One third of the sum of 5 times a number and 3 is less than one fourth the sum of six times that number and 5

Answer:

[tex]\huge \boxed{z=176}\checkmark[/tex]

Step-by-step explanation:

Add by 135 from both sides of equation.

[tex]\displaystyle z-135+135=41+135[/tex]

Simplify, to find the answer.

[tex]\displaystyle41+135=176[/tex]

[tex]\huge \boxed{z=176}[/tex], which is our answer.

Hope this helps!

Answer: Z=176

Step-by-step explanation: All you need to do is isolate z. Add 135 to each side.

135+41=176=Z

[1, 4, 3]

Solve for the first variable in one of the equations, then substitute the result into the other equation.

**For more information on how to solve a system of equations in three variables, paste and copy this link:

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***By the way, in the final line, that "+" next to the 6 should be replaced with an "=".

Answer:

Option C. 1:11

Step-by-step explanation:

Let

x-----> dollars  spent on office space

y ----> dollars spent  on other costs

we know that

x+y=$360,000 -----> equation A

x=$30,000 ----> equation B

substitute equation B in equation A and solve for y

30,000+y=360,000

y=360,000-30,000=$330,000

Find the ratio of dollars  spent on office space to dollars spent  on other costs

Divide the dollars  spent on office space by the dollars spent  on other costs

so

x/y

substitute

30,000/330,000=1/11

Answer:

$894

Step-by-step explanation:

$27,000+$2,200+$600= $29,800

$29,800*0.03=$894

Answer:

[tex]\large\boxed{a_n=5\left(\dfrac{1}{10}\right)^{n-1}}[/tex]

Step-by-step explanation:

Check:

[tex]n=1\\\\a_1=5\left(\dfrac{1}{10}\right)^{1-1}=5\left(\dfrac{1}{10}\right)^0=5(1)=5\qquad\bold{CORRECT}\ (1,\ 5)\\\\n=2\\\\a_2=5\left(\dfrac{1}{10}\right)^{2-1}=5\left(\dfrac{1}{10}\right)^1=5\left(\dfrac{1}{10}\right)=\dfrac{5}{10}=0.5\qquad\bold{CORRECT}\ (2,\ 0.5)\\\\n=3\\\\a_3=5\left(\dfrac{1}{10}\right)^{3-1}=5\left(\dfrac{1}{10}\right)^2=5\left(\dfrac{1}{100}\right)=\dfrac{5}{100}=0.05\qquad\bold{CORRECT}\ (3,\ 0.05)[/tex]

[tex]a_{n}[/tex] [tex]= 5 (\frac {1}{10} )^{n-1}[/tex]

Mathematical sequences are the set of numbers that makes a pattern or can be simple and complicated, finite and infinite. Explore sequences, terms in a sequence, and the different kinds of mathematical sequences, including the famous Fibonacci sequence.

Check:

n=1

[tex]a_{1} = 5 (\frac {1}{10} )^{1-1} = 5 (\frac {1}{10} )^{0} = 5 (1)=5[/tex]  True (1,5)

n=2

[tex]a_{2} = 5 (\frac {1}{10} )^{2-1} = 5 (\frac {1}{10} )^{1} = 5 \frac{1}{10} = 0.5[/tex] True (2, 0.5)

n=3

[tex]a_{3} = 5 (\frac {1}{10} )^{3-1} = 5 (\frac {1}{10} )^{2} = 5 \frac{1}{100} = 0.05\\[/tex] True (3, 0.05)

sequence chart is a series of the events and actions set in the order in which they take place. this is considered to be a fantastic way to represent the necessary steps taken to reach to the outcome.

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To find out which equation has no real solutions, we need to calculate the discriminant for each of these given equations.

For calculating the discriminant, we need to first compare these equations with the general formula which is ax²+bx+c.

So, let's get started.

1) x² + 4x + 16 = 0

a=1, b=4, c=16

D = b²-4ac

= (4)² - 4(1)(16)

= 16-64

= -48

√D = √-48

2) 4x² + 4x - 24 = 0

a=4, b=4, c=-24

D = b²-4ac

= (4)² - 4(4)(-24)

= 16 - 16(-24)

= 16 + 384

= 400

√D = √400 = +20 or -20

3) 5x² + 3x - 1 = 0

a=5, b=3, c=-1

D = b²-4ac

= (3)² - 4(5)(-1)

= 9 + 20

= 29

√D = √29

4) 2x² - 4x + 4 = 0

a=2, b=-4, c=4

D = b²-4ac

= (-4)² - 4(2)(4)

= 16 - 32

= -16

√D = √-16

Now from all these above calculations, we can see that discriminant was negative in first equation and in last equation.

