Pascale leaves the office to go home. She walks 12 blocks due north and then 9 blocks due west. How far is she from the office?

Answer:

There will need to be 2 and 1/3 cups of flour according to the recipe

Step-by-step explanation:

Given the recipe, we can say that for each 2 and 2/3s cups of milk, one cup of flour is used. We can write this as ( 2 + 2/3)  cups of milk / (1) cup of flour.

We can also write 2 + 2/3 as 2*(3/3) + 2/3 = 6/3 + 2/3 = 8/3, making our ratio

(8/3) / 1

The ratio stays the same, no matter how many cups of milk or flour are used. Therefore, (8/3) /1 = (4 + 2/3) / cups of flour

Writing our final cups of flour as c, we can say

(8/3) / 1 = (4+2/3) / c

(4+2/3)/c = (12/3 + 2/3) /c = (14/3) /c

(8/3)/1 = (14/3) /c

anything divided by 1 is equal to itself

(8/3) = (14/3)/c

multiply both sides by c to make the variable not a denominator

(8/3) * c = 14/3

multiply both sides by 3 to remove the denominators

8 * c = 14

divide both sides by 8 to isolate the c

c = 14/8 = 7/3 = 6/3 + 1/3 = 2 + 1/3

There will need to be 2 and 1/3 cups of flour according to the recipe

Answer:

3x+2+6x+5x

Step-by-step explanation:

perimeter of triangle = side 1 + side 2 + side 3

expression of the perimeter of triangle 3x+2+6x+5x

perimeter of traingle = 14x + 6

The expression 14x + 2 represents the perimeter of the triangle in terms of "x."

To find an expression that represents the perimeter of a triangle.

The perimeter is the sum of all three sides of the triangle. We have three sides with different lengths given by the expressions 3x + 2, 6x, and 5x. To find the expression representing the perimeter, we just need to add these three sides together.

Let's represent the sides as follows:

- The first side of the triangle is denoted as "a," which has a length of 3x + 2.

- The second side is denoted as "b," with a length of 6x.

- The third side is denoted as "c," having a length of 5x.

Now, let's find the expression for the perimeter, which we'll call "P." To do that, we add the three sides together:

P = a + b + c

Substitute the given expressions for the sides into the equation:

P = (3x + 2) + (6x) + (5x)

Now, let's simplify the expression by combining like terms (terms with the same variable "x"):

P = 3x + 2 + 6x + 5x

To further simplify, add the coefficients of the "x" terms:

P = (3 + 6 + 5)x + 2

Now, add the coefficients: 3 + 6 + 5 = 14, so the expression for the perimeter becomes:

P = 14x + 2

The expression 14x + 2 represents the perimeter of the triangle in terms of "x."

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Answer:

Equation of Ellipse is [tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]

Step-by-step explanation:

Let's find the value for [tex]a^{2}[/tex] and [tex]b^{2}[/tex] to write the equation for vertical ellipse.

Here 'a'  is the distance from center to one of the vertices.

"b" is the distance from center to one of the Co-vertices. We need to find this using formula [tex]a^{2} -b^{2} =c^{2}[/tex]

'c' is the distance between center to one of the Foci.

In this problem center is origin.

So, a =6(because distance between(0,0) and (0,6) is 6)

c= 2 (because distance between (0,0) and (0,2) is 2)

Plug in the known values into the formula [tex]a^{2} -b^{2} =c^{2}[/tex]

36-[tex]b^{2}[/tex]= 4

Subtract both sides 36

[tex]-b^{2}[/tex] = -32

Divide both sides by -1

[tex]b^{2}[/tex] =32

So, equation would be

[tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]

Answer:

