The Equation is 10 + x= 30 and 20 actors are from third grade.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
There are 30 actors in a school play.
There are 10 actors from second grade.
The rest are from third grade.
let the actors in third grade is x.
Equation is:
Actors from second grade + Actors from third grade = Total actors
10 + x= 30
Now, solving
Subtract 10 from both side
10 +x - 10 = 30 - 10
x = 20
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Part I: Domain and Range-identify the domain and range of each graph. Problem / Work Answe 2+ 6+ 2+ 1. Week 15 Homework Packet pdf 2003
Domain is the set of input values,
In the graph x axis show the domain
Where the x values is lies at -2,-1,0,1,2
Sothe domain will be :
[tex]\text{Domain =-2}\leq x\leq2[/tex]Range is the set of output values,
In the graph the value of function at y axis is : 0,2,4,6,8-2,-4.....
So, the range will be :
[tex]\text{Range = -}\infty\leq y\leq\infty[/tex]Sarah wants to take a vacation that will cost 2,562 if sarah plans to save for 9 months, then how much needs to be saved per month
Let:
x = Number of months
y = Total savings
a = Savings per month
so:
[tex]\begin{gathered} y=ax \\ where \\ y=2562 \\ x=9 \\ so\colon \\ 2562=9a \\ solve_{\text{ }}for_{\text{ }}a\colon \\ a=\frac{2562}{9} \\ a\approx284.67 \end{gathered}[/tex]She needs to save approximately $284.67 per month
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 km5) 40,20,10,5, _,_,_a) Explain and Complete the sequence.B) write an explicit and recursive formula for the sequence
We have the sequence: 40, 20, 10, 5,...
Each term is half the previous term, so it is a geometrical sequence with common ratio r = 0.5.
We can not complete the sequence, as it becomes infinitely smaller and does not have a last term.
But we can write the three next terms to complete the blank spaces: 2.5, 1.25, 0.625.
We can start by writing the recursive formula. We know that each term is half the value of the previous term, so we wil have:
[tex]a_n=0.5\cdot a_{n-1}[/tex]From this recursive formula, we can deduce the explicit formula (in terms of n) as:
[tex]\begin{gathered} a_1=40 \\ a_2=0.5\cdot40=20 \\ a_3=0.5\cdot20=0.5\cdot(0.5\cdot40)=0.5^2\cdot40=10 \\ a_4=0.5\cdot10=0.5\cdot(0.5^2\cdot40)=0.5^3\cdot40 \\ \Rightarrow a_n=40\cdot0.5^{n-1} \end{gathered}[/tex]Answer:
a) Geometric sequence with r = 0.5.
The sequence first terms are: 40, 20, 10, 5, 2.5, 1.25, 0.625.
b) The recursive formula is a(n) = 0.5*a(n-1).
The explicit formula is a(n) = 40*0.5^(n-1).
The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Find the radius of the largerwheel in the figure if the smaller wheel rotates 70.0° when the larger wheel rotates 40.0°The radius of the large wheel is approximately ____ cm.
Let's begin by listing out the information given to us:
r (1) = 11.4 cm, θ (1) = 70°, θ (2) = 40°, r(2) = ?
The arc length is the same for the 2 circles
r (1) * θ (1) = r (2) * θ (2)
11.4 * 70° = r (2) * 40°
r (2) = 11.4 * 70 ÷ 40
r (2) = 19.95 cm
Hence, the radius of the larger circle is 19.95 cm
HELP ME OUT PLEASE!!!!!!
Answer:
The First one (1.7,3.1)
Step-by-step explanation:
3x-2=-0.5x+4
3.5x=6
x=12/7
x≈1.7
sub x back into to find y
y≈3.1
NEED HELP FAST!!
For ΔABC, m∠A = 41.3° and m∠B = 103.4°. Determine m∠C.
144.7°
72.35°
54.7°
35.3°
Answer: The answer is D. 35.3
Step-by-step explanation: Because the triangle has to add up to 180 and 41.3 + 103.4 = 144.7. Then you could either do 180-144.7 = 35.3 or you could add 144.7 + 35.3. Hope this helps
The value of angle C based on the information is A. 35.3°
How to calculate the angle?It's important to know that the total sum of angles in a triangle is 180°.