If D<0 then roots does not exist, as the square root can not contain a negative value or the equation does not have any real solutions.

Roots in such case can be calculated but those roots are known as imaginary roots, which is a higher concept.

So Final answer is,

Equation 1 => x² + 4x + 16 = 0

and

Equation 4 => 2x² - 4x + 4 = 0

has no real solutions.

Answer:

b) L+S=80 and 2.75L+3.25S=245

Step-by-step explanation:

L stands for larger softballs. S stands for smaller softballs.

If you are ordering 80 softballs, then L and S represent the number of softballs of each one (large or small) to get a total of 80.

2.75 is the price of a large softball

3.25 is the price of a small softball.

You multiply the amount of each softball to how many of those kinds of softballs you get, you will then get the sum of the amount you ordered for 80 softballs: 245 dollars.

So thus the answer is B

Answer:

L+S=80

2.75L+3.25S=245

Choice B

Step-by-step explanation:

Larger ball costs $2.75.

Smaller ball costs $3.25.

You order a total of 80 softballs for $245.

So L is for number of large balls.

S is for number of small balls.

So we have 80 balls in all, some are small and some are large. This means the number of large plus the number of small equals 80.

So we have this equation L+S=80.

Now if you buy L balls, you spend 2.75 times L on large balls altogether.

If you buy S balls, you spend 3.25 times S on small balls altogether.

So together you spend 2.75L+3.25S.  They gave us that this amount should be equal to 245.

So this equations is 2.75L+3.25S=245

We are looking for the choice that contains these equations:

L+S=80

2.75L+3.25S=245

Answer:

A is most likely the next step in the series

Step-by-step explanation:

Each step, the number of sides is increasing by 1.

4,5,6 means that the next number of sides would be 7. Option A has 7 sides.

Answer:

B. [tex]^\leftrightarrow_{AB}[/tex] and [tex]^\leftrightarrow_{CD}[/tex]  are perpendicular lines.

Step-by-step explanation:

We can quickly plot the points in the cartesian plane as shown in the attachment.

A visual representation will help us see that A,B,C, and D do not lie on the same line.

The slope of AB  is [tex]\frac{4-1}{-2--8} =\frac{3}{6}=\frac{1}{2}[/tex]

The slope of CD is [tex]\frac{5--1}{-6--3} =\frac{6}{-3}=-2[/tex]

The two slopes are negative reciprocals of each other.

It is true that line AB and line CD are perpendicular.

These two lines cannot be perpendicular and parallel at the same time.

It is also not possible that, the two lines are perpendicular but will not intersect

Therefore the correct choice is B

Answer:

B

Step-by-step explanation:

plato/edmentum

Answer:

Step-by-step explanation:

Option 3 is correct

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram

Step-by-step explanation:

Slope formula is given by:

slope = y2-y1

over      x2-x1

Properties of the parallelogram:

A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)

⇒Slope of AB =Slope of CD and Slope of BC = Slope of AD

By property of parallelogram:

⇒A(-5, -2), B(-3, 3), C(3, 5), D(1, 0) set of vertices forms a parallelogram

Answer: OPTION C.

Step-by-step explanation:

A parallelogram is defined as a quadrilateral which has two pairs of parallel sides.

Attached is shown in the parallelogram obtained by plotting the vertices provided in Option C.

If that figure is a parallelogram, then:

[tex]Slope\ AB=Slope\ CD\\\\Slope\ BC=Slope\ AD[/tex]

Let's check this:

[tex]Slope\ AB=\frac{-2-3}{-5-(-3)}=\frac{5}{2}[/tex]

[tex]Slope\ CD=\frac{0-5}{1-3}=\frac{5}{2}[/tex]

[tex]Slope\ BD=\frac{3-5}{-3-3}=\frac{1}{3}[/tex]

[tex]Slope\ DA=\frac{-2-0}{-5-1}=\frac{1}{3}[/tex]

Therefore, the set of vertices that forms a parallelogram is:

[tex]A(-5, -2), B(-3, 3), C(3, 5), D(1, 0)[/tex]

Answer:

71.4

Step-by-step explanation:

For this, we will use Heron's Formula, or

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex],

with p as the perimeter divided by 2, and a, b, and c are the side lengths.

