HELP ON THIS PROBLEM

What is the period, amplitude, and the equation of the curve of this graph?

Answer:

x=-3

Step-by-step explanation:

Given, f(x) = 10^-3 and f(x)=10^x

Compare the equations

10^-3=10^x

So, x=-3

Answer:

Answer is 32 cm is length of PQ

Step-by-step explanation:

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Answer:

the first option

Step-by-step explanation:

for a number to be rational, it should be able to be expressed as a fraction.  Non terminal decimals must have a repeating pattern. Square roots of random numbers aren’t rational. Just like the first rule with decimals, the third number cannot be expressed as a fraction

Answer:

Step-by-step explanation:

it’s the first one

Answer:

Step-by-step explanation:

y

=

1

3

x

−

3

Use the slope-intercept form to find the slope and y-intercept

Slope:

1

3

y-intercept:

(

0

,

−

3

)

Any line can be graphed using two points. Select two

x

values, and plug them into the equation to find the corresponding

y

values.

x

y

0

−

3

3

−

2

Graph the line using the slope and the y-intercept, or the points.

Slope:

1

3

y-intercept:

(

0

,

−

3

)

x

y

0

−

3

3

−

2

image of graph

Answer:

Convert the problem to an equation using the percentage formula: P% * X = Y.

P is 10%, X is 150, so the equation is 10% * 150 = Y.

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.

Find the actual Dimensions of the triangle.

Multiply the size of the triangle on paper by 1.5 feet per inch:

Width = 5 x 1.5 = 7.5 feet.

Height= 7 x 1.5 =10.5 feet

Area of a triangle is 1/2 x base x height:

Area = 1/2 x 7.5 x 10.5 = 39.375 square feet.

Answer: 39.375 square feet.

The area of the actual banner is 39.375 feet²

Scaling is used to increase or decrease the size of a figure so as to create an image.

Given that 1 inch on the drawing Is equivalent to 1.5 feet on the actual banner, hence:

Base = 5 in * 1.5 feet per in = 7.5 feet

Height = 7 in * 1.5 feet per in = 10.5 feet

Area of the actual banner = (1/2) * 7.5 * 10.5 = 39.375 feet²

The area of the actual banner is 39.375 feet²

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Answer:

Step-by-step explanation:

t says that's 4 units distant from the another vertex. So, if a square is formed by 4 equal sides and 4 right angles, then you just have to add 4 units on x or y.

-> (2, 1) -> + 4 units on X

-> = (6, 1)

or

-> (2, 1) -> +4 units on Y

-> = (2, 5)

(2, 5) isn't an answer so the unique possible answer is (6, 1)

Answer: (6, 1)

Answer:

D. He needs 6 cups of flour for 3 batches

Yes, it is a polynomial

The degree of the polynomial is 2

and it is a Quadratic polynomial

A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It is made up of indeterminates (also known as variables) and coefficients.\(x^{2}\)− 4x + 7. is an illustration of a polynomial with a single indeterminate x. Three-variable example: \(x^{3}\)+ 2xy\(z^{2}\) − yz + 1..

Numerous branches of mathematics and science use polynomials. For instance, they are used to define polynomial functions, which show up in contexts ranging from basic chemistry and physics to economics and social science, and they are used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to encode a wide range of problems, from simple word problems to complex scientific problems.

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The key features of this quadratic relation y = -3x² - 24x - 36 include;

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped.

Since the leading coefficient (value of a) in the given quadratic function y = -3x² - 24x - 36 is negative 16, we can logically deduce that the parabola would open downward and the x-intercept (roots) is given by the ordered pair (-6, 0) and (-2, 0).

When x = 0, the y-intercept can be determined as follows;

y = -3x² - 24x - 36

y = -3(0)² - 24(0) - 36

y = -36

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-24)/2(-3)

Axis of symmetry, Xmax = -4

For the vertex, we have:

y(-4) = -3x² - 24x - 36

y(-4) = -3(-4)² - 24(-4) - 36

y(-4) = 12

In conclusion, the quadratic function has a maximum value at 12.

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Answer:

Therefore, the total used car sales were $179,625.

Step-by-step explanation:

Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.

The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:

3x + 5x = 8x

So, the total sales can be expressed as:

8x = $287,400

To find the value of x, we need to divide both sides by 8:

x = $35,925

Now, we can calculate the used car sales by multiplying 5x by the value of x:

Used car sales = 5x * x = 5 * $35,925 = $179,625

Therefore, the total used car sales were $179,625.

Answer:

the explanatory variable is "the amount of practice every year" while the response variable is "the improvement in his game"

Step-by-step explanation:

In simple terms, the difference between explanatory and random variable is that the response variable is usually the focus of a question in a study/experiment while an explanatory variable is a variable that explains changes in the response variable. Which means that the explanatory variable is simply any variable that may affect the response variable.

Now, in this question, the golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.

This means that the amount of practice every year explains how much he improves every year.

