y=–6x+2
–12x – 2y=–4
How many solutions does this linear system have?

Answer:

a)  2x + 4

b)  2x + 5

c)  8

d)  9

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x+1\\g(x)=2x+3 \end{cases}[/tex]

Function composition is an operation that takes two or more functions and combines them into a single function.

(f o g)(x) means find g(x) first and then substitute the result into f(x).

(g o f)(x) means find f(x) first and then substitute the result into g(x).

Part (a)

[tex]\begin{aligned}(f \circ g)(x) & = f[g(x)]\\& = g(x)+1\\ & = (2x+3)+1\\& = 2x+4\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}(g \circ f)(x) & = g[f(x)]\\& = 2[f(x)]+3\\& = 2(x+1)+3\\ & = 2x+2+3\\& = 2x+5\end{aligned}[/tex]

Part (c)

[tex]\begin{aligned}(f \circ g)(2) & = f[g(2)]\\& = g(2)+1\\ & = (2(2)+3)+1\\ & = (4+3)+1\\& = 8\end{aligned}[/tex]

Part (d)

[tex]\begin{aligned}(g \circ f)(2) & = g[f(2)]\\& = 2[f(2)]+3\\& = 2(2+1)+3\\ & = 2(3)+3\\ & = 6+3\\& = 9\end{aligned}[/tex]

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(fog)(x)

(gof)(x)

(fog)(2))

(gof)(2)

Answer:

landline

hshdjdh

dbbdhdhdh

bdbdhdhdhe

Answer:

Router

Step-by-step explanation:

Hope this helps

DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B

Defects per unit (DPU) can be defined as the number of defects divided by the number of opportunities

It is also seen as the universal measure of quality.

For example, if there are 100 defects in 1,000 units produced, then the defects per unit will be 0.01.

Defects per million opportunities can be defined as a mathematical calculation of the estimated quality of a process

From this information, we can conclude that DPU and DPMO are measure of defects in a sample.

Thus, DPU is the number of defects in a sample divided by the number of opportunities while DPMO is the number of defects divided by the number of units tested within a sample. Option B

Complete question is;

________ is the number of defects in a sample divided by the number of opportunities while ________ is the number of defects divided by the number of units tested within a sample.

a. DPMO, DPU

b. DPU, DPMO

c. RTY, FTY

d. FTY, RTY

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The required reserve ratio is 0.226 or 22.6%.

Given that a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities.

The following equality always holds.

Total liabilities=Total assets

It is given that the institution's only liabilities are transaction deposits.

This means:

Total transaction deposits=Total assets

Total transaction deposits=Required reserves + Excess reserves + Loans + Securities

Total transaction deposits=$164+$9+$417+$137

Total transaction deposits=$727

Calculate the required reserve ratio as follows:

Required reserve ratio=(Required reserves)/(Total transaction deposits)

Required reserve ratio=($164 million)/($727 million)

Required reserve ratio=0.226 or 22.6%.

Hence, the required reserve ratio when a depository institution holds $164 million in required reserves and $9 million in excess reserves and Its remaining assets include $417 million in loans and $137 million in securities is 0.226 or 22.6%.

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

Work Shown:

width = w

length = w+9

perimeter = 2*(length + width)

P = 2(w+9+w)

P = 2(2w+9)

P = 4w+18

4w+18 = P

4w+18 = 270

4w = 270 - 18

4w = 252

w = 252/4

w = 63 meters is the width

w+9 = 63+9 = 72 meters is the length

Check:

perimeter = 2*(length + width)

perimeter = 2*(72 + 63)

perimeter = 2*(135)

perimeter = 270

The answer is confirmed.

Option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively. This can be obtained by knowing what similar triangles are and finding which sides are proportional.

Similar triangles: If two triangles have proportional sides the are similar.

For example, if ΔABC and ΔDEF are similar then

[tex]\frac{AB}{DE}= \frac{BC}{EF} =\frac{AC}{DF}[/tex]

∠ABC = ∠DEF and ∠ACB = ∠DFE

Then we can write that, ΔABC ~ ΔDEF

Here in this question,

Since A, Y, Z are midpoints of sides XW, VW, XV

XA = AW

WY = VY

XZ = VZ

To consider sides AY and XV we should take triangles ΔWAY and ΔWXV

[tex]\frac{WX}{WA} =\frac{2WA}{WA} = 2[/tex]  (since A is the midpoint of WX)

[tex]\frac{WV}{WY} =\frac{2WY}{WY} = 2[/tex]  (since Y is the midpoint of WV)  

∠AWY = ∠XWV (reflexive property)

Therefore ΔWAY and ΔWXV are similar triangles

[tex]\frac{WX}{WA}= \frac{XV}{AY} =\frac{WV}{WY}[/tex] = 2

∠WAY = ∠WXV and ∠AYW = ∠XVW

Hence,

AY || XV option A AY || XV given that A, Y, Z are midpoints of sides XW, VW, XV respectively.

