Which of the following statements about f(x)= -(x-4)² -1 are true? Select all that apply.
a) Vertex: (4, -1)
b) y-intercept: (0, -17)
c) x-intercept: (5, 0)
d) Axis of Symmetry: x = 4
e) x-intercept: (3, 0)
f) no x-intercepts

1a. The interest that Thato will pay equals to R3,840.

1b. The final amount he will pay for the bicycle will be R 11 840.

a) To calculate the interest that Thato will pay, you can use the following formula:

Interest = Principal * Rate * Time

Interest = R 8,000 * 0.14 * 3

Interest = R3 840

Final amount = Principal + Interest

Final amount = R 8,000 + R 3,840

Final amount = R 11,840

Cost price per rose = Total cost of roses / Number of roses

Cost price per rose = R 900 / 200

Cost price per rose = R 4.50

Selling price per rose = Price of bouquet of 5 roses / Number of roses in the bouquet

Selling price per rose = R 35 / 5

Selling price per rose = R 7.00

Profit per rose = Selling price per rose - Cost price per rose

Profit per rose = R 7.00 - R 4.50

Profit per rose = R 2.50

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A large tank hold 1. 9 time 10 to the 7th power gallons of oil. The amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

To find the amount of oil that can be stored in 9 tanks that each hold 1.9 x 10^7 gallons of oil, we can use the following steps:

Write down the number of gallons that one tank can hold: 1.9 x 10^7 gallons. Multiply this value by the number of tanks: 1.9 x 10^7 gallons/tank x 9 tanks.

To multiply the two numbers, we can simply multiply the coefficients (1.9 and 9) and add the exponents (7 in this case): (1.9 x 9) x 10^(7+0) gallons.

Simplifying the coefficient gives us 17.1, so the amount of oil that can be stored in 9 tanks is 17.1 x 10^7 gallons.

Finally, we can express this result in scientific notation by writing it as 1.71 x 10^8 gallons, since 17.1 is equivalent to 1.71 x 10.

Therefore, the amount of oil that can be stored in 9 tanks is 1.71 x 10^8 gallons in scientific notation.

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Answer:

Two geometric objects are perpendicular if they intersect at a right angle.

Step-by-step explanation:

How you know:

The condition of perpendicularity may be represented graphically using the perpendicular symbol, ⟂.

The side x = 9.4 approximately to nearest tenth using the cosine rule.

In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

Considering the given triangle, side x is calculated with cosine rule as follows;

a² = b² + c² - 2(b)(c)cosA

x² = 8² + 15² - 2(8)(15)cos33°

x² = 64 + 225 - 240(0.8387)

x² = 289 - 201.2809

x² = 87.7191

x = 9.3658 {take square root of both sides}

With proper application of the cosine rule, we can conclude the value of the side x of the triangle is approximately 9.37 to the nearest tenth.

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Answer: ddddddddddddddddddddddddddddddddddddddddddddddbddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddd

Step-by-step explanation:

A total of 77 new flowers can be planted on the flower bed.

New flowers has to be planted in a circular flower bed that has a diameter of 14 ft.

Each one of the flower requires to square feet of the space.

The radius of the flower bed will be 7 feet.

The area of the flower bed can be calculated by using the formula,

A = πr²

Where r is the radius.

Put in the value of radius to find the area of the flower bed,

A = 3.14 x 7 x 7

A = 153.86 ft²

Now, let us say that N number of floors can be planted,

So,

N)(2) = 153.82

N = 76.93

So we can say that about 77 flowers can be planted on the flower bed.

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The given function represents exponential growth, the value of a is 1 and the value of r is 0.45.

The quantity increases slowly after which the rate of change and the rate of growth increases over a period of time rapidly. This increase in growth is calculated by using the exponential growth formula.

The exponential growth formula is [tex]Amount = Initial value(1+\frac{r}{100} )^{\frac{t}{n}}[/tex].

The given exponential function is [tex]x(t)=(1.45)^{\frac{t}{2} }[/tex].

Now, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex]

Compare, [tex]x(t)=(1+0.45)^{\frac{t}{2} }[/tex] with [tex]y=a(1+r)^t[/tex], we get

a=1 and r=0.45

Therefore, the value of a is 1 and the value of r is 0.45.

