3 · 32 + 8 ÷ 2 − (4 + 3)

Answer:

D

Step-by-step explanation:

The two triangles are similar by the property side angle side.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

Here in the triangles, the angle is equal and the sides are dilated by factor two from 18 to 9. It means that the sides are similar to each other and the angle is the same.

To know more about similarities follow

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Answer:

Hey there!

72 athletes can eat for 6 days.

1 athlete can eat for 6(72), or 432 days.

54 athletes can eat for 432/54, or 8 days.

They can eat for 2 more days.

Let me know if this helps :)

Answer:

8 days

Step-by-step explanation:

sufficient food for 72 athlete to last 6 days

when 18 athletes are absent : 72-18=54

multiply scouts by days , to see how many food is packed :

72*6=432

then divide the amount of food packed by the number of scout attended:

432/54= 8 days

Answer:

Amount of 5% solution = 5.7 Litres

Amount of 40% solution = 4.3 Litres

Step-by-step explanation:

First, of all, let x be the amount of 5% solution used

Since, the scientist needs 10 L of solution, then;

Let 10 - x be the amount of 40% solution used

Now, we are told that she needs 10 L of a 20% acid solution.

This means that;

5%x + 40%(10 - x) = 20%(10).

Simplifying this gives;

0.05x + 0.40(10 - x) = 0.20 × 10

Expanding the bracket gives;

0.05x + 4 - 0.4x = 2

0.4x - 0.05x = 4 - 2

0.35x = 2

x = 2/0.35

x ≈ 5.7 litres

Thus, she will need to mix 5.7 liters of the 5% solution.

Since 10 - x be the amount of 40% solution used , then;

the amount of 40% solution = 10 - 5.7 = 4.3 litres

Answer:

[tex]t \: = ( \frac{2a - 7}{3} )[/tex]

Step-by-step explanation:

2a+ 2t = 5t + 7

2a - 7 = 5t - 2t

2a - 7 = 3t

t = answer

The formula for t is, [tex]t=\frac{2a-7}{3}[/tex]

Given expression is,

                              [tex]2(a + t) = 5t + 7[/tex]

Now solve above expression,

                          [tex]2(a + t) = 5t + 7\\\\2a+2t=5t+7\\\\2a-7=5t-2t\\\\2a-7=3t\\\\t=\frac{2a-7}{3}[/tex]

Hence, The formula for t is, [tex]t=\frac{2a-7}{3}[/tex]

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Answers:

25 = 5*5 which is the same as 25 = 5^2

100 = 2*2*5*5 which is the same as 100 = 2^2*5^2

16 = 2*2*2*2 which is the same as 16 = 2^4

====================================================

Explanation:

To find the prime factorization of 25, we divide by prime numbers. We see that 25/2 = 12.5 isn't a whole number, and neither is 25/3 = 8.33 (approx). But 25/5 = 5 is a whole number. The result is a prime number so we can stop here. This shows that 25 = 5*5 = 5^2

------------

We'll do the same for 100 as well. Start with dividing over 2

100/2 = 50

50/2 = 25

we can't do 25/2 as mentioned earlier, but we can say 25/5 = 5

So basically 100 = 2*2*25 = 2*2*5*5 = 2^2*5^2

-------------

The same will happen with 16 as well. We divide by 2 until we arrive at a prime number result

16/2 = 8

8/2 = 4

4/2 = 2

We have three 2's as denominators and that last result 2 is included in the set of prime factors as well to say 16 = 2*2*2*2 = 2^4

-------------

The factor tree for each is shown below. For something like 100, there are a few ways to draw out the tree. The same applies for 16 as well.

Answer:

Step-by-step explanation:

[tex](-2,3) =(x_1,y_1)\\\\Slope=m= -6\\\\[/tex]

Substitute values into point slope form

[tex]y -y_1 =m(x-x_1)\\y -3=-6(x - (-2))\\y -3 =-6(x+2)\\y -3 =-6x -12\\y =-6x -12+3\\y =-6x -9[/tex]

Answer:

y=-6x-9

Step-by-step explanation:

You can write the equation in slope intercept form.

y=mx+b

m is the slope and b is where the line intersects the y axis.

If the slope is -6,

y=-6x+b

We can find b by trying all different options until we get to the line that intersects (-2,3)

Answer:

∠ EFH = 112°

Step-by-step explanation:

∠ ACD and ∠ EFH are Alternate exterior angles and are congruent, thus

11x - 20 = 9x + 4 ( subtract 9x from both sides )

2x - 20 = 4 ( add 20 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Thus

∠ EFH = 11x - 20 = 11(12) - 20 = 132 - 20 = 112°

Answer:

The approximate length of one side of the canvas (approximate to the nearest hundredth inch)= 10.63

Step-by-step explanation:

There are two ways to solve this problem . One is the use of the calculator and the other is the use of the fraction.

