The point-slope form of the equation of a line is given by the following expression:
y - y1 = m(x - x1)
Where m is the slope of the line and (x1, y1) is a point where the line passes through.
The slope of the line can be determined with the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:
[tex]m=\frac{5-(-6)}{6-(-2)}=\frac{5+6}{6+2}=\frac{11}{8}[/tex]Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:
y - y1 = 11/8(x - x1)
By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:
y - (-6) = 11/8(x - (-2))
y + 6 = 11/8 (x + 2)
Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)
Given the following table with selected values of the linear functions g(x) and h(x), determine the x-intercept of g(h(x)).
The x–intercept of g(h(x)) is the option;
[tex] \displaystyle {-\frac{2}{3}}[/tex]
What is a The x–intercept of a function?The x–intercept of a function is given by the point where the function intersects the x–axis.
From the given table, the slope of the graph of g(x), [tex] m_1 [/tex] is given by the equation;
[tex] \displaystyle{ m_1 = \frac{ - 4 - ( - 8)}{ - 4 - ( - 6))} = \frac{4}{2} = 2}[/tex]
The equation of g(x) in point slope form is therefore;
g(x) - (-4) = 2×(x - (-4)) = 2•x + 8
g(x) = 2•x + 8 - 4 = 2•x + 4
g(x) = 2•x + 4
The slope of the function h(x), [tex] m_2 [/tex] is found using the equation;
[tex] \displaystyle{ m_2 = \frac{ 8 - 14}{ - 4 - ( - 6))} = \frac{ - 6}{2} = - 3}[/tex]
h(x) presented in point and slope form is therefore;
h(x) - 8 = (-3)×(x - (-4)) = -3•x - 12
h(x) = -3•x - 12 + 8 = -3•x - 4
h(x) = -3•x - 4
g(h(x)) = 2•h(x) + 4
Plugging in the value of h(x) gives,;
g(h(x)) = 2×(-3•x - 4) + 4 = -6•x - 8 + 4
g(h(x)) = -6•x - 4
The x–intercept of g(h(x)) is given by the point where g(h(x)) = 0, which gives;
At the x–intercept, g(h(x)) = 0 = -6•x - 4
[tex] \displaystyle{ x = \frac{4}{-6} = -\frac{ 2}{3} }[/tex]
The x–intercept is [tex] \displaystyle{ -\frac{ 2}{3} }[/tex]
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find volume of hemisphere who’s great circle has an area of 12.5 ft squared
The surface area of a hemisphere is given as 12.5 square feet. It is required to find the volume of the hemisphere.
To do this, equate the given surface area to the formula, find the radius, and then substitute the radius into the volume formula to find the volume.
The surface area of a hemisphere radius, r is given as:
[tex]S=3\pi r^2[/tex]Substitute S=12.5 into the formula and solve for r in the resulting equation:
[tex]\begin{gathered} 12.5=3\pi r^2 \\ \Rightarrow3\pi r^2=12.5 \\ \Rightarrow\frac{3\pi r^2}{3\pi}=\frac{12.5}{3\pi} \\ \Rightarrow r^2=\frac{25}{6\pi} \\ \Rightarrow r=\sqrt{\frac{25}{6\pi}} \end{gathered}[/tex]The volume of a hemisphere is given as:
[tex]V=\frac{2}{3}\pi r^3[/tex]Substitute the calculated value of r into the volume formula:
[tex]\begin{gathered} V=\frac{2}{3}\pi\left(\sqrt{\frac{25}{6\pi}}\right)^3 \\ \text{ Substitute }\pi=3.14\text{ into the equation:} \\ \Rightarrow V=\frac{2}{3}(3.14)\left(\sqrt{\frac{25}{6(3.14)}}\right)^3\approx3.2\text{ square feet} \end{gathered}[/tex]The required volume is about 3.2 square feet.
Evaluate. 43⋅(100÷25)−50 Enter your answer in the box.
Answer:
122
Step-by-step explanation:
43 * (100/25) - 50
43 * 4 - 50
172 - 50
122
Hope this helps! :)
in the figure shown Line O is parallel to line P and line M is Parallel to linea N
we have that
In this problem angle x and angle of 62 degrees are supplementary angles
that means
x+62=180
solve for x
x=180-62
x=118 degreesThis figure shows a circle with a radius of 3.
A circle with its radius labeled as 3.
