On a town map, each unit of the coordinate plane represents 1 mile. Three branches of a bank are located
at A(-3,1), B(3, 4), and C(3,-2). A bank employee drives from Branch A to Branch B and then drives
halfway to Branch C before getting stuck in traffic. What is the minimum total distance the employee
may have driven before getting stuck in traffic? Round to the nearest tenth of a mile if necessary.
The minimum total distance the employee may have driven before getting stuck in traffic is
miles.

Answer:

- 21

Step-by-step explanation:

The minimum value occurs at the vertex of the function

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

Given

f(x) = x² - 6x - 12

add/ subtract ( half the coefficient of the x- term)² to x² - 6x

f(x) = x² + 2(- 3)x + 9 - 9 - 12

     = (x - 3)² - 21

with vertex = (3, - 21 )

The minimum is the value of k, that is minimum value = - 21

The total numbers of sections are 16.

Step-by-step explanation:

Given:

Number of boys in school = 576

Number of girls in school = 448

To find: Total Number of sections such that each section has either boys or girls.

Height Common Factor ( HCF ) of both number gives the number of students in a section.

HCF of 576 and 448

576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

448 = 2 × 2 × 2 × 2 × 2 × 2 × 7

HCF = 2 × 2 × 2 × 2 × 2 × 2 = 64

Number of sections of Boys = 576/64 = 9

Number of sections of girls 448/64 = 7

Total Number of sections = 9 + 7 = 16

Therefore, The total numbers of sections are 16.

Answer:

[tex] \boxed{\sf x = \frac{13}{5} } [/tex]

Given:

(x + 4):(3x + 1) is the duplicate ratio of 3:4

To Find:

Value of x

Step-by-step explanation:

[tex] \sf Solve \: for \: x: \\ \sf \implies (x + 4) : (3x + 1) = 3 : 4 \\ \\ \sf Convert \: ratios \: to \: fractions: \\ \sf \implies \frac{x + 4}{3x + 1} = \frac{3}{4} \\ \\ \sf Cross \: multiply: \\ \sf \implies 4(x + 4) = 3(3x + 1) \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \sf \implies 4x + 16 = 3(3x + 1) \\ \\ \sf Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ \sf \implies 4x + 16 = 9x + 3 \\ \\ \sf Subtract \: 9 x + 16 \: from \: both \: sides: \\ \sf \implies - 5x = - 13 \\ \\ \sf Divide \: both \: sides \: by \: - 5: \\ \sf \implies x = \frac{13}{5} [/tex]

Answer:

Attachment 1 :-   x = 3/2

Attachment 2 :-  m + r = 154°

Step-by-step explanation:

Attachment 1 :-

[tex]9^(^2^-^x^) = 3\\=> 3^2^(^2^-^x^) = 3\\[/tex]

As the base 3 is same on both the sides , cancel the base 3 from both left & right side of eqn. After that we will get:-

[tex]2(2 - x) = 1\\=> 2 - x =\frac{1}{2} \\=> x = 2 - \frac{1}{2} = \frac{3}{2}[/tex]

Attachment 2 :-

PQR is a straight line . It's given that m + n = 110°

But we know that m + n + r = 180° ..............eqn.1

So substituting the value of m+n in eqn.1 gives :-

m+n+r = 180°

=> r + 110° = 180°

=> r = 180° - 110°

       = 70°

It's also given that n+r = 96°

So putting the value of r in the above gives ,

n+r = 96°

=> n + 70° =96°

=> n = 96° - 70°

        = 26°

Putting the value of n in eqn.1 gives

m + n = 110°

=> m + 26° = 110°

=> m = 110° - 26°

        = 84°

So m + r = 84° + 70° = 154°

Answer:

$9600.72

Step-by-step explanation:

Area of the field = length × width

Length = 1,021 feet

Width= 725 feet

Area of the field = length × width

= 1,021 feet × 725 feet

= 740,225 square feet

One bag covers 1000 square feet

There are 740,225 square feet

Find the number of bags that will cover the total of 740,225 square feet

Total bags = 740,225 / 10000

=740.225 bags

A bag cost $12.97

Total cost of 740.225 bags= 740.225 × 12.97

= $9600. 71825

Approximately

$9600.72

Answer:

