Solve the equation without using a calculator

[tex]\displaystyle\\3^\frac{x+2}{3x-4}-2\cdot3^\frac{5x-10}{3x-4}=7[/tex]

We get the expression with the powers as

a) x⁻³.x⁵= x²

b) m⁻³:m⁶= m⁻⁹

c) a⁻⁷.a⁻²= a⁻⁹

d) (m⁻³)⁻²= m⁶

Given that,

We have to find the power of the expressions.

a) x⁻³.x⁵

Bases are equal so powers must be added.

x⁻³⁺⁵

x²

b) m⁻³:m⁶

It is in ratio that means

m⁻³/m⁶

We can take the m⁶ to numerator

m⁻³.m⁻⁶

Bases are equal so powers must be added.

m⁻³⁻⁶

m⁻⁹

c) a⁻⁷.a⁻²

Bases are equal so powers must be added.

a⁻⁷⁻²

a⁻⁹

d) (m⁻³)⁻²

Powers are multiplied

m⁶

Therefore, We get the expression with the powers as

a) x⁻³.x⁵= x²

b) m⁻³:m⁶= m⁻⁹

c) a⁻⁷.a⁻²= a⁻⁹

d) (m⁻³)⁻²= m⁶

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Answer:126 children

Step-by-step explanation:

first you want to multiply 18 times 4 (72) then 18 times 3 (54) and then you add 72+54=126

your welcome :)

Answer:

graph 1

symmetry about the x and y axes

graph 2

symmetry about the y axis

graph 3

symmetry about the y axis

Step-by-step explanation:

try to imagine that you folded the graph by the x axis or y axis. If the to side of the graph are overlapping, the graph is symmetry across the axis you folded.

Hope this helps.

Solve for y by simplifying both sides of the inequality, then isolating the variable.

Inequality Form:

y<−10 or 1<y<6

Interval Notation:

(−∞,−10)∪(1,6)

The graph of g(x) = -|x + 2| + 4 is obtained after these following transformations from the parent function f(x) = |x|.

The parent function in this problem is defined as follows:

f(x) = |x|.

The transformed function in this problem is defined as follows:

g(x) = -|x + 2| + 4

The transformations are listed and described as follows:

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Answer:

see below

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Answer:

Info down in Explaination

Step-by-step explanation:

To graph this equation, start at the origin (0,0) since there is not y-intercept.

Because slope is characterized by rise/run ( i.e. how many units up or down depending on whether it is positive or negative and then however many units to the right.

Because the rise (up and down, numerator) is 1, we know that we will go up one unit.

The run (side to side, denominator) is 4, so we will go to the right 4 units.

This makes the first point (4, 1).

Continue doing this until you get an idea of the line and connect the points to get the graph

Step-by-step explanation:

I assume this means that both purchase one item every day.

so, their number of purchases are the same (x).

80 - 4.5x >= 60 - 2.5x

20 - 4.5x >= -2.5x

20 >= 2x

10 >= x

our

x <= 10

after 10 purchased drinks their balances will be equal.

before that, Ashley's card balance will be greater than Aaron's.

after that, Aaron's card balance will be greater than Ashley's.

so, for up to 10 purchased drinks Ashley's card balance will be greater or equal to Aaron's.

The mean number of students per Faculty is 326.

Mean simply means the average of a set of numbers.

In this case, the number of students in nine faculties of a university are given as 168, 285, 397, 331, 383, 359, 366, 280 and 369. The mean will be:

= Total values / 9

= (168 + 285 + 397 + 331 + 383 + 359 + 366 + 280 + 369) / 9

= 2938 / 9

= 326.44

The mean is 326.

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The number pattern for the missing numbers is 1,2,1,1,2,3,2,1,1,2,3,4,3,2,1,1,2,3,2,1,2,2

A pattern of numbers formed with a definite rule is called sequence

How to find a number pattern?

