Answer: TRUE
Step-by-step explanation:
12g+21 equals to 3(4g+7) because you have to multiply 3 and 4g which will equal 12g and then multiply 3 and 7 which will equal 21.
So your final answer would be 12g+21 equals to 12g+21.
Hope it helps!!
What is the equation X+y>3 in the slope interceptform (ie y=mx+b)?
Q14.
The diagram shows a solid shape.
The cone has a height of 10 cm.
The volume of the cone is 270π cm³.
The solid shape is made from a hemisphere and a cone.
The radius of the hemisphere is equal to the radius of the base of the cone.
Work out the total volume of the solid shape.
Give your answer in terms of pi.
The total volume of the solid shape is 756π cm³.
There is a solid shape. The shape is formed by joining a cone with a hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 10 cm. The volume of the cone is 270π cm³. We need to find the total volume of the solid shape. The total volume is the sum of the volumes of the cone and the hemisphere. Let the radius be "r". The volume of the cone is (1/3)πr²h. So, we can find the radius.
270π = (1/3)πr²h
810 = r²*10
r = √81 = 9
The volume of the hemisphere is (2/3)πr³ = (2/3)π9³ = 486π cm³. The total volume of the solid shape is V = 270π +486π = 756π cm³.
To learn more about volume, visit :
https://brainly.com/question/1578538
#SPJ9
B. A concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick, how many cubic meters of concrete are required to make the tank? 10 m 30 cm 3 m 30 cm
The concrete required to make the tank be 27.4122 m³.
Given, a concrete tank has an external diameter of 10 m and an internal height of 3 m. If the walls and bottom of the tank are 30 cm thick.
External diameter = 10 m
Height = 3 m
Thickness = 0.3 m
External radius = 5 m
Internal radius = 5 - 0.3 = 4.7 m
Volume = πh(e.r² - i.r²)
Volume = (3.14)(3)(5² - 4.7²)
Volume = 9.42(9.7)(0.3)
Volume = 27.4122 m³
Hence, the concrete required to make the tank be 27.4122 m³.
Learn more about Volumes here https://brainly.com/question/463363
#SPJ9
Graph −4 < x < 2 on the number line. Write −4 < x < 2 in interval notation.
To graph the inequality, we need to take the following steps:
0. Draw a number line.
,1. Draw circles over -4 and 2; in this case the circles are hollow since the inequality only has exact signs.
,2. Join them with a straight line.
With this in mind the graph of the inequality is:
The inequality is written in interval notation as:
[tex](-4,2)[/tex]Select the correct answer.Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?A. x = -9B. X=-6C. y=-9D. y=-4
SOLUTIONS
Step-by-step explanation:
y = 1/4 is the equation of a horizontal line parallel to the x- axis.
A line perpendicular to it will be a vertical line parallel to the y- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 6, - 9 ) with equation
x = - 6 →
Option B
Answer:
B
Step-by-step explanation:
y = [tex]\frac{1}{4}[/tex] is the equation of a horizontal line, parallel to the x- axis and passing through all points with a y- coordinate of [tex]\frac{1}{4}[/tex]
A line perpendicular to it will be a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 6, - 9 ) with x- coordinate - 6 , then
x = - 6 ← equation of perpendicular line
A spinner with 10 equally sized slices is shown below. (2 slices are red, 4 are blue, and 4 are yellow.) The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not red?Write your answer as a fraction or a whole number.
We will have the following:
Since there are 8 slices that are not red, the probability will be given by:
[tex]p=\frac{8}{10}\Rightarrow p=\frac{4}{5}\Rightarrow p=0.8[/tex]So, the probability will be of 4/5, that is 80%.
The local seven digit telephone numbers in city A have 207 as the first three digits. How many different telephone numbers are possible in City A?
Given:
There are seven total digits.
The first 3 are already selected, so there is a choice for 4 digits.
