Question 7(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)

Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.

Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?

2.5 weeks
5 weeks
15 weeks
75 weeks

Answer:

3.3 seconds

Step-by-step explanation:

To find the time it takes for the ball to hit the ground, we need to solve the equation y = 0, since the ball will be on the ground when its height (y) is zero.

The equation given is:

y = -16t^2 + 20t + 7

Setting y to zero:

0 = -16t^2 + 20t + 7

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = -16, b = 20, and c = 7. Substituting these values into the quadratic formula:

t = (-20 ± √(20^2 - 4(-16)(7))) / (2(-16))

t = (-20 ± √(400 + 448)) / (-32)

t = (-20 ± √848) / (-32)

Simplifying further:

t = (-20 ± √(16 * 53)) / (-32)

t = (-20 ± 4√53) / (-32)

Now we have two possible solutions for t:

t1 = (-20 + 4√53) / (-32)

t2 = (-20 - 4√53) / (-32)

Since time cannot be negative in this context, we can disregard the negative solution.

t ≈ (-20 + 4√53) / (-32)

Calculating this value:

t ≈ 3.3 seconds (rounded to one decimal place)

Therefore, it will take approximately 3.3 seconds for the ball to hit the ground.

Answer:

m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.

Step-by-step explanation:

To find the measures of angles H, I, and J, we can use the fact that HI is approximately equal to IJ. Let's denote the measures of angles H, I, and J as m∠H, m∠I, and m∠J, respectively.

Given that HI is approximately equal to IJ, we can say that m∠H is approximately equal to m∠J.

So, m∠H ≈ m∠J.

We're also given that m∠H = 3x + 10 and m∠I = 6x - 20.

Since m∠H ≈ m∠J, we can equate their expressions:

3x + 10 ≈ 6x - 20.

To solve for x, we can subtract 3x from both sides and add 20 to both sides:

10 + 20 ≈ 6x - 3x.

30 ≈ 3x.

Dividing both sides by 3, we find:

10 ≈ x.

Now that we have the value of x, we can substitute it back into the expressions for m∠H and m∠I:

m∠H = 3x + 10 = 3(10) + 10 = 30 + 10 = 40.

m∠I = 6x - 20 = 6(10) - 20 = 60 - 20 = 40.

Therefore, the measures of angles H, I, and J are:

m∠H = 40 degrees,

m∠I = 40 degrees,

m∠J is approximately equal to m∠H and m∠I, so it is also approximately 40 degrees.

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The minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

To calculate the minimum amount charged for a cash deposit over the counter at Standard Bank, we'll use the given information.

The deposit charge includes an initial fee of R10.39, and an additional fee of K1.95 per R100 or part thereof, with a minimum charge of R16.00.

First, we calculate the additional fee based on the deposit amount:

Additional fee = (Deposit amount / 100) x K1.95

For Mr. Khumalo's deposit of R4,550.00:

Additional fee = (4,550.00 / 100) x 1.95

Additional fee = 88.725

Next, we compare the additional fee to the minimum charge of R16.00:

If the additional fee is less than the minimum charge, the minimum charge applies. Otherwise, the additional fee is charged.

Since the additional fee of R88.725 is greater than the minimum charge of R16.00, the additional fee will be charged.

Finally, we add the initial fee and the additional fee to get the total charge:

Total charge = Initial fee + Additional fee

Total charge = R10.39 + R88.725

Total charge = R99.115

Therefore, the minimum amount that Mr. Khumalo can be charged for the cash deposit is R99.12.

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Answer:

614,818.71

Step-by-step explanation:

hope it helps

Answer:

6,25,250

Step-by-step explanation:

let initaial population be "x"

after increasing by 2%

x'=x+x*2%

x'=102x/100

x' is decreased by 2% and population reached 625000,so,

625000=102x/100-2%*102x/100

625000=102x/100-51x/2500

625000=2499x/2500

2499x=625000*2500

x=1562500000/2499

x=625250.1

complete population is only counted so,

x=625250

initial population =625250

The volume of the larger cylinder is 201 cm³.

