Triangle ABC is shown below

The value of f(4) - g(-5) if function  f(x) = 3 / 2x + 2 and g(x) = 2x² - 3 is -39.

An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Given:

f(x) = 3 / 2x + 2 and g(x) = 2x² - 3

Calculate the value of f(4) and g(-5) as shown below,

f(4) = 3 / 2 × 4 + 2

f(4) = 12 / 2 + 2

f(4) = 6 + 2

f(4) = 8

g(-5) = 2 × (-5)² - 3

g(-5) = 2 × 25 - 3

g(-5) = 50 - 3

g(-5) = 47

Now, calculate the value of f(4) - g(-5) as shown below,

f(4) - g(-5) = 8 - 47

f(4) - g(-5) = -39

Thus, the value of f(4) - g(-5) is -39.

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Answer:January

Step-by-step explanation: if it is asking to explain based on data given, you can show that -11.6<-10.4, but if it is asking based on other information that you recieved, i cant really help other then to tell you to look at the cylces of day and night, because some parts of alaska get no sun for 6 months, so that could be why january is averagly colder

Only Erica's equation (y = -0.5x) is proportional

An equation is used to show the relationship between numbers and variables.

The standard form of a linear equation graph is:

y = mx + b

Where m is the slope of the line and b is the y intercept.

Given the Erica equation:

y = -0.5x

The slope is -0.5, hence it is a negative slope and the intercept is at 0, hence it passes through the origin and is proportional

Given the Aliyah equation:

y = 2.5x - 8

The slope is 2.5, hence it is a positive slope and the intercept is at -8, hence it does not pass through the origin and is not proportional

Both equations are linear equations

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We get the number of bananas as 8 and the number of mangoes as 4.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is that Chee and her children went into a grocery store and she bought $12 worth of bananas and mangos. Each banana costs $0.50 and each mango costs $2. She bought twice as many bananas as mangos.

We can write the system of equations as -

x = 2y               .....  (1)

(1/2)x + 2y = 12   ..... (2)

We can write equation (2) as -

(1/2) x 2y + 2y = 12

3y = 12

y = 4

then -

x = 8

Therefore, we get the number of bananas as 8 and the number of mangoes as 4.

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Answer: 56

Step-by-step explanation:

Given

There are 40 bears  in a national park

After a year, Population increased by 40%

An increase in population is

[tex]=40\times 40\%\\=40\times 0.4\\=16[/tex]

So, a new population is the sum of the original and increased population

[tex]\Rightarrow 40+16\\\Rightarrow 56[/tex]

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).

Here,

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

A statistical data's confidence interval can be expressed as.

=> x+/-zr/√n

=> Knowing that;

Average Sample x = $70.00

$17.50 is the standard deviation.

n = 60 samples were used.

95% confidence interval

95% confidence interval for z = 1.96

substituting our current values;

$70.00+/-1.96($17.50/√60)

$70.00+/-1.96($2.259240285287)

$70.00+/-$4.428110959163

$70.00+/-$4.43

= ( $65.57, $74.43)

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

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Answer:

68 square cm

Step-by-step explanation:

the composite is made up of a triangle , rectangle and parallelogram

area of composite = area of triangle + area of rectangle + area of parallelogram

Area of parallelogram = base x height

9 x 2 = 18

area of triangle = 1/ 2 x base x height

1/2 x 6 x 5 = 15

Area of a rectangle = length x width

5 x 7 = 35

15 + 35 + 18 = 68

Step-by-step explanation:

968866j5x4cctyvcyvyvycycc

Answer:

Total number of outcomes = 23

number of biology and art students = 2

number of biology students = 2

Since it is given that all the students study art,

number of possible outcomes = 2

probability = number of favorable outcomes/number of total outcomes.

= 2/23

Therefore probability that the selected student studies both art and biology is 2/23.

Answer:

d.  15.3%

Step-by-step explanation:

There are a total of 4 + 10 + 7 + 5 = 26 marbles

P(pick a red) = 4/26 = 2/13 = .153 = 15.3%  

Answer:

The price of a table is rs1720

Step-by-step explanation:

Let C and T be the individual prices of the tables and chairs.

We know that 3C + 4T = rs7540

We are then told that C = rs220, so we can enter that into the equation to find T:

3C + 4T = rs7540  

3(220) + 4T = rs7540  [for C = rs220]

660 + 4T = 7540

4T = rs6880

T = rs1720

Check:

Do 3 chairs at 220 each and 4 tables at 1720 each add to a total of 7540?

Chairs:   rs660

Tables:  rs6880

Total = rs7540  YES

Answer: x= 96 degrees

Step-by-step explanation:

It we figure out the rest of the angles they would be (the outside ans inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444 96 degrees

The measure of an angle x will be equal to 96°.

A Pentagon is a two-dimensional geometric shape that consists of five straight sides and five angles. It is a type of polygon, which is a closed shape with three or more sides.

The Pentagon is often used to represent the shape of buildings, monuments, and symbols in architecture and design.

If we figure out the rest of the angles they would be (the outside and inside angles are straight angles):

123+153+49+119= 444

Since the total of angles in a pentagon = 540 degrees

540-444= 96°

Therefore, the measure of an angle x will be equal to 96°.

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Answer:

Step-by-step explanation:

Total surface area:

So

TSA

The y-intercept of the line y = 7x -38 is -38. And the x-intercept is 0

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

The equation of the line,

y-4=7(x-6)

Simplify,

y -4 = 7x - 42

y = 7x -38

And slope-intercept form:

y = mx + b,

where m is the slope and y is the intercept.

Comparing with the slope intercept form,

we get,

m = 7 and b = -38

And the x-intercept is 0

Therefore3, y-intercept is -38.

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Answer:

30%

Step-by-step explanation:

18/60 = 0.30

0.30 = 30%

Answer:

A. 13

B. 2

Step-by-step explanation:

You use order of operations.

A. 4x2=8+12=20-7=13

B. 2x-3=-6+8=2

Answer:

D. Each segment of the electorate provides significant support to Mr Quintana

Step-by-step explanation:

From the question, we have the following logic statement;

If those segment that provide significant support to Ms Puerto also provide support to Mr. Quintana then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez

Counter to the If Then Logic structure

At least one segment of the lectorate provides significant support to Mr. Quintana and Mr. Ramirez

Therefore, there is at least one segment that provides support to Mr. Quintana but not to Ms. Puerta

The segments that provide support to Ms. Puerta do not provide support to Mr. Ramirez

Mr. Quintana's support includes those from the supporters of Ms. Puerta and those from the supporters of Mr. Ramirez

Therefore, each segment of the electorate provide significant support to Mr. Quintana.

Answer:

The bases are congruent

Step-by-step explanation:

From the question, we understand that the top base and the bottom base are directly opposite one another.

When such a scenario arise, it means that the bases have the same shape, they have the same dimension (i.e. size).

With the above analysis, we can conclude that the bases are congruent.

However, the given information can not be used to determine the shape and congruence of the lateral faces.

Lastly, for the bases to be congruent, they must have the same shape (and not any shape).

Hence, only option (b) is correct

Answer:

sorry

Step-by-step explanation:

Answer:

Its gonna be a 50/50 on the coin and 20/100 chance for the spinner

Answer:

5 outcomes for the spinner and a 50/50 chance for the coin

Step-by-step explanation:

for the spinner, there are five numbers, 1,2,3,4, and 5. so, there is a 1/5 chance or you could also say there is a 20/100 chance.   For the coin, there are two sides and 100 divided by 2 is 50 therefore, there is a 50/50 chance

Hope this helps!!

Answer:

Y-intercept: (0, -7)

X-intercept: (-14,0)

Step-by-step explanation:

To find the y-intercept, we need to put 0 in for x

0 + 2y = -14

2y = -14

y = -7

So, the y-intercept is located at (0, -7)

To find the x-intercept, we need to put 0 in for y

x + 2(0) = -14

x = -14

So, the x-intercept is located at (-14,0)

Step-by-step explanation:

To find the y-intercep, we need to put 0 in for x

0 + 2y= -14

2y = -14

y = - 7

So, the y - intercept is located at ( 0, - 7)

Answer:

Vertex is at (4, 2)

Step-by-step explanation:

to find the 'x' value of the vertex, use 'x = -b/2a'

in this problem, a = 1, b = -8, c = 18

x = -(-8)/2(1)

x = 8/2

x = 4

plug 2 in for 'x' in equation and solve for 'y':

y = 4² - 8(4) + 18

y = 16 - 32 + 18

y = -16 + 18

y = 2

Vertex is at (4, 2)

This is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.

For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.

We can take a few examples to understand this concept further.

Hence, this is how you construct a parent graph - it is the simplest form of the function, and has a basic shape.

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Answer:

jake did :)

Step-by-step explanation:

hope this helps ! <3

Lance is fastest because the speed of the Lance is 4.5 miles/hour and Jale speed is 4.16 miles/hour as 4.5>4.16

Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

Jake ran = [tex]2\frac{1}{2}[/tex] miles = 5/2 miles

In 3/5 hours

Thespeed = (5/2)/(3/5) =  4.16 miles/hours

Lance ran = [tex]3\frac{3}{4}[/tex] miles = 15/4 miles

In 5/6 hours

The speed = (15/4)/(5/6) = 4.5 miles/hours

Thus, Lance is fastest because the speed of the Lance is 4.5 miles/hour and Jale speed is 4.16 miles/hour as 4.5>4.16

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Answer:

m∠8 = m∠2, option G

Step-by-step explanation:

Angles 8 and 2 are alternate interior angles, which means they are equal. Thus, the answer is option G, m∠8 = m∠2

999.06ft999.06 in feet is the ladder.

Pythagorean Theorem is a mathematical formula used to calculate the length of the sides of a right triangle. It states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side, which is known as the hypotenuse. The formula is written as a² + b² = c², where a and b are the two shorter sides, and c is the hypotenuse.

To find the length of the ladder, use the Pythagorean Theorem. The length of the ladder is equal to the square root of the sum of the squares of the side lengths of the right triangle formed by the ladder and the wall.

The two side lengths of the right triangle are 999\,\text{ft}999ft999, start text, f, t, end text and 3\,\text{ft}3ft3, start text, f, t, end text.

Therefore, the length of the ladder is equal to the square root of (999^2+3^2), which is equal to 999.06\,\text{ft}999.06ft999.06,

start text, f, t, end text.

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The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.

The Correct option is (B).

The formula to calculate the margin of error  for the true proportion is;

M = √[p(1 - p)/n]

Given:

n= 40

p = 44/70

Now, The general formula for the margin of error would be:

z x √[p (1-p) ÷ n]

where:

z = values for selected confidence level

p = sample proportion

n = sample size

Since the confidence level is not given,

√[p (1-p) ÷ n]  

=√[44/70 (1 - (44/70) ÷ 70]

=√[0.6286 (0.3714)] ÷ 70

=√0.2335 ÷ 70

= √0.0033357

= 0.05775 or 0.058

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