The perimeter of the triangle is 23x + 17.
What is the perimeter of the triangle ?Perimeter is simply the sum of all sides of a polygon.
Given the sides of the triangle;
Side one = 10x + 19
Side two = 12x - 2
Side three = x
To find the perimeter, we add the sides
Perimeter = Side one + Side two + side three
Perimeter = 10x + 19 + 12x - 2 + x
Collect and add like terms
Perimeter = 10x + 12x + x - 2 + 19
Perimeter = 23x - 2 + 19
Perimeter = 23x + 17
Therefore, the perimeter is 23x + 17.
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A function is given.
f(x) = x3 − 7x2; x = 0, x = 10
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
On solving the provided question, we can say that the function is
[tex]f(z) = 3 - 4z^2[/tex] and f(-2) = -13 and f(0) = 3.
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
the function is
[tex]f(z) = 3 - 4z^2[/tex]
[tex]f(-2) = 3 - 4(-2)^2[/tex]
= 3 - 4(4)
= 3 - 16
=-13
[tex]f(0) = 3 - 4(0)^2[/tex]
= 3 - 4(0)
= 3 - 0
= 3
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Point R is located at (1,1) on the coordinate plane. Point R is reflected over the y-axis to create point R ′ . Point R' is then reflected over the x-axis to create point R''. What ordered pair describes the location of R''?
Answer:
Step-by-step explanation:
Here's a step-by-step explanation of the reflections:
Point R is located at (1, 1) on the coordinate plane.
Reflection over the y-axis: This reflection changes the sign of the x-coordinate. In other words, if the point (x, y) is reflected over the y-axis, the reflected point will be ( -x, y). So, for point R at (1, 1), the reflection over the y-axis creates R' at (-1, 1).
Reflection over the x-axis: This reflection changes the sign of the y-coordinate. In other words, if the point (x, y) is reflected over the x-axis, the reflected point will be (x, -y). So, for point R' at (-1, 1), the reflection over the x-axis creates R'' at (-1, -1).
So the final location of R'' is at the ordered pair (-1, -1).
(a) Describe the relationship among the lengths of the segments formed by the two secants. You may use words and/or an equation.
(b) Suppose = 3 in., = 2 in. and = 5 in. Is it possible to find the length of ? If so, show how to find the length. If not, explain why not.
Answer:a
Step-by-step explanation:
At sunrise the distance from the top of the Great Sphinx in Egypt to the end of its shadow is measured to be 220 ft. The distance from the top of the head of a 6 ft-tall person who is standing next to the Sphinx to end of their shadow is measured to be 20 ft. How tall is the Great Sphinx? 100 points + brainliest
70.0 ft
66.0 ft
733.3 ft
54.5ft
Answer:
132ft
Step-by-step explanation:
The height of the Great Sphinx can be found by using the relationship between the height of an object, the length of its shadow, and the angle of elevation of the sun.
Let h1 be the height of the Great Sphinx and h2 be the height of the person. We know that the length of their shadows are 220 ft and 20 ft, respectively.
Since the sun is at the same elevation for both objects, we can set up the following proportion:
h1/220 = h2/20
Cross multiplying, we get:
h1 = (h2 * 220) / 20
Plugging in h2 = 6 ft, we get:
h1 = (6 * 220) / 20 = 132 ft
So, the height of the Great Sphinx is approximately 132 ft.
Thus, the correct answer is 132 ft, which is not in the options provided, but it is a reasonable estimate of the height of the Great Sphinx.
Cone B is the image of cone A after dilation by a scale factor of 1/4.
If the volume of cone B is 1 m³, find the volume of cone A, the preimage.
The volume of the Cone A will be 4m³.
What is a cone?
A cone is a shape constructed by connecting a common point, known as the apex or vertex, to all the points of a circular base using a collection of line segments (which does not contain the apex). The height of the cone is the distance from the vertex to the base. The radius of the circular base has been measured. The slant height is the length of the cone from the apex to any point on the perimeter of the base. Based on these values, formulae for the cone's surface area and volume have been developed. The cone in the illustration is characterised by its height, radius of base, and slant height.
Volume of cone=πr²h where r=radius of base and h=height of cone
Curved surface area=πrL , where L=slant height
Now,
As given Cone B is the image of cone A after dilation by a scale factor of 1/4. If the volume of cone B is 1 m³
After dilation volume also decreases/increases with respect to scale factor of dilation. Here scale factor is 1/4
and Then volume of A=1*4
=4 m³
hence,
The volume of the Cone A will be 4m³.