Thus, the explanatory variable is "the amount of practice every year" while the response variable is "improvement in his game"

Answer:

10

Step-by-step explanation:

Distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Let \((x_1,y_1)\) = (-4, 2)

Let \((x_2,y_2)\) = (2, -6)

Substituting given points into the formula:

\(\implies d=\sqrt{(2-(-4))^2+(-6-2)^2}\)

\(\implies d=\sqrt{(6)^2+(-8)^2}\)

\(\implies d=\sqrt{36+64}\)

\(\implies d=\sqrt{100}\)

\(\implies d=10\)

A²+B²= C²

31²+ 21²= z²

961+441 = z²

1402= z²

z= 37.443290454

Answer:

(x+2), (x-4), (x-3)

Step-by-step explanation:

Use the rational root theorem to get started, then factor the remaining quadratic to find:

x^3 − 5x^2 − 2x + 24 = (x + 2)(x − 4)(x − 3)

Explanation:

Let  f(x) =x^3 − 5x^2 − 2x + 24

By the rational root theorem, any rational zeros of  f(x)  must be expressible in the for p/q for integers p, q with p a divisor of the constant term 24 and q a divisor of the coefficient 1 of the leading term.

That means that the only possible rational zeros are the factors of 24, namely:

± 1, ± 2, ± 3, ± 4, ± 6, ± 12, ± 24

Try each in turn:

f(1) = 1 − 5 − 2 + 24 = 18

f(−1) = −1 − 5 + 2 + 24 = 20

f(2) = 8 − 20 − 4 + 24 = 8

f(−2) = −8 − 20 + 4 + 24 = 0

So  x = −2  is a zero and (x + 2) is a factor.

x^3 − 5x^2 − 2x + 24 = (x + 2)(x^2 − 7x + 12)

We can factor  

x^2 − 7x + 12 by noting that 4 × 3 = 12 and 4 + 3 = 7, so:

x^2 − 7x + 12 = (x − 4)(x − 3)

Putting it all together:

x^3 − 5x^2 − 2x + 24  =  (x + 2)(x − 4)(x − 3)

\(-1~~,~~\stackrel{-1+4}{3}~~,~~\stackrel{3+4}{7}~~,~~\stackrel{7+4}{11}~~,~~\stackrel{11+4}{15}\qquad \qquad \stackrel{\textit{common difference}}{d = 4} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\stackrel{\textit{first term}}{-1}\\ d=\stackrel{\textit{common difference}}{4} \end{cases}\implies a_n=-1+(n-1)4 \\\\\\ a_n=-1+4n-4\implies a_n=4n-5\)

Answer:

Step-by-step explanation:

solo un nino diria eso

Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =

Answer:

Step-by-step explanation:

Function representing the bacterial growth has been given as,

\(b_1(t)=1200(1.8)^t\)

a). Here 1200 represents the initial number of bacteria taken for the study (1).

b). 1.8 represents the growth factor by which the population of the bacteria is multiplying.

c). Second study is modeled by the function given as,

  \(b_2(t)=1000(1.8)^t\)

  Here, initial population of bacteria = 1000

  Difference in 1200 and 1000 in two studies means → Second study was conducted on 1000 bacteria while in study (1) number of bacteria were 1200.

Answer:

953,902

Step-by-step explanation:

The complex numbers graphed on the plane are given as follows:

Complex numbers are number that are divided into a real part and an imaginary part, according to the definition given as follows:

z = a + bi.

In which:

On the complex plane, we have that:

As the number z1 has a horizontal coordinate of 3 and a vertical coordinate of 0, it is given as follows:

z1 = 3 + 0i.

As the number z2 has a horizontal coordinate of 0 and a vertical coordinate of -2, it is given as follows:

z2 = 0 - 2i.

As the number z3 has a horizontal coordinate of -2 and a vertical coordinate of 1, it is given as follows:

z3 = -2 + i.

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Answer:

x = 50

Step-by-step explanation:

\( log_{10}(2x) = 2\)

Use the following property.

\( log_{a}(m) = n \\ {a}^{n} = m\)

\( {10}^{2} = 2x \\ 100 = 2x \\ \frac{100}{2} = x \\ 50 = x\)

Therefore, the value of x is 50.

Answer Check

Substitute x = 50 in the equation.

\( log_{10}(2x) = 2 \\ log_{10}(2(50)) = 2 \\ log_{10}(100) = 2 \\ {10}^{2} = 100 \\ 100 = 100\)

The equation is true. Therefore x = 50.

Note

If you don't write logarithm with base, it is classified as common logarithm or base 10.

Answer: -3x⁵y²

its simplified :)

To model with mathematics is to test ideas using math and computer programs to simulate an object or action.

In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.

The model frequently needs to be modified because it does not adequately capture the situation.

By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$8.75\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &\frac{1}{4} \end{cases} \\\\\\ 8.75 = (1000)(\frac{r}{100})(\frac{1}{4})\implies 8.75=\cfrac{10r}{4} \\\\\\ 8.75=\cfrac{5r}{2}\implies 17.5=5r\implies \cfrac{17.5}{5}=r\implies \stackrel{\%}{3.5}=r\)

Answer: -4, -3, 0, 2

Step-by-step explanation:

Answer:

-4,-3,0,2

Step-by-step explanation:

Decimals that are higher is the less than the smallest