[tex]\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{17}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{17-11}{4-2}\implies \cfrac{6}{2}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-11=3(x-2)\implies y-11=3x-6[/tex]
[tex]\bf y=3x+5\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Answer:
[tex]y = 3x + 5[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
-y₁ + y₂\-x₁ + x₂ = m
[tex]\frac{-11 + 17}{-2 + 4} = \frac{6}{2} = 3[/tex]
Now, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:
17 = 3[4] + b
12
5 = b
[tex]y = 3x + 5[/tex]
__________________________________________________________
11 = 3[2] + b
6
5 = b
[tex]y = 3x + 5[/tex]
You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.
I am joyous to assist you anytime.
What is the y-intercept of the line with a slope of − 1/4 that passes through the point (−2, −9/2 )?
[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-\frac{9}{2}})~\hspace{10em} slope = m\implies -\cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\left( -\cfrac{9}{2} \right)=-\cfrac{1}{4}[x-(-2)] \\\\\\ y+\cfrac{9}{2}=-\cfrac{1}{4}(x+2)\implies y+\cfrac{9}{2}=-\cfrac{1}{4}x-\cfrac{1}{2}\implies y=-\cfrac{1}{4}x-\cfrac{1}{2}-\cfrac{9}{2}[/tex]
[tex]\bf y=-\cfrac{1}{4}x-\cfrac{10}{2}\implies y=-\cfrac{1}{4}x\stackrel{\stackrel{b}{\downarrow }}{\boxed{-5}}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
The slope of a graphed line is 2/3 and the y-intercept is (0,4) what is the slope-intercept equation of the line?
Answer:
B. y = 2/3x + 4
Step-by-step explanation:
the equation is Y = mx + b
m = slope
b = y-intercept
your answer is B. y = 2/3x + 4
Answer:
Step-by-step explanation:
It's B
The general equation of a slope intercept line is
y = mx + b
m = the slope
m = 2/3
b = the y intercept
b = (0,4)
So the equation is
y = 2/3 x + 4
How do I Graph h(x)=8|x+1|-1
Answer:
Step-by-step explanation:
To graph the function h(x) = 8|x+1| - 1, plot key points at (-3, 15), (-1, -1), and (1, 15). The graph exhibits vertical stretching due to the coefficient 8 and symmetry around the line x = -1.
To graph the function (h(x) = 8|x+1| - 1), follow these steps:
1. Identify Key Points:
Determine critical points where the expression inside the absolute value becomes zero. Here, when (x = -1), (h(x) = -1). Additionally, consider points on either side of -1.
2. Plot Points:
Plot these points on the coordinate plane: (-3, 15), (-1, -1), and (1, 15).
3. Determine Behavior:
Understand that the absolute value function |x+1| ensures symmetry around the vertical line x = -1. The coefficient 8 stretches the graph vertically, and the constant -1 shifts it downward.
4. Connect Points:
Draw a smooth curve connecting the points, considering the shape of the absolute value function.
5. Label Axes:
Label the x-axis and y-axis appropriately.
The resulting graph represents the function [tex]\(h(x) = 8|x+1| - 1\)[/tex].
Nine is 4 percent of what number
Answer:
225
Step-by-step explanation:
We can model this question with:
9 = 0.04x
x represents "what number."
0.04x = 9.
Divide 0.04 from both sides
0.04x ÷ 0.04 = 9 ÷ 0.04
9 ÷ 0.04 = 225.
Therefore, 9 is 4% of 225.
Answer:
225
Step-by-step explanation:
Is means equals and of means multiply
9 = 4% * W
Change to decimal form
9 = .04 * W
Divide each side by .04
9/.04 = .04W/.04
225 = W
A playground is in the shape of a square with each side equal to 109 yards. It has skating rinks in the shape of the quadrants of a circle at each corner. If the area of the remaining field is 9055, find the radius of each skating rink. Also, find the cost of cementing the skating rinks at $2.50 per square yards. Use
Answer:
radius = 30 yd , cost of cement = $7065
Step-by-step explanation:
First we will find the area of the circular sectors. From that we can find the cost of cement and their radius.
The area of the playground is ...
playground area = (109 yd)^2 = 11,881 yd^2
Then the area of the skating rinks is:
rink area = playground area - remaining field
rink area = 11,881 yd^2 - 9,055 yd^2 = 2,826 yd^2
Then the cost of cement for the rink area is ...
(2826 yd^2)($2.50 yd^2) = $7065
The four quarter-circle skating rinks add to a total area of a full circle. That area is given by ...
A = πr^2
Put the values in the formula:
2826 = 3.14r^2
Divide both sides by 3.14
900 = r^2
By taking square root at both sides we get,
30 = r
The radius of each quadrant is 30 yards....
