How do i find the x intercept using the slope intercept form, graphing the y intercept, then using the slope to step to the x intercept.
slope intercept form is: y = mx + b where m = slope and b = y-intercept
Once you have your slope intercept equation, solve for m.
How do i know to go left or right for run?
slope = rise/run
if the number is negative, you will go left.
Please comment if you have further questions.
A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the radius is 10 cm. (Note: Enter a positive value).
The volume of the snowball is decreasing at the rate of 502.56cm/min when the radius is 10 cm.
The volume of a sphere is given by the following equation:[tex]\frac{4\pi r^{3} }{3} ^{}[/tex]
We have to do the implicit differentiation of V in function of t. The are only two variables(V and r). So
[tex]\frac{dv}{dt} = \frac{4\pi }{3} 3r^{2} \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]
We have to find[tex]\frac{dv}{dt} when[/tex] [tex]\frac{dr}{dt} = - 0.4[/tex] r = 10
[tex]\frac{dv}{dt} = 4\pi (10)^{2} \times -0.4[/tex]
[tex]\frac{dv}{dt} = -502cm/m[/tex]
The negative means that the volume is decreasing.
So the answer is 502.56 cm/min.
What is volume?Volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, cuboid, cone, cylinder or sphere.
Different shapes have different volume. In 3D geometry, we studied various three-dimensionally defined shapes and solids such as cubes, cubes, cylinders, cones, etc. For each of these shapes, we learn to find volume.
The volume of a solid substance is measured in cubic units. For example, if the dimensions are given in meters, the volume is in cubic meters. It is a standard unit of volume in the International System of Units (SI). Similarly, other units of volume are cubic centimetre, cubic meter, cubic meter, etc.
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31. Original price: ?Discount: 20%Sale price: $75What is original price
Given:
We will find the original price, let it = x
Discount: 20%
Sale price: $75
As the discount = 20%
So, the sale price = 100 - 20 = 80%
So, 80% of x = 75
Note 80% = 80/100 = 0.8
So, we can write the following equation:
[tex]\begin{gathered} 0.8x=75 \\ x=\frac{75}{0.8}=93.75 \end{gathered}[/tex]So, the answer will be the original price = $93.75
Convert 81.3 to a fraction in simplest form
Answer:
813/10
Step-by-step explanation:
convert 81.3 to fraction by shifting the point once then making it over 10 cuz you shifted your point once;then break down to the simplest form
Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=2x^2+6x–16
Where
a = 2
b = 6
c = -16
Using quadratic formula, we solve for x:
[tex]undefined[/tex]Find the value of that makes m n.
43
m
n
150°
(3x - 15)°
since m and n are || lines :
150°+(3x-15)°=180°(Co-interior angles are supplementary)
[tex]150 + 3x - 15 = 180 \\ 3x + 150 - 15 = 180 \\ 3x + 135 = 180 \\ 3x = 180 - 135 \\ 3x = 45 \\ \frac{3x}{3} = \frac{45}{3} \\ x = 15[/tex]
x=15°
HOPE THIS HELPS
Answer:
x = 15
Step-by-step explanation:
If m and were parallel then
3x - 15 and 150 would be same- side interior angles and sum to 180° , so
3x - 15 + 150 = 180
3x + 135 = 180 ( subtract 135 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
then for m and m to be parallel , x = 15
Find the value for k given the line through (-1, k) and (-7, -2) is parallel to the line y = x + 1.
The value of k is 4 , the line through (-1,k) and (-7, -2).
Given,
The line through (-1, k) and (-7, -2) is parallel to the line y = x + 1.
To find the value of k
Now, According to the question is:
For Parallel lines, We know that
It has same slope as y = x + 1
Also, We know y = x +1 has slope of 1.
Using the formula for the slope :
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now, For value k
We have, 1 = (-2-k)/(-7-1)
=> 1 = (-2-k)/(-6)
=> -6 = -2 -k
=> -6+2 = -k
=> k = 4
Hence, The value of k is 4.
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Find the value of x. I have attached a photo.
Given:
Length of sides of smaller triangle = 4 and x
Lengths of larger sides = 10 and 25
Let's solve for the value of x.
Since both triangles are similar, the corresponding sides will be proportional.
To solve for x, apply the proportionality equation:
[tex]\frac{10}{4}=\frac{25}{x}[/tex]Cross multiply:
[tex]\begin{gathered} 10x=25*4 \\ \\ 10x=100 \\ \\ \text{ Divide both sides by 10:} \\ \frac{10x}{10}=\frac{100}{10} \\ \\ x=10 \end{gathered}[/tex]Therefore, the value of x is 10.
A city is considered raising taxes to build a football stadium A survey of registered voters yielded the following results !If 400 people were surveyed,how many support the tax hike .Position : Against tax hike 7/16. For tax hike 3/16. Undecided 3/8. if 400 people were surveyed,how many support the tax hike ?
