To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.
We have the following:
[tex]\begin{gathered} g(x)=8x^2-10x-3 \\ if\text{ g(x)=0} \\ \Rightarrow8x^2-10x-3=0 \end{gathered}[/tex]we can use the quadratic formula to get the roots of the polynomial:
[tex]\begin{gathered} a=8 \\ b=-10 \\ c=-3 \\ x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \Rightarrow x_{1,2}=\frac{-(-10)\pm\sqrt[]{(-10)^2-4(8)(-3)}}{2(8)}=\frac{10\pm\sqrt[]{196}}{16} \\ \Rightarrow x_{1.2}=\frac{10\pm14}{16} \\ \Rightarrow x_1=\frac{10+14}{16}=\frac{24}{16}=\frac{3}{4} \\ \Rightarrow x_2=\frac{10-14}{16}=\frac{-4}{16}=-\frac{1}{4} \end{gathered}[/tex]therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)
What is the solution to the system of equations? Use the substitution method to solve. 6=−4x+y− 5x−y=21 Enter your answer by filling in the boxes
The x and y solution of the system is x = -3 and y = -6
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
6 = −4x + y
− 5x − y = 21
Make -y the subject in the second equation, by adding 5x to both sides of the equation
5x − 5x − y = 21 + 5x
This gives
−y = 21 + 5x
Substitute −y = 21 + 5x in 6 = −4x + y
6 = −4x - 21 - 5x
Evaluate the like terms
5x + 4x = -6 - 21
This gives
9x = -27
So, we have
x = -3
Substitute x = -3 in −y = 21 + 5x
−y = 21 + 5 * -3
Evaluate
−y = 6
So, we have
y = -6
Hence, the solution for the system of linear equations 6 = −4x + y and − 5x − y = 21 is x = -3 and y = -6
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You thought you had finished 35 pages, but you actually read 32 Pages. What was your percent error?
[tex]\frac{35-32}{32} \times 100=\frac{75}{8}=9.375\%[/tex]
Answer:
9.375%
Step-by-step explanation:
Percentage Error formula
[tex]\textsf{Percentage error}=\sf \left|\dfrac{estimated\:value\:-actual\:value}{actual\:value} \right| \times 100\%[/tex]
Given:
Estimated value = 35 pagesActual value = 32 pagesSubstitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Percentage error}&= \left|\dfrac{35-32}{32} \right| \times 100\%\\\\&=\left|\dfrac{3}{32} \right| \times 100\%\\\\&=0.09375 \times 100\%\\\\&=9.375\%\end{aligned}[/tex]
Therefore, the percentage error was 9.375%.
Determine the more basic function that has been shifted reflected stretched or compressed what does
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
Step 1
iven
[tex]g(x)=-2\sqrt{x-1}+4[/tex]g(x) is a transformation of the function f(x)we have a root in the function, note that the variable x is inside the root, so we can conclude the basic function is
square tooroot
Step 2
rove
ow, lets's check the transformation of f(x)
[tex]f(x)=\sqrt{x}[/tex]a)1 was subtracted form the argument of the fucnction
[tex]\begin{gathered} f(x)=\sqrt{x} \\ f^{\prime}(x)=\sqrt{x-1} \end{gathered}[/tex]when you subtract a number b form the argument of the function you are shifting the function b units to the rigth
so
he function was shifteed 1 unit to rigth
) the resulting function was multiplied by 2-
[tex]\begin{gathered} f^{\prime}(x)=\sqrt{x-1}\text{ *-2} \\ f^{\prime}^{\prime}(x)=-2\sqrt{x-1} \end{gathered}[/tex]when you multplie by a negavitve constant you are reflecting the funciton acrros x-axis, and is is stretched vertically.
so
he funcition was reflected across x-axis an strtched vertically by a factor of 2
c) 4 was added to the function
[tex]\begin{gathered} f^{\prime\prime}(x)=-2\sqrt{x-1} \\ g(x)=-2\sqrt{x-1}+4 \end{gathered}[/tex]when you add a constant b to any function, the graph will be shifted b units up,so
he functinon was shifted 4 units up
hrerefore, we can conclude the answer is
[tex]f(x)=\sqrt{x}[/tex]I hope this helps you
Well GIVE U BRAINLIEST HELP ASAP
Question
Drag the numbers to order them from least to greatest.
Answer : -4/9 , -4/7 , -3/5 , -5/6
Can anyone help me with this problem please and thank you !
