in a cave a stalactites gets 4 millimeters longer each year.this year it is 72 centimeters long
how many years until it is 1 meter long
we have that
the linear equation that represent this situation is equal to
y=4x+720
where
y ------> length in mm
x ----> number of years
Remember that
72 cm=720 mm
so
For y=1 m ------> y=1,000 mm
substitute in the equation
1,000=4x+720
4x=1,000-720
4x=280
x=70 years
therefore
answer is 70 yearsi inserted a picture of the questionif it helps i can give you my answer to my previous question
In order to determine the time it takes for the music player to fall to the bottom of the ravine, we shall find the solutions of t as follows;
[tex]\begin{gathered} t=\sqrt[]{\frac{8t+24}{16}} \\ \end{gathered}[/tex]Take the square root of both sides;
[tex]\begin{gathered} t^2=\frac{8t+24}{16} \\ \text{Cross multiply and we'll have;} \\ 16t^2=8t+24 \\ \text{ Re-arrange the terms and we'll now have;} \\ 16t^2-8t-24=0 \end{gathered}[/tex]We can now solve this using the quadratic equation formula;
[tex]\begin{gathered} \text{The variables are;} \\ a=16,b=-8,c=-24 \\ t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(16)(-24)_{}}}{2(16)} \\ t=\frac{8\pm\sqrt[]{64+1536}}{32} \\ t=\frac{8\pm\sqrt[]{1600}}{32} \\ t=\frac{8\pm40}{32} \\ t=\frac{8+40}{32},t=\frac{8-40}{32} \\ t=\frac{48}{32},t=-\frac{32}{32} \\ t=1.5,t=-1 \end{gathered}[/tex]We shall now plug each root back into the original equation, as follows;
[tex]\begin{gathered} \text{Solution 1:} \\ \text{When t}=1.5 \\ t=\sqrt[]{\frac{8t+24}{16}} \\ t=\sqrt[]{\frac{8(1.5)+24}{16}} \\ t=\sqrt[]{\frac{12+24}{16}} \\ t=\sqrt[]{\frac{36}{16}} \\ t=\frac{6}{4} \\ t=1.5\sec \end{gathered}[/tex][tex]\begin{gathered} \text{Solution 2:} \\ \text{When t}=-1 \\ t=\sqrt[]{\frac{8(-1)+24}{16}} \\ t=\sqrt[]{\frac{-8+24}{16}} \\ t=\sqrt[]{\frac{16}{16}} \\ t=\frac{4}{4} \\ t=1 \end{gathered}[/tex]From the result shown the ballon will deploy after 1.5 seconds for the first solution.
However t = -1 cannot be a solution since you cannot have a negative time (-1 sec)
ANSWER:
t =1.5 is a solution
. A plant grows 4 centimeters in two month. How many centimeters does it grow in one week?
it is given that
in a month the plant grows = 4 cm
and there are four complete weeks in a month
so, in four weeks the plant grows = 4 cm
in 1 weel the growth of the plant is 4/4 = 1 cm
so in a week, the plant grows 1 cm
Select the correct answer.What is the image of this figure after this sequence of dilations?1. dilation by a factor of -1 centered at the origin2. dilation by a factor of 2 centered at (-1,1)
The coordinates of the original figure are:
(-2,1)
(3,1)
(1,3)
(-2,3)
A dilation by a negative scale factor produces an image on the other side of the center of enlargement.
As the first dilation is by a factor of -1 centered at the origin, the length of the sides doesn't change, but the new coordinates will be:
[tex](x,y)\to(kx,ky)[/tex]Apply this to the given coordinates:
[tex]\begin{gathered} (-2,1)\to(-1\cdot-2,-1\cdot1)\to(2,-1) \\ (3,1)\to(-1\cdot3,-1\cdot1)\to(-3,-1) \\ (1,3)\to(-1\cdot1,-1\cdot3)\to(-1,-3) \\ (-2,3)\to(-1\cdot-2,-1\cdot3)\to(2,-3) \end{gathered}[/tex]The image after the first dilation looks like this:
Now, the second dilation is by a scale factor of 2, centered at (-1,1).
As it is not centered in the origin, we can use the following formula:
[tex](x,y)\to(k(x-a)+a,k(y-b)+b)[/tex]Where k is the scale factor and (a,b) are the coordinates of the center of dilation.