Given that,

Ratio of the heights of two cylinders = 1 : 3

We have to find the volume of the larger cylinder.

The formula to find the volume of a cylinder is,

Volume of cylinder = π r² h, where r is the radius and h is the height of the cylinder.

Let height of smaller cylinder = h

Height of larger cylinder = 3h

π r² (h) = 67

Volume of larger cylinder = π r² (3h)

                                          = 3 [π r² (h)]

                                          = 3 × 67

                                          = 201 cm³

Hence he volume is 201 cm³.

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The marked price of the article is approximately Rs. 833.33, and the cost price is Rs. 500.

Let's assume the marked price of the article is M and the cost price is C.

According to the given information:

When the shopkeeper sells the object at a discount of 25%, he incurs a loss of Rs. 125. This means that the selling price (S) is 25% less than the marked price (M) and it is equal to the cost price (C) minus Rs. 125.

S = C - Rs. 125

S = M - 0.25M

C - Rs. 125 = M - 0.25M

When the shopkeeper sells the object at a discount of 10%, he gains Rs. 250. This means that the selling price (S) is 10% less than the marked price (M) and it is equal to the cost price (C) plus Rs. 250.

S = C + Rs. 250

S = M - 0.10M

C + Rs. 250 = M - 0.10M

Now we can solve these two equations simultaneously to find the marked price (M) and the cost price (C) of the article.

C - Rs. 125 = M - 0.25M --> C = 0.75M - Rs. 125 (Equation 1)

C + Rs. 250 = M - 0.10M --> C = 0.90M - Rs. 250 (Equation 2)

Setting Equation 1 equal to Equation 2:

0.75M - Rs. 125 = 0.90M - Rs. 250

Rearranging the equation:

0.90M - 0.75M = Rs. 250 - Rs. 125

0.15M = Rs. 125

M = Rs. 125 / 0.15

M = Rs. 833.33 (approx.)

Substituting the value of M back into Equation 1 to find C:

C = 0.75M - Rs. 125

C = 0.75 * 833.33 - Rs. 125

C = Rs. 625 - Rs. 125

C = Rs. 500

Therefore, the marked price of the article is approximately Rs. 833.33, and the cost price is Rs. 500.

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Answer:

C. 2 units

Step-by-step explanation:

In right triangle ABD, BD is the hypotenuse and AB and AD are the legs of the right triangle each with a length of 1 unit

By the Pythagorean Thereom
hypotenuse² = sum of squares of each of the other sides

BD² = AB² + AD² = 1² + 1² = 1 + 1 = 2

In right triangle BCD, BC is the hypotenuse and we are given BD = DC

BC² = BD² + DC² = BD² + BD² =2 BD² = 2 · 2 = 4

BC = √4 = 2 units

Answer:

C.

Step-by-step explanation:

I think the answer is C. or a point because a point is like a location in space and the question is asking which word means a location in space.

Answer:

2 . figures have a volume that is greater than 600 in3.

Step-by-step explanation:

A. The distributions of the periods is that using the five number summary is that

B. The box and whisker plot of the periods is attached

From the question, we have the following parameters that can be used in our computation:

7th Period

66, 72, 77, 78, 78, 80, 82, 84, 84, 87, 88, 88, 89, 89, 90 92, 92, 93, 94, 94 96, 96

3rd Period

52, 60, 62, 64, 64, 65, 68, 71, 72, 74, 75, 76, 78, 79, 83, 84, 85, 88, 89, 93, 94, 97

The distributions of the periods will be compared using the five-number summaries

Using a graphing tool, the five-number summaries are:

7th Period

3rd Period

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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Answer:

99.5

Explanation:

First, you would put the numbers into order from least to greatest.

99, 88, 97, 107, 100, 109

Which would be:

88, 97, 99, 100, 107, 109

Median is the middle of the number line, so you would cross off a number from each side until you find the middle.

99, 100

You would end up with two numbers, which you will have to find the mean of. In order to do so, you need to add them together then divide by 2 because there are 2 numbers.

