To solve for g in the expression 4g=16, we need to follow these steps:
[tex]\begin{gathered} 4g=16 \\ \frac{4}{4}\times g=\frac{16}{4} \\ g=\frac{16}{4}=4 \end{gathered}[/tex]The equation for line j can be written as y =
= -5/7x-10. Line k, which is parallel to line j,
includes the point (-9, 5). What is the equation of line k?
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
What is the Relation between two Parallel Lines?
To determine whether two lines are parallel or not, apply the parallel line's formula. When we have the slope of two lines that we want to compare, the parallel line formula can be used. The separation between the parallel lines remains constant. Parallel lines are those that never cross each other. Since the two lines are equal in this situation and the angle is 180 degrees, they will never intersect.
In the given equation, we have:
The equation of the line is y = -5/7x-10.
and, Line k, which is parallel to the line of the equation :
[tex]y = \frac{-5x}{7} -10.[/tex]
[tex]y + \frac{5x}{7} +10. =0[/tex]
So, the equation of the line which is parallel to the line of the equation is:
[tex]y + \frac{5x}{7} +k. =0[/tex]
and since the two lines are parallels
So, the slope of equation 1 and the slope of equation two will be the same;
Also, It is given that the line includes the point (-9, 5).
So,
[tex]5 + \frac{5 \times -9}{7} +k. =0[/tex]
⇒[tex]k = -\frac{5 \times -9}{7} -5[/tex]
⇒[tex]k = \frac{10}{7}[/tex]
So, The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex].
Hence,
The equation of the line which is parallel to the other equation is;
[tex]y + \frac{5x}{7} +\frac{10}{7} =0[/tex]..
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Complete the statements by writing the number from the graph.
The substance is in the gas phase only in region _.
The substance is in both the liquid and the solid phase in region _.
The substance is in only the liquid phase in region _.
The melting point is the temperature at region _.
The boiling point is the temperature at region _.
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
What is meant by the term temperature?Temperature is a measure of how hot or cold something is conveyed in terms of one of several scales, such as Fahrenheit and Celsius.For the given question, the correct depiction of the expressions are is;
Melting or fusion is a process wherein the phase transitions from solid to liquid at a constant temperature.Freezing is a process wherein the phase transitions from liquid to solid at a constant temperature.Evaporation is a process where the phase transitions from liquid to gaseous at a constant temperature.Condensation is a process where the phase transitions from gaseous to liquid at a constant temperature.Sublimation is a process during which the phase transitions from solid to gaseous without passing through a liquid state at a constant temperature.Thus, the result for the graph will be-
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
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Answer:
A. The substance is in the gas phase only in region 5.
B. The substance is in both the liquid and the solid phase in Region 2.
C. The substance is in only the liquid phase in region 3.
D. The melting point is the temperature at region 2.
E. The boiling point is the temperature at region 4.
Step-by-step explanation:
is this relation a function? Justify your answer
Answer:A
Step-by-step explanation:
What is the solution to this equation?
−15(x+134)=−212
Responses
x=2114
x equals 21 and 1 over 4
x=1414
x equals 14 and 1 over 4
x=1034
x equals 10 and 3 over 4
x=334
Answer: 10 3\4
Step-by-step explanation:
I did the quiz
There are 128 teams entered in a basketball tournament. Half of the teams are eliminated each round. How many teams are left after 4 rounds?
We have 128 teams.
In each round, half of the teams remain, so if T is the number of teams and n is the number of rounds, we have:
[tex]T(n)=0.5\cdot T(n-1)[/tex]and we start with n=0 so T(0)=128.
Then, we can use this recursive expression to find T after four rounds (n=4), but it is better if we derive an explicit formula for T in function of n (and not in function of the past terms of the sequence):
[tex]\begin{gathered} T(1)=0.5\cdot T(0) \\ T(2)=0.5\cdot T(1)=0.5\cdot0.5\cdot T(0)=0.5^2\cdot T(0) \\ T(n)=0.5^n\cdot T(0)=0.5^n\cdot128 \end{gathered}[/tex]With the last expression we can calculate T for any value of n. Then, for n=4, we have:
[tex]T(4)=0.5^4\cdot128=(\frac{1}{2})^4\cdot128=\frac{1}{2^4}\cdot128=\frac{1}{16}\cdot128=8[/tex]NOTE: in this case, its better to express the factor 0.5 as a fraction instead of a decimal.
