WHich of the following correctly completes the square for the equation below ? X^2 + 2x=19

First find the x and y values because where the lines will intersect, they share the point of the intersection so they will share the x and y coordinates.

Rearrange equations

[tex]4x + y = 19[/tex]

[tex] - 2x + y = 1[/tex]

To cancel y, we must do equation 1 minus equation 2. Similarly:

[tex]4x - - 2x = 4x + 2x = 6x[/tex]

[tex]19 - 1 = 18[/tex]

[tex]6x = 18[/tex]

[tex]x = 18 \div 6 = 3[/tex]

So the x coordinate is 3.

The y coordinate can be found with substitution of x into one of the equations:

[tex]y = 2x + 1 = 2(3) + 1 = 7[/tex]

So where the two lines intersect is at the point (3, 7), which is the solution to the equations.

Answer:

The correct option is 2.

Step-by-step explanation:

The given system of equations is

[tex]y=-4x+19[/tex]           ..... (1)

[tex]y=2x+1[/tex]               ..... (2)

The slope intercept form of a line is

[tex]y=mx+b[/tex]             .... (3)

where, m is slope and b is y-intercept.

From (1) and (3), we get

[tex]m=-4,b=19[/tex]

The slope of first line is -4 and the y-intercept is 19. It means it is a decreasing line and intersect the y-axis at (0,19).

From (2) and (3), we get

[tex]m=2,b=1[/tex]

The slope of first line is 2 and the y-intercept is 1. It means it is an increasing line and intersect the y-axis at (0,1).

Put y=0, to find the x-intercepts.

[tex]0=-4x+19\Rightarrow x=\frac{19}{4}=4.75[/tex]

[tex]0=2x+1\Rightarrow x=\frac{-1}{2}=-0.5[/tex]

Therefore the x-intercept of first line is 4.75 and the x-intercept of the second line is -0.5.

Only the second graph satisfy all the above condition.

One solving the given equation we get

[tex]-4x+19=2x+1[/tex]

[tex]19-1=2x+4x[/tex]

[tex]18=6x[/tex]

Divide both sides by 6.

[tex]3=x[/tex]

Put this value in equation (1).

[tex]y=-4(3)+19=-12+19=7[/tex]

Therefore the solution of the given system of equation is (3,7).

Hence the correct option is 2.

awnser: 42

step by step:

1. find the racio of both

2.multiply the awnsers by 7

3.finally subtract

The answer is 42 because to find how meant men and women started at on the the first day you do

177/3=59 and 159/3=53

Then you times those numbers separately by 7. So 59*7=413 and 53*7=371

Then you do 413 men-371 women=42 more men then women.

Answer: b. borrow $840 for 1 week at an APR 550%, since jimmie will owe less interest this way than with the fee of $90. APEX

The "better" deal is borrowing borrow $840 for 1 week at an APR of 550%

What is APR 550% mean?

The interest on the borrowing amount for one year on the credit card.

Jimmie has a borrowing APR is 550%

One month interest 5.50÷12

                                   ⇒0.4583

For one day =0.4583/30

                      =0.01527

for one week=0.01527*7

                        =0.107

APR for borrowing $840 for 1 week is charged on  purchased amount        =$840*0.107

=$89.8

Borrowing the $840 for 1 week with a fee of $90.

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The radical symbol √ indicates the root extraction operation in mathematics. Non-examples of the radical symbol could include any symbol not associated with this concept, such as the minus sign (-), division sign (÷), or the Greek letter alpha (α).

The radical symbol √, used in mathematics, represents the operation of root extraction. A non-example of the radical symbol would be anything outside this context. Here are a few:

In summary, symbols unrelated to root extraction do not serve as examples of the radical symbol, since their usage and meaning in a given context significantly differ.

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Final answer:

In chemistry, a radical is a molecule with an odd number of valence electrons, such as the chlorine atom and the hydroxyl radical, which makes the molecule highly reactive and typically paramagnetic.