S.D = 236.5

~~~~~~~~~~~~~~~~~~

300,

785,

670,

187,

760,

724

Answer:

300, 790, 670, 190, 760, 720

Answer:

25 students take both subjects.

Step-by-step explanation:

Solve for 60% of 300 students:

60/100 = x/300

Cross multiply:

60 × 300 = 100 × x

18000 = 100x

Divide both sides by 100:

180 = x

Solve for 20% of 300 students:

20/100 = x/300

20 × 300 = 100 × x

6000 = 100x

60 = x

Solve for the percentage of students in chemistry:

x/100 = 35/300

x × 300 = 100 × 35

300x = 3500

x = 11.66666...7

x = about 11.7%

Find the difference in percentages:

100 - 60 - 20 - 11.7

8.3

8.3% take both subjects

Solve for 8.3% of students:

8.3/100 = x/300

8.3 × 300 = 100 × x

2490 = 100x

24.9

About 25 students

Check your work by adding all the students together (to get to 300):

25 + 60 + 180 + 35

300 students total

This is correct!

Answer:

x=14

Step-by-step explanation:

x - 42 = 98 – 9x

x+9x=98+42

10x=140

x=14

Answer:

[tex]x - 42 = 98 - 9x \\ x + 9x = 98 + 42 \\ 10x = 140 \\ x = 14 \\ thank \: you[/tex]

Answer:

[tex]1\frac{1}{2}[/tex] or 1.33%

Step-by-step explanation:

Answer:

[tex]\boxed {\boxed {\sf y-5= 2(x+2)}}[/tex]

Step-by-step explanation:

We are asked to find the equation of a line in point-slope form.

As the name of the form describes, we need both a point and the slope. We are given a point, but we have to find the slope.

The line is parallel to the line with the equation of 4x-2y= -5. Parallel lines have the same slope, so once we find the slope of the line with the given equation, we have the slope of the other line whose equation we are finding.

[tex]4x-2y= -5[/tex]

We can find the slope by putting the equation into slope-intercept form, or y=mx+b (where m is the slope and b is the y-intercept). We must isolate the variable y. 4x is being added to -2y. The inverse of addition is subtraction, so subtract 4x from both sides.

[tex]4x-4x-2y= -5-4x[/tex]

[tex]-2y= -5-4x[/tex]

y is being multiplied by -2. The inverse of multiplication is division, so divide both sides by -2.

[tex]-2y/-2=(-5-4x)/-2\\ y= \frac{-5}{-2} + \frac{-4x}{-2} \\ y= \frac{5}{2}+2x[/tex]

The coefficient of x is the slope, so the slope of the line is 2. Any line that is parallel also has a slope of 2.

Now we have a point and a slope, so we can use the point-slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is the point.

We know the slope is 2 and the point is (-2,5).

[tex]y-5=2(x- -2 ) \\\bold {y-5= 2(x+2)}[/tex]

The equation of the line in point-slope form is y-5= 2(x+2)

Answer:

The answer is "Option C"

Step-by-step explanation:

Given:

[tex]r= 30 \ cm\\\\\theta =60^{\circ}[/tex]

Using formula:

[tex]\frac{A}{\theta}=\frac{\pi r^2}{2\pi}\\\\\frac{A}{\theta}=\frac{\pi r^2}{2}\\\\A=\frac{r^2\times \theta}{2}[/tex]

Answer:

a, 14.13. b, 39.25

Step-by-step explanation:

so for a the diameter is 6 so the radius is 3. The equation for the area of the circle is πr2. So 3x3=9. then 9x3.14=28.26. But then we have to divide by two cause we are finding only the shaded area. 28.26/2=14.13.

A is 14.13

for b, its the same thing, so the radiu is 5 and 5x5=25. 25x3.14=78.5, and divide two, so 78.5/2=39.25.

B is 39.25

WARNING: I am not sure this is correct, so if this is wrong i'm sorry, i'm learning too :)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x₁ , y₁) = (3,-1)   &(x₂,y₂) = (-8, 0)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{0-[-1]}{-8-3}\\\\=\frac{0+1}{-11}\\\\=\frac{1}{-11}\\\\=\frac{-1}{11}[/tex]

Answer:

1st box: 49

2nd box: 7

3rd box: 7

4th box: 2

5th box (above): 1

6th box (below): 3

7th box: 7

8th box: -12

