See screenshot. Couldn't solve it myself.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions.

Examples:

The Complete Question.

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No, X² is not an exponential function.

An exponential function is a function of the form f(x) = aˣ where a is a positive constant and x is a real number. The value of the function increases exponentially as x increases.

On the other hand, x² is a polynomial function, a function that can be written as the sum of a finite number of non-negative integer powers of x. The highest power of x is 2, it's called a quadratic function. And it can be represented as f(x) = ax² + bx + c where a, b, and c are real numbers and a is not 0.

Therefore, X² is not an exponential function but a polynomial function.

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To see the graph in the bottom.

Now, According to the question:

The given equation y = 1/2x

y=1/2x [The slope is (1/2) the y-intercept is zero (but isn't shown)

y=(1/2)x + 0

Plot the y-intercept (0,0). Using the slope of 1/2, move up one space from (0,0) and move to the left two spaces. Plot point (2, 1). From (2,1) move up one space and over two spaces to point (4, 2).

Stating over, go to the y-intercept again. Using the the slope (-1/-2)(same slope, different form). Move down one space and to the left two spaces to point (-2, -1). From (-2,-1) move down one space and to the left two spaces to point (-4, -2).

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The value of a in the equation 3/4(12a+8) =27.6 is

2.4

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

The equation 3/4(12a+8) =27.6 can be solved as follow:

3/4(12a+8) =27.6

multiply both sides by 4/3

12a + 8 = 27.6 × 4/3

12a + 8 = 36.8

collect like terms

12a = 36.8 - 8

12a = 28.8

divide both sides by 12

a = 28.8/12

a = 2.4

therefore the value of a is 2.4

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3 x 5 x 7 = 105, which is the smallest result that can be obtained by the process. To reach this result, the three chosen numbers must be 3, 5, and 7. The first step is to add two of the three numbers, which in this case is 3 + 5 = 8. Then, the sum of the two numbers is multiplied by the third number, which in this case is 7.

The product of 8 x 7 is 56, which is the smallest result that can be obtained by this process.  In general, the chosen numbers must be the smallest possible numbers in order to obtain the smallest result. The process involves adding two of the three chosen numbers and then multiplying the sum by the third number.

Thus, the three chosen numbers must be the numbers with the lowest sum when added together, and the third number must be the smallest number of the three. By following this process, the smallest result that can be obtained is the product of the three chosen numbers multiplied together.

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The solution to equation 7x - 9 = 16 is x = 3.57

Consider given equation 7x - 9 = 16

We solve above equation for x.

⇒ 7x - 9 = 16

Add 9 on both the sides of equation.

⇒ 7x - 9 + 9 = 16 + 9

⇒ 7x + 0 = 25                                   ...........(simplify)

⇒ 7x = 25                                        

Now we divide each side of equation by 7.

⇒ 7x / 7 = 25/7

⇒ x = 25/7                                         ..................(simplify)

If we simplify above fraction, we get.

⇒ x = 3.57

Thus, x = 3.57 is a solution to given equation.

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The complete question is:

'How do you solve 7x - 9 = 16?

Under the sign for the square root, in the quadratic formula b2-4ac, is the discriminant.

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Sam had 3 times as much money as James. After spending  $38 on a pair of shoes, now Sam has $256.

To translate a math word problem into equations, assign the unknowns to variables.

Let:

s = the amount of Sam's money

j = the amount of James' money

"Sam and James saved $392 altogether"  can be translated into:

s + j = 392  (Equation 1)

Sam had 3 times as much money as James, means:

s = 3j  (Equation 2)

Substitute equation 2 into equation 1

s + j = 392

3j + j = 392

4j =  392

j =  392 /4 = 98

Hence,

Sam's money before he bought shoes"

s = 3j = 3 x 98 = $294

After Sam bought a pair of shoes, his remaining money:

= $294  - $38 = $256

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If she has a total of $1.45, The equation that could be used to determine the number of dimes is[tex]$$0.05(a+8)+0.10(a)+=1.45$$[/tex]

Let [tex]$\boldsymbol{a}$[/tex] be the number of dimes.

There are eight more nickels than dimes. Thus, there are [tex]$\mathbf{a}+\mathbf{8}$[/tex]number of nickels.

The total of all the coins is [tex]$\mathbf{\$ 1 . 4 5}$[/tex].

[tex]$$0.05(a+8)+0.10(a)+=1.45$$[/tex]

The above equation may be used to find the value of a which is the number of dimes.

The complete question is,

Cathy has eight more nickels than dimes.

If she has a total of $1.45, write an equation that could be used to determine the number of dimes.

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It will take the plumber 1 hour and 1/8 hour to complete the job.

To find out how long it will take the plumber to complete the entire job, we can use the formula:

time = (job size) / (rate)

where job size is the fraction of the job that is remaining (1/8 in this case) and rate is the fraction of the job the plumber can complete in a given amount of time (2/9 in this case).

So the time to complete the job is:

time = (1/8) / (2/9)

= (9/16) / (2/9)

= (9/16) * (9/2)

= 9/8

= 1 and 1/8 hour

So it will take the plumber 1 hour and 1/8 hour to complete the job.

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Complete question :

A Plumber Completes ( 1)/(8) Of A Job In( 2)/(9) Hours. At This Rate, How Long Does It Take The Plumber Complete The Job?

Answer:

The equation of the line can be written in slope-intercept form as y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line that passes through the point (-2, 1) and has a slope of 1/2, we can use the point-slope form of the equation of a line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line.

So, using the point (-2, 1) and the slope of 1/2, we can write the equation of the line as:

y - 1 = (1/2)(x + 2)

Which can be re-arranged to the slope-intercept form

y = (1/2)x + (3/2)

Therefore, the equation of the line that passes through the point (-2, 1) and has a slope of 1/2 is y = (1/2)x + (3/2)

This equation can be used to find the y-coordinate of any point on the line, given its x-coordinate.

Answer:

5

Step-by-step explanation:

The descending order sum of a quadratic term, a linear term, and a constant are several ways to express a quadratic equation.

1. Regular format

2.Vertex shape

3. Detect type

4. Point-slope form

Let's examine the format of these forms.

1. Typical form:

When utilizing factoring or the quadratic formula to locate the equation's roots, this form works well.

[tex]y=ax^2+bx+5c[/tex]

2.Vertex shape

When attempting to determine the vertex (highest or lowest point) of a quadratic equation, this form works best.

y=a[tex](x+h)^2[/tex]+k

3.Intercept type:

y=a(x-p)(x-q)

4.Point-slope form

The usual form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points.

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Answer:

X = 8

Step-by-step explanation:

1) -3x+7x-8=34+9x-2

2) -3+7x-9x=8+34-2

3) -5x=40

4) x= 40/-5= -8

Answer: I think A.  x=8 ?

Step-by-step explanation: I hope this helps<3

The speed of River's mom drove for 10 miles distance is 0.234 mph

The speed of  River's mom drove for 25 miles is 10.234 mph  

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

here, we have,

Given as :

The first distance cover by River's mom = 10 miles

The rate of speed = x mph

The second distance cover by river's mom = 25 miles

The rate of speed = x + 10 mph

The total driving time = 45 min

Now, According to question

Time = speed/distance

So, 45 =10/x  +  25/(x+10)

Or, 9 =2/x  + 5/(x+10)

Or, 9 × x × ( x + 10 ) = 2 × ( x + 10 ) + 5 x

Or, 9 x² + 90 x = 2 x + 20 + 5 x

Or, 9 x² + 90 x = 7 x + 20

Or, 9 x² + 90 x - 7 x - 20 = 0

Or, 9 x² + 83 x - 20 = 0

Solving this quadratic equation

x = 0.234 , - 9.4567

so, the value is,

I.e x = 0.234 , - 9.4567

now,

We consider x = 0.234

So, The speed for 10 miles distance = x = 0.234 mph

and The speed of 25 miles = x + 10 = 0.234 + 10 = 10.234 mph

Hence The speed of River's mom drove for 10 miles distance is 0.234 mph

and The speed of  River's mom drove for 25 miles is 10.234 mph

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The graph represents the relationship between the temperature and hours after sunrise. The slope shows the temperature changes per hour and the y-intercepts shows the temperature at the time of sunrise. The linear equation of this condition is y = 4x + 4.

From the graph, we can get some informations:

The temperature at the time of sunrise is 4 degrees celcius. This information is represented by the y-intercepts on 4 or point (0, 4). This is the initial temperature of the day.

Next, we will try to find the slope of the graph. We take 2 points:

(0, 4)

(1, 8)

Slope (m) = y₂ - y₁

                    x₂ - x₁

m = (8 - 4)

       (1 - 0)

m = 4

However, as the hour goes by, the temperature increases by 4 degrees celcius. This information is known based on the slope of the graph. The slope represents the degree celcius of temperature change per hour.

Based on the found y-intercepts and slope, we can formulated the linear equation of the graph as:

y = 4x + 4

where:

y = temperature

x = hours after sunrise

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A monic polynomial in algebra is a non-zero univariate polynomial, or a polynomial with a single variable, whose leading coefficient (the highest degree nonzero coefficient) is equal to 1.

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a 0 is true is known as a quadratic equation. x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer might be simple or complicated. In mathematics, a quadratic equation is one with degree 2, which means that its highest exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero.

Here,

In algebra, a monic polynomial is a non-zero univariate polynomial (i.e., a polynomial with a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

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The statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1].

A function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.

Since f is defined on the closed interval [0, 1], which includes the endpoints 0 and 1, it also does not attain a maximum or minimum value on the entire closed interval.

For the function f to attain a minimum value, the function must be defined for all x in the closed interval and all x in the domain and at least one point x in the domain must be a global minimum.

For the function to attain a maximum value, at least one point x in the domain must be a global maximum, in this case, the function is continuous and strictly increasing on the open interval (0, 1) which means that the function doesn't have a minimum or a maximum.

In conclusion, the statement that is true is (d) f attains neither a minimum value nor a maximum value on the closed interval [0, 1] because a function that is strictly increasing on an open interval is not bounded above or below, meaning that it does not attain a maximum or minimum value within that interval.

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The two numbers used by mumtaz are 70 and 33

Let p and q be the two-digit numbers chosen by Mumtaz.

When these two two-digits number is divided one by the other, the answer was 2.1212...

Let us assume that r = p/q

and p/q = 2.1212...

we need to find the number r .

We know that a decimal number that consists of digits repeating after a fixed interval after the decimal point is a repeating decimal.

We can write a decimal number 2.1212... as [tex]2.\bar{12}[/tex]

[tex]r = 2.\bar{12}\\\\r=2+0.\bar{12}\\\\r=2+\frac{12}{99}\\\\r=\frac{70}{33}[/tex]

We can observe that 70/33 = 2.1212...

p/q = 70/33

So 70 and 33 are the required numbers.

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No, a triangle cannot have two sides.

A triangle is a three-sided polygon with three edges and three vertices in geometry. The total of a triangle's internal angles equals 180 degrees, which is its most important feature. This is known as the angle sum property of a triangle.

Triangle is a closed two-dimensional shape. It is a three-sided polygon. All sides are made of straight lines.

If ABC is a triangle, it is denoted as ABC, where A, B, and C are the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape represented by three non-collinear points in a single plane.

Thus, No, a triangle cannot have two sides.

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The amount of string left after cutting 25 strings of 7 inches in length is

5 inches.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 km = 1000 m

We have,

1 feet = 12 inches

Multiply 15 on both sides.

15 feet = 15 x 12 inches

15 feet = 180 inches

Now,

Length of the string = 15 feet

Length of each string = 7 inches

The number of strings of 7 inches is 25 and 5 inches left over.

i.e

7 x 25 = 175

The string that is left over.

= 180 - 175

= 5 inches

Thus,

5 inches of the string is left after cutting 25 strings of 7 inches in length.

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Answer:1

Step-by-step explanation:

The complete factorization of the quadratic equation 6x² + 15x - 36 is given by:

How to factor a quadratic equation?

A quadratic equation is modeled by:

Considering the roots and , it can be factored as:

In this problem, the function is:

Hence the coefficients are , and:

Hence:

Answer:

Step-by-step explanation:

Answer:

To factor the expression 6x² + 15x - 36 = 0, we can use the technique of factoring by grouping.

First we will write the expression as two binomials:

6x² + 15x - 36 = (6x² + 18x) - (3x + 36) = 0

Next we will factor out the greatest common factor (GCF) of the first binomial:

6x² + 18x = 3x(2x + 6)

Next we will factor out the GCF of the second binomial:

3x + 36 = 3x(1 + 12)

Bring the factors out of the parentheses:

3x(2x + 6) - 3x(1 + 12) = 3x(2x-1+6-12) = 3x(2x-6) = 0

So the expression is factored completely as 3x(2x-6) = 0.