Can some help me with this pleaseeee :(((; asappp
8cos20°.cos40°.cos80°=1
Answer:
Correct.
Step-by-step explanation:
I am assuming you want to verify the above. If you enter this product into your calculator you'll get a result of 1.
Answer:
see explanation
Step-by-step explanation:
Using the double angle identity
sin2x = 2sinxcosx
Consider the left side
cos20. cos40. cos80
= [tex]\frac{1}{2sin20}[/tex] (2sin20cos20)cos40.cos80
= [tex]\frac{1}{2sin20}[/tex] (sin40cos40cos80
= [tex]\frac{1}{4sin20}[/tex] (2sin40cos40)cos80
= [tex]\frac{1}{4sin20}[/tex] (sin80cos80)
= [tex]\frac{1}{8sin20}[/tex] (2sin80cos80)
= [tex]\frac{1}{8sin20}[/tex] sin160
= [tex]\frac{1}{8sin20}[/tex] sin(180 - 20)
= [tex]\frac{1}{8sin20}[/tex] sin20
= [tex]\frac{1}{8}[/tex]
Hence
8(cos20cos40cos80) = 8 ×[tex]\frac{1}{8}[/tex] = 1 = right side
Rewrite the polynomial -9x5 + 36x4 + 189x3 in factored form.
Answer:
-9x^3(x - 7)(x + 3)
Step-by-step explanation:
The sequence a, = 2, 4, 8, 16, 32, ... is the same as the sequence ay = 2,
an = 2an-1.
true or false
Answer:
TRUE
Step-by-step explanation:
TRUE
a_1 = 2
a_n = 2*(an_1)
if we start with 2, we would get
a_2 = 2*(a_1) = 2*(2) = 4
a_3 = 2*(a_2) = 2*(4) = 8
a_4 = 2*(a_3) = 2*(8) = 16
a_5 = 2*(a_4) = 2*(16) = 32
.
.
.
and so on
Answer:
the answer is TRUE
3x+5y=25
Please asap
distribute and simplify the radicals below (√12+6)(-√8-√2)
Answer:
Its A. on edge
Step-by-step explanation:
could that really be simplified anymore!!!!!
The simplified expression of (√12+6)(-√8-√2) is -6(√6 + √2).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
(√12 + 6) ( -√8 - √2)
√12 x -√8 - √12 x √2 + 6 x -√8 - 6 x -√2
-√96 - √24 - 6√8 + 6√2
-√(16x6) - √(4x6) - 6√(4x2) + 6√2
-4√6 - 2√6 - 12√2 + 6√2
-6√6 - 6√2
-6(√6 + √2)
Thus,
-6(√6 + √2) is our final expression.
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Spencer surveyed five of his friends to find out how many pets they have. His results are shown in the table below. What is the mean number of pets? Lara has 4, Cody has 2, Sam has 5, Ella has 1, Maria has 3
Answer:
3
Step-by-step explanation:
You add the total number of pets, and get 15. Then divide it by the number of people and get 3.
Answer: The mean is 3
Step-by-step explanation: In order to find the mean, you must add all the numbers (4+2+5+1+3) and then in this problem, you have to divide it by five since Spencer surveyed only five of his friends.
4+2+5+1+3=15
15 divided by 5 equals 3
As shown in the accompanying diagram, a dog is tied to a 16-foot leash,
which is attached to a corner where the house and fence meet. At this
corner, the angle between the house and the fence is 130°. When the dog
pulls the leash tight and walks from the house to the fence, what is the
distance that the dog walks, to the nearest tenth of a foot?
Backyard
Fence
(1) 11.6 feet
(2) 18.2 feet
(3) 32.0 feet
(4) 36.3 feet
House
(Not drawn to scale)
Find the circumference of the full circle:
Circumference = 2 x PI x radius.
The radius is given as the length of chain 16 feet.
Circumference = 2 x 3.14 x 16 = 100.48 feet.
The dog can walk 130 degrees.
Multiply the circumference by the fraction of a complete circle ( 360 degrees)
Distance = 100.48 x (130/360) = 36.28 feet
Round to 36.3 feet.
The answer is (4) 36.3 feet.
50% of the class are boys and 20% of class are blonde haired and there are three times as many boys are blonde haired.huv much percentage of blonde haired boys are in class
Answer:15%
Step-by-step explanation:
Divide 20 by 4 then 3/4th are boys so take the answer and add it 3 times.
Given that 50% of the class are boys and 20% are blonde-haired, if there are three times as many blonde boys, the percentage of blonde boys in the class is 60%.
Explanation:The question can be interpreted as looking for the percentage of boys with blonde hair in the entire class. We know that 50% of the class are boys and that there are three times as many boys that are blonde as the 20% that are generally blonde-haired. This means that 60% of the class are boys who have blonde hair.