Answer: after 4 rounds there will be 8 teams left.
Write the first five terms of the geometric sequence with a1 = 16 and common ratio r= 3/2
From the problem, we need to find the first five terms of the geometric sequence.
The first term, a1 = 16 and the common ratio, r = 3/2
Note that the succeeding term is the previous term multiplied by the common ratio.
This will be :
[tex]\begin{gathered} a_2=a_1r=16(\frac{3}{2})=24 \\ a_3=a_2r=24(\frac{3}{2})=36_{} \\ a_4=a_3r=36(\frac{3}{2})=54 \\ a_5=a_4r=54(\frac{3}{2})=81 \end{gathered}[/tex]The geometric series is :
an = {16, 24, 36, 54, 81, ...}
The answer is B. an = {16, 24, 36, 54, ...}
Twenty-five of 75 fifth-grade students went to a bake sale after school. Which fraction shows, in simplest form, the part of the class that did NOT go to the bake sale?
Answer:1/3
Step-by-step explanation:
25/75
25/25=1
75/25=3
Answer is 25/75=1/3
Determine weather the statement is true or false. Justify your answer
As we know:
[tex]\begin{gathered} \cos (x)=0 \\ for \\ x=\pi n-\frac{\pi}{2} \\ n\in Z \end{gathered}[/tex]For:
[tex]\begin{gathered} n=2 \\ x=2\pi-\frac{\pi}{2}=\frac{3\pi}{2} \\ for \\ n=-3 \\ x=-3\pi-\frac{\pi}{2}=-\frac{7\pi}{2} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \cos (-\frac{7\pi}{2})=0 \\ and \\ \cos (\frac{3\pi}{2})=0 \\ so\colon \\ 0=0 \\ This_{\text{ }}is_{\text{ }}true \end{gathered}[/tex]Therefore, the statement is true
What is 106/200 written as a decimal
Answer:
0.53
Step-by-step explanation:
you just take 106 and divide it by 200
Write an inequality for the graph below.
Answer: y < -4
Step-by-step explanation:
Answer the question below.
The formula that can be used to find the nth term of the sequence is aₙ = 4n + 1
How to find the formula of an arithmetic sequence?The sequence follows an arithmetic patterns. Therefore, the formula for arithmetic progression can be used to find the nth term as follows:
aₙ = a + (n - 1)d
where
n = number of termsd = common differencea = first termTherefore, using the sequence 5, 9, 13, 17, 21
a = 5
d = 9 - 5 = 4
Hence,
aₙ = 5 + (n - 1)4
aₙ = 5 + 4n -4
aₙ = 5 - 4 + 4n
Therefore,
aₙ = 4n + 1
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A towns population is 53,350 about 100 people move out of the town each month 200 people on average move into town. A nearby town has a population of 56,375.It has no one moving in and an average of 175 people moving away every month in about how many months will be population of the town be EQUAL?
11
this is just words because it doesn't let me submit this with just the answer
compare -2/5 and -0.3 -2/5 = /10 and -0.3 = /10. -4 is ? , so -2/5 ? than -0.3
-4 is less than -3
so:
[tex]\frac{-2}{5}\text{ is less than }-0.3[/tex]What is an equation of the line that passes through the points (-5, -7) and
(-5, 6)?
I believe it would be x = -5.
Hope this helps!
Question 2(Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -16+√40 to the nearest tenth.
The value of an irrational number [tex]-16 + \sqrt{40}[/tex] Is approximate, the nearest tenth is -9.675.
What are irrational numbers?Irrational numbers include all real numbers that cannot be stated as the ratio of two integers, or p/q, where p and q are both integers.
Given expression:
[tex]-16 + \sqrt{40}[/tex]
Factorize the square part as
[tex]-16 + \sqrt{10\times2^2 }[/tex]
Simplify the above expression as
[tex]-16 + 2\times \sqrt{10}[/tex]
We know that [tex]\sqrt{10} = 3.132[/tex]
Hence, -16 + 2 × 3.132
= -9.675
Therefore, the value of an irrational number [tex]-16 + \sqrt{40}[/tex] is approximately the nearest tenth is -9.675.
