what is the solution to this set of equations? show your work.

y=5x-9

y=x^2-3x+7

Answer:

[tex]\large\boxed{C.\ domain:\ \{x\ |\ x\ \text{is a real number}\};\ range:\ \{y\ |\ y>2\}}[/tex]

Step-by-step explanation:

[tex]f(x)=\left(\dfrac{1}{6}\right)^x+2\\\\\text{The domain:}\ x\in\mathbb{R}\to\{x\ |\ x\ \text{is a real number\}}\\\\\lim\limits_{x\to\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=0+2=2\\\\\lim\limits_{x\to-\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to-\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\{y\ |\ y>2\}\\\\\bold{Look\ at\ the\ picture}[/tex]

Answer: Option C

domain: {x | x is a real number}; range: {y | y > 2}

Step-by-step explanation:

We have the function [tex]f(x) =(\frac{1}{6})^x + 2[/tex]

Note that f(x) is an exponential function.

By definition the exponential functions of the form [tex]a(b)^x +k[/tex]  have as domain all real numbers and as range {y | y > k}  if [tex]a>0[/tex], [tex]b>0[/tex]

Where a is the main coefficient, b is the base and k is the vertical displacement.

In this case [tex]k = 2[/tex], [tex]b=\frac{1}{6}[/tex], [tex]a=1[/tex]

Therefore the domain of f(x) is all real numbers and the range of f(x) is

{y | y > 2}

Answer:

[tex]Area=1,325\ yd^2\\Perimeter=204\ yd[/tex]

Step-by-step explanation:

You can use the following formula to calculate the area of the triangle:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

You can observe in the figure that:

[tex]b=53\ yd\\h=50\ yd[/tex]

Then, the area is:

[tex]A=\frac{(53\ yd)(50\ yd)}{2}=1,325\ yd^2[/tex]

To find the perimeter you must add the lenght of each side of the triangle. Then, this is:

[tex]P=97\ yd+53\ yd+54\ yd\\\\P=204\ yd[/tex]

[tex]\bf \textit{area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=64\pi \end{cases}\implies 64\pi =4\pi r^2 \\\\\\ \cfrac{64\pi }{4\pi }=r^2\implies 16=r^2\implies \sqrt{16}=r\implies 4=r[/tex]

The radius of the sphere will be 4 meters. Thus, the correct option is D.

Let r be the radius of the sphere. Then the surface area of the sphere will be given as,

SA = 4πr² square units

The surface area of the sphere is 64π square meters. Then the radius of the sphere is calculated as,

64π = 4 x π x r²

r² = 16

r = 4 meters

Thus, the correct option is D.

More about the surface area of the sphere link is given below.

https://brainly.com/question/29251585

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Answer:

Each burrito platter costs $_31__ and each taco platter costs $_23__ .

Step-by-step explanation:

Let the cost of a burrito platter be x and the cost of a taco platter be y;

4 burrito platters and 5 taco platters would cost;

4x  + 5y = 239

3 burrito platters and 5 taco platters would cost;

3x + 5y = 208

We can solve the two equations simultaneously via elimination method. We subtract the two equations in order to eliminate y and solve for x;

4x - 3x = 239 - 208

x = 31

Using the first equation, substitute x = 31 and solve for y;

4(31) + 5y = 239

124 + 5y = 239

5y = 115

y = 23

Simplify 6/9 to 2/3

2/3 = x + 2/24

Simplify 2/24 to 1/12

2/3 = x + 1/12

Subtract 1/12 from both sides

2/3 - 1/12 = x

Simplify 2/3 - 1/12 to 7/12

7/12 = x

Switch sides

x = 7/12

Answer:

The measure of angle LMN is 68° ⇒ the last answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- The rhombus has 4 equal sides in length

- Every two opposite angles are equal in measure

- Every two adjacent angles are supplementary (their sum = 180°)

