Answer:
[tex]\frac{x}{3} \leq 5[/tex]
Hope this helps! :)
Identify the measure of angle x:
Answer:
79°
Step-by-step explanation:
All three of the angles form a straight line = 180°
28 + x + 73 = 180
x = 79°
Answer:x=79
Step-by-step explanation:
Find the equation of a line perpendicular to 4x + 3y = -24 that passes through
the point (-8, 3).
The equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.
What is the equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
4x + 3y = -24 and point (-8, 3).
Calculate the slope,
3y = -4x - 24
y = -4 / 3 x - 8
so, m = -4 / 3
The slope of the perpendicular line, M = - 1 / m
M = - 1 / -4 / 3 = 3 / 4
Calculate the equation of the line as shown below,
y - 3 = 3 / 4 [x - (-8)]
y - 3 = 3 / 4 [x + 8]
4y - 12 = 3x + 24
4y = 3x + 36
Therefore, the equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.
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5. An isosceles triangle is shown below with side lengths of 12 and a base length of 20. If a line segment AD is drawn from A to side BC such that D lies on BC and AD 1 BC then find the length of AD in simplest radical form.
Answer:
AD = 16
Step-by-step explanation:
Using the Pythagorean Theorem:
A2 + D2 = C2
122 + D2 = 202
144 + D2 = 400
D2 = 256
D = 256 = 16
Samra's guardians invested money for her into a 529 college savings plan, which compounds annually. The growth of the savings plan per year, x, can be represented by the exponential function f(x) = 400(1. 02)x. What is the meaning of the y-intercept in the context of the problem?.
The exponential function f(x) = 400(1. 02)ˣ is $400 does the y-intercept mean in the context of the issue.
Given that,
Samra's guardians made a yearly compounding investment on her behalf in a 529 college savings plan. The exponential function f(x) = 400(1. 02)ˣ can be used to describe the growth of the savings plan on an annual basis, x.
We have to find what does the y-intercept mean in the context of the issue.
We know that,
The exponential function is f(x) = 400(1. 02)ˣ.
In this instance, the significance of the y-intercept in relation to the situation at hand is that the beginning value of the investment is equal to $400.
Therefore, The exponential function f(x) = 400(1. 02)ˣ is $400 does the y-intercept mean in the context of the issue.
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a bag contains 80 balls numbered 1, . . . , 80. before the game starts, you choose 10 different numbers from amongst 1, . . . , 80 and write them on a piece of paper. then 20 balls are selected (without replacement) out of the bag at random. (a) what is the probability that all your numbers are selected? (b) what is the probability that none of your numbers is selected? (c) what is the probability that exactly 4 of your numbers are selected?
The required probability for P(all numbers are chosen), P(none of them are chosen), P (precisely four are chosen) are 0.24094, 0.75906, 0.1473 respectively.
What is probability?A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.
According to question:The complete likelihood of picking any 20 arbitrary balls out of 80 is ⁸⁰C₂₀ . We use mix since the request for determination doesn't make any difference
a) P(all numbers are chosen)
¹⁰C₁₀ are our numbers,⁷⁰C₁₀ is the choice of other ten numbers separated from our numbers.
So, ¹⁰C₁₀×⁷⁰C₁₀ /⁸⁰C₂₀ = 0.24094
b) P(none of them are chosen)
Since our numbers are not really chosen, we accept that every one of the numbers chose are from the other 70.
So, 1 - 0.24094 = 0.75906
c) P (precisely four are chosen)
Just four from our numbers are chosen and the rest 16 from the other 70 numbers.
Then, ¹⁰C₄×⁷⁰C₁₆ /⁸⁰C₂₀ = 0.1473
Thus, required probabilities are 0.24094, 0.75906, 0.1473 respectively.
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Please help!!! i need this done by tonight!! 50 points!!
The equation of best fit is y = (-22/5)x + 10.
What is an equation of a line?
The equation of a line is given by:
y = mx + c where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The following coordinates are given:
Pick two coordinates.
(0, 10) and (25, -100)
The equation of best fit.
y = mx + c
Now,
m = (-100 - 10) / (25 - 0)
m = -110 / 25
m = -22/5
Now,
(0, 10) = (x, y)
10 = (-22/5) x 0 + c
c = 10
Now,
y = mx + c
y = (-22/5)x + 10
Thus,
Using the coordinates the equation of best fit is y = (-22/5)x + 10.