Answer:
d = 7
For step by step explaintion I am so sorry but I don't rember enough of my geometry class to properly explain this, but triangles BDC and ABD are congruent (I swear I can prove this if I dig up my old notes but I really do not feel like doing that) so these 2 equations (sides) are equal. So we just solve for d!
6d + 3 = 10d - 25
(we all know how to solve something this simple so I won't bore you with the details of inverse operations and such)
d = 7
Match the following.
The match of the given equations and choices of the properties of equality are;
If a = b and b = c then a = c ; Transitive Property
If a = b then a ÷ c = b ÷ c; Division property of =
a = a; Reflexive property
If x + a = b and x = c then c + a = b; Substitution Property
If a = b then a + c = b + c; Addition Property of =
If a = b then a•c = b•c; Multiplication Property of =
If a•b = a•c then a•c = a•b Symmetric Property
a•(b + c) = a•b + a•c; Distributive property
If a = b then a - c = b - c; Subtraction Property of =
What are the properties of equality?Properties of equality includes; addition, subtraction, transitive, reflexive, and symmetric properties of equality
Transitive PropertyThe transitive property of equality can be stated as follows; If two variables are each equal to a third variable, then the two variables are equal to each other.
Therefore; a = b and b = c then a = c represents the transitive property
Division property of equalityThe division property states that both sides of an equation remain equal, following a division of both sides by the same non zero number
Therefore;
If a = b then a ÷ c = b ÷ c; represents the division property of equality
Reflexive propertyThe reflexive property of equality states that a measure or number is always equal to itself
Therefore;
a = a represents the reflexive property
Substitution PropertySubstitution property indicates that if two variables are equal, then one can replace the other in an equation and the results will remain the same
Therefore;
If x + a = b and x = c then c + a = b; represents the substitution property
Addition and Subtraction Property of EqualityThe statement of the addition (and subtraction) property of equality is that both sides of an equation remain equal following the addition or subtraction of the same amount from both sides the same
Therefore;
If a = b then a + c = b + c; represents the addition property of equality
If a = b then a - c = b - c; represents the subtraction property of equality
Multiplication Property of EqualityThis states that both sides of an equation remain equal following the multiplication of both sides by the same value
Symmetric PropertyThe symmetric property states that two sides of an equation remain equal when their relative positions are interchanged
Distributive PropertyThis states that two sides of an equation remain equal following a distribution with multiplication over addition or subtraction.
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The second angle of a triangle is 10 more than the first angle. The third angle is three times the first. Find the three angles.
First angle:
Second angle:
Third angle:
Answer:
First, let one angle be a variable (eg: x) so that you can form expressions and solve.
Let the first angle be x°.
Then we can form expressions for the second and third angles using the information given.
First angle = x°
Second angle = (x + 10)°
Third angle = (3x)°
Since sum of angles in a triangle is 180°, we can form an equation.
x + (x + 10) + 3x = 180
Simplify and solve for x.
5x + 10 = 180
5x = 170
x = 34
Substitute x into the expressions to find the angles.
First angle = 34°
Second angle = 34 + 10
= 44°
Third angle = 3(34)
= 102°
6
The exchange rate between pounds and US dollars is £1 = $1.27
a) Annie goes on holiday to the USA.
She buys £500 worth of dollars
She spends $550 and converts the rest back to £ at the same rate.
How much money does she receive?
Annie will receive 66.92 euros after converting the dollars into euros post her trip
The exchange rate between pounds and US dollars: 1 Euro = $1.27
Exchange rate: An exchange rate determines the price at which one currency will be exchanged for another and has an impact on international trade and money transfers.
Euro Annie spends to buy dollars = 500
Equivalent dollars received by Annie for 500 euros = 500*1.27
= $635
The money she spent in dollars = $550
Dollars remaining = 635-550 = $85
Euro she will receive after conversion = Dollars remaining/Conversion rate 85/1.27 = 66.92 Euros
So, After changing the dollars into euros after her vacation, Annie will receive 66.92 euros.
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Given that log 2 = a and log 3 = b, express the following in terms of a and b:
a) log 72
Answer:
Step-by-step explanation:
=a, log 3 = b Log 2 log 1.5= log 23/20 год 1.5 = = log 3-log 2 b-a The other terms log 1.2 log 0.24, log 0.5, log 0.836 cannot be expressed only. of in terms a or bor both. [Answer: Log 1.5 Option A
Answer:
[tex]\log 72=3a+2b[/tex]
Step-by-step explanation:
Given:
[tex]\log 2 = a[/tex][tex]\log 3 = b[/tex]Rewrite 72 as a product of 2s and 3s.