99 + 100 = 199

199/2 = 99.5

The solution is: Option D has the correct data points and so is the right answer.

We have,

A function is a mathematical way of representing relation between two variables.

The function given is

y = 2x²

For x = - 2, y = -2(- 2)² = -8

For x = - 1, y = -2(- 1)² = -2

For x = 0, y = -2(0)² = 0

For x = 1, y = -2(1)² = -2

For x = 2, y = -2(2)² = -8

the  table of x-y will be:

x  - 2    - 1    0    1    2

y    -8     -2   0  -2   -8

The graph is attached with the answer.

The parabola opens downward and has the data points as mentioned above .

The Graph B  best represents a parabola ,

Therefore Option D is the correct answer.

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complete question:

Complete the following table using the equation: Y = negative 2 x Squared x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (0, 0), and goes through (1, 2). Graph B On a coordinate plane, a parabola opens down. It goes through (negative 1, negative 1), has a vertex at (0, 0), and goes through (1, negative 1). a. 8, 2, 0, 2, 8; Graph A b. -8, -2, 0, -2, -8; Graph A c. 8, 2, 0, 2, 8; Graph B d. -8, -2, 0, -2, -8; Graph B Please select the best answer from the choices provided A B C D

The cosD is √53/9 from the given triangle which is adjacent side by hypotenuse

The triangle DEF is a right triangle

We know that cosine function is a ratio of adjacent side and hypotenuse

The adjacent side of angle D is DE

We have to find the length of DE by using Pythagoras theorem

DE²+EF² =DF²

DE²+28=9²

DE²=81-28

DE²=53

Take square root on both sides

DE=√53

So cosD=√53/9

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(a) The expected profit of the game is $0. (b) The variance of the profit is 0. (c) The probability of gaining $20 in 10 plays is 0.

To solve the given problem, we'll calculate the expected profit, variance of the profit, and the probability of gaining $20 in 10 game plays.

(a) Expected Profit:

To calculate the expected profit, we need to multiply the potential profit or loss with its corresponding probability and sum them up.

Profit (X) = Gain - Loss = $10 - $10 = $0

Probability of gaining: P(X = $0) = P(Z > 5) = 0 (since Z is only defined up to 5)

Expected Profit (E(X)) = $0 * P(X = $0) = $0

(b) Variance of the Profit:

The variance can be calculated using the formula: Var(X) = E(X^2) - (E(X))^2.

In this case, since the profit is always zero, the variance will also be zero.

Variance of the Profit (Var(X)) = 0 - (0)^2 = 0

(c) Probability of Gaining $20 in 10 plays:

Since each play is independent, the probability of gaining $20 in a single play is 0. Since the probability of gaining is 0 for each play, the probability of gaining $20 in 10 plays will also be 0.

Probability of gaining $20 in 10 plays = 0

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The order of convergence of the formula as h approaches 0 is at least 1.

To determine the order of convergence as h approaches 0 for the approximation of f'(z) using the given formula, we need to analyze the behavior of the formula as h becomes smaller.

Let's rewrite the formula in a more structured form for better clarity:

f'(z) ≈ [F(z + 2h) - 8F(z + h) + 8F(z - h) - F(z - 2h)] / (12h)

As h approaches 0, we can rewrite the formula using the limit notation:

f'(z) ≈ lim(h→0) [F(z + 2h) - 8F(z + h) + 8F(z - h) - F(z - 2h)] / (12h)

In this case, we can simplify the limit expression by dividing both the numerator and denominator by h:

f'(z) ≈ lim(h→0) [F(z + 2h)/h - 8F(z + h)/h + 8F(z - h)/h - F(z - 2h)/h] / 12

f'(z) ≈ lim(h→0) [F'(z) - 8F'(z) + 8F'(z) - F'(z)] / 12

f'(z) ≈ lim(h→0) 0 / 12

f'(z) ≈ 0

From this analysis, we see that as h approaches 0, the f'(z) approaches 0. This means that the order of convergence of the given formula is at least 1.

