The sum of three numbers is 100. The first number is 5 more than the second. The third number is 3 times the second. What are the numbers?
Answers
Answer: first number = 24
second number = 19
third number = 57
Explanation:
Let the second number be x. From the information given,
the first number is 5 more than the second. This means that
the first number is x + 5
The third number is 3 times the second. This means that
the second number is 3x
If the sum of the three numbers is 100, it means that
x + 5 + x + 3x = 100
5x + 5 = 100
5x = 100 - 5 = 95
x = 95/5
x = 19
The first number = 19 + 5 = 24
The second number = 19
the third number = 3 * 19 = 57
Related Questions
If x is 3 what is there value of 4x^2 - 5
Answers
To evaluate the given at x = 3, substitute x by 3, and evaluate the expression accordingly
[tex]\begin{gathered} 4x^2-5 \\ =4(3)^2-5 \\ =4(9)-5 \\ =36-5 \\ =31 \end{gathered}[/tex]Therefore, the value of the given at x = 3, is 31.
i need help with my homework PLEASE CHECK WORK WHEN DONENUMBER 10 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: B
[tex]\frac{log_{2}(4.72)}{0.32}[/tex]Explanation:
Step 1. The expression that we have is:
[tex]P(t)=18,785\cdot2^{0.32t}[/tex]This represents the population P after t years.
Step 2. We need to find the expression that represents the amount of time, t, in years, for the population to be 88,740:
[tex]P(t)=88,740[/tex]Step 3. Substituting this value of P(t) into the given equation:
[tex]88,740=18,785\cdot2^{0.32t}[/tex]Step 4. To solve for t, first, we divide both sides by 18,785:
[tex]\frac{88,740}{18,785}=2^{0.32t}[/tex]The result of the division is:
[tex]4.72=2^{0.32t}[/tex]Step 5. Then, to continue solving for x, we apply the logarithm base two to both sides:
[tex]log_2(4.72)=log_2(2^{0.32t})[/tex]We simplify applying this property of logarithms:
[tex]log_2(a^x)=x\cdot log_2(a)[/tex]The result is:
[tex]log_2(4.72)=0.32t\cdot log_2(2^)[/tex]And since:
[tex]log_2(2^)=1[/tex]The expression now is:
[tex]log_2(4.72)=0.32t[/tex]Step 6. Dividing both sides by 0.32 to solve for t:
[tex]\frac{log_2(4.72)}{0.32}=t[/tex]This expression is shown in option B:
[tex]\frac{log_{2}(4.72)}{0.32}[/tex]Answer: B
[tex]\frac{log_{2}(4.72)}{0.32}[/tex]Q1:a when -a lies between -4 and 7.Answer: -7) didn't change and the position of all integers were same as the start of the equation.If there is any rules applied in these two questions answers.What is that?& How I will know and apply that in terms of solving Equations like this?
Answers
When -a lies between -4 and 7, we can write an inequation like:
-4 < -a < 7
However the answer have a with a positive sign, so to transform the initial expression, we need to multiply by -1
When we multiply or divide by a negative number, the sign of the inequation change, so:
-4*(-1) > -a*(-1) > 7*(-1)
4 > a > -7
This last expression can also be written as -7 < a < 4
For question 2, we had that x lies between 8 and 9, so the initial inequation is:
8 < x < 9
Then, we need to transform the x into x², so we need to elevate all the expression to the power of 2, so:
[tex]\begin{gathered} 8In this case, we don't need to change the sign because we multiply every number by itself.
The point A(4, 1) is reflected over the point (0, -3) and its image is point B. What are the coordinates of point B?
Answers
A reflection over the point (0,0) is given by:
[tex](x,y)\rightarrow(-x,-y)[/tex]Nevertheless, the reflection is being made over the point (0,-3). We can first make a traslation of the point (0,-3) to the origin. Then, reflect the new coordinates of the point A through the origin and then bring back the new origin to (0,-3).
