The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?

O 24
O 15
O 30
O 33

Answer:

x = -1, y = 1.5

Step-by-step explanation:

3x + 6y = 6 -----> x + 2y = 2

-3x + 2y = 6 -----> -3x + 2y = 6

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

4x = -4

x = -1, y = 1.5

Answer: 15 goats

Step-by-step explanation:

h = hens - they have 2 legs

g = goats - they have 4 legs

The equations would be:

h + g = 19

2h + 4g = 68

To solve this, I personally prefer substitution, we're isolating h since we need to find g:

h + g = 19

h = 19 - g

Now that we have h, we can plug this into the second equation:

2h + 4g = 68

2(19 - g) + 4g = 68

38 - 2g + 4g = 68

2g = 30

g = 15

There are 15 goats.

Adding onto this, 19 - 15 = 4, so there are 4 hens.

Answer:

A = 42 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 6 and h = 7 , then

A = 6 × 7 = 42 cm²

Answers:

height = 4.46 units

area = 26.73 square units

Both values are approximate

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

Explanation:

h = height of the triangle

Focus on the smaller triangle on the left.

Use the cosine ratio to find h

cos(angle) = adjacent/hypotenuse

cos(27) = h/5

h = 5*cos(27)

h = 4.4550326 approximately

Your calculator needs to be in degree mode.

We can now find the area of the overall largest triangle.

area = 0.5*base*height

area = 0.5*12*4.4550326

area = 26.7301956

area = 26.73

Answer with a step-by-step explanation:

1) First, let us find the height of the triangle.

For that let us use cos theta to find the triangle's height.

Let us use the below formula to find it.

Let the height (adjacent ) be h.

Let us find it now.

cos Θ = Adjacent ÷ hypotenuse

cos 27° = h ÷ 5

0.8910 = h ÷ 5

0.8910 × 5 = h

4.455 = h

Therefore the height of the triangle is 4.455 units.

2) And now let us find the area of the triangle.

The formula to find the area of a triangle is:

Let us find it now.

A =  [tex]\frac{1}{2}[/tex] × base × height

A =  [tex]\frac{1}{2}[/tex] × 12 × 4.455

A =  [tex]\frac{1}{2}[/tex] × 53.46

A = 26.73 units²

The perimeter of the triangle is 21.4 units

The points are given as:

A(−2,2), B(5,−3), and C(−4,−1)

Calculate the side lengths using:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]

So, we have:

[tex]AB = \sqrt{(-2 -5)^2 + (2 + 3)^2} = 8.6[/tex]

[tex]AC = \sqrt{(-2 +4)^2 + (2 + 1)^2} = 3.6[/tex]

[tex]BC = \sqrt{(5+4)^2 + (-3 + 1)^2} = 9.2[/tex]

The perimeter is then calculated as:

P = AB + AC + BC

This gives

P = 8.6 + 3.6 + 9.2

Evaluate

P = 21.4

Hence, the perimeter of the triangle is 21.4 units

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5[tex]\sqrt{3}[/tex]

Special right triangles, such as the one shown, have unique equations that can be used to find missing sides.

30-60-90 Triangles

The angle measurements show us that this is a 30-60-90 triangle. This name refers to the 3 angle measurement. There are 2 types of special right triangles, 45-45-90 and 30-60-90. For most triangles, it would take the law of sine or cosine to find a missing side with only 1 side given. But, with special right triangles, we can use shortcuts to find a.

Formulas

For all 30-60-90 triangles, there are 3 sides: the hypotenuse (c), the long leg (a), and the short leg (b). The shortcuts for 30-60-90 triangles are based on the length of the short leg.

The formulas are as follows (the variables match the variable given in the figure):

Solving for a

So, to find a, we must first find b. Since b is equal to half of c, we can divide the value of c by 2.

Thus, b = 5

Next, plug this value into the formula for b

Answer:

Last option

Step-by-step explanation:

cos30° = a/10  

a = 10cos30°

     [tex]cos30=0.8660=\frac{\sqrt{3} }{2}[/tex]

[tex]a=10(\frac{\sqrt{3} }{2} )=5\sqrt{3}[/tex]

Hope this helps

Answer:

7*36=21*x

252=21x

x=12

Hope it helps!

Answer:

12

Step-by-step explanation:

Let x be the unknown number.

Method 1

[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]

[tex]\implies \sf 252 = 21x[/tex]

[tex]\implies \sf \dfrac{252}{21} = \dfrac{21x}{21}[/tex]

[tex]\implies \sf 12=x[/tex]

[tex]\implies \sf x=12[/tex]

Method 2 (using mental arithmetic)

[tex]\implies \sf 7 \times 36 = 21 \times x[/tex]

As 7 and 21 are both multiples of 7, divide both sides by 7:

[tex]\implies \sf 36=3x[/tex]

Divide both sides by 3:

[tex]\implies \sf 12=x[/tex]

[tex]\implies \sf x=12[/tex]

The conditional probability values are 0.57 and 0.43

               Has Eaten before   Have not           Total

Snack A     144                               108                252

Snack B      92                               228                320

Total          236                              336                572

Using the data in a table, the company that makes snack A calculates probabilities related to a random selected person.

