Which equation could be represented by the number line?
A. -3+(-4) = -7
B. 7+ (-6) = 1
C. 4+(-7) = -3
D. -5 + 7 = 2

When the root of x²-bx+c = 0 is decreased by 2, the resulting equation is x²-2x+1, then b = 2 and c = 1

The values of variables satisfying the given quadratic equation are called its roots.

if the roots of a quadratic equation ax²+bx+c = 0 are alpha and beta

alpha + beta = -b/a and

alpha × beta = c/a

when the roots are reduced by 2

alpha-2+ beta-2 = -b/a

(alpha+beta)-4 = -b/a

alpha+ Bata = -b/a + 4

the resulting equation is x²-2x+1 = 0

a = 1, b = -2 and c = 1

therefore alpha +beta = -b/a = -(-2)/1 = 2

therefore 2 = -b/a+4

a = 1

2 = -b+4

b = 4-2 = 2

alpha×beta = c/a = 1/1

(alpha -2)× ( beta -2) = (alpha)( beta) -2(alpha+beta) + 4 = 1-2(2)+4 = 1

therefore b = 2 , c = 1

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Answer:

16 - 3x5

Step-by-step explanation:

In the expression -2x4+16+2x4+9-3x5

-2x4 will eliminate +2x4 so we have 16 - 3x5 these two are not like terms so we can't add or subtract them

Answer:

See below.

Step-by-step explanation:

\(-2x^4+16+2x^4+9-3x^5\)

A helpful thing to do is to rearrange them in descending order:

\(=-3x^5-2x^4+2x^4+16+9\)

We can see that the second and third term cancel. The fourth and fifth term are able to be added:

\(-3x^5+25\)

Note: If you're confused on why \(-2x^4+2x^4\) cancel, use the distributive property:

\(-2x^4+2x^4=x^4(-2+2)=x^4(0)=0\)

Answer:

Step-by-step explanation:

1. -9x+2>18

-9x>18-2

-9x>16

x>-16/9

2. 13x+15≤4

13x≤-11

x≤-11/13

Answer:

x > 16/9

x < -11/13

Step-by-step explanation:

There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

To determine the number of possible outcomes when rolling a number cube and picking a cube from 4 colored cubes,

we need to multiply the number of outcomes for each event.

For rolling a number cube (assuming it has 6 sides), there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

For picking a cube from 4 colored cubes, there are 4 possible outcomes (one for each color).

Now, to calculate the total number of outcomes, multiply the outcomes of each event:

6 (number cube outcomes) x 4 (colored cube outcomes) = 24 possible outcomes.

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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There are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

When rolling a number cube, there are six possible outcomes (numbers 1-6). When picking a cube from four colored cubes, there are four possible outcomes. Therefore, the total number of possible outcomes is the product of the number of outcomes from each event: 6 x 4 = 24 possible outcomes.

When rolling a number cube, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6), since a standard number cube has 6 faces, each with a different number.

When picking a cube from 4 colored cubes, there are 4 possible outcomes, one for each color.

To find the total number of outcomes when performing both actions, you can multiply the number of outcomes for each individual action:

Total outcomes = outcomes from rolling a number cube × outcomes from picking a colored cube
Total outcomes = 6 × 4
Total outcomes = 24

So, there are 24 possible outcomes when rolling a number cube and picking a cube from 4 colored cubes.

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Answer:

hi

Step-by-step explanation:

hi

Step-by-step explanation:

yesyes jehdbshhshshshshsgs

There are 42 teachers 30 male 12 female. 30:12.  male teachers to the total number of teachers 42:30. total of teachers to the female teachers 42:12

Answer:

The slope of the line is 1

Step-by-step explanation:

To figure out the slope, you just have to do rise over one, if the line is going up from left to right then the slope is positive, which is the case shown

Answer:

Step-by-step explanation:

1.80 + 1.05 = 2.85

3.00 - 2.85 = .15 inches

The price of a senior citizen ticket is 12 and  the price of a student ticket is 6.

Two or more expressions with an Equal sign is called as Equation.

The first day of ticket sales the school sold 1 senior citizen ticket and 7 student tickets for a total of $54.

x+7y=54

x=54-7y

The school took in $156 on the second day by selling 6 senior citizen tickets and 14 student tickets.

6x+14y=156

6(54-7y)+14y=156

324-42y+14y=156

324-28y=156

Subtract 156 on both sides

168-28y=0

168=28y

y=6

Now x=54-7y

x=54-7(6)=54-42

x=12

Hence,  the price of a senior citizen ticket is 12 and  the price of a student ticket is 6.

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Answer:

Part A: 3 3/4 Part B: 5 1/4

Step-by-step explanation:

Part A: 3/4x5=3 3/4

Part B: 3 3/4 +1 2/4=5 1/4

The use and interpretation of an R or s chart are critical when examining an X-bar chart because they provide additional information about the variation within the subgroups. This allows for a more comprehensive analysis of the process and helps identify any issues or sources of variability.

