120S+3500 gives C as a function of S.
Identify the correct description of the values in both the domain and range of the function. Then, for each, choose the most appropriate set of values.
1. What is domain? (amount of sugar transported (in tons), cost to transport sugar (in dollars)
2 .What is range? (amount of sugar transported (in tons), cost to transport sugar (in dollars)
3. What is set of values of domain?
4. What is set of values of range?
The potential input and output values of a function are its domain and range respectively as ( 3500 , ∞)
It is specified as follows
the region
This is a list of the function's potential S values
Due to the fact that S refers to a physical quantity, it cannot be less than 0. (i.e. tons of sugar)
Any number greater than zero may be used as S's value.
Thus, the following is the function's domain:
The variety
This represents the function's potential C values.
It is specified as follows:
When S = 0
C = 120 x 0 + 3500 = 3500
The preceding implies that:
C must be more than 3500.
Any number higher than 3500 can be used as the value of C.
Thus, the function's range is as follows: (3500 , ∞ )
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To order tickets online to a hockey game,
there is a processing fee plus the
cost per ticket. The cost for 5 tickets is $174.45. The cost for 8 tickets is
$271.95. Write and solve a linear equation to find the total cost to order 12 tickets.
Answer: The total cost to order 12 tickets is $378.05
Step-by-step explanation:
Let y represent the cost for x number of tickets.
Since the cost for 5 tickets is $174.45, it can be represented by the point (5, 174.45).
The cost for 8 tickets is $271.95, it can be represented by the point (8, 271.95).
y = 32.5x - 11.95
The cost for 12 tickets is:
y=32.5(12) - 11.95 = 378.05
Hence the total cost to order 12 tickets is $378.05
Kylie was out at a restaurant for dinner when the bill came. to find the total plus tip, she multiplied the cost of the meal by 1.2. what percent tip did she leave?
The percentage of tip that Kylie left is 20%
Finding percentage:
To find the percentage of the number in a given whole number divide the number by the whole number and multiply by 100. To find the percentage of the tip we will calculate the percentage of tips in the total cost.
Here we have,
To find the total plus tip, Kylie multiplied the cost of the meal by 1.2
Let $ x be the cost of the meal
Then total cost plus including tip = x × 1.2 = 1.2x
From the above calculations,
The amount of tip paid by Kylie = 1.2x - x = 0.2x
There percentage of tip = (0.2x)/x × (100) = 20%
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10 800 seconds expressed in hours is?
Answer: 3 hours
Step-by-step explanation:
10,800 seconds divided by 60 would make it 180 minutes. Divide 180 by 60 (to get hours), and you get 3. So the answer is 3 hours.
What is the distance from John’s house to Peter’s house?
Please answer number 4
The distance between the peter's house and John's house is found as √116 units.
What is termed as the mid point?The coordinate plane is indeed the standard graphing grid, with the x-axis horizontal as well as the y-axis vertical. The axes meet at (0,0), which is recognised as the origin.The coordinate point at the center of the distance line connecting two points is the midpoint. As a result, the midpoint formula is just the average of the x- and y-coordinates.For the given question;
Let the coordinates of the John's house be (x₁, y₁).
Let the coordinates of Paul's house M be (x, y) = ( 3, -5).
Let the coordinates of Peter's house be (x₂, y₂) = (5, -4).
Then, by the formula of mid point.
x = (x₁ + x₂)/2
Put the values and simplifying.
x₁ = (2×3) - 5
x₁ = 1
Similarly for the y coordinates.
y = (y₁ + y₂)/2
Put the values and simplifying.
y₁ = (2×-5) - 4
y₁ = -14
Thus, the coordinates of the John's house is found as (1, -14).
Now, the distance between peter's house and john's house is;
d = √(x₁ - x₂)² + (y₁ - y₂)²
Put the values;
d = √(5-1)² + (-4+14)²
d = √(4)² + (10)²
On simplification,
d = √116 units.
Thus, the distance between the peter's house and John's house is found as √116 units.