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Answer: it is actually 64m^3
Step-by-step explanation:
i did it and this was the right answer
Kai, a seventh grader, wants to determine the average number of times the families in his neighborhood visit the pool during the summer. He samples the families of four of his classmates. Which improvements could Kai make to his sample to increase the validity of the results? Check all that apply. Sample more families/ sample families that have children who are not in seventh grade/ sample families that do not have children /sample families whose answer to the survey question is predetermined/ sample families living in every third house in the neighborhood
The correct options are sample more families, sample families having children who are not in seventh grade.
Sample families that do not have children. Sample families living in every third house in neighborhood.
To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:
Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.
Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.
Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.
Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of
sampling bias.
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Question 30
A hacker is trying to guess someone's password. The hacker knows (somehow) that the password is 4 digits
long, and that each digit could be a number between 0 and 4. Assume that the hacker makes random
guesses. What is the probability that the hacker guesses the password on his first try? Round to six decimal
places.
Probability:
The probability that the hacker guesses the password on his first try is, 0.001600.
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The probability of a hacker guessing the correct password on their first try would be 1 in 10,000, since there are a total of 5⁴ possible combinations of 4 digits, each between 0 and 4, inclusive.
The probability can be calculated as:
= 1 / 5⁴
= 1 / 625
= 0.0016
Rounded to six decimal places, the probability is: 0.0016 = 0.001600.
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What is the value of x? enter your answer, as a decimal, in the box. Do not round your answer. X= a right triangle with vertices labeled as a, b, and c. Side c b is the base and the top vertex is a. Side a b contains a midpoint d. A line segment drawn from c to d bisects angle a c b into two parts labeled as a c d and b c d. Angles a c d and b c d are marked with single arc. Side a c is labeled as 4. Base c b is labeled as 7. 5. Segment a d is labeled as 3. Segment b d is labeled as x.
In right triangle ACB with CD bisects angle ACB and intersects at midpoint of AB at point D the value of x is equal to 5.625.
In right triangle ABC,
BC is the base.
Midpoint of AB is D.
CD bisects ACB.
Measure of ∠ACD = Measure of ∠BCD
AC = 4
BC = 7.5
AD = 3
BD = x
CD bisects angle ACB and intersect at midpoint of AB at point D.
This implies
BD / AD = BC / AC
⇒x / 3 = 7.5 / 4
⇒ x = ( 7.5 × 3 ) / 4
⇒ x = 22.5 / 4
⇒ x = 5.625
Therefore, the value of x in the right triangle ACB with given dimensions is equal to 5.625.
The above question is incomplete , the complete question is :
What is the value of x? Enter your answer, as a decimal, in the box. x= A right triangle with vertices labeled as A, B, and C. Side C B is the base and the top vertex is A. Side A B contains a midpoint D. A line segment drawn from C to D bisects angle A C B into two parts labeled as A C D and B C D. Angles A C D and B C D are marked with single arc. Side A C is labeled as 4. Base C B is labeled as 7.5. Segment A D is labeled as 3. Segment B D is labeled as x.
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A figure has a perimeter of 12 units. Which describes the perimeter of the figure after a dilation with a scale factor of 4?
The perimeter of the figure after a dilation with a scale factor of 4 is
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}\\[/tex]
Thus, scale factor is the ratio of the new measurement to the old measurement.
Given;
The perimeter= 12units
Scale factor=4
Now,
Dilation with the given scale factor;
= 12*1/4
=12/4
=3
Therefore, dilation by the given scale factor will be 3.
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Find an equation of the plane.
the plane that contains the line
x = 2 + t,
y = 4 − t,
z = 3 − 3t
and is parallel to the plane
5x + 2y + z = 3
The equation of the plane containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3 is 5x + 2y + z = 21
What is a plane?
Any flat, three-dimensional, infinitely long surface is considered to be a plane. It can alternatively be thought of as the two-dimensional equivalent of a point with zero dimensions, a line with one dimension, and a space with three dimensions.
Given that, a plane is containing the line x = 2 + t, y = 4 − t, z = 3 − 3t and is parallel to the plane 5x + 2y + z = 3
Any plan e parallel to the plane 5x + 2y + z = 3 , should be in the form of 5x + 2y + z = k
Now, this plane should contain the line mentioned above
On substituting the terms,
5(2 + t) + 2(4 - t) + (3 - 3t) = k
10 + 5t + 8 - 2t + 3 -3t = k
21 = k
Therefore, The equation of the required plane is 5x + 2y + z = 21
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Thomas peters purchased a new suv for $32,984. He received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. What is the final price?.
The final price of Thomas Peters' new SUV is $30,309 , can be calculated by subtracting the rebates from the initial cost.
The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:
Final Price = $32,984 - $2,175 - $500
Final Price = $30,309
Therefore, the final price of Thomas Peters' new SUV is $30,309.
