Two trains leave Stations 396 miles apart at the same time and travel towards each other. One train travels at 95 mph while other travels 85 mph. How long will it take two trains to meet?

Let us take 'a' in the place of 'y' so the equation becomes

(y+x) (ax+b)

Step-by-step explanation:

Step 1:

(a + x) (ax + b)

Step 2: Proof

Checking polynomial identity.

(ax+b )(x+a) = FOIL

(ax+b)(x+a)

ax^2+a^2x is the First Term in the FOIL

ax^2 + a^2x + bx + ab

(ax+b)(x+a)+bx+ab is the Second Term in the FOIL

Add both expressions together from First and Second Term  

= ax^2 + a^2x + bx + ab

Step 3: Proof

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

Identity is Found .

Trying with numbers now

(ax+b)(x+a) = ax^2 + a^2x + bx + ab

((2*5)+8)(5+2) =(2*5^2)+(2^2*5)+(8*5)+(2*8)

((10)+8)(7) =(2*25)+(4*5)+(40)+(16)

(18)(7) =(50)+(20)+(56)

126 =126

The probability of drawing a red marble out of the bag without looking is 1/3.

The probability of drawing a red marble out of the bag without looking can be calculated by dividing the number of red marbles by the total number of marbles in the bag. In this case, there are 3 red marbles out of a total of 9 marbles, so the probability is 3/9, which simplifies to 1/3.

Answer:

0.60

Step-by-step explanation:

Again, we have a 10x10 space, which means there are 100 squares.

In this case, there are 60 shaded squares. This gives the probability of [tex]\frac{60}{100}[/tex] which simplifies to 0.60

Answer:

0.60

Step-by-step explanation:

Because there are 100 squares and 60 out of it is shaded if you chose a random point amongst these 100 square the probability of choosing a shaded one is 60/100 which is equal to 0.60.

By completing the square, the equation x²- 20x + 100 = 0, we get, (x-10)²=0

Here, we have,

To rewrite the equation x² - 20x + 100 = 0 by completing the square, we can follow these steps:

Step 1: Move the constant term to the right side of the equation:

x² - 20x = -100.

Step 2: Take half of the coefficient of the x-term (-20/2 = -10) and square it to get (-10)² = 100.

Step 3: Add the result from step 2 to both sides of the equation:

x² - 20x + 100 = -100 + 100.

Simplifying:

x² - 20x + 100 = 0.

Step 4: Factor the left side of the equation. In this case, the left side is a perfect square trinomial:

(x - 10)² = 0.

Therefore, by completing the square, the equation x²- 20x + 100 = 0,

we get, (x-10)²=0

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Final answer:

The equation [tex]x^2 - 20x + 100 = 0[/tex] is already a perfect square and does not need to be completed. However, completing the square involves moving the constant to the other side, squaring half the coefficient of x, and solving for x, which leads us back to the original equation [tex](x - 10)^2 = 0[/tex] and reveals that x = 10.

Explanation:

The equation given is [tex]x^2 - 20x + 100 = 0[/tex]. This equation appears to already be a perfect square, as the constant term (100) is the square of half the coefficient of the x term (which is 10), thus completing the square is actually not needed. However, to illustrate the method of completing the square, let's ignore for a moment that it's already a perfect square and proceed with the steps:

We've found that x = 10 is the solution to the equation, which is the same result you would get by recognizing the equation was already a perfect square in its original form.

Answer:

A

Step-by-step explanation:

Given sequence [tex]-8,\ -1,\ 6,\ ...[/tex]

In this sequence,

[tex]a_1=-8\\ \\a_2=-1\\ \\a_3=6\\ \\...[/tex]

Hence,

[tex]d=a_2-a_1=-1-(-8)=7\\ \\d=a_3-a_2=6-(-1)=7[/tex]

Find 56th term:

[tex]a_{n}=a_1+(n-1)\cdot d\\ \\a_{56}=-8+(56-1)\cdot 7\\ \\a_{56}=-8+385\\ \\a_{56}=377[/tex]

The sum of 56 terms is

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\ \\S_{56}=\dfrac{-8+377}{2}\cdot 56=\dfrac{369}{2}\cdot 56=369\cdot 28=10,332[/tex]

The ratio of the vertical rise to the horizontal distance on the ramp is equal to tan B.