The required probabilities are conditional probabilities, and they are calculated using:

P(A | B) = P(A and B)/P(B)

Using the above formula, we have:

The probability that a customer eats snack A given that the customer has eaten snack A before, to be:

P = n(Have eaten snack A)/n(Snack A)

This gives

P = 144/252

Evaluate

P = 0.57

Also, we have:

The probability that a customer eats snack A given that the customer has not eaten snack A before, to be:

P = n(Have not eaten snack A)/n(Snack A)

This gives

P = 108/252

Evaluate

P = 0.43

Hence, the probabilities are 0.57 and 0.43

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Answer:

Two angles and a side

Step-by-step explanation:

In order to prove triangles congruent, you'd have to either have an angle, angle, and then a side in that exact order for AAS or you can have two angles and a side in the middle of them for ASA.

Answer:

y=160

Step-by-step explanation:

y=90+14(x)

x=5

y=90+14(5)

y=90+70

y=160

Hope this helps!

If not, I am sorry.

Answer:

40 square units

Step-by-step explanation:

The question gives that both the large shape and the small missing shape are rectangles.  The formula for the area of a rectangle is [tex]A=bh[/tex] where "A" is the "Area", "b" is the "base" (bottom edge), and "h" is the height (side edge).

For rectangles, opposite sides (example: top & bottom) have the same length, so the top of the missing rectangle must also be 3.

To find the area of the figure, we must find the difference (subtraction) between the large rectangle (without a hole out of it) and the rectangular hole.

[tex]A_{\text{figure}}=A_{\text{large rectangle without hole}}-A_{\text{hole}}\\A_{\text{figure}}=(7)(7)-(3)(3)\\A_{\text{figure}}=49-9\\A_{\text{figure}}=40[/tex]

So, the area of the figure is 40 square units.

Answer:

40

Step-by-step explanation:

We can make a big square by making a line at the top open edge (as shown in the image attached below). We will first solve for [tex]A_{2}[/tex] and then [tex]A_{1}[/tex], and then finally solving for out answer by subtracting [tex]A_{1}[/tex] from [tex]A_{2}[/tex] .

[tex]A_{2}[/tex] is a square with side lengths of 7, so the area is 7 * 7 = 49.

[tex]A_{1}[/tex] is a smaller square with side lengths of 3, so the area is 3 * 3 = 9.

[tex]A_{2} - A_{1} = 49 - 9 = 40[/tex]

∴ Our final answer is 40

Answer:

14

Step-by-step explanation:

to find f(value), we plug that x value into the equation

so, if..

f(x)= 3x² -x

f(-2)= 3 · (-2)² - (-2)

f (-2) = 3 · 4 + 2

f (-2) = 12 + 2

f (-2)  = 14

Answer:

14

Step-by-step explanation:

f(x) =3x^2-x

here,

f(-2)= 3(-2)^2 -(-2)

=3*4+2

=12+2

=14 Answer.

Answer:

This point is not on the line, NOT TRUE

Step-by-step explanation:

The equation of the line is written in the slope-intercept form,

y = mx + b

where m represents the slope

          b represents the y-intercept

where the format of a point is (x, y)

Given: y = 3x - 5.1, (-1.2, -3.1)

we can plug in the point (-1.2, -3.1)

-3.1 = 3(-1.2) - 5.1

-3.1 = -3.6 - 5.1

-3.1 = -8.7

-3.1 does not equal -8.7 so this point is not on the line

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Answer:

2.4 × 10⁶

Step-by-step explanation:

Given:

To calculate the value of R, substitute the given values into the given formula:

[tex]\begin{aligned}\sf R & = \sf \dfrac{x^2}{y}\\\\ \implies \sf R& = \sf \dfrac{(3.8 \times 10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{3.8^2 \times (10^5)^2}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44 \times 10^{10}}{5.9 \times 10^4}\\\\& = \sf \dfrac{14.44}{5.9} \times \dfrac{10^{10}}{10^4}\\\\& = \sf 2.4474... \times 10^{(10-4)}\\\\& = \sf 2.4474... \times 10^6\\\\\end{aligned}[/tex]

Therefore, the value of R to 1 decimal place is 2.4 × 10⁶

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

Exponent Rules used

[tex](a^b)^c=a^{bc}[/tex]

[tex]{a^b}{a^c}=a^{b-c}[/tex]

[tex]R = \frac{ {x}^{2} }{ y} \\ \\ R = \frac{ {(3.8 \times {10}^{5})}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{ ({3.8})^{2} \times ( { {10}^{5} )}^{2} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10} }{5.9 \times {10}^{4} } \\ \\ R = \frac{14.44 \times {10}^{10 - 4} }{5.9} \\ \\ R = 2.45 \times {10}^{6} [/tex]

Answer:

-8x²-3x+5

Step-by-step explanation:

First, add like terms.