What is the circumference of the circle?
The circumference of the circle has a value of 18.86 units
How to determine the circumference of the circle?From the question, we have the following parameters:
Radius, r = 3 units
The circumference of the circle can be calculated using the following circumference formula
C = 2πr
Where
π = 22/7 (a constant)
r = 3
Substitute the known values in the above equation
So, we have the following equation
C = 2 * 22/7 * 3
Evaluate the products
So, we have the following equation
C = 18.86
Hence, the circumference is 18.86 units
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A student incorrectly simplifies an expression. The expression and work is shown below.
-(-6)(-3) - 2/3 (22 - 7)
3/5
Step 1: -(-6) (-3) - 2/3 (15)
3/5
Step 2: 18 - 2/3 (15)
3/5
Step 3: 18 - 10
3/5
Step 4: 8_3_5
Answer they got: 4 4/5
Idetnfiy which step is incorrect.
.
PLSSS HELP MEEEEEE
Answer:
so in the second step you see how the 18 is a positive
its supposed to be a negative
in the step 1, the part is -(-6)(-3), right?
so the negative symbol outside the negative 6 cancels out the negative, making it a positive number
it becomes 6(-3), which them multiplies into -18
so, i think the explanation is "the person forgot to change the 18 to a negative in the second step"
yea lol i think thats it
Oscar drew a scale drawing of a house. The garage, which is 8 meters long in real life, is 4centimeters long in the drawing. What is the drawing's scale factor?Simplify your answer and write it as a fraction.
Answer:
1/200
Explanation:
Length of the garage in the drawing = 4 centimeters
Length of the garage in real life = 8 meters
The ratio of the lengths = 4 cm : 8m
Divide both sides by 4
[tex]\begin{gathered} \frac{4\operatorname{cm}}{4}\colon\frac{8m}{4} \\ 1\operatorname{cm}\colon2m \end{gathered}[/tex]1 m =100cm
2m= 2 x 100 =200cm
Converting both to the same unit, we have:
[tex]\begin{gathered} 1\operatorname{cm}\colon200\operatorname{cm} \\ =\frac{1}{200} \end{gathered}[/tex]The drawing's scale factor in fraction form is 1/200.
Elijah and his brother ran a race. Elijah reached the finish line in 60.26 seconds and his brother reached the finish line 6 seconds later. How long did it take Elijah's brother to run the race?
Convert compressions to simplified faction or integer. If it’s not a real number, enter None
Given an expression:
[tex](-81)^{\frac{1}{4}}[/tex]We have to simplify the expression, if it does not result in a real number then the answer is NONE.
Let:
[tex]x=(-81)^{\frac{1}{4}}[/tex]Then,
[tex]\begin{gathered} x=(-81)^{\frac{1}{4}} \\ \Rightarrow x^4=((-81)^{\frac{1}{4}})^4 \\ \Rightarrow x^4=-81 \end{gathered}[/tex]There is no real number whose power 4 is a negative number.
Thus, the answer is not a real number. The answer is NONE.
Which four groups make up nearly one half of the male population?
We are given the percentages for males on the left side and the percentages for females on the right side.
We are trying to find four groups that make up nearly 1/2 of the male population, so we want the percentages for these groups to add up to nearly 50%.
Let's take a look at the lowest age groups of the male population, which in turn make up the highest proportion of the male population.
We have the age group 0-4, which makes up roughly 12%.
We have the age group 5-9, which makes up roughly 11%.
We have the age group 10-14, which makes up roughly 11%.
We have the age group 15-19, which makes up roughly 12.5%.
