Day 1 Weight of Baby Panda = 100 grams
Day 52 (after 51 days) Weight of Baby Panda = 2.17 kg
To determine the weight increase of our baby panda, we have to convert first the units from kg to grams.
[tex]1kg=1000grams[/tex]Please know that 1kg = 1000 grams. Therefore, 2.17 kg is equal to:
[tex]2.17kg\times1000grams=2170grams[/tex]So now, the weight of our baby panda after 51 days is 2170 grams. To determine weight increase, we will subtract 100 grams from 2170 grams.
[tex]2,170grams-100grams=2,070grams[/tex]Therefore, the panda cub gained 2,070 grams after 51 days or 2.07kg.
If you pay Php 38,500.00 at the end of 3 years and 3 months to settle an obligation of Php 35,800. What simple interest rate was used?
Mr. Jones owned his car for 12 years. The car has 169,344 miles recordedon the odometer. What is the average number of miles driven per year?
total distance travelled by the car is 169344 miles, for 12 years,
the distance travelled in 1 year is
[tex]=\frac{169344}{12}=14112[/tex]so the average number of miles der
function "p" is in the form y = ax² + c if the values of "a" and "c" are both less than 0, which graph could represent "p" ?A) graph AB) graph BC) graph CD) graph D
INFORMATION:
We know that:
- function "p" is in the form y = ax² + c
- the values of "a" and "c" are both less than 0
And we must select the graph that can represent p.
STEP BY STEP EXPLANATION:
To select the correct option we must know that:
- the form y = ax² + c is the form of a parabola
- the sign of "a" determines whether the parabola opens up or down
- "c" will move the function c units up or down about the origin.
Now, since "a" and "c" are both less than 0 we can conclude that:
- the parabola opens down because "a" is negative (less than 0)
- the parabola will be c units down about the origin because "c" is negative
Finally, we can see that the option which met the conditions is graph B.
ANSWER:
B) graph B
Find and graph the intercepts of the following linear equation:5x-2y=-10
x-intercept = -2
y-intercept = 5
Explanation:[tex]\begin{gathered} Given: \\ 5x\text{ - 2y = -10} \end{gathered}[/tex]x-intercept is the value of x when y = 0
To get the x-intercept, we will substitute y with zero:
[tex]\begin{gathered} 5x\text{ - 2\lparen0\rparen = -10} \\ 5x\text{ = -10} \\ divide\text{ both sides by 5:} \\ x\text{ = -10/5} \\ \text{x = -2} \\ So,\text{ the x-intercept = -2} \end{gathered}[/tex]y-intercept is the value of y when x = 0
To get the y-intercept, we will substitute x with zero:
[tex]\begin{gathered} 5(0)\text{ - 2y = -10} \\ -2y\text{ = -10} \\ divide\text{ both sides by -2:} \\ \frac{-2y}{-2}\text{ = }\frac{-10}{-2} \\ division\text{ of same signs give positive sign} \\ y\text{ = 5} \\ So,\text{ the y-intercept = 5} \end{gathered}[/tex]Plotting the graph:
(6-5g)(-3g+9)Multiply polynominals
The two polynomials are multiplied as follows:
[tex](6-5g)(-3g+9)[/tex]Open the first bracket as follows:
[tex](6-5g)(-3g+9)=6(-3g+9)-5g(-3g+9)[/tex]Open the two brackets as follows:
[tex]\begin{gathered} 6(-3g+9)-5g(-3g+9)=-18g+54+15g^2-45g \\ =15g^2-63g+54 \end{gathered}[/tex]Hence the multiplication of the polynomials results in:
[tex](6-5g)(-3g+9)=15g^2-63g+54[/tex]I dont understand how the answer is 1/3. how do you calculate that answer????
1/3
Explanation:To convert repeating decimals to fraction, we need to represent it with a variable
let n = 0.3333...
Multiply the above by 100:
100n = 33.3333...
The 3 dots after the 3333 means the numbers continues; hence indicating a repeating decimal
n = 0.3333 ...equation 1
100n = 33.3333 ...equation 2
subtract equation 1 from 2:
100n - n = 33.3333 - 0.3333
100n - n = 99n
99n = 33
divide both sides by 99:
99n/99 = 33/99
n = 1/3
Therefore, 0.3 repeating decimal in fraction is 1/3
find a point slope equation for a line containing the given point and having the given slope y-y1 = m (x-x1 )7. (7, 0), m = 48. (0,9), m = -2
We have the following:
7. (7.0), m = 4
replacing:
[tex]\begin{gathered} y-0=4\cdot(x-7) \\ y=4x-28 \end{gathered}[/tex]8. (0,9), m = -2
[tex]\begin{gathered} y-9=-2\cdot(x-0) \\ y=-2x+9 \end{gathered}[/tex]Angel X is 2n +12°, and angle why is 3n+18° find the measure of angle X
When two angles together form a straight line, they form a 180º angle.