Explanation:

The term radical in chemistry usually refers to a molecule that has an odd number of valence electrons, rendering it highly reactive. These radicals do not follow the conventional complete octets in terms of electron configuration; they are typically short one or more electrons, which gives them an odd number of electrons in total. A familiar example of a radical is the gaseous chlorine atom, which has seven valence electrons and is denoted by its elemental symbol with a dot (Cl·). This makes the chlorine atom a radical because the unpaired electron can easily participate in chemical reactions.

Another example is the hydroxyl radical (OH·), which contains an unpaired electron. Radicals are generally considered to be paramagnetic due to their odd electrons, which can align with a magnetic field. The presence of these unpaired electrons makes radicals highly reactive and an important subject in chemical reactions.

Answer:

1/6

Step-by-step explanation:

We know this because we have to first add up all of the coins, bringing us to 18. Then, to make the fraction of the probability of selecting a penny at random, we'd simply do 3/18. This simplified would be 1/6

The probability of selecting a penny is 1/6.

Given that, a jar contains 3 pennies, 5 nickels, 4 dimes, and 6 quarters.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Total number of outcomes =3+5+4+6

= 18

Number of favourable of outcomes = 3

So, probability of an event =3/18

= 1/6

Hence, the probability of selecting a penny is 1/6.

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it should be 31.5 kids get balloon animals

Answer:

Balloon Animals: 10 children

Face Paint: 35 children

Step-by-step explanation:

To find out how many children get balloon animals, divide 105 by 10. Your answer will be 10.5, but ten and a half children can't get balloon animals (it's physically impossible) so we would have to round down to 10. To find out how many children get their faces painted, you would divide 105 by 3, which would give you 35. So 35 children would get their faces painted.

Hope this helps ya :D

Answer:

If y=2x+7 were changed to y=5x+7, then the graph of the new function would be steeper than the graph of the original function. On the other hand, the y-intercept would be unchanged; ( 0, 7)

Step-by-step explanation:

If y=2x+7 were changed to y=5x+7, then the graph of the new function would be steeper than the graph of the original function. On the other hand, the y-intercept would be unchanged; ( 0, 7)

Answer:

(x - 2i)(x + 2i)(x + 1)

Step-by-step explanation:

Factor x³ + x² + 4x + 4.

Note that x² is common to the first two terms, and that 4 is common to the last two terms.

Thus:  x³ + x² + 4x + 4 = x²(x + 1) + 4(x + 1).

We see that x + 1 is common to both terms.  Thus, we have:

(x² + 4)(x + 1).  

Note that x² + 4 has two imaginary roots:  2i and -2i.  Thus, the complete

factorization of the polynomial is (x - 2i)(x + 2i)(x + 1).

Answer:

[tex](x+1)(x+2i)(x-2i)[/tex]

Step-by-step explanation:

[tex]x^3+x^2+4x+4[/tex]

Factor the given polynomial

Group first two terms and last two terms

[tex](x^3+x^2)+(4x+4)[/tex]

Factor out GCF from each group

[tex]x^2(x+1)+4(x+1)[/tex]

Factor out x+1

[tex](x^2+4)(x+1)[/tex]

Now factor out x^2+4 that is x^2  + 2^2

[tex]x^2+4= (x+2i)(x-2i)[/tex]

[tex](x+1)(x+2i)(x-2i)[/tex]

Answer:

The median, because the data distribution is skewed to the right

Step-by-step explanation:

Min= 10.5

Q1 = 11.5

Median = 12.5

Q3= 13.5

Maximum = 15

The data is skewed towards the right because more values towards the right side as compared to the left side.

For data to be symmetrical, it has same shape on both sides of the median, which in our case is not possible.