First, make a traslation such that the new coordinates of (0,-3) are (0,0):
[tex](x,y)\rightarrow(x,y+3)[/tex]Then, apply a reflection through the origin:
[tex](x,y+3)\rightarrow(-x,-y-3)[/tex]Finally, make a traslation reciprocal to the first one:
[tex](-x,-y-3)\rightarrow(-x,-y-3-3)=(-x,-y-6)[/tex]Therefore, the reflection over the point (0,-3) can be written as:
[tex](x,y)\rightarrow(-x,-y-6)[/tex]Substitute (x,y)=(4,1) to find out the new coordinates of A after the reflection:
[tex]\begin{gathered} A\rightarrow B \\ \Rightarrow(4,1)\rightarrow(-4,-1-6)=(-4,-7) \end{gathered}[/tex]Therefore, the coordinates of the point B are (-4,-7).
Factor 5m² + 19m + 12.
Answers
Answer:
(5m+4)(m+3)
Explanation:
Given the quadratic expression:
[tex]5m^2+19m+12[/tex]To factor the quadratic expression, follow the steps below:
Step 1: Multiply the coefficient of m² and the constant.
[tex]5\times12=60[/tex]Step 2: Find two numbers that multiply to give 60, and add to give the coefficient of m, 19 To do this, list the factors of 60: 1,2,3,4,6,10,15,20,30, and 60.
[tex]\begin{gathered} 15\times4=60 \\ 15+4=19 \end{gathered}[/tex]Step 3: Rewrite the middle term with those numbers.
[tex]=5m^2+15m+4m+12[/tex]Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =5m(m+3)+4(m+3) \\ =(5m+4)(m+3) \end{gathered}[/tex]The factored form of the expression is:
[tex]\begin{equation*} (5m+4)(m+3) \end{equation*}[/tex]Please make sure you answer both parts of the question. Remember to properly format your function.The hat that George bought turned out to previously belong to a magician! Initially, 3 rabbits hopped out of the hat. Each day after that, double thenumber of rabbits from the previous day appeared.1: Write an exponential function that can be used to model this function.2: How many rabbits appeared on the 13th day?
Answers
Solution
Question 1:
[tex]\begin{gathered} \text{ On day 1, 3 rabbits hopped out} \\ \text{ On day 2, }3\times2=6\text{ rabbits hopped out} \\ \text{ On day 3, }3\times2\times2=3\times2^2\text{ rabbits hopped out} \\ \text{ On day 4, }3\times2\times2\times2=3\times2^3\text{ rabbits hopped out} \\ \\ \text{Following this pattern, we can find the number of rabbits that will hop out on a day n.} \\ \\ \text{ On day }n,3\times2\times2\times2\ldots\times2=3\times2^{n-1}\text{ rabbits hopped out} \\ \\ \text{Thus, the exponential function to model this scenario is given below as } \\ \\ f(n)=3\times2^{n-1} \end{gathered}[/tex]Question 2:
[tex]\begin{gathered} \text{The question is asking for the number of rabbits that will hop out on day 13} \\ \text{ We can simply apply our formula and this implies that }n=13 \\ \\ \therefore f(13)=3\times2^{13-1} \\ \\ f(13)=3\times2^{12}=12,288 \\ \\ \text{Thus, the number of rabbits that will hop out of the hat on the 13th Day is 12,288} \end{gathered}[/tex]Final Answer
Question 1:
The exponential function to model the scenario is
[tex]f(n)=3\times2^{n-1}[/tex]
Question 2:
The number of rabbits that will hop out of the hat on the 13th Day is 12,288 rabbits
Multiply choice question of scaled factors
Answers
So it’s a and b questionsA) use the graph to determine when the helicopter is at H=30B) set up and solve an equation using the Quadratic Formula to determine when the remote controlled helicopter is at ground (H=0). Please report your answer to the first decimal place. Show all work One question multiple steps.