- The two diagonals bisect each other

- The two diagonals perpendicular to each other

- The two diagonals bisect the vertices angles

* Lets solve the problem

∵ LMNO is a rhombus

∴ ∠LMN and ∠MNO are adjacent angles

∴ ∠LMN and ∠MNO are supplementary

∴ m∠LMN + ∠MNO = 180°

∵ m∠MNO = 112°

∴ m∠LMN + 112° = 180° ⇒ subtract 112 from both sides

∴ m∠LMN = 68°

* The measure of angle LMN is 68°

Answer:

68

Step-by-step explanation:

Answer:28 + 10i

Step-by-step explanation: You first distribute.

(3i+4-i+4(6+2i)

3i +4-i+24+8i (Distribute)

3i - i = 2i + 8i= 10i and 4 + 24= 28 (Combine like terms)

10i + 28 or 28 + 10i

Answer:

Answer: 28 + 10i

Step-by-step explanation:

A P E X

Answer:

Well I think it is A because domain is the x values.

Step-by-step explanation:

So when you plug this in your calculator (mine is a ti-84 plus ce) you would hit graph. After it graphs it press Zoom, 0 to center it then press 2nd, trace which pulls up parabola menu's. Press 0 and find the left bound, right bound and then press enter which would give you x values of 2.9375 < t< 6

At the same time I don't know if this is right. I never really excelled at parabolas just trying to help.

Check the picture below.

so the domain will be the values that "x" gets, now, the maximum height of the ball is when it reaches the vertex or U-turn up above, well, what is the x-coordinate anyway?

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+94}t\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left( -\cfrac{94}{2(-16),}\qquad \qquad \right)\implies \left( \cfrac{487}{16},\qquad \qquad \right)\implies (2.9375,\qquad \qquad )[/tex]

so then x = 2.9375 at the vertex, now, what is "x" when it hits the ground? recall y = 0 at that instant.

[tex]\bf \stackrel{f(t)}{0}=-16t^2+94t+12\implies 0=-2(8t^2-47t-6) \\\\\\ 0=(8t+1)(t-6)\implies t= \begin{cases} \boxed{6}\\ \begin{matrix} -\frac{1}{8} \\[-0.5em]\cline{1-1}\\[-5pt]\end{matrix} \end{cases}[/tex]

so then, the values for "x" or namely the domain from the vertex till the ball hits the ground is 2.9375 < t < 6.

The answer is 18 inches.

Let r=radius and d=diameter

2r=d

2(9)=d

18=d

Hope this helps!

Answer:

18 inches

Step-by-step explanation:

Answer:

The answer is 450

Step-by-step explanation:

V = l*w*h

V = 15*10*3

V= 450

ANSWER

[tex]450 {cm}^{3} [/tex]

EXPLANATION

The prism shown is a rectangular prism or cuboid.

The volume of a cuboid is given by:

[tex]Volume=l \times b \times h[/tex]

From the diagram, the length is l=15cm ,the breadth is b=10cm and the height is h=3cm.

We substitute the values into the formula to obtain,

[tex]Volume=15 \times 10 \times 3[/tex]

We simplify to get,

[tex]Volume=450 {cm}^{3} [/tex]

Answer:

[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]

Step-by-step explanation:

From the Venn diagram:

So, in total,

6+11+15+12=44 participants took part in survey.

The two-way table looks like

[tex]\begin{array}{cccc}&\text{Like fish}&\text{Don't like fish}&\text{Total}\\\text{Like turtle}&6&15&21\\\text{Don't like turtle}&11&12&23\\\text{Total}&17&27&44\end{array}[/tex]

Answer:

12 I think........?....

Answer:

The answer is 12

Step-by-step explanation:

In this case, we just have to try with all of them:

Then it is not divisible (it is not integer). This proves the statement false.

Let's try with the others as well, just to check:

All the others don't prove false that statement.

