You have to multiply the numbers:
9x6 =54
Multiply is the same as adding the number 6 times
9+9+9+9+9+9 =54
How many solutions will each equation have?x^2+6x+5
To solve the quadratic equation, factor the expression and then clear x from each of the factors obtained.
[tex]\begin{gathered} x^2+6x+5=0 \\ (x+5)(x+1)=0 \\ x+5=0 \\ x=-5 \\ x+1=0 \\ x=-1 \end{gathered}[/tex]This equation has 2 solutions which are -5 and -1.
If X persons are admitted in a hospital during the last five years and Y persons
are recovered out of them during this period then find the average number of
persons admitted in one year.
The average number of persons admitted in one year is X/5.
What is average number?
Average By adding a collection of numbers, dividing by their count, and then summing the results, the arithmetic mean is determined.
If X persons are admitted in last 5 years in a hospital.
Then we get the average value of admitted persons are X/5 per year.
If Y persons are recovered in last 5 years in a hospital.
Then we get the average value of recovered persons are Y/5 per year.
Therefore, the average number of persons admitted in one year is X/5.
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Kuta Software - Infinite Precalculus Angles and Angle Measure Find the measure of each angle.
Explanation:
We are to draw the angle that is equivalent to 5pi/4
First we need to convert the radian value to degree
Since pi rad = 180degrees
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x = 5/4 * 180
x = 5 * 45
x = 225 degrees
This can also be written as 225 = 180 + 45
225degrees = 180 + pi/4
Note that 180degrees is an angle on a straight line. Find the digaram attached
The remaining angle which is pi/4 is the reason for the angle extensionon for the angle extension
5pi/4 = x
Cross multiply
pi * x = 5pi/4 * 180
x =
6 Equations of parallel and perpendicular lines VEB
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Answer:
y = 4/9x +10/3
Step-by-step explanation:
You want the slope-intercept equation of the line through point (-3, 2) that is perpendicular to the line y = -9/4x +1.
Slope-intercept equationThe slope-intercept form of the equation for a line is ...
y = mx + b . . . . . . m is the slope, b is the y-intercept
In order to write the desired equation, we need to know the desired slope and the y-intercept that makes the line go through the given point.
SlopeThe slope of the perpendicular line is the opposite reciprocal of the slope of the given line. The given line equation is in slope-intercept form, so the coefficient of x is the slope of it: -9/4.
The slope of the perpendicular line is the opposite reciprocal of this:
m = -1/(-9/4) = 4/9
Y-interceptSolving the slope-intercept form equation for b, we find ...
b = y - mx
Using the values of x and y for the given point, and the slope we just found, we have ...
b = 2 -(4/9)(-3) = 2 +4/3 = 10/3
Desired equationThe slope-intercept equation for a line with slope 4/9 and y-intercept 2/3 is ...
y = 4/9x +10/3
__
Additional comment
It can also be useful to start from the point-slope equation:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
Your line is ...
y -2 = 4/9(x +3) . . . . . . use m=opposite reciprocal of -9/4; (h, k) = (-3, 2)
y = 4/9x +(4/9)(3) +2 = 4/9x +10/3 . . . . . . add 2 and simplify
May I please get help with this. For I have tried many times but still could not get the rotation correct
Let us write out the coordinates of the parent image given
Let us name the triangle ABC
[tex]\begin{gathered} A\rightarrow(1,5) \\ B\rightarrow(-3,2) \\ C\rightarrow(-5,4) \end{gathered}[/tex]Therefore, the rule for the rotation 90 degrees counterclockwise about the origin is,
[tex]A(x,y)\rightarrow A^{\prime}(-y,x)[/tex]Let us now obtain the coordinates of the transformed image
[tex]\begin{gathered} A(1,5)\rightarrow A^{\prime}(-5,1) \\ B(-3,2)\rightarrow B^{\prime}(-2,-3) \\ C(-5,4)\rightarrow C^{\prime}(-4,-5) \end{gathered}[/tex]Hence, the coordinates of the transformed image are
[tex]\begin{gathered} A^{\prime}(-5,1) \\ B^{\prime}(-2,-3) \\ C^{\prime}(-4,-5) \end{gathered}[/tex]Let us now plot the transformed image
SOMEONE please help.
