Drag the tiles to the correct boxes to complete the pairs.
Match the systems of equations with their solution sets.
y + 12 = 1² + s
s+y = 3
y - 17 = 12 -9r
- + y = 1
Solution Set
(2,3) and (8,9)
(-2,3) and (7-6)
(-2,5) and (3,-5)
(-5,8) and (3,0)
y-15 = -12 + 4s
=+y=1
y + 5 = 1²-3r
2s + y = 1
Linear-Quadratic System of Equations

The first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13

The formula of the sequence is given as:

an = 3(n -1) + 1

The above sequence is an arithmetic sequence, and the first five terms are the values of the sequence when the value of n is from 1 to 5

i.e. n = 1, 2, 3, 4 and 5

Next, we set n = 1, 2, 3, 4 and 5, and substitute these values for n in an = 3(n -1) + 1

So, we have the following equations

First term

a1 = 3(1 -1) + 1 = 1

Second term

a2 = 3(2 -1) + 1 = 4

Third term

a3 = 3(3 -1) + 1 = 7

Fourth term

a4 = 3(4 -1) + 1 = 10

Fifth term

a5 = 3(5 -1) + 1 = 13

Hence, the first five terms of the sequence represented as an = 3(n -1) + 1 are 1,4, 7, 10 and 13

Read more about sequence at:

https://brainly.com/question/15412619

#SPJ1

The system of inequalities that represents the graph are y >  -x + 3 and y ≤  2x - 2

A line is the shortest distance between two points. The equation of a line in slope-intercept form is y = mx + b

For the broken line, the coordinate points will be(0, 3) and (3, 0)

m = -3/3

m = -1

The equation of the line will be y >  -x + 3

For the solid line, the coordinate points will be(0, -2) and (1, 0)

m = 2/1

m = 2

The equation of the line will be y ≤  2x - 2

Hence the system of inequalities that represents the graph are y >  -x + 3 and y ≤  2x - 2

Learn more on inequality here; https://brainly.com/question/24372553

#SPJ1

Answer:

D, x = 9

Step-by-step explanation:

[tex]x\left(2+5\right)=63[/tex]

=> divide both side by 7

[tex]\frac{x\left(2+5\right)}{7}=\frac{63}{7}[/tex]

x=9

Answer:

D) 9

Step-by-step explanation:

Given :

⇒ 18 + 45 = x (2 + 5)

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

Simplify both sides :

⇒ 18 + 45 = x (2 + 5)

⇒ 63 = 7x

⇒ 7x = 63

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

Divide both sides by 7 :

⇒ 7x/7 = 63/7

⇒ x = 9

The scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Scaling is the way of enlarging or reducing the image of an object.

Given scale model of a building is 3 inches, if the building is 90feet tall, to write the scale;

Convert both measures to same units

Since 1 feet. = 12 in

90 feet = 90/12 in = 7.5 in

Take the ratio

3 : 7.5 = 30: 75

Reduce to lowest term

30: 75 = 2 : 5

Hence the scale model of a building 3 inches tall if the building is 90 feet tall is 2:5

Learn more on scale model here: https://brainly.com/question/261465

#SPJ1

Answer:

[tex]P(36 < X < 43)\approx83.5\%[/tex]

Step-by-step explanation:

Use a TI-84 to calculate the probability

[tex]P(\text{Lower} < X < \text{Upper})=\text{normalcdf}(\text{Lower},\text{Upper},\mu,\sigma)\\\\P(36 < X < 43)=\text{normalcdf}(36,43,38,2)\approx0.8351\approx83.5\%[/tex]

Step-by-step explanation:

a = hours at job A

b = hours at job B

a + b = 24

a = 24 - b

5.8a + 7.4b = 158.4

note we can use the a = 24 - b identity in the second equation :

5.8×(24 - b) + 7.4b = 158.4

139.2 - 5.8b + 7.4b = 158.4

1.6b = 19.2

b = 12 hours

a = 24 - b = 24 - 12 = 12 hours

she worked 12 hours on job A and 12 hours on job B.

Answer: X = 6

Step-by-step explanation:

Substitute the x’s in the equation for the answer options that are provided.

Solutions of quadratic equation x = √(-2x + 48) are x = -8 and x = 6.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given, quadratic equation;

x = √(-2x + 48)

Squaring on both sides,

x² = -2x + 48

x² + 2x - 48 = 0

Now, we have to solve for x.

Simplifying,

x² + 8x - 6x - 48 = 0

(x + 8)(x -6) = 0

(x + 8) = 0 and (x -6) = 0

x = -8 and x = 6

After eliminating the extraneous solutions;

we have,

x = -8 and x = 6.

Therefore, the solutions are x = -8 and x = 6.