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In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )

In triangle LMN,

Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.

Measure of side m = 450 inches

Measure of ∠M = 74°

Measure of ∠N = 41°

Sum of all the angles in a triangle is equal to 180°

m ∠M + m ∠N + m ∠L = 180°

⇒ 74° + 41° + m ∠L = 180°

⇒ m ∠L = 180° - 115°

⇒ m ∠L = 65°

Using sine law of triangle we have,

sin L / l  = sin M / m = sin N / n

⇒sin L / l  = sin M / m

Substitute the value we get,

⇒ sin 65° / l  = sin 74° / 450

⇒ l = sin 65° × ( 450 / sin 74°)

⇒ l = 0.9063 × ( 450 / 0.9613 )

⇒ l = 42.43 inches

⇒ l = 42.4 inches ( nearest tenth )

Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).

The above question is incomplete, the complete question is:

In ΔLMN, m = 450 inches,  m ∠M=74° and  m ∠N=41°. Find the length of l, to the nearest 10th of an inch.

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Answer: 424.3

Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and

m∠N=41°. Find the length of l, to the nearest 10th of an inch.

A.A.S.→Law of Sines

Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3

l=

sin74

450sin65

​

≈424.2742≈424.3

To make 50 ounces of a 40 percentage alcohol solution, eight ounces of the 30% solution must be mixed with the 70% solution.

1. Round the two solutions' initial concentrations to the nearest tenth (30% alcohol = 0.3; 70% alcohol = 0.7).

2. Determine the combined solution's overall alcohol content

(30% + 70%): 0.3 + 0.7 = 1.

3. Multiply 50 ounces by 0.4 to get the total amount of alcohol required for a 40% solution:

50 x 0.4 = 20 ounces.

4. Determine how much 30% solution is required to reach the desired concentration. 1 divided by 20 equals 20 ounces.

5. Subtract the quantity of the existing 70% solution:

(50 ounces x 0.7)/20 ounces = 8 ounces.

6. The outcome is that 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

The original concentrations of the two solutions must first be converted to decimals (30% alcohol = 0.3; 70% alcohol = 0.7) in order to determine how much of a 30% alcohol solution has to be added to a 70% alcohol solution to create 50 ounces of a 40% alcohol solution. The two decimals can then be added to determine the total amount of alcohol present in the combined solution: 0.3 + 0.7 = 1. In order to determine the entire amount of alcohol required for a 40% solution, multiply 50 ounces by 0.4, which results in 20 ounces. The amount of the 30% solution required to reach the specified concentration can be estimated by dividing 20 ounces by 1, which is 20 ounces. Then, 20 ounces must be divided by the amount of the 70% solution that is already present to get 8 ounces. As a result, 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

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Answer:

The first/top option

Step-by-step explanation:

First, we can find the inequality that the line is representing. X is the number of hours she has already done, and she has five hours more to do to fulfill the 12 or more hours of required service. The inequality would be x+5≥12.

The minimum that X has to be is 7 because any value lower than 7 would make the inequality false[ ex. 6 + 5 ≠ 12 ]. The arrow would be pointing to the right, because 7 is the minimum value, not the max, so any value higher than 7 would still make the inequality true. Lastly, the circle would be filled, because 7 is included in the set of values that make the inequality true[ 7 + 5 = 12 ].

So, the answer would be the first option.

Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high, since the ratio of ice cream to caramel is much higher than her ideal ratio.

Ari's ideal ratio of ice cream to caramel for a milkshake is 5 scoops of ice cream for every 3 spoonfuls of caramel. Freeze Zone's milkshakes, however, have a ratio of 10 scoops of ice cream for every 7 spoonfuls of caramel, which is significantly higher than Ari's ideal ratio. Therefore, Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high. The higher ratio of ice cream to caramel means that the milkshake will be sweeter, and may not have the desired balance of flavors that Ari prefers. Ari may also think the milkshake is too heavy or overly sweet, since the extra caramel creates a consistency that is different from what she is used to. Ultimately, Ari will likely think that the amount of caramel in Freeze Zone's milkshakes is too high for her liking.

