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Algebraically solve the following system of equations.


(x+2)2+(y-3)2=16
x+y-1=0

Answer:

You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then

5 g - 12%,

x+5 g - 100%.

mathematically you can write a proportion;

5/x+5=12/100

=>500=12(x+5)

,500=12x+60

,12x=400,

x=440/12

=110/3

36.66 grams of water is added  to make 12% sugar syrup using 5g sugar.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Let the amount of water is added be 'x'.

Amount of sugar = 5 g

We need to make 12% of sugar syrup.

x grams of water is added to 5 g of sugar, to 12% of sugar syrup.

5/5+x=12/100

Apply cross multiplication

5×100=12(5+x)

500=60+12x

Subtract 60 from both sides

440=12x

Divide both sides by 12

x=36.66

Hence, 36.66 grams of water is added  to make 12% sugar syrup using 5g sugar.

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Answer:

60 divided by 8

Step-by-step explanation:

60 divided by 8

Answer:

Perpendicular

Answer:

parabola

Step-by-step explanation:

Answer:

(d+5)^2

Step-by-step explanation:

Answer:

x [tex]\geq[/tex] 5

Step-by-step explanation:

step 1: subtract 6 from both sides

step 2: divide both sides by 7

answer: x [tex]\geq[/tex] 5

interval notation: [5,∞)

Answer:

a) x ≤ -8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-3 + x ≤ -11

Step 2: Solve for x

Here we see that any value x smaller than or equal to -8 would work as a solution to the inequality.

Answer:

volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Step-by-step explanation:

Given the data in the question and as illustrated in the image below;

R is in the region first quadrant with vertices; 0(0,0), A(a,0) and B(0,b)

from the image;

the equation of AB will be;

y-b / b-0 = x-0 / 0-a

(y-b)(0-a) = (b-0)(x-0)

0 - ay -0 + ba = bx - 0 - 0 + 0

-ay + ba = bx  

ay = -bx + ba

divide through by a

y = [tex]\frac{-b}{a}[/tex]x + ba/a

y = [tex]\frac{-b}{a}[/tex]x + b

so R is bounded by  y = [tex]\frac{-b}{a}[/tex]x + b and y =0, 0 ≤ x ≤ a

The volume of the solid revolving R about x axis is;

dv = Area × thickness

= π( Radius)² dx

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

V = π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

Therefore,  volume of the solid generated when region R is revolved about the x-axis is π ₀∫^a ( [tex]\frac{-b}{a}[/tex]x + b )² dx

The volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

Equation of the line AB

[tex]y-0 = \frac{b-0}{0-a} (x-a)[/tex]

[tex]y = \frac{-b}{a} (x-a)[/tex]

The volume generated when a curve f(x) is rotated about the x-axis in x∈(c,d) is given by:

[tex]V=\int\limits^d_c {y^2} \, dx[/tex]

So, the volume generated when line AB is rotated about the x-axis will be [tex]V=\int\limits^b_0 ({\frac{-b}{a} (x-a))^2} \, dx[/tex]

[tex]V=\frac{b^{5} }{3a^{2} }[/tex]

Therefore, the volume of the solid generated when region R is revolved about the x-axis is [tex]\frac{b^{5} }{3a^{2} }[/tex].

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First, let's write what we know.

We can represent the number of students in the play from each class as L, G, and C. We know that L = 7, and if Gardener has 4 more students than Cho, then G = C + 4.

Then, taking the third line, we can write an inequality:

C < L < G

C < 7 < C + 4

C - 4 < 3 < C

3 < C < 7

If C is greater than 3 and less than 7 and is an integer, than means C is 4, 5, or 6.

Then, we need to find how many students are in the play.

C + L + G

C + 7 + C + 4

2C + 11

So we have our expression for the number of students in the play. Then, we need to find the total number of students. We know that 2C + 11 will be 30% of the total, so if T is the total, we can find T.

0.3T = 2C + 11

(Divide by 3/10 or multiply by 10/3 on both sides)

T = 20/3 C + 110/3

We know from before that C is 4, 5 or 6. We can plug these into our equation here to find which one produces a whole number.

T = 20/3 * 4 + 110/3

T = 190/3

T = 20/3 * 5 + 110/3

T = 210/3

T = 70

T = 20/3 * 6 + 110/3

T = 230/3

We can see here that only when C is 5 will the total be a whole number. That means Mrs. Cho has 5 students in the play. If Mrs. Gardner has 4 more than that, she has 9 students in the play in her class.  We now need to figure out the number of student in her class.

The total students are Cho's, Logan's, and Gardner's classes added together. We know that Logan's class is 23 students, so if we subtract that from the total, we can see that Cho's and Gardner's class have 47 students. If Mrs. Cho has 24 students in her class, we can subtract that from the 47, so we know that Mrs. Gardner has 23 students in her class.