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Ashley is ordering pizza. When ordering the pizza, she must choose one type of crust, one type of cheese, one type of meat, and one type of vegetable. The restaurant that Ashley is ordering from has 3 types of crust, 5 types of cheese, 6 types of meat, and 4 types of vegetables. How many different pizza combinations are available?
250/100 in simplest form
Answer:
5/2 is the simplest g will form.....
how to make 90/450 a percent
Answer:
20%
Step-by-step explanation:
90 of 450 can be written as:
90
450
To find percentages, we need to find an equivalent fraction with a denominator of 100. Multiply both the numerator & denominator by 100
90
___
450
×
100
100
= (
90 × 100
450
) ×
1
100
=
20
100
Therefore, the answer is 20%
If you are using a calculator, simply enter 90÷450×100 which will give you 20 as the answer.
Is the domain of a square root all real numbers?
Domain of square root is not all real numbers.
Domain of a function:
The domain of a function is the set of input values (x) for which it produces an output value.
Like if we consider a function y = f(x)
then input inside function that is x is know as domain of function.
First we write square root function as y =
So inside root negative numbers are not allowed so value of x should be positive numbers means x>=0.
So domain of square root function [0, ∞).
Domain of square root function is positive real numbers.
Not all real numbers because in all real numbers both positive and negative real numbers come.
Negative real numbers can not be input for square root function.
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Sam and Julia are running a lemonade stand. Sam is selling regular lemonade for $0.50 per cup, while Julia is selling pink lemonade for $0.75 per cup. In total, they sell 140 cups of lemonade and make $90. Define x = number of regular lemonade cups that Sam sells Define y = number of pink lemonade cups that Julia sells (a) Write a system of equations that represents this situation. (b) Find how many cups of regular lemonade that Sam sold. Response area (c) Find how many cups of pink lemonade that Julia sold. Response area
a) The system of equations that represents this situation is given as follows:
x + y = 140.0.5x + 0.75y = 90.b) The number of cups of regular lemonade sold is given as follows: 60.
c) The number of cups of pink lemonade sold is given as follows: 80.
How to obtain the amounts?The amounts are obtained with a system of equations, in which the variables are as defined in the problem.
Variable x: number of regular lemonade cups.Variable y: number of pink lemonade cups.They sell 140 cups, hence:
x + y = 140.
y = 140 - x.
They earn a total of $90, hence, considering the amount earned per cup:
0.5x + 0.75y = 90.
Replacing the first equation into the second, the variable x is obtained as follows:
0.5x + 0.75(140 - x) = 90.
0.25x = 15
x = 15/0.25
x = 60.
Then the variable y has a value of:
y = 140 - x = 140 - 60 = 80.
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find the next three terms.
-3, 12,-48, 192,-768...
Answer:
3072, -12288, 49152
Step-by-step explanation:
[tex]-3*-4=12\\12*-4=-48\\-48*-4=192\\192*-4=-768\\-768*-4=3072\\3072*-4=-12288\\-12288*-4=49152\\\\Answer= -3,12,-48,192,-768,3072,-12288,49152[/tex]
write the function in terms of unit step functions. find the laplace transform of the given function. f(s)
The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x
Rewrite f in terms of the unit step function:
[tex]f(t) \left \{ {{y=5} for 0\leq t \leq 7\atop {x=-3}} \rightfor t\leq 7[/tex]
⇒ f(t) = 5{u(t) -u(t -7) - 3u (t -7)}
= 5u(t) - 8u (t-7)
Recall the time-shifting property of the Laplace transform:
L I u(t - c)f(t -c) I
= e⁻ᵃˣ L[f(t)]
and the Laplace transform of a constant function,
L(K) = [tex]\frac{k}{a}[/tex]
So we have
L{f(t)} = 5u(t) - 8u (t-7)
= 5 L[1] - 8e⁻⁷ˣ
= 5 - 8e⁻⁷ˣ/ x
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Which of the correlation values represent a perfect linear relationship between x and y?
a. 0.5
b. 1
c. 100
d. -1
e. 0
The correlation values 1 and -1 represent a perfect linear relationship between the two variables x and y.
Step to Step explanation:
To represent perfect linear relationship between two variables the correlation values should be 1 and -1.When correlation value is equal to 1 it represent the positive linear relationship between two variables x and y.Slope of the correlation value positive 1 indicates the increasing slope.When correlation value is equal to -1 it represent the negative linear relationship between two variables x and y.Slope of the correlation value negative 1 indicates the decreasing slope.Therefore, the perfect linear relationship between two variables x and y is given correlation value 1 and -1.
