The equation of the line that passes through the given points is y= -4x+23.
Linear FunctionA line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:
a= the slope
b=constant term that represents the y-intercept.
From the stardard form equation:
For point (5,3) : 3=5a+b ( equation 1)For point (9,-13) : -13=9a+b (equation 2)Solving the system for equations 1 and 2.
3=5a+b
-13=9a+b * (-1)
3=5a+b
13=-9a-b * (-1)
16= -4a
4= -a
a= -4
If a= -4 from equation 1, you have
3= 5 * (-4)+b
3= -20+b
b=23
Therefore, the line equation is y= -4x+23.
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5. Find the quadratic equation with root alpha and beta,given that alpha-beta=2 and alpha^2-beta^2=3.
Answer:
[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
Step-by-step explanation:
[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]
Then
2α = 2 + 3/2 = 7/2
2β = (3/2) - 2 = -1/2
Then
Then
α = 7/4
β = -1/4
Then
a quadratic equation with root α and β can be :
[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]
[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
Need help with this geometry question
Answer: 59
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle intercepted by it.
Hello, I would like help with his question. Please do as quickly as you can, Thank you.
Answer:
Step-by-step explanation:The answer is 45
Find the length of AB.
OA. 89 units
OB. About 3.6 units
OC. 13 units
O D. About 9.4 units
Applying the distance formula, the length of AB is: D. About 9.4 units.
What is the Distance Formula?Distance formula is given as: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the following:
A(4, 2) = (x1, y1)
B(9, 10) = (x2, y2)
Apply the distance formula
AB = √[(9−4)² + (10−2)²]
AB = √[(5)² + (8)²]
AB = √89
AB ≈ 9.4 units
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Find two functions f(x) and g(x) such that h(x) = ( f∘ g)(x) , if h(x) = √ + 5
f(x) = ____________________
g(x) = ____________________
If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.
How to find the two functions behind a composed function
Let be f and g two functions, h is a composition of f with respect to g when the input variable of f is equal to g. The composed function is h(x) = √x + 5 and there may be more than a solution. One of these solutions are f(x) = x + 5 and g(x) = √x.
If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.
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John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.
David will be 10 and John will be 9
Please help I’m confused
Answer:
Step-by-step explanation:
in 1979 the Wincom river was 33 feet below the bridge. Because of silt build-up in the river bottom, the
river was only 12 feet below the bridge by 1986. Write an equation for the distance of the river from the
bridge, d, with t = 0 representing 1979. If the silt build-up continues at the same rate, what year will the
river reach the bridge?
Answer: d = 40 - 5/2t; 1995
Hope it helps :)
The temperature of a chemical reaction ranges between -10 degrees Celcius and 50 degrees Celcius. The temperature is at its lowest point when t=0, and the reaction completes 1 cycle during a 6 hour period. What is a cosine function that models this reaction?
Answer:
The cosine function is f(t) = -30sin(π÷3)t + 20
Step-by-step explanation:
Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.
To find : What is a cosine function that models this reaction?
General form of cosine function is f(x) = A cos(Bx)+C
Where A is the amplitude
B=2π÷Period
C is the midline
Now, We have given
The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.
A is the average of temperature,
i.e,
A=(-10-50)÷2 = -30
Period of 1 cycle is 6 hour
So,
B = 2π÷6 = π÷3
The temperature is at its lowest point when t = 0 and we know lowest point is -10
So,
f(t) = A cos t + C
-10 = -30 cos 0 + C
Therefore, C = 20
Substituting the values, we get
The cosine function is f(t) = -30sin(π÷3)t + 20
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An entrance examination for a job consists of 25% English, 50% Mathematics, 5% Typing and 20% Accounting, and the passing mark is 50. If an applicant sat for the examination and scored 48% in English, 35% in Mathematics, 80% in Typing and 50% in Accounting, do you think she will be accepted? Why?
Answer:
No, the total is 43.5 which is below 50.
Step-by-step explanation:
English: 25% × 48 = 12
Mathematics: 50% × 35 = 17.5
Typing: 5% × 80 = 4
Accounting 20% × 50 = 10
12 + 17.5 + 4 + 10 = 43.5
Total: 43.5
Passing: 50
Answer: No. The total is too low.