To learn more about the quadratic equation;

https://brainly.com/question/17177510

#SPJ2

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of the translated line segment will be A' (3,6) and B' (5,6).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Since AB is a line segment the changes will occur on both the coordinates, therefore, if the line segment is translated 2 units down and 2 units left, the coordinates will be,

A = (5,8) → 2 units down ⇒ (5, 8-2) → 2 units left ⇒ (5-2, 8-2) = (3, 6)

B = (7,8) → 2 units down ⇒ (7, 8-2) → 2 units left ⇒ (7-2, 8-2) = (5, 6)

Hence, the coordinates of the translated line segment will be A' (3,6) and B' (5,6).

Learn more about Coordinates:

https://brainly.com/question/23450276

#SPJ1

The points on the line are points B and D

The equation is given as:

y = x + 4

The above means that the output value is 4 more than the input value

Using the above rule, the points that satisfy the equation are:

B) 2, 6 and D) 2, 4

This is so because:

6 = 2 + 4

4 = 2 + 2

Hence, the points on the line are points B and D

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer:

Find the area land of each town.

Let x be the area of town D

then, x+ 30000 is the area of town C

we know that,

the total area of town C and town D is 120,000 square miles.

x+x+30000=120000

2x= 90000

x=45000

Area of town D= 45000 square miles

Area of town C= 45000+30000= 75000 square miles.

Step-by-step explanation:

if the squares of the two shorter sides add up to the square of the hypotenuse, the triangle contains a right angle

bbc

10 squared = 100

13 squared = 169

17 squared = 289

100 + 169 = 269 NOT 289 so

there is no right angle and so its not a right triangle

Answer:

Step-by-step explanation:

if the volume of a cube is 27cm³ what are the dimensions of the cube​

Cube Volume = l³

we use the inverse formula

∛V = l

so

∛27 =

3 cm

Answer:

Step-by-step explanation:

Area A(t) = πR² = π x 400 (t + 2) = 400π (t + 2)

A(2) = 400π (2 + 2) = 1600π = 5026.5 in²

Answer:

2x+15 =6x-45 [Alternate Angles]

or, 15+45 =6x-2x

or, 60 =4x

or 60/4 =x

or 15 = x

# x=15

Answer:  [tex]y^9[/tex]

This is the same as saying y^9

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

Explanation:

When we apply the square root to the expression [tex]a^{2b}[/tex], we end up with [tex]a^b[/tex]

[tex]\sqrt{a^{2b}} = a^b[/tex]

The exponent 2b divides in half to get b

Based on that rule, we can then say:

[tex]\sqrt{y^{18}} = y^{18/2} = y^9[/tex]

A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

If we plot the function, y = 4x⁴ - 8x² + 4, then it can be observed that the lists all of the turning points of the graphs are (–1, 0), (0, 4), and (1, 0).

Hence, the correct option is C.

Learn more about Function:

https://brainly.com/question/5245372

#SPJ1

Answer:

z = 86 °

and, x = 2

Step-by-step explanation:

We know that a straight line is a 180 degree-angle. So, we know that

94 + z must equal 180, because they are the only two angles that make up the straight line.

from this information, (that 94 + z = 180) we can easily find z.

(this is typically an intuitive method of subtracting 94 from 180)

94   +   z   =   180

-94                  -94

z = 86 °

-- we know that the relation between z and (10x + 74) must also be equal to 180, as they make up a straight line

if z = 86, then we can know that (10x + 74) must be equal to

(10x + 74) + 86 =    180

                - 86        -86

(10x + 74) = 94

10x + 74 = 94

      - 74   - 74

  10 x     =    20

÷ 10            ÷ 10

     x    =   2

so, z = 86 °

and, x = 2

(I am assuming that this "unprotected placement assessment" has already taken place, and you would like to understand a question. Or, this is a practice assessment. Because there is no point to cheating on a placement assessment--you will just skip over material you don't know. And, it wouldn't align with Brainly's honor policy. Hope you learn from this!!)

The number of children and adults who bought the tickets at the circus was 500 and 900 respectively.

let

x + y = 1400

22x + 46y = 52,400

From equation (1)

x = 1400 - y

Substitute into (2)

22(1400 - y) + 46y = 52,400

30,800 - 22y + 46y = 52,400

- 22y + 46y = 52,400 - 30,800

24y = 21,600

y = 21,600 / 24

y = 900

substitute y into

x + y = 1400

x + 900 = 1400

x = 1400 - 900

x = 500

Learn more about equation:

https://brainly.com/question/1214333

#SPJ1

The number of children's ticket that was bought is 500.

