Recall the product rule of logarithms
[tex]\log _b(xy)=\log _b(x)+\log _b(y)[/tex]Apply the product rule to the given and we get
[tex]\log _7(343x)=\log _7(343)+\log _7(x)[/tex]y=x-6y=x+2 how to solve this problem
No solutions
Explanation
[tex]\begin{gathered} y=x+6\text{ Eq(1)} \\ y=x+2\text{ Eq(2)} \end{gathered}[/tex]
Step 1
replace Eq(1) in Eq (2)
[tex]\begin{gathered} y=x+2\text{ Eq(2)} \\ x+6=x+2 \\ \end{gathered}[/tex]Step 2
subtract x in both sides
[tex]\begin{gathered} x+6=x+2 \\ x+6-x=x+2-x \\ 6=2 \end{gathered}[/tex]6=2 is false, it means there is not solution for both equations,
Assume that Jim Bruce and Valerie are 3 of the 17 members of the class, and that of the class members will be chosen randomly to deliver their reports during the next class meeting. What is the probability that Jim Bruce and Valerie are selected in that order?
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
Given,
Number of students in a class = 17
Jim, Bruce and Valerie are 3 of the 17.
Three of students from the class are randomly chosen to deliver their reports during the next class meet.
We have to find the probability that Jim, Bruce and Valerie are selected in that order;
Here,
The total number of possible selection;
S = ⁿCr
Where, n = 17 and r = 3
Then,
S = ¹⁷C₃
S = 17! / 14! x 3!
S = 680
Therefore,
The probability that Jim, Bruce and Valerie are selected in that order is P = 1/680
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The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)
To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:
[tex]\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}[/tex]Let us subtract the second equation to the first one:
This implies that
[tex]\beta_1=\frac{-1}{-21}=\frac{1}{21}[/tex]Now, let us replace this value we just got into the second equation to find beta_0:
[tex]\begin{gathered} 4=\beta_0+\frac{1}{21}\cdot11, \\ 4=\beta_0+\frac{11}{21}, \\ \beta_0=4-\frac{11}{21}=\frac{4\cdot21}{21}-\frac{11}{21}=\frac{84-11}{21}=\frac{73}{21} \end{gathered}[/tex]At last,
[tex]\beta_1=\frac{1}{21},\beta_0=\frac{73}{21}[/tex]Then, the equation of the line is just
[tex]y=\frac{73}{21}+\frac{1}{21}x[/tex]An electronic store discounted a tablet computer by 30%. The discounted price of the computer was $486.50. Determine the original price of the tablet
The discounted price of the computer was $486.50.
An electronic store discounted a tablet computer by 30%.
So, the original price was
[tex]\begin{gathered} C=486.50+(486.50\times30percent) \\ =486.50+(486.50\times\frac{30}{100}) \\ =486.50+145.95 \\ =632.45 \end{gathered}[/tex]So, the original price of the tablet computer was $632.45.
What is the independent and dependent variable for k(d) =2d^2 - d +32
Given:
[tex]k(d)=2d^2-d+32[/tex]Required:
To find the independent and dependent variable.
Explanation:
In the given equation,
The dependent variable = k(d)
The independent variable = d
Final Answer:
The dependent variable = k(d)
The independent variable = d
A collection of dimes and quarters has a value of $1.35. List all possible combinations of dimes and quarters. Remember to write a let statement
3 combinations:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
1) Remember that a dime corresponds to $0.10 and a quarter to $0.25. And the value we want to find is $1.35
2) As we can see the last digit on $1.35 is 5 then we can infer that we're going to need an odd number of quarters ($0.25). Also, notice that we need whole numbers for the quantities of each coin. In other words, multiples of 0.10 and 0.25 whose sum yields to $1.35. So let's do it step by step:
So, we can write out the following list of combinations:
q (quarter) 3 q = 3 x 0.25 = $ 0.75
d (dimes) 6 d = 6 x 0.10 = $ 0.60
0.60 + 0.75 = 1.35
2.2) Another possible combination:
q (quarter) 5 q = 5 x 0.25 = $ 1.25
d (dimes) 1 d = 1 x 0.10 = $ 0.10
0.10+1.25= 1.35
2.3)
q (quarter) 1 q = 1 x 0.25 = $ 0.25
d (dimes) 11 d = 11x 0.10 = $ 1.10
0.25+1.10 = 1.35
3) Hence, considering that we need to combine dimes and quarters and their sum must be lesser than $1.35 We have three combinations with whole numbers of dimes and quarters:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
determine the domain and range of the piecewise function graphed below
The domain is all the possible input values, and the range is all the possible output values.
