Solve the equation -2 =
k=
k+7
3

Step-by-step explanation:

complementary means together they are 90°.

x = 3y - 6

x + y = 90

(3y - 6) + y = 90

4y - 6 = 90

4y = 96

y (the smaller angle) = 24°

x (the larger angle) = 3y - 6 = 3×24 - 6 = 72 - 6 = 66°

Answer: B. 24

Step-by-step explanation:



Answer:

The slope would be [tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Answer:

-4/-5

Step-by-step explanation:

Remember the formula to slope:

(y2 - y1)/(x2-x1) given two points on the line that are (x1, y1) and (x2, y2).

The two points given on this line are: (2,2) from the top left and (-3,-2) from the bottom left. Let's say (2,2) = (x1, y1) and (-3,-2) = (x2, y2). Plug the points into the formula:

(-2 - 2)/(-3-2) = -4/-5

FINAL ANSWER: -4/-5

The numerical length and width of the rectangular picture are 9in and 12in respectively.

Area of a rectangle is expressed as;

A = length × width

Given the data in the question;

To determine the numerical length and width of the rectangular picture, first plug the given values into the equation and solve for x.

A = length × width

108 = (2x -1)(x+7)

Expand

108 = 2x² + 14x - 1x -7

108 = 2x² + 13x -7

Reorder

2x² + 13x -7 = 108

2x² + 13x - 7 - 108 = 0

2x² + 13x - 115 = 0

Solve by grouping

(x-5)(2x+23) = 0

x-5 = 0, 2x+23 = 0

x = 5, 2x = -23

x = 5, x = -23/2

x = 5, x = -11.5

But the dimension cannot be negative, hence;

x = 5

Next, determine the numerical length and width.

Length = 2x - 1 = 2(5) - 1 = 10 - 1 = 9in

Width = x + 7 = 5 + 7 = 12in

Therefore, the numerical length and width of the rectangular picture are 9in and 12in respectively.

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Answer:

b= p-(a+c)

Step-by-step explanation:

The error of interval for x will be [12.25, 12.35) for rounding off to 12.3 to 1 decimal place

In the given question, a number supposed to be 'x' is rounded off to the 1 decimal place, so that the number rounded off becomes 12.3. So, it is given that the number x is rounded off to 12.3 by 1 decimal place.

From this, we get that x should be greater than or equal to 12.25 and x should be smaller than 12.35. The equations will be :

     =>  x ≥ 12.25   and x < 12.35

So, the x lies between 12.25 and 12.35 which defines the error of interval for x.

Hence, the error of interval for x will be [12.25, 12.35)

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The probability that at least one of the births requires a cesarean delivery is 0.897.

To calculate prob(x >= 1):

prob(x>=1) = 1 - prob(x = 0)

                  = 1 - (1-0.248)^8

                  = 0.897

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Answer:

Flying Disc should be 72

Step-by-step explanation:

circumference = πd

HD Coin    C = 3π

                  9.42477796077

Flying Disc.  C = 23π
                      72.2566310326

Jar Lid      C = 8π

                  25.1327412287

Flower Pot     C = 15π

                        47.1238898038

Step-by-step explanation:

The absolute value of x is g(x)=f(x)+k.

Answer: 77 yd^2

Step-by-step explanation:

S=Area of Square. s=side length of square. w=width of rectangle

l=length of rectangle. R=Area of Rectangle

S=s^2

S=7^2

S=49 yd^2

R=l*w

R=9*14

R=126 yd^2

R-S=

126-49=77 yd^2

Answer: 3.32  

Step-by-step explanation:

√11=

3.3166=

3.3166=3.32      ==>When rounding to the hundredth place, if the thousandth's digit is 5 or greater, increase the hundredth's digit by 1.

set, in mathematics and logic, any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.

Let C=15, 16, 17, 18, and 19) and U=x | x is a full number and 0 x 19). Use the listing technique to write U U C.

UUC=

D U E = { 16, 18, 19, 20, 21 }

U stands for the union of sets.

We combine all of the components from the two groups.

16, 19, 21, and 16, 18, 19, 20 are the elements in sets D and E, respectively.

Therefore, we combine all of their components. The shared components of both sets are written just once.

As a result, there are 16, 18, 19, 20, and 21 elements in the set D U E.