Plugging our values in, (11.6+20+13)/2 = 22.3 = p, and

[tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex] = [tex]\sqrt{5103.8679} =71.4[/tex] rounded to the nearest tenth

Answer:

[tex]\large\boxed{2^{4x}=2^{3x-9}}[/tex]

Step-by-step explanation:

[tex]8=2^3\to 8^{x-3}=(2^3)^{x-3}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{3(x-3)}\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=2^{(3)(x)+(3)(-3)}=2^{3x-9}[/tex]

If you want a solution of this equation:

[tex]2^{4x}=8^{x-3}\\\\2^{4x}=2^{3x-9}\iff4x=x-3\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x=-3\qquad\text{divide both sides by 3}\\\\x=-1[/tex]

Answer:  the correct option is

(D)  [tex]2^{4x}=2^{3x-9}.[/tex]

Step-by-step explanation:  We are given to select the correct equation that is equivalent to the following equation :

[tex]2^{4x}=8^{x-3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

Equivalent equations means  two equations that can be obtained from one another using some properties of formula.

We will be using the following formula :

[tex](a^b)^c=a^{b\times c}.[/tex]

From equation (i), we have

[tex]2^{4x}=8^{x-3}\\\\\Rightarrow 2^{4x}=(2^3)^{x-3}\\\\\Rightarrow 2^{4x}=2^{3\times(x-3)}\\\\\Rightarrow 2^{4x}=2^{3x-9}.[/tex]

Thus, the required equivalent equation is [tex]2^{4x}=2^{3x-9}.[/tex]

Option (D) is CORRECT.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (-1, -3). Substitute:

[tex]y-(-3)=-5(x-(-1))\\\\y+3=-5(x+1)[/tex]

Convert to the slope-intercept form (y = mx + b):

[tex]y+3=-5(x+1)[/tex]          use the distributive property

[tex]y+3=-5x-5[/tex]            subtract 3 from both sides

[tex]y=-5x-8[/tex]

Answer:

Second option: False

Step-by-step explanation:

We need to remember this property:

 [tex]\sqrt[n]{x^n}=x^{\frac{n}{n}}=x[/tex]

In this case we have the following expressions provided in the exercise:

[tex]\sqrt{3x}[/tex] and [tex]x\sqrt{3}[/tex]

Based on the property mentioned before the expression [tex]\sqrt{3x}[/tex] cannot be simplified. So 3 and  [tex]x[/tex] stays inside the square root.

Therefore, the conclusion is: The expression [tex]\sqrt{3x}[/tex] is not equivalent to the expression [tex]x\sqrt{3}[/tex]

Deciphering the expressions reveals that 'square root 3x' is not equivalent to 'x square root 3'. They interpret differently on the terms inside and outside of the square root, thus they are not the same.

The statement 'the expression square root 3x is equivalent to the expression x square root 3' is False. To understand why, we need to understand the properties of square roots and multiplication. The expression square root 3x means that the square root is being taken over the entire product of 3x. This is not the same as x square root 3, where the square root is only being applied to 3, and then that result is being multiplied by x.

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Answer:

Table for y = 2|x-4| + 3 on domain {2,3,4,5,6} is given as:

x                           y

2         2|x-4| + 3 = 2|2-4| + 3 = 7

3         2|x-4| + 3 = 2|3-4| + 3 = 5

4         2|x-4| + 3 = 2|4-4| + 3 = 3

5         2|x-4| + 3 = 2|5-4| + 3 = 5

6         2|x-4| + 3 = 2|6-4| + 3 = 7

The graph of the absolute value function y = 2|x-4| + 3 for the given domain is attached.

Step-by-step explanation:

The absolute value parent function, written as function(x) = | x |, is defined as:

|x| = x          and           |-x| = x

In our case;

For x = 2        

y = 2|x-4| + 3

= 2|2-4| + 3

= 2|-2| + 3

= 2*2 + 3

= 4 + 3

= 7

Similarly, for all other values of x in the given domain, value of y can be calculated.

Answer:

Step-by-step explanation:

[tex]|a|=\left\{\begin{array}{ccc}a&for\ a\geq0\\-a&for\ a<0\end{array}\right[/tex]

Put each value of x from the set {2, 3, 4, 5, 6}

to the equation y = 2|x - 4| + 3:

x = 2 → y = 2|2 - 4| + 3 = 2|-2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (2, 7)

x = 3 → y = 2|3 - 4| + 3 = 2|-1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (3, 5)

x = 4 → y = 2|4 - 4| + 3 = 2|0| + 3 = 2(0) + 3 = 0 + 3 = 3 → (4, 3)

x = 5 → y = 2|5 - 4| + 3 = 2|1| + 3 = 2(1) + 3 = 2 + 3 = 5 → (5, 5)

x = 6 → y = 2|6 - 4| + 3 = 2|2| + 3 = 2(2) + 3 = 4 + 3 = 7 → (6, 7)

Mark the points in the coordinates system.

