what is the value of z? (multiple choice)

The logarithmic equation that is equivalent to this exponential equation 2,400=7,500 (10) ^ -x is [tex]x = -log_{10} \frac{8}{25}[/tex]. Option C

from the question we have:

2400 = 7500(10)⁻ˣ

we would have to transform the equation that we have here into the logarithm form.

This is written as:

[tex]\frac{2400}{7500}=10^-^x[/tex]

from here we are to reduce the division

hence we would have:
[tex]10^-^x = \frac{8}{25}[/tex]

-x = log₁₀8/25

then

[tex]x = -log_{10} \frac{8}{25}[/tex]

option c is correct

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Three variable lines are drawn in the three dimensional coordinate system.

Three-dimensional coordinate system is also called rectangular coordinate system. The system has three reference axes named X, Y and Z axis which are perpendicular to each other.

The above three axes intersect at the origin.

In the analytical geometry, location of each point is represented by three coordinate system. They give mathematical statement by using three-dimensional space.

In order to plot in the three-dimensional plane, we need to determine the value of x, y and z. At first, we start from the origin and approach to the positive x direction if our x value is positive, otherwise we need to go to the negative x direction. After identifying the x coordinate, we need to move parallel to y direction and locate the y coordinate and finally we identify the z coordinate in the same way. In the last, we will join the points.

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Answer: 12 km\h north

Step-by-step explanation:

I actually have good guesses

Velocity = 12 km/h

-

Velocity can be defined as the division between distance traveled and the time it took for that distance to be traveled:

Velocity = Distance / Time

With the above information in mind, we can calculate the velocity of the bicycle:

Velocity = 18 km / 1.5 h

Velocity = 12 km/h

Thus the velocity of the bicycle is 12 kilometers per hour.

Answer:

B) 7^2 x 7^3

Step-by-step explanation:

B is 7^5 , everything else is 7^4

Given:

Length of escalator = 26 ft

Angle of depression = 41 degrees

To find:

The horizontal distance x the escalator covers to the nearest tenth of a foot.

Solution:

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

Using this formula for the given triangle, we get

[tex]\cos 41^\circ=\dfrac{x}{26}[/tex]

[tex]26\cos 41^\circ=x[/tex]

[tex]26(0.7547)=x[/tex]

[tex]19.6222=x[/tex]

Round the value to the nearest tenth.

[tex]x\approx 19.6[/tex]

Therefore, the escalator covers 19.6 ft horizontally.

Answer:

7

Step-by-step explanation:

So the log thingy is loga(b) = c

a^c = b

So in this one, a = a

b = 7

c = 4

a^4 = 7

Answer: 6x-48

Step-by-step explanation:

Use the distributive property

6x-48

6x-6*8

6x-48

In question 1;

The student multiplied without flipping the second expression.

In second question;

The negative should only be distributed to the numerator.

In third question,

3/2 should be remove from the x - value which make the expression undefined.

In fourth student;

Neither student is correct.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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

In question 1;

The expression is,

⇒ x² + 2x - 3 / (x² - 3x - 10) ÷ (2x + 12) / (8x + 16)

= (2x³ + 16x² + 18x - 36) / (8x³ - 8x² - 128x - 100)

Cleary, The student multiplied without flipping the second expression.

In question 2;

⇒ (-2y - 2) / (y² + 2y - 8) - (y - 1) / (2 - y)

⇒ (-2y - 2) / (y² + 2y - 8) + (-y + 1) / (-2 + y)

Clearly, The negative should only be distributed to the numerator.

In Question 3;

The student make mistake is ''3/2 should be remove from the x - value which make the expression undefined.''

In fourth student;

Neither student is doing correct solution.

In fifth question,;

Sarah didn't cancel incorrectly in step 3.

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The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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The 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

5⁻³

This can be written as 1/5³ which is equal to 1/125

-5⁻³

This can be written as -1/5³ which is equal to -1/125

(-5⁻³)⁻¹

We have an exponential property

[tex](x^{a} )^{b} =x^{ab}[/tex]

So (-5⁻³)⁻¹=(-5)³=-125

(-5⁻³)⁻¹  equivalent expression is -125

(-5⁻³)⁰

=(-5)⁰=1

Hence, the 5⁻³ is equivalent to 1/125, - 5⁻³ is equivalent to -1/125,  (-5⁻³)⁻¹ is equivalent to -125 and (-5⁻³)⁰ is equivalent to 1

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Answer:

The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.

Step-by-step explanation:

We shall use the Pythagorean Theorem to determine the length of the two oblique line of the figure. From Geometry, we know that the perimeter of the parallelogram is the sum of the lengths of the four sides of the parallelogram.