Answers
Solution:
The equation is given below as
[tex]H=20+40T-16T^2[/tex]Step 1:
To determine the time when the height is at H=30, we will substitute the value of H=30 in the equation above and solve for T
[tex]\begin{gathered} H=20+40T-16T^{2} \\ 30=20+40T-16T^2 \\ collect\text{ similar terms, we will have} \\ 16T^2-40T+30-20=0 \\ 16T^2-40T+10=0 \end{gathered}[/tex]Using the quadratic formula below, we will find the value of T as
[tex]\begin{gathered} T=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=16,b=-40,c=10 \\ by\text{ substituting the values, we will have} \\ T=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ T=\frac{-(-40)\pm\sqrt{(-40)^2-4(16\times10)}}{2\times16} \\ T=\frac{40\pm\sqrt{1600-640}}{32} \\ T=\frac{40\pm\sqrt{960}}{32} \\ T=\frac{40\pm30.98}{32} \\ T=\frac{40+30.98}{32},T=\frac{40-30.98}{32} \\ T=2.2seconds,T=0.3seconds \end{gathered}[/tex]Graphically,
Hence,
The time at which the height of the helicopter will be H=30 is at
[tex]\Rightarrow T=2.2seconds,T=0.3seconds[/tex]Part B:
To figure out the time at which the height will be H=0, we will substitute the value of H=0 in the equation below and solve for T
[tex]\begin{gathered} H=20+40T-16T^2 \\ H=0 \\ 20+40T-16T^2=0 \\ 16T^2-40T-20=0 \end{gathered}[/tex]To figure out the value of T, we will use the formula below
[tex]\begin{gathered} 16T^{2}-40T-20=0 \\ T=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ T=\frac{-(-40)\pm\sqrt{(-40)^2-4(16\times-20)}}{2\times16} \\ T=\frac{40\pm\sqrt{1600+1280}}{32} \\ T=\frac{40\pm\sqrt{2880}}{32} \\ T=\frac{40\pm53.67}{32} \\ T=\frac{40+53.67}{32},T=\frac{40-53.67}{32} \\ T=\frac{93.67}{32},T=-\frac{13.67}{32} \\ T=2.9seonds,T=-0.4seconds \end{gathered}[/tex]Hence,
The time at which the remote control helicopter will hit the ground at H=0 will be
[tex]\Rightarrow T=2.9seconds[/tex]Given a four digit number XXXX, are there more permutations if repetition is allowed or not allowed? Explain your answer.
Answers
Answer:
There are more permutations when repetitions are allowed.
Explanation:
There are more permutations if repetition is allowed because in this case, we can include numbers like 1122, 4444, and 1321, which won't be included when repetitions are not allowed.
PLS HELP!! PThe tables show functions representing the growth of two types of bacteria on certain days within an experiment that lasted a total of 10 days. How do the functions in the table compare?Since x-intercepts indicate the amount of eachbacteria at the start of the experiment, there wasmore of bacteria B than bacteria A at the start.O Since y-intercepts indicate the amount of eachbacteria at the start of the experiment, there wasmore of bacteria B than bacteria A at the start.O Since the maximum value in the table for bacteria Ais greater than the maximum value in the table forbacteria B, bacteria A has a faster growth rate thanbacteria B.O Since the minimum value in the table for bacteria Ais less than the minimum value in the table forbacteria B, bacteria A has a slower growth rate thanbacteria B
Answers
Solution
The answer
Since y-intercepts indicate the amount of each
bacteria at the start of the experiment, there was
more of bacteria B than bacteria A at the start.
what is the probability of serving a student that is in math Spanish and chemistry round to the three decimal places
Answers
In this problem the total number of students are: 260 students
so the probablility is:
[tex]p=\frac{15}{260}=0.058[/tex]A person's weekly wage is worked out using the formula
Wage= Number of hours of overtime * £16 + Basic pay
a)
Find a person's Wage when the Number of hours of overtime is 9
and the Basic pay is £140.
b)
Find the Number of hours of overtime, when the Wage is £300
and the Basic pay is £124.