By applying this formula to the actual coordinates we obtain:
[tex]\begin{gathered} (2,-1)\to(2(2-(-1))+(-1),2(-1-1)+1)\to(5,-3) \\ (-3,-1)\to(2(-3-(-1))+(-1),2(-1-1)+1)\to(-5,-3) \\ (-1,-3)\to(2(-1-(-1))+(-1),2(-3-1)+1)\to(-1,-7) \\ (2,-3)\to(2(2-(-1))+(-1),2(-3-1)+1)\to(5,-7) \end{gathered}[/tex]If we place these coordinates in the coordinate plane we obtain:
The answer is option B.
Answer:
B .
Step-by-step explanation:
Got the answer right.
four times a number increased by 2 is less than -24
Four times a number increased by 2 is less than -24
The number (x)
4x +2 < -24
_________________
Solving
4x +2 < -24
4x < -24 -2
4x < -26
x<-26/4
x < -6.5
__________________
Answer
x < -6.5
13. Solve the inequality and share a graph on a number line
Given the following inequality:
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex]We get,
[tex]-3(t\text{ - 2) }\ge\text{ -15}[/tex][tex]\frac{-3(t\text{ - 2)}}{-3}\text{ }\ge\text{ }\frac{\text{-15}}{-3}[/tex][tex]t\text{ - 2 }\ge\text{ }5[/tex][tex]t\text{ }\ge\text{ }5\text{ + 2}[/tex][tex]t\text{ }\ge\text{ }7[/tex]Graphing this on a number line will be:
how long must $1000 be invested at an annual interest rate of 3% to earn $300 in sinple interest?
I’ve attached my problem thank youfind the area of the shaded area
Giving the circle with 2 radius
Radius 1= 12
Radius 2=10
this figure is also known as a ring
the area of the ring is given by
[tex]A=\pi r1^2-\pi r2^2[/tex]this is just the difference of the area of the bigger circle less the smaller circle
then
[tex]A=\pi(r1^2-r2^2)[/tex][tex]A=\pi(12^2-10^2)[/tex][tex]A=\pi(44)[/tex][tex]A=44\pi=138.230[/tex][tex]2x ^{2} - 6x + 10 = 0[/tex]solve by completing the square
We know that we can use the quadratic equation
Using this we have
[tex]\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot2\cdot10}}{2\cdot2}=\frac{6\pm\sqrt[]{36-80}}{4} \\ =\frac{6\pm\sqrt[]{-44}}{4}=\frac{6\pm\sqrt[]{4\cdot-11}}{4}=\frac{6\pm2\cdot\sqrt[]{-11}}{4} \\ =2\cdot(\frac{3\pm\sqrt[]{-11}}{4})=\frac{3\pm\sqrt[]{-11}}{2}=\frac{3\pm\sqrt[]{11}i}{2} \\ =\frac{3}{2}\pm\frac{\sqrt[]{11}}{2}i \end{gathered}[/tex]So the answer is B)
There are currently 400,000 cats in the San Diego area. The number of cats in San Diego increases each year by 2.5 % A) how many cats will there be in the year 2036 ? B) how long will it be before the number of cats doubles ?
a) 436529 cats b) Approximately 278 years
1) Gathering the data
400,000 cats
Increases yearly by 2.5%
2) Let's write that growth as a function. Note that we must rewrite 2.5% as purely decimal 0.0025. A growth of 2.5 must be written as 1.0025.
Because every time we multiply by 1.0025 we are multiplying the number and 2.5%. Considering that there are currently, in this 1st year 400,000 cats 2036 then this will be 35 years after
[tex]\begin{gathered} y=400000(1.0025)^n \\ y=400000(1.0025)^{35} \\ y=436529.23\text{ }\cong436,529\text{ } \end{gathered}[/tex]So considering we're in the first year, 35 years after in 2036 there'll be 436,529
b) Since n= is the number of years in that function, and y stands for the number of cats.
[tex]\begin{gathered} 800,000=400,000(1.0025)^n \\ \frac{800,000}{400,00}=\frac{400,000}{400,000}(1.0025)^n \\ 2=(1.0025)^n \\ \log 2\text{ =}\log (1.0025)^n \\ 0.3=^{}n1.08\cdot10^{-3} \\ n=\frac{0.3}{1.08\cdot10^{-3}} \\ n=277.8 \\ \end{gathered}[/tex]So, it will take at this rate approximately 278 years for the population of cats doubles.
The diameter of a grain of sand measures at about 0.0046 inches, while the diameter of a dust particle measured at about 0.00005 inches. About how many times larger is the diameter of a grain of sand than a dust particle? Estimate the following problem using powers of 10.
