Solve (x - 2 < 5) ∩ (x + 7 > 6).

Ø
{x | x < -1 x < 7}
{x | -1 < x < 7}

Answer:

51 cm²

Step-by-step explanation:

Let's ASSUME that the vertical measurements are taken perpendicular to the roughly horizontal baselines.

The three yellow triangles are all similar

the upper small triangle has height 3 and base 6 cm. The ratio of the lengths is 6/3 = 2

This means the medium (overlapping) triangle has lengths 10 - 3 = 7 and 7(2) = 14 cm

Area of the large triangle is ½(14 + 6)(10) = 100 cm²

Area of the overlapping yellow triangle is ½(7)(14) = 49 cm²

Exposed area of the blue triangle is 100 - 49 = 51 cm²

Both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.

Based on the information given from statement, we can determine the missing length of the yellow triangle by means of simmilarity ratios, that is:

[tex]\frac{3\,cm}{6\,cm} = \frac{10\,cm}{x}[/tex] (1)

Where [tex]x[/tex] is the base of the yellow triangle, in centimeters.

Now we proceed to find the length base:

[tex]x = \frac{6\,cm}{3\,cm}\times 10\,cm[/tex]

[tex]x = 20\,cm[/tex]

The area of the triangle can be found by means of the following expression:

[tex]A = \frac{1}{2}\cdot b\cdot h[/tex] (2)

Where:

If we know that [tex]b = 20\,cm[/tex] and [tex]h = 10\,cm[/tex], then the area of the triangle is:

[tex]A = \frac{1}{2}\cdot (20\,cm)\cdot (10\,cm)[/tex]

[tex]A = 100\,cm^{2}[/tex]

The area of the yellow triangle is 100 square centimeters and the area of the blue triangle is also 100 square centimeters due to congruency. The dimensions of the section of the yellow triangle overlapping the blue triangle are [tex]b = 14\,cm[/tex] and [tex]h = 7\,cm[/tex]. The area of this section is:

[tex]A' = \frac{1}{2}\cdot (14\,cm)\cdot (7\,cm)[/tex]

[tex]A' = 49\,cm^{2}[/tex]

And the area of the rest of the blue triangle is:

[tex]A'' = A - A'[/tex] (2)

[tex]A'' = 100\,cm^{2}-49\,cm^{2}[/tex]

[tex]A'' = 51\,cm^{2}[/tex]

In a nutshell, both triangles have an area of 100 square centimeters and the area of the blue triangle showing is 51 square centimeters.

We kindly invite to check this question on triangles: https://brainly.com/question/23103213

Start at 3, subtract 5 and you get -2

[tex]\boxed{\sf \displaystyle{\lim_{x\to a}}(x^n)=a^n}[/tex]

[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}(\sqrt{3x}-\sqrt{x-5})[/tex]

[tex]\\ \sf\longmapsto \displaystyle{\lim_{x\to \infty}}\sqrt{3x}-\displaystyle{\lim_{x\to \infty}}\sqrt{x-5}[/tex]

[tex]\\ \sf\longmapsto \infty^{\dfrac{1}{2}}-\sqrt{\infty-5}[/tex]

[tex]\\ \sf\longmapsto \infty-\sqrt{\infty}[/tex]

[tex]\\ \sf\longmapsto\infty-\infty[/tex]

[tex]\\ \sf\longmapsto\infty[/tex]

Answer:

can you answer this first

The discussion is shown below:

In computing, data is information that has been translated into a form that is efficient for movement or processing.

A hall way with laser imagine that you must cross the hall way while staying at equal distance from each laser.

So, from the question we can consider the a point o which is in between laser 1 and laser 2.

Learn more about data here:

https://brainly.com/question/10980404

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Answer:

y=-1/2x+2

Step-by-step explanation:

for x-intercept

put y=0

0= -1/2x+2

1/2x=2

x=4

(4,0)

for y-intercept

put x=0

y= 2

(0,2)

Answer:

a. solution

Area = 50 m^2

Area of square = l^2

or, 50 m^2 = l^2

or, √50m^2 = l

or, 5√2 m= l

Hence, The exact length of the playground is 5√2 m.