They are called supplementary angles.
x and y are supplementary (they together form a straight line).
This is
x + y = 180
Equation for nSince x = (2n +12)º. Instead of x we are going to write 2n + 12.
And y = (3n + 18)º. Then we are going to write 3n + 18 instead of y.
This is
x + y = 180
↓
(2n + 12) + (3n + 18) = 180
2n + 12 + 3n + 18 = 180
Now we have an equation taht we can use to find n.
2n + 12 + 3n + 18 = 180
Solving the equationWe have the equation and we are going to simplify it:
2n + 12 + 3n + 18 = 180
↓ since 2n + 3n = 5n
5n + 12 +18 = 180
↓ since 12 + 18 = 30
5n + 30 = 180
Now, we can solve it:
5n + 30 = 180
↓ taking 30 to the right side (substracting 30 both sides)
5n + 30 - 30 = 180 - 30
↓ since 30 - 30 = 0
5n + 0 = 180 - 30
5n = 180 - 30 = 150
5n = 150
↓ taking 5 to the right side (dividing by 5 both sides)
5n = 150
5n/5 = 150/5
↓ since 5n/5 = n
n = 150/5 = 30
n = 30
Then, we have n = 30
Finding xSince
x = 2ºn + 12º
then, replacing n = 30
x = 2º · 30 + 12º
x = 60º + 12º
x = 72º
Answer: C. 72ºGiven the line segment with points P (1,6) andQ (9,-4). What is the length of PQ?(2 Points)
When 2 coordinate points are given, we can find its length by using the distance formula. Which is
[tex]\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]We
• take differences in y coordinates and x coordinates
,• square them
,• take their sum
,• take square root of the answer
Tha's all.
So, let's do the steps:
y diff: -4 -6 = -10
x diff: 9-1 = 8
Now, it becomes:
[tex]\begin{gathered} \sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2} \\ =\sqrt[]{(-10)^2+(8)^2} \\ =\sqrt[]{164} \\ =2\sqrt[]{41} \end{gathered}[/tex]The length of PQ (exact) is:
[tex]2\sqrt[]{41}[/tex]In decimal: 12.81
A curve has equation x3 - 5x2 + 7x - 2dyDifferentiate the function to obtaindxa) Find the x coordinates of the points where = 0 and hence the coordinates of thed.xturning points on the curve.dyb) With the aid of a table consider the sign of on either side of the turning points,dxdetermine whether the turning points are maximum or minimum points.c) Sketch the curve showing the turning points clearly and label any other points ofinterest.
SOLUTION
Write our the function given
To differentiate the function, we apply the differentiation rule
[tex]y=x^n,\frac{dy}{dx}=nx^{n-1}[/tex]Hence
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{Then} \\ \frac{d}{dx}\mleft(x^3-5x^2+7x-2\mright) \end{gathered}[/tex]Then Apply the sum and difference rule for derivative, we have
[tex]\begin{gathered} =\frac{d}{dx}\mleft(x^3\mright)-\frac{d}{dx}\mleft(5x^2\mright)+\frac{d}{dx}\mleft(7x\mright)-\frac{d}{dx}\mleft(2\mright) \\ =3x^2-10x+7-0 \\ =3x^2-10x+7 \end{gathered}[/tex]For dy/dx =0,we have
[tex]3x^2-10x+7=0[/tex]solve quadratic equation, we have
[tex]\begin{gathered} 3x^2-3x-7x+7=0 \\ 3x(x-1)-7(x-1)=0 \\ (3x-7)(x-1)=0 \end{gathered}[/tex]Equation each factor the zero, we have
[tex]\begin{gathered} 3x-7=0,x-1=0 \\ 3x=7,x=1 \\ x=\frac{7}{3},1 \end{gathered}[/tex]Hence
The x coordinates are
x= 7/3 and x=1
To obtain the coordinate of the turning point, we substitute into the equation given
[tex]\begin{gathered} y=x^3-5x^2+7x-2 \\ \text{for x=7/3} \\ y=(\frac{7}{3})^3-5(\frac{7}{3})^2+7(\frac{7}{3})-2 \end{gathered}[/tex]Then by simplification, we have
[tex]y=-\frac{5}{27}[/tex]Then, one of the turning point is
[tex](\frac{7}{3},-\frac{5}{27})[/tex]Then, we substitute the other value of x,