We have the following:
To know how many times one grain is bigger than the other, we must calculate the quotient of them, as follows:
[tex]\frac{0.0046}{0.00005}=\frac{4.6\cdot10^{-3}}{5\cdot10^{-5}}=0.92\cdot10^{-3-(-5)}=0.92\cdot10^2=92[/tex]Therefore it is 92 times larger
Conner left his house and rode his bike into town at 6mph. Along the way he got a flat tire so he had to turn around and walk his bike to his house traveling 3 mph. If the trip down and back took 15 hours, how far did he get before his tire went flat?Conner went ___ miles before his tire went flat.
The main point in this question, that the distance of the first part = the distance of the second part
[tex]d_1=d_2[/tex]Since the speed of the first part is 6 mph
Let the time of it be t1
Since distance = speed x time, then
[tex]\begin{gathered} d_1=v_{1_{}}\times t_1_{} \\ d_1=6\times t_1 \\ d_1=6t_1 \end{gathered}[/tex]Since the speed of the second part is 3 mph
Let the time of it be t2, then
[tex]\begin{gathered} d_2=3\times t_2 \\ d_2=3t_2 \end{gathered}[/tex]Equate d1 and d2 to find t2 in terms of t1
[tex]3t_2=6t_1[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3t_2}{3}=\frac{6t_1}{3} \\ t_2=2t_1\rightarrow(1) \end{gathered}[/tex]Since the total time of the two parts is 15 hours, then
[tex]t_1+t_2=15\rightarrow(2)[/tex]Substitute (1) in (2)
[tex]\begin{gathered} t_1+2t_1=15 \\ 3t_1=15 \end{gathered}[/tex]Divide both sides by 3
[tex]\begin{gathered} \frac{3t_1}{3}=\frac{15}{3} \\ t_1=5 \end{gathered}[/tex]Now, let us find d1
[tex]\begin{gathered} d_1=6\times5 \\ d_1=30 \end{gathered}[/tex]Conner went 30 miles before his tire went flat
33<=105/p what is the answer
The answer is p≤35/11.
From the question, we have
33≤105/p
⇒p≤105/33
⇒p≤35/11
Inequality:
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
When the symbols ">", "", "", or "" are used to connect two real numbers or algebraic expressions, that relationship is known as an inequality.
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When factored completely, which is a factor of 3x3 − 9x2 − 12x A. L(x − 3) B. (x − 4) C. (3x − 1) D. <(3x − 4)
Solution:
[tex]3x^3-9x^2-12x[/tex]Step 1:
Factor out the common term
The common term is 3x
By doing this, we will have
[tex]\begin{gathered} 3x^3-9x^2-12x=3x(\frac{3x^3}{3x}-\frac{9x^2}{3x}-\frac{12x}{3x}) \\ =3x(x^2-3x-4) \end{gathered}[/tex]Step 2:
Factorise the quadratic expression in the bracket
[tex]3x(x^2-3x-4)[/tex]By doing this, we will have to look for two factors to multiply to give i4 and if we add them together, we will have -3
The two factors are -4 and +1
therefore,
Replace -3x with -4x + x
[tex]\begin{gathered} 3x(x^2-3x-4) \\ =3x(x^2-4x_{}+x-4) \\ =3x(x(x-4)+1(x-4) \\ =3x(x+1)(x-4) \end{gathered}[/tex]Hence,
The final answer is = (x-4)
568,319,000,000,000,000,000,000,000 in standard form
To write in standard form;
568,319,000,000,000,000,000,000,000
Move the decimal point backward till you reach the last number
Multiply by ten raise to the number of times you move the decimal point
That is;
568,319,000,000,000,000,000,000,000 = 5.68319 x 10^26
[tex]5.68319\text{ }\times10^{26}[/tex]Please help on average rate of change!
The average rate of change on the interval [-1, 2] is 1/3.
How to get the average rate of change?For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the function is graphed, and the interval is [-1, 2]
On the graph we can see that:
f(-1) = -3
and
f(2) = -2
Replacing these we will get:
r = ( f(2) - f(-1))/(2 - (-1))
r = (-2 + 3)/(3) = 1/3
The average rate of change is 1/3.
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if frita goes to the mall, then alice will go to the mall
Given
The statements,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
To find: The conclusion using the law of Syllogism.
Explanation:
It is given that,
If Frita goes to the mall, then Alice will go to the mall.
If Wally goes to the mall, then Frita will go to the mall.
That implies,
If Wally goes to the mall, then Frita will go to the mall.
If Frita goes to the mall, then Alice will go to the mall.
Here, consider the statement Wally goes to the mall as p, the statement Frita will go to the mall as q, and the statement Alice will go to the mall as r.
Therefore,
[tex]Conclusion:\text{ }If\text{ }Wally\text{ }goes\text{ }to\text{ }the\text{ }mall,\text{ }then\text{ }Alice\text{ }will\text{ }go\text{ }to\text{ }the\text{ }mall.[/tex]Hence, the answer is option C).
if the endpoints of KB are K(-4, 5) and B(2, -5), what is the length of KB?
The length of the line can be found by distance formula as,
[tex]\begin{gathered} KB=\text{ }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ KB=\sqrt[]{(2-(-4)_{})^2+(-5-5)^2} \\ KB=\sqrt[]{(2+4)^2+(-10)^2} \\ KB=\sqrt[]{6^2+100} \\ KB=\sqrt[]{36+100} \\ KB=\sqrt[]{136} \\ KB=11.66 \end{gathered}[/tex]"Name the property used in the equation below
a) 3 x+9 y-1=3(x+3 y)-1
b) 7 x+5 y-5 y=7 x
c) (x-4)(x+3)=0
d) 4 x+5 x=5 x+4 x"
The property used in each equation are
a) 3x + 9y - 1 = 3(x + 3y) - 1 distributive property
b) 7x + 5y - 5y = 7x additive inverse property
c) (x - 4)(x + 3) = 0 distributive property
d) 4x + 5x = 5x + 4x commutative property
What is distributive property?The distributive property states that multiplying the total of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and adding the products together.
Additive inverse involves adding which involves two numbers that has opposite sign. the addition lead to zero
b) 7x + 5y - 5y = 7x
= 7x + 0
= 7x
What is commutative property?
This law basically asserts that while adding and multiplying numbers, you can rearrange the numbers in a problem without changing the solution.
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f (x)=2^ x -10 and the domain of f(x) is the set of integers from 1 to 3which values are elements of the range of f(x) Select all that apply.a. -12b. -10c. -9d. -6e. -2
We have to find the range of the function f(x).
The definition of f(x) is:
[tex]f(x)=2^x-10[/tex]The domain of this function is defined as: D: {-1, 0, 1, 2, 3}, which represents all the integers from -1 to 3.
Then, we have to find the range by applying the function to each of the elements of the domain:
[tex]f(-1)=2^{-1}-10=\frac{1}{2}-10=-9.5[/tex][tex]f(0)=2^0-10=1-10=-9[/tex][tex]f(1)=2^1-10=2-10=-8[/tex][tex]f(2)=2^2-10=4-10=-6[/tex][tex]f(3)=2^3-10=8-10=-2[/tex]Then, the range of f(x) is R: {-9.5, -9, -8, -6, -2}.
Answer:
The options that apply from the list are -9, -6 and -2. [Options c, d and e]
Which statement about this figure is true ? ○ it has rotational symmetry with an angle of 45°.○ it has no reflectional symmetry.○ it has reflectional symmetry with one line of symmetry. ○ it has point symmetry
The figure has different measure in all their parts, then, it has no reflectional symmetry.
For a point symmetry evey part has matching part, the same distance form a central point but our figure has the same 2 ellipses but with different measure. The figure dont have rotational symmetry because there is a little ellipse in the middle of the others.
Lotsa Boats requires 75$ plus payment of 10$ an hour for each hour for which the boated is rented.Which equation could be used to find the number of hours h the johnsons rented the boat for if they paid 125$ need answer helpp.
The required equation will be 75 +10 [tex]x[/tex] =125
and the value of x = 5 hours
Linear equation in one variable:
Equation having one variable and degree of the equation is one, called linear equation in one variable.
Example: 3x+2 =5
Given,
Base price of boat is 75$
charge per hour is 10$
johnsons rented the boat and he paid 125$
let,
he has taken the boat for rent for x hours
then,
according to question,
75 +10 [tex]x[/tex] =125
now solving the equation to get the value of x
10x = 125 - 75
10x = 50
x = 50/10
x = 5 hours
Hence,
The required equation will be 75 +10 [tex]x[/tex] =125
and the value of x = 5 hours
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Simplified What is the ratio of Π to Δ ? = What is the ratio of A to ( +Δ) ? ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ ΔΔΔΔΔΔΔΔΔ
• The ratio of ⬛ to △.
First count the number of ⬛ and the number of △ given.
We have:
Number of ⬛ = 45
Number of △ = 81
The ratio of ⬛ to △ = Number of ⬛ : Number of △
= 45 : 81
To Simplify the ratio, divide by the GCF which is 9.
= 45 ÷ 9 : 81÷9 = 5 : 9
Therefore the simplified ratio of ⬛ to △ = 5 : 9
• The ratio of △ to (⬛ + △)
81 : (45 + 81)
= 81 : 126
Simplify the ratio by dividing it with its GCF which is 9:
81 ÷ 9 : 126 ÷ 9 = 9 : 14
Therefore, the simplified ratio of △ to (⬛ + △) = 9 : 14
ANSWER:
⬛ to △ = 45 : 81 Simplified = 5 : 9
△ to (⬛ + △) = 81 : 126 Simplified = 9 : 14
the five number summary for a set of data is given in the picture.what is the interquartile range of the set of data?
ANSWER
[tex]IQR=13[/tex]EXPLANATION
The interquartile range can be found by finding the difference between the first quartile, Q1, and the third quartile, Q3.
That is:
[tex]IQR=Q3-Q1[/tex]Therefore, the interquartile range is:
[tex]\begin{gathered} IQR=81-68 \\ IQR=13 \end{gathered}[/tex]A board game of chance costs $2 is play You have a 20% chance dans is the expected value of playing the game you lose your bet 15% of the m
Given
Cost to play game = $2
Find
Expected value of playing
Explanation
10% chance to win 1 = 1 x 10% = $0.1
25% chance to win 2 = 2 x 25% = $0.5
50% chance to win 5 = 5 x 50% = $2.5
15% chance to lose 2(being cost) = 2 x 15% = $0.3
= 1.5 -0.1 - 0.3 = 1.1
Final Answer
The expected value of playing is $1.10
Hence option (d) is correct
On 14 would I solve the 32x + 72 or is that the answer. The app stopped in the middle of the other tutor
The given expression is 8(4x+9)
Multiplying 8 to each term of (2x+9), we get
[tex]8(4x+9)=8\times4x+8\times9[/tex][tex]=32x+72.[/tex]Write equation of circle in standard form. Quadrant lies in 2 tangent to x=–12 and x=–4
Solution
Explanation:
The diameter of the circle is defined by the distance between (-12, 0) and (-4, 0).
The distance from the mid point of the line joining points (-12, 0) and (-4, 0) to point is the radius of the circle = 4
ActiveApplying the Triangle Inequality Theoremin triangle ABC, AB measures 25 cm and AC measures 35 cm.The inequalitycentimeters.
Using the Triangle inequality:
[tex]zso:[tex]undefined[/tex]Find PR.Write your answer as an integer or as a decimal rounded to the nearest tenth. PR = ___
In triangle PQR, RQ is 4 units and angle P is 29 degrees.
Use the trigonometric ratio of tan to find PR as follows:
[tex]\begin{gathered} \tan 29=\frac{RQ}{PR} \\ PR=\frac{RQ}{\tan 29} \\ PR=\frac{4}{0.5543090} \\ PR=7.21619 \\ PR\approx7.2 \end{gathered}[/tex]Hence the value of PR is 7.2 rounded to one decimal place.
- 10f - 4 = -24 can you help
Let's solve the equation
[tex]\begin{gathered} -10f-4=-24 \\ -10f=-24+4 \\ -10f=-20 \\ f=\frac{-20}{-10} \\ f=2 \end{gathered}[/tex]Therefore, f=2.
If y varies inversely as x and y=−97 when x=28, find y if x=36. (Round off your answer to the nearest hundredth.)
For this problem, we were informed that two variables "x" and "y" vary inversely to each other. We were also informed about one data point on the relation between the two (28, -97). From this information, we need to determine the value of "y" when "x" is equal to 36.
We can write the expression between two variables that vary inversely according to a constant, K, as shown below:
[tex]\begin{gathered} y\cdot x=k \\ y=\frac{k}{x} \end{gathered}[/tex]We can find the value of k by applying the known datapoint.
[tex]\begin{gathered} -97=\frac{k}{28} \\ k=-97\cdot28 \\ k=2716 \end{gathered}[/tex]The full expression is:
[tex]y=\frac{2716}{x}[/tex]Now we can apply the value of "x" to calculate the desired "y".
[tex]y=\frac{2716}{36}=75.44[/tex]The value of "y" is 75.44, when "x" is 36