Choose the correct graph of the given system of equations.


y + 2x = −1

3y − x = 4


A.) graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1


B.) graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1


C.) graph of two parallel lines with positive slopes with text on the graph that reads No Solution


D.) graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions

Answer:

Graph of the following function is attached with the answer.

Domain : ( - ∞ , + ∞ )

Range : ( 3 , + ∞ )

Step-by-step explanation:

[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]

Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.

So, Domain : ( - ∞ , + ∞ )

The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:

Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )

(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.

(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.

(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.

[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.

{a,b} means only 'a' and 'b'.

{a,b] or (a,b} doesn't mean anything. )

Answer:

The number of  people that received copies of the letter at the twentieth stage is 9.537 × 10¹³ .

Step-by-step explanation:

Using the discrete model,

a_k = r a_(k-1) for all integers k ≥ 1 and a₀ = a

then,

aₙ = a rⁿ for all integers n ≥ 0

Let a_k be equal to the number of people who receive a copy of the chain letter at a stage k.

Initially, one person has the chain letter (which the person will send to five other people at stage 1). Thus,

a = a₀ = 1

The people who received he chain letter at stage (k - 1),  will send a letter to five people at stage k and thus per person at stage (k - 1), five people will receive the letter. Therefore,

a_k = 5 a_(k - 1)

Thus,

aₙ = a rⁿ = 1 · 5ⁿ = 5ⁿ

The number of  people that received copies of the letter at the twentieth stage is

a₂₀ = (5)²⁰ = 9.537 × 10¹³ copies

Answer:

C) AC=DC

Step-by-step explanation:

In the figure of question attached below:

In Δ ACB and  Δ DCE, AB and DE are hypotenuse respectively.

According to HL theorem:

"If hypotenuse and one leg of right angle triangle is congruent to Hypotenuse and one leg of other right angle triangle then triangles are congruent"

According to above statement if AB and DE are hypotenuse of Δ ACB and  Δ DCE respectively then either

AC = DC    (leg)

BC = EC     (leg)

In order to prove  congruence of triangles using HL theorem, AC must be equal to DC.

So option C is correct.

Answer:

C ) AC=DC

Step-by-step explanation:

edge 2021

Answer:

36°

Step-by-step explanation:

Like your other question, the angles of the triangle must add up to 180. The tangent line is perpendicular to the center, so the angle must be 90°.

90° + 54° + 36° = 180°

Answer:

√1 1

√4 2

√9 3

√16 4

√25 5

√36 6

√49 7

√64 8

√81 9

√100 10

√121 11

√144 12

√169 13

Step-by-step explanation:

1. = 49

2. = 169

3. = 81

4. = 100

5. = 441

6. = 36

I just finished the assignment, trust me.

Answer:

The Area of the actual garden is 294 square feet.

Step-by-step explanation:

The scale model of a rectangular garden is 1.5 ft by 4 ft.

Length of scale model=1.5 ft

Breath of scale model=4 ft

The scale model is enlarged by a scale factor of 7 to create the actual garden.

It means that the dimension of the garden are multiplied with the scale factor to find the actual dimension.

Hence,

Length of actual garden=[tex]1.5\times 7= 10.5\ ft[/tex]

Breath of actual garden=[tex]4\times 7 = 28\ ft[/tex]

Now Area of garden can be calculated by multiplying length and breadth.

Framing the equation we get;

Area of actual garden=[tex]10.5\ ft \times 28\ ft = 294\ ft^2[/tex]

Hence, area of the actual garden is 294 square feet.

Answer:294 took test

Answer:

For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.

Step-by-step explanation:

[tex]A_2[/tex] = 18°

[tex]A_3[/tex] = 4(18°) = 72°

Given:

Angles:

[tex]A_1[/tex] = 90°

[tex]A_2[/tex] = x

[tex]A_3[/tex] = 4x

Solution Pathway:

Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:

Now let's solve for x.

Now that we know x is 18°, lets plug this value into the two unknown acute angles.

Answer:

72 degrees and 18 degrees.

Step-by-step explanation:

If the 2 angles are x and y, we have the system:

x + y = 90           (as it is a right triangle)

x = 4y                  (given).

Substitute x =- 4y in the first equation:

4y + y = 90

5y = 90

y = 18.

So  x + 18 = 90

x = 90 - 18

x = 72.

Option a. 26; the cheetah's rate in miles per hour is the correct answer.

