unit 1 algebra 1 test apex

If you invest $3,750 at the end of each of the next six years at an interest rate of 1.9% per annum, you will have approximately $23,596 after 6 years.

To calculate the total amount accumulated after 6 years, we can use the formula for the future value of an ordinary annuity. The formula is given as:

Future Value = Payment * [(1 + Interest Rate)^n - 1] / Interest Rate

Here, the payment is $3,750, the interest rate is 1.9% per annum (or 0.019 as a decimal), and the number of periods (years) is 6.

Substituting the values into the formula:

Future Value = $3,750 * [(1 + 0.019)^6 - 1] / 0.019

= $3,750 * (1.019^6 - 1) / 0.019

≈ $23,596

Therefore, after 6 years of investing $3,750 at the end of each year with a 1.9% interest rate per annum, you would have approximately $23,596. Hence, the correct answer is $23,596.

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The range of numbers in the data series that controls the minimum, maximum, and incremental values on the value axis is referred to as the "axis scale" or "axis range."

It determines the span of values displayed on the value axis of a graph or chart. The axis scale is typically set based on the minimum and maximum values present in the data series, and the incremental values (tick marks) are placed at regular intervals within that range.

It represents the span of values that will be displayed on the value axis of a graph or chart. The data range determines the scale and divisions of the axis, allowing the viewer to interpret the data accurately and understand the relative magnitude of the values being presented.

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Answer:

Slope=3

Step-by-step explanation:

m=y2-y1/x2-x1

m=19-10/6-3

m=3

Answer: The answer is C which is "m = 3"

Step-by-step explanation: To find the slope, the formula is change of y / change of x. The change of y in the graph is 9, and the change of x is 3. 9 divided by 3 is 3. Therefore, the option "m=3" is the correct answer.

Answer:

             \(\bold{m=-\dfrac16}\)

Step-by-step explanation:

\(\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}\)

(1, 3)    ⇒   x₁ = 1,  y₁ = 3

(7, 2)    ⇒   x₂ = 7,  y₂ = 2

So the slope:

                    \(\bold{m=\dfrac{2-3}{7-1}=\dfrac{-1}6=-\dfrac16}\)

The velocity of the ball thrown by your friend is approximately 4.17 meters per second.

To ascertain the speed of the ball, we want to utilize the condition of movement that relates distance, time, and speed increase. For this situation, we expect that the ball goes in an orderly fashion, and its speed increase is because of the power applied by your companion's toss. We can utilize the recipe:

distance = speed x time

We realize that the distance among you and your companion is 5 meters, and the time taken for the ball to travel that distance is 1.2 seconds. Hence, we can revise the equation to tackle for the speed:

speed = distance/time

Subbing the qualities, we get:

speed = 5/1.2 = 4.17 meters each second (approx.)

So the speed of the ball tossed by your companion is around 4.17 meters each second.

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Answer:

\(0.1212...=\dfrac{4}{33}\)

Step-by-step explanation:

A repeating decimal is a decimal number with a digit (or group of digits) that repeats forever.

There are three ways to show a repeating decimal:

0.1212... is a repeating decimal as there are two duplicates of the repeating block of digits "12" followed by an ellipsis.

To express a repeating decimal as a rational number, begin by assigning the decimal to a variable:

\(x=0.1212...=0.\overline{12}\)

Multiply both sides by 100:

\(\implies x \cdot 100=0.\overline{12}\cdot 100\)

\(\implies 100x=12.\overline{12}\)

Subtract the first equation from the second to eliminate the part after the decimal:

\(\begin{array}{crcr}& 100x & = & 12.\overline{12}\\- & x & = & 0.\overline{12}\\\cline{2-4} & 99x & = & 12\phantom{.12}\\\end{array}\)

Divide both sides of the equation by 99:

\(\implies \dfrac{99x}{99}=\dfrac{12}{99}\)

\(\implies x=\dfrac{12}{99}\)

Reduce the fraction to is simplest form by dividing the numerator and denominator by 3:

\(\implies x=\dfrac{12 \div 3}{99 \div 3}=\dfrac{4}{33}\)

\(\textsf{Therefore, $0.1212...$ expressed in the form of a rational number is\;$\dfrac{4}{33}$}.\)

The correct answer and explanation is:

B. No; 10 servings equals 2,500 mL, or 2.5 L, which is greater than 2 liters.

The true statement is that ten servings will not fit in a 2-liter bowl

Here, we have,

to determine the true statement:

The size of the serving punch is given as:

One serving of punch = 250 milliliters

For ten servings, we have:

Ten servings = 10 * 250 milliliters

Evaluate the product

Ten servings = 2500 milliliters

Convert to liters

Ten servings = 2.5 liters

2.5 liters is greater than liters

Hence, ten servings will not fit in a 2-liter bowl

The correct answer and explanation is:

B. No; 10 servings equals 2,500 mL, or 2.5 L, which is greater than 2 liters.

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Answer:

There are 10 different outcomes of flipping a coin five times.