The Bun-and-Run is a franchise fast-food restaurant located in the Northeast specializing in halfpound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French fries are
also available. The planning department of Bun-and-Run Inc. reports that the distribution of
daily sales for restaurants follows the normal distribution and that the population standard
deviation is $3,000. A sample of 40 showed the mean daily sales to be $20,000. Find the 95%
confidence interval for the population mean.
Answer:
franchise fast-food restaurant located in the Northeast specializing in halfpound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French fries are
also available. The planning department of Bun-and-Run Inc. reports that the distribution of
daily sales for restaurants follows the normal distribution and that the population standard
deviation is $3,000. A sample of 40 showed the mean daily sales to be $20,000. Find the 95%
confidence interval for the population mean.
6(2x²-5) = [?]
x = -3
Answer:
78
Step-by-step explanation:
plug in -3 as x
6(2(-3)^2-5)
6(2(9)-5)
6(18-5)
6(13)
78
Need help with this! Brainliest to who answers.
Answer: K
Step-by-step explanation:
The subtraction with the negatives can cancel out, resulting in a possible positive answer.
Answer:
k
Step-by-step explanation:
K you CAN get a positive number....
example :
-3 - (-5) = -3 + 5 = + 2
Adriana can ride her bicycle
6 miles in one hour. How long will it
take her to ride 15 miles?
I need someone to do this for me please!
Thank you so much in advance :D
Answer:
[tex] \cfrac{61}{24} [/tex]
Step-by-step explanation:
Given expression:
[tex] \cfrac{2}{3} + \bigg(\cfrac{5}{2} \bigg) {} ^{ 2} \times \cfrac{3}{10} [/tex]
Solution:
Simplify using PEMDAS.
[tex] = \sf \cfrac{2}{3} + \cfrac{25}{4} \times \cfrac{3}{10} \\ \\ = \cfrac{2}{3} + \cfrac{15}{8} \\ \\ = \cfrac{16 +45 }{24} \\ \\ = \boxed{\cfrac{61}{24} }[/tex]
Done!
Answer:
[tex]\frac{61}{24}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] + ( [tex]\frac{5}{2}[/tex] )² × [tex]\frac{3}{10}[/tex] ← evaluate exponent
= [tex]\frac{2}{3}[/tex] + [tex]\frac{25}{4}[/tex] × [tex]\frac{3}{10}[/tex] ← evaluate multiplication ( cancel 25 and 10 by 5 )
= [tex]\frac{2}{3}[/tex] + [tex]\frac{5}{4}[/tex] × [tex]\frac{3}{2}[/tex]
= [tex]\frac{2}{3}[/tex] + [tex]\frac{15}{8}[/tex] ← evaluate addition
= [tex]\frac{2(8)}{3(8)}[/tex] + [tex]\frac{15(3)}{8(3)}[/tex]
= [tex]\frac{16}{24}[/tex] + [tex]\frac{45}{24}[/tex]
= [tex]\frac{61}{24}[/tex]
square root of 0.98 simplified
Answer:
0.98994949366117
√0.98 = 0.98994949366117
Step 1:
Divide the number (0.98) by 2 to get the first guess for the square root.
First guess = 0.98/2 = 0.49.
Step 2:
Divide 0.98 by the previous result. d = 0.98/0.49 = 2.
Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).
Error = new guess - previous value = 0.49 - 1.245 = 0.755.
0.755 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.
Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).
Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.
0.2289257028 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.
Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).
Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.
0.0257889495 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.
Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).
Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.
0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.
So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.
Note: There are other ways to calculate square roots. This is only one of them.
To round it to the tenths, it's 1
To round to the hundredths, it's.99
Thousandth is.990
Which of the following is most likely the next step in the series?
⠀⠀
The next step in the series is choice D.
Answer:
D
Step-by-step explanation:
if we define the diagrams in terms of their rows and columns, then
1st : 2 by 1
2nd : 3 by 2
3rd : 4 by 3
note that the rows and columns both increase by 1
then the next likely diagram is
5 by 4 , that is diagram D
An equation is shown below:
6(3x − 7) = 2
Which of the following correctly shows the beginning steps to solve this equation?