Step-by-step explanation:

Given

[tex]f(x) = 6x+8\\g(x) = x-2[/tex]

As the function f is in miles and function g is is hours, and we are dividing the function f by function g so the new unit will be:

miles/hour = miles per hour

Now

[tex]\frac{f}{g}(x)= \frac{f(x)}{g(x)}\\\frac{f}{g}(x) = \frac{6x+8}{x-2}[/tex]

We have to find (f/g)(3) so putting 3 in place of x

[tex]\frac{f}{g}(x) = \frac{6(3)+8}{-2}\\= \frac{18+8}{1}\\= 26[/tex]

Hence,

Option a. 26; the cheetah's rate in miles per hour is the correct answer.

Keywords: Functions, function operations

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Answer: Sequence B is more probable than A.

Step-by-step explanation:

This two sequences are not equally probable. Sequence B is more probable than A due to the equal chances of getting head (H) and a tail (T). The probability of getting a head is equal to the probability of getting a tail which is 4/8 i.e 0.5

The sequence A is less probable because the head(H) occur more than tail (T). The probability of head occurring is almost a sure event i.e 1 which is not feasible.

Answer:

50 grams

Step-by-step explanation:

Let the amount of cheese required by the recipe be "x"

Ann increased 60% from original amount and then used up 80 grams. Thus:

Original, increased by 60%, became 80

This translated to algebraic equation would be:

x + 0.6x = 80

Note:  60% = 60/100 = 0.6

So we can solve the above equation for "x" and get our answer. Shown below:

[tex]x + 0.6x = 80\\1.6x=80\\x=\frac{80}{1.6}\\x=50[/tex]

Hence,

the recipe required 50 grams of cheese

Final answer:

The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.

Explanation:

Let's create a table to represent the given information:

Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70

To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.

Now, let's analyze the changes in cost for each additional pound of dried cherries:

Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:

y = (10.60/2)x

Answer:

  y^2/25 -x^2/4 = 1

Step-by-step explanation:

The equation can be written as ...

  y^2/a^2 -x^2/b^2 = 1

where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.

Answer:

See proofs below

Step-by-step explanation:

a) Suppose that aRb. Let y∈Sa , then y∈A and yRa. We have that yRa and aRb. Since R is a partial order, R is a transitive relation, therefore yRa and aRb imply that yRb. Now, y∈A and yRb, thus y∈Sb. This reasoning applies for all y∈Sa that is, for all y∈Sa, y∈Sb, threrefore Sa⊆Sb.

b) Suppose that Sa⊆Sb. Since R is a partial order, R is a reflexive relation then aRa. Thus, a∈Sa. The inclusion Sa⊆Sb implies that a∈Sb, then aRb.

c) Denote this set by S={Sb:b∈B}. We will prove that supS=Sx with x=supB.

First, Sx is an upper bound of S: let Sb∈S. Then b∈B and since x=supB, x is an upper bound of B, then bRx. Then b∈Sx. Now, for all y∈Sb, yRb and bRx, then by transitivity yRx, thus y∈Sx. Therefore Sb⊆Sx for all Sb∈S, which means that Sx is an upper bound of S (remember that the order between sets is inclusion).

Now, let's prove that Sx is the least upper bound of S. Let Sc⊆A be another upper bound of S (in the set F). We will prove that Sx⊆T.

Because Sc is an upper bound, Sb⊆Sc for all b∈B. Thus, if y∈Sb for some b, then y∈Sc. That is, if yRb then yRc. In particular, bRb then bRc for all b∈B. Thus c is a upper bound of B. Byt x=supB, then xRc. Now, for all z∈Sx, zRx and xRc, which again, by transitivity, implies that z∈Sc. Therefore Sx⊆Sc and Sx=sup S.

In a partial order set, if aRb, then Sa ⊆ Sb. If Sa ⊆ Sb, then aRb. If B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}.

a) To show that if aRb, then Sa ⊆ Sb, we need to prove that if x ∈ Sa, then x ∈ Sb. Since x ∈ Sa, that means xRa holds. And since aRb, we can conclude that xRb holds as well. Therefore, x ∈ Sb, which implies that Sa ⊆ Sb.

b) To show that if Sa ⊆ Sb, then aRb, we need to prove that if aRb does not hold, then Sa ⊆ Sb does not hold. If aRb does not hold, it means that b is not in Sa. However, if Sa ⊆ Sb, it implies that every element in Sa is also in Sb. Hence, we arrive at a contradiction, which proves that if Sa ⊆ Sb, then aRb.

c) To show that if B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}, we need to prove that Sx is an upper bound for {Sb : b ∈ B} and that it is the least upper bound. Since x is the least upper bound for B, this means that every element of B is contained in Sx. Therefore, Sx is an upper bound for {Sb : b ∈ B}. Additionally, if there exists an upper bound U for {Sb : b ∈ B}, then every element of {Sb : b ∈ B} must be contained in U. Since Sb is a subset of Sa for every b ∈ B, it follows that every element of Sa is contained in U. Therefore, Sa ⊆ U for every a ∈ A. In particular, Sx ⊆ U, which proves that Sx is the least upper bound for {Sb : b ∈ B}.

