A function, f, passes through the points (1,1), (2,7) and (3,25). A function, g, passes through the points (1,36), (2,43) and (3,50).

Select the correct answer.

Option B:

Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].

Solution:

Take two points on the line (0, 1) and (4, 3).

So, [tex]x_1=0, y_1=1, x_2=4, y_2=3[/tex].

Slope of the line:

[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]$m=\frac{3-1}{4-0}[/tex]

[tex]$m=\frac{2}{4}[/tex]

[tex]$m=\frac{1}{2}[/tex]

y-intercept means the point which crosses at y-axis.

Here the point on the y-axis is (0, 1).

y-intercept (b) = 1

Slope-intercept form:

y = mx + b

[tex]$y=\frac{1}{2}x+1[/tex]

Equation of the line of best fit in slope-intercept form is [tex]y=\frac{1}{2}x+1[/tex].

Option B is the correct answer.

Answer:

This is false

Step-by-step explanation:

xy is one term, x+y would be two terms

Answer:

False

Step-by-step explanation:

In an algebraic expression with terms, the terms are added together. Here all you have is x multiplied by y. xy is a single term. Since no term is being added to the term xy, all you have is one term, not two.

Answer:

A. When x = 3, both expressions have a value of 30.

Step-by-step explanation:

The first expression is 4(x+3)+2x

The second expression is 6(x+2).

When we substitute x=3 into the first equation, we get:

[tex]4(3 + 3) + 2(3) = 4 \times 6 + 6 = 24 + 6 = 30[/tex]

When we substitute x=3 into the second expression we get:

[tex]6(3 + 2) = 6(5) = 30[/tex]

This proves that the two expressions are equivalent.

The correct choice is A

Answer: A

Step-by-step explanation:

Hope this helps can i have brainly-est please

Here we need to solve some expressions. Remember the following rules:

[tex](+)(+)=+ \\ \\ (-)(-)=+ \\ \\ (+)(-)=- \\ \\ (-)(+)=-[/tex]

Then, from the left side:

[tex]5-2\cdot 7=5-14=\boxed{-9} \\ \\ 5-2\cdot 4=5-8=\boxed{-3} \\ \\ 5-2\cdot 0=5-0=\boxed{5} \\ \\ 5-2\cdot -3=5+6=\boxed{11} \\ \\ 5-2\cdot 10=5-20=\boxed{-15} \\ \\ 5-2\cdot -8=5+16=\boxed{21} \\ \\[/tex]

from the right side:

[tex]-(-4)+3=4+3=\boxed{7} \\ \\ -(6)+3=-6+3=\boxed{-3} \\ \\ -(-8)+3=8+3=\boxed{11} \\ \\ -(-5)+3=5+3=\boxed{8} \\ \\ -(2)+3=-2+3=\boxed{1} \\ \\ -(15)+3=-15+3=\boxed{-12} \\ \\ -(-6)+3=6+3=\boxed{9}[/tex]

Answer:

32

Step-by-step explanation:

let a = 5

a² + 7 | Original equation

5² + 7 | Substitution of a as 5

25 + 7 | 5 to the power of 2 is 25, as 5*5 = 25.

32       | 25 + 7 = 32

Answer:

2-2-2

History

The 2-2-2 configuration appears to have been developed by Robert Stephenson and Company in 1834, as an enlargement of their 2-2-0 Planet configuration, offering more stability and a larger firebox. The new type became known as Stephenson's Patentee locomotive.[1] Adler, the first successful locomotive to operate in Germany, was a Patentee supplied by Robert Stephenson and company in component form in December, 1835 was one of the earliest examples. Other examples were exported to the Netherlands, Russia and Italy.[2] By 1838 the 2-2-2 had become the standard passenger design by Robert Stephenson and Company.[3]

Eighteen of the first nineteen locomotives ordered by Isambard Kingdom Brunel for the opening of the Great Western Railway in 1837/8 were of the 2-2-2 type.[4] These included six 2-2-2 locomotives built by Charles Tayleur at his Vulcan Foundry. Also in 1837 the successful North Star broad gauge locomotive was delivered to the Great Western Railway by Stephenson, becoming the first of a class of twelve locomotives by 1841.

Great Western Railway North Star at Swindon

Later UK developments

Sharp, Roberts and Company constructed more than 600 2-2-2 locomotives between 1837 and 1857. Ten of these supplied to the Grand Junction Railway became the basis of Alexander Allan's successful designs for the railway from 1845 (the first of which, formerly named Columbine, is preserved). J. & G. Rennie supplied 2-2-2 locomotives to the London and Croydon Railway from 1838 and the London and Brighton Railway in 1840.[5] Arend ("eagle") was one of the two first steam locomotives in the Netherlands, built by R. B. Longridge and Company of Bedlington, Northumberland in 1839.