The class interval of the median is 1 ≤ x ≤ 2 and the mean of the distribution is 1.8
How to determine the class interval of the median class?From the question, we have
Number of students = 30
This represents the total frequency
So, we have
Total frequency = 30
The median position is then calculated as
Median = (Total frequency + 1)/2
Substitute the known values in the above equation
So, we have
Median = (30 + 1)/2
Evaluate
Median = 15.5th
The 15.5th element is located in the second class
i.e. the class with the interval 1 ≤ x ≤ 2
So, the class interval in this case is 1 ≤ x ≤ 2
The mean of the distributionTo do this, we start by calculating the average of the class interval
This is represented as
0 ≤ x ≤ 1 ⇒ 0.5
1 ≤ x ≤ 2 ⇒ 1.5
2 ≤ x ≤ 3 ⇒ 2.5
3 ≤ x ≤ 4 ⇒ 3.5
So, we have
x f
0.5 6
1.5 13
2.5 7
3.5 4
The mean is calculated as
Mean = ∑fx/∑f
So, we have
Mean = (0.5 * 6 + 1.5 * 13 + 2.5 * 7 + 3.5 * 4)/30
Evaluate
Mean = 1.8
Hence, the mean value is 1.8
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What are the rotations that will carry this equilateral triangle onto itself?A. 90° counterclockwise rotation about its center PB. 270° counterclockwise rotation about its center PC. 120° counterclockwise rotation about its center PD. 240° clockwise rotation about its center PE. 225 clockwise rotation about its center PF. 200 counterclockwise rotation about its center Prights reserved
Given -
Equilateral Triangle
To Find -
The number of rotations that will carry this equilateral triangle onto itself =?
Step-by-Step Explanation -
We know that in an equilateral triangle each question is of 60°
So,
Since it is a three-sided symmetry So, a rotation of 120° will carry this equilateral triangle onto itself.
Final Answer:
C. 120° counterclockwise rotation about its center P
is H less than 9?[tex]h \leqslant 9[/tex]
3) The given inequality is
[tex]h\text{ }\leq\text{ 9}[/tex]The inequality symbol is that of less than. Since it has an equal to sign attached, then, the meaning is h is less than or equal to 9. In words, h is at most 9, no more than 9.
Nguyen deposited $35 in a bank account earning 14% interest, compounded annually. How much interest will he earn in 72 months?
Given:
a.) Nguyen deposited $35 in a bank account.
b.) It earns 14% interest.
To be able to determine how much interest will he earn in 72 months, the following formula will be used for Compound Interest:
[tex]\text{ Interest Earned = P(1 + }\frac{\frac{r}{100}}{n})^{nt}\text{ - P}[/tex]Where,
P = Principal amount
r = Interest rate
n = No. of times the interest is compounded = annually = 1
t = Time in years = 72 months = 72/12 = 6 Years
We get,
[tex]\text{ Intereset Earned = (35)(1 + }\frac{\frac{14}{100}}{1})^{(1)(6)}\text{ - 35}[/tex][tex]\text{ = (35)(1 + }0.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}1.14)^6\text{ - 35}[/tex][tex]\text{ = (35)(}2.19497262394)^{}\text{ - 35}[/tex][tex]\text{ = 76.82404183776 - 35}[/tex][tex]\text{ = 41.82404183776 }\approx\text{ 41.82}[/tex][tex]\text{ Interest Earned = \$41.82}[/tex]Therefore, the interest he will be earning is $41.82
2-x+ 3-X-4
where a and b are integers.
Work out the value of a and the value of b.
can be written as a single fraction in the form
ax+b
x²-16
Answer:
2-×+3-×-4=0
Step-by-step explanation:
×=1\2
0.5,2`1
Please show me how to solve this step by step im really confused
Given
[tex]-16t^2+v_0t+h_0[/tex]initial velocity = 60 feet per second
initial height = 95 feet
Find
Maximum height attained by the ball
Explanation
we have given
[tex]\begin{gathered} h(t)=-16t^2+60t+95 \\ h^{\prime}(t)=-32t+60 \end{gathered}[/tex]put h'(t) = 0
[tex]\begin{gathered} -32t+60=0 \\ -32t=-60 \\ t=\frac{60}{32}=1.875sec \end{gathered}[/tex]to find the maximum height find the value of h(1.875)
[tex]\begin{gathered} h(1.875)=-16(1.875)^2+60(1.875)+95 \\ h(1.875)=-56.25+112.5+95 \\ h(1.875)=-56.25+207.5 \\ h(1.875)=151.25 \end{gathered}[/tex]Final Answer
Therefore , the maximum height attained by the ball is 151.25 feet
Identify the type(s) of symmetry for the graph below.Select all that apply. aSymmetry with respect to the line \small \theta=\frac{\pi}{2} bSymmetry with respect to the polar axis cSymmetry with respect to the pole
The line θ=π/2 is the vertical line in the polar grid, the polar axis is the horizontal line and the pole is the center of coordinates. Now let's analyze the symmetries:
If the grpah is symmetric with respect to θ=π/2 then the graph at the left of this line has to be the mirrored image of the graph at the right side. This is the case of this graph so it does have symmetry with respect to θ=π/2.
For the polar axis is the same, the graph above the axis has to be the mirrored image of that below the axis. However in this case we have two "petals" above the polar axis and one below so the upper part is not the mirrored version of the lower part so it has no symmetry with respect to this axis.
For the pole we must rotate the graph 180°. If the graph remains unchanged then it is symmetric with respect to it. In this case if we rotate the graph 180° the lower petal ends up in the opposite direction so the graph changes after a 180° rotation and it has no symmetry with respect to the pole.
Then the only type of symmetry is with respect to the line θ=π/2 and the answer is option a.
Find the time it would take for the general level of prices in the economy to double at an average annual inflation rate of 4%. The doubling time is aboutyears.
The doubling time for the general price levels in the eonomy given the average annual inflation rate is 18 years.
What is the doubling time?Inflation is a period where the general price levels in an economy rise persistently. When there is an inflation, the prices of goods and services increase. Inflation can either be as a result of an increase in the cost of production or an increase in the demand of a good.
The rule of 72 can be used to determine the doubling time. The rule of 72 is a rule of thumb that determines the number of years it would take an investment to double given its rate of growth.
The rule of 72 = 72 / inflation rate
72 / 4 = 18 years
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what will the y-intercept be if the graph is proportional?
A graph is proportional if the line intersects at the origin (0, 0)
and the y-intercept will always equal to 0
Since y-intercept is the value of y when x =0, and it passes the origin at x = 0, y= 0.
The answer is 0
Express the interval using inequality notation(1,6)
The interval (1, 6) contains all the real numbers between 1 and 6, not including any of the endpoints.
This can be written in inequality notation as:
x >1 AND x < 6
But there is a shorter way to write the interval by combining both inequalities:
1 < x < 6
The Hughes family and the Gonzalez family each used their sprinklers last summer. The Hughes family's sprinkler was used for 15 hours. The Gonzalez family's sprinkler was used for 35 hours. There was a combined total output of 1475 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65 L per hour?
Answer:
Hughes Family: 40 L/ hour
Gonzalez family: 25L/hour
Step-by-step explanation:
Let us use the following variables to denote the output rates for each sprinkler.
Let H = water output rate for the Hughes family
Let G = water output rate for the Gonzalez family
(I am using H ang G rather than the traditionally used X and Y to easily identify which rate belongs to which family)
The general equation for the volume of water outputted, V, in time h hours at a rate of r per hour is
V = r x h
Given r
Using this fact
Water Output for Hughes family at rate H for 15 hours = 15H
Water Output for Gonzalez family at rate G for 35 hours = 35 G
The total of both outputs = 1475
That gives us one equation
15H + 35G = 1475 [1]
We are given the combined rate as 65 L per hour
Sum of the two rates = combined rate
H + G = 65 [2]
Let's write down these two equations and solve for H and GDr Taylor just started an experiment he will collect data for 5 days how many hours is this
In one day the total number of hours is 24 hours.
So, in 5 days the number of hours is,
[tex]24\times5=120\text{ hours}[/tex]So, the required number of hours is 120 hours.
please help me with this. four potential solutions.450, 780, 647, 354
So first of all let's take:
[tex]x_1=x\text{ and }x_2=y[/tex]Then we get:
[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ x+y\ge300 \\ 2x+y\ge400 \\ 2x+5y\leq750 \\ x,y\ge0 \end{gathered}[/tex]The next step would be operate with the inequalities and the equation so we end up having only the term y at the left side of each:
[tex]\begin{gathered} \text{Min}z=1.5x+2y \\ 1.5x+2y=\text{Min}z \\ 2y=\text{Min}z-1.5x \\ y=\frac{\text{Min}z}{2}-0.75x \end{gathered}[/tex][tex]\begin{gathered} x+y\ge300 \\ y\ge300-x \end{gathered}[/tex][tex]\begin{gathered} 2x+y\ge400 \\ y\ge400-2x \end{gathered}[/tex][tex]\begin{gathered} 2x+5y\leq750 \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]So now we have the following inequalities and equality:
[tex]\begin{gathered} y=\frac{\text{Min}z}{2}-0.75x \\ y\ge300-x \\ y\ge400-2x \\ y\leq150-\frac{2}{5}x \end{gathered}[/tex]If we take the three inequalities and replace their symbols by "=' we'll have three equations of a line:
[tex]\begin{gathered} y=300-x \\ y=400-2x \\ y=150-\frac{2}{5}x \end{gathered}[/tex]The following step is graphing these three lines and delimitating a zone in the grid that meets the inequalities:
Where the blue area is under the graph of y=150-(2/5)x which means that it meets:
[tex]y\leq150-\frac{2}{5}x[/tex]And it is also above the x-axis, y=400-2x and y=300-x which means that it also meets:
[tex]\begin{gathered} x\ge0 \\ y\ge0 \\ y\ge400-2x \\ y\ge300-x \end{gathered}[/tex]All of this means that the values of x and y that give us the correct minimum of z are given by the coordinates of a point inside the blue area. The next thing to do is take the four possible values for Min(z) and use them to graph four lines using this equation:
[tex]y=\frac{\text{Min}z}{2}-0.75x[/tex]Then we have four equations of a line:
[tex]\begin{gathered} y=\frac{450}{2}-0.75x \\ y=\frac{780}{2}-0.75x \\ y=\frac{647}{2}-0.75x \\ y=\frac{354}{2}-0.75x \end{gathered}[/tex]The line that has more points inside the blue area is the one made with the closest value to Min(z). Then we have the following graph:
As you can see there are two lines that have points inside the blue area. These are:
[tex]\begin{gathered} y=-\frac{3}{4}x+\frac{450}{2} \\ y=-\frac{3}{4}x+\frac{354}{2} \end{gathered}[/tex]That where made using:
[tex]\begin{gathered} \text{Min }z=450 \\ \text{Min }z=354 \end{gathered}[/tex]Taking a closer look you can see that the part of the orange line inside the blue area is larger than that of the red line. Then the value used to make the orange line would be a better aproximation for the Min z. The orange line is -(3/4)x+450/2 which means that the answer to this problem is the first option, 450.
