1. What is the solution of the system of equations?
y = -3x + 8
y = -5x - 2

They have a total time of 3 hours and they equally spend at each exhibit which means that they spent 18 minutes on each exhibit.

The four fundamental operations of arithmetic are addition, subtracting, multiplying, and dividing two or more numbers. Included is the study of integers, especially the order of operations, which is essential for all other aspects of mathematics, notably algebra, information management, and geometry.

As per the given information in the question,

Total time = 3 hours

Time in minutes = 3 × 60 = 180 minutes

They have 10 exhibits to visit.

The time spent on each exhibit is,

180/10 = 18 minutes on each exhibit.

To know more about arithmetic operations:

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Answer:

Let z=−4+0i. Then, ∣z∣=

(−4)

2

+0

=4

Clearly, the point (−4,0) representing z=−4+0i lies on the negative side of real axis. Therefore, principal argument of z is π.

Answer:

d am

Step-by-step explanation:

Answer:

The one in the middle 100% correct

Answer:

second option

Step-by-step explanation:

Ratio of square to circle = 1 : 3

In the second option:

Square = 2  & circles = 6

Ratio = 2 : 6  and after simplifying, Ratio = 1 : 3

Answer:

The answer is 3x-y-2=0

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate the slope using the slope formula

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

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (2, 4) ← 2 points on the line

m = [tex]\frac{4-1}{2-1}[/tex] = 3

The line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = 3x - 2 ← in slope- intercept form

subtract y from both sides

0 = 3x - y - 2 , that is

3x - y - 2 = 0 ← in general form

Answer:

(-5,31/2)

Step-by-step explanation:

open bracket

y=1/2x^2+5x+28

compare with y=ax2+bx+c

use formula (-b/2a,4ac-b2/4a)

the arc length is calculated by the formula                                                                    [tex]\displaystyle\bf C=\frac{2\pi r}{360} \cdot\alpha[/tex]   then   [tex]\displaystyle\bf C=\frac{2\cdot 8 \pi }{360} \cdot180=8\pi=3,14\cdot8=25.12[/tex]   or it can be calculated using the circumference of the circle since we have a semicircle the circumference 2πr must be divided by 2  С=2πr:2=πr =8π=25,12

Respuesta:

Significar

Explicación paso a paso:

Las medidas del centro incluyen la media, la mediana y la moda. La media se obtiene tomando la suma de los valores dividida por el número de valores individuales (frecuencia). La mediana es el percentil 50 de la distribución y la moda es el valor que ocurre con mayor frecuencia si se trata de una distribución. De todas las medidas, la media es la más afectada por la presencia.

Dados los datos:

2,4, 5, 2, 3, 3, 3, 5

La media = Σx / N = 2.3

Modo = 3

Mediana = 2, 2, 3, 3, 3, 4, 5, 5 = 1/2 * nth = 1/2 * 8 = 4to término = 3

Si se agrega un valor extremo: digamos 80

2, 2, 3, 3, 3, 4, 5, 5, 2, 80

Nueva media = Σx / N = 11,88

Mediana = 1/2 (n + 1) th término

Mediana = 1/2 (10) término = 3

Modo = 3

Podemos ver que la inclusión de 80, que es un valor extremo, cambia significativamente el valor medio.

Answer:

A) y = -5/8x + 6

Step-by-step explanation:

y2 - y`1 / x2 - x1

7/2 - 11 / 4 - (-8)

-15/2  / 12

= -5/8

y = -5/8x + b

11 = -5/8(-8) + b

11 = 5 + b

6 = b

Answer:

Option (A)

y = - 5 / 8 x + 6

Step-by-step explanation:

Two points are

(x', y') = ( - 8, 11 )

(x'', y'') = (4, 7/2)

The equation o line passing through two points is given by

[tex](y - y') = \frac{y'' - y'}{x''-x'}(x-x')\\\\(y - 11)= \frac{\frac{7}{2}-11}{4+8} (x + 8)\\\\y - 11 = \frac{-5}{8}(x + 8)\\\\y -11 = \frac{-5x}{8} - 5\\\\y = \frac{-5x}{8} + 6[/tex]

So, option (A) is correct.  

Answer:

The slope is -2/3 and the y-intercept is -1.

Step-by-step explanation:

In a linear equation like this, the slope is the coefficient in front of the x after the expression has been completely simplified. In this case, the slope is -2/3.

For the y-intercept, that is simple too; since it is simplified, it is just the number that comes after the x package. So, for this, the y-intercept is -1.