[tex]\begin{gathered} \text{for x=1} \\ y=x^3-5x^2+7x-2 \\ y=(1)^3-5(1)^2+7(1)-2 \\ y=1-5+7-2 \\ y=1 \\ \text{turning point =(1,1)} \end{gathered}[/tex]Therefore the other turning point is (1,1)
The turning point are (7/3, -5/27) and (1,1)
B(q-L)--------- =3. its all divided by h but I don't. hunderstand how to solve for q
Given the equation below,
[tex]\frac{B(q-L)}{h}=r[/tex]Solving for q, by making q the subject of formula from the above equation
Multiply both sides by h
[tex]\begin{gathered} h\times\frac{B(q-L)}{h}=r\times h \\ B(q-L)=rh \end{gathered}[/tex]Divide both sides by B
[tex]\begin{gathered} \frac{B(q-L)}{B}=\frac{rh}{B} \\ (q-L)=\frac{rh}{B} \end{gathered}[/tex]Add L to both sides
[tex]\begin{gathered} q-L+L=\frac{rh}{B}+L \\ q=\frac{rh}{B}+L \end{gathered}[/tex]Hence, the answer is
[tex]q=\frac{rh}{B}+L[/tex]Solve the following quadratic function by factoring f(x) = x2 – X – 12 Enter the number that belongs in the green box. x = 4; x = [?] Enter
The given function is
[tex]f(x)=x^2-x-12[/tex]To solve it by factoring, we have to look for two numbers whose product is 12 and whose difference is 1. Those numbers are 4 and 3.
[tex]f(x)=(x-4)(x+3)=0[/tex]Then, we use the zero property
[tex]\begin{gathered} x-4=0\rightarrow x=4 \\ x+3=\rightarrow x=-3 \end{gathered}[/tex]Hence, the answer is -3.Select the correct answer.Which expression is equivalent to this quotient?+++55 + 15OA.1 + 35(1 + 5)2I + 31 + 5ОВ.O C.1 + 3ODI + 5ResetNext2022 Edmentum. All rights reserved.
Given
[tex]\frac{\frac{1}{x+5}}{\frac{x+3}{5x+15}}[/tex]Answer
[tex]\begin{gathered} \frac{\frac{1}{x+5}}{\frac{x+3}{5x+15}} \\ =\frac{1}{x+5}\times\frac{5(x+5)}{x+3} \\ \frac{5}{x+3} \end{gathered}[/tex]Tyra works as a hostess. She earns $6.75 per hour and works 35 hours a week. She also earns an average of $200 per week in tips. How much will Tyra earn in a year? A. $436 B. $5,235 C. $22,685 D. $27,300
Answer:
C. $22,685
Step-by-step explanation:
(35x6.75+200)x52(weeks in a year)=$22,685
Which shows how to use similar right triangles to find the equation of the line through (0,6) and any point (x,y), on the line?
By the given triangles in the figure, you can notice that the following proportion must be equal, because the involved sides are congruent:
[tex]\frac{y-b}{x-0}=\frac{m+b-b}{1-0}[/tex]In the left side, side of triangle with length y - b, divided by side with length x, must be equal to the quotient between side with length m + b - b and side with length 1.
Solve the previous equation for y, just as follow:
[tex]\begin{gathered} \frac{y-b}{x}=m \\ y-b=mx \\ y=mx+b \end{gathered}[/tex]Find the area of a triangle ABC when c = 15 m, a = 20 meters, and b = 10 meters.
Recall Heron's Formula to find the area of a triangle with sides a, b and c.
We define a new quantity s given by:
[tex]s=\frac{a+b+c}{2}[/tex]Then, the area of the triangle is given by the formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]For a=20, b=10 and c=15 we have:
[tex]s=\frac{20+10+15}{2}=22.5[/tex]Then, the area of the triangle is:
[tex]\begin{gathered} A=\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)} \\ =\sqrt{22.5(2.5)(12.5)(7.5)} \\ =\frac{75\sqrt{15}}{4} \\ =72.61843774... \\ \approx72.6 \end{gathered}[/tex]Therefore, the exact answer is:
[tex]A=\frac{75\sqrt{15}}{4}[/tex]And the approximate area of the triangle ABC when c=15m, a=20m and b=10m is 72.6 m^2.