The Great Western Railway continued to order both broad gauge and standard gauge locomotives on the railway, including the Firefly and Sun classes (1840–42), which were enlarged versions of North Star. Bury, Curtis, and Kennedy supplied six 2-2-2 locomotives to the Bristol and Gloucester Railway in 1844, and fourteen to the Great Southern and Western Railway in Ireland in 1848, (the last of these has been preserved at Cork Kent railway station.

The original "Jenny Lind" locomotive, 1847.

The Jenny Lind locomotive, designed by David Joy and built in 1847 for the London Brighton and South Coast Railway by the E.B.Wilson and Company of Leeds, became the basis of hundreds of similar passenger locomotives built during the 1840s and 1850s by this and other manufacturers for UK railways. The London & North Western Railway Cornwall locomotive was designed at Crewe Works as a 4-2-2 by Francis Trevithick in 1847, but was rebuilt as a 2-2-2 in 1858.

Although by the 1860s the 2-2-2 configuration was beginning to be superseded by the 2-4-0 type with better adhesion, the invention of steam sanding gave 2-2-2 singles a new lease of life, and they continued to be built until the 1890s. Notable late examples include William Stroudley's singles of 1874-1880, William Dean's 157 class of 1878-79,[6] and his 3001 class (1891–92),[7][8] both for the Great Western Railway. James Holden of the Great Eastern Railway created some 2-2-2 singles in 1889 by removing the coupling rod from a 2-4-0.

Belgium

Replica of 'Le Belge' 1835

The first steam railway locomotive built in Belgium in 1835, and was built by John Cockerill under license to a design by Robert Stephenson & Co. It was built for use on the first main line on the European mainland, the Brussels-Mechelen line.[9] A replica was built at the workshops of Boissellerie Cognaut for the 150th anniversary of the formation of Belgium.[10]

Italy

Two 2-2-2 locomotives were imported from Longridge and Co of Bedlington Ironworks England for the Naples–Portici railway in 1839 named Bayard and Vesuvio. A replica of 'Bayard is at the Naples Railway Museum.[11]

Germany

Most of the earliest locomotives to operate in what is now Germany before the mid-1840s were 2-2-2s delivered by UK manufacturers. However, by 1839 the type was also being built locally see List of Bavarian locomotives and railbuses. The Pegasus of 1839 was the first locomotive to be built by the Sächsische Maschinenbau-Compagnie in Chemnitz. August Borsig and Company manufactured Beuth in 1843 which was highly successful; its valve design became de facto standard for locomotives for decades to come.[12] By 1846 he had manufactured more than a hundred similar locomotives. Both the Leipzig-Dresden Railway and Royal Bavarian State Railways (Königlich Bayerische Staatsbahn) built several 2-2-2 classes 1841-1859. Similarly, the Grand Duchy of Mecklenburg Friedrich-Franz Railway grouped various 2-2-2 steam locomotives procured from German manufacturers between 1848 and 1863 into its Mecklenburg I class.

Answer: /2 is not greater than 6/8 and the answer to the question "Is 1/2 greater than 6/8?" is no. Note: When comparing fractions such as 1/2 and 6/8, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.

Answer:

6/8 is greater than 1/2

Step-by-step explanation:

Answer:

[tex]r=3.93\%[/tex]

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=18\ years\\ P=x\\A=2x\\ r=?\\n=1[/tex]  

substitute in the formula above

[tex]2x=x(1+\frac{r}{1})^{1*18}[/tex]  

[tex]2=(1+r})^{18}[/tex]  

Elevated both sides to 1/18

[tex]2^{\frac{1}{18}} =1+r[/tex]

[tex]r=2^{\frac{1}{18}} -1[/tex]

[tex]r=0.0393[/tex]

convert to percentage

Multiply by 100

[tex]r=3.93\%[/tex]

Answer:

A. 1

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The other dude did have the right answer, but for an explanation, you:

1. Take the 51,000 and multiply it by 22.65% (The sum of taxes for this job). You get 39448.5. You take 39448.5 and divide it by 12 (for monthly net income) and you get 3287.375 a month.

Then you:

2. Take 54,000 and multiply it by 28.65 (the sum of taxes for this job (remember that this job has an extra tax of 6%)). You get 38529. You take 38529 and divide it by 12 (for monthly net income) and you get 3210.75 a month.