The given figure represents a ramp with a length of 17 feet, rising 8 feet above the floor, and covering a horizontal distance of 15 feet. To find the ratio of the vertical rise to the horizontal distance (tan B), we can use the trigonometric function tangent (tan).

Tan B = vertical rise / horizontal distance = 8 feet / 15 feet = 0.5333

Answer:

1/8(A)+(3/4)(168-A)=76 is an equation to find the mass of A, the mass of A is 80 grams.

Step-by-step explanation:

What do we know?

Both sacks together are 168 grams. Therefore;

A+B=168

One eighth of sack A and three quarters of sack B is equal to 76 grams. Therefore;

1/8(A)+(3/4)B=76

Let's solve using the substitution method to find A. First, we need to isolate and then substitute B for an expression containing A.

A+B=168

B=168-A

Now that we have isolated B, we can substitute '160-A' for B in the other equation.

1/8(A)+(3/4)(168-A)=76

1/8(A)-3/4(A)+126=76

1/8(A)-3/4(A)+126=-50

-5/8(A)=-50

A=80

Answer:

39mm

Step-by-step explanation:

Final answer:

Using the scale factor of 3:1, the length of side WZ from trapezoid WXYZ can be calculated by dividing the known length of side SV from trapezoid STUV by the scale factor. The length of WZ is found to be 51 mm.

Explanation:

If trapezoid STUV is a scaled version of trapezoid WXYZ with a scale factor of 3:1, we can use this scale factor to determine the length of side WZ given the lengths of ST and SV. To find the length of WZ, we divide the length of SV by the scale factor. Since SV = 153 mm and the scale factor is 3, we perform the division 153 mm / 3 to get 51 mm as the length of WZ.

A proportion is a mathematical statement that two ratios or fractions are equal. It is used to express the equality of two fractions that compare two numbers or quantities to each other. For example, if we have two fractions a/b and c/d, a proportion states that these two fractions are equivalent: a/b = c/d. Proportions are fundamental in various branches of mathematics and applications, including solving problems involving scales, maps, and ratios in real-life scenarios.

Answer:

if f(x)=24

24=-12x+72

24-72=-12x

-48=-12x

x=48/12

x=4

so it's (C)

Answer:

x=4; Option C is your answer.

Step-by-step explanation:

Plug in 24:

[tex]f(x)=24\\[/tex]

[tex]24=-12x+72[/tex]

Solve For X:

[tex]-12x+72-72=24-72\\-12x=-48\\\frac{-12x}{-12} =\frac{-48}{-12}\\ x=4[/tex]

Answer:

The actual distance is 127 miles.

Step-by-step explanation:

Given:

On a map, the distance from Los Angeles to San Diego is 6.35 cm.

The scale is 1 cm = 20 miles.

Now, to find the actual distance.

Let the actual distance be [tex]x\ miles.[/tex]

And the distance on map is 6.35 cm.

So, 6.35 cm is equivalent to [tex]x\ miles.[/tex]

And as given on the scale 1 cm is equivalent to 20 miles.

Now, to get the actual distance by using cross multiplication method:

[tex]\frac{6.35}{x} =\frac{1}{20}[/tex]

By using cross multiplication we get:

⇒  [tex]127=x[/tex]

⇒  [tex]x=127\ miles.[/tex]

Therefore, the actual distance is 127 miles.

Equation for line: y=mx+b where m is the slope and b is the y-intercept

We have the slope. We just need to find the y-intercept. Plug in the point and the slope and solve for b.

y=mx+b

1=4(-5)+b

b=21

Answer: y=4x+21

Answer:

[tex]x\sqrt{7} - 49\sqrt{x}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) & = & \sqrt{7x}\times\sqrt{x}- 7\sqrt{7}\times\sqrt{7x} \\ & = & \sqrt{7}\times\sqrt{x}\times\sqrt{x} - 7\sqrt{7}\times\sqrt{7}\times\sqrt{x}\\& = & \sqrt{7}\times x - 7\times 7\times\sqrt{x}\\& = &\mathbf{ x\sqrt{7} - 49\sqrt{x}}\\\end{array}[/tex]

Answer:

Step-by-step explanation

But the question does not say exactly what should be solve for.

