Using the given linear function, we have that:
a) The equation in standard form is: h - 3.34r - 81.2 = 0.
b) The intercepts are given as follows: h-intercept = 81.2, r-intercept = -24.31.
c) The predicted height is of 164.7 centimeters.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In standard format, the equation is given by:
y - mx - b = 0.
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, the equation is:
h = 81.2 + 3.34r.
In standard format, the equation is:
h - 3.34r - 81.2 = 0.
From the equation, the h-intercept is of 81.2. To find the r-intercept, we have to solve for r when h = 0, hence:
3.34r + 81.2 = 0.
3.34r = -81.2
r = -81.2/3.34
r = -24.31.
For item c, the radius is given by r = 25, hence the height will be given as follows:
h = 81.2 + 3.34(25) = 164.7.
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What number is composed of 6 ones,22 tenths,33 thousandths and 44 thousandths.
Answer:
8.277
Step-by-step explanation:
Pretty simple, just add up the values but convert the word form into decimals.
[tex]6+2.2+0.033+0.044=8.277[/tex]
Also, your question said 33 thousandths, so it is what I answered.
Answer:
8.277
Step-by-step explanation:
Write as a percent
23 out of 100.
Answer:
%23
Step-by-step explanation:
23/100
Answer:
23%
Step-by-step explanation:
Hi, can someone help me answer
In two or more complete sentences, describe the transformation(s) that take place on the parent function f(x)=log(x) to achieve the graph of g(x)=log(-3x+9)+4.
The transformation that takes place on the parent function ( f (x) = log (x) ) to achieve the graph of g(x)=log(-3x+9)+4 can be described as a reflection across the y-axis. Then you horizontally shrink a factor of three; shift three units to the right, and shift four units upwards.
The explanation is as follows:Step 1: The parent graph is to be translated 3 units to the right side to achieve: y = log (x-3)
2. Shrink the graph by a factor of three by multiplying x by three:
⇒ y = log 3(x-3)
3. Reflect the function y = log 3(x-3) across line -3 = x to achieve:
y = -3(x-3)
4. Translate the function y = log 1-3(x-3) four units upwards to achieve
y = log (-3 + 9) +4
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question in screenshot
The value of tan33° is 11/20.
What is a right triangle?A triangle with an angle measure of 90° is called a right triangle.
Given that, tan(x) = (length of the opposite side)/ (length of an adjacent side)
Therefore, for the given triangle, it follows:
tan33° = 11/20
Hence, the value of tan33° is 11/20.
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Write the vertex form of the following function. (fill in each blank with the correct numerical
value: include the sign where needed)
An absolute value function with a vertex of (-12,10) and passes through the points (4, 6) and
(-8, 9).
Answer:
-1/4 Abs(x+12) + 10
Step-by-step explanation:
The vertex form of an absolute function is of the form
y = a|x -h| + k here |x-h| is the absolute value
where (h, k) are the coordinates (x, y) of the vertex
The vertex is given as (-12, 10)
So h = -12, k = 10
Plugging these in we get the vertex form as
y = a|x - (-12)| + 10
y = a|x + 12| + 10
All it remains is to find a
Given point (4, 6) as a point on the graph, plug these values
y = 6 = a|4 + 12| + 10
6 = a|16| + 10
6 = 16a + 10 since absolute value of a positive number is the number
Switch sides
16a + 10 = 6
Subtract 10 from both sides:
16a + 10 - 10 = 6 - 10
16a = -4
a = -1/4
So the equation of the function is
y = -1/4|x + 12| + 10
The second point is not needed to derive the function equation but let's use it to verify our calculated equation
Point (-8, 9)
Plug x = -8, into y = -1/4|x + 12| + 10
=> y = -1/4|-8+12| + 10
=> y = -(1/4)·4 + 10
=> y = -1 + 10
= y = 9 which matches with the y -coordinate of the second point
So everything looks cool
Final Solution
-1/4 Abs(x+12) + 10
For - 1/4 if it does not accept fractions, enter -0.25
I have also provided a screenshot which shows what should go into each box to help you out
Hope that helps and feel free to ask any clarifications
The temperature during a very cold day is recorded every 2 hours for 12 hours. The data are given in the table below. What type of polynomial would best model these data?
cubic
linear
quartic
quadratic
Answer: A. Cubic
Step-by-step explanation:
Which function's graph has a vertex at (3, 5) and contains the point (5, 13)?
