Solve the following system of equations algebraically. Be sure to show each step of your work.

y = 2x² - 5x+9
y = 2x² + 5x - 1

Answer:

0.67

Step-by-step explanation:

10/15＝0.666666......

＝0.67

The conclusions reached in steps 4 and 5 are invalid. This is a flawed argument for the existence of isosceles triangles.

An isosceles triangle has two equal sides and two equal angles as a result. The term comes from the Greek words iso (same) and skelos (leg). An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal.

Each step is valid, but the conclusion is not. At the end of step 4,

here are a series of isometric maps that lead A to D and C to F, as claimed..

After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.

If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar

But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.

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Question:

This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.

The equation in terms of log(x), log(y)  and log(z) is,  

log x + 1/4 log y -1/2 log z.

A logarithmic equation is one in which a variable-containing expression's logarithm is used as a solution. If you can write both sides of the equation as powers of the same number, that will help you answer exponential equations.

here, we have,

log x√√y/z = log(x√(√y)/z)

Consider, the given logarithmic expression,

we get,

By using the logarithmic rule: log(ab) = log(a) + log(b)

So, log(x√(√y)/z)

   =logx + log(√(√y)/z)

   =log x + 1/2 log (√y)/z

   =logx + 1/2 log (√y) - 1/2 log z

   = log x + 1/4 log y -1/2 log z

Hence, the expression in terms of x , y and z is, log x + 1/4 log y -1/2 log z.

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Answer:

x = 4  rounded to the nearest whole number (actually 4.0801)

Step-by-step explanation:

The triangle formed by the sides of length 0.9x, 2.8x and 12 form a right triangle with the side of length 12 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

12² = (0.9x)² + (2.8x)²

144 = 0.81x² + 7.84x² = 8.65x²

Switching sides:

8.65x²= 144

x² = 144/8.65 = 16.6473

x = √16.6473= 4.0801

Rounded to the nearest integer, x = 4

Answer:

60

Step-by-step explanation:

3/5 = 0.6 meters = 60 cm

Answer:

2X-3=0

2X=3

X=3/2

Step-by-step explanation:

Answer:

2x- 3 = 0

2x=3

x = 3/2

Step-by-step explanation:                                                                                   best of luck to you

Hey  there!

[tex]\huge\textbf{Assuming:}[/tex]

[tex]\mathsf{f(x) = x^2 + 3x - 5}[/tex]

[tex]\mathsf{f(x) = 3^2 + 3(3) - 5}[/tex]

[tex]\mathsf{f(x) = 3 \times 3 + 9 - 5}[/tex]

[tex]\mathsf{f(x) = 9 + 9 - 5}[/tex]

[tex]\mathsf{f(x) = 18 - 5}[/tex]

[tex]\mathsf{f(x) = 13}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\mathsf{f(x) = 13}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

the maximum number of caps she can order is 162.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Laura is the fundraising manager for a local charity she is ordering caps for an upcoming charity walk.

Let "x" be the number of caps she ordered.

Since, manufacturing cost for a cap = $6

shipping charges for the lot = $25

Thus,

Total price she paid for x caps = 6*x + 25

Since she had only 1000$

So,

6x + 25 ≤ 1000

6x ≤ 975

x ≤ 975/6

x ≤ 162.5

therefore, the maximum number of caps she can order is 162.

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Answer:

sin 28 = 8 /17

Step-by-step explanation:

Since this is a right triangle, we can use trig functions.

sin theta = opp side / hypotenuse

sin 28 = 8 /17

Answer: 1.+900

2. -24

3.  -5

4. +10

Step-by-step explanation:

Answer:

[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]

Step-by-step explanation:

[tex]B'=\{1,5,8,9\}[/tex]

[tex](B'\cap A)=\{1,5\}[/tex]

[tex](B'\cap A)\cup C=\{1,5,6,7,8\}[/tex]

The complement of a set, notated with a prime symbol ('), are all other elements that are not in that set.

The intersection of two sets, notated by [tex]\cap[/tex], are just the elements that are contained in both sets.

The union of two sets, notated by [tex]\cup[/tex], are all the elements that are contained in both sets (any duplicates are not included).

When x is 4, the output of the equation is greater.

The value for x that produces the same output in both the graph and the equation is equal to 6.

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of any proportional relationship such as the linear equation (y = 4) is characterized by a straight line that crosses the y-coordinate as shown in the image attached below.

By critically observing the graphs of the equations, we can reasonably infer and logically deduce that they both would produce the same output (dependent value or y-value) at the ordered pair (4, 6).

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Answer: The annual premium for a 27-year-old female purchasing a 20-Year Endowment insurance policy with a face value of $25,000 is $42.67.

Step-by-step explanation:

1: cscX = 1/sinX = 5/2√5.

2: Using the reciprocal identity of tanA and sinA,

tanA/sinA = 1/cosA

√2/2 / -√3/3 = 1/cosA

-2√2/2√3 = 1/cosA

cosA = -2√3/2√2.

