Answer:
The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:
l + d ≤ 14
This is because the sum of the hours worked in both jobs should not exceed 14 hours.
Rewrite the quadratic function in standard form. f (x) = x2 - 8x + 23 Get Hint Enter Your Step Here 7 4
The quadratic function in standard form of f (x) = x2 - 8x + 23 is (x) = (x - 4)2 + 7.
The quadratic function given is f (x) = x2 - 8x + 23. To rewrite this function in standard form, we need to complete the square for the x terms. Standard form for a quadratic function is f (x) = a(x - h)2 + k, where (h, k) is the vertex of the parabola.
f (x) = 1(x2 - 8x) + 23
Step 2: Take half of the coefficient of the x term, square it, and add it inside the parentheses. In this case, half of -8 is -4, and -4 squared is 16.f (x) = 1(x2 - 8x + 16) + 23 - 16
Step 3: Simplify the constant term outside of the parentheses.f (x) = 1(x2 - 8x + 16) + 7
Step 4: Factor the quadratic inside the parentheses.f (x) = 1(x - 4)2 + 7
Step 5: Simplify the coefficient of the quadratic term, if necessary. In this case, the coefficient is 1, so there is no need to simplify further.The final answer is f (x) = (x - 4)2 + 7, which is the standard form of the given quadratic function.
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Jason jumped off of a cliff into the ocean in Acapulco while vacationing with same friend. His height could be modeled by the equation [tex]h= -16x^{2}+16x+480[/tex] , where t is the time in seconds and h is the height in feet.
After how many seconds, did Jason hit the water? Step by step.
Solving a quadratic equation we can see that Jason will hit the water after 6 seconds.
After how many seconds, did Jason hit the water?We know that the height of Jason is modeled by the quadratic function:
h = - 16x² + 16x + 480
The water is at h = 0, so we need to solve the quadratic equation:
0 = - 16x² + 16x + 480
If we divide all the right side by 16,we will get:
0 = (- 16x² + 16x + 480)/16
0 = -x² + x + 30
Now we can use the quadratic formula to get the solutions:
[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*(-1)*30} }{2*-1} \\\\x = \frac{-1 \pm 11 }{-2}[/tex]
We only care for the positive solution, which is:
x = (-1 - 11)/-2 = 6
Jason will hit the water after 6 seconds.
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Question 1 1.1. Given: √9+25; π-4; √-27 ::: √-27 3 3 ; 2 From the list given above, write down: Question 2 1.1.1. A natural number. 1.1.2. A negative irrational number. 1.1.3. A non-real number. 1.1.4. A rational number which is not an integer. 1.2. Between which two consecutive integers does √138 lie? 1.3. Rewrite 0,26 as a proper fraction (in the form of), show all steps.
√(9 + 25) is real; π - 4 is negative irrational ; √-27 is a non-real ; 3 3/2 is a rational that is not an integer.
√138 lies between 11 and 12; 0.26 as fraction = 13/50
What are types of numbers?A number is an arithmetic value which is used to represent the quantity of an object. There are different types of numbers as natural numbers, whole numbers, integers, real numbers, rational numbers, irrational numbers, complex numbers and imaginary numbers.
Given numbers,
a) √(9 + 25)
= √34
square root of a real number is real number.
b) π - 4
∵π is irrational and less than four,
∴π - 4 is negative irrational number
c) √-27
Square root of -27 is not possible,
√-27 is a non-real number
d) 3 3/2
= 9/2
= 4.5
3 3/2 is a rational number that is not an integer.
e) √138 = 11.747
∴ two consecutive integers between which √138 lies are 11 and 12
f) 0.26
multiplying and dividing with 100
= 26/100
Simplifying
= 13/50
Hence,
√(9 + 25) is real number; π - 4 is negative irrational number;
√-27 is a non-real number; 3 3/2 is a rational number that is not an integer.