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The range
feet
4. A penny is dropped from the top of the Statue of Liberty, which is 305 feet tall. The height of the
penny, h, at time t seconds can be represented by the equation h(t) = -16t² + 305. After 4 seconds,
how much further does the penny need to travel before it hits the ground?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Explain about equation?Expressions that add up to one another make form an equation. A formula is an equation containing two or more variables that shows how the variables relate to one another. A line with the equation y=mx+b, where m denotes the slope and b the y-intercept, is an example of a linear equation.
Given that we've done it
h(t)=-16t²+305
Here, h stands for the penny's height.
The time is expressed as t in seconds.
Now, t equals 4 seconds.
The distance the penny must travel before it touches the earth is explained by
h(4)=- 16(4)² + 305
h(4)=- 16 x 16+ 305
h(4)= 256 - + 305
h(4)= 49 feet
Hence, penny need to travel 49 feet before it hits the ground
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Point U is on the line segment TV given TU = 4 UV =5x and TV =3x+6
I need help
Solving a linear equation that comes from the relation:
TV = TU + UV
We will see that the value of x is 1.
How to find the value of x?I'm answering the question you wrote.
We know that point U is on the line segment TV, then we can write:
TV = TU + UV
This says that the total length of TV is equal to the sum of the two segments in it.
It says:
"the length of segment TV is equal to the sum between the lengths of segments TU and UV"
Here we know that:
TU = 4
UV = 5x
TV = 3x + 6
Then we can write the linear equation:
3x + 6 = 4 + 5x
And solve this for x.
3x + 6 = 4 + 5x
6 - 4 = 5x - 3x
2 = 2x
2/2 = x
1 = x
The value of x is 1.
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Hamid has gained weight
He now weighs 88kg,which is 10% higher than his normal weight.
What is his normal weight?
You can get the answer by reciprocating the multiplying factor of 10%
88*10/11
= 80 kg
Therefore, Hamid's original weight was 80 kgs
A container is shaped like a cylinder and has a volume of 125.7 cm³. If
the height of the container is 10 cm, what is the radius of the container?
The radius of the cylindrical container with a volume and height of 125.7cm³ and 10cm is 2cm.
What is the radius of the cylindrical container?The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Volume of the cylinder V = 125.7cm³Height of the cylinder h = 10cmRadius of the cylinder r = ?To determine the radius of the cylindrical container, plug the given values into the formula above and solve for r.
V = π × r² × h
r² = V / ( π × h )
r² = 125.7cm³ / ( 3.14 × 10cm )
r² = 125.7cm³ / ( 31.4cm )
r = √( 125.7/31.4 cm² )
r = 2cm
Therefore, the radius of the container is 2 centimeters.
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maths helppppppppppp
Answer:
Acute
Step-by-step explanation:
Answer:
It is Acute.
Step-by-step explanation:
To be right triangle it has to be all perfect sides same length, to be obtuse has to be wider to the sides but this one is acute because it goes inside.
Evaluate 2a +7-8a-14+5a
Answer: -a-7
Step-by-step explanation:
Answer:
−a −7
Step-by-step explanation:
group the 'a's. 2a-8a+5a. It is -a. Next, group the numbers and simplify them. 7-14. It is equal to -7. If you put -a and -7 together, you get "-a-7" as an answer.
please help, ive been stuck on this for a while
Answer: A≈1922.46
Step-by-step explanation: A=6a^2=6·17.92≈1922.46
Rectangle A is a scaled version of rectangle B. The dimensions of rectangle B are twice the dimensions of rectangle A. The area of rectangle B is 512 sq cm. What is the area of rectangle A?
A. 256 sq cm
B. 192 sq cm
C. 128 sq cm
D. 64 sq cm
The area of rectangle A is (A) 256 cm².
What are Rectangles?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.So, the area of rectangle A:
The dimensions of rectangle B are twice the dimensions of rectangle A.So, rectangle A = 1/2 Rectangle BRectangle A = 512/2 = 256 cm²Therefore, the area of rectangle A is (A) 256 cm².
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Answer:
128 cm^2
Step-by-step explanation:
The area of rectangle B is 512 cm2. Since the dimensions of rectangle B are two times larger than the dimensions of rectangle A, the scale factor is 2.