Anna is 10 years older than Brad. The sum of their ages is 26. The system of equations representing their ages is _ Solve the system using inverses. Then select the correct calculation and the ages of Anna and Brad.
Answer:
The correct answer is option B.
[tex]undefined[/tex]the table below gives the side lengths and surface areas of different cubes.
Given
Relationship between sides and surface areas
Find
Conclusion from the table
Explanation
From the table we can see that sides double in 1st, 2nd and 4th case
So comparing them
When side =1 then Surface area = 6 cm sq
When side = 2 then Surface area = 24 cm sq
Here we can see that when the side doubles, the surface area quadruples
Similar result is obtained when in relation of side = 2 and side 4
Final Answer
When the side doubles, the surface area quadruples
option (a) is correct
Solve the inequalities. State whether the inequalities have no solutions or real solutions.4( 3 - 2x) > 2( 6 - 4x)
Given an inequalities show if it have no solutions or real solutions:
[tex]4(3-2x)>2(6-4x)[/tex]Step 1: Expand the inequalities
[tex]\begin{gathered} 4(3-2x)>2(6-4x) \\ 12-8x>12-8x \end{gathered}[/tex]Step 2: Subtract 12 from both side of the inequalities
[tex]\begin{gathered} 12-8x>12-8x \\ \text{subtract 12 from both side} \\ 12-8x-12>12-8x-12 \\ -8x>-8x \end{gathered}[/tex]Step 3: Add 8x to both side of the inequalities
[tex]\begin{gathered} -8x>-8x \\ \text{add 8x to both side} \\ -8x+8x>-8x+8x \\ 0>0 \end{gathered}[/tex]Therefore the solution for the above inequalities is No solution
Line segments, AB, BC, CD, DA create the quadrilateral graphed on the coordinate grid above. The equations for two of the four line segments are given below. Use the equations of the line segments to answer the questions that follow. AB: y = -x + 1 1
Given the equations of the side length as shown;
AB y = 1/3 x + 1
CD = y = -3x+11
Before we determine whether they are parallel or perpendicular, we must first know that;
Two parallel lines have the same slope i.e Mab = Mcd
For two lines to be perpendicular then the product of the slopes must give -1 i.e MabMcd = -1
Comapring both equations with the general equation of a line y = mx+c;
For line AB: y = 1/3 x + 1
Mab = 1/3
For line CD: y = -3x+11
Mcd = -3
Taking the product of the slope;
MabMcd = 1/3 * -3
MabMcd = -1
Is AB perpendicular or parallel to CD? Since the product of their slope gives -1, hence the lines AB and CD are PERPENDICULAR to each other.
(word sentence) Pooky eats three cans of cat food each day. How long will 27 cans of food last?
ANSWER:
9 days
Solution:
[tex]\frac{27\text{ cans}}{3\text{ cans per day}}\text{ = 9 days}[/tex]Answer: The 27 cans of food will last 9 days since 27 ÷ 3 = 9.
Step-by-step explanation:
A cyclist rides her bike at a speed of 15 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 5 hours? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers. Speed: Distance traveled in 5 hours:
Given: The cyclist rides her bike at a speed of 15 miles per hour
To Determine: The speed in kilometers per hour and the kilometers cycles in 5 hours
Solution
Please note that 1 miles equal to 1.6kilometers. Let us convert 15miles to kilometers as shown below
[tex]\begin{gathered} 1miles=1.6kilometers \\ 15miles=15\times1.6kilometers \\ 15miles=24kilometers \end{gathered}[/tex]Therefore the speed of 15miles per hour is equivalent to 24kilometers per hour
The kilometers travelled in 5 hours would be
[tex]\begin{gathered} distance=speed\times time \\ speed=24kilometers-per-hour \\ time=5hours \\ distance=24\times5 \\ distance=120kilometers \end{gathered}[/tex]Hence, the speed in kilometers per hour is 24 kilometers per hour,
And the kilometers travelled in 5 hours is 120 kilometers
2. Mason was able to sell 35% of his vegetables before noon. If Mason had 200 kg of vegetables in the morning, how many kilograms of vegetables did he NOT sell?
130kg
1) Since Mason was able to do 35% He wasn't able to make 65%
2) Then we can write it :
65% x 200 Rewriting it in decimal form
0.65 x 200
130
3) So Mason could not sell 130kg of his crop.
What is 5x100? Pls tell me
We want to calculate;
[tex]5\times100=500[/tex]Thus the answer is 500.