Two consecutive integers between which √138 lies are 11 and 12
0.26 as fraction = 13/50
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The sum of Eli's age and Cecil's age is 15 Eli is twice as old as Cecil
eli=e
Cecil=c
e+c=15
e=2c
2c+c=15
3c=15
c=5
e=10
Suppose 10 quarters, 10 dimes, 2 nickels, and 7 pennies are in a box. One coin is selected at random. What is the expected value of this experiment? The expected value of this experiment is
$
. (Round to the nearest cent.) The chart on the right shows the numbers of symbols on each of the three dials of a slot machine. Find the probability of three oranges, and find the probability of no oranges. The probability of three oranges is 0 . (Simplify your answer. Type an integer or a fraction.) The probability of no oranges is (Simplify your answer. Type an integer or a fraction.)
The probability of no oranges is 125/216.
The expected value of this experiment can be calculated by multiplying the probability of selecting each coin by its value, and then adding these products together.
First, let's find the probability of selecting each type of coin:
- The probability of selecting a quarter is 10/29 (since there are 10 quarters out of 29 total coins).
- The probability of selecting a dime is 10/29 (since there are 10 dimes out of 29 total coins).
- The probability of selecting a nickel is 2/29 (since there are 2 nickels out of 29 total coins).
- The probability of selecting a penny is 7/29 (since there are 7 pennies out of 29 total coins).
Next, let's multiply each probability by the value of the corresponding coin:
- The expected value from selecting a quarter is (10/29) * $0.25 = $0.0862
- The expected value from selecting a dime is (10/29) * $0.10 = $0.0345
- The expected value from selecting a nickel is (2/29) * $0.05 = $0.0034
- The expected value from selecting a penny is (7/29) * $0.01 = $0.0024
Finally, let's add these expected values together to find the overall expected value of the experiment:
$0.0862 + $0.0345 + $0.0034 + $0.0024 = $0.1265
So the expected value of this experiment is $0.1265, or $0.13 when rounded to the nearest cent.
As for the second part of the question, we can find the probability of three oranges by multiplying the probability of getting an orange on each dial:
(1/6) * (1/6) * (1/6) = 1/216
So the probability of three oranges is 1/216.
To find the probability of no oranges, we can multiply the probability of not getting an orange on each dial:
(5/6) * (5/6) * (5/6) = 125/216
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find the domain and range of the rational function w(x)=3x-21/3x^2-20x-7
A) factor of the numerator and denominator
B) determine the point of discontinueity if it exist
C) determine the vertical asymptote
D) determine the horizontal asymptote
E) graph the function
1) fill in the table of values to find three or four points to plot for each curve. Use a graphing calculator.
include the point of discontinuity:
We can also plot the vertical asymptote at x = -1/3 and the horizontal asymptote at y = 0.
What are a few illustrations of sensible behaviour?A rational function can be represented by a polynomial that has been divided by another polynomial. The set of all numbers omitting the zeros in the denominator makes up the domain of a rational function because polynomials are defined everywhere. First example: x = f(x) (x - 3).
A) Factor the denominator and numerator together:
w(x) = 3(x - 7)/(3x + 1) = (3x - 21)/(3x2 - 20x - 7) (x - 7)
B) Locate the discontinuity point, if one exists:
With x - 7 = 0 or 3x + 1 = 0, the denominator is 0. As a result, the function exhibits discontinuity points at x = -7 and x = -1/3.
C) Identify the vertical asymptote: For x = -1/3, the function has a vertical asymptote.
D) Locate the horizontal asymptote: The numerator and denominator each have degrees of 2 and 1, respectively. As a result, the horizontal asymptote is y = 0.
E) Visualize the function
Using the value table:
x y
-5 4.5
-2 -1.4
-0.4 -4.11
0 -7
1 -2.4
5 -0.5
7 undefined
The horizontal asymptote at y = 0 and the vertical asymptote at x = -1/3 can also be plotted.
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Please answer this question
The value of x, given the equation, can be found to be 2 .
How to find the value of x ?We are given the equation:
( 5x + 4 ) / 2 = 7
The first step is to remove the denominator using cross - multiplication :
2 x ( 5x + 4 ) / 2 = 7 x 2
5 x + 4 = 14
Solving directly for x then gives:
5 x + 4 = 14
5 x = 14 - 4
x = 10 / 5
x = 2
In conclusion, the value of x in the equation which needed to be simplified to 5 x + 4 = 14 , and then solved, is 2.
