Instructions: Factor the polynomial expression.
25x² + 20x - 50

Answer:

Step-by-step explanation:

[tex]15+2x-4=9x+11-7x \rightarrow 2x+11=2x+11[/tex]  True for all x.

[tex]2x+3(4x-1)=2(5x+3)+4x \rightarrow 2x+12x-3=10x+6+4x[/tex]

                                                [tex]\rightarrow 14x-3=14x+6[/tex]

                                               [tex]\rightarrow 14x=14x+9[/tex]   Cannot be true.                                        

Answer:

I used Desmos Graphing Calculator  

Step-by-step explanation:

The value of the question are:

S(k) - T(k) = k² + 2k + 10.

(f.g)(2) = 2.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

To find S(k) - T(k), we first need to find the expressions for S(k) and T(k):

S(k) = k² + k + 4

T(k) = k - 6

So, S(k) - T(k) = (k² + k + 4) - (k - 6)

= k² + k + 4 - k + 6 (distributing the negative sign)

= k² + 2k + 10

Therefore, S(k) - T(k) = k² + 2k + 10.

To find (f.g)(2), we first need to find the expression for f.g:

f.g(x) = f(g(x)) = f(x + 3) = (x + 3) - 3 = x

So, (f.g)(2) = f(g(2)) = f(2 + 3) = f(5) = 5 - 3 = 2.

Therefore, (f.g)(2) = 2.

Hence, the value of the question are:

S(k) - T(k) = k² + 2k + 10.

(f.g)(2) = 2.

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This isosceles trapezoid's median dimension is 10 inches.

from the question:

The two bases of the trapezoid have measures 8 inches and 12 inches. We can use the formula for the area of a trapezoid to find the length of the median:

Area of trapezoid = (sum of bases) x (height) / 2

We can rearrange this formula to solve for the height:

height = 2 x (Area of the trapezoid) / (sum of bases)

The area of the trapezoid is:

Area of trapezoid = (1/2) x (sum of bases) x (height)

Substituting the expressions for the bases and height, we get:

Area of trapezoid = (1/2) x (8 + 12) x (height) = 10h

So, we have:

10h = (1/2) x (8 + 12) x (h)

10h = 10h

Therefore, the equation is true for any value of h, including the height that we are interested in.

Now, to find the length of the median, we need to find the length of the segment that connects the midpoints of the two non-parallel sides. Since the trapezoid is isosceles, the length of this segment is equal to the average of the lengths of the two bases:

median = (8 + 12) / 2 = 10

Therefore, the measure of the median of the trapezoid is 10 inches.

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Penny needs 7 adults for 56 children, if the ratio of adults to children is 1:8.

In a ratio, two or more quantities are compared. The terms "a:b" or "a/b" are frequently used to denote ratios, where a and b represent the two values being compared. For instance, a class may have a 3:5 ratio between the number of males and girls. By dividing both components by their largest common factor, ratios can be made simpler. Ratios can also be written as fractions or percentages. Several fields, including banking, engineering, and statistics, employ ratios often.

Given that, the ratio of adults to children is 1:8.

Thus, for 56 children the number of adults should be:

If the ratio of adults to children is 1:8, then for every adult there are 8 children. So, if Penny has 56 children at the nursery, the number of adults she needs can be found by dividing 56 by 8:

Number of adults = 56/8 = 7

Therefore, Penny needs 7 adults for 56 children.

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The index card's perimeter is 15 inches square because its οriginal measurements are 3 inches by 5 inches.

This is the bοundary οr cοntοur length οf a 2D geοmetric shape.

Depending οn their size, multiple shapes may have the same circumference. Fοr example, imagine a triangle made up οf wires οf length L.

The same wire can be used tο create a square if all sides are the same length.

The length cοvered by the perimeter οf the shape is called the perimeter. Therefοre, the units οf circumference are the same as the units οf length.

As we can say, the surrοundings are οne-dimensiοnal. As a result, yοu can measure in meters, kilοmeters, millimeters, etc.

