Answer:
The domain of a function is the complete set of possible values of the independent variable.
In plain English, this definition means:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero
The number under a square root sign must be positive in this section
Step-by-step explanation:
Answer and explanation:
The set of all possible values of x that will make the function work, giving an output of real y values is said to be the domain of a function.
The domain of a function is determined by looking for the values of the independent variable (which is usually x) that are allowed to use.
While the complete set of all possible output values of the dependent variable (usually y), when we substitute the x values is called the range.
Range can be determined by the spread of the possible y-values (minimum y-value to maximum y-value).
Please explain your answer.
Answer:
x=4.4
Step-by-step explanation:
To get from A to B, the scale factor is 2.5, since 4*2.5 = 10
So, to get from B to A, you divide by 2.5.
11/2.5 = 4.4
Elise took out a payday loan for $500 due in 2 weeks that charges an $80 fee. What is the periodic interest rate of the loan?
The periodic interest rate of Elise's payday loan is calculated by dividing the $80 fee by the $500 borrowed, resulting in a rate of 16% for the 2-week period.
To calculate the periodic interest rate of Elise's payday loan, we need to consider the fee charged as the interest for the period of the loan, since the loan is due in 2 weeks, which is a half-month period. Elise is being charged an $80 fee on a $500 loan, and this fee represents the interest for the loan's term.
Therefore, we can calculate the periodic interest rate by dividing the interest by the principal and the number of periods.
Here's the calculation:
Interest (Fee) = $80
Principal (Amount borrowed) = $500
Periodic interest rate = Interest / Principal
Periodic interest rate = $80 / $500 = 0.16 or 16%
Since the period is 2 weeks, we could express this interest rate on a monthly basis if needed by scaling the bi-weekly rate to a monthly rate. However, the loan terms only mention a 2-week period, so the periodic interest rate for the loan's duration is 16%.
Each year, the number of students taught by Mr. Wright increases by 2. The first year, he taught 18 students. The total number of students taught after 25 years can be represented using the expression . How many students has Mr. Wright taught in 25 years?
450
500
1,050
2,100
Answer:
Mr. Wright taught 1,050 students in 25 years.
Step-by-step explanation:
Given,
The number of students Mr. Wright taught = 18,
Also, every year the number of student is increased by 2,
So, in second year, the number of students = 18 + 2 = 20,
In third year = 20 + 2 = 22,
In fourth year = 22 + 2 = 24,
.............., so on,
Hence, we get an A.P. that shows the given situation,
18, 20, 22, 24, ............. till 25 years.....
First term, a = 18,
Common difference, d = 2,
And, number of terms, n = 25,
Hence, the total number of students that have been taught by him are,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{25}=\frac{25}{2}[36+(25-1)2][/tex]
[tex]=\frac{25}{2}[36+24\times 2][/tex]
[tex]=\frac{25}{2}[36+48][/tex]
[tex]=\frac{25}{2}(84)[/tex]
[tex]=\frac{2100}{2}[/tex]
[tex]=1050[/tex]
Third option is correct.
2t + 15 = 40 – 3t please solve
Answer:
t=5
Step-by-step explanation:
Add 3t to the other side to cancel it out
2t+3t+15=40
Subtract 15 to the other side to cancel it out
2t+3t=40-15
Simplify
5t=25
t=5
What is the geometric mean of 5 and 4
Answer:
[tex]2\sqrt{5}[/tex]
Step-by-step explanation:
Geometric mean of two numbers of the square root of their product:
[tex]\sqrt{20}=\sqrt{4\cdot5}=2\sqrt{5}[/tex]
The geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
What is the geometric mean of two numbers?The Geometric mean of the two numbers formula is defined as the square root of the product of 2 numbers.
The following formula is used to calculate the geometric mean;
[tex]\rm Geometric \ mean = \sqrt{a \times b}[/tex]
Where a is the first term and b is the second term.
Therefore,
The geometric mean of 5 and 4 is;
[tex]\rm Geometric \ mean = \sqrt{a \times b}\\\\a=5 \ and \ b=4\\\\\rm Geometric \ mean = \sqrt{5 \times 4}\\\\\rm Geometric \ mean = \sqrt{20}\\\\\rm Geometric \ mean = 2\sqrt{5}[/tex]
Hence, the geometric mean of 5 and 4 is [tex]2\sqrt{5}[/tex].
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use the diagram to answer the questions
1. which ray is a bisector of ABC
A. BC
B. BD
C. BA
D. BF
2. what is GH
A. 5
B. 10
C. 15
D. 25
3. what is the value of y
A. 2
B. 4
C. 16
D. 20
Answer:
1. B. BD
2. C. 15
3. A. 2
Step-by-step explanation:
1. From the figure,
∠DAB = ∠DAC
Therefore, BD is the bisector of ∠ABC.