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Which image shows a pair of similar polygons? A. An image showing pair of Similar Polygons with an X-axis showing the Value range from 0 to 16 and Y-axis values from 0 to 16. B. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. C. Graphic Image showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. D. Graph showing a pair of similar polygons. The X-axis shows the Value range from 0 to 16 and the Y-axis values from 0 to 16. Reset Next
The correct answer is option C. A graphic image showing a pair of similar polygons with an X-axis showing the value range from 0 to 16 and a Y-axis values from 0 to 16.
What are polygons?Polygons are two-dimensional shapes with straight sides that are joined together. They are closed shapes, meaning all the sides are connected. Polygons can have anywhere from three sides to an infinite number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, and octagons.
This correct image is showing two polygons that are similar, or which have the same shape. This means that the sides of the two polygons are equal in length and each angle is the same. In other words, they are exactly the same shape, but can be different sizes. The X-axis and Y-axis values shown in the image are the coordinates of the points that make up the polygons. The X-axis values indicate the horizontal distance from the origin, while the Y-axis values indicate the vertical distance from the origin. By looking at the coordinates of the points that make up the polygons, we can see that the two polygons are similar.
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4k^(11)m^(22) If (z^(34))(z^(19))^(4) is equivalent to (z^(a)), then what is the value of a?
If (z³⁴)(z¹⁹)⁴ is equivalent to (zᵃ), The value of a is 110.
we can solve it by the rules of exponential :
Any nonzero real number raised to the power of zero will be 1. Any nonzero real number raised to a negative power will be one divided by the number raised to the positive power of the same number.When multiplying two exponents with the same nonzero real number base, the answer will be the sum of the exponents with the same baseWhen dividing two exponents with the same nonzero real number base, the answer will be the difference of the exponents with the same base.If an exponent is raised to another exponent, you can multiply the exponents. If the product of two nonzero real numbers is being raised to an exponent, you can distribute the exponent to each factor and multiply individually.f the quotient of two nonzero real numbers are being raised to an exponent, you can distribute the exponent to each individual factor and divide individually.To find the value of a, we need to use the laws of exponents. Specifically, we need to use the law that states (x^(y))(x^(z)) = x^(y+z) and the law that states (x^(y))^(z) = x^(y*z).
So, let's apply these laws to the given expression:
(z³⁴)(z¹⁹))⁴ = z³⁴ * z^(19*4) = z³⁴* z⁷⁶ = z^(34+76) = z¹¹⁰
Therefore, the value of a is 110.
So, the expression If (z³⁴)(z¹⁹)⁴ is equivalent to (z¹¹⁰).
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a) write RS as a column vector
b) write SR as a column vector
Answer:14
Step-by-step explanation:
The total of monthly payments for a 4-year loan is $4,200. 0. The APR is 9. 25%. How much money was originally borrowed?
The original amount borrowed was approximately $34,211.1.
To compute the first sum acquired, we can involve the recipe for the current worth of a customary annuity, which addresses a progression of equivalent installments made toward the finish of every period. The recipe is:
PV = [tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]
where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the total number of periods.
In this case, we have monthly payments, so we need to convert the APR to a monthly interest rate by dividing it by 12. We also have a 4-year loan, which means 48 monthly payments.
APR = 9.25%
Monthly interest rate = APR / 12 = 0.0925 / 12 = 0.00771 (rounded to five decimal places)
Total number of payments = 48
Total amount of payments = $4,200.0
Substituting these values into the formula, we get:
PV =[tex]PMT * (1 - (1 + r)^{(-n)}) / r[/tex]
PV = [tex]$4,200.0 * (1 - (1 + 0.00771)^{(-48)}) / 0.00771[/tex]
PV = $4,200.0 x (1 - 0.5180) / 0.00771
PV = $34,211.1 (rounded to the nearest tenth)
Therefore, the original amount borrowed was approximately $34,211.1.
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True or False with explanation (e.g. a piece of the Invertible Matrix Theorem) or a counterexample. All matrices aren×n. - (a) If the equationAx=0has only the trivial solution, thenAis row equivalent to the identity matrix. - (b) If the columns ofAspanRn, then they are linearly independent. - (c) IfATis not invertible, then neither isA. - (d) If there is a matrixDwithAD=I, thenDA=Ialso.