Answer:

the answer is 500cm^3 and 250cm^3

Step-by-step explanation:

This is the correct answer to your question. Btw I wasn't able to answer it before so I commented on the answer above but now I can answer it like this, hope it helps! :)

The on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have:

A helium balloon is filled with 1,000 cm3 of helium.

First day of the balloon has 1000 cubic cm helium gas

Each day, the balloon loses half its helium.

After second day the amount of helium gas = 1000/2 = 500 cubic cm

After third day, the amount of helium gas = 500/2 = 250 cubic cm

Thus, the on second day and third day the amount of the helium gas will be left in the balloon gas will be 500 and 250 cubic cm respectively.

Learn more about the sequence here:

brainly.com/question/21961097

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Answer:

a) The sold games of Jezebel had the greatest spread.

b) The middle 50% of the games sold by Colin has the least spread.

c) Jezebel sold more games than colin.

Step-by-step explanation:

Range is sued to calculate the spread of the given data.

Range is given by:

[tex]Range=Max\ Value-Min\ Value[/tex]

So,

Part a)

For Collin:

Range=21-3=18

For Jezebel:

Range=26-5=21

Part b)

Middle 50% of the values will be the values between 1st quartile and 3rd quartile

So, to find quartiles:

For Colin:

=3,9,9,14,15,16,17,20,21

The median is 15.

The lower half is 3,9,9,14

Q1 = (9+9)/2= 18/2 = 9

The upper half is 16,17,20,21

Q3 = (17+20)/2= 37/2= 18.5

The middle 50% is first quartile subtracted from third quartile

So, the spread is:

18.5-9=9.5

For Jezebel:

4,5,8,10,11,14,20,20,26

The median is 11.

The lower half is 4,5,8,10

Q1 = (5+8)/2=13/2=6.5

The upper half is 14,20,20,26

Q3 = (20+20)/2=40/2=20

The middle 50% values' spread is:

20-6.5=13.5

Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..

ANSWER

C. Factoring a perfect square trinomial.

EXPLANATION

The first step shown is:

[tex] {x}^{2} + \frac{b}{a}x + ( \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]

Observe that the left hand side is a perfect square trinomial.

In other words, the left hand side is of the form,

[tex] {m}^{2} + 2mn + {n}^{2} [/tex]

which can be factored as:

[tex] {m}^{2} + 2mn + {n}^{2} = {(m + n)}^{2} [/tex]

When we factor the perfect square trinomial on the left hand side, we obtain:

[tex]( x + \frac{b}{2a} )^{2} = - \frac{c}{a} + ( \frac{b}{2a} )^{2}[/tex]

The correct answer is C

Answer:

FACTORING A PERFECT SQUARE TRINOMIAL!

Step-by-step explanation:

GOT IT CORRECT ON 3.8.3 AP-EX...

it's not sq root because that comes afterwards.

it's not completing the square because that's

x^2+ bx/a +(b/2a)^2=-c/a+(b/2a)^2

Then from there it's

x^2 + bx/a + b^2/4a^2 = -c/a + b^2/4a^2

(x + b/2a)^2 = b^2/4a^2 -c/a

Then that step ends. If you don't believe me look at study 3.3.1 page 13.

This will help!

Answer:

x=9

Step-by-step explanation:

(x+3)/2=6​

Multiply each side by 2

2*(x+3)/2=6*2

x+3 = 12

Subtract 3 from each side

x+3-3 = 12-3

x = 9​

Answer:

rate per month = .01 agreed = r

Luckily they only ask for the first month so it is 0.01 * 20 .

Later months get more complicated and it is like paying off a mortgage with the term unknown but the rate and payment known.

Payment = principal value [ r / {1-(1+r)^-n } ]

100 = 2000 [ .01 / {1 - (1.01)^-n } ]

5 = 1/ {1 - (1.01)^-n }

.2 = 1 - (1.01)^-n

.8 = 1.01^-n

log .8 = -n log 1.01

n = 22.4 months :)

so over the almost two years pay 2240 total :)

* Hopefully this helps:) Mark me the brainliest:)!!!