We can calculate this by multiplying the total percent of blondes (20%) by 3, as we are told there are three times as many blonde boys. Hence, the percentage of blonde boys in the entire class is 60%.
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A line passes through the points one, four and three, -4 which is the equation of the line
ANSWER
[tex]y = - 4x + 8[/tex]
EXPLANATION
The given line passes through (1,4) and (3,-4).
The slope of this line is calculated using the formula:
[tex]m =\frac{y_2-y_1}{x_2-x_1} [/tex]
We substitute the points into the slope formula to get:
[tex]m = \frac{ - 4 - 4}{3 - 1} [/tex]
[tex] \implies \: m = \frac{ - 8}{2} [/tex]
[tex]m = - 4[/tex]
We substitute the first point and slope into the point-slope formula
[tex]y-y_1=m(x-x_1)[/tex]
This implies that
[tex]y - 4 = - 4(x - 1)[/tex]
We expand to get
[tex]y - 4 = - 4x + 4[/tex]
[tex]y = - 4x + 2/4+ 4[/tex]
[tex]y = - 4x + 8[/tex]
Howard flips a coin 335 times. What is the probability (p) of having ALL tails?
Step-by-step explanation:
The probability of getting tails is 0.5. The probability of getting tails 335 times is:
P = (0.5)^335
P = 1.43×10^-101
P ≈ 0
digits to write the value of the 5 in this number.
587,096
Answer:
Step-by-step explanation:
hundred thousandths
In the number 587,096, the value of the digit 5 would be 500,000 because it is in the hundred thousands position. We can express this as 5*100,000.
Explanation:In the number 587,096, the digit 5 is in the hundred thousands place. This means that the value of the digit 5 is not simply 5, but rather 500,000. To express this, we can write the number as 5*100,000. We multiply the actual digit (5) by its place value (100,000).
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The state of Alaska is the largest state in the United States and has a surface area of approximately 588,000 square miles. The state of Arizona has a surface area that is approximately 19.4% of the surface area of Alaska. What is the approximate surface area of the state of Arizona?
The approximate surface area of Arizona is calculated as 19.4% of Alaska's surface area, which is 588,000 square miles. By converting the percentage to a decimal and multiplying, we find that Arizona's surface area is approximately 114,072 square miles.
The question asks us to find the approximate surface area of the state of Arizona if it is 19.4% of the surface area of Alaska. To find this, we can use the known surface area of Alaska, which is approximately 588,000 square miles.
Here are the steps to calculate the surface area of Arizona:
Convert the percentage to a decimal by dividing it by 100: 19.4% \/ 100 = 0.194.Multiply this decimal by Alaska's surface area to find Arizona's surface area: 588,000 square miles * 0.194 = 114,072 square miles.So, the approximate surface area of the state of Arizona is 114,072 square miles.
The approximate surface area of the state of Arizona is 114,072 square miles, calculated as 19.4% of Alaska's surface area of 588,000 square miles.
To find the surface area of Arizona, we utilize the fact that it constitutes approximately 19.4% of Alaska's surface area.
This means that the surface area of Arizona is roughly 19.4% of the surface area of Alaska.
Given that the surface area of Alaska is approximately 588,000 square miles, we can calculate the surface area of Arizona by multiplying this value by 19.4%.
Mathematically, this can be expressed as:
[tex]\[ \text{Surface area of Arizona} = 0.194 \times \text{Surface area of Alaska} \][/tex]
Substituting the known value for the surface area of Alaska:
[tex]\[ \text{Surface area of Arizona} = 0.194 \times 588,000 \][/tex]
Calculating this yields:
[tex]\[ \text{Surface area of Arizona} \approx 0.194 \times 588,000 \][/tex]
[tex]\[ \text{Surface area of Arizona} \approx 114,072 \][/tex]
Therefore, the approximate surface area of the state of Arizona is 114,072 square miles, calculated as 19.4% of Alaska's surface area of 588,000 square miles.
This demonstrates the relative size of Arizona compared to Alaska.
Write the equation in general quadratic form: plz help!!!
Answer:
7x² - 40x - 12 = 0
Step-by-step explanation:
Solve the rational equation by combining expressions and isolating the variable. After doing that, then apply the Quadratic Formula to the listed answer choices to see if they give you the exact same x-intercepts, EXCEPT for this one, where you can easily factor this one. It is "process of elimination". Sometimes you have to try it.