Answer:

-1

Step-by-step explanation:

1. Sets the exponents equal

3b-1 = b-3

2. collect like terms and calculate it

3b-b=1-3

2b= -2

(divide both side by 2)

b=-1

find the DB =[tex]\displaystyle\bf \sqrt{17^2-8^2} =15[/tex]  ; now find AD=AB-DB=21-15=6  .Then                AC=[tex]\displaystyle\bf \sqrt{AD^2+CD^2} =\sqrt{6^2+8^2} =10[/tex]  

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD = [tex]\sqrt{225}[/tex] = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC = [tex]\sqrt{100}[/tex] = 10 → C

Answer:

[tex]{ \tt{LM = ON}} \\ { \bf{6x - 7 = 2x + 9}} \\ { \bf{4x = 16}} \\ x = 4 \\ \\ { \bf{LM = 6(4) - 7}} \\ { \boxed{ \tt{LM = 17 \: units}}}[/tex]

Answer:

8(X^2+1)

Step-by-step explanation:

(X²+3)²-(X²-1)

(X²+3)(X²+3)-(X²-1)(X²-1)

X⁴+3X²+3X²+9-(X⁴-X²-X²+1)

X⁴+6X²+9-(X⁴-2X²+1)

X⁴+6X²+9-X⁴+2X²-1

8X²+8

Answer:

The height of the tree=8.42 m

Step-by-step explanation:

We are given that

Height of Joshua, h=1.45 m

Length of tree's shadow, L=31.65 m

Distance between tree and Joshua=26.2 m

We have to find the height of the tree.

BC=26.2 m

BD=31.65m

CD=BD-BC

CD=31.65-26.2=5.45 m

EC=1.45 m

All right triangles are similar .When two triangles are similar then the ratio of their corresponding sides are equal.

[tex]\triangle ABD\sim \triangle ECD[/tex]

[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]

Substitute the values

[tex]\frac{AB}{1.45}=\frac{31.65}{5.45}[/tex]

[tex]AB=\frac{31.65\times 1.45}{5.45}[/tex]

[tex]AB=8.42m[/tex]

Hence, the height of the tree=8.42 m

Answer:

Only 10 base units to learn

Step-by-step explanation:

The metric system is a decimal based system developed to be universally acceptable by making use of base units from obtained from nature and the use of prefixes for multiples and submultiples of the base units, decimal ratios, which allows easy representation of quantities, as well as having a coherent structure of base and derived units which are obtained from the base units

During conversion in the metric system, which is decimal based, it is only required to move the decimal point

The prefixes which are used to specify multiples and submultiples are the same through out

The decimal system is based on the powers of ten

The number of base units to learn are 7 including; 1. Meter (m), 2. Kilogram (kg), 3. Second (s), 4. Ampere (A), 5. Kelvin (k), 6. Candela (cd), and 7. mole (mol)

Therefore the metric system has several advantages that include all of the following except; Only 10 base units to learn

Answer:

1.25% and 16 times

Step-by-step explanation:

Since the interest is compounded quarterly it will be compounded 4 times a year. So 4 x 4 is 16, so it will be compounded 16 times.

Then you have to divide the 5% by four to get how much will be compounded each quarter. So, (0.05 / 4) = 0.0125, which is 1.25%.

Answer:

1.25% and 16 times

Step-by-step explanation:

Answer: C

Step-by-step explanation: A straight angle is 180 degrees:

180-130 = 50

Triangle angles equal up to 180.

50 + 2y =180

y =65

SUM OF INTERIOR OPPOSITE ANGLES = EXTERIOR ANGLE .

[tex]130 = y + y \\ 130 = 2y \\ \frac{130}{2} = y \\ \frac{ \cancel{130}^ { \tiny \: \: \: \: 65} }{ \cancel{2}} = y \\ y = 65 \degree[/tex]

Answer:

t ≈ 3.65 s

Step-by-step explanation:

Let the distance the object travels after leaving the balloon be x.

