What is the golden rule for solving an equation?

Answer:

 3 hours

Step-by-step explanation:

Hours/Lawn = (1/5 h)/(1/15 lawn) = 15/5 h/lawn = 3 h/lawn

It will take the sprinkler 3 hours to water the lawn.

Answer:

3 hours 100%

Step-by-step explanation:

Answer:

y = 5x - 39

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 5, hence

y = 5x + c ← is the partial equation

To find c substitute (8, 1) into the partial equation

1 = 40 + c ⇒ c = 1 - 40 = - 39

y = 5x - 39 ← equation of line

To write the equation of a line, we will use the slope-intercept form of the equation of a line, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept of the line.
Given the point (8, 1) through which the line passes, and the slope \( m = 5 \), we will plug these values into the equation to find \( b \).
The coordinates of the point give us values for \( x \) and \( y \); specifically, \( x = 8 \) and \( y = 1 \). Using these, we can substitute into the slope-intercept formula:
\[ 1 = 5(8) + b \]
This simplifies to:
\[ 1 = 40 + b \]
To find \( b \), we'll isolate it on one side:
\[ b = 1 - 40 \]
\[ b = -39 \]
Now that we have \( b \), we can write the equation of the line with the given slope \( m \) and y-intercept \( b \):
\[ y = 5x - 39 \]
So the equation of the line that passes through the point (8, 1) with a slope of 5 is:
\[ y = 5x - 39 \]

Answer: 120 people

Step-by-step explanation: To do this problem, you want to find common denominators. The lowest common denominator is 900. So to get the denominator to 900 from 30, multiply it by 30. 30 x 30=900. Multiply 4 by 30. 4 x 30=120. Another way to do this is to set up a proportion. It would be 4/30=x/900. Cross multiply and solve for x. 3600=30x. X=120.

Answer:

Step-by-step explanation:

In each parallelogram opposite sides have the same length.

Therefore we have the equations:

2x - 4 = x + 12 and 3y - 2 = y + 6

2x - 4 = x + 12         add 4 to both sides

2x = x + 16         subtract x from both sides

x = 16

3y - 2 = y + 6            add 2 to both sides

3y = y + 8           subtract y from both sides

2y = 8            divide both sides by 2

y = 4

AB = 3y - 2 → AB = 3(4) - 2 = 12 - 2 = 10

BC = x + 12 → BC = 16 + 12 = 28

Answer:

D

Step-by-step explanation:

Answer:

1) false

2) true

3) true

4) false

5) -0.75 > - 0.5 false

6) 0.625 < 0.875 true

Step-by-step explanation:

7) July 10, 1913 - - > 134°

January 23, 1971 - - > - 80°

134 ___ - 80

134 > - 80

-80 represents the smaller value

Answer:

A = 95.03in² or 95.03 ( rounded to the nearest hundredth )

Step-by-step explanation:

The approximate area of a circle that has a diameter of 11 inches, rounded to the nearest hundredth is 95.03.

Formula: A=1/4πd²

A=1

4πd^2=95.03.

4·π·11^2≈95.03318in²

Answer:

There will be 96 lemmings in 7 years

Step-by-step explanation:

we have

[tex]f(x)=200(0.901)^{x}[/tex]

This is a exponential function

where

x ------> the time in years

f(x) ----> lemming population

so

For x=7 years

substitute in the function

[tex]f(7)=200(0.901)^{7}[/tex]

[tex]f(7)=96.4[/tex]

There will be 96 lemmings in 7 years

Final answer:

The missing term in the polynomial 36x³ - 22x + ___ that ensures a GCF of 2x must be ax, where 'a' is an even number. Possible terms could be 4x, -8x, or any other term with an even coefficient and an x factor.

Explanation:

The student's question asks which term can be used in place of the blank in the polynomial 36x³- 22x + ___ so that the greatest common factor (GCF) of the resulting polynomial is 2x. To determine the missing term, we need to look at the existing terms of the polynomial. The first term, 36x³, has a GCF of 2x because 36 is divisible by 2 and x³ has x as a factor. Similarly, the second term, -22x, also has a GCF of 2x since 22 is divisible by 2 and there's already an x present. To ensure that the GCF of the final term with the others is 2x, the term must have both a coefficient divisible by 2 and at least one factor of x.

