what is the slope to the perpendicular line to y=7/8x-9

Using a system of equations, it is found that the amounts of money that each of Gabriel, Daniel and Edgar have are given as follows:

A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the context of the problem.

In the context of this problem, the variables are given as follows:

Gabriel has double the amount of Daniel, hence:

x = 2y.

Gabriel has five times the amount of Edgar, hence:

x = 5z.

If Gabriel loans Q14 to Daniel and Q33 to Edgar, they will have the same amount, hence:

x - 47 = y + 14 = z + 33.

Since x = 2y, we can replace into the first two sides of the equality above and solve for y as follows:

2y - 47 = y + 14

y = 61. (Daniel's amount).

The solution for x is given as follows:

x = 2y = 2(161) = 122 (Gabriel's amount).

The solution for z is given as follows:

x - 47 = z + 33

122 - 47 = z + 33

75 = z + 33

z = 75 - 33

z = 42 (Edgar's amount).

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Explanation

Given the trigonometric expression

We can find the solutions below;

From trigonometry identities;

Therefore; we will have;

Therefore, the general solutions for the above is given as;

Answer:

Answer: the slope of this equation is 8

Step-by-step explanation: y = 8x - 15, the 8x represents the slope of this equation

The perimeter of the triangle is 29.31 units and the area of the triangle is 38.87 units^2

To find the perimeter and area of the triangle, we have to use the formula of distance between two points.

Distance between AB

[tex]d_a_b = \sqrt{(a_1+a_2)^2 + (b_1 + b_2)^2} \\d_a_b = \sqrt{(3+1)^2 + (-3-3)^2}\\ d_a_b = \sqrt{4^2 + 9^2} \\d_a_b = 9.85 units[/tex]

Distance between BC

[tex]d_b_c = \sqrt{(b_1+b_2)^2 + (c_1+c_2)^2}\\d_b_c = \sqrt{(-9)^2 + (7)^2}\\d_b_c = \sqrt{130} \\d_b_c = 11.40 units[/tex]

Distance between AC

[tex]d_a_c = \sqrt{(a+1_a_2)^2 + (c_1+c_2)^2} \\d_a_c = 8.06 units[/tex]

The perimeter of the triangle is equal to

[tex]p = 9.85 + 11.40 + 8.06 = 29.31 units[/tex]

The area of the  triangle is 38.87 units^2

Kindly find the attached graph below;

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The graph of the linear equation 4x - y = 8, with two points on the line is shown in the image attached below.

If we know the slope, m, of the linear equation, which is the rise of the line over the run of the line, and also know the y-intercept value, b, we can graph a linear equation such that the slope of the line would be the value of m, and the point where the line intercepts the y-axis would be the value of b in the linear equation that is represented as y = mx + b.

Given the linear equation, 4x - y = 8, we can rewrite this in slope-intercept form as y = mx + b:

4x - y = 8

-y = -4x + 8 [subtraction property of equality]

y = 4x - 8 [division property of equality]

The slope, m, is 4, while the graph of the linear equation must intercept the y-axis at y = -8, because the y-intercept of the linear equation is b = -8.

Thus, the graph of 4x - y = 8 is shown below.

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The tunnel A will be damaged and truck can pass through tunnel B.

Given that, tunnel A is modeled by x² + y² + 30x + 56 = 0, and tunnel B is modeled by x² – 30x + 16y – 95 = 0.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y²= = 4ax.

Part A: x²+y²+30x+56=0

Add 15² on both the sides of a equation

That is, x²+30x+15²+y²=-56+15²

⇒ (x+15)²+y²=169

⇒ (x+15)²+y²=13²

Divide 13² on both the sides of the equation

⇒ (x+15)²/13² + y²/13² =1

Part B:

x²-30x+16y-95=0

Now, x²-30x+16y=95

Add 15² on both the sides of a equation

That is, x²-30x+15²+16y=95+15²

⇒ (x-15)²=320-16y

⇒ (x-15)²=16(20-y)

Part C:

Maximum height:

A: 13 feet

B: 20 feet

Width = 8 feet

A: x+15=8/2=4 y=12.37<13.5

B: x-15=8/2=4 y=19>13.5

Hence, the tunnel A will be damaged and truck can pass through tunnel B.

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Hello!

Here are both solutions to your equation.

Fraction Form:

[tex]\frac{37}{100}[/tex]

OR

Decimal Form:

[tex]0.37[/tex]

Hope this helps!

The number of mosquitoes on the colony after 4 days is 2800.

The number of days that there are 70,000 mosquitoes will be 114 dad.