So, for skewed data we always prefer median because it is less affected by the outliers and if mean is chosen, the value of mean is biased towards the side that has larger values while median does not get affected by it. So, we choose median.

our correct option will be:

The median, because the data distribution is skewed to the right

Answer: The answer is A the other options are wrong I took the rest

Step-by-step explanation:

Answer:

301.59

Step-by-step explanation:

167.55 + 134.04 = 301.59

Answer:

109.38

Step-by-step explanation:

Recall the formula for compound interest is as follows:

         A  =  P·(1  +  r/n)nt ,   where

    P = principal amount (initial amount deposited)

     r = annual rate of interest (in decimal form)

     t = # of years amount is deposited for

    n = # of times interest is compounded per year

    A = amount accumulated after t years, including interest

The problem asks how much money Heather will have in the bank by her 16th birthday when she deposited $100 on her 13th birthday in a bank with 3% interest compounded quarterly. From this, we have the following information:

    P = $100

    r = 0.03     ==>     3%/100% = 0.03

    t = 3 years     ==>     16 - 13 = 3

    n = 4     ==>     since there are 12 months per year and 12/4 = 3 months,

                then interest is compounded  every 3 months which is a total of 4 times per year

Therefore,

         A = P(1 + r/n)nt

            = 100(1 + 0.03/4)4·3

            = 100(1 + 0.0075)12

            = 100(1.0075)12

            = 109.38069

            ≈ 109.38

Thus, Heather will have $109.38 in the bank by her 16th birthda

To find how many gallons of seawater contain 2.5 pounds of salt, convert the salt to ounces (40 ounces) and divide by the salinity concentration (1.2 ounces per liter) to get 33.33 liters. Then convert liters to gallons, resulting in approximately 8.8 gallons of seawater.

To solve this problem, we need to convert all units to be compatible and calculate the amount of seawater needed to obtain 2.5 pounds of salt based on the salinity given.

First, we convert 2.5 pounds of salt to ounces because the salinity is given as 1.2 ounces per liter. Since 1 pound is equal to 16 ounces, we have 2.5 pounds * 16 ounces/pound = 40 ounces of salt.

Next, we divide the total ounces of salt by the salinity concentration to find out how many liters of seawater we need:

40 ounces of salt / 1.2 ounces of salt per liter = 33.33 liters of seawater.

Then, we convert liters of seawater to gallons. There are approximately 3.785 liters in a gallon, so:

33.33 liters / 3.785 liters per gallon = 8.8 gallons

Therefore, to the nearest tenth of a gallon, it would take 8.8 gallons of seawater to contain 2.5 pounds of salt.

3/5 is the answer to the question

Answer:

3/5 is the awnser

Step-by-step explanation:

Step-by-step explanation:

Well you got a good start.  #16 = 105°, #17 = 27°, and #15 = 48°.

Inscribed angles are half the arc angle, so #3 = #10 = 21°, and #4 = #5 = 39°.

That means #14 = #12 = 120°, and #11 = #13 = 60°.

The sum of the angle arcs is 360°, and AD is the diameter, so it splits it in half.  So arc BC is 180 - 78 - 42 = 60°, so #1 = 30°.

Therefore, #2 = 90°.

AG and FG are both radii, so AGF is an isosceles triangle.  Therefore, #8 = #9 = 66°.

Similarly, FG and DG are both radii, so FGD is an isosceles triangle.  So #6 = #7 = 24°.

That means #18 = 129°.  So #20 = 129° and #19 = #21 = 51°.

That's all of them.

Answer:

x | x ≥ 0 and x ≤ 8

Step-by-step explanation:

The domain of the function is defined as the possible x values that can be used in this function. Now, taking a look at the given graph, we would find that the line starts from x = 0 and continues taking x values till it reaches x = 0This means that for this function, we are allowed to use x values that are greater than or equal to zero and less than or equal to 8Therefore, the domain is any x value greater than or equal to zero and less than or equal to 8

29+5m should be the expression!

Answer:

the correct answer is the third one.  (1, 16), (2, 20), (3, 24)

Step-by-step explanation:

A perimeter is a path that surrounds a two-dimensional shape.