Let's say the missing term is ax, where 'a' is an even number to keep the common factor of 2x. Therefore, a term like 4x or -8x could work. If the resulting polynomial had a term without x, then the GCF would just be 2, not 2x. Hence, adding a term with a factor of 2 and x not only completes the polynomial but also ensures that the GCF is 2x.

Answer:

Graph 1: Consistent Dependent

Graph 2: Consistent Independent

Graph 3: Consistent Dependent

Graph 4: Inconsistent

Step-by-step explanation:

Consistent means they have at least one solution.  So lines that intersect once or lines that intersect infinitely many times are both consistent systems.

If they are the system that has one solution they are considered independent.

If they are the system that has infinitely many solutions then are considered dependent.

Inconsistent means they won't intersect at all.

First graph shows the same line graphed onto itself.  That means they have infinitely many solutions and is therefore a consistent dependent system.

Second graph shows the lines intersecting once.  That means they have one solution and therefore is a consistent independent system.

Third graph shows the same description of graph one and is therefore a consistent dependent system.

The last graph shows parallel lines. Parallel lines do not intersect and therefore do not have a solution.  So this system is inconsistent.

Answer:

x < -3

Step-by-step explanation:

using the distributive property, distribute 9(2x +1) so it's 18x + 9, subtract 9x from 18x, subtract 9 from -18, divide both sides by 9, x < -3

Inequality is a relationship between two numbers or two expressions.

The value of x in the solution set of 9(2x + 1) < 9x – 18 is

x < -3

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

9(2x + 1) < 9x – 18

Remove the parenthesis.

9 x (2x) + 9 x 1 < 9x - 18

18x + 9 < 9x - 18

Subtract 9x on both sides.

18x + 9 - 9x < 9x - 18 - 9x

9x + 9 < -18

Subtract 9 on both sides.

9x + 9 - 9 < -18 - 9

9x < -27

Divide both sides by 9.

9x/9 < -27/9

x < -3

This means x is less than -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

Thus,

The value of x in the solution set is x < -3.

i.e -2, -1, 0, 1, 2, 3, 4, ,,,,,,∞

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Answer: B

Step-by-step explanation:

Because m<7 and m<6 share a vertex and doesn’t share any common sides and they are across from each other which means they are vertical and vertical angles are congruent

The missing reason for the 3rd step will be vertical angles are congruent. Then the correct option is B.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

The diagram is given below.

Then the missing reason for the 3rd step will be vertical angles are congruent.

Thus, the correct option is B.

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Answer:

D.)  240 miles.

Step-by-step explanation:

By proportion the distance between the 2 cities

= (3 / 1/8) * 10

= 3*8*10

= 240 miles.

The 2 cities are D.) 240 miles away.

By proportion of the distance between the 2 cities

= (3 / 1/8) * 10

= 3*8*10

= 240 miles.

This means that in case your journey is twice as lengthy, you will move two times as a long way. in case you journey three times as long, you will pass 3 instances as a ways. At the same time as in case you tour half as long, you may go 1/2 as far. By something ratio the time adjustments, the distance will alternate proportionally, that is, within the identical ratio.

The made of approach within the ratio is identical to the made from extremes. Two ratios are stated to be identical if their cross products are identical. The sharing formula is given as, a : b :: c : d ⇒ a b = c d.

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Answer:

10a-4b+2c

Step-by-step explanation:

Answer:

10a -4b +2c

Step-by-step explanation:

6a-4b+c and 4a+c

6a-4b+c + 4a+c

Combine like terms

6a+4a   + (-4b) + c+c

10a -4b +2c

Answer:

[tex]\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}[/tex]

Step-by-step explanation:

[tex]\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2[/tex]

Answer:

611.04 mm³

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 30.4 and h = 20.1, hence

A = 30.4 × 20.1 = 611.04 mm³

Answer:

611.04 mm³

Step-by-step explanation:

Formula for finding the area of a parallelogram: A = B * H

B is base, H is height, * is multiply.