If we add all of these percentages together, we get:
12% + 11% + 11% + 12.5% = 46.5%
Since we cannot go any smaller than 46.5% because this is the closest percentage to 50%, the four groups that make up nearly one half of the male population must be:
Ages 0-4, 5-9, 10-14, and 15-19
I need help with this practice Please read below ‼️‼️Use pencil and paper to graph the function, if you can’t, please use a drawing/writing tool that is *NOT* a graphing tool. If you cannot do this let me know
Answer:
Step-by-step explanation:
The trigonometric functions are represented by the following function form:
[tex]\begin{gathered} f(x)=\text{Atrig(Bx-C)}+D \\ \text{where,} \\ A=\text{ amplitud} \\ B,C=\text{ phase shift} \\ D=\text{ vertical shift} \end{gathered}[/tex]Then, for the following function:
[tex]f(x)=-\cot (x+\frac{\pi}{6})[/tex]Since it is an arctan function reflected the y-axis:
Find the solution of the system of equations.6x – 3y = -303x – 6y = 12
6x - 3y = -30 -------------------------------(1)
3x - 6y = 12 ---------------------------------(2)
Multiply through equation(1) by 3 and then multiply through equation (2) by 6
18x - 9y = - 90 ---------------------------------(3)
18x - 36y = 72 ----------------------------------(4)
subtract equation (4) from equation (3)
What is the magnitude (size) of -7.5?_______________________________O A. -7.5, because |-7.5| = 7.5O B. 7.5, because |-7.5 = 7.5O C. 7/5, because |-7.5| = 7/5O D. 7.5, because | -7.5| = - 7.5
it is given that the expression is -7.5
the magnitude of -7.5 is,
I-7.5I = 7.5
thus, the answer is option A
ABC is shown . D is a point on AB,AC =7, AD=6, and , BC=18.
ok
AC = 7
AD = 6
BC = 18
It must be 12, because the sum of two sides of a triangle is higher than the other side.
And 6 + 5 = 11
AB + AC = 11 + 7 = 18
micrometers, T is measured in seconds, and D accounts for the weakening of the earthquake due to the distance from the epicenter.
If an earthquake occurred for 4 seconds and D = 2, which graph would model the correct amount on the Richter scale?
The graph that can be used to model the correct amount on the Richter scale is r = log(a/4) + 2.
How to illustrate the information?It should be noted that the magnitude of an earthquake is gotten by using the equation:
r = log(a / t) + d.
where
r = magnitude of an earthquake
a = amplitude
t = time
d = distance.
In this case, the earthquake occurred for 4 seconds and D = 2. We'll substitute the value into the equation and this will be r = log(a/4) + 2.
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A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies. You pick one candy at random. Find the probability that it is not yellow
P(not yellow)
The probability that it is not yellow candies will be 119/139.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
A bag contains;
Number of red candies = 42
Number of green candies = 45
Number of yellow candies = 20
Number of purple candies = 32
Now,
Total number of candies in a bag = 42 + 45 + 20 + 32
= 139
And, The number of candies in a bag not contain yellow candy
= 139 - 20
= 119
Thus, The probability that it is not yellow candies will be;
Probability = Number of not yellow candies / Total candies
= 109 / 139
Therefore, The probability that it is not yellow candies will be 119/139.
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A sequence is defined recursively using the formula f(n+1) =-0.5f(n) . If the first term of the sequence is 120, what is f(5)?
−15
−7.5
7.5
15
Suppose we have the recursive formula of sequence, [tex]\displaystyle{f(n+1)=0.5f(n)}[/tex]. From this formula, we know that:
[tex]\displaystyle{f(2)=0.5f(1)}\\\\\displaystyle{f(3)=0.5f(2)}\\\\\displaystyle{f(4)=0.5f(3)}\\\\\displaystyle{f(5)=0.5f(4)}[/tex]
Since the first term of sequence is 120. Therefore, [tex]\displaystyle{f(1)=120}[/tex]. Since [tex]\displaystyle{f(4)=0.5f(3)}[/tex] then substitute in [tex]\displaystyle f(5)[/tex]:
[tex]\displaystyle{f(5)=0.5\cdot 0.5f(3)}[/tex]
Then substitute f(3) down to f(1):
[tex]\displaystyle{f(5)=0.5\cdot 0.5 \cdot 0.5 \cdot 0.5 \cdot 120}\\\\\displaystyle{f(5)=(0.5)^4\cdot 120}\\\\\displaystyle{f(5)=7.5}[/tex]
Therefore, f(5) = 7.5
Quadrilatral ABCD has the following vertices
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
Angle a is right angle
is ABCD a rectangle
pls help i will give brainliest
From the calculations below, we can tell that quadrilateral ABCD is not a rectangle because AB is not parallel to CD
How to Identify a rectangle?
We are given that the quadrilateral is ABCD with the vertices as;
A(-6,-2)
B(-4,4)
C(8,1)
D(6,-6)
We are further told that Angle A is a right angle. Thus;
AB must be perpendicular to AD.