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The number of cans collected by Sasha to reach her goal is equal to 300 cans.

Number of cans collected by Sasha before reaching her final goal of recycling is equal to 180 cans.

Percent of cans collected by which is equal to 180 is 60%

Let 'y' be the total number of cans collected by Sasha to reach her goal .

60% of y = 180

⇒ ( 60 / 100 ) × y = 180

⇒ y = ( 180 × 100 ) / 60

⇒ y = 18000 / 60

⇒ y = 300 cans

Therefore, the total number of cans collected by Sasha to reach her goal of recycling is equal to 300 cans.

The above question is incomplete, the complete question is :

Sasha is collecting cans to recycle. When she collected 180 cans she knew she had reached 60% of her goal.

Question: How many more cans does Sasha need to collect to reach her goal?

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Answer:

One pecan cheesecake = $9

One apple cheesecake = $20

Step-by-step explanation:

This is a system of equations problem, so we can set up these equations (Note: p = pecan cheesecake cost | a = apple cheesecake cost):

8p + 12a = 312

9p + 6a = 201

Now, we can solve the system of equations. Below is an example of using the elimination method to solve the system:

1.    8p + 12a = 312 --> -4p - 6a  = -156        

     9p + 6a = 201  -->  9p + 6a = 201

2.                                  5p         = 45

3.                                    p         = 9

4.  8(9) + 12a = 312

    72   + 12a = 312

              12a = 240

                 a = 20

1. We try to make one of the terms equal to the negative version of the other term to eliminate that term; here, I am eliminating "a". To do this, find a multiple of one of the equations where one of the terms is the negative version of the other term. In other words, divide/multiply the equation by a number so one of the terms in the equation is the negative version of the term in the other equation (I divided the first equation by -2 so 12a becomes -6a, the negative version of 6a in the second equation.

2. Next, add the two equations' corresponding terms

(-4p + 9p = 5p; -6a + 6a = 0; -156 + 201 = 45)

3. Simplify the equation (5p = 45; p = 45/5; p = 9)

4. Substitute the term you found back into one of the equations to find the other term.

For a z-score, We  transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions i.e. D.

What exactly is the z-score?

The z-score is a statistical measurement that describes a value's relationship to the mean of a collection of values. The z-score formula is

z = (x - μ)/σ

x = data point

μ = mean

σ = standard deviation

Mean:- The sum of a collection of numbers divided by the total number of numbers in the set is known as the arithmetic mean, sometimes known as the arithmetic average or simply the mean or average. A survey, experiment, or observational research is usually used to create the collection.

Now,

As Z-scores are standardized scores that identify and define each score's exact placement within a distribution. We may conduct meaningful comparisons of z-scores across various samples or groups by converting our data (raw score).

hence,

          We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions.

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Answer:  1/2of 2/3 = 1/2 of 2 Third(s)= 1 third

1) Given that the perimeter of the rectangle is at least 40 cm, the  inequality and show that it reduces to x ≥ 3 2/3 is:  12x - 4 >= 40

2) The smallest possible value of x is 4

3) The area of the rectangle is  57 cm²

(i) The perimeter of a rectangle is given by the formula P = 2(l + b), where l is the length and b is the breadth. Substituting the given values, we get:

P = 2(4x + 3 + 2x - 5) cm

P = 2(6x - 2) cm

P = 12x - 4 cm

We are given that the perimeter is at least 40 cm, so we can write the inequality:

12x - 4 ≥ 40

Simplifying this inequality, we get:

12x ≥ 44

Dividing both sides by 12, we get:

x ≥ 11/3

x ≥ 3 2/3

So the inequality reduces to x ≥ 3 2/3

II) Note that if x is a perfect square, the smallest possible value of x is 4, because 4 is the smallest perfect square.

III) Substituting x = 4 in the length and breadth of the rectangle, we get:

Length = 4x + 3 = 19 cm

Breadth = 2x - 5 = 3 cm

Therefore, the area of the rectangle is:

Area = Length x Breadth = 19 cm x 3 cm = 57 cm²

Thus, it is correct to state that the area of the rectangle is 57cm².

