solve using completing the square.

[tex] {x}^{2} + 2x - 15 = 0[/tex]
​

The side x of the rectangle is 36.0 cm

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

All four angles of a rectangle are right angles.

The diagonal of a rectangle are equal in length to each other and they bisect each other at there point of intersection.

Therefore,

∠ COD = 48°

∠OCD = ∠ODC = 132 / 2 = 66°

Using sin law

OD / sin 66  = 16 / sin 48

OD sin 48 = 16 sin 66

OD =  16 sin 66 / sin 48

OD = 14.6167273223 / 0.74314482547

OD = 19.6687105931

OD = 19.7 cm

∠AOD = 180 - 48

∠AOD = 132°

∠OAD = ∠ODA = 48 / 2 = 24°

Hence, using sine law let's find x

19.7 / sin 24 = x / sin 132

x sin 24 = 19.7 sin 132

x = 19.7 sin 132 / sin 24

x = 14.6399530619 / 0.40673664307

x = 35.9935605802

Therefore,

x = 36.0 cm

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Answer: 11

Step-by-step explanation:

The sum of the angles of a triangle is 180. So, 3x + 8 + 4x + 11 + 84 = 180

7x = 180 - 8 - 11 - 84

7x = 77

x = 11

Answer:

9.043

Step-by-step explanation:

i just divide

Answer: 9.043 centimeters/grams

Step-by-step explanation:

All you have to do it divide!

The stem-and-leaf diagram is:

Stem   Leaf

0          9

1           0,  5, 5, 8      

2          1, 4, 8      

3             0, 3, 5, 6, 6      

4             2, 3, 4, 5, 5, 6, 7, 7, 8    

5               1, 4, 5, 6, 8, 8, 8, 8, 9, 9, 9, 9,9,9      

The mode is 59

The range is 50

The median is 45.50

The interquartile range is 6.5.

A stem-and-leaf plot is a table that is used to display numerical data.  A  stem-and-leaf plot has two column, one for the stem and the other for the leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 59, 5 would be the stem and 9 would be the leaf.

Mode is the number that occurs most frequently in a dataset. The mode is 59 because it appears 6 times in the dataset.

Range is the difference between the highest number and the lowest number

Range = 59 - 9 = 50

Median is the number at the center of the dataset.

Median = (n + 1) / 2

37 / 2 = 18.5th term = (45 + 46) / 2 = 45.5

The interquartile range is the difference between the third quartile and the first quartile.

Third quartile = 3/4(n + 1)

3 / 4 x 37 = 27.75 term = 58

First quartile = 1/4 x (n + 1)

1/4 x 37 = 9.25term = (50 + 53) / 2 = 51.5

Interquartile range = 58 - 51.5 = 6.5

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The combination of number tiles resulting in -1 will be -4 + 3 and 2 - 3.

From the information, Huyen has round tiles and she must combine the positive and negative signs on the tiles to obtain a result equivalent to -1.

It should be noted that sone of the examples of the numbers that will give a value of -1 include:

= -4 + 3

= -1

= 2 - 3.

= -1

Note that an overview was given since you don't given enough information as options.

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Answer:

The distance between (-6, 4) and (-8, 6) is 4 units.

Step-by-step explanation:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\AB = \sqrt{(-8+6)^2+(6-4)^2}\\AB = \sqrt{(-2)^2+(2)^2}\\AB = \sqrt{16}\\AB = 4[/tex]

Just apply the distance formula, quite simple.

Answer: this is just the first one

y = -3.5x + 2

subtract the 7x from both sides to get 2y = -7x + 4

divide by 2 to get rid of the 2 so you get y = -3.5 + 2

For the third the mistake was adding 3.

You're meant to subtract the 10x from both sides to get -3y = -10x + 6

Divide everything by -3 to get y = 3.3 - 2

Answer:

-6x-18

Step-by-step explanation:

in class

Answer:-24

Step-by-step explanation: you do -6(x)+(-6)(3) and u get -6+-18 and get -24 hope it helps .

3x + 4y = 25 is an example of a line that is parallel to the supplied line.

