We can see the problem states that P = 2(x+3) and also states that P=4x
Those equations lead to the expression
2(x+3)=4x
Operating
2x+6=4x
Subtracting 2x
6 = 2x
Solving for x
x = 6/2 = 3
Thus, the perimeter is
P = 2(3+3) = 12 units
Convert 7π/6 radians to degrees
ANSWER:
210°
STEP-BY-STEP EXPLANATION:
In order to convert from radians to degrees, we must take into account that π is equal to 180°, knowing this, let's do the conversion:
[tex]\begin{gathered} \pi=180\degree \\ \\ \text{ We replacing} \\ \\ 7\cdot\frac{180\degree}{6}=210\degree \end{gathered}[/tex]Therefore, 7π/6 radians is equal to 210°
Help Please, I don’t understand and it’s really confusing me
We have this expression:
[tex]\frac{15}{y}[/tex]Let's substitute y = 1/4 into this expression.
[tex]\frac{15}{\frac{1}{4}}[/tex]Multiply the top and bottom by 4/1 in order to get rid of the double fractions.
[tex]15(\frac{4}{1})=60[/tex]The answer to this problem is C) 60.
Rational Expression and EquationsClassify each equation as direct inverse or joint variation then state the constant of variation
2. Given:
[tex]y=7z[/tex]To classify the equation as direct, inverse or joint variation then state the constant of variation:
It is of the form,
[tex]y=kz,\text{ whe}re\text{ }k\text{ is the constant}[/tex]If y increases then z increases and if y decreases then z decreases.
Therefore, it is direct variation.
We know that the ratio between two variables in a direct variation is a constant of variation.
Thus, the constant of variation is k = 7.
Lisa is saving $50 that she received from her grandmother. She earns $6 each time she walks her neighbor's dog, which she also saves. Which function can be used to find f, the amount of money Lisa will have saved after walking the neighbor's dog d times?
Let
f ------> the amount of money Lisa will have saved
d -----> number of times that she walking the neighbor's dog
so
Remember that
The linear equation in slope intercet form is equal to
f=md+b
where
m is the unit rate or slope
b is the y-intercept or initial value
in this problem we have
m=6
b=50
therefore
substitute
f=6d+50
answer is last one option
I’m just starting writing these and I don’t understand it much
In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line, and plane, and are referred to as the "three undefined terms of geometry".
a. Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single endpoint. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them.
b. Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the endpoint, and all points extending infinitely to one side of the endpoint.
In the circle below, if arc AB = 48 °, and arc CD = 122 °, find the measure of < CPD.
SOLUTIONS
In the circle below, if arc AB = 48°, and arc CD = 122°, find the measure of < CPD.
[tex]\begin{gathered}Therefore the measure of angle CPD = 85 degree
Hence the correct answer = Option C
Question 8 of 10
If the Federal Reserve decreases the reserve rate from 10% to 8%, how does
this affect the amount of
money that would result because of fractional-
reserve banking from an initial deposit into a bank of $40,000?
C A. It increases the amount by $100,000.
•
B. It decreases the amount by $400,000.
•
C. It increases the amount by $400,000.
• D. It decreases the amount by $100,000.
The amount of money that would result because of fractional reserve banking from an initial deposit of $40,000 into a bank will increase by $100,000.
The initial reserve rate of the Federal Reserve was 10%. The final reserve rate of the Federal Reserve is 8%. Hence, the reserve rate decreased from 10% to 8%. We need to find the affect, due to this decrease, on the amount of money that would result because of fractional-reserve banking from an initial deposit of $40,000 into a bank.
The formula for the reserve is used here.
Reserve = (Deposit/Final Reserve rate) - (Deposit/Initial Reserve rate)
Reserve = ($40,000/0.08) - ($40,000/0.10)
Reserve = $500,000 - $400,000
Reserve = $100,000
Hence, the reserve amount is increased by $100,000.