In every number patter, first term of this number pattern is 1; and the terms after the first term are obtained by adding, subtracting or multiply by 1 to the previous term.

1+1=2

2-1=1

1*1=1

1+1=2

2+1=3

3-1=2

2-1=1

1*1=1

.1*1=1

1*1=1

2+1=3

3+1=4

4-1=3

3-1=2

2-1=1

1*1=1

1+1=2

2+1=3

3-1=2

2-1=1

1+2=2

2*1=2

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The yards of roadside that Ben is cleaning more than Adam is 26 yards. Sheridan is correct.

The first step is to determine the length of Oakley Street. Pythagoras theorem would be used to determine the length.  Oakley Street is the hypotenuse of the right triangle that is formed by the streets.

The Pythagoras theorem: a² + b² = c²

where:

39² + 52² = c²

1,521 +  2704 = c²

c² = 4,225

c = √4225

c = 65 yards

Total yards Ben picked = 39 + 52 = 91 yards

Yards picked by Adam = 65 yards

Difference in the yards of litters picked = 91 - 65 = 26 yards

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Answer:

Step-by-step explanation:

Perpendicular lines have opposite-reciprocal slopes.

It means the product of the slopes is - 1.

Let's find the slopes of the two lines and their product.

Find the product of slopes:

This is not  - 1, therefore the lines are NOT perpendicular.

Answer:

x = 3/2 and -4/3

Step-by-step explanation:

[tex] \rm \implies 6 {x}^{2} - x - 12 = 0 \\ \\ \rm \implies 6 {x}^{2} - 9x + 8x - 12 = 0 \\ \\ \rm \implies 3x(2x - 3) + 4(2x - 3) = 0 \\ \\ \rm \implies (2x - 3)(3x + 4) = 0 \\ \\ \rm \implies 2x - 3 = 0 \: \: and \: \: 3x + 4 = 0 \\ \\ \rm \implies 2x = 3\: \: and \: \: 3x = - 4 \\ \\ \rm \implies x = \frac{3}{2} \: \: and \: \: x = - \frac{4}{3} [/tex]

Answer:  median = 61

Reason:

A normal distribution is perfectly symmetric. Such distributions have mean = median = mode.

Answer:

A.  (x - 80)² = -320(y = 20)

B.  Focus:  (80, -60)

     Directrix:  y = 100

     Axis of symmetry:  x = 80

Step-by-step explanation:

If the spider's movement is modeled by a parabola, and its maximum height is 20 mm halfway across a horizontal distance of 160 mm, then:

Standard form of a parabola with a vertical axis of symmetry:

[tex]\boxed{(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0}[/tex]

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

Substitute one of the x-intercepts and the vertex into the formula and solve for p:

[tex]\implies (0-80)^2=4p(0-20)[/tex]

[tex]\implies (-80)^2=4p(-20)[/tex]

[tex]\implies 6400=-80p[/tex]

[tex]\implies p=-80[/tex]

Substitute the found value of p and the vertex into the formula to create the equation of the parabola in standard form:

[tex]\implies (x-80)^2=4(-80)(y-20)[/tex]

[tex]\implies (x-80)^2=-320(y-20)[/tex]

Given:

[tex]\begin{aligned}\textsf{Focus}&=(h,k+p)\\&=(80,20-80)\\&=(80,-60)\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Directrix}:y&=(k-p)\\ \implies y&=(20-(-80))\\ \implies y&=100\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Axis of symmetry}:x&=h\\ \implies x&=80\end{aligned}[/tex]

As per the unitary concept,

a) There are 5/8 cups of flour would you need for half the recipe

b) There are 6 1/4 cups of flour would you need for 5 dozen cookies.

Unitary method:

The method by which first we find the value of single unit and then the value of the required number of units is known as the Unitary Method.

Given,

Here we have given that,  A recipe that makes 3 dozen chocolate chip cookies calls for 2 and 2/5 cups of flour.