Total sample popuation = 400
Fraction of those for the tax hike = 3/16
fraction of those against the tax hike = 7/16
The number of those that support the tax hike is
3/16 of 400
=> 3/16 x 400
=> 1200/ 16
=>75 people
Solving systems y=2-2x. x=y-5
we get that:
[tex]x=2-2x-5\rightarrow x+2x=-3\rightarrow3x=-3\rightarrow x=-1[/tex]so we get
[tex]y=2-2\cdot-1=2+2=4[/tex]Find the measure of angles 1-7 that lines m and n are parallel and t is transversalm<1 =
First, from the diagram and the fact that lines m and n are parallel we get that:
1)
[tex]39^{\circ}+\measuredangle1=180^{\circ}.[/tex]Therefore:
[tex]\measuredangle1=180^{\circ}-39^{\circ}=141^{\circ}.[/tex]2) Angles 1 and 3 are opposed by the vertex, and the same occurs for angles 5 and 7, 4 and 6, and the angle of measure 39 degrees and 2, therefore:
[tex]\begin{gathered} \measuredangle1=\measuredangle3\text{ }\Rightarrow\measuredangle3=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle5=\measuredangle7, \\ \measuredangle4=\measuredangle6. \end{gathered}[/tex]3) Angles 3 and 5 are alternate interior angles, and the same occurs for angles 2 and 4, therefore:
[tex]\begin{gathered} \measuredangle5=\measuredangle3=141^{\circ}, \\ \measuredangle4=\measuredangle2=39^{\circ}. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} \measuredangle1=141^{\circ}, \\ \measuredangle2=39^{\circ}, \\ \measuredangle3=141^{\circ}, \\ \measuredangle4=39^{\circ}, \\ \measuredangle5=141^{\circ}, \\ \measuredangle6=39^{\circ}, \\ \measuredangle7=141^{\circ}. \end{gathered}[/tex]State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.A No; it is a ratioBYes; degree 1CNo; x is a negative termDYes; degree 4
Given:
The function is,
[tex]\frac{8-x^4}{9}[/tex]It can be written as,
[tex]\frac{8}{9}-\frac{x^4}{9}[/tex]Polynomial is a combination of terms seperated using + and - sign which does not contain,
1) Variable in demominator
2) Variables under radical
3) special features like trigonometric function, absolute values etc.
So, it shows that the given function is polynomial with degree 4.
Answer: option D)
Find the value of x. Round to thenearest tenth.1.47 2.1ft2xx = [? ]ft=Enter
To find the value of x:
Consider the right angle triangle,
The opposite side is 1.4 ft
The adjacent side is x
The hypotenuse side is 2.1ft
Using Pythagoras theorem,
[tex]\begin{gathered} \text{Hyp}^2=\text{Opp}^2+\text{Adj}^2 \\ (2.1)^2=(1.4)^2+x^2 \\ 4.41=1.96+x^2 \\ x^2=4.41-1.96 \\ x^2=2.45 \\ x=1.5652 \\ x\approx1.57ft \end{gathered}[/tex]Hence, the value of x is 1.57 ft.
4. A construction company pays carpenters $15 an hour for the first 40 hours they work in a week, and $20 for each additional hour they work. Which expression could be used to find a carpenter's salary if he worked h hours over 40? A (15 X 40) + (20 H) B. (20 x 40) + (15 x h) c. (15 X 40) X (20 x h) D. (15 x 40) X (20 + h) Х
Let h be the number of additional hours. Since the fixed pay is 15 dollars for the first 40 hours, this means that from there, each hour will be paid with 20 dollars. We can write the following equation to represent this situation:
[tex]y=40\cdot15+20h[/tex]Find a polynomial function that has zeros of -3 and +6
Answer
P(x) = x² - 3x - 18
Explanation
We are asked to find the polynomial function which has zeros -3 and +6.
x = -3 and x = 6
(x + 3) (x - 6) = 0
x (x - 6) + 3 (x - 6) = 0
x² - 6x + 3x - 18 = 0
x² - 3x - 18 = 0
Hope this Helps!!!
1) Given that f(x)
2x²-3x - 7, where x ER
a) Show that the equation f(x) = 0 has two real roots.
b) Solve the equation f(x) = 0.
=
Answer:
Step-by-step explanation:
1) Given that f(x)= 2x²-3x - 7
a) Show that the equation f(x) = 0 has two real roots.
Calculate the discriminant Δ
f(x) = ax²+bx+c
f(x) = 2x²-3x - 7
Δ= b²-4ac = (-3)²-4·2·(-7) = 9 +56 = 65
Δ =65 is
Δ > 0 so the equation has 2 real distinct roots because the discriminant is not 0 or negative, it is a positive number.
b) Solve the equation f(x) = 0.
x= (-b ±√Δ)/2a
x= (3 ±√65)/2·2
One root is x=(3 + √65)/4, the second root is x=(3 - √65)/4
Solutions are x≈2.77 and x≈ -1.27
The sum o{ the squares of two
consecutive positive even integers
is one hundred. Find the two integers.
A starship is orbiting Milgram, a large moon of the planet Bourbakon. The ship's sensor arraydetects that the temperature on the surface of the moon is -3.8 °F. What is this temperature indegrees Celsius (°C)?Use the given formulas as necessary, and round your answer to the nearest tenth of a degree.
Concept use formula for converting degree Fahrenheit to degree celsius
[tex]\begin{gathered} ^oC\text{ = }\frac{5}{9}^{}(^oF\text{ }-\text{ 32 )} \\ ^oC\text{ = }\frac{5}{9}\text{ ( -3.8 - 32 )} \\ ^oC\text{ = 0.5555556 }\times\text{ (- 35.8 )} \\ ^oC\text{ = -19.888} \\ ^oC\text{ = -19.9} \end{gathered}[/tex]Final answer = - 19.9
At a store, a hat has a regular price of x dollars. During a sale, the price of the hat is discounted by 20%.
The final discounted price of the hat can be calculated by subtracting the discount from the regular price, like this:
discounted price = regular price - discount
By calling x to the regular price, we can rewrite the equation to get:
discounted price = x - discount
The discount, is calculated by multiplying the regular price by the discount percentage, in this case, a 20% (0.2) discount is applied, then we can rewrite the above equation to get:
discount price = x - 0.2x
Then, option D x - 0.2x describes the discount price
Select the correct answer.Rectangle is dilated by a scale factor of 3 with the origin as the center of dilation, resulting in the image . If the slope of is , what is the slope of ?
Hello there. To solve this question, we'll have to remember some properties about finding slopes of lines and dilations.
Given that the rectangle KLMN is dilated by a scale factor of 3 with the origin being the center of the dilation, resulting in the image K'L'M'N', we need to find the slope of K'L' knowing the slope of KL is -3.
We start by drawing the situation:
Just as an example. The rectangle many not pass through the same points, but the center is at the origin, which means it intersects the x and y axis at symmetric points.
Now, remember a dilation is a transformation that stretches every side at once, or in other words, re-scales the entire figure by a factor.
Since this factor is 3, we would have something like the following:
For the curve, estimate the instantaneous rate of change at x=5 without the use of derivatives
Answer: -0.733
Step-by-step explanation:
To estimate the instantaneous rate of change, we can take the slope of the secant through two points on the curve that are close to x=5.
In this case, we will consider [tex](4.9, f(4.9))[/tex] and [tex](5.1, f(5.1))[/tex].
[tex]\frac{f(5.1)-f(4.9)}{5.1-4.9} \approx -0.733[/tex]
Find the x-and y-intercepts.3x – 2y =-6The x-interceptisThe y-intercept is
The x-intercept -2 is and the y-intercept is 3
Here, we are tasked by finding the x-intercept and the y-intercept of the given straight line
The x-intercept is the point on the graph where we have the coordinates as (x,0)
What this mean is that at the x-intercept, the value of y = 0
Thus by substituting y = 0 into the equation, we can get the value of the x-intercept
Making the substitution, we have
3x - 2(0) = -6
3x = -6
x = -6/3
x = -2
The y-intercept is the point on the graph where we have the coordinates as (0,y)
What this mean is that at the y-intercept, the value of x = 0
Thus by substituting x = 0 into the equation, we can get the value of the y-intercept
Making the substitution, we have
3(0) - 2y = -6
-2y = -6
divide both sides by -2
y = -6/-2
y = 3
Please help with math problem FAST
You draw one card from a 52-card deck. Then the card is replaced in the deck and the deck is shuffled, and you draw again. Find the probability of drawing a nine the first time and a heart the second time
SOLUTION:
Step 1:
In this question, we are given the following:
You draw one card from a 52-card deck.
Then the card is replaced in the deck and the deck is shuffled, and you draw again.
Find the probability of drawing a nine the first time and a heart the second time
Step 2:
From the question, we can see that the probability of drawing a nine the first time and a heart the second time is:
[tex]\frac{4}{52\text{ }}\text{ x }\frac{13}{52}=\text{ }\frac{52}{52\text{ x 52}}=\frac{1}{52}[/tex]CONCLUSION:
The probability of drawing a nine the first time and a heart the second time is:
[tex]\frac{1}{52}[/tex]
The maximum distance d in kilometers that you can see from a height of h meters is given by d=3.2/h. Findhow far you can see from the top of the building, a height of 290.7 meters. Round to the nearest tenth of akilometer.
Explanation
We are told that the maximum distance, d in kilometres that can be observed is given by
[tex]d=\frac{3}{2}h[/tex]If the height of the building is 290.7 meters, then
The value of d will be calculated as
[tex]\begin{gathered} d=\frac{3}{2}\times h=\frac{3}{2}\times290.7 \\ \\ d=436.05\text{ Km} \end{gathered}[/tex]Thus, the value of d will be 436.1 km
what is -4 7/22 wrriten as a decimal
Answer:
-4.31818 or 2.13636
Step-by-step explanation:
I can't really tell how its written if it's -4 and 7/22 it would be -95/22 or -4.31818. if it is -47/22 it would be 2.13636. I did this by dividing the numerator by the denominator
Answer:
-4.31818 or -2.13636
Step-by-step explanation:
if its -4 and 7/22 then the first one and if its -47/22 then the second one
In the United States nearly 8 x 10^9 text messages are sent everymonth About how many text messages is this! Find the primefactorization of this number and write the result using exponents.
1) Since in the USA 8 x 10 ^9 messages are sent every month, that means that approximately 8 billion messages are sent.
2) We can Prime factorize it:
Note that on the right side we've picked only prime numbers. In this case, 2 and 5.
So we can rewrite 8 x 10^9 as prime factors.
[tex]8\times10^9=2^{12}\times5^9[/tex]3) Hence, the answer is:
[tex]8\times10^9=2^{12}\times5^9[/tex]Find the range of allowable values based on the given information. Round to the nearest tenth 49; can vary by 8.1%
49 rounded to the closest tenth; possible 8.1% variation. The range of allowable values to the nearest tenth is 4.
Given that,
We have to find using the information provided, determine the permissible value range. 49 rounded to the closest tenth; possible 8.1% variation.
The range in statistics refers to the distribution of your data between the lowest and greatest value in the distribution.
Measurements of variability provide you with descriptive statistics for summarizing your data set in addition to measures of central tendency.
By deducting the lowest value from the greatest value, the range is computed. A short range indicates low variability in a distribution, whereas a big range denotes significant variability.
We now,
49×8.1%=3.969
The nearest tenth is 4.
Therefore, the range of allowable values to the nearest tenth is 4.
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Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator and simplify.)A.B.C.2D.
Given: A fraction
[tex]\frac{2-\sqrt{2}}{2+\sqrt{2}}[/tex]Required: To simplify the given fraction.
Explanation: The given fraction can be simplified by rationalizing the denominator of the fraction. The rationalizing factor is
[tex]2-\sqrt{2}[/tex]Hence,
[tex]\begin{gathered} \frac{(2-\sqrt{2})}{2+\sqrt{2}}\times\frac{(2-\sqrt{2})}{(2-\sqrt{2})} \\ \frac{(2-\sqrt{2})^2}{(2)^2-(\sqrt{2}^{)2}} \end{gathered}[/tex]Which gives
[tex]\begin{gathered} \frac{4+2-4\sqrt{2}}{4-2} \\ \frac{2(3-2\sqrt{2})}{2} \\ 3-2\sqrt{2} \end{gathered}[/tex]Final Answer: Option A is correct.
help meeeeeeeeeeeeeeeeeeeeeee
thank you
The value of the function f(-5) is -6
How to evaluate the function?The given parameters are the graphs in the figure
From the question, we have the function definition to be f(-5)
When the graphs are analysed, we have the following highlights
The equation of the first graph is illustrated by the function f(x), while the second is illustrated by the function g(x)
Recall that the function definition is f(-5)
So, we use the function represented by f(x) i.e. the first graph
The function f(-5) means the value of x is -5
Looking at the values on the first graph, we have the following representation
f(-5) = -6
Hence, the function f(-5) has a value of -6
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The fee for charging an electric car at Station A is $2 to start and $4 for each hour or fraction of an hour. Which point is NOT included in the graph of this step function?A.(2.5, 14)B.(2, 10)C.(0, 0)D.(1, 6)Part BThe fee for charging an electric car at Station B for x hours is modeled by the function shown:f(x)={4x, if 0
The station cost $2 to start and after that $4 for every hour or fraction of hour.
For 2.5 hours, the charge is $2 to start after that 4$ for first hour, $4 for second hour and $4 for next 1/2 hours. Total cost is,
[tex]2+4+4+4=14[/tex]Simillarly for 2 hours total cost is,
[tex]2+4+4=10[/tex]For 0 hours there is start cost of $2 so point (0,2) must be included or (0,0) NOT included.
PART B
Determine the cost to charge a car at station A for 4 hours.
[tex]2+4+4+4+4=18[/tex]Determine the cost to charge a car at station B for 4 hours.
[tex]2\cdot4+3=15[/tex]So cost to charge a car for 4 hours is less for station B and fee for charging the car for 4 hours there is $15.