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The graph of a function g is shown below.Find g (0) and find one value of x for which g(x) = 4,
From the graph provided,
a) For g(0), on the graph,
[tex]g(0)=-2[/tex]b) One value of x for which g(x) = 4 is given below as,
[tex]\begin{gathered} g(x)=4 \\ x=3\text{ where g(x) = 4} \end{gathered}[/tex]Hence, g(0) = -2 and one of the value of x for which g(x) = 4 is 3
Um Im in fith grade and i need help with some of my math questions if your able to help me with five or 10 questions that will be great
Solution
For this case we can do the following:
Then the solution would be:
21 6/24 = 21 1/4
For this case we can do the following for 21 1/4
[tex]21\cdot\frac{1}{4}=\frac{21\cdot4+1}{4}=\frac{85}{4}[/tex]For the second part we can do this:
[tex]\frac{1}{3}\cdot5=\frac{5}{3}[/tex]Then the answer is 5/3
I’m not quite sure on why I’m not getting the correct solution. Please help!The questions are A) what is the initial value of Q, when t = 0? What is the continuous decay rate? B) Use the graph to estimate the value of t when Q = 2 C) Use logs to find the exact value of t when Q = 2
The given exponential function is
[tex]Q=11e^{-0.13t}[/tex]The form of the exponential continuous function is
[tex]y=ae^{rt}[/tex]a is the initial amount (value y at t = 0)
r is the rate of growth/decay in decimal
Compare the given function by the form
[tex]a=11[/tex][tex]\begin{gathered} r=0.13\rightarrow decay \\ r=0.13\times100\text{ \%} \\ r=13\text{ \%} \end{gathered}[/tex]a)
The value of Q at t = 0 is 11 and the decay rate is 13%
The initial value of Q is 11
The continuous decay rate is 13%
From the graph
To find the value of t when Q = 2
Look at the vertical axis Q and go to the scale of 2
Move horizontally from 2 until you cut the graph
Go down to read the value of t
The value of t is about 13
b)
At
Q = 2
t = 13
c)
Now, we will substitute Q in the function by 2
[tex]2=11e^{-0.13t}[/tex]Divide both sides by 11
[tex]\frac{2}{11}=e^{-0.13t}[/tex]Insert ln on both sides
[tex]ln(\frac{2}{11})=lne^{-0.13t}[/tex]Use the rule
[tex]lne^n=n[/tex][tex]lne^{-0.13t}=-0.13t[/tex]Substitute it in the equation
[tex]ln(\frac{2}{11})=-0.13t[/tex]Divide both sides by -0.13
[tex]\begin{gathered} \frac{ln(\frac{2}{11})}{-0.13}=t \\ \\ 13.11344686=t \end{gathered}[/tex]At
Q = 2
t = 13.11344686
Jed bought a generator that will run for 2 hours on a liter of gas. The gas tank on the generator is a rectangular prism with dimensions 20 cm by 15 cm by 10 cm.If Jed fills the tank with gas, how long will the generator run? [1000 cm ^3 = 1 Liter]
Volume of the rectangular-shaped gas tank = Length x Width x Height
Directions: Drag each tile to the correct box.Put the recursive formulas below in order from least to greatest according to the value of their 10th terms.For all of the formulas, let n be equal to the whole numbers greater than or equal to one.