[tex]\implies 72 = 2 \times 2 \times 2 \times 3 \times 3[/tex]
[tex]\implies 72=2^3 \times 3^2[/tex]
Therefore:
[tex]\implies \log 72=\log(2^3 \times 3^2)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log xy=\log x + \log y[/tex]
[tex]\implies \log 72=\log(2^3)+\log(3^2)[/tex]
[tex]\textsf{Apply the log power law}: \quad \log x^n=n\log x[/tex]
[tex]\implies \log 72=3\log2+2\log3[/tex]
Substitute the given values of log 2 and log 3:
[tex]\implies \log 72=3a+2b[/tex]
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There are 4 corners at an intersection. A pole at each corner holds 2 traffic light, 1 streetlight, and 2 crosswalk light. How many lights are at the intersection in all ?
Using multiplication we calculate that there are 56 lights in the cross-section.
When two integers are multiplied together in mathematics, the result is a product, or an expression that describes the factors to be multiplied.
The commutative law of multiplication states that the outcome is unaffected by the sequence in which real or complex numbers are multiplied. For instance, the sum of 6 and 5 is 30. (the outcome of multiplication). Usually, the order of the factors determines the outcome of a multiplication of matrices or the constituents of other associative algebras. For instance, multiplication in general and in matrices are non-commutative operations in other algebras.There are many other kinds of products in mathematics: in addition to multiplying just numbers, polynomials, or matrices, one may also define products on a wide range of algebraic expressionsTotal number of lights in each pole = 2 + 1 + 2 = 5 lights
There are 4 corners
Total number of poles = 5 × 4 = 20
So by multiplication we get there are 20 lights in the intersection.
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Review and evaluate the following: By the given y = 2x + 1 ÷ x, what is the value of y when: 1. x=0 2. x = 1 3. x = 2.5 4.x = 1/3 5. x=a
ANSWER
[tex]\begin{gathered} 1)\text{ Undefined} \\ \\ 2)\text{ }3 \\ \\ 3)\text{ }2.4 \\ \\ 4)\text{ }5 \\ \\ 5)\text{ }2+\frac{1}{a} \end{gathered}[/tex]EXPLANATION
We want to find the value of y:
[tex]y=\frac{2x+1}{x}[/tex]for the values of x.
To do this, for each value of x, substitute the values of x into the equation and simplify.
1. x = 0:
[tex]\begin{gathered} y=\frac{2x+1}{x} \\ \\ y=\frac{2(0)+1}{0}=\frac{0+1}{0}=\frac{1}{0} \\ \\ y=\text{ Undefined} \end{gathered}[/tex]The value of y is undefined for x = 0 since any value divided by 0 is undefined.
2. x = 1:
[tex]\begin{gathered} y=\frac{2(1)+1}{1}=\frac{2+1}{1} \\ \\ y=\frac{3}{1} \\ \\ y=3 \end{gathered}[/tex]3. x = 2.5:
[tex]\begin{gathered} y=\frac{2(2.5)+1}{2.5}=\frac{5+1}{2.5} \\ \\ y=\frac{6}{2.5} \\ \\ y=2.4 \end{gathered}[/tex]4. x = 1/3:
[tex]\begin{gathered} y=\frac{2(\frac{1}{3})+1}{\frac{1}{3}}=\frac{\frac{2}{3}+1}{\frac{1}{3}} \\ \\ y=\frac{\frac{5}{3}}{\frac{1}{3}}=\frac{5}{3}*\frac{3}{1} \\ \\ y=5 \end{gathered}[/tex]5. x = a:
[tex]\begin{gathered} y=\frac{2(a)+1}{a}=\frac{2a+1}{a} \\ \\ y=2+\frac{1}{a} \end{gathered}[/tex]That is the answer.
The sales tax is $52 on the purchase of a dining room set for $1040. Find the sales tax rate.
Answer:
Total price including tax: $ 1,092.00
Sales tax rate: 5%
Step-by-step explanation:
Brainlest, Please!
if we take 1040 to be the 100%, what is 52 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1040 & 100\\ 52& x \end{array} \implies \cfrac{1040}{52}~~=~~\cfrac{100}{x} \\\\\\ 20=\cfrac{100}{x}\implies 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
A coffee shop currently sells 440 lattes a day at $2.50 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 60 less lattes a day.
a). Assume that the number of lattes they sell in a day, N, is linearly related to the sale price, p (in dollars). Find an equation for N as a function of p.