(a) If the equation Ax=0has only the trivial solution, then A is row equivalent to the identity matrix is True.
(b) If the columns of Aspan Rn, then they are linearly independent is True.
(c) If AT is not invertible, then neither is A is True.
(d) If there is a matrix D with AD=I, then DA=I also is True.
If the equation Ax=0 has only the trivial solution, then the matrix A has a pivot in every column and is therefore row equivalent to the identity matrix.
If the columns of A span Rn, then they are linearly independent because if they were not, there would be a nontrivial linear combination of the columns that equals the zero vector, which would contradict the fact that they span Rn.
If AT is not invertible, then it has a nontrivial null space, which means that there is a nonzero vector x such that ATx=0. This implies that xTA=0, which means that x is in the null space of A. Since A has a nontrivial null space, it is not invertible.
If there is a matrix D with AD=I, then DA=I also because the inverse of a matrix is unique and both AD and DA must be equal to the inverse of A.
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A family buys 6 airline tickets online. The family buys travel insurance that costs $18 per ticket. The total cost is $1,128. Let x represent the price of one ticket. Then find the price of one ticket.
Answer: $170
Step-by-step explanation:
6x + 18(6) = 1128.
6x + 108 = 1128
6x = 1020
x = 170
The price of one ticket is 170
A car travels 1 mile every
minute, what is its speed in
mi/hr?
Answer:
Step-by-step explanation:
60mi/hr
An investment company provides strategies for improving return on your investment. It believes that it can increase a customer’s returns by 2. 3%. Which statistical method would be best to use in this situation?
A statistical method would be best to use in this situation - Hypothesis testing
We know that the hypothesis testing is nothing but a form of statistical inference that uses data from a sample to draw conclusions about a population probability distribution. Here, first we made a tentative assumption about the distribution. This assumption is called the null hypothesis , which is denoted by H₀. An alternative hypothesis is the opposite of the null hypothesis. It is denoted by [tex]H_a[/tex]
Hypothesis testing is used for confirming a business claim or idea. It is useful for investors who trying to decide what to invest in and whether the it would provide a satisfactory return.
In this case, an investment company provides strategies for improving return on your investment. It believes that it can increase a customer’s returns by 2. 3%.
Here, hypothesis testing which is one of the statistical method that would be best to use.
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Does $10,000 invested at 6% interest double its value in half the time as $10,000 invested at 3% interest? Show your work.
The answer is $21,989.34 and Yes, $10,000 invested at 6% interest will double its value in half the time as $10,000 invested at 3% interest.
Now, For the 6% investment:
$10,000 invested at 6% interest will double in 12 years:
$10,000 × (1.06)^12 = $21,989.34
For the 3% investment:
$10,000 invested at 3% interest will double in 24 years:
$10,000 × (1.03)^24 = $21,989.34
Therefore, it will take half the time (12 years) for the 6% investment to double its value compared to the 3% investment (24 years).
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The Pressure in the bulb of a constant volume gas thermometer 82cm at 0degree 105.2 cm at loo°c and 68.4cm. When the bulb is surrounded by solid Carbon(iv ) oxide calculate the temperature of the Carbon (iv )
Oxide
The temperature of the Carbon (IV) Oxide surrounding the thermometer is approximately -46.83 °C (226.32 K).
What is the temperature of the Carbon (IV) Oxide?We can use Charles's Law and Boyle's Law to relate the pressure of the gas in the thermometer to the temperature of the surrounding Carbon (IV) Oxide. Since the volume of the gas in the thermometer is constant, we can assume that the pressure is directly proportional to the absolute temperature.
Therefore, we can use the following equation:
P₁/T₁ = P₂/T₂
where;
P₁ and T₁ are the pressure and temperature at the first measurement (0 °C), and P₂ and T₂ are the pressure and temperature at the second measurement (100 °C).Solving for T₂, we get:
T₂ = (P₂/P₁) * T₁
T₂ = (105.2/82) * 273.15 K
T₂ = 348.85 K
Similarly, we can use the pressure at the third measurement (68.4 cm) and the temperature we just calculated (348.85 K) to find the temperature of the surrounding Carbon (IV) Oxide using the same equation:
T₃ = (P₃/P₁) * T₁
T₃ = (68.4/82) * 273.15 K
T₃ = 226.32 K
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HELP PLS HURRY...............................................................................