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Disclaimer: The question was given incomplete on the portal. Here is the complete question.  

Question: Analyze the diagram below and answer the question that follows. If Z, Y and A are midpoints of ΔVWX what is true about AY and XY?

A. AY || XV

B. 1/2 AY = XV

C. AY = XV

D. AY ≅ XV

Answer:

A

Step-by-step explanation:

The Volume of the Cylinder B is gotten as; 720 cm³

We are given 2 similar cylinders with;

ratio of heights = a : b

Thus;

ratio of areas = a² : b²

We are given that;

Height of A is 5cm.

Height of B is 10cm.

Thus;

Ratio of heights = 5 : 10 = 1 : 2

Therefore;

ratio of areas = 1² : 2² = 1 : 4

The cross sectional area of B is 4 times the cross sectional area of A. Thus;

Cross sectional area of B = 4 × 18 = 72 cm²

Volume of cylinder = cross section area × height

Volume of cylinder B = 72 × 10 = 720 cm³

The complete question is;

A and B are two cylinders that are mathematically similar.

The area of the cross-section of cylinder A is 18cm².

Height of A is 5cm.

Height of B is 10cm.

Work out the volume of cylinder B

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Esta estrategia se puede aplicar sumando  15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.

La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos  1,4 + 0,6  + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.

Este estrategia es beneficiosa porque facilita sumar números decimales.

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The ratio of bananas to fruit is 13 : 21

The given parameters are

Banana = 13

Apple = 8

The total number of fruits is

Fruit = Banana + Apple

Substitute the known values in the above equation

Fruit = 13 + 8

Evaluate the sum

Fruit = 21

The ratio of bananas to fruit is then represented as:

Ratio = Banana : Fruit

Substitute the known values in the above equation

Ratio = 13 : 21

Hence, the ratio of bananas to fruit is 13 : 21

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Answer:

SAVE WATER

Step-by-step explanation:

i)

x + 1 = 20

subtract 1 from both sides

x + 1 - 1 = 20 - 1

x = 19

19 = S

ii)

15 = 2x + 13

subtract 13 from both sides

15 - 13 = 2x + 13 - 13

2 = 2x

divide both sides by 2

2/2 = 2x/2

1 = x

1 = A

iii)

2x + 5 = 49

subtract 5 from both sides

2x + 5 - 5 = 49 - 5

2x = 44

divide both sides by 2

2x/2 = 44/2

x = 22

22 = V

iv)

[tex]\frac{3x + 3}{2}[/tex] = 9

multiply both sides by 2

[tex]\frac{3x + 3}{2}[/tex] x 2 = 9 x 2

3x + 3 = 18

subtract 3 from both sides

3x + 3 - 3 = 18 - 3

3x = 15

divide both sides by 3

3x/3 = 15/3

x = 5

5 = E

v)

8(x - 7) = 128

apply the distributive law

8x - 56 = 128

add 56 to both sides

8x - 56 + 56 = 128 + 56

8x = 184

divide both sides by 8

8x/8 = 184/8

x = 23

23 = W

vi)

16 = 2(x + 7)

apply the distributive law

16 = 2x + 14

subtract 14 from both sides

16 - 14 = 2x + 14 - 14

2 = 2x

divide both sides by 2

2/2 = 2x/2

1 = x

1 = A

vii)

[tex]\frac{7y}{7}[/tex] = 20

sevens cancel out

y = 20

20 = T

viii)

2x - 1 = 9

add 1 to both sides

2x - 1 + 1 = 9 + 1

2x = 10

divide both sides by 2

x = 5

5 = E

ix)

2(x - 8) = 20

apply the distributive property

2x - 16 = 20

add 16 to both sides

2x - 16 + 16 = 20 + 16

2x = 36

divide both sides by 2

2x/2 = 36/2

x = 18

18 = R

Code Word/s: SAVE WATER

hope this helps :)

Answer:

Save Water

Step-by-step explanation:

(I’m sorry it took so long, I had to write it out Σ(＝д＝ﾉ)ﾉ

I hope this helps! ヾ(>ꇴ<) xx

Equation (A) C= 1.46n shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n.