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Step-by-step explanation:

fund the slope then use the two point form

The probability of winning $2 without getting below $0 at any time is 1/4  or 0.25.

To calculate the probability of winning $2 without getting below $0 at any time, we can use a branching diagram to track the possible outcomes.

Starting from $0, there are two possible outcomes for the first flip: heads or tails. If the first flip heads, the outcome is $1 and there are two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is $2 and we have won the game. If the second flip is tails, the outcome is back to $0 and we have to start over. If the first flip is tails, the outcome is $-1 and we also have two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is back to $0 and we have to start over. If the second flip is tails, the outcome is $-2 and we have lost the game.

Putting all of the possible outcomes together, we get the following branching diagram:

              H                              T

         /          \                       /     \

       H             T                  H      T

     /     \          /                      \

    H      T     T                        H

   $2    $0   -$1                       -$2

The only way to win $2 without getting below $0 at any time is to get two heads in a row. This can only happen along the top branch of the diagram, which has a probability of (1/2) * (1/2) = 1/4.

Therefore, the probability of winning $2 without getting below $0 at any time is 1/4 or 0.25.

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The percentage increase is given by the equation A = t + 0.24t = 1.24t

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage increase be represented as A

Now , the equation will be

The initial quantity be represented as t

Now , the increased quantity be represented as p = 24 %

So , the increased quantity = 24 % x initial quantity

Substituting the values in the equation , we get

The increased quantity = ( 24/100)t

The increased quantity = 0.24t

So , the final quantity = initial quantity + increased quantity

On simplifying the equation , we get

The final quantity = t + 0.24t

The final quantity = 1.24t

Hence , the equation is A = 1.24t

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The initial length of the scarf is 50 centimeters.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

We can use the given information to find the rate at which Cassandra is knitting the scarf and the initial length of the scarf.

Let L be the initial length of the scarf in centimeters, and let r be the rate at which Cassandra is knitting the scarf in centimeters per hour. Then, we have:

L + 25h = length of scarf after h hours

Substituting h = 3 and the length of the scarf after 3 hours = 125, we get:

L + 25(3) = 125

L + 75 = 125

L = 50

Therefore, the initial length of the scarf is 50 centimeters.

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Cassandra is knitting a scarf. She increases the length of

the scarf by 25 centimeters each hour she knits. After 3

hours, the scarf is 125 centimeters long what is initial length of scarf.

The points A(-4,3) ; B(-3,4) ; C(4,3) ; D(4,-3) are plotted on the graph.

What is meant by a coordinate plane?

Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line which is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.

The given points are

A is 4 units to the left and 3 units up which means  A is (-4,3).

B is 3 units to the left and 4 units up which means B is (-3,4).

C is 4 units to the right and 3 units up which means C is (4,3).

D is 4 units to the right and 3 units down which means D is (4,-3).

All these 4 points are plotted on the coordinate plane and the graph is attached below.

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If 18% of middle school student voted in a school election and number of students who voted is 213 , then the total students in the middle school is approximately 1184 students .

Let "x" be = total number of middle school students.

We know that 18 percent  of the students voted = 0.18x, and is equal to 213  ;

that means , ⇒ 0.18x = 213 ;

Now we need to solve for x,

We divide both sides by 0.18 ;

⇒ x = 213/0.18  ;

Simplifying, we get:

⇒ x = 1183.33

Since the number of students cannot be in decimal ,

So ,  the actual number of students must be greater than or equal to 1183.33.

Therefore, the middle school has approximately 1184 students.

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The measure of x is 14, by using the definition of secants.

A straight line that intersects a circle in two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is in a unique secant line and every secant line defines a unique chord. In geometry, a secant is a line that cuts any curve in at least two different points.

Given that, two secants are intersecting inside the circle making two arcs measuring 55° and 75° and an angle measuring 3x+23

We know that,

If two secants intersect inside a circle, then the measure of the angle formed is equal to half the sum of the measures of the intercepted arcs.

Therefore,

3x+23 = 1/2[55° + 75°]

3x+23 = 1/2 × 130

3x+23 = 65

3x = 42

x = 14

Hence, the measure of x is 14, by using the definition of secants.

