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A photographer needs a frame for an 8 x 10 inch picture, such that the total area is 168 in2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?

Answer:

x= ½, y= 7

Step-by-step explanation:

[tex]\textcolor{steelblue}{\text{\textcircled{1} Label the equations}}[/tex]

6x -y= -4 -----(1)

2x +2y= 15 -----(2)

[tex]\textcolor{steelblue}{\text{\textcircled{2} Make y the subject of formula}}[/tex]

We could also make x the subject of formula in one equation, however the equation can be easily rearranged so that the coefficient of y is 1. This can be done by moving the y term to the right hand side of the equation, and the rest to the left. Note that each time you bring a term or constant over to the other side of the equation, its sign changes (e.g. positive to negative).

From (1):

6x +4= y

y= 6x +4 -----(3)

Label the equation as equation (3) so we can refer to it easily later.

[tex]\textcolor{steelblue}{\text{\textcircled{3} Substitute (3) into (2)}}[/tex]

Now that we have an equation of y that is written in terms of x, we can replace all the y in equation (2) so that the whole equation is only in terms of x.

Subst. (3) into (2):

2x +2(6x +4)= 15

Expand:

2x +12x +8= 15

Simplify:

14x +8= 15

14x= 15 -8

14x= 7

x= 7 ÷14

x= ½

[tex]\textcolor{steelblue}{\text{\textcircled{4} Find y}}[/tex]

Substitute x= ½ into (3):

y= 6(½) +4

y= 3 +4

y= 7

About the minus sign with 16, square root of -1 is an imaginary number i(iota). Also we know that square root of -16 will be multiplication of square root of -1 and square root of 16. So the final answer becomes, + or - 4i. Hope this helps

The z-statistic is 1. 68, so the null hypothesis cannot be rejected.

The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches.

To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years.

Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches.

Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches.

To compute for the z-score,

we have z-score = (x – μ) / (σ / √n)

where x is the computed/measured value,

μ is the expected mean, σ is the standard deviation,

and n is the number of samples.

Using the information we have,

z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68

In order to reject the null hyptohesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05.

Hence The z-statistic is 1. 68, so the null hypothesis cannot be rejected.

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Answer:

B. The z-statistic is 1.68, so the null hypothesis cannot be rejected.

Step-by-step explanation:

edg 22, got 100 on unit test

Answer:

Area of a rectangle

A = lw

‎[tex] \qquad\quad\hookrightarrow{\sf { 1000(e-1)}}[/tex]

[tex] \begin{aligned}&\longrightarrow \int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e ^{x - |x| }dx \\ \\ &\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999} \int_{k}^{k + 1}e^{x - k}dx \\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^{999}e^{x - k \big |_{k}^ {k + 1}} \\ \\& \longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = \sum_{k = 0}^ {999}(e - 1)\\\\&\longrightarrow\int_{0} ^{1000} {e}^{ - |x| }dx = 1000(e - 1)\end{aligned}[/tex]

Answer:

96

Step-by-step explanation:

L=6

W=2

H=8

LxWxH=8x6x2=96

8x6=48

48x2=96

Answer:

76

Step-by-step explanation:

the answer is 76 because I took the test

The length of the ribbon needed to cross from one corner of the rectangle to the other corner is 7 1/2 feet.

The length of the ribbon needed can be determined using the Pythagoras theorem.

The Pythagoras theorem: a² + b² = c²

where

a = length

b = base

c = hypotenuse

√4.5² + 6²

√36 + 20.25 = 7.5 feet

To learn more about Pythagoras theorem, please check: https://brainly.com/question/14580675

Answer:

true

Step-by-step explanation:

Answer:

150 cm^2

Step-by-step explanation:

A cube has 6 surfaces

Each surface square = 5 by 5

So.....

5 x 5 (or 25) times 6

25 x 6 = 150

Hope this helps!

The final statement is: The rate of interest is 7% and simple interest is $12.60

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Principal =$180 And amount after one year=$192.60

Therefore simple interest= 192.60-180

                                          =12.60

∴12.60=180×r×1/100

 r=7%

Hence, The rate of interest is 7% and simple interest is $12.60

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Answer:

C

Step-by-step explanation:

Givens

You are given 2 tangent lines.

You are also given a 4 sided figure.

All 4 sided figures have 360 degrees

A radius meets a tangent at 90 degrees

Formula

<BDA + <DCA + <BCA + <BDC = 360

Solution

90 + 90 +40 + <BDC = 360               Combine

220 + <BDC = 360                             Subtract 220 from both sides

220- 220 +BDC =360 - 220

<BDC = 140

Answer: C

Answer:

Step-by-step explanation:

5x^2 - 125 factors into 5 (x^2 - 25)

x^2 - 25 factors into  (x + 5)(x - 5)

So the answer to this part is 5(x + 5)(x - 5)

x^2 -  10x + 25 factors into

(x - 5)(x - 5)

So the HCF is (x - 5)

Answer:

  (d)  as a triangle, a rectangle, and a semicircle

Step-by-step explanation:

The description of the shape tells you how to decompose it. The shape is described as a semicircle, a rectangle, and a triangle. The appropriate decomposition is ...

  as a triangle, a rectangle, and a semicircle

Answer:

d

Step-by-step explanation:

Answer:

m = 4

Step-by-step explanation:

(80, 40) and (90, 80)

40/10= 4

Answer:

4

Step-by-step explanation:

choose two points

I chose (80,40) and (90,80)

(80-40)÷(90-80)

40/10

4

Answer:

0.125 = ⅛

Step-by-step explanation:

Both are equal.......

Answer:

divide the number of pages by the time

Step-by-step explanation:

=50/40

=5/4

= 1.25/per minute

Answer:

$279

Step-by-step explanation:

10% off $310 is $31

310-31 is 279

Answer: the sale price of the suit is $279 or $31 dollars off

Step-by-step explanation:

$310 x 0.10= $31

$310 - $31= $279

Answer:  (x + 4)(x + 4)

                x² + 8x + 16

                x² + 4x + 4x + 16                

Step-by-step explanation:

See the image below.

Answer:

100 quarters = 2500 cents = $25

500 dimes = 5000 cents = $50

total = $75

Step-by-step explanation:

Using the z-distribution, as we are working with a proportion, it is found that the buyers need a sample of 1505.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is z = 2.327.

There is no estimate of the percentage, hence [tex]\pi = 0.5[/tex], and the margin of error is of M = 0.03, hence we solve for n to find the desired sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 2.327\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.03\sqrt{n} = 2.327(0.5)[/tex]

[tex]\sqrt{n} = \frac{2.327(0.5)}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{2.327(0.5)}{0.03}\right)^2[/tex]

[tex]n = 1504.2[/tex]

Rounding up, the buyers need a sample of 1505.

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Answer:

surface area of cylinder is 126cm²

Step-by-step explanation:

Height of a cylinder is 8cm

Radius of a cylinder is 2cm

surface area = ?

surface area of cylinder= 2πr(r + h)

=2×22/7×2(2+8)

=44/7×2(10)

=44/7×20

=880/7

=125.71

A = 2πrh + 2πr² π=3.14

Answer:

I think answer C

Step-by-step explanation:

You can display how many toothbrushes were distributed each month on the dot plot :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

0.5

Step-by-step explanation:

0.5

I guess i am 70% sure

Answer:

6 carnations

Step-by-step explanation:

0.5x +15 = 3x

x = 6

perimeter = turn of the figure

P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36

the triangle has 2 équal sides => isosceles

and 1 angle is 60° so the triangle is equilateral

The amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the percentage symbol '%'.

Miki, a resident of kyoto, earns an annual salary of ¥6,760,950. The Japanese government levies a 29.12% income tax on miki’s tax bracket.

The amount of tax Miki pay to the government as income tax is,

[tex]I=\dfrac{29.12}{100}\times6760950\\I=1968788.64[/tex]

Miki, earns an annual salary of ¥6,760,950. Thus, her yearly take-home pay after the deduction of income tax is,

[tex]M=6760950-1968788.64\\M=4792161.36\\M\approx4792161[/tex]

Thus, the amount of yearly take-home pay of Miki, a resident of Kyoto after the payment of income tax is ¥4,792,161.

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Answer:

A

Step-by-step explanation:

:) good luck

The figure below is composed of eight circles, seven small circles and one large circle containing them all. Neighboring circles only share one point, and two regions between the smaller circles have been shaded. Each small circle has a radius of 5 cm.