Finally:

3. You just compare the monthly net incomes and see that marketing manager job pays around 70 more dollars a month. Hope that helped!

Answer:

Step-by-step explanation:

In the image attached you can notice that line ZY is tangent at point Y.

Remember that the radius is always perpendicular to tangents, by definition, that means [tex]XY \perp ZY[/tex].

That means [tex]\triangle XYZ[/tex] is a right triangle where [tex]\angle Y = 90\°[/tex].

All these facts are deducted form having ZY as a tangent.

We know by given that

[tex]XZ=8+9=17[/tex]

[tex]XY=8[/tex], becaus it's the radius.

Using Pythagorean Theorem

[tex]17^{2} =8^{2}+ZY^{2}[/tex]

Solving for [tex]ZY[/tex]

[tex]ZY=\sqrt{17^{2} -8^{2} } \\ZY=\sqrt{289-64}\\ ZY=\sqrt{225}\\ ZY=15[/tex]

Therefore, the length of ZY must be 15 units to be tangent to circle X.

Answer:

15 units

Step-by-step explanation:

The guy above me has got it right! :D

Step-by-step explanation:

Total area of merged figure = area of vertical rectangle + area of horizontal rectangle.

[tex] \therefore \: 3x(2x - 7) + (3x + 4)x = 85 \\ \\ \therefore \: 6 {x}^{2} - 21x+ 3 {x}^{2} + 4x = 85 \\ \\ \therefore \: 6 {x}^{2} + 3 {x}^{2} - 21x + 4x - 85 = 0 \\ \\ \huge \red {\boxed {\therefore \: 9 {x}^{2} - 17x - 85 = 0}} \\ hence \: proved.[/tex]

Answer:

Step-by-step explanation:

(3x + 4)(x) + (2x - 7)(3x) = 85

3x² + 4x + 6x² - 21x = 85

9x² - 17x - 85 = 0

Answer:

See below

Step-by-step explanation:

Let's check:

34*1/2 does equal 17, so Yes

51*2/3 does equal 34, so Yes

34*3/8 does not equal 12, so No

300*1/9 does not equal 34, so No

Answer:

This is a statement not a question

Answer:

Y=1/3x

Step-by-step explanation:

1) there is no y intercept as x=0 when y=0 so that rules out y=x-2

2) next, we will use the formula for slope to find the value of m

Y2-Y1/X2-X1

Where y2=-1

Y1=0

X2=-3

X1=0

So

-1-0/-3-0=-1/-3

Aka 1/3

So y=1/3x

Hope this helps!

Answer: 3% (3/100), 4% (1/25), and 5% (1/20)

Step-by-step explanation:

So, there are 100 recordable DVDs, and 5 are defective. The way you find the answer is by dividing 100 by 100, which equals one. That means you have a one percent chance to select one random DVD. But, since you need to find the probability of selecting at least three non-defective DVDs, you would need to multiply 1 by 3, 4 or 5 to get the percentages for you probability.

Final answer:

The probability of selecting at least three non-defective disks from a pack with 5 defective ones among a total of 100 is found by summing the probabilities of selecting exactly three non-defective disks plus the probability of selecting all four non-defective disks.

Explanation:

The question asks for the probability of selecting at least three non-defective disks from a pack that contains 100 recordable DVDs, with 5 being defective. To solve this, we consider the scenarios where 3 or 4 non-defective disks are chosen out of the 4 disks we pick. We will calculate these probabilities using the hypergeometric distribution, which is apt for scenarios where we have a finite population without replacement.

Calculating the Probability:

Let X represent the number of non-defective disks selected.

There are two outcomes where at least three disks are non-defective: when exactly 3 are non-defective (one is defective) or when all 4 are non-defective.

Probability of selecting 3 non-defective disks and 1 defective disk (X = 3):
P(X = 3) = [number of ways to choose 3 non-defective from 95]
imes [number of ways to choose 1 defective from 5] / [number of ways to choose 4 from 100].

Probability of selecting 4 non-defective disks (X = 4):
P(X = 4) = [number of ways to choose 4 non-defective from 95] / [number of ways to choose 4 from 100].

The total probability of selecting at least three non-defective disks is the sum of these two probabilities: P(X = 3) + P(X = 4).

Answer: 4*p=8

Step-by-step explanation:

You can use inverse operation to answer this equation.

Answer:

4*p=8

Step-by-step explanation: I took the test

Value of x is 5. I remember doing this last year..