So, here we need to find the following:

a) Exactly how much flour would you need for half the recipe?

b) Exactly how much flour would you need to make 5 dozen cookies?

In order to find these value, we have to calculate the amount of flour need for 1 dozen.

In order to calculate that, one we need to divide the total amount by the cups of flour need.

Then we get,

=> 3/ (2 2/5)

=> 3/ (12/5)

=> 15/12

=> 1.25

So, for half dozen cookies, we need

=> 1.25/2

=> 0.625

Which is in the fraction form of,

=> 5/8

And for 5 dozen of cookie we need.

=> 5 x 1.25

=> 6.25

The fraction equivalent is

=> 6 1/4 cups.

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Answer:

It will take them 3.5 hours to paint the room.

Step-by-step explanation:

Step 1: Add the number of hours it takes them together

    A. 6 + 8

Step 2: Divide the total number of hours by two (since two people are working together)

    B. 12 / 2 = 7 hours

Step 3: Divide by two again since you now have twice the speed

    C. 7 / 2 = 3.5 hours

Answer:

angle LHJ is congruent to angle IKL

Answer:

segment JL is congruent to segment JK

segment HL is congruent to segment KI

Angle LJH is congruent to angle KJI

Step-by-step explanation:

we flip the triangles to look for the corresponding sides

Hopes this helps please mark brainliest

The variable X has a binomial distribution, as:

There are three requirements for the binomial distribution to represent a variable, as follows:

In the context of the variable X, these requirements are respected as follows:

Hence yes, the variable X has a binomial distribution.

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The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

Now,

Let the cost of 1 slices of cheese pizza = x

And, The cost of 1 slices of soda = y

Since, Richard bought 3 slices of cheese pizza and 2 sodas for $8.75.

Hence, We get;

⇒ 3x + 2y = $8.75  ..(i)

And, Jordan bought 2 slices of cheese pizza and 4 sodas for $8.50.

So, We get;

⇒ 2x + 4y = $8.50  ..(ii)

Multiply by 2 with (ii);

⇒ 2 (3x + 2y) = 2 × $8.75

⇒ 6x + 4y = $17.5  

Subtract from (ii), we get;

⇒ 6x + 4y - 2x - 4y = $17.5 - $8.50

⇒ 4x = $9

⇒ x = $2.25

And, ⇒ 2x + 4y = $8.50

⇒ 2 × $2.25 + 4y = $8.50

⇒ $4.5 + 4y = $8.50

⇒ 4y = $8.50 - $4.5

⇒ 4y = $4

⇒ y = $1

Thus, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $2.25 + 3 × $1

⇒ $2.25 + $3

⇒ $5.25

Therefore, The cost of 1 slice of cheese pizza and 3 sodas cost will be;

⇒ $5.25

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The inequality that represents the graph is y < 4

The graph is shown in the figure

The graph is the pictorial representation of the collection of data. It has 2 axis . The x axis and y axis

Consider the each block of the graph as 1 units

At y = 4 there is dotted line parallel to the x axis of the graph

The dotted line represents the inequality symbol less than, Therefore the value of y is less than 4

From the graph, the entire region of the graph that y less than 4 are shaded therefore for all the value of x the value of y is less than 4

The inequality will be

y < 4

Hence, the inequality that represents the graph is y < 4

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Answer:

0.5867  (or 58.7%)

Step-by-step explanation:

The probability that a randomly selected student has a score between 350 and 550 is  59%.

Standard score or z score in statistics is defined as the number of standard deviations by which that the value of a score is above or below the mean value.

Given that,

The scores of the students on a standardized test are normally distributed.

Mean, μ = 500

Standard deviation, σ = 110

z score = (x - μ) / σ

For x = 350,

z = (350 - 500) / 110 = -1.36

Probability = 1 - 0.9131 = 0.0869

For x = 550,

z = (550 - 500) / 110 = 0.45

Probability = 0.6736

Probability that a randomly selected student has a score between 350 and 550 is,

P = 0.6736 - 0.0869 = 0.5867 ≈ 59%

Hence the required probability is 0.5867 or 58.67%.