The population of a colony of mosquitoes obeys the law of uninhibited growth and there are 1000 mosquitoes initially and there are 1600 after 1 day. The common difference will be:

= 1600 - 1000

= 600

The formula for the arithmetic sequence will be:

= a + (n - 1)d

a = 1000

d = 600

n = 4

The colony after 4 days will be:

= a + (n - 1)d

= 1000 + (4 - 1)600

= 1000 + 1800

= 2800

The number of days that there are 70,000 mosquitoes will be:

a + (n - 1)d = 70000

1000 + 600(n - 1) = 70000

1000 + 600n - 600 = 70000

Collect like terms

600n = 70000 - 1000 + 600

600n = 68400

n = 68400/600

n = 114 days

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Answer:

Answer down below!

Step-by-step explanation:

If we draw this out, we already know that m<7 = 96

Using what we already know, we can figure out the rest

m<6 also equals 96 because m<7 and m<6 are verticle angles

m<3 also equals 96 because m<6 and m<3 are opposite interior angles

m<2 also equals 96 because m<3 and m<2 are verticle angles

Now, to find m<4, simply subtract 96 from 180. That should give you 84

Thus, m<2 = 96 and m<4 = 84

The height of the yellow mark above the water is 1 foot.

This is further explained below.

Generally, The radius of a waterwheel is 4 feet, and its center is 1 foot below the waterline.

Estimation of feet:

cos π/3 = OB/OA

1/2 = OB/4

OB = 2

t

In conclusion,A yellow mark should be placed above the water

= OB - OD

= 2 - 1

= 1 foot

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Answer:

the other answer is correct is A. 1 foot

Step-by-step explanation:

Got it right on edge

The range of F(x) = 7.4* is all positive real numbers is true

What is Range ?

When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.

Currently, the function is

f(x) = 7 x 4^x

Suppose,

y = f(x) = 7 x 4^x.

=> y = 7 x 4^x

Hence,

lny = ln (7 x 4^x).

We obtain using the logarithm equation

Hence,

ln y = ln7 + ln 4^x.

= ln y = ln7 + x ln4 .

Hence,

y equals e^(ln7 + x ln4).

=> y = e^ln7.e^(xln4) (xln4)

Using the exponential formula, we obtain

=> y = 7xln4

Consequently, y=f(x)=7.x.ln4

To determine function f's value (x)

7.x.ln7 = 0

As a result, For all possible values of x (x€R). To date,

=> 7x ≥ 0

=> 7xln4 ≥ 0

Therefore interval notation will be (0,∞)

Notation for set builders:

{y|y>0}

The graph will be plotted as follows if all the values of x (x€R) are used:

Hence, it is true that the range of f(x)=7*4x is all positive real integers.

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Answer:

Step-by-step explanation:

Find the burning rate of candle per hour:

The rate is the slope of the linear function and the initial length of the candle is the y-intercept:

The equation is:

Correct choice is the first one.

Answer:

C

Step-by-step explanation:

I'm to lazy to type it out so...I took a photo

I hope this helps :D

and I need brainiliest so bad...

Answer:

38333333333333/10000000000000

Step-by-step explanation:

The z-scores for a 67-inch- man and a 62-inch woman are -0.9667 and -0.5526, respectively.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

For a 67-inch- man, use the formula to solve for the z-score.

x = 67

μ = 69.9

σ = 3.0

z-score = (x – μ) / σ

z-score = (67 - 69.9) / 3.0

z-score = -0.9667

Do the same for a 62-inch- man, use the formula to solve for the z-score.

x = 62

μ = 64.1

σ = 3.8

z-score = (x – μ) / σ

z-score = (62 - 64.1) / 3.8

z-score = -0.5526

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The circumference of a circle whose area is 9π cm² in terms of pi is 6π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed mathematically as;

C = 2πr

Given that the area of the circle is 9πcm², we determine the radius of the circle.

A = πr²

9πcm² = π × r²

r² = 9πcm² / π

r² = 9cm²

r = √9cm²

r = 3cm

Now, we determine the circumference of the circle.

C = 2πr

C = 2 × π × 3cm

C = 6cm × π

C = 6π cm

Therefore, the circumference of the circle is 6π centimeters.

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Answer:

   -6.4, -5 1/2, -5, and -2 6/4.

Step-by-step explanation:

Arranging these negative values in order from least to greatest may be tricky if you are not familiar with your integer rules and operations. However, if you seem to understand, even a little, this way may be helpful to you.

All you need to know is this. positive and negative are opposites. Thus, if, for example, +2 is greater than +1 in positives, then -2 is less than -1 in negatives. So, in other words, think about it this way when you see a negative number, but you are used to positive numbers, just assume that the biggest number on the positive side is the smallest number on the negative side.

Therefore, if we were to use this method, we would result in -6.4, -5 1/2, -5, and -2 6/4. Since it would be the opposite in positives.

The ages of Victoria and tyee are 72 and 74.

A linear equation is an algebraic equation of the form y=mx+b that only contains a constant and a first-order (linear) component, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where y and x are the variables. Ax+By=C is the accepted form for two-variable linear equations. Finding both intercepts of an equation in this form is rather simple (x and y). If an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is said to be linear. The point-slope form, standard form, and slope-intercept form are the three primary types of linear equations.