Final answer:

For Sheila's first payment on her new computer financed at 12% annual interest with $100 monthly payments, she will pay $20 towards interest and the remaining $80 will go towards the principal.

Explanation:

Sheila bought a new computer for $2000 and agreed to finance it at 12% annual interest, with $100 monthly payments. To calculate the interest she will pay with the first payment, we need to find 1% of $2000 (since 12% per year is equivalent to 1% per month).

(1% of $2000) = 0.01 * $2000 = $20

Therefore, when Sheila makes her first monthly payment of $100, $20 will go towards interest, and the remaining $80 will reduce the principal on her loan.

Answer:

x = - 2

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

f(x) + g(x) = x² - 2x + 6x + 4 = x² + 4x + 4 ← equating to 0

x² + 4x + 4 = 0 ← in standard form

(x + 2)² = 0 ← in factored form, thus

x + 2 = 0 ⇒ x = - 2

Answer:

-3/4

Step-by-step explanation:

Perpendicular slopes are reciprocal opposites of the original slope. This means that the reciprocal of 4/3 is 3/4, and the opposite of 3/4 is -3/4.

To find the perpendicular slope you must take the given slope take the opposite reciprocal (aka switch the sign and flip the fraction)

so...

[tex]\frac{-3}{4}[/tex]

^^^slope perpendicular to 4/3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

cdc

Step-by-step explanation:

1. The option is (A) mean = –25; median = –26.5; mode = –28; range = 40.

2. The option is (C) 13; 17.6; 20.

The median is the value that splits the mathematical numbers or expressions in the half. The median value is the middle number of data points. to find the median first arrange the data points in ascending order.

To find the mean, median, mode, and range of the data set, we first need to arrange the data in order:

–46, –39, –28, –28, –25, –17, –11, –6

Mean: To find the mean, we add up all the values and divide by the total number of values:

Mean = (-46 + -39 + -28 + -28 + -25 + -17 + -11 + -6) / 8

Mean = -25

Median: To find the median, we need to find the middle value of the data set.

Since there are 8 values, the median is the average of the 4th and 5th values:

Median = (-28 + -25) / 2

Median = -26.5

Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is –28, since it appears twice and no other value appears more than once.

Range: To find the range, we subtract the smallest value from the largest value:

Range = -6 - (-46)

Range = 40

Therefore, the answer is (A) mean = –25; median = –26.5; mode = –28; range = 40.

2.

A. The outlier in the data set is 37, since it is much larger than the other values.

B. To find the mean with the outlier, we add up all the values and divide by the total number of values:

Mean = (21 + 13 + 13 + 37 + 13 + 23 + 25 + 15) / 8

Mean = 17.6

C. To find the mean without the outlier, we need to exclude the value 37 and then calculate the mean using the remaining values:

Mean = (21 + 13 + 13 + 13 + 23 + 25 + 15) / 7

Mean = 17.6

Therefore, the answer is (C) 13; 17.6; 20.

To learn more about the median;

https://brainly.com/question/28060453

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Answer:

360 radical 2 or 509.11688

Step-by-step explanation:

simplify the radicals

12 =2 radical 3

calculate the products

10* 2 radical 3 * 6 radical 6

= 120 radical 18

again simplify

360 radical 2  

Answer:

360 radical 2

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Substitute y=6 into 2x+3y=36

2x+3(6) =36

2x + 18 = 36

2x = 18

x = 9

Answer:

x = 9

Step-by-step explanation:

Substitute y=6 into 2x+3y=36

2x+3(6) =36

2x + 18 = 36

2x = 18

x = 9

Answer:

x=3

Step-by-step explanation:

i just did it on ttm  

the y=14x-6

y=-4x=48

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Answer:

the answer would be 4

Step-by-step explanation:

The number 39□,077 to the nearest thousand and get 394,000, the thousands place digit must be 5 since that's the digit which would lead to rounding up. Hence, the correct digit to replace the □ would be 5.