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Answer:

A 1.44 cm cubed

Step-by-step explanation:

Just multiply all the numbers to get the area of the block

Answer:

A 1.44 cm cubed

Step-by-step explanation:

Answer:

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

Step-by-step explanation:

Given that the diameter of a sphere is 14cm.

That is d=14

First find the radius of the sphere with diameter

[tex]r=\frac{d}{2}[/tex]

[tex]r=\frac{14}{2}[/tex]

Therefore r=7cm

Now to find the volume of the sphere:

[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]

[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex]  (here[tex]\pi=\frac{22}{7}[/tex] and r=7)

[tex]V=\frac{4}{3}(22)(7)^2[/tex]

[tex]V=\frac{4}{3}(22)(49)[/tex]

[tex]V=\frac{4}{3}(1078)[/tex]

[tex]V=\frac{4312}{3}[/tex]

[tex]V=1437.33cm^3[/tex]

Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]

The exact volume of a sphere is [tex]V=1437cm^3[/tex]

Answer:

Step-by-step explanation:

Looking at both triangles, angle P in triangle PQR = 38 degrees. Angle N in triangle LMN = 38 degrees. Both angles are equal.

Side PQ in triangle PQR = 16

Side MN in triangle LMN = 8

Therefore,

PQ/MN = 16/8 = 2

Side PR in triangle PQR = 14

Side LN in triangle LMN = 7

Therefore,

PR/LN = 14/7 = 2

Therefore, triangle PQR is similar to

triangle LMN because

1) the length of PQ is proportional to the length of MN.

2) the length of PR is proportional to the length of LN

3) angle P = angle N

4) Therefore, QR is also proportional to ML

Therefore,

PQ/MN = PR/LN = QR/ML = 2

Step-by-step explanation:

Let the small mass be m and position on x axis be y.

A 20 kg sphere is at the origin.

Distance to 20 kg mass = y

A 10 kg sphere is at x = 20 cm

Distance to 10 kg sphere = 20 - y

We have forces between them are equal

We have gravitational force   

                    [tex]F=\frac{GMm}{r^2}[/tex]              

          Where G =  6.67 x 10⁻¹¹ N m²/kg²

                      M = Mass of body 1

                      M = Mass of body 2

                      r = Distance between them

Here we have

            [tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]

So the small mass should be placed at x = 11.72 cm or x = 68.28 cm

The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.

Recall the force of universal gravitational attraction :

Sphere 1 :

Sphere 2 :

Gravitational force ; sphere 1 :

Gravitational force ; sphere 2 :

Equate (1) and (2)

[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]

[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]

20(400 - 40d + d²) = 10d²

8000 - 800d + 20d² = 10d²

10d² - 800d + 8000 = 0

Divide through by 10

d² - 80d + 800 = 0

Using a quadratic equation solver :

d = 68.28 cm or d = 11.72 cm

The possible positions are 68.28 cm and 11.72 cm

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Answer: 68

Step-by-step explanation:

range=47 lowest score = 21 let highest score =x

Range=highest score - lowest score

47 = x - 21

x = 47 + 21

x = 68

Therefore the highest score is 68

The highest score is 68.

Range = Highest Score - Lowest Score

In this case,

the lowest score is 21 and

the range is 47.

So, we can rearrange the formula to solve for the highest score:

Highest Score = Range + Lowest Score

Substituting in the given values:

Highest Score = 47 + 21

Thus, the highest score will be 68.

Answer:

$115.67

Step-by-step explanation:

given that the markdown rate is 53%, that means that the markdown is 53% of the original price, or,

markdown = 53% of $229.99 = 0.53 x 229.99 = $121.89

sale price before tax = Original Price - Markdown

= 229.99 - 121.89

= $108.10

sales tax = 7% of sale price before tax

= 0.07 x 108.10

= $7.57

Final price =  price before tax + tax

= 108.1 + 7.57

= $115.67

I would say it as "the letter F is greater than negative four."

Answer:

high glycemic carb with some protein

Step-by-step explanation:

Food like white bread made from dextrose supplement and chocolate milk that contains some protein for muscle repair.

Due to the spongelike characteristic of the muscle would make it soak up glucose from high glycemic carb.

The expression which  gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD.  option C is correct.

The area of rectangle is obtained by multiplying the length and width.

The length of the rectangle is C+D

The width of the rectangle is A+B.