As given

ages are consecutive even integers

Victoria > Tyee

So

Victoria's age = x

Tyee's age = x + 2

x(x + 2) = 80

= x² + 2x - 80

= x²  + 8x - 10x - 80

Hence , the ages are 72 and 74.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 2i [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3 {x}^{2} + 12 = 0[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 3{x}^{2} = - 12[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: {x}^{2} = - \frac{12}{3} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x {}^{2} = - 4 [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ (- 1)(4)} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = \sqrt{ - 1} \sdot \sqrt{4} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = i \sdot2[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: x = 2i[/tex]

[ i represents iota, i² = -1, (complex number) ]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]x=2i[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2+12=0[/tex]

Factor 3 from the left side of the equation:

[tex]\implies 3(x^2+4)=0[/tex]

Divide both sides of the equation by 3:

[tex]\implies\dfrac{3(x^2+4)}{3}=\dfrac{0}{3}[/tex]

[tex]\implies x^2+4=0[/tex]

Subtract 4 from both sides:

[tex]\implies x^2+4-4=0-4[/tex]

[tex]\implies x^2=-4[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{-4}[/tex]

[tex]\implies x^2=\sqrt{-4}[/tex]

Rewrite -4 as 2² · -1:

[tex]\implies x=\sqrt{2^2 \cdot-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies x=\sqrt{2^2}\sqrt{-1}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies x=2\sqrt{-1}[/tex]

[tex]\textsf{Since $\sqrt{-1}=i$}[/tex]

[tex]\implies x=2i[/tex]

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter i.

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

Answer:

27

Step-by-step explanation:

x + y = 23

x - y = 27

(x + y) + (x - y) = 23 + 27

2x = 50

x = 25

y = - 2

How to find distance:

|25 -(-2)| = |27| = 27

Answer:-4+27

Step-by-step explanation:

Answer:

the answer is 29              

Answer:

3 feet

Step-by-step explanation:

s= sandra

L= Lamp

if you know that the lamp is four feet away, and the bird is five feet away. go vertically up from the lamp until the distance from the lamp vertically equals five feet back to sandra.

According to the given line, the points are L and M and the segment is LM.

Lines:

The line is defined as the one-dimensional figure, which has length but no width. It is made of a set of points which is extended in opposite directions infinitely.

Given,

Here we have the diagram.

Through the given diagram we have to identify the points and segments from it.

We know that, the points refers the is a dimensionless shape, since it represents a dot only, whereas a line is a one-dimensional shape.

Based on this definition , we have two points that L and M in the given diagram.

Next one we have to identify from the graph is segment,

Segment means the part of the line that connects two points.

So, LM is the segment of the line.

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The pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

The Janitor find the leakage in the pipe at a rate of [tex]23[/tex] fl oz per hour.

We have to find how fast was the pipe leaking in gallons per day​.

To find the leaking in gallons per day​ we have to convert [tex]23[/tex] fl oz per hour into gallons per day.

As we know that

[tex]1[/tex] gallon[tex]=128[/tex] fl oz

So [tex]1[/tex] fl oz[tex]=\frac{1}{128}[/tex] gallons

There are [tex]24[/tex] hours in a day so we multiply with [tex]24[/tex] to convert in day.

So the expression should be

[tex]=23[/tex] fl oz/hours[tex]\times\frac{1}{128}[/tex] gallons/fl oz[tex]\times24[/tex] hours/day

[tex]=\frac{23\times24}{128}[/tex] gallons/day

[tex]=\frac{23\times3}{16}\\[/tex] gallons/day

[tex]=\frac{69}{16}[/tex] gallons/day

Hence, the pipe leaking in gallons per day is [tex]\frac{69}{16}[/tex] gallons/day.

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Yes, the system of inequalities listed to the represent the wants of the campaign manager are correct

This refers to the term in mathematics that uses some expressions to typify statements.

The following are the statements in inequalities

Considering the question here:

r = each 60-second radio spot

t = 30 seconds of television time

The budget is limited to $48,000 means less than or equal to

The manager wants at least 45 radio spots, but no more than 90

means radio spots from 45 to 90 hence 45≤ r ≤ 90

at least 20 means television spots of 20 and above hence t ≥ 20

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The number of time Easton's song was played on commercials is 10 times.

The number of time Easton's song was played during a movie is 4 times.

The first step is to form a system of equations:

40c + 110m = 840 equation 1

c - m = 6

c = 6 + m equation 2

Where:

The system of equations would be solved using the substitution method.

Substitute for c in equation 1 using equation 2

40(6 +  m) + 110m = 840

240 + 40m + 110m = 840

40m + 110m = 840 - 240

150m = 600

m = 600 / 150

m = 4

Substitute for m in equation 2.

c = 6 + 4

c = 10

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