So according to this function (Given in the question).
The domain is [-3, 5] and the range is [-5, 4]
That is all to this question.
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Last year, Susan had $20,000 to invest. She invested some of it in an account that paid 10% simple interest per year, and she invested the rest in an account that paid 7% simple interest per year. After one year, she received a total of $1790 in interest. How much did she invest in each account?
Let
x ------> amount invested in an account that paid 10% simple interest per year
20,000-x ------> amount invested in an account that paid 7% simple interest per year
so
The formula of simple interest is equal to
I=P(rt)
In this problem we have that
10%=0.10
7%=0.07
x*(0.1)+(20,000-x)*(0.07)=1,790
solve for x
0.10x+1,400-0.07x=1,790
0.03x=1,790-1,400
0.03x=390
x=$13,000
therefore
amount invested in an account that paid 10% simple interest per year was $13,000and amount invested in an account that paid 7% simple interest per year was $7,000what is the value of x in the solutions to the system of equations below3x-8y=112y+x=13
Given system of equations
3x - 8y = 11 ______________________1
2y + x = 13 ______________________ 2
Use the substution method
How to use the substitution method
1. pick one of the equation
2. make one of the variable subject of relation
3. substitute
From equation (1)
2y + x = 13
x = 13 - 2y
substitute x from equation 1 to 2.
3(13 - 2y) - 8y = 11
39 - 6y - 8y = 11
39 - 11 = 6y + 8y
28 = 14y
y = 28/14
y = 2
Next, substitute y in equation 2 to find x.
x = 13 - 2y
x = 13 - 2(2)
x = 13 - 4
x = 9
Final answer x = 9
L1 : y=−4x+3L2 : y=4x−1
Answer:
Assuming you're trying to find where the lines intersect (their solution), the point where they intersect is (1/2 , 1).
Step-by-step explanation:
When you are trying to find the point where two lines intersect, you have to find the x and y values of that point. To do that, just set the lines equal to each other.
First, since y must equal y:
y = y
-4x + 3 = 4x - 1
Now solve for x:
-8x + 3 = -4
-8x = -4
8x = 4
x = 1/2
We just found the x value of the shared point. Now we need to find the y value of that point. Again, since the two lines share this point, plugging in the x value will result in the same y value for both lines.
So just plug in x to any of the equations: (I think y=4x-1 is easier)
y(1/2) = 4(1/2) - 1 or y = 4(1/2) - 1 (it doesn't matter how you write it)
y(1/2) = 2 - 1 or y = 2 - 1
y(1/2) = 1
So the point is:
(1/2 , 1)
To check you can plug in the y value you find, 1 in this case, and solve for x. If you get the same x value as before, everything is correct.
So:
(1) = -4x + 3
-2 = -4x
1/2 = x or x = 1/2
Great! Everything is correct.
This may seem like a very long process, but it is very easy. Just find the x and y values that the lines share by setting the lines equal to each other.
You bought your first car for $3,000 and make payments of $150 each month. Letting B represent the balance (what still needs to be paid), which function rule represents how much money is still owed (the balance) after m months?
The function rule represents how much money is still owed is B = 3000 - 150m
What is a function?A function is used to show the relationship between the data given. This can be illustrated with the variables.
Here, the person bought the first car for $3,000 and make payments of $150 each month.
Let B represent the balance.
The function to illustrate this will be:
B = 3000 - 150(m)
B = 3000 - 150m
where B = balance
m = number of months
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f(x) = -2x² + 2x
Find f(-8)
Answer:
f(-8)= -112
Step-by-step explanation:
-2(-8)^2 + 2(-8)
-2(-64) + 16
-128 + 16
= -112
hope this helped
have a good day :)
i need help with this too
a The value of (2.3 × 10⁴) × (1.5 × 10^-2) is 3.45 × 10^2
b. The value of (3.6 × 10^-5) ÷ (1.8 × 10^2) is 2 × 10^-3. This illustrates the concept of standard form.
What is standard form?The standard form is simply used in Mathematics to illustrate the numbers that are either too large or too small.
It's important to note that the multiplication of exponents is an addition and the division of the power is subtraction.
Therefore, (2.3 × 10⁴) × (1.5 × 10^-2) will be:
= (2.3 × 1.5) × (10^(4-2)
= 3.45 × 10^2
Also, (3.6 × 10^-5) ÷ (1.8 × 10^2) will be:
= (3.6 ÷ 1.8) × 10^(-5 + 2)
= 2 × 10^-3.
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Grade 12 math can you please explain each step, what are you doing, why and the final result that contributes to the sketch.
ANSWER and EXPLANATION
We want to sketch the graph of the given function:
[tex]y=\frac{2x^2-7x+5}{2x-1}[/tex]First, we have to check for the asymptotes of the function.
To find the vertical asymptote, we have to equate the denominator to 0 and solve for x:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]That is the vertical asymptote.
To find the horizontal asymptote, we have to check the degrees of the numerator and denominator. Since the degree of the numerator is greater than the denominator's, there is no horizontal asymptote.
To find the slant asymptote, divide the numerator by the denominator and identify the quotient:
This implies that the slant asymptote is:
[tex]y=x-3[/tex]The asymptotes will provide the boundaries for the graph of the function as follows:
Now, we have to find some coordinate points that satisfy the function.
Let us solve for y for values of x = -2, -1, 0, 1, 2, 3:
[tex]\begin{gathered} \Rightarrow x=-2 \\ y=\frac{2(-2)^2-7(-2)+5}{2(-2)-1}=-5.4 \\ \Rightarrow x=-1 \\ y=\frac{2(-1)^2-7(-1)+5}{2(-1)-1}=-4.67 \\ \Rightarrow x=0 \\ y=\frac{2(0)^2-7(0)+5}{2(0)-1}=-5 \\ \Rightarrow x=1 \\ y=\frac{2(1)^2-7(1)+5}{2(1)-1}=0 \\ \Rightarrow x=2 \\ y=\frac{2(2)^2-7(2)+5}{2(2)-1}=-0.33 \\ \Rightarrow x=3 \\ y=\frac{2(3)^2-7(3)+5}{2(3)-1}=0.4 \end{gathered}[/tex]We also have to identify the x and y intercepts of the function.
For the x-intercept, solve for x when y = 0:
[tex]\begin{gathered} 0=\frac{2x^2-7x+5}{2x-1} \\ \Rightarrow2x^2-7x+5=0 \\ 2x^2-2x-5x+5=0 \\ 2x(x-1)-5(x-1)=0 \\ (2x-5)(x-1)=0 \\ x=\frac{5}{2};x=1 \end{gathered}[/tex]For the y-intercept, solve for y when x = 0:
[tex]\begin{gathered} y=\frac{2(0)^2-7(0)+5}{2(0)-1} \\ y=\frac{5}{-1} \\ y=-5 \end{gathered}[/tex]Let us draw the table of values:
Now, we can use the calculated points, the intercepts, and the asymptotes to sketch the graph of the function:
That is the sketch of the function.
Determine whether each expression can be used to find the length of side RS.
ANSWER:
[tex]\begin{gathered} \sin (R)\rightarrow\text{ Yes} \\ \tan (T)\rightarrow\text{ No} \\ \cos (R)\rightarrow\text{ No} \\ tan(R)\rightarrow\text{ No} \end{gathered}[/tex]STEP-BY-STEP EXPLANATION:
Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.
Therefore, if we want to know that side we must apply sine or cosine, just like this:
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{therefore, in this case:} \\ \sin R=\frac{21}{35} \\ \cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}} \\ \cos R=\frac{\text{unknown}}{35} \end{gathered}[/tex]Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R
McGraw-H….A ALEKS - Mi...O POLYNOMIAL AND RATIONAL FUNCTIONSThe Factor Theorem
SOLUTIONS
Using factor theorem to solve the equation below:
[tex]-x^3+4x^2-8=0[/tex][tex]\begin{gathered} -x^3+4x^2-8 \\ -x(x^2-4x+8) \end{gathered}[/tex]i have test tomorrow i will love you to help me with thisClassify the following as a monomial, binomial, trinomial, or polynomial andstate the degree.a) 7^5b) 5^7 + 7^2c) 7^3 + 11^2 − 13 + 112d) + 2 + 3^2e) 11^3 − 7^3
Answer:
a) degree 5; monomial
b) degree 7; polynomial
c) degree 3; polynomial
d) degree 2; polynomial
e) degree 3 polynomial
Explanation.
A polynomial is a mathematical expression containing coefficients and variables.
An example of a polynomial is 42x^5 + 23 x^3 - 2x.
A monomial is a polynomial that contains only one term. For example, x^4, 34x^5, 2x, etc.
Having that in mind, we go through the expressions and place them in one of either category.
a) 7^5
This contains only one term, meaning it is monomial; its highest exponent is 5, meaning it is of degree 5.
b) 5^7 + 7^2
This contains two terms, meaning it is a polynomial; its highest exponent is 7, meaning its degree is 7.
c) 7^3 + 11^2 − 13 + 112
This expression contains four terms - it is a polynomial; its highest exponent is 3, meaning its degree is 3.
d) + 2 + 3^2
This contains three terms, meaning it is a polynomial; its highest exponent is 2, meaning its degree is 2.
e) 11^3 − 7^3
This contains 2 terms, meaning it is a polynomial; its highest exponent is 3, meaning it is of degree 2.
Leila runs at 12 mph find the number of miles she can travel if she runs for 2 hours
20 POINTS ANSWER I WILL MARK BRAINLIEST!!!!!!!!!!
Answer: 24 mph
Step-by-step explanation:
If she can run 12 mph/ 12 miles per hour
She runs for 2 hours
12 · 2 = 24
two ships leave a port at the same time. the first ship sails on a bearing of 55° at 12 knots (natural miles per hour) and the second on a bearing of 145° at 22 knots. how far apart are they after 1.5 hours (round to the nearest nautical mile)
Given that one of the ships travels at 12 nautical miles per hour, then after 1.5 hours, it will travel 12*1.5 = 18 miles
The other ship will travel 22*1.5 = 33 miles
The angle of 145° is measured with respect to the positive x-axis. Then, respect the negative x-axis, its measure is 180° - 145° = 35°
We have to use trigonometric functions to find x1, y1, x2, and y2, as follows:
sin(55°) = y1/18
sin(55°) *18 = y1
14.7 = y1
cos(55°) = x1/18
cos(55°)*18 = x1
10.3 = x1
sin(35°) = y2/33
sin(35°)*33 = y2
18.9 = y2
cos(35°) = x2/33
cos(35°)*33 = x
-27 = x2 (the minus sign comes from the graph)
The distance between two points (x1, y1) and (x2, y2) is computed as follows:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Substituting with the values found,
[tex]\begin{gathered} d=\sqrt[]{(-27-10.3)^2+(18.9-14.7)^2} \\ d=\sqrt[]{(-37.3)^2+4.2^2} \\ d=\sqrt[]{1391.29+17.64} \\ d\approx38\text{ miles} \end{gathered}[/tex]A skier is trying to decide wheter or not to buy a seaskn ski pass. A daily pass cost $71. a season ski pass costs $350. the skirr would have to rent skis with either pass for $30 per day. how many days would the skier have to go skiing i. order to make the season pass less expensive than the daily passes?
The most appropriate choice for linear equation will be given by -
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , \geq, < , \leq[/tex] sign
A one degree inequation is known as linear inequation.
Here,
Let the number of days the skier have to go skiing in order to make the season pass less expensive than the daily passes be d days
A daily pass cost $71
A season ski pass costs $350.
The skier would have to rent skis with either pass for $30 per day.
Cost of skiing with daily pass = $(71d + 30d) = $101d
Cost of skiing with season pass = $(350 + 30d)
By the problem,
[tex]101d > 350 + 30d\\101d - 30d > 350\\81d > 350\\d > \frac{350}{81}\\d > 4.3[/tex]
The skier would have to go atleast 5 days to make the season pass less expensive than the daily pass
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Find the values of the variables in the parallelogram. The diagram is not drawn to scale. (Image is attached below)thank you in advance :)
For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.
Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:
[tex]x=33º[/tex]The opposite angles in a parallelogram are congruent, therefore:
[tex]z=109º[/tex]The sum of internal angles is 360º, therefore we have:
[tex]\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}[/tex]The value of x is 33º, the value of y is 38º and the value of z is 109º.
f(x) = - 3x + 4; g(x) = f(x) + 1
Graph it and then describe the graph
The graph of function f(x) and g(x) is parallel lines separated by 1 unit.
In this question we have been given two functions f(x) = - 3x + 4 and g(x) = f(x) + 1
We need to graph these functions and then describe the graph.
The graph of given functions is as shown below.
The graph of function f(x) is a straight line with slope -3 and y-intercept 4.
The function g(x) is nothing but but function f(x) translated upward by 1 unit.
The graph of function g(x) is also a straight line with slope -3 and y-intercept 5.
Therefore, the graph of function f(x) and g(x) is parallel lines separated by 1 unit.
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Given the equation y = 6sin(2x - 10) + 3
We have the equation:
[tex]y=6\sin(2x-10)+3[/tex]We have to find the amplitude, the period, the horizontal shift and the midline.
The amplitude can be calculated as half the difference between the maximum and minimum value of the function.
The maximum value will happen when the sine is equal to 1 and the minimum when the sine is equal to -1.
We can then calculate the amplitude A as:
[tex]\begin{gathered} A=\frac{y_{max}-y_{min}}{2} \\ A=\frac{6(1)+3-(6(-1)+3)}{2} \\ A=\frac{6+3-(-6+3)}{2} \\ A=\frac{9-(-3)}{2} \\ A=\frac{12}{2} \\ A=6 \end{gathered}[/tex]Now we have to calculate the period.
The period will be equal to the horizontal distance at which the function starts repeating itself (or complete a period).
As we have a sine function we know that:
[tex]\sin(u)=\sin(u+2n\pi)\text{ }n\in Z[/tex]That means that it will repeat itself for any multiple of 2π.
We can calculate the period as:
[tex]\begin{gathered} y(x+2\pi)=y(x+T) \\ 6(2x-10+2\pi)+3=6(2(x+T)-10)+3 \\ 2x-10+2\pi=2(x+T)-10 \\ 2x+2\pi=2x+2T \\ 2\pi=2T \\ T=\pi \end{gathered}[/tex]The period is π.
The horizontal shift will be given by the constant value inside the argument of the sine function. We can ignore the other terms and factors and use only the sine function in this case.
For example, for sin(2x) = 0, this value corresponds to x = 0.
In the case of sin(2x-10) = 0 this corresponds to an x that is 5.
That is because the function has a frequency that is twice as the frequency of the hpure sine function.
If the function wasn't periodice we would see it translated by 10 to the right.
We can calculate the midline as the average of the function.
This average value will be given by the average value of the sine function, which is 0, so we can calculate the midline as:
[tex]y_{avg}=6(0)+3=3[/tex]Answer:
The amplitude is 6.
The period is π.
The horizontal shift is 10 units to the right.
The midline is y = 3.
Metric area unit conversion with decimal valuesTammy has a rectangular poster. The poster is 1.2 meters long and 0.9 meters wide. What is the area of the poster in square centimeters? Do not round youranswer.cmcm²cm³
We are asked to find the final area in square centimeters.
We must first convert the measurements of the poster into centimeters:
1.2m = 120cm
0.9m = 90cm
Area = length * width
= 120*90
= 10800 square centimeters.
27. A race consists of 7 women and 10 men. What is the probability that the top three finishers were(a) all men (b) all women (c) 2 men and 1 woman (d) 1 man and 2 women
Given 7 women and 10 men;
a) the top 3 are all men:
[tex]\begin{gathered} ways\text{ to choose 3 men out of 10 men is:} \\ 10C_3=\frac{10!}{(10-3)!3!} \\ \Rightarrow\frac{10!}{7!3!}=\frac{10\times9\times8\times7!}{7!\times3\times2\times1} \\ \Rightarrow\frac{10\times9\times8}{3\times2\times1}=120 \\ \text{ways to choose 3 men from 17 people(10men +7women) is:} \\ 17C_3=\frac{17!}{(17-3)!3!} \\ \Rightarrow\frac{17!}{14!\times3!}=\frac{17\times16\times15\times14!}{14!\times3\times2\times1} \\ \Rightarrow\frac{17\times16\times15}{3\times2\times1}=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all men is:
[tex]P_{all\text{ men}}=\frac{120}{680}=0.1765[/tex]b) the top 3 are all women:
[tex]\begin{gathered} \text{ways to choose 3 women from 7 women is:} \\ 7C_3=35 \\ \text{ways to choose 3 women from 17 people is:} \\ 17C_3=680 \end{gathered}[/tex]Therefore, the probability that the top 3 are all women is:
[tex]P_{\text{all women}}=\frac{35}{680}=0.0515[/tex]c) 2 men and 1 woman;
[tex]\begin{gathered} ways\text{ to choose 2 men out of 10 men is:} \\ 10C_2=45 \\ \text{ways to choose 1 woman from 7 women is:} \\ 7C_1=7 \\ \text{Thus, ways to choose 2 men and 1 woman }=45\times7=315 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 2 men and 1 woman is:
[tex]P=\frac{315}{680}=0.4632[/tex]d) 1 man and 2 women;
[tex]\begin{gathered} \text{ways to choose 1 man from 10 men is;} \\ 10C_1=10 \\ \text{ways to choose 2 women from 7 women is:} \\ 7C_2=21 \\ \text{Thus, ways to choose 1 man and 2 women is 10}\times21=210 \end{gathered}[/tex]Therefore, the probability that the top 3 finishers are 1 man and 2 women is:
[tex]P=\frac{210}{680}=0.3088[/tex]#Classify each number as a natural number, a whole number, or an integer.
If a number belongs to more than one set, list all possible sets it belongs to.
a) 1
b) -20
c) -3
(a) Whole number and integer
(b) Negative integer
(c) Negative integer
What are whole numbers an integers?Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers. A number line is a graphic representation of positive and negative integers. The use of integers on a number line facilitates mathematical procedures. The right-side number is always greater than the left-side number. Due to the fact that they are greater than 0, positive numbers are positioned to the right of zero. All natural numbers and 0 are included in a group of numbers known as whole numbers. They belong to the category of real numbers, which excludes fractions, decimals, and negative numbers. Numbers used for counting are also regarded as whole numbers.
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to find the height of a tree, a group of students devised the following method. A girl walks toward the tree along it's shadow until the shadow of the top of her head coincide with the shadow of the top of the tree. if the girl is 150 cm tall, her distance to the foot of the tree is 13 meters, and the length of her shadow is 3 m, how tall is the tree?