To find the area of rectangle A, first square the scale factor, 2.
2^2 = 4
Next, divide the area of rectangle B by 4.
512 cm^2 ÷ 4 = 128 cm^2
The regression equation y=3.610*1.194^x approximates the cost to go on a safari, y,given the number of years since it opened in 2005, X.What is the best estimate of the cost to go on a safari in 2,022 ? Round your answerto the nearest dollar.
Step 1:
Write the regression line equation.
[tex]y\text{ = 3.610 }\times1.194^x[/tex]Step 2:
y represents the cost and x represent the number of years.
From 2005 till 2022
x = 17 years
Step 3:
Let find the cost to go on a safari in 2022.
[tex]\begin{gathered} y\text{ = 3.610 }\times1.194^x \\ \text{Substitute x = 17} \\ y\text{ = 3.610 }\times1.194^{17} \\ y\text{ = 3.610 }\times\text{ 20.37387116} \\ y\text{ = 73.54967489} \\ y\text{ = \$74} \end{gathered}[/tex]Final answer
The cost to go on a safari in 2022 = $74
HELP!!!
Graph y=1/2x- 3
Answer: See the graph I attached below.
Step-by-step explanation: Remember to use the slope-intercept form of the equation:
y = mx+b
m = slope
b = y-intercept
Therefore, y=1/2x-3 has a slope of 1/2 and intercepts the y-axis at -3
there may be more then one answer
will give brainlest
Answer:
6(4u+3u)
Step-by-step explanation:
4u+3u= 7u
you add the 4u and the 3u because they're inside the parentheses
and then you get 6(7u)
Alyssa rode her bicycle 14.2 miles in 0.8 hours. What is the number of miles she rode per hour?
Answer:
17.75
Step-by-step explanation:
.
Parcel A is heavier than parcel B by
2.5 kg. Parcel C is lighter than parcel
B by 4.86 kg. How heavy is parcel A if
parcel C is 6.2 kg?
Answer: 13.56 kg
Step-by-step explanation:
We can make two equations:
1) A = B + 2.5
2) C = B - 4.86
Replace C with 6.2.
(6.2) = B - 4.86 can be rewritten as 6.2 + 4.86 = B.
B = 11.06
Add 2.5 to 11.06 and you get 13.56 kg.
a number divided by 3 decreased by 2 is at most 2
"A number divided by 3 decreased by 2 is at most" in equation form is 2y/3 -2 ≤ 2
How to convert word problems to equations?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Given that: a number divided by 3 decreased by 2 is at most 2
We need to translate the word into an equation:
First, we will assign a letter to the said number. So let the number be y
The number divided by 3: y/3
Then decreased by 2: y/3 -2
And everything is at most 2 (it is less than or equal to 2): y/3 -2 ≤ 2
Therefore, the given word problem can be written as y/3 -2 ≤ 2
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Triangle ABC and triangle DEF are similar. What is the measure of side DF?
2 right triangles. First has points A, B, C. Distance from A to C is 9 centimeters. Distance from B to C is 15 centimeters. Second has points D, E, F. Distance from E to F is 25 centimeters. Distance from D to F is question mark centimeters.
The given side lengths of AC, BC, and EF, of the similar triangles, using the ratio of similarity between segments of similar figures, gives;
The measure of side DF as 15 centimeters
What is the ratio of similarity?When two figures are similar, the corresponding side pairs have the same ratio of one to the other.
The given information on the two triangles are;
Triangle ∆ABC is similar to triangle ∆DEF
Triangle ∆ABC and triangle ∆DEF are right triangles
The length of segment AC = 9 centimeter
Length of segment BC = 15 centimeters
In triangle ∆DEF, we have;
Length of segment EF = 25 centimeters
Required;
The length of segment DF
Solution;
By comparison, the corresponding sides of the two triangles are;
AC corresponds to DF
BC corresponds to EF
In similar triangles, the ratio of the corresponding sides are the same, which gives;
[tex] \displaystyle{ \frac{AC}{DF} = \frac{BC}{EF} }[/tex]
[tex] \displaystyle{ \frac{9}{DF} = \frac{15}{25} }[/tex]
[tex] \displaystyle{ DF = \frac{9 \times 25}{15} = 15 }[/tex]
The measure of side DF is 15 centimeters
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Can you guys please explain the whole thing of converting I don't know how to do it?
Answer:
y=6/5x+6
Step-by-step explanation:
so for this you gotta see how far up/down the 2 points are apart as well as how far left/right and should be shown as 'y/x'. this will be your slope. Simplify it as far down as you can but keep it as a fraction.
After that you need to find where it crosses the y axis. lucky for us its stated in the problem. thats the process of finding y= m/x +b
PLS HELP ASAP! 20 PT+Brainliest
Answer:
The graph of a line with 1/2 is only half of 1/4 the line with 4 is greater and way bigger than just half of 1/4.
if 3x=5 what’s 3^4x=
Answer:
135
Step-by-step explanation:
If 3x = 5, x = 5/3
3^4 = 81
3^4 x = 81x = 81 x 5/3 = 135
Solve this quadratic equation by factoring.
(x-3)^2 =3(x-3)
Please help me i’m very stuck on this equation
The expression of the given quadratic equation in factor form is (x - 3)(x - 6) = 0 with a solution of x = 3 or 6.
How to factor quadratic equations?
We are given the quadratic expression;
(x - 3)² = 3(x - 3)
By expansion of the brackets, we have;
x² - 6x + 9 = 3x - 9
x² - 6x + 9 - 3x + 9 = 0
x² - 6x - 3x + 18 = 0
By grouping into brackets we have;
(x² - 6x) - (3x - 18) = 0
By bringing out common factors, we have;
x(x - 6) - 3(x - 6) = 0
Thus, we can write it in factor form as;
(x - 3)(x - 6) = 0
x = 3 or 6
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1: En el triángulo rectángulo de la figura, si a =30°, entonces ¿cuál es el valor de P
A) 2
B) 0,5
C) 30°
D) No se puede saber.
Answer:
can you translate this because I don't understand
solve each of the pairs of simulations equations by elimination
5g+2h=14
3g-4h=-28
We need to know to solve equations by elimination method to solve the problem. The solution for the given pair of equations is g=0 and h=7.
When we solve a given pair of equations by elimination method, we need to express one of the variables in terms of the other variable and then substitute this value in the other equation to find the value of one of the variables. We use the value of this variable to find the value of the other variable. In this question we have a pair of equations and we need to solve for the variables g and h.
5g+2h=14..(i)
3g-4h=-28..(ii)
From equation (i)
2h=14-5g⇒h=7-5g/2
Substitute this in equation (ii)
3g-4(7-5g/2)=-28
3g-28+10g=-28
13g=0
g=0
Using value of g to find out h
h=7-5g/2=7
Therefore the solution of the given pair of equations is g=0 and h=7.
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A spinner with 10 equally sized slices has 3 yellow slices, 2 blue slices, and 5 red slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a yellow or blue slice? Write your answer as a fraction in simplest form.
The probability that the dial stops on a yellow or blue slice is 50%.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 indicates certainty.
An event's likelihood of occurring increases with its probability. The flip of a fair (unbiased) coin serves as a straightforward illustration. Since there are no other possible outcomes and the coin is fair, the probability of both the outcomes, "heads" and "tails," is half.
The total no. of outcomes in the events = 10
Outcomes favourable to yellow and blue = 3 + 2
= 5
Probability = outcomes favourable/total no. of outcome
= 5/10
= 1/2
= 1/2 × 100%
= 50%
Thus, The probability that the dial stops on a yellow or blue slice is 50%.
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Question 14 (1 point)
Write the equation for the following graph.
Answer:
The correct equation is b, x = 4.
Triangle PQR is a right triangle. The triangle has vertices P(-2,4), Q(3,4) and R(-2,-2) What is the length of segment PQ?
Answer:
Length of segment PQ = 5
Step-by-step explanation:
Coordinates of P (-2, 4) and coordinates of Q are (3,4)
y coordinates are the same so the segment PQ is a horizontal line
The length is simply the difference between the x coordinates = 3 -(-2) = 3 + 2 = 5