9th box: -2

Answer:

b

Step-by-step explanation:

i just answered it

Answer:

D

I can suggest some insight how to analyze this type of problem...

1) the y intercept has to be 1... they all are so no help

2) the slope is negative, they all are so no help

3) the sign is ≥ so the "fill" goes up ... A or D

4) the ≥ means that the line has to be SOLID not a dash ONLY D left.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Common difference is 3.

Let x be a term in the sequence. The next term in the sequence is x+3.

x(x+3) = 598

x² + 3x - 598 = 0

x = [-3 ± √(3²-4⋅1(-598))]/[2⋅1] = [-3 ± 49]/2 = 23, -26

-26 is an extraneous solution, so x = 23.

The two terms are 23 and 26.

Answer:

a=2   b = 3   c=8

Step-by-step explanation:

2^5

-------

4

Rewrite 4 as 2^2

2^5

------

2^2

We know that x^y / x^z = x^(y-z)

2^(5-2)

2^3

8

Answer: the answer is 2 or C

-8/2 x -3/6

*Always do the recipical*

(-8 x -3) / (2 x 6)

-8 x -3= +24

2 x 6= 12

24/12= 2

The solution of the given expression -8/2 x -3/6 is 2. The correct option is B.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

Given that the expression is,

-8/2 x -3/6

The expression will be solved as below,

E = (-8 x -3) / (2 x 6)

The numerator will get reciprocal and multiplied to the denominator,

E = 24 / 12

Divide the number 24 by 12 and get the solution,

E = 2

Therefore, the solution of the expression will be 2. The correct option is B.

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Answer:

2.4 miles

Step-by-step explanation:

0.4 / 20 = 0.02

0.02 x 120

= 2.4

Answer:

466.67

Step-by-step explanation:

Let p be the original price

p - 10 % p = 420

p - .10p = 420

.9p = 420

Divide each side by .9

.9p/.9 = 420/.9

p =466.666666

Rounding to the nearest cent

p = 466.67

Answer:

y = -3x+14

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

y = -3x+b

Substitute the point into the equation to solve for b

2 = -3(4)+b

2 = -12+b

2+12 = -12+b+12

14 = b

y = -3x+14

Answer:

= (6/x - 2)^3

Answer:

favricis 1/3 yard bt 3 5/8 yards wich it will be 64

Answer:

domain[-infinity, infinity]

range[2, infinity]

Answer:

in which class you are if you are in 7 the ans will be -3.

Answer:

34

Step-by-step explanation:

We are here given a modulus expression and we need to find out the value when m = -5 and n = 3 .

Modulus :- It always gives positive value . For example ,

[tex]\rm\implies |-a| = a [/tex]

[tex]\rm\implies |a| = a [/tex]

The given modulus expression is :-

[tex]\rm\implies |m^2+ n^2| [/tex]

As the number inside the modulus operator are already squared therefore they will always give positive value for real numbers . Here we can omit the modulus .

[tex]\rm\implies m^2 + n^2 [/tex]

Plug in the given values ,

[tex]\rm\implies (-5)^2 + 3^2 [/tex]

Solve 5² and 3² and add them ,

[tex]\rm\implies 25 + 9 [/tex]

On adding ,

[tex]\rm\implies 34 [/tex]

Therefore ,

[tex]\rm\implies \boxed{\blue{\rm |m^2+n^2| = 34 }}[/tex]

Hence the required answer is 34 .

Answer:

Step-by-step explanation:

[tex]4[/tex] ± [tex]\frac{\sqrt{(-4)^{2} - 4(11) 8} }{2(11)}[/tex]

Answer:

what are the answer choicesss

Step-by-step explanation:

Answer:

30.28 yd²

Step-by-step explanation:

Area enclosed = area of trapezoid + area of semicircle

= ½(a + b)*h + ½(πr²)

Where,

a = 5 yd

b = 2 + 5 = 7 yd

h = 4 yd

r = ½(4) = 2 yd

Plug in the known values

Area enclosed = ½(5 + 7)*4 + ½(π*2²)

Area enclosed = ½(12)*4 + ½(π*4)

= 6*4 + π*2

= 24 + 2π

= 30.2831853

≈ 30.28 yd² (2 decimal places)

Answer:

58.480766068854

Step-by-step explanation:

hope it will help you