In the formula
[tex]\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_2}[/tex]putting in the given values of R_1, R_2, and R_3 gives
[tex]\frac{1}{R}=\frac{1}{10.0}+\frac{1}{14.0}+\frac{1}{35.0}[/tex]We add the fractions on the right-hand- side to get:
[tex]\frac{1}{R}=\frac{1\cdot7}{10.0\cdot7}+\frac{1\cdot5}{14.0\cdot5}+\frac{1\cdot2}{35.0\cdot2}[/tex][tex]\frac{1}{R}=\frac{7}{70}+\frac{5}{70}+\frac{2}{70}[/tex][tex]\frac{1}{R}=\frac{14}{70}=\frac{1}{5}[/tex]Taking the reciprocal both sides gives
[tex]R=5.0[/tex]Which is our answer!
Hi guys.I was sick today and I’m still not feeling good.I missed out on class and I’ll be giving 25 points to whoever helps me.Thank you
Answer:
x = -12
Step-by-step explanation:
these two angles are same side interior angles. These two angles will add up to 180.
so we have the equation:
(x + 142) + (x + 62) = 180
Now just simplify:
(x + 142) + (x + 62) = 180
___-142_________-142
x + (x + 62) = 38
_____-62___-62
x + x = -24
2x = -24
-24/2 = -12
Therefore, x = -12
Use synthetic division to determine whether or not (2 – 1) is a factor of (-32% – 2x² – 1).-- Quotient:help (formulas)- Remainder:help (numbers)- Is (2 – 1) is a factor of (-323 – 2x2 - 1)?Yes No
Answer:
Explanations:
From the question, we are to use synthetic division to divide x - 1 by the polynomial function -3x^3 - 2x^2 - 1
Next is to use the synthetic division to carry out the operation as shown below;
From the calculation above, we can conclude the following;
[tex]undefined[/tex]Robert has 3 more than twice the number of t-shirtsthat Brianne has. Robert has 19 shirts. How manyShirts does Brianne have?** 3x + 219X+ 5 = 16* 2 + 3 =19
1) Considering that we can call t-shirts "x" then we can write out the following equations to express this problem:
Robert: 2x +3
Brianne: x
2) Now, we can write out the following equation to find out how many t-shirts does Brianne have:
[tex]\begin{gathered} 2x+3=19 \\ 2x+3-3=19-3 \\ 2x=16 \\ \frac{2x}{2}=\frac{16}{2} \\ x=8 \end{gathered}[/tex]So that's the number of t-shirts Brianne has. And the equation used is:
[tex]2x+3=19[/tex]determine if the following are rotations
Answer: D and C are the other rotations
Step-by-step explanation: A is mirrored
El cargo por servicio de Julia en un salón de belleza fue de $72.60 antes de impuestos. La tasa del impuesto sobre las ventas era del 8%. Si agregó el 20% de la cantidad antes de impuestos como propina, ¿cuánto pagó por el servicio en el salón?
Answer:
20.36
Step-by-step explanation:
72.60 cuando se divide por 100 se obtiene 1% o 0.73x8=5.84
entonces 72.60/10=7.26x2=20% o 14.52
14.52+5.84=20.36
The Cougars scored a total of 84 points in their basketball game last nightagainst the Bears. The Cougars made no one-point shots, and a total of38 two-point and three-point shots. Let x represent the number of two-pointshots and y represent the number of three-point shots.a. How many two-point shots did the Cougars make? How many three-pointshots did the Cougars make? Write and solve a system of equations that canbe used to solve this problem.
Step 1: Write out the values
For Cougars
Total Points = 84
Number of 1 point shot = 0
Number of 3 and 2 points shots = 38
Step 2: Write out the system of equations
[tex]x+y=38---------------------(1)[/tex]Since there are x number of two-point shots, then the total number of points from the two-point shots is 2x
Also, there are y number of three-point shots, then the total number of points from the three-point shots is 3y
Hence, the total number of points is 2x + 3y
Therefore,
[tex]2x+3y=84----------------(2)[/tex]Step 3: Solve the system of equation simultaneously
x + y = 38 ------ equation 1
2x + 3y = 84 ------ equation 2
Using the elimination method to eliminate x
Multiply equation 1 by 2 to get a new equation
2x + 2y = 76 ------ equation 3
Step 4: combine equation 2 and 3 and solve simultaneously
2x + 3y = 84------- equation 2
2x + 2y = 76 ------ equation 3
Subtract equation 3 from 2
[tex]undefined[/tex]
2+1+What are thex-intercepts ofthis quadratic?2 B-2t(-1, [?]); ([ ], [ )-3-44- 5+57
The x intercepts of the quadratic function are the points where the graph of the parabola intersects with the x axis.
