Can someone please explain how to get the answer i've looked it up several times and i'm still stuck. I'm in algebra 2 with trig and doing my summer math packet: "The length of a rectangle is two feet less than four times the width. Find the length and width if the area is 38.2 square feet. let w= width of the rectangle" Btw websites say w is 19.1 but my answer key says its 3.35. Thanks!

Answer:

x = 6

Step-by-step explanation:

Since KN is the perpendicular bisector, that means ∠KNM = ∠KNQ = 90° and MN = NQ so therefore, since they are right triangles, ΔKNM ≅ ΔKNQ because of HL. Therefore, KM = KQ by CPCTC so:

5x - 3 = 3x + 9

2x = 12

x = 6

Answer:

2

Step-by-step explanation:

We can use 2 points to find the slope

m = (y2 -y1)/(x2-x1)

Using ( 0,1) and (1,3)

    = (3-1)/(1-0)

   = 2/1

  = 2

Answer:

2

Step-by-step explanation:

Take any two points -- I'm using (0, 1) and (1, 3). You can think of slope as (change in y)/(change in x), or simply rise/run. (3-1)/(1-0) is equal to 2.

*Note: (-1/2,1/2) is not in the same line as the other four points.

Answer:

first option

Step-by-step explanation:

Given

[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]

Multiply through by x² to clear the fractions

15x + 6x² = 9 ( subtract 9 from both sides )

6x² + 15x - 9 = 0 ( divide through by 3 )

2x² + 5x - 3 = 0 ← in standard form

Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to slit the x- term

2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Solution set is { - 3, 0.5 }

Answer:

28,000

Step-by-step explanation:

multiply 7 cars with 4,000

Answer:

[tex]\large\boxed{\sf \ \ 49 \ \ }[/tex]

Step-by-step explanation:

Hello,

we need to get the discriminant = 0 meaning

[tex]\Delta = b^2-4ac = 0\\\\<=>14^2-4c=0\\\\<=>c=\dfrac{196}{4}=49[/tex]

And then the square is

[tex]x^2-2\cdot 7\cdot x+7^2=(x-7)^2[/tex]

Hope this helps

Answer:

[tex]\boxed{F(x)>0}[/tex]

Step-by-step explanation:

The range is the set of possible values of y (the output).

The input value x is all real numbers, because there are no restrictions on x.

When the input x is all real numbers, the output is always greater than 0.

[tex]2^{-15}= 0.00003051757[/tex]

[tex]2^{8}= 256[/tex]

[tex]2^{-4}= 0.0625[/tex]

Complete question :

Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm long. How many whole cubes can Sharon make?

Answer:

About 51 ice cubes

Step-by-step explanation:

Given the following :

Height (h) of cylindrical pot = 25

Diameter = 30cm

Edge of ice cube = 7cm long

Volume of cylinder (v) = πr^2h

V = π * (30/2)^2 * 25

V = π * 15^2 * 25

V = 17671.458cm^3

Therefore, the soup occupies 17673.75cm^3

Volume of cubes to store the soup for later:

The volume of a cube is given by the formula:

V = a^3

Where a is the length of it's edge

V = 7^3

V = 343cm^3

Number of cubes required to store soup:

(Volume of cylinder / Volume of ice cube)

17671.458cm^3 / 343cm^3

= 51.520287

This is about 51 whole cubes

Answer:

10 cm overlap required to make a 30 cm long strip.

Step-by-step explanation:

Given:

Four paper strips of the same length.

Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.

To find:

Overlap required to make a strip which is 30 cm long = ?

Solution:

First of all, let us understand the concept of overlap.

Please refer to the attached image.

Let length of each strip be [tex]x[/tex] cm.

Given that there is 4 cm overlap resulting in new strip of length 36 cm.

The overlapping length is counted only once as clear from the figure attached.

So, Let us try to find the equation:

[tex]x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm[/tex]

i.e. each strip length is 20 cm.

Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.

The equation will be:

[tex](20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm[/tex]

Answer:

(a) 56 ways

(b) 6 ways

(c) 56 ways

Step-by-step explanation:

Given:

candidates: 6 mail, 1 female

number to hire : 3

a) In how many different ways can choose new employees?

use the combination formula to choose r to hire out of n candidates

C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways

b) In how many different ways can choose a single male candidate?

6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways

c) In how many different ways can choose at least one male candidate?

To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.

Since there are only two females, there is no way to choose 3 female candidates.

In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.

Answer:

  9.1 mph

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  s = √(30×drag factor×skid distance×braking efficiency)

  s = √(30×0.90×3.8×0.80) = √82.08 ≈ 9.06

The car was traveling about 9.1 mph before it started skidding.

Answer :Answer: Did you get helped on this one?          