The equation y = 2x² - 12x + 23 describes the function graph that includes a vertex at (3, 5) and passes through the point (5, 13).
What does a parabolic equation look like in vertex form?The vertex of a parabolic equation is at the point and the vertex form is y = a(x - h)2 + k, where a, h, and k are constants (h, k).
How do you answer this dilemma?Find the function whose graph has the vertex at (3, 5) and passes through the point in the question (5, 13).
Assuming it to be a parabolic function, we know that a parabolic equation's vertex form is y = a(x - h)2 + k, where a, h, and k are constants, and the vertex is located at the position (h, k).
As the vertex of the necessary function is at the position (3, 5), we may substitute h = 3 and k = 5 to obtain the following equation in the above equation:
y = a(x - 3)² + 5
Now that we know that the graph passes through the point (5, 13), we can change the original equation to read:
13 = a(5 - 3)² + 5,
or, 13 = 4a + 5,
or, 4a = 13 - 5 = 8,
or, a = 2.
We obtain the following from the equation y = a(x - h)2 + k by inserting a = 2, h = 3, and k = 5:
y = 2(x - 3)² + 5,
alternatively, y = 2(x² - 6x + 9) + 5,
alternatively, y = 2x² - 12x + 18 + 5,
Alternatively, y = 2x² - 12x + 23.
As a result, the function graph with the vertex at (3, 5) and the point of intersection (5, 13) yields the equation y = 2x² - 12x + 23.
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(6z³ + 3z² - 4x + 8) - (4z²-3z + 2)
A. 6z-z²-z+6
B.
10z³ + 3z² - 4z + 10
C. 6z³-z² - 4z + 10
D. 10z³ +7z² - 4z+6
Which is equivalent
Answer:
6z³ -z² - z + 6
Step-by-step explanation:
By using the negative sign to open the bracket and collecting like terms, we have:
6z³ + 3z² - 4z + 8 - 4z² + 3z - 2 I'm guessing it suppose to be 4z and not 4x.
= 6z³ -z² - z + 6
Option A is correct.
Write the equation of the line that passes through the points (-1,4)and (−1,0). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
well, the tell-tale part in the points will be the coordinates, hmmm now, the x-coordinate for both points is the same, well, that simply means is a vertical line. Check the picture below.
*PLEASE SOLVE!!!*
In late 1897, Amos Dolbear published an article called “The Cricket as a Thermometer." He had determined that the outside temperature (in Fahrenheit) shared a linear relationship with the number of times the snowy tree cricket would chirp per . If you count the number of cricket chirps per (while sitting inside your warm house), then you can find the temperature outside. In his research, Dolbear concluded that for every extra cricket chirp per second, the temperature was 1/4*F higher. Furthermore, he found that when the number of cricket chirps per minute was 120, the temperature outside was 70*F.
What are the quantities in this scenario?
What in the problem suggests or indicates that the relationship between the temperature and the number of chirps per minute should be linear?
If you graph the relationship, what will be the value of the slope of the graph?
What is the y-intercept?
Answer:
The equations is t = 1/4n + 40
The slope is 1/4 and the y-intercept is 40
t is the temperature.
n is the number of chirps per minute.
Step-by-step explanation:
Question 1 of 10
The following graphs have no scales assigned to them. Which of them could
be density curves for a continuous random variable if they were provided with
the right scale?
Check all that apply.
B.
my
nh
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
What is variable?A symbol (often a letter) used in algebra to represent an unknowable numerical value in an equation. Variables can have a wide range of values, which is why they are called variables. Thus, a variable can be thought of as a quantity that can take on different values depending on the circumstances of a given issue. As the program executes, we may store, modify, and access this data thanks to variables. All types of information can be stored in variables.
Four graphs of different nature as options.