Answers
Answer:
a) £284
b)11
Step-by-step explanation:
To find the weekly wage you have to solve this equation where y=wage, x=number of hours overtime and z=basic pay:
y=x*£16+z
a) y=9*£16+£140 = £284
b) You need to invert the formula, letting on the left side of the equal only the x:
x=(y-z)/£16
so you have:
x=(£300-£124)/£16 = 11
What is the solution set to 8(2^(x – 3)) ≤ 20 – 4^x
Answers
The solution of 8(2^(x – 3)) ≤ 20 – 4^x is (-∞,6/5]
We need to find the solution set to 8(2^(x – 3)) ≤ 20 – 4^x
[tex]8(2^{x - 3})\leq 20 - 4^{x\\\\} \\8(2^{x - 3})\leq 16 + 4 - 4.4^{x-1\\\\} \\2(2^{x - 3})\leq 4 + 1 - 4^{x-1\\\\} \\2(2^{x - 3})\leq 4 + 1 - 4.4^{x-2\\\\} \\(2^{x - 3})\leq 2 + 1/2 - 2.4^{x-2\\\\} \\(2^{x - 3})\leq 2^1 + (2^{-1} ) - 2.2^{2(x-2)}\\ (2^{x - 3})\leq 2^1 + (2^{-1} ) - 2^{4x-4+1)}\\ x-3 \leq 1 - 1 -4x +3\\x-3 \leq -4x +3\\x+ 4x \leq 3+3\\5x \leq 6\\x\leq 6/5[/tex]
The solution set is (-∞,6/5]
Therefore, the solution of 8(2^(x – 3)) ≤ 20 – 4^x is (-∞,6/5]
To learn more about inequality refer here
https://brainly.com/question/24372553
#SPJ1
You buy 3.17 pounds of grapes, 1.45 pounds of pears, and 2.26 pounds of apples. What is you total bill
Answers
We buy:
• 3.17 pounds of grapes,
,• 1.45 pounds of pears,
,• 2.26 pounds of apples.
The total bill is just the sum of the money spent on each product:
Total bill = 3.17 pounds + 1.45 pounds + 2.26 pounds = 6.88 pounds.
Answer
The total bill is 6.88 pounds.
Given the function, fx=x+4 a).Write the transformed equation g(x), if g(x) = -f(x) + 2. b). Describe the transformation(s) that takes place. i. What does the -f(x) do to the function? ii. What does the +2 do to the function?
Answers
Since the given function is
[tex]f(x)=x+4[/tex]Since the function after transformation is
[tex]g(x)=-f(x)+2[/tex]Then we will find g(x) by substituting f(x) by (x + 4)
[tex]g(x)=-(x+4)+2[/tex]Simplify it
[tex]\begin{gathered} g(x)=-(x)+-(4)+2 \\ \\ g(x)=-x-4+2 \\ \\ g(x)=-x-2 \end{gathered}[/tex]a) The transformed equation is
[tex]g(x)=-x-2[/tex]b)
When we change the sign of f(x), that means we made a reflection on the x-axis
i. -f(x) means reflect f(x) about the x-axis
When we add f(x) by a number, then that means we translate the f(x) by a number
ii. +2 means translate the function 2 units up
I don't know if I got the correct answer for the behavior goes to the positive or negative?
Answers
Given the function:
[tex]f(x)=-x^5[/tex]by looking at the exponent of x, we can see that it is an odd exponent, then, the graph must look something like this:
but since we have a negative sign (-x^5) ,then, it looks like this:
now we can see that the following limits are true:
[tex]\begin{gathered} \lim _{x\rightarrow\infty}f(x)=-\infty \\ \lim _{x\rightarrow-\infty}f(x)=\infty \end{gathered}[/tex]Given the radius r of a sphere, calculate it's volume V using the formula V= 4 3 Calculate V when r = 7 feet and use T = 3.14. Round your answer to two decimal places
Answers
The volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]In this case we have r=7, then:
[tex]V=\frac{4}{3}(3.14)(7)^3=1436.03[/tex]Therefore the volume is 1436.03 cubic feet.
You roll a dye pick a marble and pick a card how many outcomes are possible
Answers
SOLUTION
The die has 6 faces, that is 6 outcomes
They are 2 marbles that is 2 outcomes
They are 2 cards, that is 2 outcomes
Number of possible outcomes become
[tex]6\times2\times2=24[/tex]Hence the answer is 24 possible outcomes
I need help with this problem, does anybody know how to do it?