Using Newton's equation of motion, we have;

s = ut + ½gt²

We are given;

s = 30 m

u = -10 m/s (negative because it is an upward motion)

Thus;

30 = -10t + ½(10)t²

30 = -10t + 5t²

5t² - 10t - 30 = 0

Using quadratic formula, we have;

t ≈ 3.65 s

Answer:

well your answer should be "F"

Step-by-step explanation:

we have

Y<-2x+10  -----> inequality A

The solution of the inequality A is the shaded area below the dashed line

Y = -2x+10

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

Y<1/2x-2 ----> inequality B  

The solution of the inequality B is the shaded area below the dashed line

Y= 1/2x-2

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G

i hope this helps

Answer:

0.037

Step-by-step explanation:

Given that,

Let a and b be the solutions to [tex]x^2 + x -3 = 0[/tex]

It can be solved using quadratic formula where a = 1, b = 1 and c = -3

So,

[tex]x=\dfrac{-1+\sqrt{1^2-4\times 1\times (-3)}}{2(1)},\dfrac{-1-\sqrt{1^2-4\times 1\times (-3)}}{2(1)}\\\\x=1.30,-2.3[/tex]

Let a = 1.3, b = -2.3

The value of [tex]a^3 -4b^2 + 19[/tex] can be given by :

[tex]a^3 -4b^2 + 19=(1.3)^3-4\times (-2.3)^2+19\\\\=0.037[/tex]

So, the value of the given expression is 0.037.

Answer:

(-7, -3)

Step-by-step explanation:

So the formula is (x, y) --> (-y, x) for a 90 degrees counterclockwise rotation.

To apply this formula to (-3,7), first identify which is the x-coordinate and which is the y-coordinate.

x-coordinate is -3 & y-coordinate is 7

Then you literally just substitute it into the formula like so:

(-y, x) -->(-(7), (-3)) --> (-7, -3)

Try to put parantheses around the coordinate when substituting to prevent confusion & incorrect negative signs.

Hope it helps and good luck (●'◡'●)

Answer:

(-7,-3)

Step-by-step explanation:

You could read (x,y)->(-y,x) as if I have the point (x,y), the image point is (opposite of y,x).

So shorthand the rule is just saying

(x,y)->(opposite of y, x)

(-3,7)->(-7,-3)

A few more examples:

(5,7)->(-7,5)

(-5,7)->(-7,-5)

(-5,-7)->(7-,5)

(5,-7)->(7,5)

This whole explanation comes down to reading-u as opposite of u.

Opposite just means to change the sign.

Another way to read -u is -1×u.

Example:

Q: evaluate -u if u=8

A: -8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×8=-8 or the opposite or 8 is -8.

Example:

Q: evaluate -u if u=-8

A: 8

Why? -u means -1×u or opposite or u. Take your pick in reading it. It's the same meaning just different ways of reading. -1×-8=8 or the opposite or -8 is 8.

Answer: Commutative property of addition

Step-by-step explanation:

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\text{1 + 3 + 4 = 4 + 3 + 1}[/tex]

[tex]\large\text{1 + 3 + 4}[/tex]

[tex]\large\text{4 + 4}[/tex]

[tex]\large\text{= \bf 8}[/tex]

[tex]\large\text{4 + 3 + 1}[/tex]

[tex]\large\text{7 + 1}[/tex]

[tex]\large\text{= \bf 8}[/tex]

[tex]\large\text{\bf 8 = 8}[/tex]

[tex]\large\textsf{We could remove Option C. because there’s no sign of multiplication.}[/tex]

[tex]\large\textsf{This leaves us to Option A and Option B because the equation(s) has}\\\large\textsf{sum/addition}[/tex]

[tex]\large\textsf{Associative Property of Addition formula is:}[/tex]

[tex]\bullet\large\text{ \bf (a + b) + c = a + (b + c)}[/tex]

[tex]\large\textsf{Commutative Property of Addition formula is:}[/tex]

[tex]\bullet\large\text{ \ \bf a + b = b + a}[/tex]

[tex]\boxed{\boxed{\large\textsf{Answer: \huge \bf Commutative Property of Addition}}}\\\boxed{\huge\textsf{(Option B.)}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Option (1)

Step-by-step explanation:

Given inequality is,

-4(x + 3) ≤ -2 - 2x

Further solve this inequality,

-4x - 12 ≤ -2 - 2x

-4x + 2x - 12 ≤ -2 - 2x + 2x

-2x - 12 ≤ -2

-2x - 12 + 12 ≤ -2 + 12

-2x ≤ 10

-x ≤ 5

x ≥ -5

Therefore, on a number line draw an arrow starting with a solid circle (because of equal to sign) and moving towards the numbers greater than -5.

Option (1) is the answer.

Answer:

A.

Step-by-step explanation:

4y = 12x + 16

3x = y - 4

=>

y = 3x + 4

using that in the first equation

4(3x+4) = 12x + 16

12x + 16 = 12x + 16

=> both lines/equations are identical, so they have infinitely many solutions.

The equation will be:

25 + d = t

where t is total money