Answer:
C) - 1/10--------------------------------
Given two points:
[tex](-3, -7/2}) \ and \ (2, -4)[/tex]Find the slope of the line containing these points.
Slope equation:
[tex]m=(y_2-y_1)/(x_2-x_1)[/tex]Substitute coordinates and find the slope:
[tex]m=(-4-(-7/2))/(2-(-3))=(-4+7/2)/(2+3)=(-1/2)/5=-1/10[/tex]Answer:
-1/10
Step-by-step explanation:
To find:-
The slope of the line passing through the points (-3,-7/2) and (2,-4) .Answer:-
We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;
[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]
where ,
(x1,y1) and (x2,y2) are the coordinates of the two points.Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .
So on substituting the respective values, we have;
[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]
[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]
[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]
[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]
[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]
[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]
Hence the slope of the line is -1/10 .
Find two numbers that multiply to -24 and adds to 2
Answer:
6 and -4
Step-by-step explanation:
Let the first number be n.
Other number= [tex]\frac{-24}{n}[/tex]
Their sum= 2
n + [tex]\frac{-24}{n}[/tex]= 2
[tex]\frac{n^{2-24} }{n}[/tex]= 2
n²-24= 2n
You can solve this problem in either of these 2 ways:
i) Square Completion method:
n²-2n = 24
Half of the coefficient= [tex]\frac{2}{2}[/tex] =1
Its square= 1²= 1
n²-2n+1= 24+1
(n-1)²= 25
n-1= [tex]\sqrt{25}[/tex]
n-1= ±5
If n-1= 5,
n= 5+1
n= 6
If n-1= -5,
n= -5+1
n= -4
∴ the numbers are 6 and -4
ii) Equation Method:
n²-24= 2n
n²-2n-24= 0
a= 1,
b= -2,
-b= 2,
c= -24
n= -b±[tex]\sqrt{b^{2}-4ac }[/tex]/2a
n= 2±[tex]\sqrt{-2^{2}-4x1x-24[/tex]/2x1
n= 2±[tex]\sqrt{4+96}[/tex]/2
n= 2±[tex]\sqrt{100}[/tex]/2
n= 2±10/2
If n= [tex]\frac{2+10}{2}[/tex],
n= [tex]\frac{12}{2}[/tex]
n= 6
If n= [tex]\frac{2-10}{2}[/tex],
n= [tex]\frac{-8}{2}[/tex]
n= -4
∴ the numbers are 6 and -4
A recipe calls for mixing 8/5 cups of blueberries and 7/5
cups of strawberries. The mix is divided equally among 18 items. What fraction of a cup is used for each item?
3 cups of fruit mix is divided equally among 18 items.
Each item will contain 1/6 cup of fruit mix.
How to find out what fraction of a cup is used for each item ?First we need to divide the total amount of fruit mix by the number of items.
The total amount of fruit mix is :
8/5 cups of blueberries + 7/5 cups of strawberries
= (8/5 + 7/5) cups
= 15/5 cups
= 3 cups
So, 3 cups of fruit mix is divided equally among 18 items.
To find the fraction of a cup used for each item, we need to divide 3 cups by 18:
Copy code
3 cups ÷ 18 = 1/6 cup
Therefore, each item will contain 1/6 cup of fruit mix.
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Jack is w years old now his brother
is 3 years older than he is now if his brother is x years old express x in terms of w
The expression for Jack's brother's age is x = 3 + w
How to determine the valueIt is important that we know algebraic expressions are defined as expressions which are composed of variables, coefficients, constants, factors and terms.
These algebraic expressions are also identified with mathematical operations, such as;
SubtractionMultiplicationDivisionAdditionBracketParenthesesFrom the information given, we have that;
Jack is w years old
His brother is 3 years old than him
His brother's age is also x
This is represented as;
x = 3 + w
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3.5c – 1.5d > 50
Esa's Pastries sells cupcakes for $3.50 each and donuts for $1.50 each. The inequality above
represents the difference, in dollars, between cupcake sales and donut sales on a typical day
based on C, the number of cupcakes sold and d, the number of donuts sold. If Esa sold 200
donuts on a typical day, what is the minimum number of cupcakes she sold on that day?