9/10 divided by (-3/5) as a mixed number
Answer:
-1 1/2
Step-by-step explanation:
9/10 ÷ -3/5
Copy dot flip
9/10 * -5/3
-45/30
Divide the top and bottom by 15
-3/2
Change this to a mixed number
-1 1/2
The equation of a line is y-4=3(x+2) , which of the following is a point on the line? A (2, 4) B (4, -2) C (-2, 4) D (-4, 2)
Answer:
C (-2, 4)Step-by-step explanation:
The point-slope equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation
[tex]y-4=3(x+2)\\\\y-4=3(x-(-2))[/tex]
Therefore
m = 3
(x₁, y₁) = (-2, 4)
Solve for x. 4−2x · 4x = 64
[tex]4-2x \cdot 4x = 64\\-8x^2=60\\x^2=-\dfrac{15}{2}\\x\in\emptyset[/tex]
What is the measure, in degrees, of angle 1?
Answer:
Think simple.
angle 1 and the angle with the measurement of 110° are subplementary angles, therefore:
∠1 + 110° = 180°
∠1 = 180° - 110° = 70°
the point (5,-2) is rotated 90degrees about the orgin it’s image is what ?
What is the value for this expression?
2e-5
Answer:
[tex]0.0134[/tex]
Step-by-step explanation:
we have
[tex]2(e^{-5})[/tex]
Using a calculator
[tex](e^{-5})=0.0067[/tex]
substitute
[tex]2(0.0067)=0.0134[/tex]
find the equation of the line graph below in point slope form. show your work. (will make brainiest.)
Answer:
y-2=4/3(x-2)
Step-by-step explanation:
Pick one coordinate and then plug the x value and the by value into the formula and then to find the slope and count up 4 and to the right 3.
Subtract these polynomials. (6x2-x+8)-(x2+2)?
Answer:
5x2 - x + 6
Step-by-step explanation:
(6x2-x+8)-(x2+2)
We gonna use KCC which is Keep Change Change and distributing property
multiple (6x2-x+8) by 1 and (x2+2) by -1
6x2-x+8 -x2 - 2
combine the like terms
6x2 - x2 + 8 - 2 - x
5x2 + 6 - x
arrange in order
5x2 - x + 6
Here is the histogram of a data distribution. All class widths are 1.
4 5 6 7 8 9 10
Which of the following numbers is closest to the mean of this distribution?
From the given histogram, the mean of the distribution is 5. Therefore, option B is the correct answer.
What is mean?In statistics, the mean refers to the average of a set of values. The mean can be computed in a number of ways, including the simple arithmetic mean (add up the numbers and divide the total by the number of observations).
From the given histogram, the frequency distribution is
Number Frequency
1 1
2 2
3 3
4 1
5 1
6 2
7 3
8 1
9 1
Now, the mean is (1×1+2×2+3×3+4×1+5×1+6×2+7×3+8×1+9×1)/15
= (1+4+6+4+5+12+21+8+9)/15
= 70/15
= 4.67
≈ 5
Therefore, the mean is 5.
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The mean of the data distribution is 6.3.
The mean of a data distribution can be calculated by summing all the values and dividing by the total number of values. Considering the data set 4, 5, 6, 6, 6, 7, 7, 7, 7, 8, the mean is:
(4 + 5 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8) / 10 = 63 / 10 = 6.3
Julia went to the movies and spent $15 on her ticket and popcorn, if the popcorn cost $7 how much did her ticket cost ?
Final answer:
To find out how much Julia's movie ticket cost, we subtracted the cost of the popcorn ($7) from the total amount spent ($15) to get the movie ticket price of $8.
Explanation:
The student's question asks how much Julia's movie ticket cost if she spent a total of $15 on a movie ticket and popcorn combined, given that the popcorn cost $7. To solve this, we subtract the cost of the popcorn from the total amount spent.
Here's the calculation step by step:
Start with the total amount spent: $15.
Subtract the cost of the popcorn: $15 - $7.
The result gives us the cost of the movie ticket: $8.
Therefore, Julia's movie ticket cost $8.
Solve for X, please show work!
Answer:
the solution set consists of {x < -2 ∪ x > 10/3}
Step-by-step explanation:
|3x - 2| > 8 is equivalent to the following set of inequalities:
1) 3x - 2 > 8
and
2) -(3x - 2) > 8
In case 1, above, add 2 to both sides, obtaining 3x > 10, or x > 10/3.
In case 2, above, carry out the indicated multiplication first:
-3x + 2 > 8. Next, subtract 2 from both sides: -3x > 6.
Next, divide both sides by -3, remembering to reverse the direction of the inequality sign: x < -2.
Thus, the solution set consists of {x < -2 ∪ x > 10/3}
Answer:
x < -2 or x > 10/3
Step-by-step explanation:
3x - 2 > 8
3x > 10
x > 10/3
-3x + 2 > 8
-3x > 6
x < -2
x < -2 or x > 10/3