In this case, the following can be deduced:
Angle A = 41.3°
Angle B = 103.4°
Therefore, Angie C will be:
= Total angle - {Angle A + Angle B}
= 180° - (41.3° + 103.4°)
= 180° - 144.7°
= 35.3°
Therefore, the correct option is D.
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Is my answer correct help please
Answer:
Yes your answer is right !
Step-by-step explanation:
steps
X= 3 and y = 7
So first replace [tex]2^{x}[/tex] with [tex]2^{3}[/tex] an that will give you 8Then 8-Y and so you replace y with 7 and so it becomes
8-7 = 1So the correct answer is D (1)
Hope this helps
~~Wdfads~~
I have answer for the question it in the image but I don't know if it right and I don't know any other formulas to find the area of a triangle
Hello there. To solve this question, we'll have to remember which other formulas for area of triangles can be used.
Most specifically, it asks for a formula that works on an obtuse triangle, that is, a triangle that haves an angle that measures more than 90º.
Besides the formula BH/2, that refers to half of the product between the measurements of the base and the height of the triangle, of course, this height must be a projection perpendicular to the base, as in the following drawing:
Another formula that can be used is Heron's formula;
Knowing the measures of all the sides of the triangle (no matter if it is an obtuse, acute or right triangle), say a, b and c, Heron's formula states that the area S of the triangle is given by:
[tex]S=\sqrt{\rho\cdot(\rho-a)\cdot(\rho-b)\cdot(\rho-c)}[/tex]Where
[tex]\rho=\dfrac{a+b+c}{2}[/tex]is the semiperimeter of the triangle.
This is the answer we've been looking for.
Sam rides at a rate of 14.5 miles per 1 hour. If he rides at a constant rate, how many miles would he ride in 1 hour and 15 minutes?
Sam would ride 18.125 miles when hw would ride at the rate of 14.5 miles/hour.
According to the question,
We have the following information:
Speed of Sam = 14.5 miles/hour
Distance to be covered = ?
Time taken to cover the distance = 1 hour and 15 minutes
Now, we will convert the time given in minutes into hour.
We have 15 minutes.
We know that 1 hour is equal to 60 minutes.
So, we will convert 15 minutes into hour:
15/60 hour
0.25 hour
So, the total time taken = (1 + 0.25) hour
Time taken = 1.25 hour
We know that the following formula is used to find the speed:
speed = distance/time
Distance = speed*time
Distance = 14.5*1.25
Distance = 18.125 miles
Hence, the distance covered by Sam in 1 hour and 15 minutes is 18.125 miles.
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From question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*
Answer:
The complete table:
6 18 2 42
9 27 3 63
Explanation:
We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is
[tex]\frac{\min}{\text{song}}=\frac{9}{6}[/tex]Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get
[tex]song\times\frac{\min}{\text{song}}=\frac{9}{6}\times\text{song}[/tex]which gives
[tex]min=\frac{9}{6}\times\text{song}[/tex]This means the number of minutes practised is 9/6 of the number of songs played.
Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get
[tex]\frac{9\div3}{6\div3}=\frac{3}{2}[/tex]therefore, we have
[tex]min=\frac{3}{2}\times\text{song}[/tex]Now we are ready to fill the table.
If Montell plays 18 songs then we have
[tex]\min =\frac{3}{2}\times18[/tex][tex]\min =27[/tex]the minutes practised is 27 for 18 songs.
If Montell practices for 3 minutes then we have
[tex]3=\frac{3}{2}\times\text{song}[/tex]then the value of song must be song = 2, since
[tex]\begin{gathered} 3=\frac{3}{2}\times2 \\ 3=3 \end{gathered}[/tex]Hence, for 3 minutes of practice, Montell sings 2 songs.
Now for 42 songs, the number of minutes played would be
[tex]\min =\frac{3}{2}\times42[/tex]which simplifies to give
[tex]\min =63[/tex]Hence, for 42 songs played, the practice time is 63 minutes.
To summerise, the complete table would be
songs 6 18 2 42
minutes 9 27 3 63
Find the slope and the equation of the line having the points (0, 2) and (5, 5)
Answer:
The slope is 3/5 and the equation is:
[tex]y=\frac{3}{5}x+2[/tex]Explanation:
Given the points (0,2) and (5, 5)
The slope of a line is the ratio of the difference between the y coordinates to the x coordinates. The x coordinates are 0 and 5, the y coordinates are 2 and 5.