Now the square has equal sides length = breadth .

So we can simply find the length on one side by taking square root with the help of the calculator .

So when you press the symbol of square root after entering the number 113 we get the answer 10.63

Square = Length * breadth

Square = Length * length

Square = L²

One side =√ L²= L so √113= 10.63

The approximate length of one side of the canvas (approximate to the nearest hundredth inch)= 10.63

Answer:

Consecutive par .. 2,4,6,8 .....

positive difference between 6 and 8

8-6 = 2; this difference will always be 2 regardless of the number if it is consecutive even.

Step-by-step explanation:

Answer:

The length of the rectangle is 15 cm.

Step-by-step explanation:

breadth(b)=?

length(l)= 3+2b

perimeter(P)= 42 cm

Now,

  P = 2 ( l+b )

or, 42= 2 ( 3+2b+b)

or, 42 = 2 ( 3+3b)

or, [tex]\frac{42}{2}[/tex] = 3+3b

or, 21 = 3+3b

or, 21-3 =3b

or, 18 = 3b

or, [tex]\frac{18}{3}[/tex] = b

or, 6 = b

Here, Breadth(b)= 6 cm

Length (l) = 3 + 2*6

              = 3 + 12

              =15 cm

Answer:

40 points

Step-by-step explanations

divide 50 by 5 to get the number of answers

you get 10 answers so then you subtract 2 and get 8

times that by 5 and you get the answer 40

Answer:

x > -7

Step-by-step explanation:

Step 1: Translate

Twice a number = 2x

Six more = + 6

At least = >

-8 = -8

Step 2: Write out inequality

2x + 6 > -8

Step 3: Solve

2x > - 14

x > -7

Answer:

The value of a mathematical expression is the result of the computation described by this expression when the variables and constants in it are assigned values. The value of a function, given the value(s) assigned to its argument(s), is the value assumed by the function for these argument values.

Step-by-step explanation:

Yes, the value of an expression does mean the answer.

The value of an expression is a variable that is assigned to a number.

Lets say we have 3n + 2 = 10.

"n" is the variable and we need to find the value of it.

In that kind of question, that is the answer for an expression.

But there are cases where we have the value and we need to solve with it. Then, the value would not be the answer.

Best of Luck!

Answer:

No Real Solutions

Step-by-step explanation:

So we have:

[tex]x-2\sqrt{x-3}=0[/tex]

First, determine the domain restrictions. The expression under the radical cannot be less than 0. Therefore:

[tex]x-3\geq 0\\x\geq 3[/tex]

Therefore, our final answers must be greater than or equal to 3:

Now, going back to the original equation, subtract x from both sides:

[tex]-2\sqrt{x-3}=-x[/tex]

Now, square both sides:

[tex]4(x-3)=x^2[/tex]

Distribute:

[tex]4x-12=x^2[/tex]

Subtract 4x and add 12 to both sides:

[tex]0=x^2-4x+12[/tex]

This isn't factor-able. Let's use the quadratic formula. a is 1, b is -4 and c is 12:

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

Substitute:

[tex]x=\frac{4\pm\sqrt{(-4)^2-4(1)(12)}}{2(1)}[/tex]

Simplify the radical:

[tex]x=\frac{4\pm\sqrt{-32}}{2(1)}[/tex]

The number under the radical is negative. In other words, there are no real solutions.

Answer:

in the intersection region of all the solution in the system.

Answer:

8

Step-by-step explanation:

Remember median is the middle. What you have to do is put them in oder from least to greatest. Then go from the left to right and cross one out until you get to the midde.

Answer:

SOHCAHTOA.

TOA=opposite/adjacent.

Tan45=100/h.

h tan45=100.

h×1=100.

h=100m

Answer:

[tex]\Huge \boxed{\mathrm{100 \ meters}}[/tex]

Step-by-step explanation:

The base of the right triangle created is 100 meters.

The angle between the base and the hypotenuse of the right triangle is 45 degrees.

We can use trigonometric functions to solve for the height of the tower.

[tex]\displaystyle \mathrm{tan(\theta)=\frac{opposite}{adjacent} }[/tex]

Let the height be x.

[tex]\displaystyle \mathrm{tan(45)}=\frac{x}{100}[/tex]

Multiplying both sides by 100.

[tex]\displaystyle 100 \cdot \mathrm{tan(45)}=x[/tex]

[tex]100=x[/tex]

The height of the tower is 100 meters.