Answer: 8m
Explanation:
Given:
To find the height(h) of the tree, we can use ratio since they are similar triangles.
Triangle 1
Triangle 2
So,
[tex]\begin{gathered} \frac{1.5}{3}\text{ = }\frac{h}{16} \\ \text{Simplify and rearrange} \\ h=\text{ }\frac{1.5}{3}(16) \\ \text{Calculate} \\ h=\text{ 8 m} \end{gathered}[/tex]Therefore, the height of the tree is 8m.
Find the equation of the line with slope = 5 and passing through (-7,-29). Write your equation in the form
y = mz+b.
Answer:
[tex]y =5x+6[/tex]
Step-by-step explanation:
In the equation, [tex]y=mx+b[/tex], the "m" represents the slope, and the b represents the y-intercept.
We know the slope is 5, so we already know part of the equation: [tex]y=5x+b[/tex]
To solve for the "b" part or y-intercept, we can simply plug in a known point on the line, which was given to be (-7, -29)
This gives us the following equation:
[tex]-29 = 5(-7) + b\\\text{simplify}\\-29 = -35 + b\\\text{add 35 to both sides}\\6=b[/tex]
Answer: y = 5x + 6
Step-by-step explanation:
1. Do point-slope formula {(y - y1) = m(x - x1})
(y - 29) = 5(x - 7)
Distribute
(y - 29) = 5x - 35
Subtract 29 on both sides
Cancel out y - 29 - 29
y = 5x + 6
8) Use the graph to determine the independent variable. Money Saved 240 210 180 A Number of Weeks 150 120 Amount of Money ($) B) The Amount of Money 90 © Money Saved 60 30 0 1 2 6 7 8 3 4 5 Number of Weeks
Generally equations are in the form:
y = mx + b
Where
x is the independent variable, you can choose any value for x
y is the dependent variable. The value of y depends on x.
In the graph, the x-axis is number of weeks and y-axis is amount.
Amount depends on the number of weeks, which is the independent variable, here in this graph.
can you explain what the 8th question is asking then answer it please
Answer:
Options A and C
Explanation:
We want to find out which arithmetic sequence(s) contain the term 34.
For an arithmetic sequence to contain the term, 34, the corresponding n-value must be an integer.
Option A
Set tn = 34
[tex]\begin{gathered} t_n=6+(n-1)4 \\ 34=6+(n-1)4 \end{gathered}[/tex]Solve for n:
[tex]\begin{gathered} 34-6=4n-4 \\ 28=4(n-1) \\ n-1=\frac{28}{4}=7 \\ n-1=7 \\ n=7+1 \\ n=8 \end{gathered}[/tex]The 8th term of this sequence is 34.
Option B
[tex]\begin{gathered} t_n=3n-1 \\ 34=3n-1 \\ 34+1=3n \\ 35=3n \\ n=\frac{35}{3}=11\frac{2}{3} \end{gathered}[/tex]A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.
Option C
T1 = 12, d=5.5
[tex]\begin{gathered} 12+5.5(n-1)=34 \\ 5.5(n-1)=34-12 \\ 5.5(n-1)=22 \\ n-1=\frac{22}{5.5} \\ n=4+1 \\ n=5 \end{gathered}[/tex]The 5th term of this sequence is 34, therefore, it contains the term 34.
Option D
3,7,11,...
[tex]\begin{gathered} t_1=3 \\ d=7-3=4 \end{gathered}[/tex]Using the nth term of an arithmetic sequence formula:
[tex]\begin{gathered} t_n=t_1+(n-1)d \\ 34=3+4(n-1) \\ 34-3=4(n-1) \\ 31=4(n-1) \\ n-1=\frac{31}{4} \\ n-1=7\frac{3}{4} \\ n=8\frac{3}{4} \end{gathered}[/tex]A sequence cannot have a decimal nth term, therefore, the sequence does not contain 34.
The sequences in Options A and C contain the term 34.