3: Using the Pythagorean theorem, sinX = √(1 - cos^2X)

√(1 - cos^2X) = √((1/cot^2X) - 1) = √((√3/2)^2 - 1) / (-√3/2)

sinX = √2/2.

4: Using the Pythagorean theorem,

cotθ = cosθ / sinθ = 1 / tanθ = 1 / (√(1 - cos^2θ) / cosθ) = cosθ / √(1 - cos^2θ) = 1 / (√(1 - (1/7)^2)) = √(48) / 7.

5: Using the cofunction identity, tan(-x) = -tan(x).

Using the identity that tan(π/2 -x) = cot(x),

-tan(x) = -1/cot(π/2 -x) = -1/(-1.84) = 1.84.

6: Using the even-odd identity, cos(-θ) = cos(θ), and

sin(-θ) = -sin(θ),

cos(θ-π/2) = cosθcos(π/2) + sinθsin(π/2) = 0cos(π/2) + (-0.57)sin(π/2) = -0.57.

7: Using the identity sin^2X + cos^2X = 1,

secX ⋅ sin^2X + cosX = secX ⋅ (1 - cos^2X) + cosX = secX - secXcos^2X + cosX = secX + cosX.

8: Using the identity 1 + tan^2θ = sec^2θ,

(sinθ + 1)(tanθ - secθ) = (sinθ + 1)(tanθ - 1/cosθ) = (sinθ + 1)(tanθcosθ - 1) = (sinθ + 1)sinθ(tanθ/sinθ) - (sinθ + 1) = sinθ + sin^2θ - sinθ - 1 = sin^2θ - 1.

Proof:

Using the identity tan^2X = sin^2X / cos^2X,

1+sec^2X / 1+tan^2X = (1 + 1/cos^2X) / (1 + sin^2X / cos^2X) = cos^2X / (cos^2X + sin^2X) = cos^2X / (1) = 1 + cos^2X.

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I think that it could be b but I'm not 100 percent sure

[tex]\textit{sum of all exterior angles in a polygon}\\\\ S=360^o \\\\[-0.35em] ~\dotfill\\\\ x+2x+3x+4x+5x+6x+7x+8x=360\implies 36x=360 \\\\\\ x=\cfrac{360}{36}\implies x=10[/tex]

Answer:

The exterior angles of an octagon add up to 360°. So, 8x° = 360°, and x = 45°.

Answer: Let's call the number of adults admitted "A" and the number of children admitted "C". We know that:

A + C = 4900 (total number of people admitted)

And the total revenue is:

2.75A + 0.25C = $6,962.50

We can use the first equation to solve for one of the variables in terms of the other:

C = 4900 - A

Substitute this expression for C into the second equation:

2.75A + 0.25(4900 - A) = $6,962.50

Expand and simplify the right side:

2.75A + 1225 - 0.25A = $6,962.50

2.5A = 5737.5

Solve for A:

A = 2298

So there were 2298 adults and 4900 - 2298 = 2602 children admitted.

Step-by-step explanation:

The two plans cost the same when the amount is $200.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us suppose the miles driven = x.

Given that,

The first plan has an initial fee of $40 and costs an additional $0.70 per mile driven. This is represented as:

A = 40 + 0.70x

The second plan has no initial fee but costs $0.90 per mile driven.

B = 0.90x

The two plans cost the same when A = B:

40 + 0.70x = 0.90x

40 = 0.90x - 0.70x

40 = 0.20x

x = 200

The two plans cost the same when the amount is $200.

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Answer:

30

Step-by-step explanation:

Add all the sides and you get 30.

Hope this helps! Pls give brainliest!

Answer:

30

Step-by-step explanation:

6+9.5+6.5+4+4 = 30

From the graph the range of the function is obtained as option 1: -5 ≤ y ≤ 8.

What is the range of data?

The range of data is defined as a measure of the difference between the maximum value of data and the minimum value of data.

From the graph, the following observations are made -

The endpoints of the graph have closed circles this means that, the endpoints are inclusive of the range.

For closed circles the inequality symbols used is (≤,≥).

The y-axis values suggests the range of the function.

The minimum y-axis value in the fourth quadrant is -5.

The maximum y-axis value in the first quadrant is 8.

The range of the function is [-5 , 8]

Therefore, the range is found to be -5 ≤ y ≤ 8.

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Given that the volume of the rectangular prism is 120 cubic inches, we can write the equation:

l * w * h = 120

where l, w, and h are the length, width, and height of the prism, respectively.

Since the length is 3 and the width is 10, we can plug in these values into the equation:

3 * 10 * h = 120

Solving for h, we get:

h = 120 / (3 * 10) = 120 / 30 = 4

So the height of the rectangular prism is 4 inches.

To find the surface area of the rectangular prism, we can add up the areas of all six faces:

2 * l * w + 2 * w * h + 2 * h * l

Plugging in the known dimensions, we get:

2 * 3 * 10 + 2 * 10 * 4 + 2 * 4 * 3 = 60 + 80 + 24 = 164 square inches

So the surface area of the rectangular prism is 164 square inches.

Answer: Hight 4 inch, surface area 164 square inch

Step-by-step explanation: multiply with l * w * h  

* = x

A: Mai answered 5  open-ended questions correctly,

B: Priya answered 15 multiple-choice questions correctly,

C: expression for the condition is y = 10 + 4a + 6b.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given points on each multiple choice question = 4

points on each open-ended question = 6

extra credit for winners = 10 points

A. If Mai answered 13 multiple-choice questions correctly and earned a total score of 92,

the total score of multiple choice questions = 13*4

the total score of multiple choice questions = 52

score left  = 92 - 52 - 10 (reducing 10 for extra points)

score left  = 30

open-ended questions she answers correctly = 30/6

open-ended questions she answers correctly = 5

B:  If Priya answered 4 open-ended questions correctly and earned a total score of 94,

the total score of open-ended questions = 4*6

the total score of open-ended questions = 24

the score left  = 94 - 24 - 10 (reducing 10 for extra points)

score left  = 60

multiple choice questions she answers correctly = 60/4

multiple choice questions she answers correctly = 15

C:  an expression that will represent a student's score in first period,

let y be the total score,

a be the number of multiple choice questions answered,

the total score of multiple choice questions = 4a

and b be the number of  open-ended questions answered,

the total score of open-ended questions = 6b

expression is,

y = 10 + 4a + 6b  (adding 10 for extra points)

Hence Mai answered 5  open-ended questions correctly,

Priya answered 15 multiple-choice questions correctly,

and expression is y = 10 + 4a + 6b.

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Answer:

M = 10 + 2f

Step-by-step explanation:

Please see the attachment for detail explanation

Best Mortgage Option 3 because this mortgage option offers a lower interest rate.

After reviewing all three mortgage options available to Demarco and Tanya, I would recommend that they choose option 3. This option offers a lower interest rate compared to the other two options and a longer loan term, which means that their monthly payments will be lower and more manageable for their budget. Additionally, option 3 offers a fixed interest rate, which provides them with more stability and predictability in their mortgage payments, as opposed to options 1 and 2 that offer adjustable interest rates.

Option 1 has the highest interest rate and the shortest loan term, making their monthly payments the highest of all three options. Option 2 offers a slightly lower interest rate, but it still higher compared to option 3, and has a shorter loan term compared to option 3, making their monthly payments still relatively high.

In conclusion, the best financial choice for Demarco and Tanya would be option 3. Its lower interest rate, longer loan term, and fixed interest rate make it the most affordable and stable option for them in the long run.

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Answer:

$199.98

Step-by-step explanation:

To calculate the amount that Kendall will save in finance charges during the six-month promotional rate period, we need to calculate the finance charges he would have incurred with his standard APR and then compare it to the finance charges he will incur with the promotional rate.

First, let's calculate the monthly finance charges with the standard APR. To do this, we need to know the average daily balance for each month. Assuming Kendall has a previous unpaid balance, let's say it is $500. And assuming he makes no other purchases, his average daily balance for each month would be:

$1,014 + $500 = $1,514The finance charges for each month with the standard APR would be:

$1,514 * (22.65/100) / 12 = $38.37

So, the total finance charges for the six-month promotional rate period with the standard APR would be:

$38.37 * 6 = $230.22

Next, let's calculate the finance charges with the promotional rate:

$1,514 * (3/100) / 12 = $5.04

So, the total finance charges for the six-month promotional rate period with the promotional rate would be:

$5.04 * 6 = $30.24

Finally, we can calculate the amount that Kendall will save in finance charges during the six-month promotional rate period:

$230.22 - $30.24 = $199.98

Therefore, Kendall will save $199.98 in finance charges during the six-month promotional rate period.

1) The sales tax is an additional rate that is paid along with the cost of the meal.

2) The amount paid in taxes for a meal costing $15.00 and a rate of 7% is given as follows: $1.05.

The sales tax is obtained applying the proportions in the context of this problem.

A proportion is applied as the sales tax is obtained with the multiplication of the cost of the meal by the decimal equivalent of the percentage of tax.

The decimal equivalent for a percentage of 7% is given as follows:

7/100 = 0.07.

Hence the amount of tax paid is given as follows:

0.07 x 15 = $1.05.

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The y-intercept is calculated using a table or a graph by substituting x = 0.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The y-intercept value is calculated when the x-coordinate is zero.

Now,

Example:

(0, 3), (0. 5), (0, 7) are all y-intercepts of the graph.

Thus,

The y-intercept is calculated when x = 0.

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Answer:

The answer is 6t-9. This can be calculated by dividing the numerator (54t2−81t) by the denominator (9t). This gives 6t-9.

Step-by-step explanation:

Answer:

81t2+16

Step-by-step explanation:

(9t-4)(-9t-4)   : Equation

Distribute parentheses using:(a + b)(c + d) = ac + ad + bc + bd.

Where :  a=9t, b=-4, c=-9t, d=-4.

This leads to 9t(-9t) +9t (-4) -4- (9t) -4 (-4).

Now we have to Apply minus-plus rule.

Where: -(-a)=a.+(-a)=-a

-9t.9t - 9t.4 + 4.9t = 4.4

=81t2+16

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