Step-by-step explanation: okay yup yup have a good day OKAY

Step-by-step explanation: HAVE A GOOD ONE OKAY

Answer:

BC = 8

Step-by-step explanation:

16 ( sin 30 degrees ) = BC

16 (0.5)

16/2

BC = 8

Give the other person brainliest they deserve it.

Answer:

A ( -4, -7)

Step-by-step explanation:

if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )

Answer:

A.

Step-by-step explanation:

Answer:

NL=10.82

Step-by-step explanation:

Start by finding the area of the triangle.  We do this by using c as the base.

1/2bh=1/2(12)(25)=150

Now that we know the area is 150, we turn the triangle so b is the base and use the formula again.  This time we’re looking for the height, which is NL.

1/2bh=

1/2(27.73)h=150

13.865h=150

h=10.8186

Rounded to the nearest hundredth, it’s NL=10.82

Answer:

x = 30

(30, 0)

Step-by-step explanation:

The x-intercept is when the graph crosses the x-axis when y = 0. In that case, simply plug in 0 for y:

x + 6(0) = 30

x + 0 = 30

x = 30

Answer: (30,0)

Step-by-step explanation:

x-intercept can be found in the form x = my + b, where b is the x-intercept. Thus, simply turn x+6y=30 into x-6y+30, to find that the x-intercept is (30,0)

Hope it helps <3

Answer:

Step-by-step explanation:

In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°

Looking at the diagram, angle X and angle W are adjacent angles. It means that

X + W = 180

Since X = 105, then

105 + W = 180

W = 180 - 105 = 75°

Since W = b + 25°, then

b + 25° = 75

b = 75 - 25 = 50°

Answer: In an isosceles trapezoid, two pairs of adjacent angles are supplementary. It means that the sum of the adjacent angles is 180°Looking at the diagram, angle X and angle W are adjacent angles. It means that X + W = 180Since X = 105, then105 + W = 180W = 180 - 105 = 75°Since W = b + 25°, thenb + 25° = 75b = 75 - 25 = 50°

Step-by-step explanation:

Answer:

SAA or AAS

Step-by-step explanation:

∠BAC = ∠BCA   Given

∠BDA = 90° and ∠BDC = 90°   Given

∠BDA = ∠BDC All 90° angles are congruent

BD = DB Reflexive property

ΔADB = ΔCDB   SAA

Answer:

x is less than or equal to -18

Step-by-step explanation:

When doing this problem, I had to do -6 x 3 and x/3 x 3. This should cancel out the 3 in x/3, leaving you with just x. -6 x 3 is less or equal to -18. To check, I converted -18/3 into a whole number, which gave me -6. This is true to the original inequality. Hope this helped!

Answer:

12 feet

Step-by-step explanation:

Use the Pythagorean Theorem to find how high up the tree the top of the ladder reaches.

13 feet - hypotenuse

5 feet - can be a or b

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 144

b = √144

b = 12

The top of the ladder reaches 12 feet up the tree.

Hope that helps.

Answer:

12 ft

Step-by-step explanation:

These circumstances describe a triangle with hypotenuse 13 ft and bottom side 5 ft.  The vertical side (height above ground to top of ladder) is to be found.  According to the Pythagorean Theorem,

5^2 + (vertical side)^2 = 13 ft = 169, and so

(vertical side) = sqrt( 169 - 25 ) = 144 (ft)

The top of the ladder is s 12 ft above the ground.

Answer: A rectangle is a type of parallelogram but there are other parallelograms like rhombi so a parallelogram is not a type of rectangle

Answer:

27/2 units^3

Step-by-step explanation:

Formula for volume: l * w * h   or   a * h  because l * w = area.

27/5 ( which is area ) * 5/2 ( the height ) = 27/2

i hope this helps

The volume of the following rectangular prism is 27/2 units^3

We know that the rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism = Length X Width X Height

We are given the dimensions as Length = 5/2

Area = 27/5

Here a * h  because l * w = area.

Volume = Length X Width X Height

= area X Width

= 27/5 x 5/2

= 27/2

The volume is 27/2 units^3.

Learn more about a rectangular prism;

https://brainly.com/question/21308574

#SPJ2

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]

[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

Answer:

0.15x + 0.20y = 1.80

Step-by-step explanation:

Here, we are interested in writing an equation for the total cost of the apples and bananas

before we write , kindly understand that 100p = £1

So the cost of apple which is 15p will be 15/100 =£ 0.15

The cost of bananas which is 20p will be 20/100 = £0.2

Thus, the total cost of the apples bought will be number of apples bought * price of apple bought = 0.15 * x = £0.15x

The cost of bananas = number of bananas bought * price of bananas = 0.2 * y = £0.2y

So the total cost of the apples and bananas will be;

0.15x + 0.20y = 1.80

Answer:

Max would be 4y meters ahead by 4pm

Step-by-step explanation:

What we want to calculate here is the difference in the distance they have covered by 4pm given the speed at which they traveled.