There are 10 possible choices for each of the other 4 digits, so there are a total of 10×10×10×10 choices. Therefore:
[tex]10\times10\times10\times10=10000[/tex]Answer: 10000
There are 6 mice in an attic. Their population is growing at a rate of12% per month.a. Write an exponential growth function to model this situation.
general equation of a population is
[tex]y=a(1+\frac{b}{100})^x[/tex]where a is the initial population and b the percent of growing
then replacing a=6 and b=12
[tex]y=6(1+\frac{12}{100})^x[/tex]and simplify
[tex]\begin{gathered} y=6(1+0.12)^x \\ y=6(1.12)^x \end{gathered}[/tex]It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.
I need a inequality
The inequality to represent the given situation is 2s+12a≤50.
Given that, it costs $2 to download a song and $12 to download an entire album.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Jorge has $50 to spend on downloading music.
Let the number of songs be s and the number of albums be a.
So, inequality to represent the given situation is
2s+12a≤50
Therefore, the inequality to represent the given situation is 2s+12a≤50.
To learn more about the inequalities visit:
https://brainly.com/question/20383699.
#SPJ1
The table below shows the changes in the value of a company's stock over the past four weeks. By how many points would the stock value need to change in Week 5 to return to its value before Week 1? Explain.
ANSWER:
+ 4 7/8
STEP-BY-STEP EXPLANATION:
Assuming that we start in week 0, with a total of 0 points, we must operate the changes in each week and the value opposite to that result must be the change necessary to return to the original value.
Just like that:
[tex]\begin{gathered} 9\frac{1}{2}+6\frac{5}{8}-12\frac{3}{4}-8\frac{1}{4}=\frac{19}{2}+\frac{53}{8}-\frac{51}{4}-\frac{33}{4}=-\frac{39}{8}=-4\frac{7}{8} \\ -4\frac{7}{8}+4\frac{7}{8}=0 \end{gathered}[/tex]Which means that to return to the initial value, 4 7/8 points must be added
What is the value of 0 in the following image
We will determine the value of theta as follows:
[tex]\begin{gathered} cos(\theta)=\frac{10}{21}\Rightarrow\theta=cos^{-1}(\frac{10}{21}) \\ \\ \Rightarrow\theta\approx61.6 \end{gathered}[/tex]So, the measurement of the angle is approximately 61.6°.
2. The volume of a 3-D shape is 13 cubic feet. The shape is scaled up and the new volume is 832 cubic
feet. What was the scale factor?
Scale factor of given equation is 64 : 1
What is scale factor ?Scale Factor is used to scale the shape in various dimensions. In Geometry you will learn about different geometric shapes in 2D and 3D. A scale factor is a measure of similar figures that look the same but have different scales or measurements. Suppose two circles are similar but may have different radii. The scale factor indicates how much larger or smaller the figure is than the original figure. Scale allows you to scale the original shape up or down and draw it. The amount by which a shape is magnified or shrunk is called the scale factor. Used when you need to increase the size of 2D shapes such as circles, triangles, squares, and rectangles. Magnification is also well understood from the basic theorem of proportionality.Calculationinitial volume = 13 cubic feet
final volume = 832 cubic feet
scale factor = 832 / 13
= 64 : 1
learn more about scale factor here :
brainly.com/question/22312172
#SPJ1
Which angles are coterminal with -6pie/5
4π/5 and -16π/5 are Coterminal angles with -6π/5
What is Angle?an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle
Coterminal angles are angles that share the same initial and terminal sides. To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians.
The given angle is -6π/5
We need to add 2π for finding coterminal angle
-6π/5+2π
4π/5
We need to subtract 2π for finding coterminal angle
-6π/5-2π
-6π-10π/5
-16π/5
Hence 4π/5 and -16π/5 are Coterminal angles with -6π/5
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ1
These ordered pairs represent a proportional relationship. Use the interactive and the constant of proportionality to find the missing coordinates for the ordered pairs.