Now the complete area of rectangle :

Area = (A+B)(C+D)

Now to find area of rectangle which is red we have to subtract the red rectangle which are in blue:

The area of left side rectangle which is blue:

Area =C(A+B)

The area of rectangle below red rectangle:

Area =BD

So the area of red rectangle : (A+B)(C+D)-C(A+B)-BD.

Hence, option C is correct, the expression which  gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD.

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Answer:

12.584 N

Step-by-step explanation:

To solve this problem you need to use Hokke's law, this is a physics lar which states the force (F) you need to compress a spring for some distance (x) can be easily calculated with the equation F=kx. The constant k (the stiffness of the spring) is the value of 242 N/m and x is the distance 5.2 cm = 0.052 m. So if you multiply 242 N/m by 0.052 m you will obtain 12.584 N, which is the necessary force to compress the spring 5.2 cm. The mass of the spring is a nonrelevant data in this problem.

Answer:

5.30 PM

Step-by-step explanation:

time taken=(1/2)×(1/35)×245=7/2 hrs=3hrs 30 min.

so time =2+3.30=5.30 PM

Answer: 5:30pm

Step-by-step explanation:

Distance of family destination from the starting point = 245miles

Average speed = 35miles/1/2hour

Therefore 245 miles = 245/35 x 30mins.

7 x 30 = 210minutes.

Converted to hour by dividing by 60

210/60 = 3hours 30minutes.

Current local time at the point of commencement

Therefore, the arrival time at their destination = 14hours + 3hours 30mins.

= 17hours 30minutes. Convert to local time

17hours 30minutes = 12hours

= 5:30 pm in the evening

They have succeeded in spending 3hours 30minutes on the road. The final answer = 5:30pm.

Answer:

The correct answer is C. 129.

Step-by-step explanation:

Let's recall that the Inscribed Quadrilateral Theorem states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.

In the case of the inscribed quadrilateral ABCD in the graph attached, we have that:

m∠C= 51°, therefore its supplementary angle, ∠A, should be the difference between 180° and m∠C.

m∠C= 180° - m∠A

Replacing with the real values:

51 = 180 - m∠A

m∠A = 129°

The correct answer is C. 129.

Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:

Interest = Principal (loan amount) x Rate x Time

Where:

Principal (loan amount) = $7,900

Rate = 4.29% (0.0429 as a decimal)

Time = 4.5 years

Now, plug these values into the formula:

Interest = $7,900 x 0.0429 x 4.5

Interest = $7,900 x 0.19205

Interest ≈ $1,518.45

So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.

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Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.

Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.

To calculate the interest that will accrue during the 4.5 years, we can use the formula:

Interest Accrued = Principal x Interest Rate x Time

Substituting the values, we get:

Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75

Therefore, the interest that will accrue during the non-payment time is $1,146.75.

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Sarah has received £ 294

Solution:

Given that £980 is divided between Caroline, Sarah & Gavyn

Let "c" be the amount received by caroline

Let "s" be the amount received by sarah

Let "g" be the amount received by gavyn

Caroline gets twice as much as Sarah

amount received by caroline = twice as much as Sarah

amount received by caroline = 2(amount received by sarah)

c = 2s ---- eqn 1

Sarah gets three times as much as Gavyn

amount received by sarah = three times as much as Gavyn

amount received by sarah = 3(amount received by gavyn)

s = 3g ------- eqn 2

Given that total amount is 980

c + s + g = 980 --- eqn 3

Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"

From eqn 2,

[tex]g = \frac{s}{3}[/tex]  --- eqn 4

Substitute eqn 1 and eqn 4 in eqn 3

[tex]2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294[/tex]

Thus sarah has received £ 294

Final answer:

To solve for the amount Sarah receives, set up ratios based on the information provided and solve the resulting equation. The total amount divided among them is £980, which when divided by the total parts (10) gives Gavyn's share as £98. Sarah's share is three times Gavyn's share, resulting in £294.

Explanation:

The problem described is a classic division in ratio mathematics question where £980 is being divided among Caroline, Sarah, and Gavyn following certain rules.

According to the problem, Caroline receives twice the amount that Sarah receives and Sarah receives triple the amount that Gavyn receives.

We can set up the following ratios: C = 2S and S = 3G, where C stands for Caroline's amount, S for Sarah's, and G for Gavyn's. If we denote Gavyn's amount as G, then Sarah's amount is 3G and Caroline's is 2 × 3G which is 6G.

To find the value of G, we can write the equation G + 3G + 6G = £980 or 10G = £980. Solving for G gives us G = £98.

Therefore, Sarah, receiving three times as much as Gavyn, gets 3 × £98 = £294.

Answer:

$307.60

Step-by-step explanation:

multiple $76.90 by the 4 nights he stayed. $76.90×4

Answer:

76.00

Step-by-step explanation: