The equation y= √(x-1) + 3 is a function of radical function.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Type of function:
linear, power, quadratic, polynomial, rational, exponential, logarithmic, radical etc.
Given equation is
y= √(x-1) + 3
In the equation there is a term √(x-1).
A square root presents in the equation.
This means it is a radical function.
The given equation is of a radical function.
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23 inches of wire cost 92 cents at the same rate, how much (in cents) will 34 inches of wire cost?
Answer:
Step-by-step explanation:
Let's use the formula rate = cost/length to find the cost of one inch of wire. We know that 23 inches of wire cost 92 cents, so the rate of one inch of wire can be found by dividing 92 cents by 23 inches:
rate = cost/length = 92 cents/23 inches = 4 cents/inch
Now that we have found the rate of one inch of wire, we can use it to find the cost of 34 inches of wire. We simply multiply the rate by the length:
cost = rate * length = 4 cents/inch * 34 inches = 136 cents
So, 34 inches of wire will cost 136 cents.
Step-by-step explanation:
the trick is to find the "norm" rate, which is the rate for one unit.
from there we can get the rate for any number of units just by multiplying.
so,
23 in for 92 cents.
that means the rate is
23/92 = 23/(23×4) = 1/4
so, by dividing numerator and denominator by 23 (in this case it has an integer result also for the denominator) we get the price for 1 inch of wire : 4 cents.
so, 34 inches then have the length/price ratio (we multiply numerator and denominator by 34)
1/4 × 34/34 = 34/136
that means 34 inches cost 136 cents (= $1.36).
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 vears and making monthly payments. What would their monthly payment be?
Answer:
a) payment: $1082.84
b) interest: $194,822.40
Step-by-step explanation:
The monthly payment on the mortgage can be found using the given formula with the given values of principal (P=195000), interest rate (r=0.053), and time period (t=30). The value of n is 12, corresponding to the number of months in a year.
a)The monthly payment is ...
\(k=\left(1+\dfrac{r}{n}\right)^{nt}=\left(1+\dfrac{0.053}{12}\right)^{12\cdot30}\approx 4.88661119\\\\\text{monthly payment}=\dfrac{P\cdot\dfrac{r}{n}\cdot k}{k-1}=\dfrac{195000\cdot0.0044166667\cdot4.88661119}{4.88661119-1}\\\\\boxed{\text{monthly payment}=\$1082.84}\)
__
b)The interest owed is the difference between the total of monthly payments and the principal of the loan:
interest owed = (360)(1082.84) -195000 = 194,822.40
The interest owed over 30 years is $194,822.40.
an 8cm cube is cut into several small cubes of edge 2cm.how many cubes are formed???
helppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
first second sum
5 2 7
7 -3 4
-10 6 -4
second picture
D, C, B, A
Step-by-step explanation:
Answer:
Step-by-step explanation:
First second sum
5 2 7
7 -3 4
-10 6 -4
Second question
d,c,a,b
A group of friends ordered two pizzas, one with pepperoni and one with mushrooms and green peppers. A plain pizza costs 9 dollars. Each extra topping costs 1 dollar. How much did the two pizzas cost?
Answer:
23
Step-by-step explanation:
Todd rolled a 12-sided die marked with the numbers 1 to 12. These are his experimental probabilities.
P(odd number) = 18/48
P(greater than 8) = 16/48
P(9) = 12/48
1. Which experimental probability matches the theoretical probability exactly?
2. Which experimental probability is farthest from the theoretical probability?
The experimental probability farthest from the theoretical probability is P(greater than 8). The theoretical probability of rolling a 9 is 1/12 because there is one 9 out of twelve total possible outcomes.
Experimental probability refers to the probability of an event based on data acquired from repeated trials or experiments.
Theoretical probability is the probability of an event occurring based on logical reasoning or prior knowledge. In Todd’s case, he rolled a 12-sided die marked with the numbers 1 to 12.
The probabilities are as follows:P(odd number) = 18/48P(greater than 8) = 16/48P(9) = 12/48To answer the questions:1. Which experimental probability matches the theoretical probability exactly?The theoretical probability of rolling an odd number is 6/12 or 1/2 because there are six odd numbers out of the twelve total possible outcomes.