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a 20 foot ladder is placed 5 feet from the base of a building. how high on the building will the ladder reach?
As calculated with the help of Pythagorean theorem, The ladder will reach 19.36 feet high on the building.
What is Pythagorean theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle. The square whose side is the hypotenuse, or the side across from the right angle, has an area equal to the sum of the areas of the squares on its other two sides. The Pythagorean equation, which connects the lengths of the sides B, P, and the hypotenuse H, can be used to express this theorem.
H² = B² + P²
As given in the question,
the length of the ladder is 20 ft. which will work as a hypotenuse of a right angled triangle,
The base is 5 ft.
we need to find the perpendicular line to the base.
Applying Pythagorean theorem.
H² = B² + P²
20² = 5² + P²
400 = 25 + P²
400 - 25 = P²
P = 19.36 ft.
Therefore, the ladder will go 19.36 ft. high on the building.
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Please hleppp me memmemm
Tariq went shopping for a new pair of pants. Sales tax where he lives is 4%. The price of the pair of pants is $30. Find the total price including tax. Round to the nearest cent.
Answer:
Step-by-step explanation:
4% = 4/100
4/100 x 30 = 1.2
30 + 1.2 = 31.20 (nearest cent)
Answer:
31.20
Step by step explanation: I got it from delta
In 2012, there are approximately 275 students in the Delaware High School band. In 2018, that number increased to 305. Find the annual rate of change from 2012 to 2018 in the number of students.
Using exponential function, the annual rate of change in the school is 1.74%
Exponential FunctionExponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function)
In this problem, the annual rate of change can be calculated as
A = P(1 + r)ˣ
r = ratex = timeLet's substitute the values into the equation and solve;
305 = 275(1 + r)⁶
r = 0.0174
r = 0.0174 * 100
r = 1.74%
The annual rate of change is 1.74%
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two dice are tossed. what is the probability that their sum will be 6, given that exactly one face shows 2? (round your answer to three decimal places.)
The probability that their sum will be 6 is 1/6.
What is probability?
The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.
Here are all rolls of the dice, the sample space,
which contains 36 elements:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
If one face shows a 2, then there are 6 possible faces on the other die.
Only one of those is a 4 which would make the sum of 6.
Hence, the probability that their sum will be 6 is 1/6.
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A survey is given to children and adults about their favorite meal of the day.
*Breakfast is preferred by one and half times more children than adults.
*Children and adults both had 24 respondents for dinner.
*There were 62 adults who responded lunch, twice as great as the number of children who responded lunch. The results are shown in the table.
Which category has an error in the table?
Breakfast
Lunch
Adults
Children
Table below:
The category has an error in the table is A. breakfast.
How to illustrate the survey?A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted by phone, mail, or the internet, as well as on street corners or in shopping malls.
Historically, survey research has included large amounts of population-based data collection.
The primary goal of this type of survey research was to quickly obtain information describing the characteristics of a large sample of individuals of interest.
The category has an error in the table is breakfast. In this case, the children should be 45 and not 30.
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what does the central limit theorem say about the shape of the distribution of the sample means? the distribution will be approximately normal regardless of sample size. the distribution will be normal when all sample means within 2 standard deviations of the actual mean are considered. the distribution will be approximately normal when the standard deviation of the sample means is the same as the population standard deviation. the distribution will be approximately normal when the sample size is large. the distribution will be approximately normal when the sample size is small.
Thus, the distribution will be approximately normal when the sample size is large.
What is central limit theory ?According to the central limit theorem, even if a population isn't normally distributed, if you take sufficiently big samples from it, the sample means will be.
Here,
the central limit theorem say about the shape of the distribution of the sample means because
If the sample size is big, the solution will be when the distribution is roughly normal.
thus, the distribution will be approximately normal when the sample size is large.
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Select the correct answer. Which statement is true about this equation? 3(-y + 7) = 3(y + 5) + 6 A. The equation has one solution, y = 0. B. The equation has one solution, y = -1. C. The equation has no solution. D. The equation has infinitely many solutions.
Answer:
The statement that is true about the given equation is that it has no solution. This can be seen by rearranging the terms on both sides of the equation and then solving for y. When we do this, we get:
3(-y + 7) = 3(y + 5) + 6
-3y + 21 = 3y + 15 + 6
-6y = -12
y = 2
However, when we substitute this value of y back into the original equation, we find that it does not satisfy the equation. This means that there is no value of y that can make the equation true, so the equation has no solution.
Step-by-step explanation:
I need help with quadrilateral proofs
The completed two-column table to prove that ABCD is a rectangle is presented as follows;
Step Statement [tex]{}[/tex] Reason
1 [tex]{}[/tex] ΔABD ≅ ΔDCA Given
[tex]{}[/tex] [tex]\overline{AD}[/tex] ≅ [tex]\overline{BC}[/tex]
2. [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex] Reflexive property
3. [tex]\overline{CA}[/tex] ≅ [tex]\overline{CA}[/tex] [tex]{}[/tex] Reflexive property
4. [tex]{}[/tex] ∠CAD ≅ ∠BDA CPCTC
5. [tex]{}[/tex] [tex]\overline{AE}[/tex] ≅ [tex]\overline{ED}[/tex] Side length of isosceles triangle ΔAED
6. [tex]{}[/tex] [tex]\overline{AB}[/tex] ≅ [tex]\overline{ED}[/tex] CPCTC
7. [tex]{}[/tex] ΔABD ≅ ΔBCD SSS
8. ΔDCA ≅ ΔABC [tex]{}[/tex] SSS
9. ∠B ≅ ∠C ≅ ∠D ≅ ∠A [tex]{}[/tex] CPCTC
10. [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A [tex]{}[/tex] Definition of congruency
11. [tex]{}[/tex] ∠B + ∠C + ∠D + ∠A = 360° [tex]{}[/tex] Angles in quadrilateral
12. [tex]{}[/tex] 4·∠B = 360° Substitution property
13. [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A = 90° Substitution property
14. [tex]{}[/tex]ABCD is a rectangle Definition of a rectangle
What is a rectangle?A rectangle is a quadrilateral that has four interior angles that are right angles (90°) each and in which the length of the adjacent sides are different.
The details of the reasons used to prove that ABCD is a rectangle are presented as follows;
Reflexive property
The reflexive property of congruency states that a part is congruent to itself
CPCTC
CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent
Isosceles triangle
An isosceles triangle is a triangle with a pair of congruent sides and a pair of congruent base angles
SSS
The Side-Side-Side (SSS) congruency postulate states that two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle
Definition of congruency
A geometric shape is congruent to another geometric figure if they have the same measurement
Angles in a quadrilateral
The sum of the interior angles in a quadrilateral is 360°
Substitution property
The substitution property of equality states that if a = b then b can substitute a in equations and expressions, without changing their value
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6x+2=4x+3
Please help asap I been doing the work for so long and can’t get a final answer
Answer x=1/2
Step-by-step explanation:
6x+2=4x+3
2x+2=3
2x=1
x=1/2
Answer:
x= 1/2
Step-by-step explanation:
x=1/2
6x+2=4x+3
-4x -4x
2x+2=3
-2 -2
2x=1
/2 /2
x=1/2
A football field i 300 ft long. A loth moving very quickly travel 60 ft every 5 min. Baed on thi ratio how many minute would it take the length of a football field
Using simple unitary method, the time taken to take the length of the football field is 25min.
What do you mean by number system?The system for naming or representing numbers is known as the number system or numeral system. We are aware that a number is a mathematical value that aids in the measurement and counting of items as well as in several mathematical operations.
What do you mean by unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Loth travels 60 ft in 5 min.
Loth travels 1 ft in 5/60 min.
Loth travels 300 ft in 5/60 * 300 min.
=1/12 * 30
=25min
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6. Tom's cousin, George, is three times as old as Tom. In 15
years, Tom will be two-thirds as old as his cousin, George.
How old is each of them in 15 years?
The answer to this Question based on ages is 20 years and 30 years
What is age?
The age is measure of how old the person is. It also gives us idea about how many years before he was born This data is used at various places in application forms medical form etc
Let age of Tom be x and age of George be y
given 1st condition george is 3 times as old as Tom
hence we can write y = 3x
After 15 years age of tom = x + 15 and age of George be y + 15
according to 2nd condition
x + 15 = 2/3(y + 15)
3x + 45 = 2y + 30
2y - 3x = 15
put y = 3x here
2(3x) - 3x = 15
3x = 15
x = 5
and y = 3(5)
y = 15
present age of tom = 5 years and after 15 years he will be 20 years old
present age of george = 15 tears and after 15 years he will be 30 years old
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A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup (in cm) that will use the smallest amount of paper. (round your answers to two decimal places. ).