Mathematically, distance = speed * time

The time is just the difference between 12 noon and 4pm which is 4 hours

Let’s tackle Max’s

He’s biking at x km/h, so the distance he would have covered by 4pm would be 4 * x = 4x meters

Now let’s tackle Sven

Sven is biking at a speed which is y mph less than Max’s x mph

Thus his speed would be (x-y) mph

His distance covered would be 4(x-y) meters

Now the difference between their bikes distance at 4pm would be;

4x - [4(x-y)]

= 4x -(4x -4y)

4x -4x + 4y

= 4y

Hence, Max would be 4y meters ahead by 4pm

Answer:

The temperature at 5376 ft is approximately 63°F

The assumption made was that the temperature varies linearly with elevation

Step-by-step explanation:

The parameters given are;

Temperature at 6288 feet = 56°F = 286.5

Temperature at 2041 feet = 87°F = 303.71

We are to find the temperature at 5376 feet

Let the temperature be the y-coordinate value and the elevation be the x-coordinate value, to find the temperature, we have the temperature gradient given by the relation;

[tex]m = \dfrac{y_2-y_1}{x_2 - x_1} = \dfrac{303.71-286.5}{2041 - 6288}= -4.05 \times 10^{-3} \ K/ft[/tex]

The temperature at 5376 ft will be the temperature at 2041 added to the decrease in temperature from climbing to 5376 ft

The increase in elevation is 5376 - 2041 = 3335 ft

The decrease in temperature = 3335 ft × (-4.05 × 10⁻³) K/ft = -13 .5 K

The temperature at 5376 ft will then be 303.71 - 13.5 = 290.196 K = 62.68°F ≈ 63°F

The assumption made was that the decrease in temperature with elevation is linear.

Answer:

L = 18 = hours worked by Lisa

a = 12 = hours worked by Abigail

Step-by-step explanation:

Given the following :

Abigail's earning = $20

Lisa's earning = $25

Last week :

Let number of hours worked by Abigail = a

Number of hours worked by Lisa = L

Total earning = $690

Total hours worked :

a + L = 30 - - - - (1)

To obtain their total earning:

(Lisa's earning per hour * hours worked) + (Abigail's earning per hour * hours worked)). $690

($25 * L) + ($20 * a) = $690

25L + 20a = 690 - - - - (2)

a + L = 30 - - - - (1)

25L + 20a = 690 - - - - (2)

L = 30 - a

25(30 - a) + 20a = 690

750 - 25a + 20a = 690

-5a = 690 - 750

-5a = - 60

a = 12

From (1)

a + L = 30 - - - - (1)

12 + L = 30

L = 30 - 12

L = 18

L = 18 = hours worked by Lisa

a = 12 = hours worked by Abigail

Answer: E. 1.561.

Step-by-step explanation:

Given, Total choices for each question =4

Probability that a particular answer is correct : p = [tex]\dfrac{1}{4}=0.25[/tex]

Sample size : n= 13

Formula for standard deviation: [tex]\sigma=\sqrt{np(1-p)}[/tex]

Put all values, we get

[tex]\sigma=\sqrt{13(0.25)(1-0.25)}=\sqrt{13(0.25)(0.75)}[/tex]

[tex]\sigma=\sqrt{2.4375}\approx1.561[/tex]

Hence, the standard deviation is 1.561.

So, the correct option is E.

Answer:

Step-by-step explanation:

you have the hypotenuse side and adjacent side, so you would use cosine (adj/hyp). since you are trying to find the angle, you use the inverse operation.

put it in the calculator and you should get 0.98176535657.

Answer: 17.75

Step-by-step explanation:

The interquartile range(IQR) is the 3rd quartile - the 1st quartile.

How to get quartiles:

First get the median:

3.5, 10.4, 16, 21.7, 27.7

10.4, 16, 21.7

16

Then find the median of the first half of data(3.5, 10.4)

(3.5+10.4)/2 = 6.95

Then find the median of the last half of data(21.7, 27.7)

(21.7+27.7)/2 = 24.7

Then to get the IQR subtract 6.95 from 24.7 to get 17.75

Hope it helps <3

Answer11.3

Step-by-step explanation:

Since there is an odd amount of values

find you lower median by taking the 3 lower numbers and using the middle number 10.4 (Q1)

then find your higher median with the 3 higher numbers and using the middle number 21.7 (Q3)

Then subtract Q3 - Q1

21.7-10.4 giving you the answer 11.3

Answer:

what are you going to do with that?