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Answer:

The slope is 4 and the equation is y = 4x + 18

Step-by-step explanation:

Okay, so you start by solving for the slope. The formula for slope is

m = y1-y2 over x1-x2 (it looks lke a fraction)

then you plug in your coordinates, so it becomes:

m = 7-3 over -4 - (-4) which then you get your slope as 4, but because it has to be perpendicular, the slope becomes -1/4. this is because the slope has to be the reciprocal and the opposite sign to be perpendicular.

Then, you can continue to create the equation by using point-slope form, which is y - y1 = m (x-x1)  (y1 and x1 are from the coordinates btw)

so the point-slope equation is:

y - 3 = -1/4 (x + 4)

y - 3 = -1/4x - 1

   +3            +3

y = -1/4x + 2 (this is your equation in slope - intercept form)

I hope this helps!!

Considering the two figures the value of x is

The value of x is found by the external angle theorem which states that the sum of the two opposite internal angels of a triangle gives the external angle

The value of x is calculated as below

8)  70 + 5x = 9x + 22

70 - 22 = 9x - 5x

48 = 4x

x = 12

9)  65 + 8x + 11 = 16x + 12

65 + 11 - 12 = 16x - 8x

66 = 8x

x = 8.25

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The direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

What are the component of force?

If a force acting at some angle [tex]\theta[/tex] with respect to x axis then the force can be resolved into two perpendicular forces ([tex]Fcos\theta[/tex] and [tex]Fsin\theta[/tex]). These perpendicular forces are known as component of forces.

Consider the following diagram of the sialboat.

The component of force along the heading direction is 480N and the component of force perpendicular to the heading is 650N.

If F is the foce the direction of wind then then component of force in the East direction will be [tex]Fcos\theta[/tex] and the component of force in the heading direction is [tex]Fsin\theta[/tex]. Now, take the ratio of these two compnents to find the angle [tex]\theta[/tex] as follows:

[tex]tan\theta=\frac{Fcos\theta}{Fsin\theta}\\tan\theta=\frac{650N}{480N}\\\\\theta=tan^{-1}(1.354)\\=53.6^0[/tex]

Now, calculate the force exerted by the wind. Equate the force in heading direction to find the force.

[tex]Fsin\theta=480N\\F=\frac{480N}{sin\theta}\\=\frac{480N}{sin53.6^0}\\=596.4N[/tex]

Hence, the direction of force is [tex]53.6^0[/tex] South of West and force exerted by the wind is 596.4N.

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Answer:

========================

The difference between two consecutive integers is 1.

A) x + (x + 1) + (x + 2) = 42,

B) x + (x + 2) + (x + 4) = 42

C) (x minus 1) + x + (x + 1) = 42

D) (x minus 2) + x + (x + 2) = 42

E) x + 2 x + 3 x = 42

Answer:

x + (x + 1) + (x + 2) = 42

(x minus 1) + x + (x + 1) = 42

Step-by-step explanation:

Integer: A whole number that can be positive, negative, or zero.

Consecutive integer:  Integers that follow each other in order.

Let x be an integer.

Consecutive integers of x are one more or one less than each other in order.

This equation represents 3 consecutive integers as each value is one more than the previous value.

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

This equation represents 3 consecutive integers as each value is one more than the previous value.

This equation does not represent 3 consecutive integers as each value is 2 more than the previous value.

This equation does not represent 3 consecutive integers as each value is x more than the previous value.

Answer:

0.3125

Step-by-step explanation:

10 / 2 is 5

5 / 2 is 2.5

2.5 / 2 is 1.25

1.25 / 2 is 0.625

0.625 / 2 is 0.3125