Jacob stated that he solved the equation 2x + 3 = 5 using the addition and multiplication property of equality. Which statement is true

Using the same-side interior angles theorem,

\(8x+30+6x+24=180 \\ \\ 14x+54=180 \\ \\ 14x=126 \\ \\ \boxed{x=9}\)

Using vertical angles,

\(6(9)+24=10y+2 \\ \\ 78=10y+2 \\ \\ 10y=76 \\ \\ \boxed{y=7.6}\)

Answer:

the collection center should be located at Collection Option (D).

Step-by-step explanation:

To determine the best location for the collection center, you can calculate the average coordinates of the four collection points and choose the location that is closest to this average.

To calculate the average coordinates, you can add the coordinates of each collection point and divide the result by the number of collection points. For example, to find the average X coordinate, you can add the X coordinates of all four collection points and divide by 4. Similarly, to find the average Y coordinate, you can add the Y coordinates of all four collection points and divide by 4.

Using this method, the average coordinates for the four collection points are (5.75,3.25). The collection point that is closest to these average coordinates is Collection Point D, which is located at (7,3). Therefore, the collection center should be located at Collection Point D.

I hope this helps to clarify the process for determining the best location for the collection center. Please let me know if you have any other questions.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 7.2

For the alternative hypothesis,

H1: µ ≠ 7.2

This is a two tailed test.

Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7.2

x = 7.3

σ = 0.8

n = 250

z = (7.3 - 7.2)/(0.8/√250) = 1.976

Test statistic is 1.976

Given:

Chris has a collection of dimes and quarters worth $4.25.

To number of coins = 22

To find:

The number of quarters.

Solution:

Let x be the number of dimes and y be the number of quarters.

Total coins : \(x+y=22\)          ...(i)

we know that, 1 dime = $0.10 and 1 quarter = $0.25.

Total value : \(0.10x+0.25y=4.25\)      ...(ii)

Multiply equation (i) by 0.10 and subtract the result form (ii).

\(0.10x+0.25y-0.10(x+y)=4.25-0.10(22)\)

\(0.10x+0.25y-0.10x-0.10y=4.25-2.20\)

\(0.15y=2.05\)

Divide both sides by 0.15.

\(y=\dfrac{2.05}{0.15}\)

\(y=13.6667\)

Number of quarter cannot be a decimal value.

\(y\approx 17\)

Therefore, the number of quarter is about 17.

Answer:

x = 0.21

Step-by-step explanation:

\(\frac{.15}{100} = \frac{x}{140}\)

.15(140) = 100x

21 = 100x

x = 0.21

The number of milligrams of zinc provided by 140 grams of banana will be 0.21 milligrams. Then the correct option is B.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

According to the department of agriculture consuming 100 grams of banana provides 0.15 milligrams of zinc.

Then the number of milligrams of zinc provided by 140 grams of banana will be given by the ratio.

Let x be the amount of zinc. Then the equation is given as,

x / 140 = 0.15 / 100

x / 1.4 = 0.15

x = 0.21 milligrams

The number of milligrams of zinc provided by 140 grams of banana will be 0.21 milligrams. Then the correct option is B.

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Answer:

what do you want me to do actuallt the pic is Unclear?

Answer:

-9 -15 9 i think

Step-by-step explanation:

Answer:

-15,-9,9

Step-by-step explanation:

Ordering that from least to greatest would be -15,-9,9 but unfortunetly i cant answer the second half. Hope this helps :).

The function g(x) = x² + 4x has a: A. minimum.

The minimum value occur at x = -2.

The function's minimum value is -4.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function g(x) = x² + 4x, we have:

a = 1, b = 4, and c = 0

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(4)/2(1)

Axis of symmetry, Xmax = -2

Next, we would determine vertex as follows;

g(x) = x² + 4x

g(-2) = -(-2)² + 4(-2)

g(-2) = -4.

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Rounding to the nearest hundredth, the probability that the player gets the bonus on the 4th coin collected is approximately 0.07.

To find the probability that the player gets the bonus on the 4th coin collected, we can analyze the situation.

The probability of getting the bonus on any given coin collected is 1/10, since there is a 1 in 10 chance that the last digit of the milliseconds in the game's timer equals 1.

Since the events of collecting each coin are independent, we can use the probability of getting the bonus on a single coin to calculate the probability of not getting the bonus on the first three coins and then getting it on the fourth coin.

The probability of not getting the bonus on a coin is 9/10, as there are 9 out of 10 possible last digits that do not satisfy the condition.

So, the probability of not getting the bonus on the first three coins is (9/10)^3, as each event is independent.

Therefore, the probability of getting the bonus on the 4th coin is:

P(C=4) = (9/10)^3 * (1/10) = 729/10000 ≈ 0.0729.

Hence, rounding to the nearest hundredth, the probability that the player gets the bonus on the 4th coin collected is approximately 0.07.

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Answer:

21.2, 25.2, and 12.6 meters

Step-by-step explanation:

If this was a rectangle, the perimeter would be 3.6 + 3.6 + 7 + 7 = 21.2 m. The area of this figure would be 3.6 × 7 = 25.2 m. If this was a triangle, then the area of the figure would be 12.6 m.