2. From the figure, IG = GH
3x = 5x - 10
10 = 5x - 3x
2x = 10
x = 5
So, GH = 5x - 10
= 5(5) - 10
= 25 - 10
= 15
Therefore, GH = 15.
3. From the figure,
∠DAB = ∠DAC
10y = 8y + 4
10y - 8y = 4
2y = 4
y = 2
In combining like terms, what do these equations equal?
1: 5+6(2x+3)-2x
2: 3(4x+8) + 3(2x-6)
3: (32-8x)
____
4
4: 24x+18
____
6
If you can, please explain it! Thanks!
Answer:
Look below. The answers are bolded!
Step-by-step explanation:
1. 10x + 23
5+6(2x+3)-2x
Distribute first!
5 + 12x + 18 -2x.
Now you can combine like terms.
23 + 10x
2. 18x + 6
3(4x+8) + 3(2x-6)
Distribute first!
12x + 24 + 6x - 18
Now you can combine like terms.
18x + 6
3. -2x + 8
(32-8x)
____ ___
4
Divide 32 and -8x by 4.
32/4 = 8
-8x/4 = -2x
-2x + 8
4. 4x + 3
24x+18
______
6
Divide 24x and 18 by 6
24x/6 = 4x
18/6 = 3
4x + 3
Name the angle in 2 different ways and name the 2 rays from the diagram below please show work
Answer:
3) TB and NT
4) ∠KLM and ∠MLK
Step-by-step explanation:
3) those two rays intersect to form the angle shown in the diagram
4) an angle can always be named from left to right or right to left as long as the middle letter is always the vertex of the angle
A rectangle has an area (x2-17x+72) square units.Since the area of a rectangle is determined using the formula, A= lw, what could be the length and width of the rectangle
Answer:
length: 9
width: 8
Step-by-step explanation:
you would need to factorise the equation in order to work out the length and width of the rectangle
so to factorise x^2 -17x +72, you will need to numbers that multiply to make 72 and add to make -17
the numbers are -9 and -8
so the factorised equation is (x-9)(x-8)
if you equate it to 0 you get 9 and 8 as values for x
since the length is longer than the width
the length is 9 and the width is 8
you are a plumber installing a pipe the ratio of the outside diameter to the inside diameter is 1.5 to 1. you use a pipe with a 0.5 inch inside diameter what is the smallest diameter that you will need to drill to allow the pipes to pass through the wall
The smallest diameter needed to drill through the wall is 0.75 inches, which is calculated by multiplying the inside diameter of the pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). Always measure and plan ahead to avoid mistakes.
Explanation:The subject matter of this question is mathematics, specifically ratios. To find the smallest diameter you would need to drill into the wall, you would need to multiply the inside diameter of your pipe (0.5 inches) by the ratio of the outside diameter to the inside diameter (1.5). So, 0.5 inches * 1.5 = 0.75 inches.
This means, to allow the pipes to pass through the wall, you will need to drill a hole at least 0.75 inches in diameter. This is assuming the wall is thin enough that the entire length of the pipe that needs to pass through the wall is less than the thickness of the wall.
Remember, it's always better to pre-measure and plan ahead to avoid unnecessary work and potentially costly mistakes.
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Which inequality best represents that ice cream at −3°C is cooler than ice cream at 1°C?
A. −3°C > 1°C
B.−3°C < 1°C
C. 1°C > 3°C
D. 1°C < −3°C
Answer: Choice B
"ice cream at -3 degrees C is cooler than ice cream at 1 degree C"
-3 is smaller than 1
-3 < 1
Keep the order the same even though 1 > -3 is also possible, but fortunately this isn't listed.
On a car trip Sam drove m miles Kara drove twice as many miles as Sam and Darin drove 20 fewer miles than Kara in terms of m many miles did Darin drive
Answer:
Darin drove '2m - 20' miles.
Step-by-step explanation:
We are given that Sam drove 'm' no. of miles.
As, it is also given that Kara drove twice as many miles as Sam. Therefore we get that Kara drove '2m' no. of miles.
Now, it is given that Darin drove 20 miles fewer than Kara .i.e. Darin drove '2m - 20' no. of miles.
Hence, in terms of m, Darin drove '2m - 20' miles.
Point M is the midpoint of AB. The coordinates of point A are (-7,2) and the coordinates of M are (-2,2). What are the coordinates of point B?
Answer:
(-9/2,2)
Step-by-step explanation:
Midpoint equals (x1+x2)/2, (y1+y2)/2
Answer:
(-9/2,2)
Step-by-step explanation:
These triangles are similar. find Y and X
It these triangles are similar, then the sides of the triangles are in proportion:
[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex] cross multiply
[tex]15y=10(y+4)[/tex] use distributive property
[tex]15y=10y+40[/tex] subtract 10y from both sides
[tex]5y=40[/tex] divide both sides by 5
[tex]\boxed{y=8}[/tex]
[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex] cross multiply
[tex]8x=(4)(6)[/tex]
[tex]8x=24[/tex] divide both sides by 8
[tex]\boxed{x=3}[/tex]
"If parallel lines have a transversal, then corresponding angles are congruent."
On the fence, lines A and B are parallel and line C is a transversal. How many pairs of corresponding angles are available on the picture to use to prove the theorem? Which given pair of angles can be used?
A) 2 pairs; ∠5 and ∠1;
B) 2 pairs; ∠5 and ∠7;
C) 4 pairs; ∠2 and ∠4
D) 4 pairs; ∠3 and ∠5;
Answer:
Option C. 4 pairs; ∠2 and ∠4
Step-by-step explanation:
we know that
In the figure
[tex]m<6=m<1[/tex] -----> by corresponding angles
[tex]m<3=m<7[/tex] -----> by corresponding angles
[tex]m<5=m<8[/tex] -----> by corresponding angles
[tex]m<2=m<4[/tex] -----> by corresponding angles
therefore
Are available [tex]4[/tex] pairs of corresponding angles
The answer is the option C
A jet plane can travel 567 miles per hour. How many mile can it travel in 4hour
Answer: 2268 miles
Step-by-step explanation: 1 hour = 567 miles
4 hours= n miles
multiply 567 miles by four hours
= 2268 miles
Answer:
2304
Step-by-step explanation:
567 x 4
Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 50% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution? Gabe needs 30 liters for a 50% solution .
He also needs a ___ for a 70% solution . whats __?
Answer:
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Step-by-step explanation:
Equation:
acid + acid = acid
0.40x + 0.70(60-x) = 0.60*60
40x + 70*60 - 70x = 60*60
-30x = -10*60
x = 20 liters
Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Identify the slope of the line shown in the graph below: slope = -1
Slope = 0
Slope = undefined
Slope = 1
It's a vertical line. The slope of vertical line is undefined.
The equation of a vertical line is x = a (a - any real number).
Answer: Slope = undefinedEquation of line: x = -1Answer:
Slope = undefined
Step-by-step explanation:
A vertical STRAIGHT line that represents a slope is undefined.
Mr. Geyer dog weighs 32.01 pounds if he goes on a die and loses 5.89 pounds how much will he weigh
Answer: 27.12
Step-by-step explanation:
32.01
-5.89
27.12
Your parents are renting an apartment for you when you go away to college. An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. How much is the difference in payments if you stay the whole year?
Answer:
The month-to-month contract will cost an extra $1356.
Step-by-step explanation:
"An annual contract is $502.00/month with a 2-month penalty if you break the lease."
If you stay the whole year, and you pay $502 per month, you pay 12 * $502 = $6024 for the entire year.
"The month-to-month contract is $615.00/month."
If you stay the entire year, you pay 12 * $615 = $7380.
The difference is $7380 - $6024 = $1356
An equation that expresses a mathematical rule or relationship is a ___.
proportion
conversion factor
formula
ratio
Answer:
formula
Step-by-step explanation:
3rd option is correct which is formula.
What is a formula ?
A mathematical relationship or rule which expressed only in symbols and which is the connection between two or more variable.
What is the correct option ?An equation that expresses a mathematical rule or relationship is a formula.
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(((FIND THE MEASUREMENT INDICATED IN EACH PARALLELOGRAM)))
Help please
Thanks
Answer:
LM=12
V =90
Step-by-step explanation:
4. If it is a parallelogram, the two sides have to be equal.
2x-6 = x+3
Subtract x from each side
2x-x -6 = x+3-x
x-6 =3
Add 6 to each side
x-6+6 = 3+6
x=9
LM =2x-6
= 2*9 -6
= 18-6
= 12
5.
<U + < T = 180 Adjacent corners in a parallelogram are supplementary
11x+2 + 12x-6 = 180
Combine like terms
23x -4 = 180
Add 4 to each side
23x-4+4 = 180+4
23x = 184
Divide by 23
23x/23 = 184/23
x=8
<V = <T Opposite corners in a parallelogram are equal.
<V = 12x-6
<V = 12(8) -6
<V = 96-6
<v =90
The question involves solving algebra and geometry problems related to parallelograms, focusing on transformations, coordinates, and area calculations to find the equation for y.
Explanation:The student is asked to solve a series of algebra and geometry problems related to the properties of a parallelogram. These include finding coordinates, proving algebraic expressions, computing distances, and determining areas. The goal is to find the equation for y given a series of transformations and conditions on a square that becomes a parallelogram. Important concepts include the area of a parallelogram, vector addition using the parallelogram rule, and the determinant relating to a change of basis in vectors.
For example, part (e) involves finding the area of the parallelogram by computing twice the area of triangle PQO, using PQ as the base of the triangle. Solving for y in part (f) by setting this area equal to 1 involves understanding the effects of transformation on geometrical shapes and employing algebra to arrive at the desired equation.
How do I do this please dumb this down
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept fprm is
y = mx + b ( m is the slope and b the y-intercept )
y = [tex]\frac{5}{4}[/tex] x - 4 is in this form
with m = [tex]\frac{5}{4}[/tex] and b = - 4
Plot the point (0, - 4)
using the slope add 5 to the y-coordinate and 4 to the x-coordinate
(0, - 4 ) → (0 + 4, - 4 + 5) → (4, 1) ← point on the line
Plot the points (0, - 4) and (4, 1) and draw a straight line through them to obtain a sketch of the graph
Jian’s family sells honey from beehives. They collected 3,311 ounces of honey from the beehives this season. They will use the honey to completely fill 4-ounce jars or 6-ounce jars. Jian’s family will sell 4-ounce jars for $5 each or 6-ounce jars for $8 each. Jian says if they use only 4-ounce jars, they could make $4,140 because 3,311 / 4 =827 R3. That rounds up to 828, and 828 multiplied by $5 is $4,140. Part A-Explain the error that Jian made when finding the amount of money his family could make if they use only 4-ounce jars. Enter your explanation in the space provided. Part B- Explain how to determine the money Jian’s family could make if they use only 6-ounce jars. Include the total amount of money and the total number of 6-ounce jars in your explanation. Enter your answers and your explanation in the space provided.
Answer:
A. Jian rounded the number of 4-ounce jars to 828 which is wrong. There are only 827 jars that can be completely filled.
B. Total number of 6-ounce jars = 551
Total money earned from 6-ounce jars = $4408
Step-by-step explanation:
A. Jian's family's collection = 3311 ounces
Number of 4-ounce jars = [tex]\frac{3311}{4}[/tex]
= 827.75
Jian rounded it to 828 which is wrong. There are 827 jars that can be completely filled.
Cost per 4-ounce jar = $5.
Total cost = 827 × 5 = 4135
B. Now, number of 6-ounce jars = [tex]\frac{3311}{6}[/tex]
= 551.83
≅ 551 jars
Cost per 6-ounce jar = $8
Total cost = 551 × 8 = 4408
Sin (3pi/4) =_____ please help!!!
[tex]sin\frac{3}{4}\pi=sin(\pi-\frac{\pi}{4})=sin\frac{\pi}{4}=\frac{\sqrt2}{2}[/tex]
PLEASE HELP ME !! Carter has 3 statues of various sizes in his garden. Statue A is one foot taller than statue B. Statue is one-half of a foot taller than statue B. A) write an algebraic expression for the total combined height of statue A and c. (equations for statues A and C) B) If the total combined height of the 3 statues is 10 feet, find the height of statue B in inches.
Answer:
Step-by-step explanation:
Find the value of x such that PQ = QRwhere P, Q and Rare the pints (2, 5), (x, -3) and (7, 9) respectively.
Answer: x = 12.5
Step-by-step explanation:
P = (2, 5)
Q = (x, -3)
R = (7, 9)
[tex]d_{PQ}=d_{QR}[/tex]
[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]
[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]
[tex]4x+68 = -14x+193[/tex]
[tex]10x+68 = 193[/tex]
[tex]10x= 125[/tex]
x = 12.5
How many centimeters are in 7 feet, given that 1 inch = 2.5 centimeters?
Answer:
210 cm
Step-by-step explanation:
We need to convert 7 ft to cm
We know that 1 ft = 12 inches
7 ft * 12 inches/1 ft = 84 inches
We know that 1 inch = 2.5 cm
( 1 inch is really 2.54 cm but you question says 2.5 cm)
84 inches * 2.5 cm/1 inch = 210 cm
a train travels 160 km in 2 h what is the trains average speed in km/h
Answer:
80km/h
Step-by-step explanation:
we know that the train is 160 km in 2 hours we need to find how much is in 1 hour you divide 160÷2= 80 so it means that there is 80 km in 1 hour which is "80 km/h"
Find the value of
[tex] {x}^{i} [/tex]
for all x belongs to Real Numbers and i = √(-1).
Answer: cis (ln x) ; x > 0
Step-by-step explanation:
[tex]x^i[/tex]
[tex]= e^{ln(x^i)}[/tex]
[tex]=e^{i \ln(x)}[/tex]
= cos (ln x) + i sin (ln x)
AKA: cis (ln x)
NOTE: I found this following formula which you may find useful:
[tex]A^i = x + iy[/tex]