First, we calculate the length of the oblique line, that is:

[tex]l_{O} = \sqrt{5^{2} + 3^{2}}[/tex]

[tex]l_{O} = \sqrt{34}[/tex]

Second, we determine the length of the vertical line by direct observation, that is:

[tex]l_{V} = 12[/tex]

Lastly, the perimeter is determined by the following formula:

[tex]p = 2\cdot (l_{O}+l_{V})[/tex]

[tex]p = 24+2\sqrt{34}[/tex]

The perimeter of the paralellogram is [tex]24 + 2\sqrt{34}[/tex] units.  

Answer: 35.7

(This is the answer squared by the way)

Step-by-step explanation:

Answer:

I believe it is (C), the length of the golfers.

The things measured in the experiment are the bracelet and the length of the shots based off of it. The response variable is basically the dependent variable, and theyre trying to figure out if the lengths of shots are dependent on the bracelet.

Because of this, we know A and B are already wrong.

Now we're left with C and D.

If you think of graphing D as the y variable, it just doesn't make sense. Because how would you do that? But, if you made C the y variable, you can make a bar graph, which I think would make sense in this scenario.

Which is why I believe, the length of the shots is the response variable.

ED2021

Goodluck :)

it is (C), the length of the golfers.

A response variable is a type of dependent variable. It is the one that changes the results. Furthermore, a response variable is the expected effect, and it responds to explanatory variables.

Here, we have,

The things measured in the experiment are the bracelet and the length of the shots based off of it. The response variable is basically the dependent variable, and they are trying to figure out if the lengths of shots are dependent on the bracelet.

Because of this, we know A and B are already wrong.

Now we're left with C and D.

If you think of graphing D as the y variable, it just doesn't make sense. Because how would you do that? But, if you made C the y variable, you can make a bar graph, which I think would make sense in this scenario.

This  is why, the length of the shots is the response variable.

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Answer:

-x^2+7

Step-by-step explanation:

I dont exactly know how to write a quadratic equation, however my TI-84 calculator can make equations from points

Answer:

10,260 in³

Step-by-step explanation:

Please find attached an image of the chest

The ice chest is shaped like a rectangle. Thus the formula for the volume of a cuboid can be used to determine the volume of the chest

volume of a cuboid = length x width x height

18 in x 19 in x 30 in = 10,260 in³

Answer:

what does x mean, like what number does it represent in this situation

Answer:

x = 27

Step-by-step explanation:

I made '3' into 9/3

x/3 - 9/3 = x/9 + 9/3

convert terms to fractions with a denominator of 9

x/3 = 3x/9

9/3 = 27/9

3x/9 - 27/9 = x/9 + 27/9

(3x-27)/9 = (x+27)/9

since each denominator equals 9 we can set the numerators equal to each other:

3x - 27 = x + 27

3x = x + 54

2x = 54

x = 27

With an accuracy of within $0.01, the student will be able to recognize

and determine the total worth of a given assortment of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills.

TEKS stands for Texas Essential Knowledge and Skills. It is a set of state standards for public schools in Texas, that outline what students should know and be able to do in each grade level and subject area. The standards cover subjects such as English language arts, mathematics, science, social studies, and languages other than English.

The TEKS are used to guide the development of curriculum and instruction in Texas schools.

The clear learning goal for the Texas Essential Knowledge and Skills (TEKS) skill of determining the value of a collection of coins and bills could be: "The student will be able to accurately identify and calculate the total value of a given collection of coins and bills, including pennies, nickels, dimes, quarters, half-dollars, and dollar bills, to within $0.01."

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Answer:

298.24 mph at an angle of 89 degrees

Step-by-step explanation:

[tex]v_p[/tex] = Velocity of plane = 300 mph at 50 degrees

[tex]v_j[/tex] = Velocity of jet stream = 200 mph at 160 degrees

The velocity of the plane in component form is

[tex]v_p=300\cos50^{\circ}\hat{i}+300\sin50^{\circ}\hat{j}[/tex]

The velocity of the jet stream in component form is

[tex]v_j=200\cos160^{\circ}\hat{i}+200\sin160^{\circ}\hat{j}[/tex]

Resultant velocity is given by

[tex]v=(300\cos50^{\circ}+200\cos160^{\circ})\hat{i}+(300\sin50^{\circ}+200\sin160^{\circ})\hat{j}\\\Rightarrow v=4.9\hat{i}+298.2\hat{j}[/tex]

Magnitude is given by

[tex]|v|=\sqrt{4.9^2+298.2^2}\\\Rightarrow |v|=298.24\ \text{mph}[/tex]

Angle is given by

[tex]\theta=\tan^{-1}\dfrac{298.2}{4.9}=89^{\circ}[/tex]

The velocity of the plane is 298.24 mph at an angle of 89 degrees.