Digits in the thousands place of the number 39□,077 would make it round to 394,000 when rounded to the nearest thousand. When rounding to the nearest thousand, we look at the hundreds place to decide whether to round up or down. The rules for rounding are if the hundreds place digit is 5 or higher, we round up, and if it is 4 or lower, we do not round up.

Therefore, to round up to 394,000, the digit in the hundreds place should be 5 or higher. This means that the options provided as possible answers:

3

4

5

Can be evaluated based on this rule. The digit 3 or 4 in the thousands place would not cause the number to round up, but the digit 5 would result in the number being rounded up to 394,000. Thus, the correct answer is 5.

To find the answer, I used:

Volume = Length • Height • Width

Each book in box 1 has a volume of 132 inches^3 and there are 16 of them, so I multiplied 132 inches^3 by 16 and got a total volume of 2,112 inches^3 in box 1

Each book in box 2 has a volume of 30 inches^3 and there are 30 of them, so I multiplied 30 inches^3 by 30 and got a total volume of 900 inches^3 in box 2

2,112 inches^3 is greater than 900 inches^3 so box 1 should be more than twice as big as box 2

2112 cubic inches.

To determine which of the two boxes is larger, we need to calculate the volume of each box. For the first box, containing books each measuring 3/2 in by 8 in by 11 in, the volume of one book is calculated as:

For the second box, containing books each measuring 3/4 in by 5 in by 8 in, the volume of one book is calculated as:

Comparing the two totals, the second box, with a total volume of 4500 cubic inches, is larger than the first box, which has a total volume of 2112 cubic inches. Hence, we know that the second box is larger because it has a greater total volume.

The wide side of the garden is 12 feet, so the other side would be 12 feet aswell.

12+12=24

To find the length of each long side, you subtract 60-12, then divide by 2.

60-12=48/2=24

Answer:

Step-by-step explanation:

The perfect square:

[tex](a+b)^2=a^2+2ab+b^2[/tex]

Q4

We have

[tex]y^2+14y+49=0\\\\y^2+2(y)(7)+7^2=0\\\\(y+7)^2=0\iff y+7=0\qquad\text{subtract 7 from both sides}\\\\\boxed{y=-7}[/tex]

Q5

We have

[tex]y^2+16y+64=0\\\\y^2+2(y)(8)+8^2=0\\\\(y+8)^2=0\iff y+8=0\qquad\text{subtract 8 from both sides}\\\\\boxed{y=-8}[/tex]

Hello There!

None of them would be the correct answer

Have a great day!

ANSWER

[tex]f(x + h) = \frac{4x + 4h}{1 - x - h}[/tex]

EXPLANATION

The given expression is

[tex]f(x) = \frac{4x}{1 - x} [/tex]

To find an expression for f(x+h), we substitute x+h, wherever we see x in the given expression.

This implies that,

[tex]f(x + h) = \frac{4(x + h)}{1 - (x + h)} [/tex]

We simplify to obtain;

[tex]f(x + h) = \frac{4x + 4h}{1 - x - h} [/tex]

Answer:

A

Step-by-step explanation:

(4x+4h)/(1-x-h)

Let a,b & c be the number of cookies Adrian, Bobby and Calvin baked respectively.

(a+b+c)/3 =138

(a+b)/2 =136

a+b=272

a=272-b

(b+c)/2 =125

b+c=250

c=250-b

Sub a=272-b and c=250-b into (a+b+c)/3 =138,

(a+b+c)/3 =138

[(272-b)+b+(250-b)]/3 = 138

272-b+b+250-b = 414

-b = -108

b=108

From the above,

a=272-b

=272-108

a=164

c=250-b

=250-108

c=142

∵ a=164

b=108

c=142

∴ Adrian baked 164 cookies.

Bobby baked 108 cookies.

Calvin baked 142 cookies.