[tex]\begin{gathered} m=\frac{5-2}{5-0} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The equation of a straight line is given as:
y = mx + b
Where m is the slope and b is the y-intercept
Using any of the given points, we can find b
Use (0, 2), with x = 0, y = 2
2 = (3/5)(0) + b
b = 2
Now the equation is:
[tex]y=\frac{3}{5}x+2[/tex]The oil tank in your car is leaking at a rate of 1.2 oz per mile driven you drove 15 miles how many cups of oil did your car leak
we know that
The unit rate is equal to
1.2 oz per mile
so
To obtain the number of ounces
multiply the unit rate by the number of miles driven
1.2*(15)=18 oz
step 2
Convert ounces to cups
Remember that
1 oz=0.125 cups
so
18 oz=18*0.125=2.25 cups
therefo
I got stuck and I need help on this I would appreciate the help:0
1) In this problem, we can see that this is an isosceles right triangle.
2) So, one way of solving it is to make use of the Pythagorean theorem. Note that an isosceles triangle has two congruent sides, so we can write out:
[tex]\begin{gathered} a^2=b^2+c^2 \\ b=c \\ 9^2=x^2+x^2 \\ 81=2x^2 \\ 2x^2=81 \\ \frac{2x^2}{2}=\frac{81}{2} \\ x^2=\frac{81}{2} \\ \sqrt[]{x^2}=\sqrt[]{\frac{81}{2}} \\ x=\frac{9}{\sqrt[]{2}} \end{gathered}[/tex]Usually, we rationalize it. But since the question requests the denominator to be a rational one, so this is the answer.
What is the equation of the line that passes through the point (7,6) and has a slope of 0
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
Given,
The points which the line passes, (x₁, y₁) = (7, 6)
Slope of the line, m = 0
We have to find the equation of the line:
We know that,
y - y₁ = m(x - x₁)
So,
y - 6 = 0(x - 7)
y - 6 = 0
y = 6
That is,
The equation of the line that passes through the point (7, 6) with slope 0 is y = 6
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Equation of the line that passes through points (8,7) and (0,0)
Equation of the line:
y = mx+b
where:
m= slope
b= y-intercept
First, we have to find the slope:
m = (y2-y1) / (x2-x1)
Since we have:
(x1,y1) = (8,7)
(x2,y2)= (0,0)
Replacing:
m = (0-7)/ (0-8) = -7/-8 = 7/8
Now, that we have the slope:
y = 7/8 x +b
We can place the point (8,7) in the equation and solve for b:
7 = 7/8 (8) +b
7=7 +b
7-7=b
b=0
Since the y-intercept=0
The final equation is:
y= 7/8x
“Use the properties to rewrite this expression with the fewest terms possible:3+7(x - y) + 2x - 5y”
Expanding 7(x - y) in the above expression gives
[tex]-5y^{}+2x+7x-7y+3[/tex]adding the like terms (2x+ 7x) and (-5y-7y) gives
[tex](-5y-7y)+(2x+7x)+3[/tex][tex]\rightarrow\textcolor{#FF7968}{-12y+8x+3.}[/tex]The last expression is the simplest form we can convert our expression into.
Carmen has 12 loaves of pumpkin bread. She cuts each loaf into 1/8 pieces and gives one piece to each of her friends. How many friends can Carmen give a piece of pumpkin bread?
12 loaves of pumpkin bread.
Each loave is cut into 1/8 pieces.
So, there are 8 pieces per loaf:
8 pieces per loaf x 12 loaves = 96 pieces
If she gives one piece to each friend she can give it to 96 friends:
96 pieces / x friends = 1 per friend
96/x =1
96 = x(1)
96= x
translate the following verbal statement into an algebraic equation and solve. Paid 24,998 for a car which was 1,815 less than sticker price what was the sticker price of the caruse x for your vairableequation_______x=______
paid price = 24,998
it is the amount that is 1815 less than the sticker price,
so the sticker price or price of the car is x
so x = 24,998 + 1815
x =26,813
so the price of car is x = 26,813.
I need help in math can you please help me
We have the following:
[tex]\begin{gathered} \sin \theta=-\frac{8}{17} \\ \theta=\sin ^{-1}(-\frac{8}{17}) \\ \theta=-28.07 \end{gathered}[/tex]now, in Quadrant III (180° to 270°):
[tex]\theta=180+28.07=208.7[/tex]now, for cosine:
[tex]\cos 2\theta=\cos (2\cdot208.7)=0.538=\frac{539}{1000}[/tex]The answer is 539/1000
Rectangle WXYZ has vertices located at W(−6, 4), X(−6,−1), Y(2,−1), and Z(2, 4) on a coordinate plane. It is translated 4 units right and 2 units down to produce rectangle W'X'Y'Z'. What is the location of the vertices of the transformed rectangle?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Rectangle WXYZ
W(−6, 4)
X(−6,−1)
Y(2,−1)
Z(2, 4)
Step 02:
Translated
4 units right ===> x + 4
2 units down ===> y - 2
W' (−6+4, 4 -2) = W' (-2, 2)
X' (−6+4,−1 - 2) = X' (-2,-3)
Y' (2+4,−1-2) = Y' (6,-3)
Z' (2+4, 4-2) = Z' (6, 2)
The answer is:
W' (-2, 2)
X' (-2,-3)
Y' (6,-3)
Z' (6, 2)
Determine whether the arc is a minor arc, a major arc, or a semicircle of R. Questions 25 nd 27
We can find the missing angles using the drawing below.
Then,
[tex]\begin{gathered} 360=60+60+55+x+y \\ \text{and} \\ 55+y=x \\ \Rightarrow240=2(55+y) \\ \Rightarrow120=55+y \\ \Rightarrow y=65 \\ \Rightarrow x=120 \end{gathered}[/tex]Therefore
25)
Arc JML covers an angle equal to 65+55+60=180; thus, ArcJML is a semicircle of R.
27)
Using the equation and the ordered-pairs found previously, plot the points on the graph that would best satisfy theequation.y= 2^x
Given the following equation:
[tex]y=x^2[/tex]We will graph the given function using the points that will be written in ordered-pairs.
The given function is a quadratic function with a vertex = (0, 0)
We will graph the points using five points
The vertex and 4 points, 2 points before the vertex and 2 points after the vertex.
So, we will substitute x = -4, -2, 2, 4
[tex]\begin{gathered} x=-4\rightarrow y=16 \\ x=-2\operatorname{\rightarrow}y=4 \\ x=2\operatorname{\rightarrow}y=4 \\ x=4\operatorname{\rightarrow}y=16 \end{gathered}[/tex]So, the points are: (-4, 16), (-2, 4), (0, 0), (2, 4), (4, 16)
The graph using the points will be as follows:
Differentiate. f(x) = (x3 - 3)2/3 2x f'(x) 3 x 8 х f'(x) 3 | 23-8 2x2 f'(x) 3 S x2 f'(x) 3 8
1) Let's calculate the derivative of f(x) = (x³-8) ^(2/3)
Let's start applying the power rule :
[tex]undefined[/tex]3. What is the vertical shift for the absolute value function below?F(x) 9|x + 1|+ 2
Answer:
The vertical shift is of 2 units up
Step-by-step explanation:
We have a function in the following format:
F(x) = a(x+b) + c
The vertical shift is given by c.
If c > 0, the shift is up.
If c < 0, the shift is down.
In this question:
F(x) = 9|x+1| + 2
So c = 2
The vertical shift is of 2 units up
im not sure the steps to this math problem, from step one to step three
The equation of the second line is written in standard form. To know the slope of this line, we can rewrite its equation in slope-intercept form by solving for y.
[tex]\begin{gathered} ax+by=c\Rightarrow\text{ Standard form} \\ y=mx+b\Rightarrow\text{ Slope-intercept form} \\ \text{ Where m is the slope and b is the y-intercept} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} 4x-5y=-10 \\ \text{ Subtract 4x from both sides of the equation} \\ 4x-5y-4x=-10-4x \\ -5y=-10-4x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-10-4x}{-5} \\ y=\frac{-10}{-5}-\frac{4x}{-5} \\ y=2+\frac{4}{5}x \\ \text{ Reorganize} \\ y=\frac{4}{5}x+2 \\ \text{ Then} \\ $$\boldsymbol{m=\frac{4}{5}}$$ \end{gathered}[/tex]Now, two lines are perpendicular if their slopes satisfy the following equation:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ \text{ Where }m_1\text{ is the slope of the first equation and} \\ m_2\text{ is the slope of the second equation} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} m_2=\frac{4}{5} \\ m_1=-\frac{1}{\frac{4}{5}_{}} \\ m_1=-\frac{\frac{1}{1}}{\frac{4}{5}_{}} \\ m_1=-\frac{1\cdot5}{1\cdot4} \\ $$\boldsymbol{m}_{\boldsymbol{1}}\boldsymbol{=-\frac{5}{4}}$$ \end{gathered}[/tex]Step 2Since we already have a point on the line and its slope, then we can use the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ \text{ Where } \\ m\text{ is the slope and} \\ (x_1,y_1)\text{ is a point through which the line passes} \end{gathered}[/tex]Then, we have:
[tex]\begin{gathered} (x_1,y_1)=(6,3) \\ m=-\frac{5}{4} \\ y-3=-\frac{5}{4}(x-6) \\ \text{ Apply the distributive property} \\ y-3=-\frac{5}{4}\cdot x-\frac{5}{4}\cdot-6 \\ y-3=-\frac{5}{4}x+\frac{5}{4}\cdot6 \\ y-3=-\frac{5}{4}x+\frac{30}{4} \\ \text{ Add 3 from both sides of the equation} \\ y-3+3=-\frac{5}{4}x+\frac{30}{4}+3 \\ y=-\frac{5}{4}x+\frac{30}{4}+\frac{12}{4} \\ y=-\frac{5}{4}x+\frac{30+12}{4} \\ y=-\frac{5}{4}x+\frac{42}{4} \\ \text{ Simplify} \\ y=-\frac{5}{4}x+\frac{21\cdot2}{2\cdot2} \\ y=-\frac{5}{4}x+\frac{21}{2} \end{gathered}[/tex]Step 3Therefore, the equation of the line that passes through the point (6,3) that is perpendicular to the line 4x - 5y = -10 is
[tex]$$\boldsymbol{y=-\frac{5}{4}x+\frac{21}{2}}$$[/tex]I was doing this with a tutor but there was a connection problem.
ANSWER:
[tex](x-3)^2+(y+7)^2=113[/tex]The point (7,6) is not on the circle
STEP-BY-STEP EXPLANATION:
(a)
The equation of the circle is given as follows:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ where (h,k) is the center and r is the radius } \end{gathered}[/tex]We replace to calculate the radius of the circle, like this:
[tex]\begin{gathered} \mleft(-4-3\mright)^2+\mleft(1-\mleft(-7\mright)\mright)^2=r^2 \\ (-7)^2+(8)^2=r^2 \\ r^2=113 \end{gathered}[/tex]Therefore, the equation would be:
[tex](x-3)^2+(y+7)^2=113[/tex](b)
We replace the point, and if the value is greater than the radius, it means that this point is not on the circle:
[tex]\begin{gathered} (x-3)^2+(y+7)^2\le113 \\ \text{ replacing:} \\ \mleft(7-3\mright)^2+\mleft(6+7\mright)^2\le113 \\ 4^2+13^2\le113 \\ 16+169\le113 \\ 185\le113 \end{gathered}[/tex]Therefore, the point (7,6) is not on the circle
True or False? The end behaviors of each end of any quadratic function are always inthe same direction.
In general, given a quadratic function,
[tex]\begin{gathered} f(x)=ax^2+bx+c \\ a,b,c\rightarrow\text{ constants} \end{gathered}[/tex]The end behaviors of each end of the function are given by the limits of f(x) when x approaches +/-infinite.
Therefore,
[tex]\lim_{x\to\infty}f(x)=\lim_{x\to\infty}ax^2=a\lim_{x\to\infty}x^2=a*\infty[/tex]and
[tex]\lim_{x\to-\infty}f(x)=\lim_{x\to-\infty}ax^2=a\lim_{x\to-\infty}x^2=a*\infty[/tex]Thus, the two limits are the same and depend on the sign of a.
Hence, the answer is True, the statement is True.Joyce paid $154.00 for an item at the store that was 30 percent off the original price. What was the original price?
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You are purchasing a snack at the store for $3.50. The sales tax is 6%. How much is the sales tax?
price = $3.50
Sale tax = 6%
Multiply the price by the tax percentage in decimal for ( divided by 100)
3.50 x (6/100) = 3.50 x 0.06 = $0.21