We are required to find how much the polygon has rotated after 12 minutes

The number of times the polygon has rotated after 12 minutes is 72°

Number of sides of the polygon = 60

The polygon rotates every minute, that is

1 rotation = 1 minutes

12 rotation = 12 minutes

one rotation of the clock is 360°

Number of times the polygon has rotated after 12 minutes = one rotation of the clock / Number of sides of the polygon × number of minutes

= 360°/60 × 12

= 6 × 12

= 72°

Learn more about polygons and clock:

https://brainly.in/question/5841490

Hey there!

I believe x might be 1296.

Look at the question closely, the square root of a number minus thirty-six equals zero.

The square root of 1296 would equal 36, so, 36 - 36 = 0.

Hope this helps!

Have a wonderful day!

Answer:

slope is 28.7/6

Step-by-step explanation:

m= y2-y1/x2-x1

subtitute value in formula:

m=28.8-0.1/7-1

m=28.7/6

2 3/4m for textbooks + 1 1/2m for Notebooks

2 3/4 + 11/2

11/4 + 3/2

11/4 + 6/4

17/4

4 1/4

5 1/2 - 4 1/4

11/2 - 17/4

22/4 - 17/4

5/4

1 1/4

1 1/4 meters of plastic cover will be left

HOPE THIS HELPS. GOODLUCK:)

Answer:

There are 240 boys.

Step-by-step explanation:

There are five boys to every three girls in an introductory Chinese course. Given that there are 384 students enrolled in total, we want to determine the amount of students which are boys.

Let b represent the number of boys and g girls.

Since the ratio is 5:3, we can write that:

[tex]\displaystyle \frac{5}{3} = \frac{b}{g}[/tex]

And since the total number of students is 384:

[tex]b + g = 384[/tex]

From the first equation, cross-multiply:

[tex]5g = 3b[/tex]

Solve for g:

[tex]\displaystyle g = \frac{3}{5} b[/tex]

Substitute:

[tex]\displaystyle b + \left (\frac{3}{5} b\right) = 384[/tex]

Simplify:

[tex]\displaystyle \frac{8}{5} b = 384[/tex]

Solve for b:

[tex]\displaystyle b = \frac{5}{8}\left(384\right) = 240[/tex]

In conclusion, 240 of the total students are boys.

Answer:

1/4

Step-by-step explanation:

its 0.25 which is rational. and its between the two.

The argument; if he did not get a good wage, then he must not have studied medicine is valid.

Let P represent "He studies medicine"

Let Q represent "He gets a good job"

Let R represent "He gets a good wage"

The argument can be written as:

P → Q

Q → R

¬R

∴ ¬P (conclusion: he did not study medicine)

Assume for contradiction that the argument is invalid:

P → Q

Q → R

¬R

P (assumption for contradiction: he studied medicine)

Use modus ponens to derive Q from (5) and (1):

Q (from 1 and 5 using MP)

Use modus ponens again to derive R from (6) and (2):

R (from 2 and 6 using MP)

This contradicts ¬R in (3), so our assumption in (5) must be false. Therefore, we can conclude that the argument is valid:

¬P (from contradiction of assumption in (5))

Learn more about valid proof:https://brainly.com/question/30458110

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Answer:

D. rectangles

Step-by-step explanation:

Perpendicular is when they cross but the base isn't perpendicular

Parallel is when two lines never touch, but in the base of a prism there are lines that touch

Intersecting is when two or more lines meet and cross over each other

Answer:

B

Step-by-step explanation:

(7×2)⁶

when we put a number to the power of something, we need to include the whole number. bit just a part of it.

so, it must be 7⁶×2⁶

just think about the simple example 6², which we could write as (2×3)².

would it be sufficient to e.g. square only one of the factors ?

6² = 36

but e.g. 2×3² = 18. so, that's really not it.

or add the two factors and then square them ?

2+3 = 5. 5² = 25. so, that's not it either.

or multiply the exponent in ?

2×3×2 = 12. so that's not it either.

no, it truly is you need to do the operation to all parts.

2²×3² = 4×9 = 36. yes, that fits.

therefore, B is the right answer.

Answer:

2 sorry i don't know that's what answer i got

Answer:

Go to multiple schools in urban and rural areas and find out how much exercise they get. Compare the data/research to find out if one gets more than the other, less, or equally the same amount of exericise.

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The parallel lines cut the transversals proportionally, so we have ...