In the given graph, the parabola intersects the x axis at points with coordinates (-1, 0) and (3, 0).
Therefore, the x intercepts of the quadratic are:
(-1, 0) ; (3, 0).
Segment AB has endpoints A (-5, 7) and B (4, 4). The segment is reflected over the line y =4 to create endpoints A'B' and then rotated 90° CW to form points A"B". Find the location of A" and B".
A(-5,7)
B(4,4)
The segment is reflected over the line y =4
The line y=4 is a horizontal line, coordinate in x doesn't change after reflection.
To find coordinate y after reflection:
Find the distance of each point from y=4
Point A: (-5,7)[tex]\lvert7-4\rvert=3[/tex]As y=4 is below the point A, the point A' will have a coordinate y of: 4-3=1
Point A': (-5,1)Point B: (4,4)[tex]\lvert4-4\rvert=0[/tex]As point B is on line y=4 the point B' will have a coordinate y of 4-0:4
Point B': (4,4)_____________________________then rotated 90° CW:
Rule for a rotation 90º CW:
[tex]P(x,y)\rightarrow P^{\prime}(y,-x)[/tex]Then, you get the next coordinates for A'' and B'':
[tex]\begin{gathered} A^{\prime}(-5,1)\rightarrow A^{\doubleprime}(1,5) \\ B^{\prime}(4,4)\rightarrow B^{\doubleprime}(4,-4) \end{gathered}[/tex]Evaluate the function f(x) = x² + 9x− 7 at the given values
a. f(2) b. f(x+8) c. f(-x)
b. f(x+8)
c. f(-x)
The given values the equation evaluate is:
f(2) = 15,
f(x+8) = x² + 25x + 129,
f(-x) = x² - 9x - 7
What in mathematics is a quadratic equation?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. Since it is a second-order quadratic equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution might be straightforward or difficult.
According to the given data:f(x) = x² + 9x− 7
a) At, f(2)
f(2) = (2)² + 9(2) - 7
f(2) = 4 + 18 - 7
f(2) = 15
b) At, f(x+8)
f(x+8) = (x + 8)² + 9(x + 8) - 7
f(x+8) = x² + 8² + 16x + 9x + 72 - 7
f(x+8) = x² + 64 + 25x + 72 - 7
f(x+8) = x² + 25x + 129
c) At, f(-x)
f(-x) = (-x)² + 9(-x) - 7
f(-x) = x² - 9x - 7
Hence,
The given values the equation evaluate is:
f(2) = 15,
f(x+8) = x² + 25x + 129,
f(-x) = x² - 9x - 7
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find figure 0 for the tile pattern below. write a rule that will give the number of tiles in any figure, record the data for the first six tiles 0-5 in a table, and graph the data
Solution
for this case we can see that for
Figure 0 = 6 tiles
Figure 1 = 7 tiles
Figure 2 = 8 tiles
Figure 3= 9 tiles
Figure 4 = 10 tiles
Figure 5= 11 tiles
Then the table would be given by:
Figure number (x) 0 1 2 3 4 5 x
Number of tiles (y) 6 7 8 9 10 11 6+x
And the line should be like this:
will you kindly please work the math expressionpls brake in detail numbers
We are given the expression below:
[tex]\lbrack44+(4\times7)\rbrack\div9-5[/tex]To find the solution to the expression, we would make use of PEDMAS to other our steps on finding the solution. PEDMAS implies
[tex]\begin{gathered} P-Parenthesis \\ E-Exponential \\ D-Division \\ M-Multiplication \\ A-Addition \\ S-Subtraction \\ \end{gathered}[/tex]The order of PEDMAS would then be utilized in finding the value in the question.
[tex]\begin{gathered} \lbrack44+(4\times7)\rbrack\div9-5 \\ =\lbrack44+28\rbrack\div9-5 \\ =72\div9-5 \\ =8-5 \\ =3 \end{gathered}[/tex]Therefore, the answer is
[tex]3[/tex]The right option is option C
Simplify.10(15 + n)150 n150 + n150 + 10 n50 + n
The Solution:
Given:
[tex]10(15+n)[/tex]We are required to simplify.
[tex]\begin{gathered} 10(15+n) \\ 150+10n \end{gathered}[/tex]Therefore, the correct answer is:
[tex]undefined[/tex]express your answer as a polynomial in Itandard form.
Answer:
f(x) = x + 5
g(x) = x² - 4x + 8
Find: g(f(x))
The answer to g(f(x)) expressed as a polynomial in Standard form is x² + 6x + 13.
What is the Composition of Functions?The composition of the functions f(x) and g(x), where g(x) acts first, is denoted by f(g(x)) or (fog)(x). A new function is created by combining two or more existing functions. The output of the function inside the parenthesis that is being composed becomes the input for the function outside of the parenthesis. i.e.,In f(g(x)), g(x) is the input to f(x).In g(f(x)), f(x) is the input to g(x).Given the composition of functions g(f(x)),
For which f(x) = x + 5, and g(x) = x² - 4x + 8.
Considering f(x) as input we substitute it in g(x) in place of x.
g(f(x)) = (x+5)²- 4(x+5) + 8
= x² + 25 + 10x - 4x -20 + 8
= x² + 6x + 13
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state if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.ABC
Remember that
If two triangles are similar, then the ratio of their corresponding sides is proportional and their corresponding angles are congruent
Verify the proportionality between corresponding sides
so
[tex]\begin{gathered} \frac{AB}{AV}=\frac{AC}{AW} \\ substitute\text{ given values} \\ \frac{42}{27}=\frac{24}{16} \\ 1.561.5\text{ } \\ \end{gathered}[/tex]that means
The triangles are not similar
Option AWrite a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two workers in a holiday boutique are filling stockings with small gifts and candy. Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour. Peter, who just arrived to help, can fill 4 stockings per hour. At some point, Peter will catch up with Katie and they will have completed the same number of stockings. How long will that take? How many stockings will each worker have filled by then?In ____ hours, the workers will each have filled _____ stockings.
Two workers in a holiday boutique are filling stockings with small gifts and candy.
Katie has already filled 3 stockings and will continue to fill them at a rate of 1 stocking per hour.
3 + x
Peter, who just arrived to help, can fill 4 stockings per hour.
4 x
At some point, Peter will catch up with Katie and they will have completed the same number of stockings.
3 + x = 4x
3 = 4x -x
3 x =3
x = 3/3
x =1 hour How long will that take?
How many stockings will each worker have filled by then?
Katie = 3 + 1 = 4
Peter = 4 x 1 = 4
Solve for x.Question options:A) 11 B) 13 C) 12 D) 10
Notice that triangles QRS and YRZ are similar, therefore:
[tex]\frac{YZ}{QS}=\frac{YR}{QR}=\frac{1}{2}\text{.}[/tex]Substituting YZ=x+2, QS=3x-8, and solving for x we get:
[tex]\begin{gathered} \frac{x+2}{3x-8}=\frac{1}{2}, \\ 2(x+2)=3x-8, \\ 2x+4=3x-8, \\ x=12. \end{gathered}[/tex]Answer: Option C).
In ∆VWX, w=680 cm, < X =80° and
1) We know that the sum of the interior angles within a triangle is 180º
So we can state that :
∠X = 80º , ∠V=32º and ∠W = 180º-(80+32), ∠W=68º
2) The area of a triangle can be found by the Heron formula, but before that, we need to find out the other legs. Let's sketch this and use the Law of Sines:
The Law of Sines:
[tex]\begin{gathered} \frac{v}{\sin(V)}=\frac{w}{\sin(W)}=\frac{x}{\sin(X)} \\ \frac{v}{\sin(32)}=\frac{680}{\sin(68)} \\ 680\text{ sin(32) = vsin(68)} \\ \frac{680\text{ }\sin(32_{}}{\sin(68)}=v \\ v\text{ =}388.65 \\ \\ \end{gathered}[/tex]Now let's proceed to find the length of side x:
[tex]\begin{gathered} \frac{w}{\sin(W)}=\frac{x}{\sin(X)} \\ \frac{680}{\sin(68)}=\frac{x}{\sin (80)} \\ x\sin (68)=680\cdot\sin (80) \\ x=\frac{680\cdot\sin (80)}{\sin (68)} \\ x\approx722.26 \end{gathered}[/tex]Now we can add the three sides and find out the Perimeter:
2p: 722.26 +388.65 +680
2p=1790.91
And the semi perimeter is p =2p/2, p =895.455.