Answer:

30%

Step-by-step explanation:

We can translate the question into an equation.

500x=150

x=150/500

x=3/10=30%

answer: 30%

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]

In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.

coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.

Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].

Answer:

82

Step-by-step explanation:

Mean of a set of data is simply the average. It's calculated by adding up all the numbers, then divide by how many numbers there are.

57 + 59 + 64 + 72 + 76 + 77 + 77 + 78 + 85 + 87 + 88 + 88 + 88 + 92 + 94 + 96 + 98 + 100 = 1,476

1476/18 = 82

Therefore 82 is the mean of the set of numbers

Answer:

Median = 86

Step-by-step explanation:

the middle of the data set is 85 and 87. to find the median you would do 85+87/2= 172/2 median = 86

Answer:

She traveled 13 23/56 miles on the third day.

Step-by-step explanation:

HOPE THIS HELPED ;3

Answer:

The difference is [tex]\frac{3}{4}[/tex] inches.

Step-by-step explanation:

See the attached number line where the worm lengths in inches are plotted.

From the number line plotted in the attached photo, it is clear that the shortest worm has the length of [tex]\frac{3}{4}[/tex] inches and the longest worm has the length of [tex]1\frac{1}{2}[/tex] inches i.e. [tex]\frac{3}{2}[/tex] inches.

Therefore, the difference in length between the shortest and longest worm is [tex](\frac{3}{2} - \frac{3}{4}) = \frac{3}{4}[/tex] inches. (Answer)

Answer:

x=-5, x=9

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2} -8x-90[/tex]  

equate to zero

[tex]2x^{2} -8x-90=0[/tex]  

so

[tex]2=-1\\b=-8\\c=-90[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(2)(-90)}} {2(2)}[/tex]

[tex]x=\frac{8\pm\sqrt{784}} {4}[/tex]

[tex]x=\frac{8\pm28} {4}[/tex]

[tex]x=\frac{8+28} {4}=9[/tex]

[tex]x=\frac{8-28} {4}=-5[/tex]

therefore

The solutions are x=-5, x=9

Answer:

B. x² + 16x + 15

Step-by-step explanation:

Area of parallelogram = base x height

A = (x + 15) (x + 1) = x² + 16x + 15

Answer:

7.2

Step-by-step explanation:

You divide 225 by 30 and get 7.2

Answer:

c

Step-by-step explanation:

The other answer is wrong the following is the sample response.

Answer:

Sample Response: The population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.

Step-by-step explanation:

just finished the assignment and this was the sample response.

(please mark brainliest)

Have a great day!

Alan's survey population encompasses all students at the high school with art preferences. A sample could be randomly chosen from students from each grade or art class, reflecting the school's diversity and maintained by a random sampling method for fairness and representation.

The population of Alan's survey is all the students at the town’s high school who have preferences for types of art. To conduct his survey, Alan needs to choose a sample, which is a smaller group from the population that can provide reliable information about the entire population's art preferences. An example of a possible sample would be selecting a certain number of students from each grade level or art class to ensure a variety of perspectives. It could also involve stratification by demographic characteristics such as age, gender, socioeconomic status, or ethnicity if these factors are believed to influence art preferences.

An efficient method to create a representative sample could be to use a random sampling technique where each student has an equal chance of being selected. For instance, Alan could use a random number generator to pick students from a list, or he might use a stratified random sampling by first dividing the student body into subgroups (such as by grade or art class) and then randomly selecting students from each subgroup.

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Answer:

[tex]\frac{14}{6}[/tex]

Step-by-step explanation:

A mixed fraction of the form [tex]a\frac{b}{c}[/tex] can be converted into an improper fraction by writing it in the form [tex]\frac{(ac)+b}{c}[/tex] . By applying this formula , we can see that [tex]2\frac{2}{6} = \frac{12 +2}{6} =\frac{14}{6}[/tex] . As numerator is greater than the denominator , we can see that the answer is greater than one and thus it is an improper fraction.

Answer:

2 1/2 or 2.5

Step-by-step explanation:

The area is the length times the width. To solve for the length, you have this equation using the data you already have. 8 1/2 = 3 2/5 x length. 8 1/2 / 3 2/5 = length. 8.5/3.4 = length. length = 2.5 OR to do this fraction wise, you can make them fractions and divide, making 8/1 -> 16/2 + 1/2 = 17/2 and 3/1 - 15/5 + 2/5 = 17/5 and divide those, which ends up at 2 1/2 but fraction wise makes it more complicated

Answer:

[tex]m\angle KLM=53.13^o[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

[tex]KO=MO=r=5\ units[/tex]

[tex]KM=8\ units[/tex]

Applying the law of cosines

[tex]8^2=5^2+5^2-2(5)(5)cos(KOM)[/tex]

[tex]64=50-50cos(KOM)[/tex]

[tex]50cos(KOM)=50-64[/tex]

[tex]50cos(KOM)=-14[/tex]

[tex]cos(KOM)=-14/50[/tex]

[tex]m\angle KOM=cos^{-1}(-14/50)[/tex]

[tex]m\angle KOM=106.26^o[/tex]

step 2

Find the measure of the arc KM

we know that

[tex]arc\ KM=m\angle KOM[/tex] ----> by central angle

we have

[tex]m\angle KOM=106.26^o[/tex]

so

[tex]arc\ KM=106.26^o[/tex]

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising  

[tex]m\angle KLM=\frac{1}{2}[arc\ KM][/tex]

we have

[tex]arc\ KM=106.26^o[/tex]

substitute

[tex]m\angle KLM=\frac{1}{2}[106.26^o][/tex]

[tex]m\angle KLM=53.13^o[/tex]

Answer:

Equation of line is given by:

[tex]y=2x+14[/tex]  

Step-by-step explanation:

Given points:

[tex](-8,-2)\ and\ (-4,6)[/tex]

Slope of line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]  is a point on the line

[tex]m=\frac{6-(-2)}{-4-(-8)}[/tex]

[tex]m=\frac{6+2}{-4+8}[/tex]

[tex]m=\frac{8}{4}[/tex]

∴ [tex]m=2[/tex]

Point-slope equation of line is given by:

[tex]y-y_1=m(x-x_1)[/tex]  

where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is slope of line.

Using point [tex](-8,-2)[/tex] and slope [tex]m=2[/tex] point-slope equation of line is given by:

[tex]y-(-2)=2(x-(-8))[/tex]  

Simplifying.

[tex]y+2=2(x+8)[/tex]  

Using distribution.

[tex]y+2=2x+16[/tex]  

Subtracting 2 to both sides.

[tex]y+2-2=2x+16-2[/tex]  

[tex]y=2x+14[/tex]  

Thus, equation of line is [tex]y=2x+14[/tex]  

Answer:

The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.

Step-by-step explanation:

Given order of fractions from least to greatest:

[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]

To check if the fractions are in correct order.

Solution:

The fractions given have same numerators but different denominators.

For fractions the higher the denominator the lower is the value of that fraction.

Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]

So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.

The correct order from least to greatest should be:

[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].

For this case we must simplify the following expression:

[tex]\frac {1} {2} (6 \frac {2} {3} + \frac {1} {4}) - \frac {5} {24} =[/tex]

We convert the mixed number to an improper fraction:

[tex]6 \frac {2} {3} = \frac {3 * 6 + 2} {3} = \frac {20} {3}[/tex]

So, by rewriting we have:

[tex]\frac {1} {2} (\frac {20} {3} + \frac {1} {4}) - \frac {5} {24} =\\\frac {1} {2} (\frac {4 * 20 + 3 * 1} {4 * 3}) - \frac {5} {24} =\\\frac {1} {2} (\frac {80 + 3} {12}) - \frac {5} {24} =\\\frac {1} {2} (\frac {83} {12}) - \frac {5} {24} =[/tex]

[tex]\frac {83} {24} - \frac {5} {24} =\\\frac {83-5} {24} =\\\frac {78} {24} =\\\frac {39} {12} =\\\frac {13} {4} =\\3 \frac {1} {4}[/tex]

Answer:

[tex]3 \frac {1} {4}[/tex]

Answer:

4

Step-by-step explanation:

3.6m = 14.4

m = 14.4 ÷ 3.6

m = 4