  (10 -x)/x = 3/2

  2(10 -x) = 3x . . . . . . . multiply by 2x

  20 -2x = 3x . . . . . . . eliminate parentheses

  20 = 5x . . . . . . . . . . add 2x

  4 = x . . . . . . . . . . . . divide by 5

Answer:

[tex]{ \underline{ \sf{x \: is \: \: \{ \frac{ - 5 + i \sqrt{35} }{10} \} } \: \: and \: \: \{ \frac{ - 5 - i \sqrt{35} }{10} \}} }[/tex]

Step-by-step explanation:

[tex]5 {x}^{2} + 4x + 3 = 0 [/tex]

from quadratic formular:

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

general equation:

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

a is 5, b is 4 and c is 3:

substitute in formular:

[tex]{ \sf{x = \frac{ - 5± \sqrt{ {5}^{2} - (4 \times 5 \times 3) } }{(2 \times 5)} }} \\ \\ { \sf{x = \frac{ - 5± \sqrt{ - 35} }{10} }}[/tex]

but from complexes, i² = -1

[tex]{ \sf{x = \frac{ - 5± \sqrt{35 {i}^{2} } }{10} }} \\ \\ = { \sf{x = \frac{ - 5±i \sqrt{35} }{10} }}[/tex]

Hi! I'm happy to help!

To solve this problem, we have to find the slope, which is rise over run, or how much the line rises and how far forward the line goes.

We find the slope using this formula (slope formula)

m(slope)=[tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

This refers to the second y point minus the first y point, divided by the second x point minus the first x point. Y refers to the y axis, so that is the rise, because it is the difference of height in the line. X refers to the x axis, so that is the run, because it is the difference in how far it travels forward.

Our second y point is -2, our first y point is also -2. Our second x point is -2, and our first y point is 4. Let's plug in our values.

[tex]\frac{-2-(-2)}{-2-4}[/tex]

Let's simplify this so there isn't a double negative.

[tex]\frac{-2+2}{-2-4}[/tex]

Now, let's solve

[tex]\frac{0}{-6}[/tex]

0 divided by -6, is still 0, so there is no slope or the slope is 0. This means that the line is horizontal and the y coordinate doesn't change.

I hope this was helpful, keep learning! :D

Answer:

1/24 chance

Step-by-step explanation:

To begin you would need to find the probability of picking a green sock which would be 3/9; and you could simplify this to 1/3.

After that you need to find the probability of picking a purple sock out of the 8 left, which would provide you with 1/8. To find the probability of both you would multiply 1/8 by 1/3 to find the combined probability which would leave you with 1/24.

9514 1404 393

Answer:

  81

Step-by-step explanation:

Rewriting the expression as powers of 3, we get ...

  [tex]\dfrac{27^x}{3^y}=\dfrac{(3^3)^x}{3^y}=3^{3x-y}=3^4=\boxed{81}[/tex]

Answer:

4d - 6

Step-by-step explanation:

-2-(-15d)+(-11d)+2-6

-2 + 15d - 11d + 2 - 6

15d - 11d - 2 + 2 - 6

4d - 6

[tex]x^2\gt2x-2[/tex]

[tex]x^2-2x+2\gt0[/tex]

You are essentially asking at this point where is the quadratic function greater than 0. To get the interval find the roots. Between the roots the function is guaranteed to be LESS THAN zero. Everywhere else the function is greater than 0.

[tex]x^2-2x+2=0[/tex]

Use Vieta's rule to get the roots,

[tex](x-1)(x-1)=0[/tex]

Both roots are the same so no value is less than 0 which means all values except at the point of root are strictly greater, the point of root is at [tex]x_{1,2}=1[/tex] which means the set for which the quadratic function is greater than 0 is [tex]\mathbb{R}-\{1\}[/tex] "all real numbers except 1".

To convert this into interval notation use all numbers up to 1 but not including and all numbers after 1 but not including,

[tex](-\infty,1)\cup(1,\infty)[/tex]

Hope this helps :)

⇛ -12 + 8

⇛ -4

‌

‌

‌

[tex] \: [/tex]

Hey there!

The word “sum” simply means “to add” or “addition” in mathematical terms

So, we have to ADD -12 from 8 from each other.

Positives are on the RIGHT side of the number line whereas negatives are on the LEFT side of the number line

Start at -12 and go UP 8 spaces to the right.

-12 + 8

= -4

Answer: -4

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)