Step-by-step explanation:

there are two sides on a coin. 2 x 5 = 10

Hope that helps!

Answer:

2

Step-by-step explanation:

it heads or tales a coin is two-sided no matter what kind unless you are talking about all together then it would be 10

Answer:

8 nine tenths

Step-by-step explanation:

In RAND function, when we click anyplace in the succeed sheet use duplicate and afterward glue as values. returns an irregular number that is more noteworthy than or equivalent to 0 and under 1.

The subject of arithmetic incorporates amounts and their varieties, conditions and related designs, shapes and their areas, and where they can be found. The expression "function" alludes to the connection between a bunch of information sources, every one of which has a related result. An association among data sources and results in which each info prompts a solitary, particular outcome is known as a capability. Each capability is given a space and a codomain, or scope. Normally, f is utilized to signify capabilities (x). input is a x. There are four fundamental sorts of capabilities open. in view of the accompanying variables: on capabilities, coordinated capabilities, many-to-one capabilities, inside capabilities, and on capabilities.

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answer done last mai btaa dena correct hai

Answer:

93/5

Step-by-step explanation:

(0, 3) and (5, 96)

m= (y2-y1)/(x2-x1)

m= (96-3)/(5-0)

m= 93/5

Flowing Water as a geological process can be described as the running of water which could be from a rivulet to a raging river, the flowing could be flowing  a path which is curved, narrow or  merging.

This can be described as the  hydrologic cycle by returning precipitation that was received on the land by spreading out to the oceans.

The Overland flow transfers of water can occur through the basin by:

In the formation of  landforms by the geologic process the  Tectonic plate movement under the Earth  can bring about the formation of  landforms gnarled through pushing up mountains as well as  hills.

The processes of shaping landforms entails the :

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The bags of takis did he bought is 9 and number of sodas is 7

Given data ,

1 bag of takis cost 2.25 dollars and 1 soda cost 1.50 dollars.

Now , total number of items = 16

And total amount spend = $ 30.75

The total number of items bought is 16, so we have the equation:

x + y = 16 (equation 1)

The total amount spent is $30.75, so we have another equation:

2.25x + 1.50y = 30.75 (equation 2)

Multiply equation 1 by 1.50 to make the coefficients of y the same

1.50(x + y) = 1.50(16)

1.50x + 1.50y = 24 (equation 3)

Subtract equation 3 from equation 2 to eliminate y:

(2.25x + 1.50y) - (1.50x + 1.50y) = 30.75 - 24

0.75x = 6.75

x = 6.75 / 0.75

x = 9

Substitute the value of x into equation 1 to find y:

9 + y = 16

y = 16 - 9

y = 7

Hence , the person bought 9 bags of Takis and 7 sodas

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Answer:

(-2,-3), (-4,-2), (-2,0), (0,3), (1,2)

Step-by-step explanation:

Answer:

(-2,-3), (-4,-2), (-2,0), (0,3), (1,2)

Step-by-step explanation:

An inverse function is just switching up the x and y of the original function.

(-3,-2) to (-2,-3)

What shape lol? Gotta snag those points ;)

Taking the square root of both sides, we finally get the Schwarz inequality: || ≤ ||f|| ||g||. And that's the proof for the Schwarz inequality.

The Schwarz in equality can be proved by taking the square root of the both sides.

To prove the Schwarz inequality, we can follow the hint provided. Let's consider the function F(a) = ||f + ag||^2, where ||g|| ≠ 0. F(a) is a second-degree polynomial in a, and it has no negative values since the square of a norm is always non-negative.

F(a) = ||f + ag||^2
=  + 2a + a^2

Now, let's examine the discriminant of this polynomial. The discriminant, Δ, is given by: Δ = B^2 - 4AC
Here, A = , B = 2, and C = . Substituting these values, we get: Δ = (2)^2 - 4

Since F(a) has no negative values, its discriminant must be non-positive, i.e., Δ ≤ 0. Thus, (2)^2 - 4 ≤ 0 (2)^2 ≤ 4

Dividing both sides by 4, we obtain: ()^2 ≤ .Taking the square root of both sides, we finally get the Schwarz inequality: || ≤ ||f|| ||g||. And that's the proof for the Schwarz inequality.

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Answer:

I think it is 3.750

Step-by-step explanation:

In the imaged attached, the most precise name for ABCD  is known to be rhombus.

Looking at the shape attached, one can see that the diagonals of a parallelogram are said to be bisecting one other and if it cross at right angles, it is said to be a rhombus.

Using the Diagonal midpoints of AC and BD, the equation will be:

(A+C)/2

(B+D)/2

To find if the midpoints are similar, then:

A +C = (3, 5) +(6, 2) = (9, 7)

B +D = (7, 6) +(2, 1) = (9, 7)

Therefore, from the solution above, the midpoints of the diagonals are the same, making the shape to be a parallelogram.