The situation is that; the parking lot has 64 cars at the end of the day

Step-by-step explanation:

Given

Initial Number of cars = 16

Additional Cars = 48

Required

Determine the situation for the day

From the question, we understand that no car left the park;

This implies that

[tex]Number\ of\ cars = Initial\ Cars + Additional\ Cars[/tex]

[tex]Number\ of\ cars = 16 + 48[/tex]

[tex]Number\ of\ cars = 64[/tex]

So, the situation is that; the parking lot has 64 cars at the end of the day

Answer:

B. (-2,-1)

Step-by-step explanation:

A continuous function is one that do not discontinue, and a little change in its input has no effect on its result. This is one major difference between continuous and discontinuous functions. Both functions has major applications in calculus.

The turning point of a function can be obtained by determining where  it is increasing or decreasing.

In the given question, though there is no detailed information about the continuous function, but the probable turning point is (-2, -1).

Answer:

(–2, –1)

Step-by-step explanation:

Answer: A. -5x-24

Step-by-step explanation:

 3(2x-8)-11x

=6x-24-11x

=6x-11x-24

=-5x-24

Hope this helps!! :)

Please let me know if you have any question

Answer:

67 inches

Step-by-step explanation:

Since the question is asking how many inches total do you have, we need to add up the 2 values given:

39 inches + 28 inches = 67 inches.

We can convert this to feet by dividing by 12:

67 in /12 in/ft ≈ a little over 5 and a half feet

Answer:

XY= 12

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

30

Step-by-step explanation: 270 divided by 9

hope it helps

Answer:

A

Step-by-step explanation:

a would be the correct answer to create a rectangle

Answer:

272cm squared

Step-by-step explanation:

figure a, a traingle... to find area formula is

1/2×b×h

1/2×18×17

153

figure b, it's rectangle.so length×width

=7×17

=119

area of the shape=153+119

=272cm squared

Answer:

D.    272 cm²

Step-by-step explanation:

will make it easy and short

use the area of a trapezoid = (a + b) * h/2

where a = 25,  b = 7,  h = 17

Area = (25 + 7) * (17/2)

Area = 32 * 8.5

Area = 272 cm²

Answer:

[tex] (x - 5)^2 + (y + 2)^2 = 81 [/tex]

Step-by-step explanation:

Standard form of the equation of a circle with center (h, k) and radius r:

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

Compare it to the given equation, and you get:

[tex] (x - 5)^2 + (y - (- 2))^2 = 9^2 [/tex]

[tex] (x - 5)^2 + (y + 2)^2 = 81 [/tex]

Answer:

i don't know

Step-by-step explanation:

Answer:

144x⁸y⁸

Step-by-step explanation:

Order of Operations: BPEMDAS

When you exponent an exponent, you multiply powers; when you multiply an exponent, you add powers.

Step 1: Write out expression

(-3xy³)² (4x³y)²

Step 2: Exponents

9x²y⁶(16x⁶y²)

Step 3: Multiply

144x⁸y⁸

Answer:

[tex]\large\boxed{{144x^8y^8}}[/tex]

Step-by-step explanation:

[tex](-3xy^3) ^2 (4x^3y) ^2[/tex]

[tex]\boxed{\text{Use the property: }(a^n b^m)^k= a^{nk} b^{mk}}[/tex]

[tex](9x^2y^6) (16x^6y^2)[/tex]

[tex]\text{Take } 9 \cdot 16, x^2 \cdot x^6, y^6\cdot y^2[/tex]

[tex]\boxed{\text{Use the property: }a^n a^m= a^{n+m}}[/tex]

[tex]144x^8y^8[/tex]

[tex]\therefore (-3xy^3) ^2 (4x^3y) ^2 = 144x^8y^8[/tex]

Answer:

Step-by-step explanation:

1. Define unknowns:

2. Make system of equations:

3. Multiply both sides of first equation by 6.4:

4. Subtract first equation from second one:

Answer:

9/10

Step-by-step explanation:

3^4/5^4 × 15^4/10^4=x^4/y^4

81/625 × 50625/10000= x^4/y^4

multiply

4100625/6250000=x^4/y^4

break it down by dividing it by 5

820125/1250000

divide by 5

164025/250000

divide by 5

32805/50000

divide by 5

6561/10000 = x^4/y^4

4√6561/4√10000=x/y

9/10= x/y

An equation is formed of two equal expressions. The value of x in the given equation is equal to 6.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved for x as shown below.