Answers
Angle relationships, where we're given a diagram containing 2+ parallel lines and a transversal, can tell us a lot about the angles.
Solving the QuestionThe two angles indicated in the diagram measure 4x + 19 degrees and 6x + 7 degrees.
These two angles form a "Z" pattern, meaning they are on opposite sides of the transversal and opposite sides of the two parallel lines. They are alternate angles.
Alternate angles are always equal. Therefore, we can set up the following equation and solve for x:
[tex]4x + 19 = 6x + 7\\19 = 2x + 7\\12 = 2x\\x = 6[/tex]
Answerx = 6
The table shows conversions of common units of length.Unit of LengthCustomary System UnitsMetric System Units1 inch2.54 centimeters1 foot0.3048 meters1 mile1.61 kilometersAbout how many inches are equivalent to 3 meters? Round the number(s) needed in the table to the nearest tenth to find the approximate answer.10 inches75 inches100 inches120 inches
Answers
2.54 cm = 1 inches
1 cm =
cross multiply
[tex]undefined[/tex]60 scholars are dancing at the Snow Ball of the scholars 1/12 are doing the Woah, 2/3 Sare Flossing, 4/30 are Dabbing, and the rest the scholars are doing the Orange Justice. How many scholars are doing the Orange Justice?
Answers
Given:
Total number of scholars = 60
Fraction of scholars doing Woah = 1/12
Fraction of scholars doing flossing = 2/3
Fraction of scholars dabbing = 4/30
The rest of the scholars are doing the Orange Justice.
To find the number of scholars doing Orange Justice, let's first find the number doing Woah, Sare Flossing and dabbing.
[tex]\text{Number of scholars doing Woah = }\frac{1}{12}\ast60=5[/tex][tex]\text{Number of scholars doing Sare Flossing }=\text{ }\frac{2}{3}\ast60=40[/tex][tex]\text{Number of scholars dabbing = }\frac{4}{30}\ast60=8[/tex]Number doing Orange Justice = Total - Woah - Sare Flossing - Dabbing =
60 - 5 - 40 - 8 = 7
Therefore, 7 scholars are doing the Orange Justice.
ANSWER:
7
Its number 7 and its pretty easy can someone help kinda lost
Answers
Answer:
7.8 cm
Step-by-step explanation:
Tan ( 1R) = opposite leg / adjacent leg = QR / 5
5 tan (1R) = QR = 7.787 cm =~ 7.8 cm
(Remember : there are 2pi R = 360 degrees
so 1R = 360 / (2pi) degrees
tan ( 360/2pi) = tan 57.296 ° = 1.5574 )
You roll six-sided dice. What is the probability of rolling a 6 on both dice??
Answers
Given
You roll six-sided dice. What is the probability of rolling a 6 on both dice??
Solution
The sample space
The probability of obtaining 6 twice occurs just once in the sample space which is 36.
The probability is thus;
[tex]\frac{1}{36}=\frac{1}{6}\times\frac{1}{6}[/tex]Thus, the answer is ;
[tex]\frac{1}{36}[/tex]Jim earns money doing yard work each week. During three weeks he earned a total of $168. If each week, his earnings doubled, how much did he make each week
Answers
He made $112 each week
Explanations:The total amount earned in three weeks before his weekly earning was doubled = $168
The amount earned each week before his weekly earning was doubles = $168/3
The amount earned each week before his weekly earning was doubled = $56
If his weekly earning was doubled:
The amount earned each week = 2 x $56
The amount earned each week = $112
Finding the surface area of a prism #5 and #6
Answers
Answer:
Area = 640 sq. meters
Explanation:
5.