N(p)= (blank)
b). Revenue (the amount of money the store brings in before costs) can be found by multiplying the cost per cup times the number of cups sold. Again using p as the sales price, use your equation from above to write an equation for the revenue, R as a function of p.
R(p)= (blank)
c). The store wants to maximize their revenue (make as much money as possible). Find the value of p that will maximize the revenue (round to the nearest cent).
p= (blank) which will give a maximum revenue of $ (blank)
Show your work!
Explain your answer!
No incorrect answer!
No nonsense answers!
No spam answers!
Thanks!
Using linear function concepts, it is found that:
a) The amount of lattes sold function is: N(p) = -240p + 1040.
b) The revenue function is: R(p) = -240p² + 1040p.
c) The revenue is maximized when p = $2.17.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For this problem, we have a linear function with the points having the following format:
(price, lattes sold).
Hence two points are given as follows:
(2.50, 440), (2.75, 380).
The slope is given by change in y divided by change in x, hence:
m = -60/0.25 = -240.
Then:
N(p) = -240p + b.
When p = 2.50, N(p) = 440, hence we solve for b as follows:
440 = -240(2.5) + b
b = 1040.
Thus the function is:
N(p) = -240p + 1040.
The revenue function is:
R(p) = pN(p)
Hence:
R(p) = p(-240p + 1040)
R(p) = -240p² + 1040p.
Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:
p = -b/2a
Hence:
p = -1040/2(-240) = $2.17.
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A data set has a correlation coefficient of 0.013. Which statement about the data is true? a. The data has little or no linear correlation. b. The data has a strong positive linear correlation. c. The data has a weak negative linear correlation. d. The data has a strong negative linear correlation.
Answer: Choice A
The data has little or no linear correlation
======================================================
Explanation:
r = correlation coefficient
The r values are within the interval [tex]-1 \le r \le 1[/tex]
In other words, r is between -1 and 1 inclusive of both endpoints.
r = -1 is the strongest negative correlationr = 1 is the strongest positive correlationr = 0 means there's no linear correlation at all. The data points are either randomly scattered about, or they perhaps fit on some kind of curve.For the case r = 0.013, it's very close to r = 0. This suggests there is very weak positive correlation or practically no linear correlation at all.
A is shaped like a rectangle whose perimeter is 378ft . The length is 8 times as long as the width. Find the length and the width.
The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.
What is the length and the width of the rectangle?The formula used in calculating the perimeter of a rectangle is expressed as;
P = 2( l + w )
Where l is length and w is width.
Given the data in the question;
Let 'x' represent the width of the rectangle.
Width of the rectangle w = xLength of the rectangle l = 8xPerimeter P = 378ftPlug the given values into perimeter formula and solve for x .
P = 2( l + w )
378 = 2( 8x + x )
378 = 2( 9x )
378 = 18x
18x = 378
x = 378/18
x = 21
Now, we find the length and width of the rectangle.
Width of the rectangle w = x = 21ft
Length of the rectangle l = 8x = 8( 21 ) = 168ft
Therefore, the width of the rectangle is 21ft while its length is 168ft.
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A serving of rice is 5/6 of a cup. How many servings are there in a 3 1/3 cup bag of rice?
Answer:
there are 7 severeings of rice
In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.80, the same as the overall proportion of complaints settled in 2016.
Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:
Mean: 160 complaints.Standard deviation: 5.66 complaints.What are the mean and the standard deviation for the binomial distribution?The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.
The mean is given as follows:
[tex]E(X) = np[/tex]
The standard deviation is given as follows:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:
n = 200, p = 0.8.
Hence the mean is:
[tex]E(X) = np = 200 \times 0.8 = 160[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66[/tex]
What is the missing information?The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.
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The value of the ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
The value of the independent variable does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.
What is an independent variable?An independent variable can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.
It is termed “independent” because it's not affected or changed by other variables in an experiment or study.
It is known as a variable that is unaffected in a function and cannot be determined by the other variables in that function.
Other names for an independent variable includes;
Explanatory variableInput variableExposure variableControlled variablePredictor variableHence, the variable is independent.
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11. At Outdoor Adventures Clothing Company, all items are marked up to maximize
profit. Life preservers cost $25 to buy from the manufacturer. They sell for $35. What
is the percent increase on life preservers, to the nearest whole percent?