1 point Esther thinks she understands how to find the midpoint of a segment on a graph. "I always look for the middle of the line segment. But what should I do if the coordinates are not easy to graph?" she asks. Find the midpoint of KL if (2.125) and L(98, 15). *
In this case, we can write out the parameters
[tex]\begin{gathered} x_1=2,_{}y_1=125, \\ x_2=98,y_2=15 \end{gathered}[/tex]Thus, substitute the coordinates in the mid-point formula and simplify
[tex]\begin{gathered} x_m=\frac{98+2}{2}=\frac{100}{2}=50 \\ y_m=\frac{125+15}{2}=\frac{140}{2}=70 \end{gathered}[/tex]Hence, the coordinate of the mid-point is (50, 70)
Use the drop-down menus to explain if the two figures below are congruent, similar, or neither. If the figures are similar, state the scale factor I v Figure IJKE congruent to Figure TUVW because rigid motions be used to map Figure IJRL onto Figure TUVW. Figure IJKE dilations similar to Figure TUVW because rigid motions and/or be used to map Figure IJKL onto Figure TUVW.
Figure IJKL is congruent to Figure TUVW because rigid motions can be used to map Figure IJKL onto Figure TUVW
Figure IJKL is similar to Figure TUVW because rigid motions and/or dilations can be used to map Figure IJKL onto Figure TUVW
Since the figures are congruent, the scale factor is 1
A paper airplane contest is being held. The following results are found: 80% of the participants used a triangle shape. The triangle shaped planes only won their trials 16% of the time. The other shaped planes won their trials 36% of the time. Create a tree diagram for this situation: What is the probability that a triangle plane won overall?Out of 100 planes, which shape has the most winners?A winning plane is selected at random, what is the chance it is triangle shaped?
Given:
Percent of participants that used triangles shape = 80% = 0.80
The triangles shaped won their trials 16% of the time = 0.16
The other shaped plane won their trials 36% of the time = 0.36
Thus, we have:
Percent of participants who used other shapes = 100% - 80% = 20% = 0.20
Amount of time the triangle shaped plane lost = 100% - 16% =84% = 0.84
Amount of time the other shaped plane lost = 100% - 36% = 64% = 0.64
Let's solve for the following:
• (a) Create a tree diagram for this situation.
We have the tree diagram below:
• (b) What is the probability that a triangle plane won overall?
To find the probability that a triangle plane won overall, we have:
[tex]P(\text{triangle)}=\frac{0.8\times0.16}{(0.8\times0.16)+(0.2\times0.36)}=\frac{0.128}{0.128+0.072}=0.64[/tex]• (c) Out of 100 planes, which shape has the most winners?
Given that 80% used triangle, the number of planes with triangle shape will be:
0.8 x 100 = 80 planes
Number of planes with other shape:
0.2 x 100 = 20 planes
Number of winners for traingles:
0.16 x 80 = 12.8
Number of winners for other shape:
0.36 x 20 = 7.2
Therefore, the shape with the most winners is the triangle shape.
• (d),. A winning plane is selected at random, what is the chance it is triangle shaped?
To find the probability a winning plane selected at random is triangle shaped, wehave:
[tex]P(\text{triangle)}=\frac{12.8}{12.8+7.2}=\frac{12.8}{20}=0.64[/tex]ANSWER:
(b) 0.64
(c) Triangle shape
(d) 0.64
use a combination of inverse operations to solve the following equations.2(x-1) = -6
Given the following question:
[tex]2(x-1)=-6[/tex][tex]\begin{gathered} 2(x-1)=-6 \\ \text{ Divide by two} \\ -6\div2=-3 \\ \frac{2(x-1)}{2}=(x-1) \\ (x-1)=-3 \\ -1+1=0 \\ -3+1=-2 \\ x=-2 \end{gathered}[/tex]Your answer is x = -2.