Secondly, for ABCD to be a rectangle, AB must be parallel to CD. Thus;
By slope formula, for AB and CD are gotten from the formula;
Slope = (y₂ - y₁)/(x₂ - x₁)
Slope of CD = (-6 - 1)/(6 - 8)
Slope of CD = -7/-2 = 7/2
Slope of AB = (4 - (-2))/(-4 - (-6))
Slope of AB = 6/2
Slope of AB = 3
Since Slope of AB and AC are not equal then ABCD is not a rectangle.
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The graph below plots the values of y for different values of x: plot the ordered pairs 1, 3 and 2, 4 and 3, 9 and 4, 7 and 5, 2 and 6, 18 What does a correlation coefficient of 0.25 say about this graph? (1 point) x and y have a strong, positive correlation x and y have a weak, positive correlation x and y have a strong, negative correlation x and y have a weak, negative correlation
The presented data for x and y show a significant, positive correlation with 0.78 serving as the coefficient of correlation.
The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset. The other variables shift in the same direction when one changes.
The intensity and direction of a relationship between two variables are indicated by a correlation coefficient, which is a number between -1 and 1. In other words, it shows how comparable two or more variables' measurements are across a dataset.
Given x and y values in this case
x 1 2 3 4 5 6
y 3 4 9 7 2 18
xy 3 8 27 28 10 108
x² 1 4 9 16 25 36
y² 9 16 81 49 4 324
∑x = 21,
∑y = 43,
∑xy = 194,
∑x² = 91,
∑y² = 483,
n = 6
the relationship between x and y now:
r = (n∑xy - ∑x.∑y)/ √[{n∑x²- (∑x)²}{n∑y² - (∑y)²}]
r = ( 6 X 194 - 21 X 43 ) / √[ {6 X 91 - (21)²}{ 6 X 483 - (43)²}]
r = ( 1164 - 903) / √( 546 - 441)(2898 - 1849)
r = 261 / √ 105 X 1049
r = 261 / √110145
r = 261 / 331.88
r = 0.78
As a result, the x and y data's correlation coefficient is 0.78.
The strong, positive association between x and y
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The figure shows a circle inscribed into a regular pentagon.Cis the center of the circle and the regular pentagon.G and H are on the edge of both the circle and the regular pentagon.The radius of the circle is 3 inches.GHCPart A. Find the area of the dark shaded region. Show your work.Part B. Find the area of the light shaded region. Show your work.
Solution
Part A: The area of the dark shaded region = S1,
where
The radius of the circle is 3 inches.
[tex]\begin{gathered} S_1=\frac{4}{5}\pi r^2 \\ =\frac{4}{5}\pi.3^2 \\ S_1=\frac{36}{5}\pi in^2 \end{gathered}[/tex]Part B: The area of the light shaded region = S,
[tex]\begin{gathered} S=S_2-S_1 \\ S=5\times\frac{1}{2}r.rtan36 \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}} \\ S=\frac{45}{2}\sqrt{5-2\sqrt{5}}-\frac{36}{5}\pi in^2 \end{gathered}[/tex]Three cubes of side 10 cm are joined end to end to form a cuboid as given in the figure. Find is total surface area.
Solution:
The cuboid is a solid-shaped figure formed by six faces. A cuboid is a simple figure. It has three dimensions - width, length, and height. Thus, the cuboid is a parallelepiped. Now, the surface area of the parallelepiped is the sum of the areas of all sides, that is:
[tex]S\text{ =2(}lw+lh+wh\text{)}[/tex]where
l is the lenght
w is the width
and
h is the height
According to the figure given in the problem, we have that:
l = 30
w = 10
h = 10
thus, the surface area of the given cuboid would be:
[tex]\begin{gathered} S\text{ =2(}lw+lh+wh\text{)} \\ \text{ = 2((}30\cdot10\text{)+(30}\cdot10\text{)+(10}\cdot10\text{))=}1400 \end{gathered}[/tex]So that, we can conclude that the correct answer is:
[tex]1400[/tex]
Find a degree 3 polynomial having zeros -8, 2 and 8 and the coefficient of x3 equal 1.
The degree 3 polynomial is "x³-2x²-64x+128".