The domain is only five numbers, therefore the graph of this function is only five points.

Answer:(4, 7)

Step-by-step explanation:

This question is about changing the coordinates of the function.

They want you to choose a value of x that will make the sentence inside the function (-3x/4) equal to -3.

-3 x / 4 = -3

x = 4

Hence, the correspondig point is (4, 7)

Answer:

The vertex of the parabola is (105 , 7)

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation of the parabola is y = a(x - h)² + k, where (h , k) are

  the coordinates of the vertex point of the parabola

- The points (0 , 27) , (52.5 , 12) , (105 , 7) ,  (157.6 , 12) , (210 , 27) are

 the points lie on the parabola

- We have three unknown a , h , k to find them we will substitute the x

 and y in the equation by the coordinates of some point on the

 parabola

- Lets start with point (0 , 27)

∵ x = 0 and y = 27

∴ 27 = a(0 - h)² + k

∴ 27 = ah² + k ⇒ (1)

- Lets use point (210 , 27)

∵ x = 210 and y = 27

∴ 27 = a(210 - h)² + k ⇒ (2)

- Equations (1) and (2) have the same L.H.S, so we can equate them

∴ ah² + k = a(210 - h)² + k ⇒ subtract k from both sides

∴ ah² = a(210 - h)² ⇒ divide both sides by a

∴ h² = (210 - h)² ⇒ take √ for both sides

∴ h = ± (210 - h)

∵ h = 210 - h ⇒ add h to both sides

∴ 2h = 210 ⇒ divide both sides by 2

∴ h = 105

∵ h = - (210 - h)

∴ h = -210 + h ⇒ no value of h from this equation so we will ignore it

∴ The value of h is 105

- Lets substitute this value of h in the equation

∴ y = a(x - 105)² + k

- Lets use the point (105 , 7)

∵ x = 105 and y = 7

∴ 7 = a(105 - 105)² + k

∴ 7 = a(0) + k

∴ k = 7

- The coordinates of the vertex point are (h , k)

∵ h = 105 and k = 7

∴ The vertex of the parabola is (105 , 7)

Answer:

105, 7 and then for the next one y= 0.0018(x – 105)2 + 7

Step-by-step explanation:

Answer:

=8/3m⁷n⁶

Step-by-step explanation:

Given the expression (2mn)⁴/6m⁻³n⁻², we first solve the numerator

(2mn)⁴ = 16m⁴n⁴

The new expression becomes 16m⁴n⁴/6m⁻³n⁻²

We now divide the coefficients and the exponents as follows:

=16/6ₓ(m⁴/m⁻³)×(n⁴/n⁻²)

Division between indices to the same base we subtract the powers.

4-⁻3=7

4-⁻2=6

=8/3m⁷n⁶

Answer:

the asnwer is A

Step-by-step explanation:

Answer:

1) 8x5

2) 8x10

3)8x20

This answer does not make sense because you can't buy half a movie ticket

Answer: If h(x) represents the amount of money spent and x the amount of friends, then we can write it as in a pair as (x, h(x))

Then the pair given is (6.5, $92.25)

Here you see a problem, x is 6.5, knowing that x represents the amount of friends, this is a problem because you need to have a whole number ( you can't have a 0.5 of a friend)

So the domain of h(x) is only the natural numbers, then the possible solution of (6.5, $92.25) doesn't make sense because 6.5 is not a natural number.

Answer:

4:3

Step-by-step explanation:

You divide 8 and 6 by 2 to simplify it

[tex]\( f(x) + g(x) \) equals \( 2x^2 - 5x - 8 \).[/tex] (option b)

To find [tex]\( f(x) + g(x) \)[/tex], we need to add the functions f(x) and g(x):

[tex]\[ f(x) + g(x) = (2x^2 + 3x - 4) + (-8x - 4) \][/tex]

[tex]\[ = 2x^2 + 3x - 4 - 8x - 4 \][/tex]

[tex]\[ = 2x^2 + (3x - 8x) + (-4 - 4) \][/tex]

[tex]\[ = 2x^2 - 5x - 8 \][/tex]

Therefore, the correct answer is:

[tex]\[ f(x) = 2x^2 - 5x - 8 \][/tex]