We are given the figure of a prism and we are to obtain its surface area
The prism has 5 faces: 2 triangular shaped faces of equal dimensions, 3 rectangular faces of different dimensions (2 out of these 3 have the same dimension while the third has a different dimension)
For the triangular-shaped face(s), its/their dimension is:
Height = 12 inches
Base = 5 inches
For the rectangular-shaped faces, their dimensions are:
Rectangle 1 & 2: Length = 20 inches, Width = 12 inches
Rectangle 3: Length = 20 inches, Width = 5 inches
The surface area of the prism is obtained by the sum of all the areas of the 5 faces itemized above. This is shown below:
[tex]\begin{gathered} Area_{prism}=Area_{triangle,1}+Area_{triangle,2}+Area_{rectangle,1}+Area_{rectangle,2}+Area_{rectangle,3} \\ Area_{triangle}=\frac{1}{2}\times base\times height \\ Area_{triangle,1}=\frac{1}{2}\times5\times12=30m^2 \\ Area_{triangle,2}=\frac{1}{2}\times5\times12=30m^2 \\ \\ Area_{rectangle}=length\times width \\ Area_{rectangle,1}=20\times12=240m^2 \\ Area_{rectangle,2}=20\times12=240m^2 \\ Area_{rectangle,3}=20\times5=100m^2 \end{gathered}[/tex]The area of the prism is obtained thus:
[tex]\begin{gathered} Area_{prism}=30+30+240+240+100 \\ Area_{prism}=640m^2 \\ \\ \therefore Area_{prism}=640m^2 \end{gathered}[/tex]Therefore, the area of the prism is 640 square meters
Kellogg increases the length of their rectangular Pop-Tarts by 10% and decreases thewidth by 10%. By what percent willthe area of their Pop-Tarts change?ANo changeB1% decreaseс21% increaseD19% decrease
Answers
Let the initial length and width Kellogg's rectangular Pop-Tarts be represented as l and b
The area of the initial rectangular Pop-Tarts will be
[tex]\begin{gathered} A_{rec\tan gle}=length\text{ }\times width \\ A_{i\text{nitial}}=l\times b \end{gathered}[/tex]If the new length is increased 10% of the initial length, then the new length L will be
[tex]undefined[/tex]? - √3 - ? what is the 2 numbers between 3
Answers
The number √3 has a result less than 2 and greater than 1. We know this because the square of 2 is 4, that is √4 = 2 and √2 is less than 2 itself.
Hence, the number √3 lies between √2 and √4.
More precisely, it lies between 1 and 2 (the result of √3 is 1.732)
√
For the function y = 2x^2(a) Find the average rate of change of y with respect to r over the interval [1,4](b) Find the instantaneous rate of change of y with respect to a at the value x = 1.Average Rate of Change= ___Instantaneous Rate of Change at x = 1: _____
Answers
Given the function
[tex]y=2x^2[/tex]The formula to find the average rate of change of y with respect to x in [a,b]
[tex]\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{f(b)-f(a)}{b-a}[/tex]Here, a = 1 and b = 4.
[tex]\begin{gathered} \text{Average rate of change =}\frac{f(4)-f(1)}{4-1} \\ =\frac{2\cdot4^2-2\cdot1^2}{3} \\ =\frac{30}{3} \\ =10 \end{gathered}[/tex]The instantaneous rate of change is the slope of the tangent line at x = 1.
[tex]\begin{gathered} \text{Slope}=\frac{d}{dx}(2x^2) \\ =2\cdot2x \\ =4x \end{gathered}[/tex]Slope at x = 1 is
[tex]4\cdot1=4[/tex]So, the instantaneous rate of change is 4.
What is an expression for the product of -3x-2y
Answers
6y
Recall that - * - = +
Hence -3 * -2y = 6y
The volume of a cylinder is 448 pi cm³ and the height is 7 cm.Find its radius.
Answers
The formula for the volume of a cylinder is given by:
[tex]V=\pi r^2h[/tex]Where r is the base radius and h is the height.
If the volume is 448*pi cm³ and the height is 7 cm, we have:
[tex]\begin{gathered} 448\pi=\pi r^2\cdot7\\ \\ 448=7r^2\\ \\ r^2=\frac{448}{7}\\ \\ r^2=64\\ \\ r=8\text{ cm} \end{gathered}[/tex]Therefore the radius is equal to 8 cm.
Drawing this cylinder, we have: