The length of a rectangle is twice as long as the width. If the diagonal length of the rectangle
is 60 cm, what is the perimeter of the rectangle (to the nearest centimetre)?
Provide a complete algebraic solution, including a supporting diagram.
I

Answer:

Option (1)

Step-by-step explanation:

System of equations has been given as

2x + 6y = 14

By dividing this equation by 2

x + 3y = 7 --------(1)

Second equation is,

-2x + 2y = -10

-x + y = -5 -------(2)

By adding equation (1) and equation (2)

(x + 3y) + (-x + y) = 7 - 5

2x = 2

x = 1

By putting x = 1 in the equation (1)

1 + 3y = 7

3y = 6

y = 2

So, we get exactly one solution pair (1, 2) where these lines are intersecting.

Therefore, the best category that defines the system of equations is Consistent/Independent

Option (1) will be the answer.

The actual pressure when the gauge shows 33.58 would be 36.5.

Used the concept of the percentage that states,

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating the hundredth part of any quantity is called a percentage.

Given that,

Ali's tire pressure gauge shows a reading which is [tex]8 \%[/tex]lower than the actual pressure.

And, the gauge shows [tex]33.58.[/tex]

Let us assume that,

The actual pressure of Ali's tires = x

Hence, we can formulate the equation,

[tex]x \times (1 - 8\%) = 33.58[/tex]

Solve the equation for x,

[tex]x \times (1 - \dfrac{8}{100} ) = 33.58[/tex]

[tex]x \times (1 - 0.08) = 33.58[/tex]

[tex]x \times 0.92 = 33.58[/tex]

Divide both sides by 0.92;

[tex]x= \dfrac{33.58}{0.92}[/tex]

[tex]x = 36.5[/tex]

Therefore, The actual pressure of Ali's tires = 36.5

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The complete question is,

Ali's tire pressure gauge shows a reading which is 8% lower than the actual pressure.

What is the actual pressure of Ali's tires when the gauge shows 33.58?

Answer: x>-2

Step-by-step explanation:

To find the values of the inequality, you treat this like it would be any other equation.

[tex]-3x<6[/tex]

[tex]x>-2[/tex]

Answer:

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Step-by-step explanation:

For this case we want to determine if mean running time has increased as a result of the new change so then the system of hypothesis are given by:

Note: we assume that the value to check in order to be consistent with the options is 8.3

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Answer:

x = 0, 4/5

Step-by-step explanation:

The zero-product property states that if the product of a and b is zero, then either a = 0, b = 0, or both terms equal zero

Answer:

[tex](3x+1)^2[/tex]

Step-by-step explanation:

[tex]9x^2+6x+1=\\(3x+1)^2[/tex]

You can confirm this by working and expanding backwards:

[tex](3x+1)^2=\\(3x+1)(3x+1)=\\9x^2+3x+3x+1=\\9x^2+6x+1[/tex]

Hope this helps!

The factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

To find the factorized form of the quadratic expression 9x² + 6x + 1 is (3x + 1)², we can expand the factorized form and compare it with the given expression to check if they are equal.

Expanding (3x + 1)² using the square of a binomial formula, we get:

9x² + 6x + 1

= 9x² + 3x + 3x + 1

= 3x (3x + 1) + 1 (3x + 1)

(3x + 1)² = (3x + 1)(3x + 1)

Comparing the expanded form of (3x + 1)² with the given expression 9x² + 6x + 1, we can see that they are equal.

Therefore, we have found that the factorized form of 9x² + 6x + 1 is indeed (3x + 1)².

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The general form for the equation of a line is:

[tex]y = mx + c[/tex]

Where:

m is the gradient of the line

c is the y intercept of the line  (y - intercept is where the graph crosses the y-axis)

So if you had the following equation:

[tex]y = 3x + 2[/tex]

Then:

m = 3

c = 2

So gradient = 3, and y intercept = 2

---------------------------------------------------

Rearranging

So first rearrange both of the equations in the form y = mx + c :

[tex]3x + 2y = -1[/tex]   becomes  [tex]y = -\frac{3}{2} x-\frac{1}{2}[/tex]      [tex](where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )[/tex]

and:

[tex]2x+7y=2[/tex]  becomes  [tex]y=-\frac{2}{7}x +\frac{2}{7}[/tex]     [tex](where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})[/tex]

---------------------------------------------

The question tells us that the equation of the line we are looking for has the same y-intercept as:

[tex]2x+7y=2[/tex]

So the line we are trying to work out will also have a y intercept of   [tex]\frac{2}{7}[/tex]

(refer to rearranging)

----------------------------

The question also tells us that the line is perpendicular to  [tex]3x + 2y = -1[/tex]

Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.

So the gradient of the new line will be the  negative reciprocal of the gradient of  [tex]3x + 2y = -1[/tex]

Gradient of  [tex]3x + 2y = -1[/tex]  is: [tex]-\frac{3}{2}[/tex]

(refer to rearranging)

Gradient of new line: = negative reciprocal of  [tex]-\frac{3}{2}[/tex] , which is  [tex]\frac{2}{3}[/tex]

(just flip fraction and change the sign)

------------------------------------

So for the new line: [tex]m = \frac{2}{3} \ and, \ c = \frac{2}{7}[/tex]

So just substitute in the values for m and c into: y = mx + c

[tex]y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}[/tex]

-----------------------------

Answer:

So equation of the new line is:

[tex]y = \frac{2}{3}x + \frac{2}{7}[/tex]

------------

Any questions, just ask.

Answer:

 4π cm

Step-by-step explanation:

The length of an arc of a circle with radius r and central angle θ is given by ...

  s = rθ

where θ is in radians.