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{7.5}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{ - 3 \div \frac{ - 2}{5} }[/tex]

If any number or fraction is divided by a fraction , we multiply the dividend by the reciprocal of the divisor

⇒[tex] \sf{ \frac{ - 3}{1} \times \frac{5}{ - 2} }[/tex]

To multiply one fraction by another , multiply the numerators for the numerator , and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

⇒[tex] \sf{ \frac{ - 3 \times 5}{1 \times ( - 2)} }[/tex]

⇒[tex] \sf{ \frac{ - 15}{ - 2} }[/tex]

Divide -15 by -2

⇒[tex] \sf{7.5}[/tex]

Hope I helped!

Best regards!!

Answers:

================================================

Explanation:

There are 3 right triangles here. They are all similar triangles allowing us to form the proportion

7/h = h/56

which solves to...

7/h = h/56

7*56 = h*h

392 = h^2

h^2 = 392

h = sqrt(392)

h = sqrt(196*2)

h = sqrt(196)*sqrt(2)

h = 14*sqrt(2)

Note: h is the geometric mean of 7 and 56.

---------------------

Use the pythagorean theorem to solve for 'a'. Focus on the smaller triangle on the left

7^2 + h^2 = a^2

7^2 + (sqrt(392))^2 = a^2

49 + 392 = a^2

441 = a^2

a^2 = 441

a = sqrt(441)

a = 21

---------------------

Then we can find b. Again use the pythagorean theorem. Focus on the largest right triangle this time.

a^2 + b^2 = (7+56)^2

21^2 + b^2 = 63^2

441 + b^2 = 3969

b^2 = 3969 - 441

b^2 = 3528

b = sqrt(3528)

b = sqrt(1764*2)

b = sqrt(1764)*sqrt(2)

b = 42*sqrt(2)

Answer:

n = -4/9

Step-by-step explanation:

8n + 9 = -n +5

Add n to each side

8n+n + 9 = -n+n +5

9n +9 = 5

Subtract 9 from each side

9n+9 - 9 = 5-9

9n /9 = -4/9

Divide each side by 9

n = -4/9

Answer:

x=-12

Step-by-step explanation:

[tex]\frac{x}{h}+1=-2\\ \frac{x}{4}=-2-1\\ \frac{x}{4}=-3\\ x=4*-3=-12[/tex]

Answer:

-2

Step-by-step explanation:

15x+6=6x-12

15x-6x=-12-6

9x=-18

x=-2

Answer: b. False

Step-by-step explanation:

The term " correlation" defines the nature of the relationship between the two quantities.

The term "causation" defines the effect of one variable one the other.

They both are used to analyse the relationship between variables such that

Presence of causation implies there is correlation between variables but correlation does not imply causation.

So, correlation coefficient (r) has nothing to do with the cause.

That means having a good correlation of r = 0.71 between the time spent playing video games each week and grade point average for a group of high school boys doesn't imply that playing video games causes students to get lower grades.

Hence, the given statement is False.

Answer:

295.936

Step-by-step explanation:

First find out what 544^2 is.  That is 295,936.  There are 100 ml in 1 liter.  So divide 295,936 by 100 to see how many liters are in 295,936 ml.  

295,936÷100=295.936

Answer:

L= 16 m

W= 12 m

Step-by-step explanation:

let us define the parameters of the parallelogram

let the length be L

and the width be W

given that the W= L-4

perimeter= 72 meters

We know that the perimeter of a parallelogram is given as

[tex]P=2L + 2W[/tex]

Substituting W= L-4 for W we have

[tex]72=2L + 2(L-4)\\\\72= 2L+2L-8 \\\\72= 4L-8\\\\4L= 72-8\\\\4L= 64[/tex]

Divide both sides by 4 we have

[tex]L= 64/4\\\\L= 16 m[/tex]

From w= L-4 we can find w by setting L= 16

W= 16-4

W= 12 m

Answer:

[tex]\huge \boxed{x=180}[/tex]

Step-by-step explanation:

15% of x = 27

[tex]\sf 15\% \cdot x =27 \\\\\\ 0.15x=27 \\\\\\ Divide \ both \ sides \ by \ 0.15. \\\\\\ \frac{0.15x}{0.15} = \frac{27}{0.15} \\\\\\ x = 180[/tex]

15% of 180 is 27.

Answer:

x = 180

Step-by-step explanation:

15% of x = 27

x = 27 / 0.15

x = 180

Answer:

ijwnecijnec

Step-by-step explanation:

ijwmcijncipjnecjn dn nnnev

Answer:

the jogger runs 80000 centimeters.

Step-by-step explanation:

1 metre = 100 centimeters (cm)

so if the jogger runs 800 metres, it means he jogs

800 × 100 cm

= 80000 cm

Answer:

237

Step-by-step explanation:

29 + 16 * 13

= 29 + 208

= 237