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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 correct option is :
A package that weighs 7 pounds will cost $17 for both options.
What is an equation ?The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.
The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.
Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.
We'll compare the equation as a whole.
In this case,
3 + 2x = 17
Compile similar terms
2x = 17 - 3
2x = 14
x = 14 divided by 2x = 7
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the mayor of a town believes that under 46% of the residents favor construction of an adjoining bridge. is there sufficient evidence at the 0.05 level to support the mayor's claim? after information is gathered from 190 voters and a hypothesis test is completed, the mayor fails to reject the null hypothesis at the 0.05 level. what is the conclusion regarding the mayor's claim?
Since the null hypothesis was not rejected, there is not enough evidence to conclude that under 46% of the residents favor construction of an adjoining bridge.
What is the relation between the decision and the conclusion?There are two decisions possible regarding the null hypothesis, as follows;
Reject the null hypothesis.Do not reject the null hypothesis.The hypothesis are given as follows:
Null hypothesis: proportion is not under 46%.Alternative hypothesis: proportion is under 46%.The null hypothesis was not rejected, meaning that the conclusion regarding the mayor's claim is that there is not enough evidence from the sample of 190 voters to conclude that the percentage is below 46%.
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Pls help i need this answered quickly
Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long. She then takes a photo of the sandbox and prints the photo. In the photo, the sides of the hexagon are each 4 inches long. Identify the scale factor that was used to create the printed photo of the sandbox. Express your answer as a decimal.
A scale factor of 0.1 was used to create the printed photo of the sandbox
How to find the scale factor used for the printed photo of the sandbox?A scale factor is the size by which a shape is enlarged or reduced. It is used in increasing or reducing the size of a 2D shape, such as circle, triangle, square, rectangle, hexagon, etc.
Given that: Tess builds a sandbox in the shape of a regular hexagon in which all the sides are 40 inches long, and in the photo, the sides of the hexagon are each 4 inches long
The scale factor will be:
4/40 = 1/10 = 0.1
This means the sandbox has been reduced by 10 times the original size
Therefore, the scale factor that was used to create the printed photo of the sandbox is 0.1
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Question 1(Multiple Choice Worth 2 points)
(Converting Between Systems MC)
I need help pleaseeee
For a craft project you need 182 inches of ribbon, but it is only sold by the meter. Determine the amount of ribbon, in meters, you need to buy for the project. (1 inch = 2.54 centimeters and 1 centimeter = 0.01 meter)
462
47
12
5
The amount of ribbon needed to buy for the project in meters is (d) 5.
According to question,
1 centimeter = 0.01 meter
2.54 centimeter = 0.01*2.54
= 0.0254 meters
1 inches = 2.54 centimeters
= 0.0254 meters
Amount of ribbon needed for project = 182 inches
= 182 * 0.0254 meters
= 4.62 meters
≅ 5 meters
Hence, 5 meters of ribbon is needed for the project.
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The library is installing new
Shelves. If the carpenter has
4/5 yard of wood to make
into 2 shelves of equal length,
how long will each shelf be?
Menth
The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
Given that,
The library is getting new shelves built.
We have to find how long will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
We know that,
We have to divide
4÷2÷5
2÷5
0.4
In percentage we write as 40%.
Therefore, The library is getting new shelves built. 40% will each shelf be if the carpenter has 4/5 yards of wood to create 2 shelves that are the same length.
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Choose the line parallel to the following equation through the given point
Answer:
y = 2x + 1
Step-by-step explanation:
→ Find the gradient of this line
2
→ Write in standard format
y = 2x + c
→ Substitute in ( 0 , 1 )
1 = 0 + c ⇒ c = 1
If given f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5, what is (f · g)(x)?
The addition of the given two functions f(x) = –4x – 2 and g(x) = 2x ^2 + 4x-5 will be (f · g)(x) = 2x²-9
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Given f(x)= -4x-2
g(x)=2x²+4x-5
For (f-g)(x) = -4x-2+2x²+4x-5
=2x²-9
(f-g)(x) = 2x²-9
Hence, The addition of the given two functions will be (f · g)(x) = 2x²-9
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Where is the center of dilation located?
inside figure A
outside figure A
on a vertex of figure A
B
A
The center of dilation is outside figure A
In this question, rectangle A is dilated to rectangle B.