In terms of Diagonal vectors, the shape will be perpendicular when the figure is a rhombus. So:

 AC = C -A = (6, 2) -(3, 5) = (3, -3)

BD = D -B = (2, 1) -(7, 6) = (-5, -5)

So the lengths will be (3√2 vs 5√2).

Note also that the dot-product of these values need to be zero if they are perpendicular and as such:

 AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

Therefore, one can say that the diagonals are known to different length and are perpendicular bisectors, so the shape above is regarded as rhombus.

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If trapezoid WXYZ is congruent to trapezoid EFGH, then each of their corresponding sides and angles are congruent.

In a trapezoid, the parallel sides are called the bases, and the non-parallel sides are called the legs. The height or altitude of a trapezoid is the perpendicular distance between the bases.

If trapezoid WXYZ is congruent to trapezoid EFGH, then each of their corresponding sides and angles are congruent. In particular, corresponding sides are parallel and have the same length.

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Answer:

\(BC=5\sqrt{2}\), \(AC=5\sqrt{4}\)

Step-by-step explanation:

In a 45-45-90 relation triangle the two shortest sides will have equal length, meaning:

\(BC=5\sqrt{2}\)

To find the hypotenuse we must multiply the shortest side by \(\sqrt{2}\), both sides are equal so it doesn't matter which we multiply.

\(AC=5\sqrt{2} \sqrt{2} \\AC=5\sqrt{4}\)

Answer:

b. 5z-10 = 5(z-2)    c. c-2c^2= c(1-2c)    d. r+r+r+r= r(1+1+1+1)= 4r   e. 2x-(1/2) = (1/2)(4x-1)

Explanation:

you just need to find a common factor that you can divide out  of each term. ex. with the 5z-10 both 5z and 10 are divisible by 5, so you can factor that out. to check the answers just multiply it. if you still don't get it, look up "factoring binomials"

Answer:

$67.83

Step-by-step explanation:

Price before tax: $85

Discount: 25%

100% - 25% = 75% = 0.75

Price after discount: 0.75 * $85 = $63.75

Tax: 6.4%

100% + 6.4% = 106.4% = 1.064

Price after discount & tax: 1.064 * $63.75 = $67.83

Answer: $67.83

Answer:

They sold

20 Roses and 20 Carnations

Step-by-step explanation:

The total sales of 40 flowers is $100 not $10 as in the question

Roses=$3

Carnations=$2

Total flowers sold=40

Total sales=$10

Let Roses=r

Carnations=c

c+r=40. (1)

3r+2c=100 (2)

From (1)

c=40-r

Substitute c=40-r into (2)

3r+2c=100

3r+2(40-r)=100

3r+80-2r=10

r=100-80

r=20

Substitute r=20 into (1)

c+r=40

c+20=40

c=40-20

=20

c=20

r=20

Check:

3r+2c=100

3(20)+2(20)=100

60+40=100

100=100

Answer:

2. $9.99

3. 45 tickets for $27

4. 20 cents

Step-by-step explanation:

2. 79.92/8 = 9.99

3. 27/45 0.6 and 15/20 = 0.75 and 60 cents is less than 75 cents

4. 6/30 = 20

Answer:

Step-by-step explanation:

79.92/8= 9.12 per cd

15/20= .75

27/45=.6 better deal because it is .60 cents per ticket

6/30= .20 per can

The area of the acute triangle can be found by the formula: area of acute triangle = (1/2) × b × h.

According to Pythagoras theorem the triangle is termed as acutely angled if the square of its longest side is less than the sum of the squares of two other smaller sides. Let a, b, and c are the length of sides of a triangle, where side "a" is the longest, then the given triangle is acutely angled if and only if a^2 < b^2 + c^2.

The area of the acute triangle can be calculated by the formula:

         area of acute triangle = (1/2) × b × h

         b = base, and

         h = height

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Answer:

See below

Step-by-step explanation:

Plug each equation in:

34-5 = 29

2^3 +18 = 26

We have an equation that gives us the height of the flagpole in terms of "m", the height of Tim. We can use this equation to find the height of the flagpole for different values of "m".

Based on the given information, we can use similar triangles to determine the height of the flagpole. The height of the flagpole is represented by the length of one side of the larger triangle, and the length of the shadow is represented by the length of one side of the smaller triangle.

Let's label the height of the flagpole as "h" and the length of the shadow as "s". We can set up the following proportion:

h/s = (distance from Tim to base of flagpole + height of Tim)/distance from Tim to base of flagpole

Substituting in the given values, we get:

h/16.60 = (12.45 + height of Tim)/12.45

To solve for "h", we can cross-multiply and simplify:

h = 16.60 * (12.45/(12.45 + height of Tim))

We don't have enough information to solve for the height of Tim, but we can still simplify the equation by substituting in "m" for "height of Tim":

h = 16.60 * (12.45/(12.45 + m))

Now we have an equation that gives us the height of the flagpole in terms of "m", the height of Tim. We can use this equation to find the height of the flagpole for different values of "m".

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