Answers:
A) 25
B) 50
C) 100
D) 350
Answer:
C) 100
Step-by-step explanation:
[tex]3.5c - 1.5d > 50[/tex]
[tex]3.5c - 1.5(200) > 50[/tex]
[tex]3.5c - 300 > 50[/tex]
[tex]3.5c > 350[/tex]
[tex]c > 100[/tex]
If the pattern below follows the rule starting with two every consecutive line has a number that is one less than twice the previos line how many marbles must be in the sith line
Answer:
The pattern described in the question follows the rule that each consecutive line has a number that is one less than twice the previous line. Starting with 2 as the first line, the pattern can be written as follows:
1st line: 2
2nd line: 2(2) - 1 = 3
3rd line: 2(3) - 1 = 5
4th line: 2(5) - 1 = 9
5th line: 2(9) - 1 = 17
6th line: 2(x) - 1 (unknown)
To find the number of marbles in the 6th line, we can use the rule of the pattern and solve for x:
2(x) - 1 = 2(17) - 1 (substitute 17 for the number in the 5th line)
2x - 1 = 33
2x = 34
x = 17
Therefore, the 6th line of the pattern would have 17 marbles
Step-by-step explanation:
The pattern is described as having a number in each line that is one less than twice the previous line.
Write out the first few lines of the pattern, starting with 2 as the first line:
1st line: 2
2nd line: 2(2) - 1 = 3
3rd line: 2(3) - 1 = 5
4th line: 2(5) - 1 = 9
5th line: 2(9) - 1 = 17
To find the number of marbles in the 6th line, use the pattern rule and substitute the value for the 5th line:
6th line: 2(x) - 1
Substitute 17 for x (the value in the 5th line):
2(x) - 1 = 2(17) - 1
Simplify the right-hand side:
2(x) - 1 = 33
Add 1 to both sides:
2(x) = 34
Divide both sides by 2:
x = 17
Therefore, the 6th line of the pattern would have 17 marbles.
The complete pattern in the given question is: 2, 3, 5, 9, 17, 33.
How to solve for the complete pattern?To solve this problem, we need to apply the given rule to generate the numbers in the sequence and then find the sixth number.
Starting with two, we can apply the rule to generate the next few numbers:
First line: 2
Second line: 2(2) - 1 = 3
Third line: 2(3) - 1 = 5
Fourth line: 2(5) - 1 = 9
Fifth line: 2(9) - 1 = 17
Now we can apply the rule again to find the sixth number:
Sixth line: 2(17) - 1 = 33
Therefore, the sixth line must have 33 marbles.
The pattern starts with two, which is the first line.
The second line follows the given rule: "every consecutive line has a number that is one less than twice the previous line". We can apply this rule to the first line by multiplying it by 2 and subtracting 1: 2(2) - 1 = 3. Therefore, the second line has 3 marbles.
To find the third line, we can apply the same rule to the second line: 2(3) - 1 = 5. Therefore, the third line has 5 marbles.
Similarly, we can find the fourth line by applying the rule to the third line: 2(5) - 1 = 9. Therefore, the fourth line has 9 marbles.
We can find the fifth line by applying the rule to the fourth line: 2(9) - 1 = 17. Therefore, the fifth line has 17 marbles.
Finally, to find the sixth line, we apply the rule again to the fifth line: 2(17) - 1 = 33. Therefore, the sixth line has 33 marbles.
So, the complete pattern is: 2, 3, 5, 9, 17, 33.
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If a patient takes 25mg of medication twice a day, how many
grams will he take in 14 days?
If a patient takes 25 mg of medication twice a day, he will take 0.7 grams in 14 days.
To find out how many grams a patient will take in 14 days, we can follow these steps:
25mg × 2 = 50mg
50mg × 14 days = 700mg
700mg ÷ 1000 = 0.7 grams
Therefore, the patient will take 0.7 grams of medication in 14 days.
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A rectangular region has an area of 299 square miles. The length of the region is 10 miles longer than its width. Find the length and width of the region.