We are required to find a graph that is not a continuous variable.
What is continuity?In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.
Continuous lines are those lines that when decreased, decrease with continuity and when increased, increase with continuity.
Given that,
When we observe graph A, graph C. In these graphs, the value of the function keeps increasing and decreasing a lot and is not in continuity.
Hence, graph A, and graph C could not possibly be density curves for a continuous random variable if they were provided with the right scale.
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A rectangular garden is 5 ft longer than it is wide. Its area is 300 ft2. What are its dimensions?
Answer:
width=x
length=5x
area= 300ft2
area=lxb
300=5x(x)
300=5x^2
x^2=60
x=7.74
7.74(5)=38.7
dimensions are 38.7ft by 7.74 ft
Please mark as brainliest
Step-by-step explanation:
the area of a rectangle is
length × width = 300 ft²
length = width + 5
(width + 5) × width = 300
width² + 5×width = 300
width² + 5×width - 300 = 0
the general solution to such a quadratic equation is
width = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 5
c = -300
width = (-5 ± sqrt(5² - 4×1×-300))/(2×1) =
= (-5 ± sqrt(25 + 1200))/2 =
= (-5 ± sqrt(1225))/2 = (-5 ± 35)/2
width1 = (-5 + 35)/2 = 30/2 = 15 ft
width2 = (-5 - 35)/2 = -40/2 = -20 ft
negative lengths for an actual object don't make sense, so width = 15 ft is our solution.
length = width + 5 = 15 + 5 = 20 ft
How do I do this question?
Round 673,432 to the place of the underlined digit , enter the rounded number in the box. The thousands place =3 is underlined.
Answer: 673, 43
Step-by-step explanation:
As the next digit coming after the underlined digit is 2, the rounded number becomes 673,43. If instead of 2 we had 5 or above, the number should have become 673,44.
write 600 as the product of prime factors
Give your answer in index form
The value of 600 as the product of prime factors will be 2³ × 3 × 5².
What's prime number?It should be noted that a prime number simply means the number that can be multiplied by itself and 1.
Therefore, it should be noted that 600 will be expressed thus:
600 = 2 × 2 × 2 × 3 × 5 × 5
600 = 2³ × 3 × 5².
Therefore, the value is 2³ × 3 × 5².
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Find the surface area of a cylinder with a height of 8 inches and base radius of 4 inches
The surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.
What is a cylinder?A cylinder is defined as a solid geometric figure with straight parallel sides and a circular or oval cross section.
What is Surface Area ?Surface area is the amount of space covering the outside of a three-dimensional shape.
Surface area of the cylinder is calculated as : - 2πr² + 2πrh
We have:
Height of the cylinder h = 8 inches
The radius r = 4 inches
π = 3.14
Surface Area = 2(3.14)(4)² + 2(3.14)(4)(8)
surface Area = 2x 3.14 x 16 + 18.28
surface Area = 100.48 + 18.28
surface Area = 118.76 square inches
Therefore , the surface area of the cylinder is 118.76 square inches if the height is 8 inches and base radius is 4 inches.
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Consider the function f(x) = 10(x2 â€"" 7x). what are the additive and multiplicative inverses? the additive inverse is g(x) = 10(x2 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 (x squared minus 7 x) endfraction. the additive inverse is g(x) = â€""10(x2 â€"" 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 (x squared minus 7 x) endfraction. the additive inverse is g(x) = 10(x2 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 endfraction (x squared minus 7 x) . the additive inverse is g(x) = â€""10(x2 â€"" 7x) and the multiplicative inverse is h(x) =startfraction 1 over 10 endfraction (x squared minus 7 x) .