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = [tex]0.06P+0.14P=1000[/tex]

[tex]\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000[/tex]

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

At the interest rate of 6%, amount invested is; $5000

At interest rate of 7%, amount invested is; $10000

Let P be the initial amount that Ms. Hagan invested in the 6% interest account that

Since she invested twice as much in the 7% interest account as in the 6% interest account, then;

Initial amount invested in the 7% interest account = 2P

Formula for Simple interest is;

I = Principal × rate × time

Interest after 1 year for the 6% interest account is,

I_1 = P × 0.06 × 1

I_1 = 0.06P

Interest after 1 year for the 7% interest account is,

I_2 = 2P × 0.07 × 1

I_2 = 0.14P

Total investment pays her $1000 after a year. Thus;

0.06P + 0.14P = 1000

0.2P = 1000

P = 1000/0.2

P = $5000

Then amount initially invested in the 7% interest account = 2P = $10000

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Answer:

a. Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [P(x,y)]  ∨ ∃x ∃y ¬ [Q(x,y)]

Step-by-step explanation:

a.∃x ∀y(P(x,y) → Q(x,y))

Negation = ¬ [ ∃x ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ¬ [ ∀y(P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [ (P(x,y) → Q(x,y)) ]

                = ∀x  ∃y ¬ [  ¬P(x,y)  ∨ Q(x,y) ]

                = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

Negation of ∃x ∀y(P(x,y) → Q(x,y)) = ∀x  ∃y P(x,y)  ∧ ¬Q(x,y) ]

b. ∃x ∀y(P(x,y) → P(y,x))

Negation = ¬ [ ∃x ∀y(P(x,y) → P(y,x)) ]

               = ∀x ¬ [ ∀y(P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ (P(x,y) → P(y,x)) ]

               = ∀x ∃y ¬ [ ( P(x,y) ∧ P(y,x) ) ∨ ( ¬P(x,y) ∧ ¬P(y,x) )]

               = ∀x ∃y ¬ [ P(x,y) ∧ P(y,x) ] ∧ ¬[ ¬P(x,y) ∧ ¬P(y,x) ]

               = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [ P(x,y) ∨ P(y,x) ]

∴ we get

Negation of ∃x ∀y(P(x,y) → P(y,x)) = ∀x ∃y  [ ¬P(x,y) ∨ ¬P(y,x) ] ∧ [P(x,y) ∨ P(y,x)]

c. ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y)

Negation = ¬ [ ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) ]

                = ¬ [ ∃x ∃y P(x,y) ]  ∨ ¬ [ ∀x ∀y Q(x,y) ]

                = ∀x¬ [  ∃y P(x,y) ]  ∨ ∃x ¬ [ ∀y Q(x,y) ]

                = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

∴ we get

Negation of ∃x ∃y P(x,y) ∧ ∀x ∀y Q(x,y) = ∀x ∀y ¬ [ P(x,y) ]  ∨ ∃x ∃y ¬ [ Q(x,y) ]

Answer:

y = -2x + 6

Step-by-step explanation:

This has sort of the same concept as your earlier question

Use the equation y = mx + b

To find the slope, take the second y value and subtract the first y value. Then take the second x value and subtract the first x value. Divide the answers. You'd get -2 in this case. -2 would be your slope (m).

The substitute any set of x and y values (either (1, 4) or (-2, 10)) and the slope into y = mx + b. You'd get 6 as your y-intercept (b).

Answer:

I'm not sure if this is a real problem and I don't think it is but the answer is 6.5

Step-by-step explanation:

first you have to add -2 and 2, then plus 3 and 2 and subtract 2 from it and then and 2+4 and subtract -5 and divide 2 and add 3 and add the answer to al of that to 2 + 3 and subtract - 10 and you get your answer of 6.5

Answer:

Where's the cone at and I might be able to help

Step-by-step explanation:

Answer: Please put a picture of the cone underneath the question!

Step-by-step explanation:

Answer: 12≠6

False

Step-by-step explanation:

Answer:

I think it's D

Step-by-step explanation:

Answer:

i think it's a or d

but d is more have percent

Answer:

El lado del cuadrado es de 20 my el área del cuadrado es de 400 metros cuadrados. Paso a paso ... El perímetro de un cuadrado es 80 m. ¿Cuál es la longitud de cada lado del cuadrado ... Para celosía & lt; L, * & gt; si a, b, ce L thena + (a e b) = a se llama.

Step-by-step explanation:

Answer:

the answer is B (graph a and c)

just did the test on edg 21

Step-by-step explanation:

i hope this helps!! have an amazing day <3

If a graph is reflected across y = x then it will be an inverse graph so graphs B and C will be inverse.

The inverse of a function is basically a reverse function or undo of the function.