Reba is playing on the slide. Over and over, she climbs the 9-foot ladder, goes down the slide, and walks 3 feet to get back to the ladder. How far does Reba travel each time she repeats this process? If necessary, round to the nearest tenth.
we have
then find c
[tex]\begin{gathered} c^2=3^2+9^2 \\ c^2=9+81 \\ c^2=90 \\ c=\sqrt[]{90} \\ c=3\sqrt[]{10} \end{gathered}[/tex]therefore the distance is:
[tex]9+3\sqrt[]{10}+3=21.5[/tex]answer: 21.5 ft
7 x 5f = 7070
HELPPPP PLEASE
f = 202
Step-by-step explanation:
[tex]7 \times 5f = 7070[/tex]
[tex]5f = \frac{7070}{7} [/tex]
[tex]5f = 1010[/tex]
[tex]f = \frac{1010}{5} [/tex]
[tex]f = 202[/tex]
Verification to check the given answer is correct, then put the value of f in the given question.
[tex]7 \times 5(202) = 7070[/tex]
[tex]35(202) = 7070[/tex]
[tex]7070 = 7070[/tex]
L.H.S. = R.H.S
[tex]{ \green { \boxed{ \red{ \sf{f = 202}}}}}[/tex]
Step-by-step explanation:
The given Eqⁿ is, [tex]{ \purple{ \sf{7 \times 5f = 7070}}}[/tex]
We need to find the value of f. So, let us cancel the numbers one by one.
First, let us cancel 7 by dividing both the sides by 7 in the given Eqⁿ.
[tex]{ \purple{ \sf \frac{ \cancel7 \times 5f}{ \cancel7}}} = { \purple{ \sf{ \frac{ \cancel{7070} ^{ \green{ \tt{1010}}} }{ \cancel 7_{ \green{ \tt{1}}}}}}}[/tex]
[tex]{ \purple{ \sf{5f = 1010}}}[/tex]
Now, let us cancel 5 by dividing both the sides by 5. then,
[tex]{ \purple{ \sf{ \frac{ \cancel5}{ \cancel5}f}}} = { \purple{ \sf{ \frac{ \cancel{1010^{ \red{ \tt{ \: \:202}}}}}{ \cancel 5_{ \red{ \tt{1}}}}}}}[/tex]
[tex]{ \boxed{ \blue{ \sf{f = 202}}}}[/tex]
Charlene and Gary want to make perfume. In order to get the right balance of ingredients for their tastes they bought 2ounces of rose oil at $4.36 per ounce, 5 ounces of ginger essence for $2.15 per ounce, and 4 ounces of black currant essence for $2.27 per ounce. Determine the cost per ounce of the perfume.
First, lets calculate how much the expended in the perfume:
[tex]2\times(4.36)+5\times(2.15)_{}+4\times(2.27)=28.55[/tex]So, for 11 ounces of perfume, they need $28.55, so the minimum that the perfume need to cost per ounce is:
[tex]\frac{28.55}{11}=2.5954\cong2.6[/tex]So, about $2.6 per ounce of perfume.
Suppose you want to have $ 749,791 for retirement in 13 years. Your account earns 9.5 % interest monthly. How much interest will you earn?$_________ (Round to the nearest DOLLAR)
ANSWER
$530,663
EXPLANATION
The amount the account will have in t years is given by,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where n = 12, t = 13 years, r = 0.095 and A = 749,791. We have to find P,
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Replace with the values and solve,
[tex]P=\frac{749,791}{(1+\frac{0.095}{12})^{12\cdot13}}\approx219,128[/tex]The interest earned is the difference between the initial deposit P and the final amount A,
[tex]i=A-P=749,791-219,128=530,663[/tex]Hence, the interest earned would be $530,663.