The Additive inverse of f(x) is 70x – 10x² and the multiplicative inverse of f(x) is [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]
We have, f(x) = 10(x² – 7x).The additive inverse of a number is a value that on adding to the given number gives zero.The multiplicative inverse of a number is a number when multiplied by a given number gives 1.According to the question,We have,f(x) = 10( x² – 7x)Assume that the additive inverse of f(x) is g(x).Thereforef(x) + g(x) = 010x² - 70x + g(x) = 0g(x) = 70x - 10x²and,Let’s assume that the multiplicative inverse of f(x) is h(x).Thereforef(x) x h(x) = 110(x² – 7x) x h(x) = 1h(x) = [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]Hence, the additive inverse of f(x) is g(x) = 70x - 10x² and the multiplicative inverse of f(x) is h(x) = [tex](x^{2} -7x)[/tex] x [tex](1/10)[/tex]Solve more questions on Additive inverse and multiplicative inverse -https://brainly.com/question/17142610#SPJ4For each sequence, decide whether it could be arithmetic or geometric or neither. 200, 40, 8
Answer:
geometric sequence
Step-by-step explanation:
an arithmetic sequence has a common difference d between consecutive terms.
40 - 200 = - 160
8 - 40 = - 32
no common difference thus not arithmetic
a geometric sequence has a common ratio r between consecutive terms
[tex]\frac{40}{200}[/tex] = [tex]\frac{4}{20}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{8}{40}[/tex] = [tex]\frac{1}{5}[/tex]
thus there is a common ratio so sequence is geometric
A 3 lb (1.36 kg) bag of carrots cost $3.25, a 75 lb (ca. 34 kg) bag of carrots cost $4.75, which is the better deal?
Answer:
The second bag (4.75)
Step-by-step explanation:
Round 0.898 to the nearest hundred
Answer:
0.900.........
Step-by-step explanation:
thats it
0.898 rounded to nearest hundred will be 0.90 .
Given,
Number = 0.898
Here,
Now when we round numbers, anything greater than 5 gets rounded up, and anything less than 5 gets rounded down.
So 9 is greater than 5 thus the number will be rounded off to 0.90 .
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Find the equation of the line.
a line that is perpendicular to the graph of y=-3x +2 and
contains the point (3,-3)
Answer: y = -3x + 6
Step-by-step explanation:
If it is perpendicular to the line -3x + 2, then it's slope should also be -3.
The standard form of a line is y = mx + b. As our slope is -3, we have that our line is y = -3x+b. Now, let's put the given point into the line. x = 3 and y = -3, so -3 = -3*3 + b. Hence, b = -3+9 = 6. The equation of the line is y = -3x + 6.
Pls help asap for math
Nara wants to determine how much ice it will take to fill her cooler . If the cooler has a length of 22 inches, a width of 12 inches, and a height of 1012 inches, how much ice will her cooler hold?
Answer:
267,168 inches
Step-by-step explanation:
If your box is a rectangular prism or a cube, the only information you need is the box's length, width, and height. You can then multiply them together to get volume. This formula is often abbreviated as V = l x w x h.
Volume = L × W × H
Where,
L means lengthW means widthH means heightVolume = 22 inches × 12 inches × 1012 inches
Volume = 267,168 inches
So, her cooler can hold 267,168 inches of ice
30 POINTS!!!!
Please turn this into an EQUATION
One-half times the difference of twenty and a variable is two thirds
Here are the possible answers
approximate √86 as a decimal to the tenths place.
-30 19/40 as a decimal
The conversion of the fraction -30 ¹⁹/₄₀ to decimal is expressed as; -30.475
How to convert fraction to Decimal?
Fractions usually have a numerator and denominator. Now, fractions can also be expressed as mixed fraction, improper fraction and proper fraction.
Now, we are given the fraction in mixed fraction. This is expressed as;
-30 ¹⁹/₄₀ = -30 - ¹⁹/₄₀
Now, the proper fraction part of the mixed fraction can be expressed as;
¹⁹/₄₀ = 0.475
Thus, our fraction is now;
-30 - 0.475 = -30.475
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0.01p + 0.05(22 – p) = 0.54
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
How many of each type of coin does Ari have?
pennies and
nickels
The number of pennies that Ari has is 14.
The number of nickels that Ari has is 8.