When using an X-bar chart, the focus is on monitoring the process mean or average. However, the X-bar chart alone does not provide information about the variation within the subgroups. This is where the R or s chart comes into play. The R chart measures the range of values within each subgroup, while the s chart measures the standard deviation.
By using an R or s chart alongside the X-bar chart, we can assess the variability within the subgroups and determine if it is stable over time. If the variation within the subgroups is high and unpredictable, it may indicate that the process is out of control or that there are sources of variation that need to be addressed. The R or s chart provides additional insights into the process performance and helps in identifying the presence of special causes of variation.
In summary, the use and interpretation of an R or s chart in conjunction with an X-bar chart allow for a more comprehensive analysis of process variation. This helps in understanding the stability and capability of the process and enables appropriate actions to be taken to improve quality and performance.

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Answer:

integer

Step-by-step explanation:

10x12=120

48/12=4

Answer:

11

Step-by-step explanation:

Just subtract ST from RT to get RS

13-2=11

The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

The system of equation line 1: y=-2x+4 and line 2: y=-2x has no solution.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given the system of equation as;

line 1: y=-2x+4

line 2: y=-2x

Here we can put x = 1

Then;

y= -2(1) + 4

y = -2 + 4

y = 2

-2x=-2x+4

x = 0

Therefore, we can see that the system of equation has no solution.

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Calculating the obtuse angle or value of a triangle.

Finding obtuse angle value:

steps:

1)  Square the length of both sides of the triangle that intersect to create the obtuse angle, and add the squares together.

For example, if the lengths of the sides measure 4 and 2, then squaring them would result in 16 and 4. Adding the squares together results in 20.

2)  Square the length of the side opposite the obtuse angle. For the example, if the length is 5, then squaring it results in 25.

3) Subtract the combined squares of the adjacent sides by the square of the side opposite the obtuse angle. For the example, 25 subtracted from 20 equals -5.

4)  Multiply the lengths of the adjacent sides together, and then multiply that product by 2. For the example, 4 multiplied by 2 equals 8, and 8 multiplied by 2 equals 16.

5) Divide the difference of the sides squared by the product of the adjacent sides multiplied together then doubled. For the example, divide -5 by 16, which results in -0.3125.

The obtuse angle value is obtained by inverse of cos:

cos^-1(-0.3125)

= 108.209 degrees.

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Answer:

21

Step-by-step explanation:

since we are looking for the value of x, we make it the subject of the formula(stand alone) and to do that + 13 would have to cross over the equality sign.when a positive number crosses over the equality sign it changes to a negative number .

Therefore,x +13=34

x=34 -13

x=21(d)

Answer:

yes, yes, no, yes, yes (x > 0)

Step-by-step explanation:

the longest side must not be greater than the other 2 sides added up.

5 + 7 > 8 (yes)

10 + 3 > 11 (yes)

16 + 5 = 21 (no)

4 + 1.4 > 5 (yes)

3x + 4x > 5x (yes, x > 0)

Answer:

x = 1187.96

Step-by-step explanation:

Let x = price before tax

tax = x* 7.6%

tax = .076x

The cost of the computer is price before tax plus tax

cost = x + .076x

cost = 1.076x

1278.24 = 1.076x

Divide each side by 1.076

1278.24/1.076 = 1.076x/1.076

x=1187.9553

Rounding to the nearest cent

x = 1187.96

… I hope this help you

Answer:6

Step-by-step explanation:

Answer:  \(\$202\)

Step-by-step explanation:

Given

Jennifer has $400 more than Brian

Suppose Brian has x amount initially

So, Jennifer has 400+x

If Jennifer gives 20% of her to Brian, then brian would have two-third of the amount Jennifer left with

\(\Rightarrow \dfrac{2}{3}\times [400+x](1-0.2)=[400+x](0.2)+x\\\\\Rightarrow \dfrac{2}{3}\times 0.8\times (400+x)=80+0.2x+x\\\\\Rightarrow 213.334+0.533x=80+1.2x\\\Rightarrow 133.334=0.66x\\\Rightarrow x=\$202.02\)

Thus, Brain has \(\$202\)

Answer:

x= 83y−17 and y= 83x+17

​

hope it helps

The mean of the new distribution will be 33 after the addition of 3 points to each score.

Here, correct option will be:- b. 33

The mean of a population is a measure of central tendency that provides an average of the data within a data set. In this question, we are given the mean of a population as 30 and are asked to determine the mean of the new distribution after 3 points have been added to each score.

To answer this question, we must recognize that adding 3 points to each score in the population will increase the mean of the population by 3 points.

Therefore, the new mean of the distribution will be 33 i.e option b. This is because the addition of 3 points to each score will increase the total sum of all the scores, which will in turn increase the mean of the population.

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Answer:

Slope of green line:

\(m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} \)

Slope of red line:

\(m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} \)

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

Answer:

Easiest and fastest way is to graph the equation in a graphing calc and determine where it crosses the x-axis.

Step-by-step explanation:

As per the combination method, there are 3,024 different designs that can be created with four different pictures placed in nine different locations on a page.

There are seven options for the third picture and six options for the fourth picture.

To determine the total number of designs, we can use the multiplication principle, which states that the number of ways two or more independent events can occur together is equal to the product of the number of ways each event can occur individually.

Therefore, the total number of designs that can be created by placing four different pictures in nine different locations on a page can be found by multiplying the number of options for each picture:

9 x 8 x 7 x 6 = 3,024

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