The experimental probability Todd obtained was 18/48. Simplifying 18/48 to lowest terms gives 3/8, which is equal to 1/2, the theoretical probability.
Therefore, the experimental probability that matches the theoretical probability exactly is P(odd number).2. Which experimental probability is farthest from the theoretical probability? The theoretical probability of rolling a number greater than 8 is 3/12 or 1/4 because there are three numbers greater than 8 out of twelve total possible outcomes.
The experimental probability Todd obtained was 16/48. Simplifying 16/48 to lowest terms gives 1/3, which is not equal to 1/4, the theoretical probability.
The experimental probability Todd obtained was 12/48. Simplifying 12/48 to lowest terms gives 1/4, which is not equal to 1/12, the theoretical probability.
However, the difference between the experimental probability and the theoretical probability for P(9) is smaller than that of P(greater than 8). Therefore, P(greater than 8) is the experimental probability that is farthest from the theoretical probability.
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i need help can someone please help me
The measure of the angle m∠ZYX of the trapezoid is equal to 139°
What is a trapezoid?A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.
3x + 19 + x + 1 = 180°
4x + 20 = 180°
4x = 180 - 20 {collect like terms}
4x = 160
x = 160/4 {divide through by 4}
x = 40
m∠ZYX = 3(40) + 19 = 139°.
WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.
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1. Find the value of the unknown angles in the following diagram.
Answer:
z= 40
y=140
x= 115
Step-by-step explanation:
look at the pics
Meggie uncovered some old plans for a dolphin habitat that a previous zoo employee created. She knows guests will enjoy watching the dolphins swim and play: The only problem is the paper has a stain covering one side length of the exhibit!
If the perimeter of the pool is 108 feet, what is the missing side length?
I think it is some ware between 20 and 200 if that helps
Step-by-step explanation:
A customer wants to book a room with a seaview.
You show her 4 options but only 3 have sea views.
What fraction has a seaview?
Determine if the equation given in slope-intercept form represents the graph. If the equation is correct support your reasoning with why it is correct. If the equation is incorrect, give the correct slope-intercept form equation explaining how you determined it.
The equation of the line would be y = (4/5)x + 4 which in slope-intercept form represents the graph.
The graph is given in the question.
As per the given line, we take two points (0, 4) and (5, 8)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 0, y₁ = 4
x₂ = 5, y₂ = 8
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 4 = (8 - 4)/(5-0 )[x -0]
⇒ y - 4 = (4/5)x
⇒ y = (4/5)x + 4
The given equation of the line y = 4x + 5 is incorrect because its slope is not correct.
So, the equation of the line would be y = (4/5)x + 4.
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3√b in exponential form
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The medium size gets the most ice cream per dollar.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given three types of soft-serve ice cream,
A; small,
ice cream for $1.96 = 3 ounces
ice cream for $1 = 3/1.96 = 1.53 ounce per dollar
B; medium,
1 ounce of icecream cost = $0.64
ice cream for $1 = 1/0.64
ice cream for $1 = 1.5625 ounce per dollar
C: Large
ice cream for $6.85 = 10 ounces
ice cream for $1 = 10/6.85 = 1.459 ounce per dollar
Hence medium size gets the most ice cream per dollar.
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Which graph represents y=x-4?
Answer:
Can you reupload your graph, I don't think you attached it to your question.
Prove that two triangles on the same base and between the same parallels are equal
in area.
follow me please .........
Answer:
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Step-by-step explanation:
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NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The measure of the hypotenuse of the right-angle triangle is 53.21 feet.
Given that:
Perpendicular, P = 50 feet
Angle, Ф = 70°
It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The measure of the hypotenuse of the right-angle triangle is calculated as,
sinФ = P/H
sin 70° = 50 / x
x = 53.21 feet
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Find an equation of the line that passes through the point
(x, y) = (3, 1) and is
perpendicular to the line
2x + 3y = 12
Considering the definition of perpendicular line, the equation of the perpendicular line that passes through the point (x, y) = (3, 1) and is perpendicular to the line 2x + 3y = 12 is y= 3/2x -7/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseIn this case, the line is 2x+3y= 12. Expressed in the form y = mx + b, you get:
3y= 12 - 2x
y= (-2x +12)÷ 3
y= -2/3x +4
Since multiplying the slopes of two perpendicular lines, you get -1, and the line has a slope of -2/3, you get:
-2/3× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (-2/3)
slope perpendicular line= 3/2
The line passes through the point (3, 1). Replacing in the expression for parallel line:
1= 3/2× (3) + b
1= 9/2 + b
1- 9/2 = b
-7/2= b
Finally, the equation of of perpendicular line is y= 3/2x -7/2.