Complete question: If f(x)=2x²+3x−4, and g(x)=−8x−4, what does f(x)+g(x) equal?

a-f(x)=2x²+5x+8

b-f(x)=2x²−5x−8

c-f(x)=2x²+11x−8

d-f(x)=2x²+5x

Answer:

The distance from the pole is 11.8 ft

Step-by-step explanation:

Let

x------> the distance from the pole

we know that

The tangent of angle of 28 degrees is equal to divide the opposite side to angle of 28 degrees ( the height of the pole) by the adjacent side to angle of 28 degrees ( the horizontal distance from the pole)

so

tan(28°)=6.3/x

Solve for x

x=6.3/tan(28°)=11.8 ft

Final answer:

The distance from the pole is found by using the tangent function with the given angle of elevation (28 degrees) and the pole's height (6.3 feet), resulting in a distance of approximately 12.04 feet.

Explanation:

To calculate the distance from the pole given the angle of elevation and the height of the pole, you can use trigonometric functions. The angle of elevation is 28 degrees and the height of the pole is 6.3 feet. You can use the tangent function, which relates the angle of a right triangle to the ratio of the opposite side to the adjacent side.

Let d represent the distance from the pole. The tangent of the angle of elevation (28 degrees) equals the opposite side (6.3 feet) over the adjacent side (distance d).

tan(28°) = 6.3 / d

To find d, rearrange the equation: d = 6.3 / tan(28°). Using a calculator for tan(28°), you obtain d ≈ 12.04 feet.

Therefore, the distance from the pole is approximately 12.04 feet.

Answer:

5

Step-by-step explanation:

(-1) + 5 - (-6) - 5 =

    v          

4 - (-6) - 5 =

   v

10 - 5 =

   v

5

e = Euler's constant

e ≈ 2.718281828459045, rounded up e = 2.7183.

= 4.17356

the number after the line is lower than 5, round the number down (keep it the same). If the number is 5 and more than it round the number upwards. therefore in example 1 you need to round 4.17356 to 4 decimal places. This means you have 2 choices, either 4.17356 or 4.17357.

When we say round to 4 it means to fewer the digits to 4 to the right of the decimal point. The basic rule of remember is, if the number in the 5th place ( to round it any decimal place, consider this next digit) is > 5 then add 1 on the 4th digit and else remains the same.

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Step-by-step explanation:

for x^a/x^b = x^(a-b)...eqn 1

thus for 5^6/5^2 = a^b,

if a = 5, following eqn 1...

then b = 6-2 = 4

Answer:

20.2

The thousandth position doesn't affect the rounding of the numbers. Since the hundredth position contains a 5, you will round up, meaning the tenth position will change from a 1 to a 2.

Answer:

20.2

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Answer:

5040 ft^2

Step-by-step explanation:

The area of rectangle is: 7 ft by 5 ft

The scaling is done by multiplying the dimensions with the sale factor.

so,

The area of actual house will be:

(7*12) x (5*12)

= 84 * 60

= 5040 ft^2

So the area of actual building is 5040 ft^2 ..

Answer:

220 miles

Step-by-step explanation:

Joe got $301 for an overnight trip.

As the employees get $125 for lodging. The lodging expense will be subtracted from the total amount to get the amount for the miles he drove.

So,

Expense by company for miles driver = 301 - 125 = $176

So, Joe received $176 for miles driven

Now,

amount for one mile = $0.80

Miles driven in $176 = 176/0.80 = 220 miles

Joe drove 220 miles ..

Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip, after considering the fixed lodging cost and the per mile reimbursement rate.

The student wishes to know how many miles Joe drove if his company reimbursed him $301 for an overnight trip wherein he receives $125 for lodging plus $0.80 per mile driven. To solve this problem, we start by subtracting the fixed lodging cost from the total reimbursement to find the total amount reimbursed for mileage. Let's denote the number of miles driven by Joe as m.

Total reimbursement for mileage = Total reimbursement - Lodging cost
$301 - $125 = $176

Now, since Joe gets reimbursed $0.80 per mile, we can calculate the number of miles driven as follows:

$176 / $0.80 per mile = 220 miles

Therefore, Joe drove 220 miles for his company to be reimbursed $301 for an overnight trip.

Answer:

D one real solution

Step-by-step explanation:

x^2 - 8x + 16 = 0

This is in the form

ax^2 +bx + c = 0

so we can use the discriminant to determine the number of solutions

b^2 -4ac

(-8)^2 -4(1)(16)

64 - 64

0

Since the discriminant is zero, there is one real solution.