Step 1: 9x − 1 = 2
Step 2: 9x = 3
Step 1: 9x − 7 = 2
Step 2: 9x = 9
Step 1: 18x − 7 = 2
Step 2: 18x = 9
Step 1: 18x − 42 = 2
Step 2: 18x = 44
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex] \texttt{Step 1: 18x − 42 = 2} [/tex][tex] \texttt{Step 2: 18x = 44 } [/tex]____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: 6(3x - 7) = 2[/tex]
Step 1 -
[tex]\qquad \tt \rightarrow \: 18x - 42 = 2[/tex]
[ distributive property ]
Step 2 -
[tex]\qquad \tt \rightarrow \: 18x = 2 + 42[/tex]
[tex]\qquad \tt \rightarrow \: 18x = 44[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
d) Step 1: 18x - 42 = 2
Step 2: 18x = 44
Step-by-step explanation:
Given equation,
→ 6(3x - 7) = 2
Now the value of x will be,
→ 6(3x - 7) = 2
→ 6(3x) - 6(7) = 2
→ 18x - 42 = 2
→ 18x = 2 + 42
→ 18x = 44
→ x = 44/18
→ [ x = 22/9 ]
Hence, value of x is 22/9.
A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 8 inches.
Part A: Write a list of 6 ordered pairs to show the height of the candle in inches (y) as a function of time in hours (x) from the first hour after it started burning. For example, the point (0, 8) would represent a height of 8 inches after 0 hours. Explain how you obtained the ordered pairs. (5 points)
Part B: Is this relation a function? Justify your answer using the list of ordered pairs you created in Part A. (2 points)
Part C: If the rate at which the candle burned was 0.4 inches per hour instead of 0.5 inches per hour, would the relation be a function? Explain your answer using input and output values. (3 points)
The ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
How to determine the ordered pairs?The given parameters are:
Initial height, h = 8 inches
Rate = 0.5 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.5x
Set x = 0 to 5
y = 8 - 0.5(0) = 8
y = 8 - 0.5(1) = 7.5
y = 8 - 0.5(2) = 7
y = 8 - 0.5(3) = 6.5
y = 8 - 0.5(4) = 6
y = 8 - 0.5(5) = 5.5
So, the ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)
Is the relation a function?In (a), we have:
y = 8 - 0.5x
The above is a linear relation.
All linear relations are functions
Hence, the relation is a function.
Would a new relation be a function?
We have
Initial height, h = 8 inches
New rate = 0.4 inches per hour
The height of the candle at x hour is:
y = Initial - rate * x
This gives
y = 8 - 0.4x
The above is a linear relation.
All linear relations are functions
Hence, the new relation is also a function.
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Because the two distributions displayed below have similar shapes, they have
the same standard deviation.
A. True
B. False
Answer:
False, distributions having the same mean and standard deviation can have very different shape of distribution.
The crime rate of a certain city is increasing by exactly 4% each year. If there were 350
crimes in the year 1990 and the crime rate remains constant each year, determine the approximate number of crimes in the year 2023.
Answer:
1277
Step-by-step explanation:
350 * (1.04)^33 =
1276.93338385
algebracom
theo(12211)
Help, Help, Brainliest available to the best Answer!
Find the Variance
Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².
What is the variance of a data-set?The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.
The mean is the sum of all observations divided by the number of observations, hence:
M = (145 + 175 + 180 + 205 + 120)/5 = 165.
And the variance, in lbs squared, is given by:
V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.
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Someone please help me!
…….
Half of the chimpanzees in a zoo weigh less than 45 kg.
of the chimpanzees weigh less than 55 kg.
No chimpanzees weigh exactly 45 kg.
What fraction of the chimpanzees weigh between 45 kg and 55 kg?
Answer:
[tex] \frac{45}{55} = \frac{3}{11} [/tex]
Step-by-step explanation:
I think that is the right answer
()
8
What is 11 - 2³
Answer:
[tex]11 - 2 {}^{3} [/tex]
[tex]11 - 8[/tex]
[tex]3[/tex]
A polynomial-function has −5+√3 as a root. Which of the following must also be a root of the function?