How many of each type of coin does Ari have?The linear equations that represent this question are:
0.01p + 0.05n = $0.54 equation 1
p + n = 22 equation 2
Where:
p = number of pennies n = number of nickelsIn order to determine the number of nickels, multiply equation 2 by 0.01
0.01p + 0.01n = 0.22 equation 3
Subtract equation 3 from equation 1:
0.04n = 0.32
Divide both sides by 0.04
n = 0.32 / 0.04
n = 8
Substitute for n in equation 2:
8 + p = 22
p = 22 - 8
p = 14
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In the following exercise, two sides and an angle are given. First determine whether the information results in no triangle, one triangle, or two triangles. Solve the resulting triangle.
a=229,b=244, and A = 37.8°
By the Law of Sines,
[tex]\frac{\sin B}{b}=\frac{\sin A}{a} \\ \\ \sin B=\frac{b \sin A}{a} \\ \\ =\frac{244\sin 37.8^{\circ}}{229} \\ \\ B \approx 37.42^{\circ}, 142.58^{\circ}[/tex]
Of these, only 37.42° is a possible value of B (sum of angles of a triangle is 180°).
So, we have that:
[tex] a=229, b=244, A=37.8^{\circ}, B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]
Angles of a triangle add to 180°, so:
[tex]C=180^{\circ}-A-B=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)
[/tex]
Using the Law of Sines again,
[tex]\frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a \sin C}{\sin A} \\ \\ =\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}}[/tex]
So, there is one possible triangle, where:
[tex]a=229 \\ \\ b=244 \\ \\ c=\frac{244\sin \left(142^{\circ}-\arcsin \left(\frac{244 \sin 37.8^{\circ}}{229} \right) \right)}{\sin 37.8^{\circ}} \\ \\ A=37.8^{\circ} \\ \\ B=\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right) \\ \\ C=142.2^{\circ}-\arcsin \left(\frac{244\sin 37.8^{\circ}}{229} \right)[/tex]
William works at a nearby electronics store. He makes a commission of 6\%6%6, percent on everything he sells. If he sells a computer for \$764.00$764.00dollar sign, 764, point, 00, how much money does William make in commission?
\$\
Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.
How to find the money made from commission?Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for.
The commission to William here can be found by the formula:
= Percentage made for commission on everything sold x Amount that the computer sold for
Solving for the commission to William gives:
= 6 % x 764
= 0. 06 x 764
= $ 45.84
In conclusion, the commission that William made from the sale of the computer which was valued at $ 764 is $ 45.84.
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Answer:
45. 84
Step-by-step explanation:
Based on the commission percentage that William makes when he sells goods at the electronics store, the amount that William made in commission from the computer is $ 45. 84.How to find the money made from commission?Commission made on goods and services are a percentage that is paid to sales people when they make a certain number of sales. The commission is based on the amount that the good or service in question is sold for. The commission to William here can be found by the formula:= Percentage made for commission on everything sold x Amount that the computer sold for Solving for the commission to William gives:= 6 % x 764 = 0. 06 x 764= $ 45.84
What is the measure of angle 1, angle 5, angle 2, angle 8, and angle 7? Angle 4 = 72 degrees.
The unknow angles are as follows:
m∠1 = 108 degreesm∠2 = 72 degreesm∠5 = 108 degrees.m∠7 = 108 degreesm∠8 = 72 degreesHow to find angles in parallel lines?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles etc.
Therefore,
m∠4 = 72 degrees
Hence,
m∠1 + m∠4 = 180 (angle on a straight line)
m∠1 = 180 - 72
m∠1 = 108 degrees
m∠2 = m∠4 (vertically opposite angles)
Vertical angles are the angles formed when two lines intersect each other. Vertical angles are congruent.
Therefore,
m∠2 = 72 degrees
m∠5 = m∠1 (corresponding angles)
Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
m∠5 = 108 degrees.
m∠7 = m∠5(vertically opposite angles)
m∠7 = 108 degrees
m∠8 = m∠2 (alternate exterior angles)
Alternate exterior angles are congruent.
m∠8 = 72 degrees
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Mr. Brown's class has 20 students. 6 of the students have blonde hair. What
percent of the students have blonde hair?
Answer:
30%
Step-by-step explanation:
6/20 = .3
.3 x 100 = 30