Using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
What is the percentage?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. By dividing the value by the total value and multiplying the result by 100, one can determine the percentage. The percentage calculation formula is (value/total value)100%.So, the percentage increase in life preserves:
Formula: (selling value - cost)/cost ×100Now, substitute the values in the formula as follows:
(selling value - cost)/cost ×100(35 - 25)/25×10010/25×1000.4×10040%Therefore, using the percentages formula, we conclude that the percentage increase in life preserves is 40%.
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in the pic.............
Given -
a = 2.5 cm
b = 3.6 cm
∠A = 43°
To Find -
Remaining angles and sides =?
Step-by-Step Explanation -
We will start by drawing the diagram:
Now, we know
By, sine rule:
[tex]\begin{gathered} \frac{\sin A}{a}\text{ =}\frac{\sin B}{b}=\frac{\sin C}{c} \\ \\ =\text{ }\frac{\sin43}{2.5}\text{ = }\frac{\sin C}{3.6} \\ \\ =\text{ }\sin C\text{ = }\frac{3.6\times\sin44}{2.5} \\ \\ =\text{ }\sin C\text{ = 0.9820} \\ \\ C\text{ = }\sin^{-1}(0.9820) \\ \\ C\text{ = 79} \\ \end{gathered}[/tex]Now, we know N
A + B + C = 180 c°°
43 + B + 79° = 180°°
B = 180° - 799 - 43°°
B = 58°
Now, Side b =
[tex]\begin{gathered} \frac{\sin A}{a}\text{ = }\frac{\sin B}{b} \\ \\ \frac{\sin43}{2.5}\text{ = }\frac{\sin58°}{b} \\ \\ b\text{ = }\frac{2.5\times\sin58°}{\sin43°} \\ \\ b\text{ = 3.1} \end{gathered}[/tex]Final Answer -
∠B = 58B°
∠C = 797°
Side, b = 3.1 cm
Please help I’ll mark you as brainliest if correct!!
Answer:The answer is 8
Step-by-step explanation:
21-13
3. Allison Separates 23 stickers into 4 4 equal piles. How many stickers does she have left over?
If X - N(-3,4), find the probability that x is between -6 and 6. Round to 3 decimal places.
The probability that x is between -6 and 6 is 18.84%.
What is defined by the term normal distribution?The symmetry of the normal distribution is well known. This means that the distribution is just not skewed. We can easily calculate probabilities using this distribution; all we need are the z scores. The Standard Normal Distribution would be a probability distribution with known and constant parameters. That really is, the parameters remain unchanged.For the given question;
The probability of x should line between -6 and 6.
The formula for calculating the z-score is;
z = (x - μ)/σ
μ = mean (-3)
σ = standard deviation (4)
Put the values in the formula.
For x = -6
z = (-6 - (-3))/4
z = -3/4
z = -0.75
Now, x = 6
z = (-6 - 3)/4
z = -9/4
z = -2.25
P(-6 < x < 6) = P(-0.75 < x < -2.25)
Find the probability using negative z score.
P(-6 < x < 6) = 0.197 - 0.0122
P(-6 < x < 6) = 0.1848
P(-6 < x < 6) = 18.84%
Thus, the probability that x is between -6 and 6 is 18.84%.
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how do you find the equation of line passing through (0,0) and (4,4)
Answer:
y = mx
Step-by-step explanation:
It depends on what form of the line that you want. Usually the slope intercept form is wanted.
y = mx + b We need to have the m (slope) and the b (the y-intercept)
The slope is the change in y over the change in x.
Ordered pairs are in the form (x,y)
(0,0) and (4,4) Have x's of 4 and 0, and y's of 4 and 0. We subtract these to find the changes in y and x.
[tex]\frac{4-0}{4-0}[/tex] This is [tex]\frac{4}{4}[/tex] which is the same as 1. The slope (m) is 1.
Now we need to find the y -intercept. The y intercept is the point where x is 0 (0,b). They give us this point (0,0,) So the y -intercept is zero.
y = 1m + 0
or y =mx
in 2018, the population of los Angeles county, California, was 10,137,915. if los Angeles County covers 4,751 square miles, what's the average population density in the county?
The average population density in the county is:
10,137,915 people / 4,751 square miles = 2133.84 people / square mile
Rounding to nearest integer, we have: 2134 people / square mile
Volunteers are preparing identical backpacks for refugees. There are 32 maps and 24 dictionaries to use for the backpacks. What is the greatest number of backpacks they can prepare using all of the maps and dictionaries?
Considering the definition of greatest common divisor, the greatest number of backpacks volunteers can prepare using all of the maps and dictionaries is 8.