How do I do I calculate the curve of best fit with the following data points given?
To determine the curve of best fit, let's look at the x-intercepts of the curve.
Based on the graph, the x-intercepts are at x = -7 and x = -1.
Since -7 and -1 are the x-intercepts, we can say that the factors of this curve are:
[tex](x+7)(x+1)[/tex]Now, we can also see that the graph is opening downward, therefore, the leading coefficient of the equation of this graph must be negative. For this, we will multiply the factors above by -1.
[tex]-(x+7)(x+1)[/tex]All we have to do now is multiply the factors above in order to get the curve of best fit.
[tex]-(x^2+x+7x+7)[/tex]Combine similar terms like x and 7x.
[tex]-(x^2+8x+7)[/tex]Then, distribute the negative sign.
[tex]-x^2-8x-7[/tex]Therefore, the curve of best fit is y = -x² - 8x - 7.
Determine the end behavior for each function below. Place the letter(s) of the appropriatestatement(s) on the line provided. A. As x approaches ∞o, y approaches ∞oB. As x approaches -œo, y approaches œC. As x approaches ∞o, y approaches -∞0D. As x approaches -c0, y approaches -00
Solution:
From the given graphs,
The first graph is the absolute function graph.
Which can be expressed in the form
[tex]y=-|x|[/tex]Since the leading coefficient is negative,
The end behavior of the graph is
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow-\infty[/tex]Hence, the answers are C and D
The second graph is a quadratic graph of the form
[tex]y=x^2[/tex]Since the leading coefficient is positive
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are A and B
The third graph is a cubic function that can be expressed in the form
[tex]y=-x^3[/tex]The leading coefficient is negative.
The end behavior will be
[tex]As\text{ x}\rightarrow\infty,y\rightarrow-\infty\text{ and as x}\rightarrow-\infty,y\rightarrow\infty[/tex]Hence, the answers are C and B
Find the equation of the circle having the given properties:
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]3.
Using the points (4, 0), (0, 2) and (0, 0), we have:
[tex]\begin{gathered} (0,0)\colon \\ h^2+k^2=r^2 \\ (0,2)\colon \\ h^2+(2-k)^2=r^2 \\ h^2+4-2k+k^2=r^2 \\ \text{Comparing both equations:} \\ h^2+k^2=h^2+4-2k+k^2 \\ 4-2k=0 \\ k=2 \\ (4,0)\colon \\ (4-h)^2+k^2=r^2 \\ 16-8h+h^2+4=r^2 \\ \text{Comparing this last equation with the first one:} \\ 16-8h+h^2+4=h^2+4 \\ 16-8h=0 \\ h=2 \\ \\ h^2+k^2=r^2 \\ r^2=4+4=8 \end{gathered}[/tex]So the equation of this circle is:
[tex](x-2)^2+(y-2)^2=8[/tex]Robbie ran 21 miles less than O'neill lastweek. Robbie ran 17 miles. How manymiles did O'neill run?
We need to find the distance, in miles, that O'Neill ran.
We know that Robbie ran 21 miles less than O'Neill. This is the same as saying that O'Neill ran 21 miles more than Robbie.
Also, we know that Robbie ran 17 miles.
Then, to find the distance O'Neill ran, we need to add 21 miles to the 17 miles Robbie ran.
We obtain:
[tex]17\text{miles}+21\text{miles}=38\text{miles}[/tex]A dilation with a scale factor of 2 maps ....
The measure of the angles is the same. After a dilation what changes is the length of the sides, but the angles are the same of
[tex]\measuredangle B\text{ = }\measuredangle E[/tex]The second choice is correct.
Help ! its not a test i just don't understand!!
An important rule before subtracting fractions, you must first make them have a common denominator. The common denominator is the LCM (Least Common Multiple) of the two different denominators.
You may use this formula:
[tex]\frac{a}{b}=\frac{(a)(\frac{c}{b})}{c}[/tex]We get,
a.) 9/12 - 1/2 ; The LCM of 12 and 2 is 12.
[tex]\frac{9}{12}-\frac{1}{2}=\text{ }\frac{9}{12}-\frac{(1)(\frac{12}{2})}{12}=\text{ }\frac{9}{12}-\frac{(1)(6)}{12}=\frac{9}{12}-\frac{6}{12}[/tex][tex]\frac{9}{12}-\frac{6}{12}=\frac{3}{12}[/tex]Therefore, the difference of 9/12 - 1/2 is 3/12. You shade letter B.