Solving for the 10th term for each of the recursive sequence
First sequence
[tex]\begin{gathered} a_1=32 \\ a_{n+1}=-5+a_n \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)(-5) \\ \\ \text{Substitute }n=10 \\ a_{10}=32+(10-1)(-5) \\ a_{10}=32+(9)(-5) \\ a_{10}=32-45 \\ a_{10}=-13 \end{gathered}[/tex]Second sequence
[tex]\begin{gathered} a_1=2048 \\ a_{n+1}=-\frac{1}{2}a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot\Big(-\frac{1}{2}\Big)^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^{10-1} \\ a_{10}=2048\cdot\Big(-\frac{1}{2}\Big)^9 \\ a_{10}=-4 \end{gathered}[/tex]Third sequence
[tex]\begin{gathered} a_1=0.125 \\ a_{n+1}=2a_n \\ \\ \text{This can be converted to} \\ a_n=a_1\cdot2^{n-1} \\ \\ \text{Substitute }n=10 \\ a_{10}=0.125\cdot2^{10-1} \\ a_{10}=0.125\cdot2^9 \\ a_{10}=64 \end{gathered}[/tex]Fourth sequence
[tex]\begin{gathered} a_1=-7\frac{2}{3} \\ a_{n+1}=a_n+1\frac{2}{3} \\ \\ \text{This can be converted to} \\ a_n=a_1+(n-1)\Big(1\frac{2}{3}\Big) \\ \\ \text{Substitute }n=10 \\ a_{10}=-7\frac{2}{3}+(10-1)\Big(1\frac{2}{3}\Big) \\ a_{10}=\frac{-23}{3}+(9)\Big(\frac{5}{3}\Big) \\ a_{10}=-\frac{23}{3}+\frac{45}{3} \\ a_{10}=\frac{22}{3} \\ a_{10}=7\frac{1}{3} \end{gathered}[/tex]Arranging the formulas from least to greatest according to their 10th terms, we have the following:
First Sequence → Second Sequence → Fourth Sequence → Third Sequence
Functions > 1.02 Function families and transformations How do we shift the graph of y = f(x) to get the graph of y = f(x) + 2?
y = f(x)
to
y = f(x) + 2
Move up the graph by 2 units along the y- axis. (vertical translation)
what is 14% of $3.40
In order to calculate the 14% of $3.40, you only calculate the multiplication of 14/100 and 3.40, just as follow:
14/100 x 3.40 = 0.14 x 3.40 = 0.476
Hence, the 14% of $3.40 is $0.476
The previous calculation can be summarized as follow:
- Divide the percentage between 100
14/100 = 0.14
- The previous result is multiplied by the quantity about you want to know what is the given percentage
0.14 x 3.40
How can I get the volume in cubic centimetres of one large cereal box? How do I calculate the total surface of a cereal box? How do I calculate the volume of the cereal box? If the height of a small box is 20cm, list two different Pairs of values which the company can use for the length and width of a small box?
The volume of the cereal box is 7200 cm³ and the surface area of the cereal box is 2776 cm².
The dimensions of the cereal box are given as:
Length = 25 cm
Width = 8 cm
Height = 36 cm
The volume of the cereal box is:
Volume = l × b × h
V = 25 cm × 8 cm × 36 cm
V = 7200 cm³
The surface area of the cereal box is:
Surface area = 2 l b + 2 b h + 2 h l
S = 2 (25) (8) + 2 (8) (36) + 2 (36) (25)
S = 400 + 576 + 1800
S = 2776 cm²
Therefore, we get that, the volume of the cereal box is 7200 cm³ and the surface area of the cereal box is 2776 cm².
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A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using thefollowing parametric equations. Rewrite the parametric equations by eliminating the parameter.
Solution
Given
[tex]\begin{gathered} x(t)=2t-1 \\ \\ y(t)=\sqrt{t}\Rightarrow y^2=t \\ \\ \Rightarrow x=2y^2-1 \end{gathered}[/tex]Hence, the correct option is D
Please see attached photo for question
For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
Domain of a function is all possible input values for that function.
Here, the domain of g(x) is set of all integers numbers
The x intercept of g(x)
The x intercept is when the value of y is zero, analysing the graph the x intercept can be interpreted as -5 and 1
The y intercept is when the value of x is zero, analysing the graph the y intercept can be interpreted as 1
From the graph,
g(4) is 1
Therefore, For the function g(x), the graph is shown and the domain of that function is set of all integer numbers.
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solve each system of equations below by graphing, please use my graphy = -2x + 1 y = x - 5
In order to find the solution to the given system of equations, find x and y intercepts for each line, as follow:
y = -2x + 1
x-intercept:
0 = -2x + 1
2x = 1
x = 1/2
y-intercept:
y = -2(0) + 1
y = 1
Then, the points of intersection for the first line are (1/2 , 0) and (0 , 1)
y = x - 5
x-intercept:
0 = x- 5
x = 5
y-intercept:
y = 0 - 5
y = - 5
Then, the points of intersection of the second line are (5,0) and (0,-5)
Next, graph the two lines by using the previous points:
The solution of the system is the point of intersection between the two lines. As you ca notice, such a point is (2,-3)
Related to your system of coordinates, you have:
Write an equation in general form of the circle with the given properties. Ends of diameter at (5,7) and (-5,-7) ?