7x = 42

Divide both the sides of the equation by 7,

7x / 7 = 42/ 7

Simplifying both sides of the equation,

x = 6

Hence, the value of x in the given equation is equal to 6.

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Answer:

a/3 + 27

Step-by-step explanation:

One third is: 1/3

then:

, the expressipn is:

a/3 + 27

The required expression, that is the sum of one-third of a number, and 27 is x / 3 + 7.

Given that,
To determine the arithmetic, the sum of one-third of a number and 27.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Let the number be x,
one-third of the number is = x/3,
Now according to the question,
Applying arithmetic operations,
Sum = x / 3 + 27

Thus, the required expression, that is the sum of one-third of a number and 27 is x / 3 + 7.

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Answer:

(0,80) (5,40)

Step-by-step explanation:

edge2020

Two points on the side view of a waterslide are (0,80) and (5, 40)

Graphs are used to visualize the relationship between datasets and variables

From the graph, we have the following coordinates

(0,80), (5,40), (10,20), (15, 10) and (20, 0)

Hence, two points on slide are (0,80) and (5, 40)

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Answer and Step-by-step explanation:

Areas of mathematics, and give a precise definition of each.

Sol: importance: mathematics can be tricky, so precise definitions are essential. Without them, there can be confusion, which will generate the wrong answer more often than not.  It teaches the students exactly how to use formulas and under what condition a mathematical statement is true.

Some words related to geometry that are quite hard to define precisely are the line, the plane, and the point. In mathematics, the unit square is area one and any other shape.

Answer:

0.25 miles per minute, travels 5 miles in 20 minutes

Step-by-step explanation:

First, we have to find out how many miles he can travel in a minute.

We know that he travels 15 miles every hour, and we know that one hour is 60 minutes.

So, we can divide 15 miles by 60 minutes in order to get his pace for miles per minute

Then we can just multiply 0.25 miles by 20 minutes

which gives us 5 miles in 20 minutes

Answer:

0.000000861

Step-by-step explanation:

Answer:

0.0000000861

Step-by-step explanation:

I took the test. Hope this helps!

Answer:

-2x² - 16x + 4

Step-by-step explanation:

Step 1: Write out expression

6x² - 9x + 3 - (8x² + 7x - 1)

Step 2: Distribute negative

6x² - 9x + 3 - 8x² - 7x + 1

Step 3: Combine like terms (x²)

-2x² - 9x + 3 - 7x + 1

Step 4: Combine like terms (x)

-2x² - 16x + 3 + 1

Step 5: Combine like terms (constants)

-2x² - 16x + 4

Answer:

-2(x^2=8x-2)

Step-by-step explanation:

Answer: It is equal to the measure of angle C.

Step-by-step explanation:

If we know that Triangle ABC isosceles, then that means two sides and two angles are congruent to each other. Angle A must the topmost angle, and Angle B and C are probably the base angles. So, saying that, the base angles and sides are congruent to each other. Hence, Angle B must be equal to Angle C.

Answer:

It is equal to the measure of angle C.

Step-by-step explanation:

If we know that Triangle ABC isosceles, then that means two sides and two angles are congruent to each other. Angle A must the topmost angle, and Angle B and C are probably the base angles. So, saying that, the base angles and sides are congruent to each other. Hence, Angle B must be equal to Angle C.

Answer:

8640

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

If FG is 19 and GH is 7 and you are trying to find the combined length of FG and GH then add 19 and 7.

The sum of line segment FG and GH will result FH as 26.

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.

Given the line FH with two segment FG and GH

So,

FH = FG + GH

FH = 19 + 7

FH = (20 - 1) + 7

FH = 20 + 7 - 1

FH = 27 - 1 = 26

Hence "The sum of line segment FG and GH will result in FH as 26".

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