We have to find a polynomial of degree 3.We are given that the polynomial has -8, 2, and 8 as its roots.We are also given that the coefficient of x³ equals 1.If x = -8 is a root, then:(x+8) is a factor of the polynomial.If x = 2 is a root, then:(x-2) is a factor of the polynomial.If x = 8 is a root, then:(x-8) is a factor of the polynomial.All the three roots are of the same polynomial.So, the polynomial is the product of these factors.(x+8)(x-8)(x-2)(x²-64)(x-2)x³-2x²-64x+128The required polynomial is "x³-2x²-64x+128".To learn more about polynomials, visit :
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Graph the image of ∆KLM after a dilation with a scale factor of 4, centered at the origin.
The red triangle is the original figure
The green triangle is the image
Scale factor is 4
PLEASEEE HELPP
Megan is in a musical production. She was at practice for 2 hours yesterday and 3 hours today. Altogether she spent of her practice hours dancing. How many total hours did Megan spend dancing yesterday and today?
Answer:
2.0833
Step-by-step explanation:
2 3/4 + 3 1/2 =6.25
6.25(1/3)=2.0833
Please explain and help me get the correct answer. Thank you. Practice work that is not graded.
First, from the formula given we solve the equation for D:
[tex]\begin{gathered} 4PD=D^2LN\pi, \\ \frac{4PD}{LN\pi}=D^2, \\ \sqrt{\frac{4PD}{LN\pi}}=D^{}. \end{gathered}[/tex]Now, substituting the given data:
(a) PD=405 cu in, L=4.7 in, and N=7,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times405}{4.7\times7\times\pi}}in=\sqrt[]{15.6736175}in\approx3.96\text{ in}[/tex](b) PD=399.4 cu in, L=2 in, and N=6,
in the above equation we get:
[tex]D=\sqrt[]{\frac{4\times399.4}{2\times6\times\pi}}in=\sqrt[]{42.37765618}in\approx6.51\text{ in}[/tex]Answer:
(a) 3.96 in.
(b) 6.51 in.
8. Tabitha made 12 out of 23 free throw attempts in the first half of practice and 20 out
of 27 attempts in the second half of practice. What is her free throw average for the
whole practice, written as a decimal?
Answer: 0.64 ...........
In 5 minutes, a conveyor belt moves 100 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans thesame distance in 9 minutes. If both belts are used, find how long it takes to move the cans to the storage area.The conveyor belts can move the 100 pounds of recyclable aluminum from the delivery truck to a storage area in minutes.(Simplify your answer. Type an integer, fraction, or a mixed number.)
we know that
a greater conveyor belt moves 100 pounds ------------> 5 minutes
so
Applying proportion
1-minute ---------> move 100/5=20 pounds
a smaller conveyor belt moves 100 pounds ------> 9 minutes
so
Applying proportion
1-minute --------> move 100/9 pounds
therefore
If both belts are used
then
1-minute --------> move 20+(100/9)=(180+100)/9=280/9 pounds
Applying proportion
Find out how long it takes to move 100 pounds
[tex]\begin{gathered} \frac{1}{\frac{280}{9}}=\frac{x}{100} \\ \\ solve\text{ for x} \\ x=\frac{100}{\frac{280}{9}}=\frac{900}{280} \end{gathered}[/tex]Simplify the fraction
45/14
Convert to a mixed number
45/14=42/14+3/14=3 3/14 minutes
The answer is 3 3/14 minutesDrop down options for 1 2 and 4 are Forest A or Forest B
Given :
[tex]A(t)=107(1.015)^t[/tex][tex]B(t)=88(1.025)^t[/tex]1)
Set t=1 we get
[tex]A(t)=107(1.015)^t[/tex]IS THIS A FUNCTION YES OR NO?? (ALGEBRA 1)
Answer: Yes
Step-by-step explanation:
Yes, the numbers in the table are a function. The equation for the equation would be
y = 2x
A rectangular garden has one side with a length of x + 7 and another with a length 2x + 3. Find the perimeter of the garden.
A rectangular garden has one side with a length of x + 7 another with a length 2x + 3
We are asked to find the perimeter of the garden
Let me draw this rectangular garden to better understand the problem
Recall that the perimeter of a rectangular shape is given by
[tex]P=2(W+L)[/tex]Where W is the width and L is the length of the rectangular garden
Let us substitute the given values into the above formula
[tex]P=2(x+7+2x+3)[/tex]Now simplify the equation
[tex]\begin{gathered} P=2(x+2x+7+3) \\ P=2(3x+10) \\ P=6x+20 \end{gathered}[/tex]Therefore, the perimeter of the rectangular garden is equal to 6x + 20.