(3, 9), (A, 12), (5, 15), (6, B
Missing coordinates for the ordered pairs given are A= 4 and B= 18.
What are coordinates ?An integer pair used to define a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes Coordinates are two numbers (Cartesian coordinates) or, less frequently, a letter and a number that identify a specific location on a grid, also known as a coordinate plane. They are frequently represented by the x-value and y-value pair (x,y). The x (horizontal) and y (vertical) axes are the two axes of a coordinate plane with four quadrants (vertical)
Calculation12/A = 9 / 3
A = 4
Same as above
B/6 = 9/3
B = 18
learn more about coordinates here :
brainly.com/question/15300200
#SPJ1
Find the slope and y-intercept of the line. Graph the line.
Answer:
Graphing the equation we have;
Explanation:
Given the equation;
[tex]x+5y=40[/tex]the slope of the line can be derived by expressing the equation in slope-intercept form;
[tex]\begin{gathered} 5y=-x+40 \\ y=-\frac{1}{5}x+\frac{40}{5} \\ y=-\frac{1}{5}x+8 \end{gathered}[/tex]So, the slope and y-intercept are;
[tex]\begin{gathered} \text{slope m = -}\frac{1}{5} \\ y-\text{intercept b = 8} \end{gathered}[/tex]to graph the equation, let us find the x-intercept;
[tex]\begin{gathered} at\text{ y=0;} \\ x+5y=40 \\ x+0=40 \\ x=40 \\ (40,0) \\ at\text{ x=0;} \\ (0,8) \end{gathered}[/tex]Graphing the equation we have;
Other points on the graph includes;
[tex]\begin{gathered} at\text{ x=10}; \\ y=-\frac{1}{5}(10)+8=-2+8=6 \\ (10,6) \\ at\text{ x=20;} \\ y=-\frac{1}{5}(20)+8=-4+8=4 \\ (20,4) \end{gathered}[/tex]Then where dose the two lines intersect needs to be (x,y) pair
Answer:
The lines are parallel, and therefore, never intersect.
Can someone answer this for me ill give a big reward
Answer:
carol
Step-by-step explanation:
Beth’s hair can be represented as 1 since everyone else is a fraction of her hair so we just convert the other 2 fractions to make them have the same denominator
4x3/5x3=12/15
2x5/3x5=10/15
10 is less than 12 so carol has the shortest hair
Hopes this helps please mark brainliest
To help visualize, let's say Beth's hair is 15 inches:
Beth = 15"
Abbey = 4/5 * 15" = 12"
Carol = 2/3 * 15" = 10"
Carol has the shortest hair.
Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?
the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
Explanation:half life = 12.4 hours
initial amount = 746g
time elapsed = 62 hours
Using the half-life formula:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}[/tex]Substitute for the values:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}[/tex][tex]\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}[/tex]Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
1/16*1/8 in exponential form
The exponential form of 1/6 × 1/ 8 = 1/32 = 3.125 × [tex]10^{-5}[/tex]
The given numbers are 1/6 and 1/8
and exponential form means that we would have to write these numbers in such a way that the number can be expressed in the form 10 raised to the power of an integer.
When we solve 1/6
we will get 1/6 = 0.166
and when we solve 1/8 we will get
1/8 = 0.125
thus when we multiply 1/6 × 1/ 8 = 1/32
which when solved will give us
0.03125
this can be expressed as 3.125 × [tex]10^{-5}[/tex]
To know more about exponents and exponential form you may visit the link which is mentioned below:
https://brainly.com/question/88070
#SPJ1
Identify the graphs of y 2|x+2|-6 and y=-2 in the same coordinate plane
The graphs of the absolute value function y = 2|x + 2| - 6 and the horizontal line y = -2 are given on the image at the end of the answer.
How to build the graphs?The definition of the absolute value function is given as follows:
y = |x - h| + k.