2.2) Finally we can find out the area using the Heron Formula:
[tex]\begin{gathered} A=\sqrt[]{p(p-v)(p-w)(p-x)} \\ A=\sqrt[]{895.455(895.455-388.65)(895.455-722.455)(895.455-680)} \\ A=130059.9757\approx130060 \end{gathered}[/tex]3) Hence, the area is 130,060 cm²
10. The value of a new car decreases by 15% each year. The value (D) of the car after t years could be modelled as D = 23000(1 - 0.15) a) Show that the cost of the new car was £23 000. b) What is the cost of the car after 6 years? c) If we drew a graph, what would be the equation of the asymptote? - I just need help with question c
Answer:
y = 0
Step-by-step explanation:
The function has a horizontal asymptote at y = 0 where y is the value of the car
[tex]\text{Since the equation for the value of the car is }[/tex] [tex]23000(1-0.15)^t[/tex]
As [tex]t \rightarrow \infty, \text{the term } (1-0.15)^t \rightarrow 0 \\[/tex]
This is because the term (1-0.15) is < 1 and a nˣ approaches 0 as x → ∞ since the values get smaller and smaller with increasing powers of x
So the equation for the horizontal asymptote is y = 0
Provided graph to illustrate
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A customer at a shipping store is planning to send a package and is considering two options. The customer can send a package for $3, plus an additional $2 per pound. The cost, y, can be represented by the equation y = 3 + 2x, where x represents the amount of pounds of the package. Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
Based on the graph of the system of equations, when will the cost of the two shipping options be the same?
A package that weighs 10 pounds will cost $17 for both options.
A package that weighs 7 pounds will cost $17 for both options.
A package that weighs 17 pounds will cost $31 for both options.
A package that weighs 17pounds will cost $37 for both options.
The cost of the two shipping options be the same when B. a package that weighs 7 pounds will cost $17 for both options.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The cost, y, can be represented by the equation: y = 3 + 2x,
x = the amount of pounds of the package
Another option is that the customer can pay a one-time fee of $17 to send the box, represented by the equation y = 17.
The equation will be equated together.This will be:
3 + 2x = 17
Collect like terms
2x = 17 - 3
2x = 14
Divide
x = 14 / 2
x = 7
The weight is 7 pounds.
In conclusion, the correct option is B.
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Which fraction divided by 3/6 is equal to -9/10?
A. -3/2
B. -9/20
C. 9/20
D. 9/40
multiply and/ or divide and put into lowest terms
the division of fractions follows the stes
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Applying this into the expression given
[tex]\frac{3\cdot(a-9)}{9\cdot(a^2-81)}[/tex]simplify the coefficients by decomposing 9 into a product and cancelling the common factors
[tex]\frac{3\cdot(a-9)}{3\cdot3\cdot(a^2-81)}[/tex]simplify
[tex]\frac{a-9}{3\cdot(a^2-81)}[/tex]In the denominators there is a difference of squares that can be rewriten as a product, in which by definition the difference of square is described as
[tex]a^2-b^2=(a+b)\cdot(a-b)[/tex]In the denominator of the expression we can see that a is squared and that 81 has an exact root which is 9, reason why we can write this as a difference of squares, it should look like this:
simplify the expression
[tex]\frac{1}{3\cdot(a+9)}[/tex]distribute the 3
[tex]\frac{1}{3a+27}[/tex]The coordinates of point T are (0,5). The midpoint of ST is (6,-7).Find the coordinates of point S.S =(
If the midpoint of ST is (6, -7) then its distance from S and T must be the same!
The distance from point T (0,5 ) to (6, -7) is from the Pythagorean theorem:
[tex]d=\sqrt{\left(0-6\right)^2+\left(5--7\right)^2}[/tex]which is
[tex]d=6\sqrt{5}[/tex]i need help fast as possible and explanation
Answer:
x>0
Step-by-step explanation:
any number less than or equal to zero does not give a negative solution and you need a negative solution so x must be greater than 0
Lucy bought four paint brushes from the Art Supply Store. She had a coupon for 25% off.
How much money does she owe? Each paint brush is 10.50
Answer: $31.50 for the four brushes after using the coupon
Step-by-step explanation:
$10.50 (Amount for EACH brush) * 0.75 (coupon 25% off) = $7.875 (Amount for each after coupon)
$7.875* 4 brushes = $31.5
or
$10.50 (regular price) * 4 brushes = $42 (4 brushes at regular price)
$42 * 0.75(25% coupon) =$ 31.5
4.5 simplified into a fraction is?
4.5 = 45/10 Using GCF
9/2
Abdul, Beckie, Cynthia and Douglas are making pancakes according to the recipe below:Which person can make the most pancakes?BeckieAbdulCynthiaDouglas
To make 12 pancakes we need 100 g flour, 2 eggs, 300 ml milk
Abdul has 175 g flour, 4 eggs and 500 g milk
The ration between Abdul's amount of each ingredient and the total needed to make 12 pancakes is: (175/100) = 1.75 flour, (4/2) = 2 eggs, (500/300) = 1.67 milk.