Write an equation in general form of the circle with the given properties.
Ends of diameter at (5,7) and (-5,-7)
we have that
the equation of the circle is
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius
step 1
Find the center
Remember that
The center of the circle is the midpoint of diameter
so
[tex]\begin{gathered} (h,k)=(\frac{5-5}{2},\frac{7-7}{2}) \\ (h,k)=(0,0) \end{gathered}[/tex]the center is the origin
step 2
Find the radius
Find the diameter
calculate the distance between two points
[tex]\begin{gathered} d=\sqrt[\square]{(-7-7)^2+(-5-5)^2} \\ d=\sqrt[\square]{(-14)^2+(-10)^2} \\ d=\sqrt[\square]{296} \end{gathered}[/tex]simplify
[tex]D=\sqrt[\square]{296}=2\sqrt[\square]{74}[/tex]the radius is half the diameter
so
r=2√74/2=√74
step 3
the equation iof the circle is
x^2+y^2=(√74)^2
x^2+y^2=74The fish population of a receding pond is 8,000. The population is expected to decrease at a rate of 8% each year.Which function represents the population of the fish in the pond after x years?
Answer: f(x) = 8000(0.92)^x
Explanation:
The formula for calculating exponential decay is expressed as
f(x) = P(1 - r)^x
where
f(x) is the population after a period of x
P is the initial population
r is the decay rate
x is the time
From the information given,
P = 8000
r = 8% = 8/100 = 0.08
By substituting r = 0.08 into the equation. We have
f(x) = 8000(1 - 0.08)^x
f(x) = 8000(0.92)^x
please help this math seem hard 50 points anyone
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.
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
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,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
This can be written as,
[ √ means 1/2, √a = [tex]a^{1/2}[/tex]]
√(xy³) = [tex]x^{1/2}y^{3/2}[/tex]
([tex]x^{1/2} y^4[/tex])² = x[tex]y^8[/tex]
Now,
√(xy³) x ([tex]x^{1/2} y^4[/tex])²
= [tex]x^{(1/2 + 1)}y^{(3/2 + 8)}[/tex]
= [tex]x^{3/2}y^{19/2}[/tex]
Thus,
The equivalent expression is
[tex]x^{3/2}y^{19/2}[/tex]
Option C is the correct answer.
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Solve the right triangle ABC for all missing parts. Express all angles in decimal degrees. a= 306.5 km, c=591.3 km(Round to the nearest hundredth as needed)
Explanation
Step 1
we have a rigth triangle, then
let
[tex]\begin{gathered} side_1=306.5 \\ side_2=b \\ \text{hypotenuse}=591.3 \end{gathered}[/tex]to find the missing side we an use the Pythagorean theorem. it states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)
so
[tex]\begin{gathered} side^2+side^2=hypotenuse^2 \\ \text{replace} \\ 306.5^2+b^2=591.3^2 \\ \text{subtract }306.5^2i\text{n both sides} \\ 306.5^2+b^2-306.5^2=591.3^2-306.5^2 \\ b^2=591.3^2-306.5^2 \\ b=\sqrt[]{591.3^2-306.5^2} \\ b=\sqrt[]{255693.44} \\ b=505.66\text{ km} \end{gathered}[/tex]hence
b=505.66 km
Step 2
angles
a)A
[tex]\begin{gathered} \sin \text{ }\alpha=\frac{opposi\text{te side}}{\text{hypotenuse}} \\ \text{replace} \\ \sin \text{ A=}\frac{a}{c}=\frac{360.5\text{ }}{591.3} \\ A=\sin ^{-1}(\frac{360.5\text{ }}{591.3}) \\ A=37.56\~ \end{gathered}[/tex]and B
[tex]\begin{gathered} \sin \text{ B=}\frac{b}{c} \\ B=\sin ^{-1}(\frac{505.66}{591.3}) \\ B=58.77\text{ \degree} \end{gathered}[/tex]I hope this helps you
You would like to make Chili, Tacos and Grilled Cheese this week. The grocery store prices and ingredients for the meals are listed above. One of each item will be enough to cover all recipes, except you will need two packages of cheese to make all three recipes. How much will you spend on groceries?