To find the right equation:

Therefore, equation (A) C= 1.46n shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n.

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The complete question is given below:
The total cost of gasoline varies directly with the number of gallons purchased. Kathy pays $23.36 for 16 gallons of gasoline. Which equation

shows the relationship between the total cost of gasoline, c, and the number of gallons purchased, n?

A.C= 1.46n

B. n = 1.46c

C.C = 23.361

D. n = 23.36c

Answer:

x + 4y = 7

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 m using the slope formula

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

with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (3, 1 )

m = [tex]\frac{1-2}{3-(-1)}[/tex] = [tex]\frac{-1}{3+1}[/tex] = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 2 )

2 = [tex]\frac{1}{4}[/tex] + c ⇒ c = 2 - [tex]\frac{1}{4}[/tex] = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex]x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form

multiply through by 4 to clear the fractions

4y = - x + 7 ( add x to both sides )

x + 4y = 7 ← equation in standard form

equation of line in two point form is needed here.

From the given information, we get the value of ABC = 120°.

Given: In the figure, O exists the center of the circle and OABC exists as a parallelogram.

Now, the radius of the circle exists

OA = OB = OC

Opposite sides of a parallelogram are equal

AB = OC and OA = BC

In ∆OAB,

OA = OB = AB and,

In ∆OCB,

OC = OB = BC

Therefore, ∆OAB and ∆OCB exist in equilateral triangles.

All angles of an equilateral triangle are equivalent to 60°.

Hence, ∠ABC = ∠OBA + ∠OBC

∠ABC = 60° + 60°

∠ABC = 120°

Therefore, the value of ∠ABC = 120°.

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Answer:

This the only one I know for sure right

I think the second one mn/on=qn/pn

I think the last one and the first one too but let me know which was right!

Step-by-step explanation:

Hi what unit of algebra or geometry is this because I did this before, and I can help you.

Answer:

C

Step-by-step explanation:

C

Answer:

Step-by-step explanation:

its c

Answer:

[tex]20a^2-70a[/tex]

Step-by-step explanation:

1) Expand by distributing terms.

[tex]10\times2a+10a\times-7[/tex]

2) Take out the constants.

[tex](10\times2)aa+10a\times-7[/tex]

3) Simplify [tex]10\times2[/tex] to [tex]20.[/tex]

[tex]20aa+10a\times7[/tex]

4) Use Product Rule:[tex]x^ax^b=x^{a+b}[/tex].

[tex]20a^2+10a\times-7[/tex]

5) Simplify [tex]10a\times-7[/tex] to [tex]-70a.[/tex]

[tex]20a^2-70a[/tex]

Thank you,

Eddie

Answer:

20a² - 70a

Step-by-step explanation:

(10a)(2a-7)

= 10a*2a + 10a*-7

= 20a² - 70a

The fraction (1/3)⁻⁴ is equal to 81.

Given that:

Fraction: (1/3)⁻⁴

Rewrite the expression by applying the rule that states a negative exponent is equal to the reciprocal of the positive exponent:

(1/3)⁻⁴= 1 / (1/3)⁴

Now, let's simplify (1/3)⁴:

(1/3)⁴ = (1/3) × (1/3) × (1/3) × (1/3)

(1/3)⁴ = 1/81

So, the expression becomes:

1 /(1/3)⁴ = 1 / (1/81)

Now, dividing by a fraction is equivalent to multiplying by its reciprocal:

1 / (1/81) = 1 × 81 = 81

Therefore, the fraction (1/3)⁻⁴ is equal to 81.

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The inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p

From the information given, we have that;

Area of the small pizza = 730 square centimeters

p  = area of the larger pizza

In writing inequality, we have to use the signs

<  less than

> greater than

Since p has greater area, we have

730 < p

Thus, the inequality that describes p, the area of a pizza that is larger than a small pizza 730 < p

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Answer:

the answer is actually p > 730

Step-by-step explanation:

i juts checked on Kahn academy and i got it right..

Answer:

A

Step-by-step explanation:

(x + 15 + 19 + 23 + 41) / 5 = 20

x + 15 + 19 + 23 + 41 = 100

x + 98 = 100

x = 2

Answer: it’s 2 (A)

Step-by-step explanation:

20 * 5 = 100

15 + 19 + 23 + 41 = 98

100-98=2

The rate of interest applied on the amount is 15%.

According to the statement

we have given that the sum of money amounts to Rs. 2175 in 3 years and to Rs. 2625 in 5 years.