In which the coordinates of the vertex are (h,k), representing the turning point of the graph of the absolute value function, the point in which the function makes the "V".
In this problem, the definition of the function is:
y = 2|x + 2| - 6.
Hence the coordinates of the vertex are:
(-2, -6).
The multiplication by 2 represents a vertical stretch but is not related to the vertex of the function.
y = -2 is a horizontal line, and the graph with these two functions is given by the image at the end of the answer.
More can be learned about the absolute value function at brainly.com/question/3381225
#SPJ1
Lacy picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries. let x represent the weight of raspberries. Which equations could be used to find the weight of the blueberries Lacey has?
Chose all correct answers.
A. [tex]\frac{1}{5} x-1\frac{1}{5}=x[/tex]
B. [tex]x-1\frac{4}{5} =\frac{1}{5}x[/tex]
C. [tex]\frac{1}{5}x=x-1\frac{4}{5}[/tex]
D. [tex]x+1\frac{4}{5}=\frac{1}{5}x-1\frac{4}{5}[/tex]
E. [tex]\frac{1}{5}x+1\frac{4}{5}=x[/tex]
F. [tex]x=1\frac{4}{5}(\frac{1}{5}+x)[/tex]
The equations that could be used to find the weight of the blueberries Lacey has are given as follows:
B. x - 1 and 4/5 = x/5.
C. x/5 = x - 1 and 4/5.
E. x/5 + 1 and 4/5 = x.
How to obtain the equations?The variable that represents the weight of the raspberries is given as follows:
x.
The variable that represents the weight of the blueberries is given as follows:
b.
She has 1/5 as many pounds of blueberries as raspberries, hence:
b = x/5.
If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries, hence:
b + 1 and 4/5 = x.
x/5 + 1 and 4/5 = x.
Thus the correct options are given as follows:
Option B, as x - 1 and 4/5 = x/5.Option C, as x/5 = x - 1 and 4/5.Option E, as x/5 + 1 and 4/5 = x.More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
In Exercises 1 and 2, solve the system using the elimination method.2. x + y - 2 = -22x – y += = 8-x + 2y + 2: = 10
(1,3,-7)
1) Let's write the following system of linear equations, and then solve them by the elimination method.
The first thing to do is to proceed with the elimination of one variable. In this case, let's chose to start with
x-6y+2z=5 x -2
2x-3y+z=4
3x+4y-z=-2
2x-12y+4z=10
2x-3y+z=4
3x+4y-z=-2
Adding these two equations:
2x-3y+z=4
-2x+12y-4z=-10
----------------------------------
9y -3z =-6
Now getting the other equations, let's eliminate another variable, in this case, "x"
-2x+12y-4z=-10 x 3
3x+4y-z=-2 x 2
Adding them
-6x +36y -12z=-30
6x+8y-2z=-4
----------------------------
0 44y -14z=-34
2) Now that we have a simpler system of two variables "y" and " z" let's operate them. Choosing a factor that we can multiply and cancel out the y variable, in this case, let's pick the Least Common Multiple between 9 and 44 = 396, so let's multiply them by
9y -3z = -6 x 44
44y-14z=-34 x -9
396y -132z = -264
-396y+126z=-306
----------------------------
6z =-42
z=-7
Plugging into the equation 9y -3z =-6
9y-3(-7)=-6
9y +21 =-6
9y=27
y=3
And for x
x-6y+2z=5
x-6(3)+2(-7)=5
x+18-14=5
x+4=5
x=1
3) So the solution for that system is (1, 3, -7).
The selling price of a refrigerator, is $548.90. The markup value was 10%. How much was the refrigerator originally?
Let the original price be p.
Then
p + (10% of p) = 548.90
1.1p = 548.90
p = 548.9 / 1.1 = $499.00
Hence the refrigerator was $499.00 originally
Look at the simultaneous equations below.
x - 6y=10
3y² = 4x + 1
a) Show that 3y² - 24y - 41 0
=
b) Use part a) to solve the simultaneous
equations.
For x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
What is a expression? What is a mathematical equation? What is degree of a equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Degree of equation is the highest power of x in the given equation.An equation of second degree is of the form -f(x) = ax² + bx + c
It has two possible roots.Given is are the following equations -
x - 6y=10
3y² = 4x + 1
It is given that -
3y² - 24y - 41 ...Eq[1]
3y² = 4x + 1
y² = (4/3)x + (1/3)
So, we can write -
3{(4/3)x + (1/3)} - 24 × √{(4/3)x + (1/3)} - 410
Refer to the graph [1] attached. We can see that, for x = 200, the equation is fulfilled.
Now, refer to the graph [2] attached. It shows there two possible solution sets.
A(66.68, 9.447)
B(1.31, - 1.447)
Therefore, for x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
brainly.com/question/15146641
#SPJ1
Which property of addition is shown? −3+ 5 = 5 + (−3)
Associative Property
Commutative Property
Distributive Property
Identity Property.
This is the Commutative Property. It states that when addition takes place, the addends may switch positions with another addend.
The given expression −3+ 5 = 5 + (−3) is showing the commutative Property. The correct option is B.
The cumulative property states that if the position of the numbers when they are in addition is changed then it will not affect the final result of the addition. If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
The given expression is −3+ 5 = 5 + (−3).
From the cumulative property, the expression can be solved. The two expressions will have the same value but the frame of writing the expression is different.
This is the Commutative Property. It states that when an addition takes place, the addends may switch positions with another added.
To know more about cumulative property follow
brainly.com/question/6838217
#SPJ2
6x+1.6=58
i dont know the answer to this
The value of x in the given equation, 6x + 1.6 = 58, is x = 9.4
Determining the value of x in an equationFrom the question, we are to determine the value of x in the given equation.
The given equation is
6x + 1.6 = 58
To determine the value of x in the equation, we will determine the value of the unknown variable.
The unknown variable in the given equation is x.
Thus, we will determine the value of x.
Solving the equation for x
6x + 1.6 = 58
Subtract 1.6 from both sides of the equation
6x + 1.6 - 1.6 = 58 - 1.6
6x = 56.4
Divide both sides of the equation by 6
6x/6 = 56.4/6
x = 9.4
Hence, the equation solved for x gives x = 9.4
Learn more on Determining the value of x in an equation here: https://brainly.com/question/27882730
#SPJ1
2) A recycling center was offering cash for different types of recyclables. For each pound of
paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for
each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of
aluminum and 7 pounds of plastic. How much money did he earn?
The money earned by Jerry at the recycling center is $11.35.
According to the question,
We have the following information:
For each pound of paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of aluminum and 7 pounds of plastic.
Now, we have the following expression when multiplied with the cost of each pound:
10*0.03+8*1.32+7*0.07
Now, we will first use multiplication and then we will use addition:
0.3+10.56+0.49
$11.35
Hence, the money earned by Jerry at the recycling center is $11.35.
To know more about money earned here
https://brainly.com/question/26156975
#SPJ1
write a fracción and a decimal for the part of the gris that is shaded.
The shaded part is 3 column
There are 10 columnn in total.
The number of grids are 100 and shaded grids are 30
Thus the fraction of shaded portion is:
3/10.
The decimal form is 0.3.
jack wants to buy a pair of trousers for $60.When he went to the store he found that the price was marked down by 20%. how much do they cost
Answer:
$48
no idea how working out would go
Answer: $48
Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.
Then multiply 60 x 0.20 which equals 12.
Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.
I hope this helps!! Good Luck!
Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
18
14
:C
PLEASE HELP 10 POINTS !!!!!!!!
Answer:
112
Step-by-step explanation:
8*14=112
3.14*4²=50.24
50.24/2=25.12
112-25.12+25.12=112