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The point of intersection can be found by setting the equations equal, dividing by the same quantity, taking the natural log, and dividing by ln(1.25).

[tex]2500(1.25^t) = 6000(0.3^t)[/tex]

[tex]2500*1.25^t = 6000*0.3^t[/tex]

Divide both sides by 2500:

[tex]1.25^t = 0.3^t * (6000/2500)[/tex]

Divide both sides by[tex]0.3^t[/tex]:

[tex]1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]

Take the natural log of both sides:

[tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]

Divide both sides by ln(1.25):

[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]

The point of intersection is t = ln((6000/2500) / [tex]0.3^t[/tex]) / ln(1.25).

The point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other and solving for the variable t. For example, if we want to find the point of intersection of [tex]2500(1.25^t) = 6000(0.3^t)[/tex], we can start by setting the two equations equal to each other and dividing both sides by [tex]2500: 1.25^t = 0.3^t * (6000/2500)[/tex]. Then we can divide both sides by[tex]0.3^t: 1.25^t / 0.3^t = (6000/2500) / 0.3^t[/tex]. We then take the natural log of both sides: [tex]t*ln(1.25) = ln((6000/2500) / 0.3^t)[/tex]. Finally, we divide both sides by ln(1.25): [tex]t = ln((6000/2500) / 0.3^t) / ln(1.25)[/tex]. This means that the point of intersection is[tex]t = ln((6000/2500) / 0.3^t) / ln(1.25).[/tex] In conclusion, the point of intersection of two exponential functions can be found algebraically by setting the two equations equal to each other, dividing both sides by the same quantity, taking the natural log of both sides, and then dividing both sides by ln(1.25).

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Answer:Part A: To determine the average test score in your math class after completing test 2, substitute 2 for x in the linear function f(x) = 0.5x + 80.

f(2) = 0.5 * 2 + 80 = 81

So, the average test score in your math class after completing test 2 is 81.

Part B: To determine the test average for your science class after completing test 2, we can use the table of values for g(x) given in the problem. When x = 2, g(2) = 83. So, the average test score in your science class after completing test 2 is 83.

Part C: To determine which class had a higher average after completing test 4, we need to calculate the average test scores for both classes after test 4.

For the math class, we can use the linear function f(x) = 0.5x + 80 to find the average test score.

f(4) = 0.5 * 4 + 80 = 82

For the science class, we can use the table of values for g(x) given in the problem. When x = 4, g(4) = 85.

So, the average test score in your science class after test 4 is higher, 85 compared to 82 in your math class.

Step-by-step explanation:

Answer:

y=5 and x=-1 are parallel

Step-by-step explanation:

Let's do a quick review on some things:

Parallel lines are the lines that never intersect and perpendicular lines are the lines that intersect at 90°.

Lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.

So, this answers to your question that it's parallel!

Hopefully this helps :)

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

The lowest point on the graph, that is referred to as the minimum, or min, is the vertex of a parabola. The highest point on the graph, that referred to as the maximum, or max, is the vertex of a parabola.

The formula for the minimum value is given by -b/2a

Here we have

The medical equipment industry manufactures X-ray machines. If x machines are made, the unit cost is given by the function
C(x) = 0.9x²-180x+20,985.  

Compare given C(x) with the standard equation ax² + bx + c  

=> a = 0.9, b = -180 and c = 20,985  

We can find the x - coordinate where the minimum value occurs using the formula -b/2a    

The x-coordinate where the minimum value occurs = - (- 180)/2(0.9)

= (180)/1.8 = 100

Hence at x = 100, the unit cost will be minimum

The unit cost can be calculated as follows

C(100) = 0.9(100)²-180(100)+20,985

= 0.9(10000) -18000 + 20,985    

= 9000 - 18000 + 20985

= 11985

Therefore,

At 100 machines the unit cost will be minimum and the minimum cost is 11985.

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Answer:

4

Step-by-step explanation:

Rate of change forumla

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

We have our X points, -7 and -2. Now to find the Y value at those places.

For -7, Y is 5

For -2, Y is 25

Now we plug this into the equation

[tex] = \frac{25 - 5}{ - 2 - ( - 7)} = \frac{20}{5} = 4[/tex]