For example y = f(x) then inverse will be x = f(y).

It means in the inverse function we need to interchange x and y.

Another example y = 3x² ⇒ x = √(y/3) will be the inverse.

An inverse function is a reflection of graph across y = x and due to that coordinate will interchange its that ;

( x ,y ) → ( y , x )

Since graph A is rotated about the x-axis to make graph B

Now,

Graph A is rotated( which is B ) and reflected across the axis y = x to form Graph C.

So B and C will be the inverse of each other.

Hence "If a graph is reflected across y = x then it will be an inverse graph so graphs B and C will be inverse".

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The given question is incomplete complete question is ;

Which graphs are inverses of one another? Graph A and B Graph A and C Graph B and C none of the graphs shown On a coordinate plane, graph A is in quadrants 1, 2, and 3. Graph A is rotated across the x-axis to form graph B. Graph A is rotated and reflected across the axis y = x  to form Graph C.

Answer:

The equation is y = (2/3)x + (4/3).

Step-by-step explanation:

First, you have to change the equation into slope-intecept formula to find its gradient (slope) :

[tex]3x + 2y = 12[/tex]

[tex]2y = - 3x + 12[/tex]

[tex]y = - \frac{3}{2}x + 6[/tex]

Given that when a line is perpendicular to the other line, their slope value multiplied, will form -1. Next, we have to find the slope for line :

[tex]m1 \times m2 = - 1[/tex]

[tex] - \frac{3}{2} \times m2 = - 1[/tex]

[tex]m2 = - 1 \div - \frac{3}{2} [/tex]

[tex]m2 = \frac{2}{3} [/tex]

Lastly, we have to subatitute the x and y values into the equation, to find its intercept value :

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

[tex]let \: x = 1,y = 2[/tex]

[tex]2 = \frac{2}{3} (1) + b[/tex]

[tex]b = 2 - \frac{2}{3} [/tex]

[tex]b = \frac{4}{3} [/tex]

[tex]y = \frac{2}{3} x + \frac{4}{3} [/tex]

Step-by-step explanation:

[tex] \underline{ \underline{ \text{Given}}} : [/tex]

[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

[tex] \underline{ \underline{ \text{Solution}}} : [/tex]

~ Plug the value of x and then multiply !

⇾ [tex] \tt{6x = 6 \times 6 \times = \boxed{36}}[/tex]

[tex] \red{ \boxed{ \boxed{ \text{Our \: final \: answer : \boxed{ \tt{36}}}}}}[/tex]

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

B

Step-by-step explanation:

Because the the contract will be in verbal form. no matter if it is videotaped or recorded or both a "videoed verbal contract" not just written. so like paper thst is notarized or not this is still the same bc the the same rules apply the contract is still valid. the rest of the options are more like what they call gentlemens agreements which would be the handshake type of thing. and no matter what any agreement someone has to witness the transaction or contract. so definitely the answer is B

Answer:

x = 3

Step-by-step explanation:

MN is exactly half of 6x + 2 (midpoint theorem)

2(2x + 4) = 6x + 2

4x + 8 = 6x + 2

-2x + 8 = 2

-2x = -6

x = 3

Answer:

340

Step-by-step explanation:

Answer:

y=-3x-13

Step-by-step explanation:

Answer:

1 .  

Step-by-step explanation:        

Answer:

r1 and r2 are the radii of two concentric circles

To find:

The length of the chord of the larger circle.

Solution:

We have given the two concentric circles which means both the circles have the same centre.

The chord of the larger circle toches the inner circle so the chord of the larger circle will be the tangent of the smaller circle.

And we know that the radius of the circle is perpendicular to the tangent of the circle.

Let 2x be the length of the chord of the circle.

r1 is the radius of the larger circle.

r2 is the radius of the smaller circle.

So by the Pythagoras theorem,

The length of the half of the chord is given by:

r1² = x² + r2²

x² = r1² - r2²

x = √r1² - r2²

So,

The length of the chord will be 2x = 2√r1² - r2² units

Step-by-step explanation:

Given:

Score in first round = 5 points

Score in second, third and fourth rounds was identical.

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round.

To find:

The inequality for the given problem.

Solution:

Let p be the number of points, p, that Steward scored in each of the second, third, and fourth rounds.

Score in first 4 rounds = Score of 1st round + Score of 2nd round + Score of  1s 3rd round + Score of 4th round

Score in first 4 rounds [tex]=5 + p + p + p[/tex]

                                     [tex]=5 +3p[/tex]

A participant has to score a total of at least 30 points in the first four rounds combined to move on to the fifth and final round. It means the total score in first 4 rounds must be greater than or equal to 30.

[tex]5+3p\geq 30[/tex]

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

I think it is A)2 because 3^2 = 9 and 9×4 = 36