3-6x-2x²+3x-6x²+2=

= 5-3x-8x²

Put it in standard form. To put in standard form, put the exponent from greatest to least.

-8x²-3x+5.

Hope this helps!

If not, I am sorry.

Answer: False

Step-by-step explanation: An expression is a sentence with a minimum of two numbers or variables and at least one math operation.

Expressions do not have an equal sign because they do not have an answer.

Answer:

ok the first point there is (-4;-3)

the second point is(0;-6)

a. The survey method is unlikely to result in a representative sample

b. Interview people on all days of the week.

A representative sample is a sub-section of a larger population and has similar characteristics of the main group population.

a. The population of the study is the entire consumers that shop at the supermarkets who shop all days of the weeks. Therefore, asking only shoppers who shopped on Monday will most likely give you a bias response as most customers may select Wednesday. The sample doesn't represent the entire population.

b. A better survey method is picking samples on all days of the week and ask them.

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Answer:

Each student ticket costs $10, and each adult ticket costs $17.

Step-by-step explanation:

Let s represent the cost of a student ticket and a represent the cost of an adult ticket.

31s + 32a = 854

31s + 31a = 837

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

a = 17

31s + 31(17) = 837

31s + 527 = 837

31s = 310, so s = 10

Answer:

Mikaela's team scored 5.3 points, in whole number form 5.

Step-by-step explanation:

If Viktoria's team's score was 7, 2 more than twice is (7*2) +2.

(7*2)+2=16

16 is three times Mikaela's team's score. Reduced by three means just to divide.

16/3=5.3

Mikaela's team scored 5 points.

Hope this helps!

If not, I am sorry.

Answer:

8

Step-by-step explanation:

Make it into an equation.

2x+2=(3x7)-3

2x+2=21-3

2x+5=21

2x=16

x=8

8

Answer:

6779

Step-by-step explanation:

69

Answer:

-4/3

Step-by-step explanation:

mtan × mline = -1

mtan× 3/4 = -1

mtan =-4/3

Answer:

The product of the Width and Length is x^2 + 4x + 3 cm^2.

Step-by-step explanation:

The volume of a box = 5x^3 + 20x^2 + 15x cm^3.

Volume of a Box = W*L*H       [Width(W), Length(L), and Height(H)]

W*L*(5x) = 5x^3 + 20x^2 + 15x cm^3

W*L = (5x^3 + 20x^2 + 15x cm^3)/5x cm

W*L = x^2 + 4x + 3 cm^2

We know the area of the base of the box (W*L).  It is x^2 + 4x + 3 cm^2.

To find the actual width and length, we need to know one of the variables, L or W.  Without that, all we can say is that their product (W*L) is x^2 + 4x + 3 cm^2.

The correct value that equates to this expression is q¹⁰

.

To solve this expression, just:

[tex]{ = \large \sf (q {}^{5} ) {}^{2} } [/tex]

[tex]{ = \large \sf q {}^{5 \times 2} } [/tex]

[tex] \pink{ \boxed{ = \large \sf q {}^{10} } } \\ [/tex]

Therefore, the answer will be q¹⁰

Answer:

Q¹⁰

Step-by-step explanation:

Given that,

Solution:

Well,there is a law of exponents,which states that:

Same case is here as well.

Just multiply both powers given.

5*2 = 10

Hence, the expression equivalent to (Q⁵)² is (Q)¹⁰

Answer:

The answer is D

Cuba, Poland, U.S., Argentina, Turkey, and Spain

Step-by-step explanation:

Basically, what it was asking, is what countries are over 90%? So, all you have to do - to put it simply - is just look at the countries that's numbers are greater than 90%

Answer:

21500

Step-by-step explanation:

21500 people would have to see the movie to recuperate their losses.

The number of people would have to see the movie is given by the equation A = 2600 people

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people to see the movie in first four weeks be A

Now , the equation will be

The cost of movie license per week = ₹ 1500

The cost of movie license per month = 4 x ₹ 1500

The cost of movie license per month = ₹ 6000

And ,

The cost of keeping the stuff and hall for a month = ₹ 20,000

So ,

The cost of movie license and the hall for a month = 20,000 + 6000

The cost of movie license and the hall for a month = ₹26,000

The cost of charge of each seat = ₹ 10

So , the number of people to see the movie in the first four weeks in order for them to recoup the costs A = cost of movie license and the hall for a month / cost of charge of each seat

Substituting the values in the equation , we get

Number of people to see the movie in first four weeks A = 26000/10

Number of people to see the movie in first four weeks A = 2600 people

Hence , the number of people is 2600 people

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