_________________________________________________

The area of the parallelogram pictured: 611.04 mm³

A=bh=30.4·20.1=611.04

_________________________________________________

Answer:

65 units²

Step-by-step explanation:

The polygon is composed of a trapezium and a triangle

Trapezium QRSU has area (A)

A = 0.5 h (a + b)

where h is the perpendicular height and a, b are the parallel bases.

h = RS = 7 , a = RQ = 6 and b = SU = 8, so

A = 0.5 × 7 × (6 + 8) = 0.5 × 7 × 14 = 49 units²

Triangle STU has area ( A )

A = 0.5 bh ( b is the base and h the perpendicular height )

here b = SU = 8 and h = 4 ( distance from vertex T to the base SU), so

A = 0.5 × 8 × 4 = 16 units²

Total area = 49 + 16 = 65 units²

Answer:

D. Y+5=-(1/2)*(x+3)

Step-by-step explanation:

Perpendicular Lines are those with the following condition:

y=a*x+b (1)

y=c*x+d (2)

Where 'a' and 'c' are the respective slope

If These two lines are perpendicular, then

a=- 1/c

Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8

Using those principles we have that the slope for our needed line ('c') has to be -(1/2).

Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:

-5=(-1/2)*(-3)+d

resulting that d=-5-(3/2)

Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)

Rearranging terms, we have the following:

y+5=(-1/2)*x-(3/2)

where you can obtain a more pretty expression:

y+5=(-1/2)*(x+3)

ANSWER

a. 12 units

EXPLANATION

According to the altitude theorem, RT which is the altitude, is equal to the geometric mean of TQ and TS, the segments created by the foot of the altitude on the hypotenuse.

This implies that:

[tex]x = \sqrt{TQ \times TS} [/tex]

From the diagram, TQ=16 and TS=9.

We substitute these values and solve for x.

[tex]x = \sqrt{9 \times 16} [/tex]

[tex]x = \sqrt{144} [/tex]

[tex]x = 12[/tex]

Therefore x is 12 units.

The correct answer is A

Step-by-step explanation:

Given that line a is parallel to line b

∠6 = ∠2 = 36.5° (property of corresponding angles)

∠8 = 180° -∠6 (property of adjacent angles on a straight line)

∠8 = 180° - 36.5° = 143.5°  

[tex]\huge{\boxed{y=\frac{1}{2} x+1}}[/tex]

First, we must find the slope of the graphed line. We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are known points on the line.

Plug in the values. [tex]\frac{4-2}{-1-0}[/tex]

Subtract. [tex]\frac{2}{-1}[/tex]

Simplify. [tex]-2[/tex]

To find the slope of the perpendicular line, we must find the opposite inverse slope. This means we first need to multiply it by [tex]-1[/tex], then we need to swap the numerator and denominator.

[tex]-2*-1=2[/tex]

Now, swap the numerator and denominator. The numerator is [tex]2[/tex], and the denominator is [tex]1[/tex] by default.

[tex]\frac{1}{2}[/tex]

The only answer choice with a slope of [tex]\frac{1}{2}[/tex] is [tex]\boxed{y=\frac{1}{2} x+1}[/tex]

Answer:

B. 10.5 units

Step-by-step explanation:

The radius of a circle is a segment that has the center of the circle as one endpoint and a point on the circle as the other endpoint. The length of a radius is also called radius.

The figure shows two radii: segments MR and MS.

The lengths of all radii of a circle are equal.

MR = MS = 10.5 units

Answer:

10.5 units

Step-by-step explanation:

The radius of Circle M is the distance from the center M to the circle

That is 10.5 units

For this case we must factor the following expression:[tex]x ^ 2-12x-20[/tex]

We have that the expression cannot be factored with rational numbers.

On the other hand, we can find the zeros, applying the quadratic formula we have:[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = 1\\b = -12\\c = -20[/tex]

[tex]x = \frac {- (- 12) \pm \sqrt {(- 12) ^ 2-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144-4 (1) (- 20)}} {2 (1)}\\x = \frac {12 \pm \sqrt {144 + 80}} {2}\\x = \frac {12 \pm \sqrt {224}} {2}\\x = \frac {12 \pm \sqrt {16 * 14}} {2}\\x = \frac {12 \pm4 \sqrt {14}} {2}[/tex]

Thus, the roots would be:

[tex]x_ {1} = 6 + 2 \sqrt {14}\\x_ {2} = 6-2 \sqrt {14}[/tex]

Answer:

the expression cannot be factored with rational numbers.