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Total amount of money in the account will be $456.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest.

The formula for simple interest is: Simple Interest = Principal × Rate × Time

Principal (P) is $300

Rate (R) is 6.5%

Time (T) is 8 years.

Simple Interest = $300 × 0.065 × 8

Simple Interest = $156

Total Amount = Principal + Simple Interest

Total Amount = $300 + $156

Total Amount = $456.

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The missing angle is 25 degrees.

We are given that;

A polygon with 6 side have interior angles 90, 98, 140, x, 155, 112

Now,

we can write:

S = (6 - 2) × 180 degrees

S = 4 × 180 degrees

S = 720 degrees

We know that the sum of the given interior angles is:

90 + 98 + 140 + x + 155 + 112 = 695 + x

Since the sum of the interior angles of a polygon with 6 sides is equal to 720 degrees, we can write:

695 + x = 720

Solving for x, we get:

x = 25 degrees

Therefore, by the polygon the answer will be 25 degrees.

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To find the values of x and y in the system of equations:

Equation 1: [tex]x + 2y = 3[/tex]

Equation 2: [tex]3x + 4y = 1[/tex]

We can solve the system using the method of substitution or elimination. Here, I will demonstrate the method of substitution:

Step 1: Solve Equation 1 for x:

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

Step 2: Substitute the value of x from Step 1 into Equation 2:

[tex]3(3 - 2y) + 4y = 1[/tex]

Step 3: Simplify and solve for y:

[tex]9 - 6y + 4y = 1[/tex]

[tex]-2y = 1 - 9[/tex]

[tex]-2y = -8[/tex]

[tex]y = \frac{-8}{-2}[/tex]

[tex]y = 4[/tex]

Step 4: Substitute the value of y back into Equation 1 to find x:

[tex]x + 2(4) = 3[/tex]

[tex]x + 8 = 3[/tex]

[tex]x = 3 - 8[/tex]

[tex]x = -5[/tex]

Therefore, the solution to the system of equations is:

[tex]x = -5[/tex]

[tex]y = 4[/tex]

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Answer: X=-2 & Y=5/2

Step-by-step explanation:

STEP 1: Find the given equations

            x+2y=3 and 3x+4y=1

STEP 2: Try to equate any of the terms by multiplying either of the equations.

HERE, we can multiply the equation x+2y=3 by 2

WE GET, 2x+4y=6 and we can see that 4y terms is common in both te equations

STEP 3: cancel out the matching terms by simple addition or subtraction of the equations.

after solving we get, x=-2.

STEP 4: put the value of x in any of the two quations to get the value of y.

WE GET, the value of y as 5/2.

check the attached image for a better understanding.

The value of the underlined digit in the number 27,416,385.( 4 is the underlined number.) is the hundred thousandths place.

The symbols, from 0 to 9 can be described as a digit. For instance, the numbers 2 and 3 are used to represent the number 23.  however amount is represented by a number.

It should be noted that It may be expressed using one, two, three, or even more digits however only single symbol used to represent a number is a digit in the case above we can see that 4 is the hundred thousandths place.

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The polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5 is P(x) = x^3 - 4x^2 - 17x + 60.  

To construct a polynomial of degree 3 with zeros at x = 3, x = -4, and x = 5, we can use the fact that the polynomial can be written as a product of linear factors corresponding to each zero.

The factor corresponding to x = 3 is (x - 3).

The factor corresponding to x = -4 is (x + 4).

The factor corresponding to x = 5 is (x - 5).

To obtain the polynomial, we multiply these factors together:

P(x) = (x - 3)(x + 4)(x - 5)

Expanding this expression gives us:

[tex]P(x) = (x^2 - 3x + 4x - 12)(x - 5)[/tex]

[tex]= (x^2 + x - 12)(x - 5)[/tex]

[tex]= x^3 - 5x^2 + x^2 - 5x - 12x + 60[/tex]

[tex]= x^3 - 4x^2 - 17x + 60[/tex].

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Answer:

see below

Step-by-step explanation:

b.

(x+2, y - 1) = (2, 3)

We have two equations:

x + 2 = 2

y - 1 = 3

Solving for x, we get:

x = 0

Solving for y, we get:

y = 4

Therefore, the values of x and y are 0 and 4, respectively.

A specific X-value for the solution ,-4 is not equal to -3/2.

The x-value of the solution to the system of equations, we need to solve the given equation and the line represented by the data in the table. Let's begin by examining the first equation, 2x + 4y = 0.

We can rewrite this equation in terms of y:

4y = -2x

y = (-2/4)x

y = (-1/2)x

Now, let's use the data from the table to create a system of equations:

For the first data point (-1, 8):

y = (-1/2)x

8 = (-1/2)(-1)

8 = 1/2

Since 8 is not equal to 1/2, the first data point does not satisfy the equation.

For the second data point (3, -4):

y = (-1/2)x

-4 = (-1/2)(3)

-4 = -3/2

Again, -4 is not equal to -3/2, so the second data point does not satisfy the equation.

We can continue this process for the remaining data points, but from the information given, it seems that none of the data points satisfy the equation. Therefore, there is no solution to the system of equations.

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One would pay $5,232.96 in interest over the 5-year loan term.

To get interest paid on the loan, we will the formula for compound interest [tex]Interest = Principal * (1 + Annual Interest Rate)^{Number of Years} - Principal[/tex]

The principal is the loan amount which is $9,000.

The annual interest rate is 9.6%

The number of years is 5.

Interest = $9,000 * (1 + 0.096)^(5) - $9,000

Interest = $9,000 * 1.58144018701 - $9,000

Interest = $5,232.96168

Interest = $5,232.96.

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Answer:

0.789 to 1 or 78.9 percent chance

Step-by-step explanation:

15 did the homework and passed

19 did the homework

therefore, only 4 people who completed the homework and failed the test.

so, 15/19= 0.789, or 78.9 percent. or a 0.789 to one chance

The height of the given triangle will be 13.416 cm.

Given a right-angle triangle that has a hypotenuse of 14 cm, height of x, and base of 4 cm.

The Pythagorean theorem is a fundamental principle in geometry that establishes a relationship between the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Applying the Pythagorean theorem, we can write:

[tex]14^2 = 4^2 + x^2[/tex]

Simplifying the equation:

[tex]196 = 16 + x^2[/tex]

Subtracting 16 from both sides:

[tex]180 = x^2[/tex]

Taking the square root of both sides:

x = √180 = 6√5

Simplifying the square root:

x ≈ 13.416 cm

Therefore, the height (x) of the right-angle triangle is approximately 13.416 cm.

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The box of pancake says that it makes 10 pancakes but sam is able to make 8 pancakes from the ingredient. Here the number 10 represents Theoretical yield.

Here,

Theoretical yield can be defined as the product received from the  complete conversion of the limiting reactant in a chemical process.

It is the amount of product resulting from a theoretical chemical reaction and it is not the same as the amount you'll actually get from a reaction in the lab.

Theoretical yield is commonly expressed in terms of grams or moles.  the actual yield is the amount of product actually produced by a reaction. Actual yield is usually a smaller quantity because few chemical reactions proceed with 100% efficiency because of loss recovering the product and because other reactions may be occurring that reduce the product.  so 10 here is a theoretical yield bot the actual yield.

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complete question:

Decide whether the following scenarios represent theoretical or actual yields. sam follows the directions on a box of pancake mix. the box says that it makes 10 pancakes, but he is able to make 8 pancakes from the ingredients. in this case, the number 10 represents which type of yield?

Answer:

4[tex]y^{\frac{3}{2} }[/tex]

Step-by-step explanation:

using the rule of exponents/ radicals

[tex]\sqrt[n]{a^{m} }[/tex] = [tex]a^{\frac{m}{n} }[/tex]

then

4 [tex]\sqrt{y^{3} }[/tex]

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