We can see that the factors of the expression 6x² + 15x - 36 = 0 are 3x and (2x-6)

When one multiplies a negative numer and a positive number, the product integer will be negative.

The rule to assist the multiplication of signed integers is -

Case I - Product of postive and negative integer will be negative.

Case II - Product of two positive integers will be positive.

Case III - Product of two negative integers will be positive.

Case IV - Product of negative and positive integer will be negative.

Let us understand this will example. Taking two integer numbers 2 and 5. Changing the signs as per the requirement.

Case I - 5 and (-2) = -10

Case II - 5 × 2 = 10

Case III - (-5) × (-2) = 10

Case IV - (-5) × 2 = -10

Thus, the result according to question will be negative number.

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To find f (-4) on a graph, plot the point (-4, f (-4)) on the graph.

B. First, identify the point (-4, 0) on the x-axis. This is the point where the x-coordinate is -4. Then, draw a line perpendicular to the x-axis that passes through the point (-4, 0).

This line represents the function f (x). Use the equation of the line to determine the value of f (-4). For example, if the equation of the line is y = 3x + 7, then the value of f (-4) is -5.

To plot the point (-4, f (-4)) on the graph, simply draw a dot at the intersection of the line and the y-axis, with the y-coordinate being f (-4). This dot represents the point (-4, f (-4)).

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Answer:

f(-1) = -2

f(-2) = -3

Step-by-step explanation:

See the attached worksheet.

f(-1) = is asking for the value of the function, f, when x = -1.

f(x) = -3 is asking what value of x will cause the function to produce a - 3.

The range in which at least 88.9% of the data will reside is (6.8,8).

mean=7.2

standard deviation=0.2

we find the range in which at least 88.9% of the data will reside

1-1/k²=0.889

⇒1/k²=1-0.889

⇒1/k²=0.111

⇒k²=1/0.111=9.009

⇒k=3.002

so, k=3

The range of values can be computed as mean±k(standard deviation).

Thus, the range in which at least 88.9% of the data will reside in

(mean-k(standard deviation), mean+ k(standard deviation))

(7.2-3(0.2),7.2+3(0.2))

=(7.2-0.6,7.2+0.6)

= (6.6, 7.8)

Thus, the range in which at least 88.9% of the data will reside is (6.8,8).

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The range of this function #( x 3x2 6x 8 is (-infinity(∞), infinity(∞)) .

What is function ?

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Have given function ,

f(x) = #( x 3x2 6x 8

The range of a function is the set of all possible output values (y-values) for a given input (x-values). Since this is a polynomial function, it can take any value for y as long as we input real numbers for x.

Therefore, the range of this function #( x 3x2 6x 8 is (-infinity(∞), infinity(∞)).

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The length of the segment SY is equivalent to 22.

Given is a triangle ΔTSU.

The medians are divided into a 2 : 1 ratio by the centroid. So, we can write that -

SY/YP = 2/1

SY/YP + 1 = 2/1 + 1

(SY + YP)/YP = 3/1

SP/YP = 3/1

(2x + 3)/11 = 3/1

2x + 3 = 3 x 11

2x + 3 = 33

2x = 30

x = 15

Now, SY = SP - YP = (2 x 15 + 3) - 11 = 33 - 11 = 22

SY = 22

Therefore, the length of the segment SY is equivalent to 22.

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The 5 steps in a division problem are understanding the problem, setting up the problem, dividing, finding the remainder and continuing the last two steps until the remainder is less than the divisor.

Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the dividend, divisor, and the quotient.

Set up the problem: Write the problem using the standard division format: dividend ÷ divisor = quotient.

Divide: Begin by dividing the leftmost digit of the dividend by the divisor. Write the quotient above the dividend, to the left of the dividend, and above the divisor.

Multiply and Subtract: Multiply the divisor by the quotient digit and write the product under the corresponding digit of the dividend. Then subtract this product from the corresponding digits of the dividend.

Bring down the next digit: Bring down the next digit of the dividend to the right of the remainder. Repeat steps 3 and 4 until the remainder is zero or until you have reached the desired level of accuracy.

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