The factorization of the polynomial x² + 3x + 2 gives (x + 1)(x + 2)

An equation is an expression that shows how numbers and variables relate with each other.

A polynomial is an expression consisting of variables and their exponents with operations of addition and subtraction. Polynomials are classified based on degree as linear, quadratic and cubic.

The standard form of a quadratic equation is:

y = ax² + bx + c

where a, b and c are constants.

Given the polynomial:

x² + 3x + 2

Factorizing the polynomial:

x² + 2x + x + 2

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

= (x + 1)(x + 2)

The factorization gives (x + 1)(x + 2)

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Answer:

Gianna has $760 to spend and she has already spent $356.46 on a new bicycle, $10.01 on 2 bicycle reflectors, and $20.72 on a pair of bike gloves.

The total amount spent on these items is $356.46 + $10.01 + $20.72 = $387.19.

Gianna has $760 - $387.19 = $<<760-387.19=372.81>>372.81 left to spend on biking outfits.

She wants to buy biking outfits that cost $45.35 each.

We can write an inequality to represent the number of outfits Gianna can purchase while staying within her budget as follows:

45.35o <= 372.81

This inequality can be solved by dividing both sides by 45.35:

o <= 8.24

Therefore, Gianna can purchase 8 biking outfits while staying within her budget.

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

the range is the difference between the lowest and the highest number on the series

here the range is 3 two members have size 6 different from 6 and 3 which range its 3

Less than 2 units separate the median from the lower quartile for customers making purchases.

The three values known as quartiles divide sorted data into four equal-sized portions, each with an equal number of observations. An example of a quantile is a quantile. First quartile: Also referred to as the lower quartile or Q1. The median or second quartile is also referred to as Q2. Third quartile: Also referred to as the higher quartile or Q3.

Half of the difference between the upper and lower quartiles can be used to define the quartile deviation analytically. Here, the upper quartile (Q3) and lower quartile (Q1) can be used to depict quartile deviation as the letters QD. The term "quartile deviation" is sometimes used to refer to the semi-interquartile range.

The coefficient of quartile deviation serves as a gauge for a collection of data's variability or spread. It is determined by taking the square root of the difference between the upper and lower quartiles, squaring the result, and dividing it by two. Comparing data sets is simple because it is expressed as a percentage.

Therefore, the correct answer is option E. The difference between the median and the lower quartile for the customers making a purchase is less than 2.

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Answer: Spent $120 originally, profited by $36

Step-by-step explanation:

The total cost Stefan earned from selling the helmet and the bicycle is $139 + $17 = $156.

130% can be rewritten as [tex]\frac{130}{100}[/tex] which is simplified to 1.3.

Set up and this equation to find 130% of this price.

[tex]1.3x = 156\\x = 120[/tex]

Stefan spent $120 on these items.

Subtract this value from the selling price and solve.

[tex]156-120 = 36[/tex]

Stefan made $36 from selling the helmet and bicycle.

Growth that is slower than the Nuttall Oak growth rate is h=5t.

An equation is a mathematical statement that expresses two values as being equal. It is the basic building block of algebra and can be used to solve for unknown values, or to show the relationships between two or more values. Equations use mathematical operators such as addition, subtraction, multiplication, and division, as well as symbols and numbers, to express relationships between values. An equation can be written in the form of an expression, a system of equations, or a single equation. In all cases, an equation requires both sides of the equation to be equal in order to be valid and have a solution.

This equation describes growth that is slower than the Nuttall Oak growth rate because it has a lower rate of growth of 5 feet per year. The Nuttall Oak grows 7 to 8 feet per year, so any equation with a growth rate lower than that would be slower. Choices B, C, and D have higher growth rates than the Nuttall Oak, so they would not be slower than the Nuttall Oak growth rate.

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Answer:

I used desmos to make the graph

Step-by-step explanation:

Hopefully this helps!

Answer:

∅ = 6 radians

Step-by-step explanation:

s = r ∅

s is arc length

r is radius

∅ is  the central angle in radians

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

Plug in the givens

30 = 5 ∅

Divide both sides by 5

∅ = 6 radians

(FYI : 6 radians is about 343.8º)

Answer:

H 40%

Step-by-step explanation:

29+27+24=80

32/80=0.4

Answer:

Step-by-step explanation:

32/80 x 100 = 40%

Answer:

It would be >

Step-by-step explanation:

> Means bigger than, and -15 is bigger than -19.

Think of it as a number line. On the positive spectrum,

a bigger number is bigger. On the negative side, a smaller

number is bigger.

Hope this helps!