Answer:
i dont get it
Step-by-step explanation:
Solve the equation involving simple interest Mike borrowed some money for 2 years at 2% simple interest. If he had to pay back a total of $3952, how much did he originally borrow?
Given that Mike borrowed an amount for 2 years at 2% simple interest, and paid back a total of $3952.
To Determine: The original money he borrowed
Solution:
The formula to find the amount for simple interest is
[tex]A=P(1+rt)[/tex]Where:
A is the Amount paid back
r is the rate
t is the time
Given that
[tex]\begin{gathered} A=3952 \\ r=\frac{2}{100}=0.02 \\ t=2 \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=P(1+rt) \\ 3952=P(1+0.02\times2) \\ 3952=P(1+0.04) \\ 3952=P(1.04) \\ 3952=1.04P \\ P=\frac{3952}{1.04} \\ P=3,800 \end{gathered}[/tex]Hence, the Mike originally borrow $3,800
If ABCD is dilated by a factor of 3, thecoordinate of D' would be:4C3B21-5 -4 -3-2 -1 012345DA-1-2D-3D' = ([?],[ ]
Answer:
(6, -6)
Explanation:
The coordinate of D is the figure = (2, -2)
If ABCD is dilated by a factor of 3, then:
[tex]\begin{gathered} D(2,-2)\to D^{\prime}(2\times3,-2\times3) \\ =(6,-6) \end{gathered}[/tex]The coordinate of D' would be (6, -6).
original price of shoes is $104.95 a discount of 30% tax 2%
Solving for the price of a $104.95 pair of shoes with 30% discount, after 2% taxes
First, we have to calculate the 70% of the original value (30% discount). Then, we calculate the 2% of that value (70% of $104.95) and add it up, as following:
[tex]\begin{gathered} 104.95\times\frac{70}{10}=73.47 \\ 73.47\times\frac{2}{100}=1.47 \\ 73.47+1.47=74.94 \end{gathered}[/tex]Thus, the retail price of the shoes, with 30% discount and after 2% taxes, would be 74.94
A cubical tank with sides 6 feet is to be painted. It costs $2 per square feet to paint. Find the total cost to paint all the six sides.
We have that the surface area of a cube is given by
[tex]SA=6s^2[/tex]where s is the measure of the side
s= 6 ft
[tex]SA=6\cdot6^2=6\cdot36=216ft^2[/tex]If the square feet cost $2 the total cost will be
[tex]TC=216\cdot2=432[/tex]the total cost is $432
write the expression x^2 / x^-6 as a product of two factors and also as a negative exponent.
Writing the given expression as a product of two factors, we'll have;
[tex]\begin{gathered} \frac{x^2}{x^{-6}}=x^2\ast x^6=x^{2+6}=x^8 \\ \end{gathered}[/tex]Now, writing it as a negative exponent, we'll have;
1. (4x3.5x2 + 3) + (2x3 - 5x²)
Then
4x3.5x2 = 28
28 + 3 = 31
31 + 2x3= 37
and so answer is
=37 - 5x^2
Lin family has completed 70% of a trip. They have traveled 35 miles. How far is the trip?A. 24.5 milesB. 50 milesC. 59.5 milesD. 200 miles
The given information is:
The family have traveled 35 miles and it represents the 70% of the trip.
To find how far is the trip we need to divide the 35 miles by the percentage that it represents:
[tex]35\text{miles}\cdot\frac{100\%}{75\%}=50miles[/tex]Thus, the trip is 50 miles.
Answer: B.