Answer:

It would be three coconuts hope this helped

Step-by-step explanation:

Answer:

a = -3/2 = -1.5

Step-by-step explanation:

(1+ax) (2+3x)³

Formula

(a+b)^3=a^3+3a^2b+3ab^2+b^3

(1 + ax) [ 2^3 + 3*2^2*3x + 3*2*(3x)^2 + (3x)^3]

(1 + ax) [ 8 + 12*3x + 6*9x^2 + 27x^3]

8 + 12*3x + 6*9x^2 + 27x^3 + 8ax + 36ax^2 + 54ax^3 + 27ax^4

coefficient of x^2 is zero

54x^2 + 36ax^2

54 + 36a = 0

36a = -54

a = -3/2

Answer:

The rate of change of Function A is less than the rate of change of function B.

Other than that, everything else you put is correct.

Step-by-step explanation:

None.

Answer:

Option A, B and D are correct options.

Step-by-step explanation:

First we will find rate of change of function A and function B

Rate of Change of Function A

The formula used to calculate rate of change is: \(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\)

We have x_1=1, y_1=5, x_2=2, y_2=7

Putting values in formula and finding rate of change

\(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{7-5}{2-1}\\Rate\:of\:Change=\frac{2}{1}\\Rate\:of\:Change=2\)

So, Rate of change of Function A = 2

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the function, we can write the equation: y=2x+3

Now, put x =0

y=2(0)+3

y=3

So, when x =0, y=3

So, y-intercept is 3 for function A.

Rate of Change of Function A

The formula used to calculate rate of change is: \(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\)

We have x_1=1, y_1=1, x_2=2, y_2=4

Putting values in formula and finding rate of change

\(Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{4-1}{2-1}\\Rate\:of\:Change=\frac{3}{1}\\Rate\:of\:Change=3\)

So, Rate of change of Function B = 3

Now, finding y-intercept.

y-intercept is found by putting x =0

Looking at the graph, when x=0, y is -2

So, y-intercept is -2 for function B.

We get following answers:

Rate of change of Function A = 2

Rate of change of Function B = 3

y-intercept is 3 for function A.

y-intercept is -2 for function B.

So, The correct options are:

The rate of change of function A and B are positive

The rate of change of function A is less than the rate of change of function B. (Because 2 is less than 3)

The y-intercept of function A is positive, while y-intercept of function B is negative.

So, Option A, B and D are correct options.

Step-by-step explanation:

This is a geometric series where our common ratio is -1/2, and a is -4

Since r is less than -1, this series converges so

The sun is

\( \frac{ - 4}{1 + 0.5} \)

\( \frac{ - 4}{1.5} = - \frac{8}{3} \)

The sum is -8)3

The third side of the triangle using the law of cosines and to the nearest hundredth is 13.15 m.

The law of cosines, commonly referred to as the cosine rule or the cosine formula, in trigonometry essentially connects the length of the triangle to the cosines of one of its angles. It claims that we can determine the length of the third side of a triangle if we know the length of the first two sides and the angle between them. It comes from:

c² = b² + a² - 2ab cos α

Given that,

a = 19 m

b = 16 m

α = 43°

Then, according to the law of cosines we have:

c² = b² + a² - 2ab cos α

Substituting the values:

c² = (16)² + (19)² - 2(19)(16) cos (43)

c² = 256 + 361 -  608(0.73)

c² = 173.16

c = 13.15 m

Hence, the third side of the triangle using the law of cosines and to the nearest hundredth is 13.15 m.

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Answer:

f(x)  :  exponential growth

g(x);  exponential growth

h(x):  exponential growth

j(x):   exponential decay

Step-by-step explanation:

In an exponential function such as
\(m(x) = a \cdot b^x\)

the factor that determines whether it is a growth or decay function depends entirely on the value of b since x cannot be negative

If b > 1, it is a growth function

If b < 1 then it is a decay function

If b = 1 neither growth or decay function values are constant

In this context
f(x) has b = 2 > 1 . Hence it is a growth function
g(x) has b = 3 > 1 hence growth function
h(x) has be = 3/2 > 1; hence growth function
j(x) has be = 0.5 < 1 hence decay function

Answer:

O f(x)  :  exponential growth

O g(x);  exponential growth

O h(x):  exponential growth

O j(x):   exponential decay

Step-by-step explanation: I used to do this before :)

Answer:

d) 189.3 in²

Step-by-step explanation:

Area of rectangle is,

→ w × l

→ 10 × 15

→ 150 in²

Area of semi circle is,

→ (1/2)πr²

→ (1/2) × 3.14 × (5)²

→ 1.57 × 25

→ 39.3 in²

Now the total area will be,

→ 150 + 39

→ 189.3 in²

Thus, total area is 189.3 in².

The correct statement about the given function is: The function is increasing for all real values of x where x < –4.

In this question, we have been given the graph of the function

f(x) = -(x + 6)(x + 2)

According to description of the graph of given function f(x), the graph of function is a parabola and on a coordinate plane, a parabola opens down.

Also, the parabola goes through (-6, 0), has a vertex at (-4, 4), and goes through (-2, 0).

We need to find to the correct statement about the function.

f(x) = -(x + 6)(x + 2)

The function is increasing until it reaches the vertex x = -4.  

The function will decrease after the vertex, so after x = -4 function decreases.

increasing: -∞ < x < -4

decreasing : -4 < x < ∞

Therefore, the correct statement about the given function is: The function is increasing for all real values of x where x < –4.

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The percentage that can be filled with $3 in 1990 is: 29.41%

To calculate percentage growth rate:

Beginning:

Calculate the difference (increase) between the two numbers you are comparing. after that:

Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.  

We are told that it cost $3 to fill a gas tank as at 1970.

Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:

Cost of a gallon in 1970 = $0.36

Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank

Now, in 1990, the cost is $1.23 and as such:

Quantity that can be bought = 3/1.23 = 2.45 gallons

Percentage of tank filled = 2.45/8.33 * 100% = 29.41%

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Answer:

D: \(\frac{3}{(6-6)}\)

Step-by-step explanation:

Option A equates to \(-\frac{0}{2}=0\)

Option B equates to \(\frac{(-4+0)}{8}=\frac{-4}{8}=-\frac{1}{2}\)

Option C equates to \(0\div11 =0\)

Option D equates to \(\frac{3}{(6-6)}=\frac{3}{0}\) which cannot be defined as division by 0 is impossible

Answer:

lollllll

Step-by-step explanation:

thanks for the points

Answer:

hope this helps

Step-by-step explanation:

To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph

Option D, which is the closest choice to 933.33, is 930. As a result, 930 fraction acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans

A fraction is a number that represents a portion of a whole or a ratio between two quantities in mathematics. It is represented as a top number (numerator) over a bottom number (denominator) divided by a horizontal line, also known as a vinculum. The fraction 3/4, for example, represents three-quarters of a whole that has been divided into four equal parts. Proper fractions, improper fractions, and mixed numbers are all ways to express a fraction. A suitable fraction is one in which the numerator is less than the denominator, for example, 2/5.

Mr. Bailey intends to plant soybeans on 4 of every 9 acres, which equates to (4/9) of the total acres he farms.

If he intends to cultivate 2,100 acres, the number of acres planted with soybeans is:

(4/9) x 2,100 = 933.33

We must round this amount to the next whole number because he cannot plant soybeans on a fraction of an acre.

Option D, which is the closest choice to 933.33, is 930. As a result, 930 acres is a plausible estimate of the amount of acres on which Mr. Bailey will plant soybeans.

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The solution is:

⇒ 6b = 95.94   (equation to determine cost of one box)

cost of one box 'b' = $`15.99

⇒ 12t = 95.94   (equation to determine cost of per tile)

cost of one tile t = $0.7995.

Given :

Jorge bought a crate of floor tiles for $95.94.

The crate had 6 boxes of floor tiles.

Each box contained 20 floor tiles .

To Find :

Write and solve equation to determine the cost per box'b'.

Write and solve a second equation to determine the cost per tile't'

Solution :

Cost of one box = b

There are 6 boxes

So, cost of 6 boxes = $  6b

Since Jorge bought 1 crate( = 6 boxes) of cost $95.94

⇒     (equation to determine cost of one box)

⇒6b = 95.94

⇒b =15.99

Thus cost of one box = $`15.99

Since 1 box 20 floor tiles

So, 6 boxes (=1 crate) contain tiles = 6*20 = 120 tiles

We are given that cost of 1 crate( = 6 boxes = 120 tiles) is $95.94

Cost of one tile = t

Cost of 120 tiles = $120t

⇒ (equation to determine cost of per tile)

⇒12t = 95.94

⇒t = 0.7995.

Thus cost of one tile t = $0.7995.

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The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).

Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.

Assuming a semiannual compounding rate of 8%,

As per the given information, the required solution would be as:

Amount to be paid into the fund each semi-annual period will be

= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))

= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))

= $1535.21

Thus, the required amount to be paid into the fund each period is $1535.21.

Hence, the correct answer would be an option (B).

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Answer:

\(9^\circ , 171^\circ\)

Step-by-step explanation

If  a  represents the measure of the angle, then 180 - a is the measure of its supplement.  (Supplements add up to 180 degrees.)

The sentence in the problem translates to an equation:

a = (180 - a) - 162

Simplify the right side.

a = 18 - a

Add a.

2a = 18

a = 9

The angle's measure is \(9^\circ\).  The supplement is \(180^\circ - 9^\circ =171^\circ\)

The symmetric property of congruence is Option C) If AB ≅ CD, then CD ≅ AB.

The symmetric property of congruence states that if one segment is congruent to another segment, then the second segment is also congruent to the first.

Therefore, the correct answer is C) If AB ≅ CD , then CD ≅ AB.

This statement shows that if segment AB is congruent to segment CD, then segment CD is also congruent to segment AB, which satisfies the definition of the symmetric property of congruence.

Answer choices A) and D) do not represent the symmetric property of congruence, as they simply state that a segment is congruent to itself or to another segment without reversing the order of the comparison.

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