We know that, the center of a dilation is nothing but a fixed point about which all points are expanded or contracted.
We can observe that B = 1/2 * A
This means, the scaling factor is k = 1/2
Let's determine the center of dilation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.
k - Scale factor
P(x, y) - Original point
P'(x, y) - Resulting point
(3, 1) = O(x, y) + 1/2 [(6, 2) - O(x, y)]
(3, 1) = O(x, y) - 1/2 O(x, y) + (3, 1)
1/2O(x, y) = (0, 0)
so, the center of dilation is the origin (0, 0)
So, in this case the center of dilation is outside figure A.
Therefore, the center of dilation is outside figure A
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Solve this system of equations by graphing. First graph the equations, and then type the solution.x+y=13x+5y=15Click to select points on the graph.
Solution
For this case we have the following system of equations:
x + y= 1
3x + 5y= 15
We can create the following plot:
Then the solution for this case is:
x= -5
y= 6
PLEASEEE HELP I REALLY NEED HELP ITS MENTAL MATH!!!!!!!!!!!!
Answer:
6y+12
Step-by-step explanation:
4(y+3)+2y
= 4y+12+2y
=6y+12
Answer:
[tex]\sf 6y+12[/tex]Step-by-step explanation:
[tex]\sf 4(y+3)+2y[/tex]
Expand (Distributive property):-
[tex]\sf 4y+12+2y[/tex]
Combine like terms:-
[tex]\sf 4y+2y+12[/tex]
[tex]\sf (4y+2y)=6y[/tex]
[tex]\sf 6y+12[/tex]
__________________
Hope this helps!
Have a great day! :)
Identify the roots of:y = x² - 12x + 32
Okay, here we have this:
Considering the provided function, we are going to calculate the requested roots, so we obtain the following:
[tex]\begin{gathered} x^2-12x+32=0 \\ x_{1,2}=\frac{-(-12)\pm\sqrt{(-12^2)-4(1)(32)}}{2(1)} \\ x_{1,2}=\frac{12\pm\sqrt{144-128}}{2} \\ x_{1,2}=\frac{12\pm\sqrt{16}}{2} \\ x_{1,2}=\frac{12\pm4}{2} \\ x_{1,2}=6\pm2 \\ x_1=6+2,x_2=6-2 \\ x_1=8,x_2=4 \end{gathered}[/tex]Finally we obtain that the roots of the function are x=8 and x=4.
help in mathematics pls i am troubled
Answer:
It's very blurry, try sending one section at a time.
Step-by-step explanation:
It is possible for 2 lines to
intersect in such a way
that 3 of the angles
formed have measures 20,
70, and 20.?
Sometimes true,
Never true,
Always true.
Answer:
sometimes true
Step-by-step explanation:
Given, two straight lines intersect each other in such a way that one of the angles formed measure 90°.
We know that, lines which intersect to form a right angle are known as perpendicular lines
In the above figure , AB is perpendicular to CD
Considering ∠AOC=90°
Now,
∠AOC+∠AOD=180° [Linear pair]
90°+∠AOD=180°
∠AOD=90°
Similarly,
∠AOC+∠BOC=180° and ∠BOD+∠AOD=180° [Both making linear pair]
So, we get ∠BOC=90° and ∠BOD=90°
Hence, ∠AOC=∠AOD=∠BOC=∠BOD=90°
What’s the answer asp
Answer:
Step-by-step explanation:
35
Area of the base of a rectangular box is 205 cm² and its height is 3 cm. Find the volume of the box
Answer:
V= 615 cm³
Step-by-step explanation:
the volume (V) of a rectangular box is calculated as
V = Ah ( A is the area of the base and h the height ) , then
V = 205 × 3 = 615 cm³
Answer:
Step-by-step explanation: In order to find the volume of box, we need to know the formula
The formula is
volume= LxBxH where L=length, B= breadth and H= height
SO, area= L x B
we can say,
Volume= area x height= 205 x 3= 615 cm^3
Hence, the volume of the box= 615 cm^3
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