In the first case, 1 rectangle, the perimeter is the sum of all the sides:

Perimeter = 6 + 2 + 6 + 2 = 16

In the second case, 2 rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 6 + 2 + 2 = 20

In the third case, three rectangles, the perimeter is the sum of all external sides:

Perimeter = 6 + 2 + 2 + 2 + 6 + 2 + 2 + 2 = 24

In none of the cases, you take into consideration the interal sides. Just the external sides, so the correct answer is the third one.

Answer:

x = 8

Step-by-step explanation:

The two angles are complementary angles, which means they add to 90 degrees

6x + (4x+10) = 90

Combine like terms

10x+10 = 90

Subtract 10 from each side

10x+10-10=90-10

10x = 80

Divide each side by 10

10x/10=80/10

x = 8

Final answer:

The mean usually has the greatest value among measures of central tendency like the median and mode, particularly in skewed distributions. The range is not a central tendency measure but represents the difference between the highest and lowest values.

Explanation:

When comparing different measures of central tendency, the mean usually has the greatest value in a skewed distribution. The mean is the arithmetic average of all the numbers, while the median is the middle value when the numbers are sorted, and the mode is the number that appears most frequently. Examples given show that in various cases, the mean tends to be larger than the median and mode, especially when the data set is right-skewed, which is when there are values that are significantly higher than the rest. Range, however, represents the difference between the highest and lowest values in the set, and is not a measure of central tendency, but rather a measure of spread.

Final answer:

To compare two-way frequencies in a relative frequency table, calculate the relative frequency by dividing each frequency by the total number of data values, and find the cumulative relative frequency by summing up the previous relative frequencies.

Explanation:

To compare two-way frequencies in a relative frequency table, you start by calculating the relative frequency. This is done by dividing the frequency by the total number of data values for that group. For cumulative relative frequency, add the relative frequencies of all preceding rows to the relative frequency of the current row. Let's clarify using an example.

In the first row, if the relative frequency is .15, this is the cumulative frequency as well since it's the first value. For the second row, if the relative frequency is .25, we add this to the .15 from the first row to get a cumulative relative frequency of .40. Continue this process down each row.

When constructing a histogram using these frequencies, scale the x-axis in increments suitable to the data range (e.g., $50 widths) and plot relative frequencies on the y-axis. The sum of the relative frequency column should total 1 (or 100% if in percentage form), as it represents the entire sample.

The difference between relative frequency and frequency is that frequency is the absolute count of occurrences, while relative frequency expresses this count as a proportion of the total number of data values. Cumulative relative frequency is the sum of all previous relative frequencies, showing the accumulation of data up to that point.

Answer:

Step-by-step explanation:

One of the easier approaches to graphing a linear equation such as this one is to solve it for y, which gives us both the slope of the line and the y-intercept.

x-3y=-6 → -3y = -x - 6,  or 3y = x + 6.

Dividing both sides by 3, we get   y = (1/3)x + 2.

So the slope of this line is 1/3 and the y-intercept is 2.

Plot a dot at (0, 2).  This is the y-intercept.  Now move your pencil point from that dot 3 spaces to the right and then 1 space up.  Draw a line thru these two dots.  End.

Alternatively, you could use the intercept method.  We have already found that the y-intercept is (0, 2).  To find the x-intercept, let y = 0.  Then x = -6, and the x-intercept is (-6, 0).

Plot both (0, 2) and (-6, 0) and draw a line thru these points.  Same graph.

Answer: Not sure if this is right but here we go.

Step-by-step explanation:

to solve for x

x-3y=-6

Add 3y on both sides, and that should give you x=-6+3y

Solve for y:

y=x/3+2

Answer:

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

Step-by-step explanation:

[tex]8x^2+4x+1=0[/tex]

Using Quadratic formula to solve this equation:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\a = 8 \,\, b = 4\,\, c = -1\\Putting \,\, values \,\, in \,\, the\,\, equation\\x= \frac{-4\pm\sqrt{(4)^2-4(8)(-1)}}{2(8)}\\x= \frac{-4\pm\sqrt{16+32}}{16}\\x= \frac{-4\pm\sqrt{48}}{16}\\x= \frac{-4+ \sqrt{48}}{16} \,\, and \,\, x= \frac{-4- \sqrt{48}}{16}\\x= \frac{-1+ \sqrt{3}}{4} \,\, and \,\, x= \frac{-1- \sqrt{3}}{4}[/tex]

The possible values of x are:

x= [tex]\frac{-1+\sqrt{3}}{4} \,\,or\,\, x= 0.18[/tex]

and

x= [tex]\frac{-1-\sqrt{3}}{4} \,\, or \,\, x= -0.68[/tex]

Answer:

2.5 mins per page

Step-by-step explanation:

2.5 x [page's Read] = Awnser

The total time William needs to read his novel is calculated by multiplying the number of pages by 2.5 minutes per page. This method allows efficient time management and scheduling for reading. By dividing the total pages by available days, one can manage the reading workload more effectively.

The total time William takes to read his novel is directly proportional to the number of pages he reads. This means that if William allots 2.5 minutes to read each page of his novel, then for every page he reads, he will spend 2.5 minutes. To find the total time spent reading, you simply multiply the number of pages by 2.5 minutes.

For example, if William wants to read 40 pages, he would calculate his total reading time as 40 pages × 2.5 minutes per page = 100 minutes. This approach allows William to plan how much time he needs to set aside for reading based on the number of pages.

Additionally, dividing the total page count by the number of available days can help in managing the reading workload efficiently. By knowing how long it takes to read a set number of pages, William can also estimate the time required for larger sections and manage his schedule accordingly.

Answer:

B. 28

Step-by-step explanation:

We are given the following system of equations

[tex]y=5x+10\\y=10x-5[/tex]

We can substitute in one of the equations for y. This will give us an equation that we can solve for x.

[tex]5x+10=10x-5\\\\5x=15\\\\x=3[/tex]

Next we can substitute in our value for x in order to find the y value.

[tex]y=5(3)+20\\\\y=15+20\\\\y=25[/tex]

Now we can check with the other equation to see if our x and y values are correct

[tex]25=10(3)-5\\\\25=30-5\\\\25=25[/tex]

Now we are certain that x=3 and y=25

[tex]x+y=?\\\\3+25=28[/tex]

Answer:

Step-by-step explanation:

The graph of y= -4x² is that of a parabola with vertex at (0, 0) that opens down.

The graph of y= -4x² - 5 is the same, except that it's the result of translating the entire graph of y= -4x² down by 5 units.

Answer:

Step-by-step explanation:

Answer:

B) Interquartile Range

Answer:

IQR, interquartile range

Step-by-step explanation:

thats what i got on algebra nation, lmk if you want an explanation :)

Answer: D. x+2y+10

Trinomial refers to the fact that the polynomial has 3 pieces (x, 2y, and 10)

Constant term means there is a term with no variable (a number with no letters attached to it: In this example, that number is 10)

The trinomial with a constant term is D. x + 2y + 10.

Trinomials are polynomials which consists of three terms in total.

Given are four polynomials.

A trinomial consists of three terms.

The only polynomials in the option which contains three terms are,

B. y⁶ + 8y³ + 64y

D. x + 2y + 10

The polynomial with constant is D.

Hence the correct option is D.

Hence the trinomial with a constant term is option D.

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Answer: 800

Step-by-step explanation:

Answer: 2.74 m

Step-by-step explanation:

You need to make the following conversions:

[tex](6dm)(\frac{1m}{10m})=0.6m[/tex]

[tex](40mm)(\frac{1m}{1,000mm})=0.04m[/tex]

[tex](10cm)(\frac{1m}{100cm})=0.1m[/tex]

Now you need to add all the values to get the sum. This is:

[tex]0.6m+0.04m+2m+0.1m=2.74m[/tex]

Answer:

48

Step-by-step explanation:

Wherever you see an x on the right, you put a 16. That's what f(16) means.

f(16) = 1/3 (4 - 16)^2

f(16) = 1/3 (- 12)^2

f(16) = 1/3 (144)

f(16) = 48