Set up the system of equations:The cost of 4 bananas and 6 pears is $1.68. Nine bananas and 2 pears cost $1.48. Set up thesystem of equations to find the cost of each banana and pear.4B + 6P = 1.689B - 2P = 1.484B + 6P + 1.689B + 2P + 1.484B + 6P = 1.689B + 2P = 1484B = 6P + 1.689B = 2P + 148
Solution:
Let b represent the cost of 1 banana
Let p represent the cost of 1 pear
From the first statement, The cost of 4 bananas and 6 pears is $1.68
4b + 6p = 1.68 ----------------------------equation (1)
From the second statement, Nine bananas and 2 pears cost $1.48
9b + 2p = 1.48 -----------------------------equation (2)
Solve both equations simultaneously
4b + 6p = 1.68 ----------------------------equation (1)
9b + 2p = 1.48 -----------------------------equation (2)
Multiply equation (2) by 3 to eliminate p
27b + 6p = 4.44
4b + 6p = 1.68
Subtract both equatuions above
23b = 2.76
b = 2.76/23
b= 0.12
Substitute b = 0.12 into equation (1)
9b + 2p = 1.48
9(0.12) + 2p = 1.48
1.08 + 2p = 1.48
2p = 1.48 - 1.08
2p = 0.4
p = 0.4/2
p = 0.2
Hence, the cost of each banana is $0.12 while the cost of each pear is $0.2
Find the domain of the function. Write the domain in interval notation.
The domain of a function is the possible values of "t" that the given function can take.
Since the variable "t" is in the denominator, the denominator cannot be equal to zero because it would make the function undefined.
Hence, t - 4 must be greater than zero. For t - 4 to be greater than zero, the value of t must be greater than 4.
In addition, since the variable is inside the radical sign, then the function itself cannot be negative.
Hence, the domain of this function must be greater than 4. In interval notation, it is (4, ∞).
50 gramos de pechuga de un pollo contiene 10.4 g de proteínas, 0.5 g de carbohidratos y 1.6 g de grasas. Los valores medios de energía alimentaria de esas sustancias son de 4.0 kcal/g para las proteínas y los carbohidratos, y de 9.0 kcal/g para las grasas. a) Al jugar baloncesto, una persona representativa consume energía a una potencia de 420 kcal/h. ¿Cuánto tiempo debe jugar para “quemar” esa pechuga?
Tenemos lo siguiente:
Lo primero es calcular las kilocalorías para las proteínas y para los carbohidratos y grasas, de la siguiente día:
[tex]\begin{gathered} \text{Protenas} \\ 10.4\text{ g}\cdot4\frac{\text{ kcal}}{g}=41.6\text{kcal} \\ \text{Carbohidratos} \\ 0.5\text{ g}\cdot4\frac{\text{ kcal}}{g}=2\text{kcal} \\ \text{Grasas} \\ 1.6\text{ g}\cdot9\frac{\text{ kcal}}{g}=14.4\text{kcal} \end{gathered}[/tex]Ahora sumamos todas las kilocalorías y nos queda lo siguiente:
[tex]41.6+2+14.4=58[/tex]Es decir que en total en los 50 gramos de pechuga hay en total de 58 kilocalorías, ahora debemos calcular el tiempo dividiendo el numero de kilocalorías por la cantidad de consumo de kilocalorías al jugar baloncesto
[tex]\frac{58\text{ kcal}}{420\text{ kcal/h}}=0.138\text{ h}[/tex]Es decir que debe jugar 0.138 horas o un total de:
[tex]0.138\text{ h}\cdot\frac{60\text{ min}}{1\text{ h}}=8.28\text{ min}[/tex]Es decir que debe jugar 8.28 minutos
Four more than the product of a number and 8 is equal to 3.
Four more than the product of a number and 8 is equal to
Let
x -----> the number
we have that
the algebraic expression is equal to
the product of a number and 8 ------> 8x
so
Four more than the product of a number and 8 is equal to 3
8x+4=3
solve for x
8x=3-4
8x=-1
x=-1/3
therefore
the number is -1/3