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Answer:

y=-7/2

Step-by-step explanation:

1=|8-2y|

1=8+2y

-7=2y

2y=-7

y=-7/2

Answer: x=2

Step-by-step explanation:

x=z/4+7

x=z/4+3+4

x=(z/4+3)+4

x=-2+4

x=2

The coordinate of the pointed that represented the weighted average of A and B is: 1

Note that X = [x1w1 + x2w2 +.......xnwn]/w1+w2 +....wn

Where x is the numbers and w is the weight.

Given,

A = - 4  : Weight = 2

B= 3    : Weight = 5

Hence, average is given as;

([-4 x 2] + [3 x 5])/2+5

= (-8 + 15)/7

= 7/7

= 1

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Answer :  7.5 ft

Step-by-step explanation:

when the length of the shadow is 8ft, the actual height of the man = 5ft

8:5

let the giraffe be 'x' ft tall.

if the length of the shadow is 12ft, actual height = x ft

12:x

8:5 x 12:x

[tex]\frac{8}{5}[/tex] × [tex]\frac{12}{x}[/tex]

x= [tex]\frac{15}{2}[/tex]

x=7.5 ft

Therefore, the giraffe is 7.5ft tall.

Answer:

[tex]7.5\; {\rm ft}[/tex].

Step-by-step explanation:

The height of objects nearby under the sun are approximately proportional to the length of their shadows.

In other words, if the man and the giraffe are near each other and under the sun:

[tex]\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}[/tex].

Given that:

Rearrange the equation to find [tex](\text{height of giraffe})[/tex]:

[tex]\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})\times \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} \times \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}[/tex].

Answer:

37.9 units (nearest tenth)

Step-by-step explanation:

As ABCD is a rectangle, AD = BC and AB = DC.

Find the length of AD and AB using the distance formula.

[tex]\boxed{\begin{minipage}{7.5 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}}[/tex]

From inspection of the given diagram:

Therefore:

[tex]\begin{aligned}AD & =\sqrt{(x_D-x_A)^2+(y_D-y_A)^2}\\& =\sqrt{(-7-(-5))^2+(-3-(-9))^2}\\& =\sqrt{(-2)^2+(6)^2}\\& =\sqrt{4+36}\\& =\sqrt{40}\end{aligned}[/tex]

[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(7-(-5))^2+(-5-(-9))^2}\\& =\sqrt{(12)^2+(4)^2}\\& =\sqrt{144+16}\\& =\sqrt{160}\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = \sf 2(length + width)\\& = 2(AB+AD)\\& = 2(\sqrt{160}+\sqrt{40})\\& = 2(18.97366596...)\\& = 37.94733192...\\& = 37.9\: \sf units\:(nearest\:tenth)\end{aligned}[/tex]

Therefore, the perimeter of the rectangle ABCD is 37.9 units (nearest tenth).

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The gross income will be $5,800.

It is given that per month salary of an individual is $4000 and from a side job he makes $20 per hour for 10 hours a week for 4 weeks and rent he got is $1000.

We have to calculate the gross income.

What do you mean by gross income ?

Gross income refers to the total income of a person or business from all resources.

As per the question ;

Per month salary = $4000

Earning from side job is given $20 per hour for 10 hours a week for 4 weeks.

i.e.,

= 20 × 10 × 4

= $800 for 4 week

and

the rent they receive = $1000

So ;

The gross income will be ;

= 4000 + 800 + 1000

= $5,800

Thus , the gross income will be $5,800.

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The slope of Line 1 is m = -2

The slope of Line 2 is m = -2

For Line 1;

(x₁, y₁) = (1, 1);

(x₂, y₂) = (-2, 7);

m₁ = (7-1)/(-2-1) = -2;

For Line 2;

(x₃, y₃) = (-1, 4);

(x₄, y₄) = (1, 0);

m₂ = (4-0)/(-1-1) = -2;

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Step-by-step explanation:

the average change rate for a function g(x) is defined for an interval of x values as

(g(interval end) - g(interval begin))/(interval end - interval begin)

in our case that is

(g(2013) - g(2008))/(2013 - 2008) =

= (24 mil. - 186 mil)/5 = -162 mil./5 =

= -162,000,000 / 5 = -32,400,000

that means that as a mean value there were 32,400,000 digital cameras shipped less every year.

in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.

actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).

Answer:

[tex]\dfrac{7}{8} \textsf{ and } -\dfrac{5}{8}[/tex]

Step-by-step explanation:

To find numbers that are [tex]\dfrac{3}{4}[/tex] units distance from [tex]\displaystyle \dfrac{1}{8}[/tex] , add and subtract [tex]\dfrac{3}{4}[/tex] to and from [tex]\displaystyle \dfrac{1}{8}[/tex]

One of the points is at [tex]\displaystyle \dfrac{1}{8} + \dfrac{3}{4}[/tex] units away and the other at [tex]\displaystyle \dfrac{1}{8} - \dfrac{3}{4}[/tex] units away

Answer:

x^21/5

Step-by-step explanation:

To change this expression to an expression with a rational exponent, we need to change the radical to a rational (fractional) exponent. Just as square root is a one half power and cuberoot is a one-third power, a fifth root is a one-fifth power.

Once the radical is changed to a fraction, we will just use the exponent rule that says when you raise a power to a power, you multiply exponents.

see image.

Answer:

5 days.

Step-by-step explanation:

The food will last her 5 days.
[tex]3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}[/tex]
[tex]=1-\frac{5}{8}[/tex][tex]=\frac{3}{8}[/tex]

1) a + b = ?

→ (9i − 4j + 3k) + (6i − 9k)

→ 15i - 4j - 6k

2) 9a + 3b = ?

→ 9(9i − 4j + 3k) + 3(6i − 9k)

→ (81i - 36j + 27k) + (18i - 27k)

→ 99i - 36j

3) |a| = ?

→ |9i − 4j + 3k|

→ 9i + 4j + 3k

4) |a − b| = ?

→ |(9i − 4j + 3k) - (6i − 9k)|

→ |3i - 4j + 12k|

→ 3i + 4j + 12k

Answer:

[tex]a+b=15i-4j-6k[/tex]

[tex]9a+3b=99i-36j[/tex]

[tex]|a| = 9i+4j+3k[/tex]

[tex]|a-b| = 3i+4j+12k[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}a = 9i-4j+3k\\b=6i-9k\end{cases}[/tex]

[tex]\begin{aligned}a+b & = (9i-4j+3k)+(6i-9k)\\& = 9i-4j+3k+6i-9k\\& = 9i+6i-4j+3k-9k\\& = 15i-4j-6k\\\end{aligned}[/tex]

[tex]\begin{aligned}9a+3b & = 9(9i-4j+3k) + 3(6i-9k)\\& = 81i-36j+27k+ 18i-27k\\& = 81i+ 18i-36j+27k-27k\\& = 99i-36j\end{aligned}[/tex]

[tex]\begin{aligned}|a| & = |9i-4j+3k|\\& = 9i+4j+3k\end{aligned}[/tex]

[tex]\begin{aligned}|a-b| & = |(9i-4j+3k)-(6i-9k)|\\& = |9i-4j+3k-6i+9k|\\& = |9i-6i-4j+3k+9k|\\& = |3i-4j+12k|\\& = 3i+4j+12k\end{aligned}[/tex]

The approximate number of guests that were children are 172 and adults are 278

From the complete question, we have the following system of equations

25x + 12y = 9014

x + y = 450

Make y the subject in x + y = 450

y = 450 -x

Substitute y = 450 - x in 25x + 12y = 9014

25x + 12(450 - x) = 9014

Expand the expression

25x + 5400 - 12x = 9014

Evaluate the like terms

13x = 3614

Divide both sides by 12

x = 278

Substitute x = 278 in y = 450 -x

y = 450 - 278

Evaluate

y = 172

Hence, the approximate number of guests that were children are 172 and adults are 278

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Answer:

x = 7, y = 45

Step-by-step explanation:

[tex]7x+13=6x+20[/tex]

[tex]x=20-13\\x=7[/tex]

Angle

[tex]7(7)+13=49+13=62^{0}[/tex]

supplementary angle

180 - 62 = 118°

[tex]3y-17=118[/tex]

[tex]y=\frac{118+17}{3} =135/3=45[/tex]

Hope this helps

Answer:

The length should equal 27.

The width should equal 13.

A: P= 2L+ 2W

B: L=2W+1

Step-by-step explanation:

Perimeter is always equal to all of the sides added up.

You can find out the width and length by subsititution.

80=2(2W+1) +2W

80=4W+2+2W

80=6W+2

78=6W

W=13

L=(13*2)+1

L=27

Answer: $52 is your new balance

Step-by-step explanation: -12+60=52