Here, your arc measures 60° = π/3 radians, so the arc length is ...

  s = (12 cm)(π/3) = 4π cm

Answer:

Option D

Step-by-step explanation:

The response variable is also known as the dependent variable. It depends on another factor which is the independent variable to cause change/ response to it.

In this study, they want to test if an increase in the number of Math workshop which is the independent variable will cause a change in the final exam scores which is the dependent variable. The response to this inquiry is thus the final exam score which is also known as the response variable.

Answer:[tex]8.75\ m^2[/tex]

Step-by-step explanation:

Given

Area of circle is [tex]A=45\ m^2[/tex]

Arc measure [tex]\theta =70^{\circ}[/tex]

and area of sector is given by

[tex]\Rightarrow \frac{\theta }{360^{\circ}}\times \text{Area of circle}[/tex]

[tex]\Rightarrow \frac{70}{360}\times 45[/tex]

[tex]\Rightarrow 0.194\times 45[/tex]

[tex]\Rightarrow 8.75\ m^2[/tex]

So, area of sector is [tex]8.75\ m^2[/tex]

Answer: $58.33

Step-by-step explanation:

Yes, Sasha is correct. The mean amount she makes is in a day.

Answer:

a: Yes, Sasha is correct. The mean amount she makes is $58.33 in a day

Step-by-step explanation:

edg2020

Answer:

  straight angle

Step-by-step explanation:

A straight angle is one whose measure is 180°. Its formative rays point in opposite directions from the vertex and make a straight line.

Answer:

I think it's 462. I'm sry if I'm wrong.

Rise over run. Or I believe. Like If I chose (-1,2) and (0,-1)  the rise or in this case since the line is going down, if I move down 4 units. I am one unit to the left of (0,-1) so 4/1 so rise/run

The equation of the line is y+2x+1 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

Line intersect x-axis at -1/2

And intersect y-axis at -1

The points are (-1/2,0) and (0,-1)

The slope of the line m = -1-0/(0-(-1/2)) = -2

The required equation of the line that passes through the point (-1/2,0) and slope is -2,

y-0 = -2(x-(-1/2))

⇒y=-2x-1

⇒y+2x+1 = 0

The equation of the line is y+2x+1 = 0.

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Answer:

Step-by-step explanation:

This is a test of 2 population proportions. Let 1 and 2 be the subscript for the occupants not wearing seat belts and occupants wearing seat belts. The population proportion of occupants not wearing seat belts and occupants wearing seat belts would be p1 and p2 respectively.

P1 - P2 = difference in the proportion of occupants not wearing seat belts and occupants wearing seat belts.

The null hypothesis is

H0 : p1 = p2

p1 - p2 = 0

The alternative hypothesis is

Ha : p1 > p2

p1 - p2 > 0

it is a right tailed test

Sample proportion = x/n

Where

x represents number of success

n represents number of samples.

For occupants not wearing seat belts,

x1 = 31

n1 = 2823

P1 = 31/2823 = 0.011

For occupants wearing seat belts,

x2 = 16

n2 = 7765

P2 = 16/7765 = 0.0021

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (31 + 16)/(2823 + 7765) = 0.0044

1 - pc = 1 - 0.0044 = 0.9956

z = (P1 - P2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.011 - 0.0021)/√(0.0044)(0.9956)(1/2823 + 1/7765) = - 0.0089/0.00145462023

z = 6.81

From the normal distribution table,

p < 0.00001

0.00001 < 0.05, we would reject the null hypothesis.

Therefore,

b. Since p <α, we conclude that this data shows that seat belts are effective in reducing fatalities

As far as I'm concerned, it still exists

What do you mean becauae nothing happened

Answer:

8

Step-by-step explanation: because its even

Answer:

Yes.

Step-by-step explanation:

Answer:

si

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

The probability of rolling an odd number is 3/6, which is 1/2

The probability of rolling a factor of 12 is 5/6 (1,2,3,4,6)

1/2 x 5/6 = 5/12

Answer:

120

Step-by-step explanation:

Answer:

Step-by-step explanation:espinal hola defryet iSight x0 do hulp

Answer:

(x-1)^2= -0.5

Step-by-step explanation:

I DID THE USA TEST PREP AND THIS ANSWER WAS CORRECT

Answer:

  A.  A horizontal shift to the right 7.5 units

Step-by-step explanation:

Replacing x with x-7.5 shifts the graph 7.5 units to the right.

__

In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.

Answer:

A. 40 degree+ 90 degree = x

The sum of the angles = 130 degree

Step-by-step explanation:

[tex]Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x[/tex]

x = 130 degree

sry my mistake wrong quesrion

Answer: Hot Dog $1.50 Drinks $2.00

Step-by-step explanation:

Answer:

17, 23

Step-by-step explanation:

First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do [tex]\sqrt{(-7-8)^2+(-1-7)^2}[/tex] which gives us 17. Therefore, the radius of the circle is 17 units.

Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be [tex](x+7)^{2} +(y-8)^{2}=289[/tex]. Now we can plug in -15 for x and solve for y. So now we have [tex](-15+7)^{2} +(y-8)^{2}=289[/tex].

Simplifying the equation we have [tex](8)^{2} +(y-8)^{2}=289[/tex]. Subract [tex]8^{2}[/tex] from 289 and now the equation is [tex](y-8)^{2}=225[/tex]. Square root both sides to get [tex]y-8=15[/tex]. We solve for y to get 23. Therefore, the point is (-15, 23).

Answer:

Well, the answer would be 17,23 Also i had the same question as you so i already know the answer

Answer:

Can you answer mine? I willl answer yours

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

So the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex]

r = 3

h = 7

[tex]9\pi *\frac{7}{3} = 21\pi[/tex]

[tex]\frac{22}{7} *21=66[/tex]