And we have to find the rate of interest on this money.

So, For this purpose,

The given equation is:

Money in 3 years = 2175

Money in 5 years = 2625

Amount increased in 2 years = 2625-2175

Amount increased in 2 years = 450

And amount increased per year = 450/2

Amount increased per year = 225.

SI in 3 years=450/2 *3=Rs. 675

Principal amount= 2175-675=1500

so again,

R=(I*100)/(P*T)

R=15%

So, The rate of interest applied on the amount is 15%.

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Applying the knowledge of fractions, the number of cups of water that will fill a bottle of 3 liters is calculated as: 13.5 cups.

Fractions are numbers that indicate a part of whole numbers. For example, 2/9 of a liter means 2/9 of a part of 1 liter.

In math, a proportion is simply and equation that sets to ratios equal to each other.

To solve the problem given, create a proportion then use cross product to find the wanted value, which is the number of cups of water that can be filled into a 3-liter bottle.

Let x represent the cups of water we are looking for.

1 cup = 2/9 liter

x = 3 liters

We would have:

(1)(3) = (2/9)(x)

3 = 2x/9

(3)(9) = 2x

27/2 = x

x = 13.5

The number of cups of water to fill a 3-liter bottle is: 13.5.

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Answer:

its A

Step-by-step explanation:

Answer: The first one (A)

Step-by-step explanation:

See attachment for the graph of the reflection of f(x) across the y-axis

The function is given as:

f(x) = 1.5(0.5)^x

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

f'(x) = 1.5(0.5)^-x

Rewrite the function as

g(x) = 1.5(0.5)^-x

So, we plot the graph of the function g(x)

See attachment for the graph of the reflection of f(x)

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step 1 :

g(x) = 1.5

step 2 :

g(0): 1.5

step 3 :

plot at (0,1.5)

step 4 :

g(1) = 3

g(-1) = .75

step 5 :

plot (1,3) & (-1,0.75)

step 6:

y=0

The expression which shows how the distributive property of the can be used to multiply 8×29 as in the task content is; 8(20 + 9).

It follows from the task content that the given product to be multiplied is; 8×29.

Consequently, it follows from convention that the distributive property of multiplication allows that the multiplication in this case can be rewritten as follows;

8×29 = 8 (20 + 9)

Hence, we have; (8×20) + (8×9).

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Based on the given parameters, the value of the printer after 9 years is $3304

The given parameters about the exponential function are

Initial value, a = $7000

Depreciation rate, r = 8%

Time, t = 9

Exponential functions are different from linear functions, and they are calculated using the following exponential function

A = a *(1 - r)^t

To calculate the value in nine years, we have:

Substitute the known values in the above equation

A = 7000 * (1 - 8%)^9

Express 8% as decimal

A = 7000 * (1 - 0.08)^9

Evaluate the difference

A = 7000 * (0.92)^9

Evaluate the exponent

A = 7000 * 0.472

Evaluate the product

A = 3304

Hence, the value of the printer after 9 years is $3304

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Answer: 5040

Step-by-step explanation

We need to find how much it will depreciate each year based of of original cost.
8% of 7000
turn the percent into a decimal
.08
multiple .08 by the 7000
.08 * 7000 = 560

The printer depreciates 560 each year , to find the total for 9 years multiply by 9

560*9 =5040

The equivalent angle in the interval [0, 2pi] is 5pi/6.

Remember that for any given angle θ in radians, we define a family coterminal or equivalent angles as:

A = θ + n*(2pi)

Where n is a whole number.

Now we want to find an angle equivalent to 17pi/6 that is on the range between 0 and 2pi.

Then we can write:

A = 17pi/6 + n*(2pi)

If we use n = -1, then we get:

A = 17pi/6 - 2pi = 17pi/6 - 12pi/6 = 5pi/6

This is the equivalent angle in the desired range.

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The measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.

A measure of central tendency (measure of centre) is a value that attempts to describe a set of data by identifying the central position of the data set.

The measure of central tendency includes the mean, median and mode.

The measure of variation describes the amount of variability or spread in a set of data.

The common  measures of variability are the range, the interquartile range (IQR), variance, and standard deviation.

Therefore, the measure of centre includes mean median and mode and the measure of variability includes range, interquartile range and mean absolute deviation.

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Answer:

7 balls

Step-by-step explanation:

Look for the worst case scenario:

Get 3 white, 2 green, and 1 black.

That adds up to: 3 + 2 + 1 = 6.

+1 red ball: 6 + 1 =7

7 balls