The factors of the given quadratic expression are: (x - 2) and (x - 10)

The quadratic expression is given as:

x² - 12x - 20

Now, to get the factors, we need to write as follows:

x² - 10x - 2x + 20

This can be factorized to get:

x(x - 10) - 2(x - 10)

= (x - 2)(x - 10)

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Answer:

A

Step-by-step explanation:

The graphs of two functions y=f(x) and y=g(x) intersect at one point. The coordinates of this point are (0,-2). This means

f(0)=-2

g(0)=-2

Thus,

f(0)=g(0)

Note that the blue line passes through the point (-2,4), so

f(-2)=4

and the red line passes through the point (-2,-4), so

g(-2)=-4

Hence,

f(-2)≠g(-2)

and f(0)≠g(-2)

Answer:

First Option

Step-by-step explanation:

It can be seen in the graph that the two plotted functions are linear, which means that if the lines are not parallel or not lying on each other, then the lines will intersect at most one point in the plane. It can be clearly seen that both the lines intersect at the point (0,-2). As far as the functions are concerned, there is an input and an associated output. The term f(0) means that 0 is the input and f(0) is the functional value, which is the output. In the graph, both lines have the y-intercept of -2. Y-intercept is the point where the value of the input (i.e. the value of x) is 0. Since both lines are intersecting at (0,-2), this implies that f(0) = g(0). This essentially means that the the functional value of f, which is -2, is equal to the functional value of g!!!

Answer:

It shows that  h varies directly with V and inversely with l and w.

Step-by-step explanation:

The given equation is:

h = V/lw

It shows that  h varies directly with V and inversely with l and w.

Inversely means if the value of one entity increases, the value of second entity decreases or vice versa. Directly related means as one quantity increases, another quantity increases at the same rate

We can show it as h=1/lw which means  h is in inverse relation with l and w and in direct relation with V....

ANSWER

[tex]y = 2( {x - 4)}^{2} - 3[/tex]

EXPLANATION

The function equation of a parabola that opens up in vertex form is given by

[tex]y = a( {x - h)}^{2} + k[/tex]

where (h,k) is the vertex and 'a' is the leading coefficient.

The given graph is a parabola that opens up and has its vertex at (4,-3).

This implies that, h=4 and y=-3

We substitute these values into the vertex form to obtain,

[tex]y =a( {x - 4)}^{2} + - 3[/tex]

This simplifies to,

[tex]y =a( {x - 4)}^{2} - 3[/tex]

The graph also contains (3,-1). We plug x=3 and y=-1 into the equation to find the value of 'a'.

[tex] - 1=a( {3 - 4)}^{2} - 3[/tex]

[tex] - 1 + 3 = a( { - 1})^{2} [/tex]

[tex]2 = a[/tex]

We substitute this value to get:

[tex]y = 2( {x - 4)}^{2} - 3[/tex]

The last choice is correct.

Answer:

125-135

Step-by-step explanation:

The standard deviation is 7. This implies that the IQ scorings can be between 123 and 137. With a 90% confidence in these numbers, 125-135 is the closest interval to 90% confidence.

Answer: (129.04,130.96)

Step-by-step explanation:

Given : Sample size : n= 145

Mean IQ in the sample : [tex]\overline{x}=130[/tex]

Standard deviation : [tex]\sigma=7[/tex]

Significance level : [tex]\alpha=1-0.9=0.1[/tex]

Critical value : [tex]z_{\alpha/2}=1.645[/tex]

The confidence interval for population mean is given by :-

[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=130\pm(1.645)\dfrac{7}{\sqrt{145}}\\\\=130\pm0.96\\\\=(129.04,\ 130.96)[/tex]

Hence, the 90% confidence interval for the students' mean IQ score is (129.04,130.96)

Answer:

f (x) = (x+5) is linear

Step-by-step explanation:

We are given the following function and we are to determine if it is a linear function or not:

[tex] f ( x ) = ( x + 5 ) [/tex]

For a function to be linear, it must be written in the standard form [tex]y=mx+c[/tex] and its graph gives a straight line.

Whereas, when an equation is squared, its graph becomes a curved one which is not linear.

Therefore, the given function f (x) = (x+5) is linear.

Answer: No, it is not a linear function. It is a Quadratic function.

Step-by-step explanation:

Given the following function:

 [tex]f(x)=x(x+5)[/tex]

You need to apply Distributive property:

[tex]f(x)=(x)(x)+(x)(5)[/tex]

[tex]f(x)=x^2+5x[/tex]

You can observe that the highest exponent of the function is "2", therefore, it is not a Linear function, but a Quadratic function in the form:

[tex]f(x) = ax^2 + bx + c[/tex]

Where a, b, and c are numbers ([tex]a\neq 0[/tex])