Equations are mathematical expressions that have two algebraic expression on either side of an equals (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left hand side = right hand side) is a fundamental mathematical formula. For an unknown quantity represented by an unknown variable, equations can be solved to determine its value. It is clear that a statement is not an equation if there is no "equal to" sign in it. The phrase will be regarded as an expression.

Given that : line that is parallel to the line 3x + 4y = 32 and contains

the point (7,1).

3x + 4y = 32 is the equation for given line

This type of line is called a slope intercept. The line has a slope of m=[tex]\frac{-3}{4}[/tex].

The slope of parallel lines is equal. As a result, all lines with slope m=[tex]\frac{-3}{4}[/tex].will be perpendicular to one another.

3x + 4y = 25 is an example of a line that is parallel to the supplied line.

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Answer:

12 hours

Step-by-step explanation:

look it up

The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.

The given question is solved using the unitary method.

The arts academy requires 4 teacher for every 68 students

The arts academy requires 1 teacher for every 68/4 students

The arts academy requires 1 teacher for every 17 students

The academy has 17 students per teacher

It requires 3 tutors for every 36 students

3 tutor = 36 student

1 tutor = 36 /3 = 12 students

The academy has 12 students per tutor

For 72 students the total number of tutor required are 72/12 = 6

The number of students per teacher is 17 and per tutor is 12. For 72 students the academy needs 6 tutors.

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Since the population increases at a rate proportional to the current number of people, the population will be three times of its initial population after 14.27 years.

The population of a community increases at a rate proportional to the number of people present at time t, means:

dP/dt = kP

where k is a constant.

Rearrange it:

(1/P) dP = k dt

Take the integral:

∫ (1/P) dP = ∫ k dt

ln P = kt + C, where C is a constant

Substitute t = 0, from the problem, it is known that P(t = 0) = P₀

Hence,

P(t) = P₀. e^(kt)

The population doubles after 9 years, means if we substitute t = 9

P(9) = P₀. e^(9k)

2P₀ = P₀. e^(9k)

2 = e^(9k)

Take the natural logarithmic:

ln 2 = 9k

k = (ln 2)/9 = 0.077

When the population grows to triple, it means P(t) = 3P₀

3P₀ = P₀. e^(kt)

ln 3 = kt

ln 3 = 0.077 t

t = (ln 3)/0.077 = 14.27 years.

Hence, the population will be three times of its initial population after 14.27 years.

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Answer:

-7

Step-by-step explanation:

2(-9)+5=-7

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{xy + 5}\\\mathsf{= 2(-6) + 5}\\\mathsf{= -12 + 5}\\\mathsf{= -7}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

a) 7 video games;

26 - x = 40 - 3x

x = 7

The formula for y in terms of x is y = 8/x^3 and x is 1/2 when y = 64

The variation statement is given as

y is inversely proportional to the cube of x

This means that

y = k/x^3

Where k represents the constant of variation

Using the points on the table, we have

(x, y) = (1, 8)

This gives

8 = k/1^3

Evaluate

k = 8

So, we have

y = 8/x^3

Here, we have

y = 64 and y = 8/x^3

This gives

8/x^3 = 64

So, we have

x^3 = 1/8

Take the cube roots

x = 1/2

Hence, the value of x is 1/2

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It will take 3 days for the cost of the car to be the same which is $740.

So,

Ben's car rental:

Dave's car rental:

Now,

Days after which the cost will be the same:

Day 1:

Day 2:

Day 3:

Therefore, it will take 3 days for the cost of the car to be the same.

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Consequently, there exist four numbers z:

√3/2 ± I 1/2

-√3/2 ± I 1/2

The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z

=(z^2-e^±iπ/3)z=0⟺z=0

or z^2=e^±iπ/3

Since we have z[tex]\neq[/tex]0, z=e^±iπ/6= ±(√3/2 ± I 1/2  )

There are thus four numbers in z:

√3/2 ± I 1/2

-√3/2 ± I 1/2

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The number of smaller squares that can fit inside a larger square with a side length of 31 units is A. 961 smaller squares if the larger square is a plane.

A side length is one part of the length of an object.

Determining the number of smaller squares in a larger square depends on if the square is an enclosure or a plane.

If the square object is an enclosure, then it has three dimensions, length, width, and height, which are squared.  In that case, the number of smaller squares will be 29,791.

But if the square object is a plane with two dimensions, the number of smaller squares is 961.

Side length = 31 units

Area of a square plane = 961 unit² (31 x 31)

Volume of a square enclosure = 29,791 unit³ (31 x 31 x 31)

Thus, the number of smaller squares depends on the dimensions of the larger square.

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As per the direct variation formula, it take  11 hours : 6 minutes : 36 seconds to earn $25,000 for the restaurant.

Direct variation:

Direct Variation is said to be the relationship between two variables in which one is a constant multiple of the other.

Direct variation equation: y = kx

Given,

A local fast food restaurant takes in $9000 in a 4 hours period. Write a direct variation equation for the relationship income and number of hours.

Here we need to estimate how many hours it would take the restaurant to earn $25,000.

a) Let us consider income (I) directly varies to number of hours (h) where k is the constant of variation.

I = kh   ⇒  Direct variation equation

Solve for k:

9,000 = (k)(4)

k = 9,000/4

k = 2,250

b) When income (I) = 25,000, find the number of hours:

I = kh

25,000 = (2,250) (h)

h = 25,000/2,250

h = 11.11

It will take approximately 11 hours : 6 minutes : 36 seconds for the restaurant to earn $25,000.

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Answer:

3. two places to the right of zero

Step-by-step explanation:

-3 + 5 = 2. On a graph, you always move right along the x axis for positive numbers, and left for negative numbers.

Answer: y= -2x+5

Step-by-step explanation:

The figure that is shaded here has the quadrant and the sector as the two parts that it has.

The area of the shaded is given as (πr²) / 4 - bh/2

We have ACD as the sector of the circle.

such that we can see that the arc of AC is the quadrant of the circle nad it has the line at point o.

We would solve the area of the shaded as:

the area of a circle / 4 - the area of the triangle

this is mathematically written as

πr²/4 - 1/2bh

where

b = base

h = height

r = radius

This is the area of the shaded

An isosceles traingle would be formed when < A = < C = x

AO is equal to radius of the circle equal to the height CO

mathematically,

< A = < C = x

180 - 90 = 90 / 2

x = 45 degrees

We have to find the area of the sector

This is

= ∅/360 * πr²  

= (45 / 360) * (πr²)

= (πr²) / 4

From the calculation we have here, we would see that

the area of the shaded is  area of sector - area of the right angle triangle

= (πr²) / 4 - bh/2

When we go on to compare the sides we would then find out that they are equal. Therefore the shaded quadrant equals to the shaded sector.

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Answer:

n x 2 + 3 = n x 4 + 11

Step-by-step explanation:

n x 2 ("two times a number) + 3 ("increased by three") = ("is equal to") n x 4 ("four times the same number") + 11 ("increased by eleven")

well, let's check how much is 30% of £158.80

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 158.80}}{\left( \cfrac{30}{100} \right)158.80}\implies 47.64~\hfill \underset{ticket~price}{\stackrel{158.8~~ - ~~47.64}{\text{\LARGE \pounds 111.16}}}[/tex]

To know how much each chocolate bar costs, knowing that ten chocolate bars cost 3 pesos, we only have to divide the total cost of the 10 chocolate bars by the total number of chocolate bars.

So that:

Tenth that; the cost of each bar is 0.3 pesos.

Answer:

When multiplying whole numbers by 10, simply add a 0 to the end of the number

When dividing by 10 remove a 0 from the end of the number.

Step-by-step explanation:

Multiplication:

10 x 2 = 20

10 x 6970 = 69750

Division

20 / 10 = 2

6970 / 10 = 697

Hope this helps! :)

the more compact hospital. The Law of Large Numbers, which makes intuitive sense, states that when there are more observations, the experimental average tends to approach the true proportion. Large hospitals have more observations, therefore their results are less likely to deviate from 50% or have a wide range of results.

An equation that states that two ratios are equal is a genuine proportion. You can utilise information about one ratio in a proportion to determine values in the other equal ratio.

The sample proportion, p′ = 0.842, which is the point estimate of the population proportion, must be determined in order to calculate the confidence interval. Given that CL = 0.95 is the requested confidence level, = 1 - CL = 1 - 0.95 = 0.05 ( 2) ( 2) follows..

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