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Juan is creating a rectangular garden in his backyard. The length of the garden is 20 feet. The perimeter of the garden must be at least 70 feet and no more than 86 feet. Use a compound inequality to find the range of values for the width w of the garden.
 The difference between the product of four and a number and six
Into algebraic expression
Calvin estimated he would need 8 hours to
complete his science project. It actually took
him 12 1/2 hours to get everything done. What
was his percent error?
Answer:45%
Step-by-step explanation:
Last week's and this week's low temperatures are shown in the table below.
Low Temperatures for 5 Days This Week and Last Week
Low Temperatures
This Week (°F)
4
10
6
9
6
Low Temperatures
Last Week (°F)
13
9
5
8 5
Which measures of center or variability are greater than 5 degrees? Select three choices.
the mean of this week's temperatures
the mean of last week's temperatures
the range of this week's temperatures
the mean absolute deviation of this week's temperatures
the mean absolute deviation of last week's temperatures
Next
Mark this and return
Save and Exit
Submit
Answer:
A, B, C
Step-by-step explanation:
bc, I think...
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
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PLEASE ANSWER UNDER 5 MIN!!!! ily!!!!
what is the period of the sinusoidal function? enter your answer in the box.
Answer:
Step-by-step explanation:
10
Ws
For which equations is 8 a solution? Select the four correct answers.
OX+6 - 2
Ox+2-10
O x-4-4
O x-2-10
2x=4
3x= 24
ož - 16
OŠ - 1
Answer:
3x = 24
x/8 = 11
x - 4 = 4
x + 2 = 10
Trent grew 12 plants with 4 seed packets. With 5 seed packets.
how many plants can he grow?
Find the measurement of each numbered angle.
The measurement of each numbered angle are,
⇒ ∠10 = 115°
⇒ ∠ 11 = 65 degree
⇒ ∠12 = 115°
We have to given that,
Two intersecting lines are shown in figure.
Since, We know that,
Opposite angle of intersecting lines are vertically opposite angle and both are equal.
Hence, We get;
⇒ ∠ 11 = 65 degree
And, By definition of linear pair angle,
⇒ ∠11 + ∠10 = 180°
⇒ 65° + ∠10 = 180°
⇒ ∠10 = 180° - 65°
⇒ ∠10 = 115°
And, ∠11 + ∠12 = 180°
⇒ 65° + ∠12 = 180°
⇒ ∠12 = 180° - 65°
⇒ ∠12 = 115°
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PLS HELP ASAP!!! I’ll give brainliest
A square rug has an area of 121 ft?. Write the side length as a square root. Then decide if the side
length is a rational number.
HELP ASAP
Select the equation that is true.
6,714 ÷ 103 = 6.714
6,714 ÷ 103 = 67.14
6,714 ÷ 103 = 671.4
6,714 ÷ 103 = 6,714
Answer: None of the choices is correct.
6,714÷103 is about 65.184
Step-by-step explanation:
The closest answer is the second choice. But there must be a typo in the question.
6,714÷100 = 67.14
I hope this helps. You might be able to ask your teacher about the mistake in the question.
1600 with a 6% interest rate
The simple interest on 1600 with a 6% interest rate for 2 years is $192.
What is the simple interest?The simple interest simply means the method that's used to calculate the interest that's charged on a loan or money given out.
In this situation, we want to calculate the simple interest on 1600 with a 6% interest rate for 2 years. This will be calculated thus:
Simple interest = Principal × Rate × Interest
Simple interest = $1600 × 6% × 2
Simple interest = $1600 × 0.06 × 2
Simple interest = $192
The interest is $192.
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Complete question
Calculate the simple interest on 1600 with a 6% interest rate for 2 years.