Definition of greatest common divisorConsidering that a divisor can be formally defined as that number that is contained in another exactly n times, the greatest common divisor is the largest number by which two or more numbers can be divided. That is, the greatest common factor is the highest number by which a set of numbers can be divided, resulting in a whole number.
To calculate the greatest common factor, the following steps must be followed:
Decompose each number into prime factors. [The prime factors of an integer are the exact divisors of that integer, that is, they have only two divisors: one and themselves]Then point out the common factors.In each of the common factors, choose the factor with the smallest exponent.Multiply the chosen factors.Greatest number of backpacks preparedIn this case, you must calculate the greatest common factor as follows:
Decomposition of 32: 2⁵Decomposition of 24: 2³×32 is the factor common to both numbers, with 3 being the smallest exponent found. Then the greatest common divisor is calculated as:
Greatest common divisor= 2³
Greatest common divisor= 8
This means that they can prepare 8 backpacks.
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Indira finds that on a typical day, 4 out of every 5 students at her school eat a
cafeteria lunch. The rest of the students bring their lunch from home. Indira's
school has 495 students. On a typical day, how many students at her school bring
their lunch from home? Show your work.
By using fractions, we can conclude that 99 students bring their lunch from home.
What is a fraction?Consider a collection of items from which some of their components have been stolen. A fraction is a name given to the portion that was taken. The denominator is the bottom portion of the fraction, and the numerator is the upper portion.So, the Fraction of students eating a cafeteria lunch at her school = 4/5
A fraction of students bring their lunch from home:
1 / 4/55/4/51/5495 students attend her school in total.
Several students bring their lunch from home, including:
1/5 × 49599Therefore, by using fractions, we can conclude that 99 students bring their lunch from home.
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HELP PLEASE WILL GIVE BRAINLIEST!!! I NEED HELP
Answer: y = -x + 3
Step-by-step explanation:
y = mx + b
We need to find the slope of the equation first.
Change in y: 7 - 0 = 7
Change in x: -4 - 3 = -7
Slope = Change in y / Change in x
slope = 7 / -7 = -1
Now, plug the slope into the equation to find b.
0 = -1(3) + b
b = 3
or 7 = -1(-4) + b
b = 3
Harry just deposited $1500 into a savings account giving 6% interest compounded monthly. How much will be in the account after 10 years and 20 years ?
Compound Interest
It occurs when the interest is reinvested rather than paying it out.
When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.
The formula is:
[tex]{\displaystyle A=P\mleft(1+{\frac{r}{n}}\mright)^{nt}}[/tex]Where:
A=final amount
P=initial principal balance
r=interest rate
n=number of times interest applied per time period
t=number of time periods elapsed
Harry deposited an initial amount of P = $1500.
The savings account gives r = 6% = 0.06 interest
Since the interest is compounded monthly, n = 12 (there are 12 months in a year)
The time is t = 10 years.
Now we apply the formula:
[tex]\begin{gathered} {\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot10}} \\ \text{Calculating:} \\ {\displaystyle A=1500(1+0.005)^{120}} \end{gathered}[/tex]Using a calculator:
A = $2729.095
Rounding to two decimals,
A = $2729.10
Harry will have $2729.10 in his account after 10 years
Now for t = 20 years:
[tex]{\displaystyle A=1500(1+{\frac{0.06}{12}})^{12\cdot20}}[/tex]Calculating again:
A = $4965.31
Harry will have $4965.31 in his account after 20 years
Which value must be added to the expression x² - 8x to make it a perfect-square trinomial?
04
O-16
O-4
O 16
Answer: 16
Step-by-step explanation:
The standard form of a perfect square trinomial is:
[tex](x-a)^{2} = x^{2}-2ax+a^{2}[/tex]
Put the equation into standard form:
[tex]x^{2} -8x+c[/tex]
Compare to to the form of a perfect square trinomial:
[tex]-8x=-2ax\\\frac{-8x}{-2x}=a\\a=4[/tex]
Plug a back into the equation to get c:
[tex]c=a^{2}=4^{2}\\c=16[/tex]
Putting everything back together gives you:
[tex](x-4)^{2} = x^{2}-8x+16[/tex]
The required, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial. Option D is correct.
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.
To make the expression x² - 8x a perfect-square trinomial, we need to add the square of half of the coefficient of x to the expression.
The coefficient of x is -8, so half of it is -4. The square of -4 is 16.
Therefore, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial.
Answer: 16.
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