O-5-√√3
0 -5+√√√31
05-√√√31
0 5+√√31
Answer:
First option.
Step-by-step explanation:
Find g(32) for g(x) = x+4−−−−√.
A. 3
B. 5
C. 6
D. 10
Answer:
6
Step-by-step explanation:
I presume you meant
[tex]g(x) = \sqrt{x + 32} \\ g(32) = \sqrt{32 + 4} \\ g(32) = \sqrt{36} \\ g(32) = 6[/tex]
Dan Barker, the chief engineer, told Ms. Silva that the company is currently making 150 units of Model Diamond per batch and 245 units of Model Gold per batch. He suggests doubling the batch sizes to cut the number of setups in half, thereby reducing the setup cost by 50 percent. Compute the cost per unit for each product if Ms. Silva adopts his suggestion.
The cost per unit for each product is given as:
x ≈ 0.0067; and
y ≈ 0.0041. See explanation below.
What is the cost per unit for each product?Given that the current production:
Model Diamond (Md) - 150 UnitsModel Gold (Mg) - 245 UnitsCurrent cost of production is given as:
Current Total Cost = 150y + 245x where;
if doubling the batch sizes will reduce the cost per unit by 50% then the new cost equation will be:
Thus, New Total Cost of production = (150 x 2) (y/2) + (245 x 2) (x/2)
= (300)(y/2) + (490) (x/2)
Since we are looking for the cost per unit of each product:
f(x) = 300 * (x/2)..........Unit cost of Model Gold
If we make x subject of the formula, then we arrive at:
1/300 = x/2
x = (1/300) * 2
x = 0.00666666666
x ≈ 0.0067
f(x) = 490* (x/2)
If we make y subject of the formula, then we arrive at:
i/490 = y/2
y = (1/490) * 2
y = 0.00408163265306122448979591836735
y ≈ 0.0041
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Write an expression in factored form for the polynomial of least possible degree graphed below.
The expression in factored form for the polynomial of least possible degree graphed will be y(x) = (x + 3)(x + 2 )(x - 1 )(x - 3 )
How to factor the polynomial?From the graph, the zeros of the polynomial of given graph are:
x = -3
x = -2
x = 1
x = 3
Equate the above equations to zero
x + 3 = 0
x + 2 = 0
x - 1 = 0
x - 3 = 0
Multiply the equations
(x + 3)(x + 2 )(x - 1 )(x - 3 ) = 0
Express as a function gives;
y = (x + 3)(x + 2 )(x - 1 )(x - 3 )
Hence, the factored form of the polynomial will be y = (x + 3)(x + 2 )(x - 1 )(x - 3 )
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Please answer this question i really want answers :(
Based on the hints of distinguishing between radical and non-radical numbers, we have the following lists:
[tex]\sqrt{3}[/tex], [tex]2.\overline{2}[/tex], 2.5, [tex]\sqrt{5}[/tex]3.01, [tex]3.\overline{01}[/tex],[tex]3.\overline{1}[/tex], [tex]\sqrt{9}[/tex][tex]-4.\overline{1}[/tex], - 4.1, 4.01, [tex]\sqrt{17}[/tex]- 2.5, [tex]-\sqrt{5}[/tex], [tex]\sqrt{6}[/tex], 2.5How to order numbers from least to greatest
In this question we must order sets of numbers in ascending order. A hint consists in comparing non-radical numbers with the closest radical numbers whose results are integers.
In consequence, we obtain the following orders:
[tex]\sqrt{3}[/tex], [tex]2.\overline{2}[/tex], 2.5, [tex]\sqrt{5}[/tex]3.01, [tex]3.\overline{01}[/tex],[tex]3.\overline{1}[/tex], [tex]\sqrt{9}[/tex][tex]-4.\overline{1}[/tex], - 4.1, 4.01, [tex]\sqrt{17}[/tex]- 2.5, [tex]-\sqrt{5}[/tex], [tex]\sqrt{6}[/tex], 2.5To learn more on sets: https://brainly.com/question/18877138
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6ac+bd-3bc-2ad help
Answer:
(2a-b)(3c-d)