Inches, feet, yards, and miles are οther glοbally recοgnized units οf circumference measurement.

Accοrding tο οur questiοn-

The map's new dimensiοns, which are 3 inches by 8 inches when it is enlarged tο 8 inches lοng, are as fοllοws:

P'=2(3 in + 2 in ) + 2 in ) = 6 in + 16 in = 22 in

and the lοcatiοn is

A' is 3 x 8 x 24 inches.

The enlarged map's area is 24 square inches, and its perimeter is 22 inches.

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For a loan of $7500 over 5 years at 6.5% fixed APR, the total amount paid is $8673. The percentage of the total amount paid that goes towards the principal is 84.32% and the percentage that goes towards interest is 13.68%.

To calculate the percentage of the total amount paid that goes towards the principal and interest, we need to first calculate the total amount to be paid over the 5 year period. We can use the formula for the present value of an annuity to calculate this:

[tex]PV = PMT \times \frac{(1 - (1 + r/n)^{(-nt)})}{(r/n)}[/tex]

Where,

PV is the present value (loan amount),

PMT is the monthly payment,

r is the annual interest rate (6.5%),

n is the number of times interest is compounded per year (12 for monthly), and

t is the number of years (5).

First, we need to calculate the monthly interest rate:

r/monthly = r/12

                = 0.065/12

                = 0.00541667

Now we can calculate the monthly payment:

[tex]PMT = PV \times \frac{(r/n)}{(1 - (1 + r/n)^{(-nt)})}[/tex]

         [tex]= \frac{7500 \times (0.00541667)}{(1 - (1 + 0.00541667)^{(-12 \times 5)})}[/tex]

         = $144.55

So the total amount paid over the 5 year period is:

Total paid = PMT x n x t

                 = $144.55 x 12 x 5

                 = $8,673.00

To find the percentage of the total amount paid that goes towards the principal and interest, we can use the following formula:

Principal % = (Principal / Total paid) x 100%

Interest % = (Interest / Total paid) x 100%

The interest for each payment can be calculated by subtracting the principal from the payment, and the principal can be calculated by subtracting the interest from the original loan amount. Since the interest and principal change with each payment, we need to calculate them for each individual payment and then sum them up over the 5 year period.

We can use a loan amortization schedule to calculate the principal and interest for each payment. Here is the amortization schedule for this loan:

Year Payment Principal Interest Balance

The total interest paid over the 5 year period is the sum of the interest for each payment, which is $1,187.81. The total principal paid over the 5 year period is the loan amount minus the final balance, which is $7,312.19.

So the percentage of the total amount paid that goes towards the principal is:

Principal % = (7,312.19 / 8,673.00) x 100%

                  = 84.32%

And the percentage of the total amount paid that goes towards interest is:

Interest % = (1,187.81 / 8,673.00) x 100%

                = 13.68%

Therefore, 84.32% of the total amount paid is for the principal, and 13.68% is for interest.

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The transformation sequence to go from g(x) to f(x) is horizontal compression by a factor of 2, horizontal shift to the left by 3 units, and vertical stretch by a factor of 1.

Explain about function g(x) ?
The function g(x) is a mathematical rule that takes an input value x and produces an output value according to the rule specified. In this case, g(x) = 1/x, which means that the output value is the reciprocal of the input value. For example, if x = 2, then g(x) = 1/2, which is equal to 0.5.

The function g(x) is defined for all real numbers except for x = 0, since division by zero is undefined. The graph of the function g(x) is a curve that approaches zero as x approaches positive or negative infinity, and it has a vertical asymptote at x = 0.

According to the question:

Starting with the function g(x) = 1/x, we can apply the following transformations to obtain the function f(x) = 1/(2x + 3):

Horizontal compression by a factor of 2: Replace x in g(x) with 2x to obtain g(2x) = 1/(2x).

Horizontal shift to the left by 3 units: Replace 2x in g(2x) with 2(x+3) to obtain g(2(x+3)) = 1/(2(x+3)).

Vertical stretch by a factor of 1: Multiply g(2(x+3)) by 1 to obtain f(x) = 1/(2x+3).

Therefore, the transformation sequence to go from g(x) to f(x) is horizontal compression by a factor of 2, horizontal shift to the left by 3 units, and vertical stretch by a factor of 1.

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The value for the limits for the function f(x) is -

x → -1, then f(x) = -1

x → 0, then f(x) = -2

x → 1, then f(x) = -1

x → 2, then f(x) = DNE

x → ∞, then f(x) = ∞

What is limit?

A limit in mathematics is a point at which a function approaches the outcome for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.

The piecewise graph of a function f(x) is given.

In the graph it can be seen that when x approaches -1, the value of f(x) is also -1.

In the graph it can be seen that when x approaches 0, the value of f(x) is also -2.

In the graph it can be seen that when x approaches 1, the value of f(x) is also -1.

In the graph it can be seen that when x approaches 2, then the limit does not exist.

In the graph it can be seen that when x approaches ∞, the value of f(x) is also infinite.

Therefore, the limit values are obtained for the function f(x).

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Answer:

-2x + 3

Step-by-step explanation:

Like terms are categorized by the variables (letters) beside them.

It is a pretty simple process. To make it easier, first group the "like terms" together:

( 3x - 5x ) + ( + 7 - 4 )

Then solve the parenthesis:

( -2x ) + ( 3 )

That is it!

The probability of the following using only the z-table (Express your answers in percentage with 2 decimal places that is the probability of -2.8 ≤ z ≤ 1.54 is 93.56%.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event (it will never happen), and 1 represents a certain event (it will always happen). In probability theory, an event is a set of outcomes or results. For example, if we flip a fair coin, the event of getting heads is the set {H}, and the event of getting tails is the set {T}. The probability of each event is given by the ratio of the number of outcomes in the event to the total number of possible outcomes.

Here,

To find the probability P(-2.8 ≤ z ≤ 1.54), we need to use the standard normal distribution table (also known as the z-table). First, we can find the area to the left of z = -2.8 by looking up -2.8 in the z-table, which gives a value of 0.0026. This represents the area to the left of -2.8.

Next, we can find the area to the left of z = 1.54 by looking up 1.54 in the z-table, which gives a value of 0.9382. This represents the area to the left of 1.54.

To find the area between -2.8 and 1.54, we need to subtract the area to the left of -2.8 from the area to the left of 1.54:

P(-2.8 ≤ z ≤ 1.54) = 0.9382 - 0.0026 = 0.9356

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Answer:

Your answer is "A".

Step-by-step explanation:

Basically, your question is asking for the side lengths after the transformation. However, the transformation it would undergo does not change the size of the rectangle, it only changes its position on the graph. This means, all you need to do is count the number of squares from one point to another.

From point A to B, there are 3 squares. From point B to C, there are 5 squares. Therefore, your answer is A.

Answer: 18.8cm

Step-by-step explanation:

From the given side pairs, DA ≅  ES is the pair which is not necessarily congruent.

When two sides in geometry are the same length, they are said to be congruent. For instance, a square has four sides that are congruent because it has four equal-length sides.

Given that, ΔDAL ≅ ΔEKS

Now we need to find the pair which is not necessarily congruent:

Option A: AL ≅  KS is congruent. Since given that the angles are equal.

Option B: DL ≅  ES is congruent. They are ends of the shapes.

Option C: DA ≅  EK is congruent. Since they are following the congruence laws.

From the list given,

Option D: DA ≅  ES  is not necessarily congruent. So option D is the correct answer for the given sum.

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Answer:

m<6 = 119

Step-by-step explanation:

m<4 + m<6 = 180 (Linear Pair)

61 + m<6 = 180

=> m<6 = 180 - 61

=> m<6 = 119

It is false that the more beautiful you are, the more problems you will face.

Beauty is a human concept that refers to the attraction or sensory pleasure that an individual or object causes to a person. Generally, beauty is associated with physical beauty, that is to say that an element is "pretty" to see it. However, this concept has developed different perspectives that refer to different aspects of an individual as her personality.

In accordance with the above, it cannot be inferred that beauty is a cause of problems because this concept is purely subjective, so we cannot generalize beauty in society and therefore we could not conclude that beauty causes problems for people.

Note: This question is incomplete. Here is the complete information:

True or False

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The fractiοn οf the plants had yellοw blοssοms with dark green leaves is 1/6

A fractiοn is divided intο additiοnal equal pieces when it is divided intο fractiοns. Fοr instance, if yοu had three-fοurths οf a pizza remaining and divided each slice intο twο pieces, yοu wοuld have received six slices, which wοuld be equivalent tο six-eighths οf the entire pizza.

The fractiοn οf the plants had yellοw blοssοms with dark green leaves

= 2/4 the οf 1/3

= 2/4 * 1/3

=1/2 *1/3

=1/6

The fractiοn οf the plants had yellοw blοssοms with dark green leaves is 1/6

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Answer:

There are 9 students in each group for a total of 9 groups.

Step-by-step explanation:

divide 72 and 9 and that gives you how many students need to be in each group!

Answer:

x = 10

Step-by-step explanation:

if BC and DE are parallel then the sides of the triangle are divided proportionally, that is

[tex]\frac{CE}{AE}[/tex] = [tex]\frac{BD}{AD}[/tex] ( substitute values )

[tex]\frac{x-2}{16}[/tex] = [tex]\frac{x-3}{14}[/tex] ( cross- multiply )

16(x - 3) = 14(x - 2) ← distribute parenthesis

16x - 48 = 14x - 28 ( subtract 14x from both sides )

2x - 48 = - 28 ( add 48 to both sides )

2x = 20 ( divide both sides by 2 )

x = 10

then for BC and DE to be parallel, x has the value x = 10

10 minutes after 10 past 4 would be 24 minutes past 4.

To calculate this, you can start with the given time of 10 past 4, which is equivalent to 4:10.

Then, adding 10 minutes gives 4:20. Finally, adding another 4 minutes (since 10 + 4 = 14, which is equivalent to the number of minutes in a quarter of an hour) gives the final answer of 4:24.

When we add 10 minutes to 4:10, we're essentially starting with a time interval of 10 minutes and adding it to another time interval of 10 minutes (which is the time between 4:00 and 4:10). The total time interval is then 20 minutes, which we can think of as two sets of 10 minutes.

So we add the first set of 10 minutes to 4:10 to get 4:20. Then we add the second set of 10 minutes to 4:20, giving us 4:30. If the problem had asked for the time 20 minutes after 10 past 4, we would have stopped here and given the answer 4:30.

But since the problem asks for the time 10 minutes after 10 past 4 specifically, we need to subtract one set of 10 minutes from the total interval of 20 minutes. We've already added one set of 10 minutes, so we just need to add the remaining 10 minutes to the time we have so far (4:20), giving us the final answer of 4:30.

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The amount of loan that Molly needs after reducing the down payment and cash allowance is $38190.

What is a loan?

In a loan, a certain quantity of money is given to another person in exchange for the value or main amount being repaid at a later date. In many circumstances, the lender increases the principal value by adding interest or finance charges, which the borrower must pay in addition to the principal sum.

Loans may be made for a predetermined, one-time sum or as an open-ended line of credit with a cap of up to a certain amount. In addition to secured and unsecured loans, there are also commercial and personal lending options.

Given,

The amount of cash Molly saved for the purchase,

Down payment = $4500

The dealer's cash allowance = $4300

It is said that the dealer's cash allowance will come straight from her total.

Then the amount of loan she needs = 46990 - 4500 - 4300

                                                    = $38190

Therefore the amount of loan that Molly needs after reducing the down payment and cash allowance is $38190.

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Answer:

Step-by-step explanation:

Green beans!!!!!!!

The measure of angle mLNKL is 315 degrees.

We can see that angle JMK and angle LNK are vertical angles and therefore congruent. Also, angle JMK and angle NIK are corresponding angles and therefore congruent.

So we have:

mJMK = mNIK = 28 + 17 = 45

Also, we know that the sum of the angles in triangle JMK is 180 degrees. So, we have:

mJMK + mJM + mMK = 180

45 + (10x + 9) + mMK = 180

10x + mMK = 126

Similarly, we know that the sum of the angles in triangle NIK is 180 degrees. So, we have:

mNIK + mNKI + mNI = 180

45 + (16x + 19) + mNI = 180

16x + mNI = 116

Since angle LNK is supplementary to angles JMK and NIK, we have:

mLNK = 180 - mJMK - mNIK

mLNK = 180 - 45 - 45

mLNK = 90

Therefore, mLNKL is the sum of the angles MKL and NKL.

mMKL = 180 - mJMK

mMKL = 180 - 45

mMKL = 135

mNKL = mMKL + mJMK

mNKL = 135 + 45

mNKL = 180

Therefore, mLNKL = mMKL + mNKL = 135 + 180 = 315 degrees.

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the upper estimate for the total amount of water that leaked out using five rectangles is 90.8 gallons (rounded to one decimal place).

Approximating the length of curves and other approximations, as well as the area of functions or lines on a graph, is a highly popular application.

from the question:

The range [0, 10] will be split into five equal-width subranges using five rectangles:

Δt = (10 - 0) / 5 = 2

Upper estimate = Δt [r(0) + r(2) + r(4) + r(6) + r(8)]

Upper estimate = 2 [12.0 + 10.6 + 8.8 + 8.0 + 6.0]

Upper estimate = 2 [45.4]

Upper estimate = 90.8

Thus, 90.8 gallons is the highest estimate for the total volume of water that flowed out utilizing five rectangles (rounded to one decimal place).

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The most likely number of people who visited the library zero times last summer based on Amy's survey is 632 people

To find the number of people who were most likely not to visit the library, you need to find the percentage of people who did not visit the library from Amy's survey.

Percentage of males:                                           Percentage of females:

= 14 / 25                                                                 = 17 / 25

= 56%                                                                     = 68%

From the population of 1,000, the males and females who went to the library zero times would be:

Number of males:                                           Percentage of females:

= 56 % x 400                                                  = 68 % x 600

= 224 males                                                    = 408 females

Total number of people :

= 224 + 408

= 632 people

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The solution of the given system of linear equation is (4,2) .

What is substitution method ?

The substitution method is a method of solving a system of two equations with two variables by solving one of the equations for one variable and substituting that expression into the other equation to solve for the other variable. This method can be used to solve systems of linear equations, where each equation represents a line in a two-dimensional coordinate system. The solution to the system represents the point where the two lines intersect.

Finding the solution using substitution method :

We can solve for one variable in terms of the other in one equation and substitute it into the other equation.

For example, we can solve for y in terms of x in the first equation:

[tex]y = -x + 6[/tex]

Then substitute this expression for y into the second equation:

[tex]({3}/{4x} )- 1 = y[/tex]

Substitute [tex]y = -x + 6:[/tex]

[tex](3/4x) - 1 = -x + 6[/tex]

Solve for x:

[tex](3/4x )+ x = 7[/tex]

[tex]x = 4[/tex]

Substitute [tex]x = 4[/tex] into either equation to find y:

[tex]y = -x + 6 = -4 + 6 = 2[/tex]

Therefore, the solution is (4, 2).

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We can say that the tree's height increased by 12.5% over the course of the six-week experiment.

To calculate the percent increase in the tree's height, we need to find the difference between its new height and its old height, and then express that difference as a percentage of the old height.

We start with the formula:

percent increase = (new value - old value) / old value * 100%

In this case, the old value is the height of the tree at the beginning of the experiment, which is 32 inches. The new value is the height of the tree six weeks later, which is 36 inches.

So, plugging in those values, we get:

percent increase = (36 - 32) / 32 * 100%

Simplifying this expression gives us:

percent increase = 4 / 32 * 100%

And when we evaluate that expression, we get:

percent increase = 12.5%

Therefore, the percent increase in the tree's height is 12.5%.

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