It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.
By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.
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The length of the dashed line in the circle
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?
The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.
In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:
d = 2r
In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get
q = 17.708 - 4.893 - 4.893
By solving this, we get
q = 7.922
Hence, the length of the dotted line would be 7.922 ft.
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Consider the function below.
f(x)=8/x−6
What would be the output if the input is 8?
8/14
8/6
2 1/3
4
The input is 8, the output of the function f(x) would be -5.
What is the function?
Function is a relationship or expression involving one or more variables. It has a set of input and outputs.
Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences. The modern definition of function was first given in 1837 by the German mathematician Peter Dirichlet
To find the output of the function f(x) when x is 8, we substitute x = 8 into the function and simplify:
f(x) = 8/x - 6
f(8) = 8/8 - 6
f(8) = 1 - 6
f(8) = -5
Hence, if the input is 8, the output of the function f(x) would be -5.
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Find R. Round to the nearest tenth.
Answer:
letter R rounded off to the nearest tenth is 40
15 is the answer because this is the nearest
Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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The depth of a certain part of the Earth's seabed is 36,078 feet. How deep is it in (a) fathoms ? (b) leagues (marine)?
Step-by-step explanation:
(a) To convert feet to fathoms, we can use the conversion factor 1 fathom = 6 feet. Hence, we can divide the depth in feet by 6 to find the depth in fathoms:
36,078 feet / 6 feet/fathom = 6,013 fathoms
So the depth of the seabed is 6,013 fathoms.
(b) To convert feet to leagues (marine), we can use the conversion factor 1 league (marine) = 5,556 feet. Hence, we can divide the depth in feet by 5,556 to find the depth in leagues (marine):
36,078 feet / 5,556 feet/league (marine) = 6.52 leagues (marine)
So the depth of the seabed is approximately 6.52 leagues (marine).
What is the Volume of the prism below
Answer:
140
Step-by-step explanation:
(5*7*8)/2= 280/2 =140
For four months, you have saved $25 per month.
You now have $175 in your savings account.
a. Use your result from Exploration 2 to
write an equation that represents the
balance A after t months.
Answer:
A=25t.
Step-by-step explanation:
..........................
solve. a certain phone call costs 75 cents for the first 3 minutes plus 15 cents for each additional minute. if the call lated x minutes and x is an integer greater than 3, what is cost in dollars
(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35
While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes
According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15
cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315
, so we need to find whether the cost is greater than 315 cents.
(1) The cost of the phone call was less than $4.16. Not sufficient.
(2) The cost of the phone call was greater than $3.35. Sufficient.
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simplify the equation
Answer:
[tex]a \sqrt[5]{b} [/tex]
Step-by-step explanation:
solution Given:
[tex] \sqrt[5]{ {a}^{3} {b}^{2} } \times \sqrt[5]{ {a}^{2}{b }^{ - 1} } [/tex]
since i indices rule if the power is same it can be multiplied or divided.
[tex] \sqrt[5]{ {a}^{3} {b}^{2} \times {a}^{2} {b}^{ - 1} } [/tex]
since power is added of like terms in multiplication
[tex] \sqrt[5]{ {a}^{3 + 2} {b}^{2 - 1} } [/tex]
again simplifying
[tex] \sqrt[5]{ {a}^{5} b} [/tex]
by using indices formula
[tex] \sqrt[x]{ {a}^{y} } = {a}^{ \frac{y}{x} } [/tex]
we get
[tex]a \sqrt[5]{b} [/tex]
Answer:
[tex]a \sqrt[5]{b}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt[5]{a^3b^2} \times \sqrt[5]{a^2b^{-1}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex](a^3b^2)^{\frac{1}{5}} \times (a^2b^{-1})^{\frac{1}{5}}[/tex]
As the exponents are the same,
[tex]\textsf{apply exponent rule} \quad a^n \cdot c^n=(a \cdot c)^n:[/tex]
[tex](a^3b^2a^2b^{-1})^{\frac{1}{5}}[/tex]
Collect like terms:
[tex](a^3a^2b^2b^{-1})^{\frac{1}{5}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex](a^{(3+2)}b^{(2-1)})^{\frac{1}{5}}[/tex]
Simplify the exponents:
[tex](a^5b^1)^{\frac{1}{5}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^bc^d)^n=(a^b)^n \cdot (c^d)^n:[/tex]
[tex](a^5)^{\frac{1}{5}} \cdot (b^1)^{\frac{1}{5}}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]a^{\frac{5}{5}} \cdot b^{\frac{1}{5}}[/tex]
Simplify:
[tex]a^1 \cdot b^{\frac{1}{5}}[/tex]
[tex]a \cdot b^{\frac{1}{5}}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]a \sqrt[5]{b}[/tex]
A cable installer charges $40.00 per hour
plus a $50.00 service charge. Your father's firm hires him to hook up his
company's Internet service.