The height and radius of the cup that will use the smallest amount of paper are 3.86 cm and 2.72 cm. The result is obtained by using the first derivative .
How to find the dimension of a cone?To find the height and radius of a cone for the smallest surface area, we can use the first derivative dS/dh. We then equate it to 0 for the maximum value.
The volume of a cone-shaped paper drinking cup is 30 cm³. Find the height and radius for the smallest amount of paper!
The radius of the cone can be expressed as
V = 1/3 (πr²h)
30 = 1/3 (πr²h)
90 = πr²h
r² = 90/πh
The surface area of the cone can be expressed as
S = πrs
[tex]S = \pi r \times \sqrt{h^{2} + r^{2}}[/tex]
[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{{h^{2} + \frac{90}{\pi h}[/tex]
[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{\frac{(\pi h^{3} + 90)}{\pi h}[/tex]
[tex]S = \sqrt{90} \times \sqrt{\frac{(\pi h^{3} + 90)}{h^{2}}[/tex]
[tex]S = \sqrt{90} \times \sqrt{\pi h + \frac{90}{h^{2}} }[/tex]
The 1st derivative is
[tex]\frac{dS}{dh} = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]
[tex]0 = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]
The height for the smallest amount of paper is
π - 180/h³ = 0
π = 180/h³
h³ = 180/π
h³ = 57.32
h = 3.86 cm
The radius for the smallest amount of paper is
r² = 90/πh
r² = 90/π(3.86)
r² = 7.42
r = 2.72 cm
Hence, the dimension of the cone-shaped paper drinking cup for the smallest amount of paper is
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Cai is ordering a taxi from an online taxi service. He has to pay a flat charge just to order the taxi, and then has to pay per mile, depending on how far he travels. He wrote an equation to represent his total cost, y=1. 3x+2y=1. 3x+2, where yy represents the total cost in dollars and cents, and xx represents the number of miles he travels. What could the number 1. 3 represent in the equation?.
The equation of cost of taxi payed by cal is,
y=1. 3x+2
here , y --> total cost of taxi
x --> distance travelled by him
Cofficient of x i.e., 1.3 represents the cost/rate of taxi per mile .
We have given a equation of total cost pay by Cal on ordering a taxi from online taxi service. The equation is
y = 1.3x+2
where, y represents the total cost in dollars
x represents the number of miles he travels ; 2 is fixed charge
Since, x represents the number of miles he travels then the cofficient of x is representing the taxi rate or cost per mile . So, that when we multiply 1.3 with number of miles he travel(i.e x ) we get the total cost on travelling x distance.
After adding the total cost of travelling with fixed charge of taxi we get total cost of journey.
Hence, 1.3 represents the cost per mile.
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Jeremy has 50 ft of fencing to enclose a rectangular-pen for his dog. He plans on using a side of his house for one side of the pen. What dimensions will produce an enclosed area of 288 ft?
The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.
What is the dimension of length and width?We know that,
P = l + 2w
50 = l + 2w
50 - 2w = l
A = l x w
288 = (50 - 2w)w
288 = 50w -2w²
2w² - 50w + 288
By dividing throughout by 2
w² - 25w + 144
This is in quadratic equation form.
By applying quadratic formula,
w = (-(-25) ± [tex]\sqrt{(-25)^{2}-4*1*144[/tex]) / 2
w = (-(-25) ± 7)/2
w1 = (-(-25) + 7)/2
w1 = (25 + 7) / 2
w1 = 16
w2 = (-(-25) - 7)/2
w2 = (25 - 7) / 2
w2 = 9
By substituting the values in eq1,
A = l x w
if w = 16
288 = l x 16
l = 288/16
l = 18
if w = 9
288 = l x 9
l = 288/9
l = 32
The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.
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PLEASE ANSWER ASAP! Choose ALL equations that would create a parallel line to y=78x+9
The equation of the parallel to y = 7/8x + 9 will be y = 7/8x+11, 7x - 8y = 3, and (y-6) = 7/8(x-1).
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the equation of the line is y = 7/8x+9. For the equation to be parallel the slope of the line must be the same.
The equations having the same slope of the line as that of y = 7/8x + 9 are,
y = 7/8x+11,
7x - 8y = 3,
(y-6) = 7/8(x-1)
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