35a+45b=80

then we would do 99-80, and that gives us the value of c, 19

Answer:

maybe just 41?

Step-by-step explanation:

It's asking for the small arc XY, so that would just be 41. Correct me if i'm wrong

Answer:

[tex]y=\frac{1}{4}x[/tex]    [tex]x=4y[/tex]

Step-by-step explanation:

Assuming

y = inches of rain

x = hours (The x latitude is usually used for time)

Answer: B) line reflection

The orientation will flip with a reflection. So if points A,B,C are going clockwise for instance, then A', B', and C' will go counterclockwise.

Answer:

51

Step-by-step explanation:

Answer:

51°

Step-by-step explanation:

90 - 39 = 51

Answer:

average = sum of observations/number

80=400/5

Therefore, the sum of the scores has to equal 400.

Step-by-step explanation:

400-(82+77+75+84)=x

400-(318)=x

x=82

That is the minimum score needed.

The scale factor of the dilation from ABCD to A′B′C′D′ is 3.

Step-by-step explanation:

Step 1:

In the pre-image ABCD, the length of one of the sides is given as 14 units.

For the other shape A′B′C′D′, the same side as the previous shape is given as 8 units.

Step 2:

To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling.

In this case, it is the given length of the sides CD and C′D′.

So the scale factor = [tex]\frac{C^{1} D^{1} }{CD} = \frac{8}{14} = \frac{4}{7} .[/tex]

So the shape ABCD is dilated by a scale factor of [tex]\frac{4}{7}[/tex] to produce the shape A′B′C′D′.

Answer: The answer is 4/7

Step-by-step explanation: the other persons work was correct!! so i got 100%

Answer:

y=mx+b broken down is in the step by step explanation.

Step-by-step explanation:

y=mx+b is the y intercept formula.it is mostly used for slopes.

y is usually equal to the total,or final answer.it is the start.

m is equal to the slope.in the formula.it can also be used as the rise over run,which means the top number is the amount of units you go up for rise,and run is the bottom number which is the amount of units you move to the right.if it is negative,you move the opposite ways.if it is a single number,the bottom number can be 1.

x is equal to the number you multiply m,or the slope by.

b is equal to where you start on the vertical line in the graph.a way to remember it is horizontal is like a horizon,it’s flat.

Answer:

Therefore,

2²+5² = c² will be matched.

The equation that could be used to find the length of the hypotenuse is 2²+5² = c².

Pythagorean theorem is a fundamental relation in between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

Given is right triangle we need to find an equation to determine the length of the hypotenuse,

To find the length of the hypotenuse of a right triangle you can use the Pythagorean theorem, that can be written as:

(base)² + (altitude)² = (hypotenuse)²

In this case, a=2, b=5 and c=c, so according to the Pythagorean theorem:

2²+5²=c²

Hence the equation that could be used to find the length of the hypotenuse is 2²+5² = c².

Learn more about Pythagoras theorem, click;

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Final answer:

The store sold 1 and 2/5 more cases of juice on Friday than on Saturday.

Explanation:

To determine how many more cases of juice the store sold on Friday than on Saturday, we need to subtract the number of cases sold on Saturday from the number of cases sold on Friday.

Friday's sales: 6 and 1/5 cases
Saturday's sales: 4 and 4/5 cases

We convert these mixed numbers to improper fractions to make the subtraction easier:

Now we subtract the two fractions:

(31/5) – (24/5) = 7/5 cases

Convert the improper fraction back to a mixed number:

7/5 = 1 and 2/5 cases

So, the store sold 1 and 2/5 more cases of juice on Friday than on Saturday.

Answer:

5.04 inches

Step-by-step explanation:

because the total rainfall in March was 3.6 inches and if the total rainfall in April was 1.4 times as much then you would take the total rainfall in March which was 3.6 inches and multiply that by 1.4 because it says the amount in April was 1.4 times as much.

The total rainfall in March was 3.6 inches. In April, the total rainfall was 1.4 times as much. The total rainfall in April is calculated by multiplying the March rainfall of 3.6 inches by 1.4, resulting in a total April rainfall of 5.04 inches.

The total rainfall in March was 3.6 inches. In April, the total rainfall was 1.4 times as much. To calculate the total rainfall in April, you multiply the March rainfall by 1.4. So, the calculation you'd do is 3.6 inches (March rain) times 1.4. This gives you 5.04 inches of rainfall in April. So, the total rainfall in April was 5.04 inches.

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