Given a polynomial function f(x) = 2x2 – 3x + 5 and an exponential function g(x) = 2x – 5, what key features do f(x) and g(x) have in common?

Both f(x) and g(x) have the same domain of (∞, -∞).
Both f(x) and g(x) have the same range of [0, -∞).
Both f(x) and g(x) have the same x-intercept of (2, 0).
Both f(x) and g(x) increase over the interval of [-4 , ∞).

Step-by-step explanation:

4x + 3y = -10

9x + 2y = 6

we have 2 general options :

substitution or elimination.

in substitution we use one equation to express one variable by the other, then use that equality in the second equation and solve for the remaining variable.

like in our case

4x = -10 - 3y

x = (-10 - 3y)/4

in elimination we multiply one or both equations by some factors and then subtract one equation from the other resulting in one equation in one remaining variable.

this is the better method, if substitution leads to more complex fractions.

like in our case.

so, I would multiply equation 1 by 2 and equation 2 by 3, and then subtract e.g. equation 2 from 1 (we could also do it the other direction, it gives the same solutions) :

8x + 6y = -20

- 27x + 6y = 18

------------------------

-19x 0 = -38

-19x = -38

19x = 38

x = 2

and then we pick any of the original equations to get the other variable :

e.g.

4x + 3y = -10

4×2 + 3y = -10

8 + 3y = -10

3y = -18

y = -6

The missing reasons that completes the proof are:

2. Definition of bisection

4. Reflexive property

5. SAS

6. CPCTC

A proof usually contains the statements on one column, and the reason that justifies each of the statement on another column.

To prove that sides XY is congruent to side ZY, the following are the statements and reasons that completes the proof:

Statement                                              Reason                                        

1. Line YW ⊥ line XZ; YW bisects XZ.  1. Given

2. Side XW ≅ side ZW                         2. Definition of bisection

3. Angles YWX and YWZ,                    3. Definition of perpendicular

so ∠YWX ≅ ∠YWZ              

4. Side YW ≅ Side YW                          4. Reflexive property

5. Triangles WXY and WZY are            5. SAS postulate

Congruent                                                      

6. 6. XY ≅ ZY                                          6. CPCTC

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Answer:

v = 9√2 ; u = 18

Step-by-step explanation:

angle 45 degrees = the legs are congruent

v = 9√2

u = [tex]\sqrt{(9\sqrt{2} )^2+{(9\sqrt{2})^2}} = \sqrt{2(9\sqrt{2)}^2} = \sqrt{2 (81 *2) }= \sqrt{4 * 81}= 2 * 9 = 18[/tex]

Answer:

Step-by-step explanation:

a triangle with an angle of 90° and an angle of 45° is an isosceles right triangle, so V equals 9√2.

to find u we use the Pythagorean theorem

u = √(9√2)²+(9√2)²

u = 9 + 9

u = 18

Answer:

i believe it's 136.666666667

Step-by-step explanation:

The remainder is 8 in the given synthetic division problem. which is the correct answer would be option (B).

In mathematics, divides left-hand operands into right-hand operands in the division operation.

In the given synthetic division, the coefficients of terms are 4,6, and -2.

Fill in the first coefficient as it appears on the bottom line.

Now multiply 1 by 4 and write the result (i.e., 4) underneath the second coefficient in the center line.

Now multiply 6 by 4 and write the result (i.e., 10) in the bottom row.

Now multiply 1 by 10 and write the result (i.e., 10) below the third coefficient in the center line.

Now add -2 with 10 and write the result (i.e., 8) in the bottom row.

The first two terms now indicate the polynomial coefficient, while the last term shows the remainder.

Therefore, the remainder is 8 in the given synthetic division problem.

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Based on the loan amount and the number of years, the monthly payment, total cost of the car, and amount of interest to be paid are as follows:

Find the loan amount first:

= Car expense x ( 1 - down payment percent)

= 14, 800 x ( 1 - 12%)

= $13024

the monthly rate and the total number of periods, then:

Daily rate calculation:

= Annual Rate / Twelve-Month Period

= 4.5% / 12

= 0.375%

Counting periods:

= Years multiplied by Months per year

6 years times 12

72 months

These enable the following formula to determine the monthly payment:

= Loan Amount / 72-period Annuity Present Value Interest Factor of 0.375%

13024 / 62.995976235992

= $206.74

Total amount repaid on the auto loan:

= Amount Due Each Month x The Number of Months

= 206. 74 x 72

= $14, 885. 52

Accordingly, the total amount of interest paid was:

= Amount borrowed - Amount paid toward the car's cost

= 14, 885.52 - 13, 024

= $1, 861.52

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Answer: its gonna be D

Step-by-step explanation:

its just zeros

Answer:

(-1,4)

Step-by-step explanation:

to find out we just fill in the values to see if it’s true

(x,f(x))

4=-1^2+3

4=1+3

4=4

True

-4=-1^2+3

-4=1+3

-4=4

Not true

-4=1^2+3

-4=1+3

-4=4

Not true

-1=-4^2+3

-1=16+3

-1=19

Not true

Hopes this helps please mark brainliest

Answer:

[tex]9-3\sqrt{3} i.[/tex]

Step-by-step explanation:

[tex]1. \ cos(-30)=\frac{ \sqrt{3}}{2}; \ sin(-30)=-0.5;[/tex]

[tex]2. \sqrt{108} (cos(-30)+isin(-30))=\frac{\sqrt{108} \sqrt{3}}{2}-i*\sqrt{108}*0.5=9-3\sqrt{3} i.[/tex]

The mistake Matt made in calculating the distance the mouse travelled each hour was that Matt should have divided the numerator but not the denominator of 3/24 by 3

The distance the mouse travelled per hour is calculated by comparison

If the mouse covers 3/24 miles in in 3 hours then in an hour the mouse will cover

3/24 = 3

? = 1

cross multiplying

3 * ? = 1 * 3/24

? = 3/24 ÷ 3

? = 3/24 * 1/3

? = 1/24

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The Center of the circle is (5, -17) and radius of the circle is 29 units.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We have given circle in the x, y-plane has the equation;

x² + y² -10x + 34y - 527 = 0

Now we will convert this equation to the standard form of the circle as;

x² -10x + y² + 34y = 527

[x² - 2(5)x] + [y² + 2(17)x] =527

[x² - 2(5)x + 5²] + [y² + 2(17)y + 17²] = 5² + 17² +527

(x - 5)² + (y + 17)² = 25 + 289 +527

(x - 5)² + (y + 17)² = 841

(x - 5)² + (y + 17)² = 29²

By comparing this equation with the standard equation of the circle →

That is;  (x - h)² + (y - k)² = r²

The Center of the circle is (5, -17) and radius of the circle is 29 units.

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Using the dimensions of the figure, Thomas will have enough money to paint the surface area.

The dimensions of a two-dimensional figure are its lengths and widths.

The product of the length and width results in the surface area, which is stated in square units.

Since Thomas has $1,300, and the squared surface of the figure is equal to 260 square units, when $5 is multiplied into 260, the product is $1,300.

This amount is equal to the money available to Thomas for the painting.

If the dimensions produced a surface area of more or less than 260 square units, we can calculate Thomas' ability to complete the painting based on the information.

The length of the figure is given as 20 units.

The width of the figure is given as 13 units.

The surface area of the figure = 260 square units

The cost of paint per square unit = $5

The total cost for painting the figure = $1,300 ($5 x 260)

The amount available to Thomas for the painting = $1,300

Difference between the total cost and the available amount = $0.

Thus, we can assert that, given the dimensions of the figure, Thomas can complete the painting with the available funds.

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Length of the figure = 20 units

Width of the figure = 13 units

Answer:

The weight of oranges growing in an orchard is normally distributed with a mean weight of 6.5 oz. and a standard deviation of 1 oz. Using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard

Step-by-step explanation:

bran leist ple

Answer:

1954

Step-by-step explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ²:

[tex]\boxed{X \sim \textsf{N}(\mu,\sigma^2)}[/tex]

Given:

First find the probability that the weight of an orange is less than 5 oz.

[tex]\text{If \;$X \sim \textsf{N}(4,0.5^2)$,\;\;find\;\;P$(X < 5)$}.[/tex]

Method 1

Using a calculator:

[tex]\implies \text{P}(X < 5)=0.977249868[/tex]

Method 2

Converting to the z-distribution.

[tex]\boxed{\text{If\;\;$X \sim$N$(\mu,\sigma^2)$\;\;then\;\;$\dfrac{X-\mu}{\sigma}=Z$, \quad where $Z \sim$N$(0,1)$}}[/tex]

[tex]x=5 \implies Z=\dfrac{5-4}{0.5}=2[/tex]

Using the z-tables for the probability:

[tex]\implies \text{P}(Z < 2)=0.9772[/tex]

To find the expected number of oranges that will weigh less than 5 oz from a batch of 2000, multiply the total number of oranges by the probability calculated:

[tex]\begin{aligned}2000 \times \text{P}(X < 5)&=2000 \times 0.977249868\\&=1954.499736\\&=1954\end{aligned}[/tex]

Therefore, 1954 oranges would be expected to weigh less than 5 oz.                                

Hi, that would be option 3 if I am correct.

Hope this helps.

Answer:

0.8461

To find the proportion of cherry tomatoes that have a diameter greater than 25 mm, we need to determine the proportion of the distribution that falls above this value. We can do this by converting the diameter of 25 mm to a z-score using the formula:

z-score = (value - mean) / standard deviation

For a diameter of 25 mm, the z-score is (3 - 22) / 2.5 = -2.8.

We can then use a z-table to find the proportion of the distribution that falls above this value. The z-table gives the area under the standard Normal curve to the left of a given z-score. To find the proportion of the distribution above the diameter of 25 mm, we need to find the area to the right of -2.8. From the z-table, we find that the area to the right of -2.8 is 0.8461. Therefore, approximately 84.61% of cherry tomatoes produced by the farm have a diameter greater than 25 mm.

The fraction of magazines that were delivered to families who were at home is 0.4 if total number of families are 25 out of which 10 were at home and rest are away.

Total number of families = 25

Families at home = 10

So the ratio of the required families

= Families at home/total number of families

= 10/25

= 2/5

To convert the fraction into decimal form, we have to divide and we get

= 0.4

Hence, the number of families in decimal to which magazines got delivered are 0.4

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The value of the unknown t, by susbtituting the values into the formula is 2

Simple interest refers to the straightforward crediting of cash flows associated with some investment or deposit.

To calculate the unknown variable in the equation, we do substitution into the formula below.

Formula:

Given:

Substitute these values into equation 1

Hence, the value of the unknown is 2.

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Answer:

(a)  x = 2

(b)  7 + 5√2

Step-by-step explanation:

Given terms of a geometric sequence:

The common ratio of a geometric sequence is found by dividing consecutive terms.  Therefore:

[tex]\implies \dfrac{a_3}{a_2}=\dfrac{a_2}{a_1}[/tex]

Substitute the given terms into the equation and solve for x:

[tex]\implies \dfrac{\sqrt{x}+1}{1}=\dfrac{1}{\sqrt{x}-1}[/tex]

[tex]\implies (\sqrt{x}-1)(\sqrt{x}+1)=1[/tex]

[tex]\implies x+\sqrt{x}-\sqrt{x}-1=1[/tex]

[tex]\implies x-1=1[/tex]

[tex]\implies x=2[/tex]

General form of a geometric sequence:

[tex]\boxed{a_n=ar^{n-1}}[/tex]

where:

Substitute the found value of x into the expressions for the given terms:

Find the common ratio:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{\sqrt{2}+1}{1}=\sqrt{2}+1[/tex]

Therefore, the equation for the nth term is:

[tex]\boxed{a_n=(\sqrt{2}-1)(\sqrt{2}+1)^{n-1}}}[/tex]

To find the 5th term, substitute n = 5 into the equation:

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{5-1}[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^{4}[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(\sqrt{2}+1)^2(\sqrt{2}+1)^2[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(3+2\sqrt{2})(3+2\sqrt{2})[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(9+12\sqrt{12}+8)[/tex]

[tex]\implies a_5=(\sqrt{2}-1)(17+12\sqrt{2})[/tex]

[tex]\implies a_5=17\sqrt{2}+24-17-12\sqrt{2}[/tex]

[tex]\implies a_5=7+5\sqrt{2}[/tex]

Answer:

1) 5

2) 3
3) 2
4) 10
5) 7
6) 36
7) 110
8) 100
9) 40
10) 8
11) 30
12) 60
13) 12
14) 63
15) 77
16) 5

Step-by-step explanation:

Answer:

1) x=5; 2) x=3; 3) x=2; 4) x=10; 5) x=7; 6) x=36; 7) x=110; 8) x=100; 9) x=40; 10) x=8; 11) x=30; 12) x=12; 13) x=12; 14) x=63; 15) x=77; 16) x=5

Step-by-step explanation:

I can't explain every problem, but I will do the first three.

1) We divide the sides by 4 to get x=5

2)We divide by 3 to get x=3

3)Divide by 4 to get x=2

Answer:  80.44 meters/seconds/ to 179.9391553 miles/hours

Step-by-step explanation:  Example:  80.44X2.2369362921=

1 m/s = 2.3469362921 that gives you the above answer.

Answer: Rational

Step-by-step explanation:

The function is not continuous, so the function cannot be exponential, logarithmic, or exponential.

This means the only possibility is that the function is rational.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes when a pair of dice is rolled is given by:

6² = 36.

As each throw has six outcomes.

The outcomes with a sum of 5 are given as follows:

(1,4), (2,3), (3,2), (4,1).

Hence 4 outcomes, and the probability that player A wins is of:

p = 4/36 = 1/9.

The outcomes with a sum of 4 are given as follows:

(1,3), (2,2), (3,1).

Hence the probability that B wins is given by:

p = 3/36 = 1/12.

Then the probability that a player wins on each trial is given by:

p = 4/36 + 3/36 = 7/36.

Then the expected number of rolls is given as follows:

E(X) = 1/(7/36) = 36/7 = 5.1 rolls.

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The number of permutation and number of combination of 10 objects taken 4 at a time are

10P₄ = 5040

10C₄ = 210

The permutation of 10 objects taken 4 at a time is given by the formula

= 10! / (10 - 4)!

= 10! / 6!

= 10 * 9 * 8 * 7 * 6! / 6!

= 10 * 9 * 8 *7

= 5040

The combination of 10 objects taken 4 at a time is given by the formula

= 10! / (4!(10 - 4)!)

= 10! / (4! * 6!)

= 10 * 9 * 8 * 7 * 6! / (6! * 4!)

= 10 * 9 * 8 *7 / 4!

= 210

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Answer: log(10)

Step-by-step explanation:

Based on the laws of logarithm attached below, the expression can be rewritten as:

[tex]log(5)+log(18)-log(9)=log(5*18)-log(9)\\\\=log(90)-log(9)=log(\frac{90}{9})=log(10)[/tex]

The area of the circle in 2 decimal place is 394.13 cm².

Area of a circle is the region occupied by the circle in a two-dimensional plane. The area of a circle is π multiplied by the square of the radius.

Therefore,

area of a circle = πr²

where

r = radius

Therefore,

area of a circle = πr²

r = 11.2 cm

area of a circle = 3.142 × 11.2²

area of a circle = 3.142 × 125.44

area of a circle = 394.13248

area of a circle = 394.13 cm²

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The Venn diagram of visit to Paris is completed and attached

The probability is 22/30

The Venn diagram is completed using the principle of inclusion exclusive

let x be the number that visited both Eiffel tower and Notre-Dame Cathedral

The calculation is done by counting as the universal set is equal to the numbers of the people

30 = 13 - x + x + 16 - x + 7

30 = 13 + 16 + 7 - x

30 - 37 = -x

-7 = -x

x = 7

ET only = 13 - 7 = 6

NDC only = 16 - 7 = 9

The probability

= (6 + 9 + 7) / 30

= 22/30

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The equation of the line that passes through (-1, -6) and (5,0). is y = x - 5.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's find the equation of the line that passes through  (-1, -6) and (5,0).

m = 0 + 6 / 5 + 1

m = 6 / 6

m = 1

Therefore, let's find the y-intercept using (5, 0)

y = x + b

0 = 5 + b

b = -5

Therefore, the equation is y = x - 5

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The required greatest rate of change is at x = 7 to x = 10. Option A is correct.

Given that,
The function is graphed. On which interval of a is the average rate of change of the function the greatest is to be determined.

Rate of change is defined as the change in value with rest to the time is called rate of change.

Here,
The average rate for,
x = 7 tot x = 10
Rate = 56 - 8 / 10 -7
Rate = 16
While the other pair has an average rate of 4, 4.46

Thus, the required greatest rate of change is at x = 7 to x = 10. Option A is correct.

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Answer:

25 advance tickets and 20 same day

Step-by-step explanation:

Answer: Advanced tickets:25
Same Day tickets: 20

Differentition of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

[tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex]

We have to differentiate with respect to x.

y'=xy'+yx'

[tex]x=log_{2}x^{3}[/tex]

[tex]y=5x^{4}+2[/tex]

[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x^{3}} .3x^{2}[/tex]

[tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

Hence, differentiation of [tex]y=log_{2}x^{3}.(5x^{4}+2)[/tex] is [tex]y'=log_{2}x^{3}(20x^{3} )+(5x^{4}+2)\frac{1}{x}[/tex]

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