So, the total amount of pancakes that Abdul can make is determined by the amount of the less abundant ingredient (milk): 1.67*12 = 20 pancakes
Doing the same steps for Beckie, we got that her less abundant ingredient is milk, with a ratio of 400/300 = 1.33. Then, she can make 1.33*12 = 16 pancakes.
For Cynthia, her less abundant ingredient is flour, with a ratio of 150/100 1.5. Then, she can make 1.5*12 = 18 pancakes.
And for Douglas, his less avundant ingredient is egg, with a ratio of 3/2 = 1.5. Then, he can make 1.,5*12 = 18 pancakes.
Therefore, Abdul is the one who can make the most pancakes
Hank has just purchased a small rectangular fish tank that holds 950.4 milliliters of water. The tank has a width of 8.8 cm and a height of 9 cm. what is the length of the fish tank?
We will investigate how to determine one of the indicator dimensions of a regular figure.
We have a rectangular fish tank which can be modeled as a cuboid. The indicator lengths of a cuboid or a rectangular fish tank are as such:
[tex]\begin{gathered} \text{Length ( L ) } \\ \text{Width ( w ) = 8.8 cm} \\ \text{Height ( h ) = 9 cm} \end{gathered}[/tex]One of the indicator lengths of the rectangular fish tank Length ( L ) is unknown. Howver, we are given the total amount of water that the fish tank can withold as follows:
[tex]\text{Water in fish tank = 950.4 mL}[/tex]We will use the conversion factor between milliLiters and centimeter cube as follows:
[tex]1\text{ mL }\to1cm^3[/tex]Therefore,
[tex]950.4\text{ mL }\to950.4cm^3[/tex]The amount of water a fish tank can hold is equivalent to the volume of the fish tank. We have modeled our rectangular fish tank as a cuboid. The volume ( V ) of a cuboid can be expressed in terms of its indicator dimensions as follows:
[tex]V\text{ = L}\cdot w\cdot h[/tex]We can use the above volume expression to determine one off our missing indicator dimension of length ( L ). We plug in the respective quantities and evaluate:
[tex]\begin{gathered} 950.4\text{ = L}\cdot(8.8\text{ ) }\cdot\text{ ( 9 )} \\ \\ L\text{ = }\frac{950.4}{8.8\cdot9}\text{ = }\frac{950.4}{79.2} \\ \\ L\text{ = 12 cm} \end{gathered}[/tex]Therefore, the length ( L ) of the fish tank must be:
[tex]12\text{ cm }\ldots\text{ Answer}[/tex]What is the percent of 80 of 62
Given the definitions of f(x) and g(x) below, find the value of (gof)(-8).
f(x) = 2x + 12
g(x) = 2x² + 2x + 12
(g o f)(-8) = 36
For f(x) = 2x + 12 and g(x) = 2x² + 2x + 12 the value of (g o f)(-8) is 36.
Solution:Given that f(x) = 2x + 12, g(x) = 2x² + 2x + 12.
to locate (g o f) (-8),
To find (g o f)(-8), we must first find g(f(x)) and then substitute x = -8.
Find g(f(x)) by substituting f(x) into g. (x)
= g(f(x)) = 2( 2x +12)² + 2( 2x + 12) + 12
x = -8 so,
g( f( - 8) ) = 2( 2(-8) +12)² + 2( 2(-8) + 12) + 12
g( f( - 8) ) = 2( -16 +12)² + 2( -16 + 12) + 12
g( f( - 8) ) = 2(-4)² + 2( -4 ) + 12
g( f( - 8) ) = 2 x 16 -8 + 12
g( f( - 8) ) = 32 - 8 + 12
g( f( - 8) ) = 36
So (g o f)(-8) = 36
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The mean of 6 numbers is 12.
The numbers are in the ratio 1 : 1 : 1 : 1 : 2 : 3.
Find the range.
Answer:
range = 16
Step-by-step explanation:
The total of all the numbers = mean x number of values = 6 x 12 = 72
The ratio of the numbers is
1: 1: 1: 1:2 :3
The sum of the ratios is 9
So the numbers in the ratio of 1 must be 1/9 x 72 = 8
The number with a ratio of 2 must be 2 x 8 = 16
and finally the number with the ratio of 3 = 3 x = 24
The range of the numbers is 24-8 = 16