Here is the cost function used to
represent this situation in terms of then number of hours worked:
c(h) = 40h +50
Find the total charges if it takes the cable installer 6.5 hours to complete the task.
__________
Enter the correct answer.
Answer:
Set up the equation ... 60 + 40X = total charges... where X is the number of hours (6.5)
60 + 40(6.5) = ?
60 + 260 = ?
320 = total charges
(1.3+0.2) divided by 5+2.7 using BODMAS/PEDMAS
Answer:
3
Step-by-step explanation:
Parenthesis
Exponent
Division
Multiplication
Addition
Subtraction
(1.3+0.2) ÷ 5+2.7
paranthesis first
1.5 ÷ 5 + 2.7
Division next
0.3 +2.7= 3
five times the sum of a number and two is nineteen less than six times the number.
Answer:
The number is 29.
Step-by-step explanation:
"five times the sum of a number and two" can be represented as 5(x + 2), where x is the number. "nineteen less than six times the number" is the same as 6x - 19. The word "is" determines that these two parts are equal. So, 5(x + 2) = 6x - 19.
Solve:
5x + 10 = 6x - 19
10 = x - 19
x = 29
Check:
5 * (29 + 2) = 5 * 31 = 155
(6 * 29) - 19 = 155
155 = 155
mz1 = (2x +29)° and mz2 = (5x+20)°. If 21 and
22 are vertical angles, what are mz1 and mz2?
Answer:
Step-by-step explanation:
m∠2 = 90° - 56° = 34°. So, m∠1 = m∠2 = 34°
here the answers
What is the distance from the origin to point A graphed on the complex plane below?
-5-4-3
O √5
O√13
O 9
-94
--
13
A
& 1 14.
543
2
1
+2+
Mark thin ond roturn
-3-
4
4
L
1 2 3 4 5 X
Save and Exit
57
The distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.
What is complex plane?The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.
Complex numbers can be geometrically interpreted using the complex plane. They add like vectors when addition is applied. Polar coordinates make it simpler to represent the product of two complex numbers, whose magnitude or modulus is the sum of their absolute values.
The coordinates of the point A are (-3, -2).
If we extend the line from the origin to the point A it forms a right angled triangle with base = 3 and height = 2.
Using the Pythagoras theorem:
c² = a² + b²
Substituting the values:
c² = (2)² + (3)²
c = √13
Hence, the distance from the origin to point A graphed on the complex plane below is √13, Option C is the correct answer.
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A student is trying to prove that the triangle XAB is similar to triangle XYZ.
Answer:
Below
Step-by-step explanation:
See image
L side goes from 3 units to 6 units so scale factor is 2
XIII.4.11. Află două numere naturale care îndeplinesc simultan condiţiile:
a) diferenţa lor este egală cu sfertul sumei lor;
b) diferenţa dintre suma şi diferenţa lor este 108. VA ROG RAPIDDD DAU COROANA
Answer:B
Step-by-step explanation:
Need help with this. Keep getting answer wrong
Answer:
see image
Step-by-step explanation:
First of all, the problem might be that we need to set this up differently than how it is written.
"Subtract THIS from THAT" means that you have to put the second thing first and minus the first thing:
THAT - THIS
Next, the minus in the middle has to go to all three of the terms in the second part. This is going to change the sign of all three parts. See image.
Last, hopefully fraction addition with positive and negative signs isn't too terribly confusing.
1/5 - 2/5 is -1/5.
And -1/4 - 1/4 is -2/4, which is -1/2.
see image.
Make sure the y^2 and the y look like they are next to the whole fraction and are not on the bottom of the fraction.
the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500
The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years
How to determine the valueTo solve this problem, we can use the formula for exponential growth:
V(t) = V₀ * (1 + r)^t
Given that the parameters are;
V(t) is the value of the equipment at a time tV₀ is the initial value of the equipment ($15,000)r is the growth rate (15.9% or 0.159)t is the time in yearsTo determine time t when the value of the equipment will be less than $7500.
Let's set up an inequality;
V(t) < 7500
Substituting the formula for V(t), we get:
V₀ * (1 + r)^t < 7500
Substitute the values
(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
Hence, the value is 2.64 years.
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1.8 The first two terms of a geometric sequence are 2 and 3 respectively. - Determine the smallest number of terms which will yield a sum larger than 12.
Answer:
I know that answer
Step-by-step explanation:
answer is -23