The number of adult's ticket that was bought is 900.

a + b = 1400 equation 1

22a + 46b = 52,400 equation 2

Where:

Multiply equation 1 by 22

22a + 22b = 30800 equation 3

Subtract equation 3 from equation 2

21,600 = 24b

b = 21,600 / 24

b = 900

Subtract 900 from 1400

1400 - 900 = 500

To learn more about simultaneous equations, please check: https://brainly.com/question/25875552

#SPJ1

Answer:

Step-by-step explanation:

[tex]\text {modulus of z } = =\sqrt{\left( -3\right)^{2} +\left( 1\right)^{2} } =\sqrt{9+1} =\sqrt{10}[/tex]

Answer:

square root of 10

Step-by-step explanation:

the answer would be 240 because wind speed is close to its median

Answer:

(x - 3) is a factor of P(x)

Step-by-step explanation:

if (x - 3) is a factor of P(x) then P(3) = 0

P(3) = 2(3)³ + 5(3)² - 28(3) - 15

      = 2(27) + 5(9) - 84 - 15

      = 54 + 45 - 99

      = 99 - 99

      = 0

since P(3) = 0 then (x - 3) is a factor of P(x)

Interpretation 1:

[tex]5x = 15 \\ [/tex]

Divide both sides by 5:

[tex]\implies \boxed{x = 3}[/tex]

(Which is the final answer.)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

Interpretation 2:

[tex] 5^{x}=15[/tex]

Take logarithm to the base 5 on both sides:

[tex]\implies log_5(5^{x})=log_5(15)\\\implies x=log_5 (15) \\\implies x= \frac{ln(15)}{ln(5)} \\\implies \boxed{x≈1.683} [/tex]

(Which is a thing too!)

[tex]\huge\mathfrak\colorbox{white}{}[/tex]

P. S.: Now please don't tell me that this is a PhD level question and this is referring to the Knuth's Up-Arrow Notation. Which translates the question into something like: [tex]^{5}x=15[/tex]

Answer:

Step-by-step explanation:

what would be the answer to this ?

Solve.

5x=15

x = 15 : 5

x = 3

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

check

5 * 3 = 15

the answer is good

Answer:

(4, -6)

Step-by-step explanation:

(x1+x2)/2 + (y1+y2)/2 = midpoint

(11+-3)/2 = 8/2 = 4.     x = 4

(-5 + -7)/2 = -12/2.      y = -6

4, -6 is the midpoint

give brainliest please! hope this helps :)

Step-by-step explanation:

this is very easy u can do urself

The What is the population of interest are:

The data collection method according to the group below

The best data collection method for the first one oatmeal  and GMC students is survey because the population is large and opinions may differ.

The best data collection method for the cars  is Experiment as one needs to study the cars that pass the red lights

For one of the three studies, a census is possible in the first one because the study population is the Georgia which is very large.

For the two studies the one that a census is not needed is GMC students and cars at red light because the population is not too big.

Based on the study I will use 500 people, 200 students, or 300 cars and the  sampling technique would be Systematic sampling, Simple random sampling and Judgmental/purposive sampling.

A  Simple random sampling is known to be the easiest method of selecting a sample as every member is known to have an equal chance of being selected in the sample.

See the other part of the question below

Write a reply

Consider the following statistical studies:

1. A study (in Georgia) of the effect of eating oatmeal on lowering cholesterol.

2. A study of current GMC students next career move after graduating or transferring from GMC.

3. A study of how many cars run the red light at a certain intersection in Macon, GA.

Learn more about statistical studies from

https://brainly.com/question/15525560

#SPJ1

[tex]\left|\dfrac{2}{13}t-11\right|-10=-16\\\\\left|\dfrac{2}{13}t-11\right|=-6\\\\x\in\emptyset[/tex]

Let's say you are paddling at 5mph and the current is 3 mph. Going upstream, you are going 2 mph and downstream, 8 mph.

8(b - c) = 464

7(b + c) = 644

b - c = 58

b + c = 92

Adding the two together

2b = 150

b = 75

75 - c = 58

c = 17

The boat's speed is 75 mph and the current's speed is 17 mph.

Answer: 32

Step-by-step explanation:

Since [tex]\overline{FG} \parallel \overline{AC}[/tex], we know that by the corresponding angles theorem, [tex]\angle BFG \cong \angle BAC[/tex] and [tex]\angle BGF \cong \angle BCA[/tex].

Thus, [tex]\triangle BFG \sim \triangle BAC[/tex] by AA.

It follows that since corresponding sides of similar triangles are proportional,

[tex]\frac{36+90}{90}=\frac{CG+80}{80}\\ \\\frac{126}{90}=\frac{CG+80}{80}\\\left(\frac{126}{90} \right)(80)=CG+80\\112=CG+80\\CG=\boxed{32}[/tex]