Answer:
Let's represent the width of the region by "w". According to the problem, the length of the region is 10 miles longer than the width, so we can represent the length as "w + 10".
The formula for the area of a rectangle is:
Area = Length x Width
So we can write an equation for the area of this region:
299 = (w + 10) x w
Expanding the right side, we get:
299 = w^2 + 10w
Now we can rearrange this equation into standard quadratic form:
w^2 + 10w - 299 = 0
We can solve for "w" by using the quadratic formula:
w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 10, and c = -299. Plugging in these values, we get:
w = (-10 ± sqrt(10^2 - 4(1)(-299))) / 2(1)
w = (-10 ± sqrt(1180)) / 2
w = (-10 ± 34.351) / 2
We can ignore the negative solution, since the width of the region cannot be negative. So the width is:
w = (-10 + 34.351) / 2
w = 12.176
We can round the width to the nearest mile, since we can't have a fractional width. So the width is approximately 12 miles.
Now we can use the equation we derived earlier to find the length:
299 = (w + 10) x w
299 = (12 + 10) x 12
299 = 22 x 12
So the length is 22 miles.
Therefore, the width of the region is approximately 12 miles and the length is 22 miles.
The construction of a tangent to a circle given a point outside the circle can be justified using the second corollary to the inscribed angle theorem. An alternative proof of this construction is shown below. Complete the proof. (5 points)
Given: Circle C is constructed so that CD = DE = AD; is a radius of circle C.
Prove: is tangent to circle C.
Answer:
Proof:
Draw circle C with center at point A and radius AD = CD = DE.
Draw point P outside the circle C.
Draw segment AP and extend it to intersect the circle at point B.
Draw segment BD.
Draw segment CP.
Note that triangle BCD is isosceles, since CD = BD. Therefore, angle BDC = angle CBD.
Since angle BDC is an inscribed angle that intercepts arc BC, and angle CBD is an angle that intercepts the same arc, then angle BDC = angle CBD = 1/2(arc BC).
Since CD = DE, then angle CED = angle CDE. Therefore, angle DCE = 1/2(arc BC).
Since angles BDC and DCE are equal, then angles BDC and CBD are also equal, and triangle BPC is isosceles. Therefore, segment BP = segment PC.
Since BP = PC, then segment CP is perpendicular to segment BD, by the Converse of the Perpendicular Bisector Theorem.
Therefore, segment CP is a tangent to circle C at point B.
Hence, the proof is complete.
Answer:
I got a good grade on it yw ;)
Jim donates 13% if his paycheck every month to a local animal shelter his pizza this month was $1398 how much money did he donate
Answer:
181.74
Step-by-step explanation:
I hope you meant the paycheck was $1398.. if not then this is wrong.
So you take 1398 and multiply it by 0.13 and then you get 181.74. So Jim donated 181.74 this month.
The y-intercept of f(x)=3(12)x
is ____________________ the y-intercept of the function in the graph. is it greater than less than or equal to
The y-intercept of the given function is 0.
What is y-intercept?A y-intercept is the place where a line or curve crosses, or touches, the y-axis the vertical, often darkened line in the center of a graph.
Given is a function f(x) = 3(12)x, we need to find the y-intercept.
The general equation of a line is given by
y = mx+c
Where m is the slope and the c is the y-intercept,
But in our equation, the y-intercept is not available that means it is zero,
We can write the equation as ;-
f(x) = 3(12)x + 0
Hence, the y-intercept of the given function is 0.
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Anyone help wit this
The value of x is equal to 10.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a line segment is intersected by a straight line which is parallel to the third (3rd) side of the line segment, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
21/(x - 3) = 27/(x - 1)
By cross-multiplying, we have the following:
21(x - 1) = 27(x - 3)
21x - 21 = 27x - 81
27x - 21x = 81 - 21
6x = 60
x = 60/6
x = 10.
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Find the rate of change between the following points:
(1,-6)
(-6,2)
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
to get the slope of any straight line, we simply need two points off of it, let's use those above
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{1}}} \implies \cfrac{2 +6}{-7} \implies \cfrac{ 8 }{ -7 } \implies - \cfrac{8 }{ 7 }[/tex]