Solve this system. Write your answer as an ordered pair.

-5x + y = -3

3x - 8y = 24

Answer:

B

Step-by-step explanation:

The area of the triangle is half the base time the height.  The height is y sub 1.  The length is the distance between the x values.

well, we know that 25 pecks is 1/4% or namely 0.25%, less than 1%, and let's say the amount of pecks per day will be "x", which is 100% of that.

[tex]\begin{array}{ccll} pecks&\%\\ \cline{1-2} 25 & \frac{1}{4}\\[1em] x& 100 \end{array} \implies \cfrac{25}{x}~~=~~\cfrac{ ~~ \frac{1}{4} ~~ }{100}\implies 2500=x\cfrac{1}{4} \\\\\\ 2500=\cfrac{x}{4}\implies 10000=x[/tex]

Pila can peck a tree approximately 10,000 times per day.

Given that Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4 % the average number of pecks that she can make each day.

We need to determine how many times per day can pila peck a tree.

Let's denote the average number of pecks Pila can make in a day as "x."

According to the information given, Pila can drill a small hole in a tree trunk with 25 pecks, which is only 1/4% (0.25%) of the average number of pecks she can make each day.

We can set up the following equation to represent the relationship:

0.25% of x = 25

To solve for x, we first convert 0.25% to decimal form by dividing by 100:

0.25% = 0.25/100 = 0.0025

Now, we can rewrite the equation:

0.0025x = 25

To isolate x, we divide both sides of the equation by 0.0025:

x = 25 / 0.0025

Simplifying the right side gives us:

x = 10,000

Therefore, Pila can peck a tree approximately 10,000 times per day.

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The total interest cost to Bette is  $145.89

What is exact interest basis?

Exact interest means that the interest is computed on 365-day per year basis rather than a 360-day per year basis, which is the case with financial institutions.

The first task in this case is to determine the number of days from May 19, when the amount was borrowed till October 8, when loan repayment was effected.

There are 142 days between the two dates, hence, we can compute exact interest on the loan as shown by the below formula:

exact interest=loan principal*number of days the borrowing last/365days *interest rate

loan principal=$3000

number of days the borrowing last=142

interest rate=12.5%(1/2%=0.5%)

Exact interest=$3000*142/365*12.5%

Exact interest=$145.89

The amount would have been different if ordinary interest where the number of days in a year is deemed to be 360, was used instead

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The value of x when the richter scale rating scale is 8.4 is 251188643.151

A richter scale is a numerical scale that is used for expressing the magnitude of an earthquake in a geographical area

The richter scale takes the amplitude of the earthquake's largest seismic as an input and calculate (and display) the magnitude of an earthquake in the geographical area using a logarithmic function

The formula of a richter scale is expressed as:

log(x) = n

Where n represents the scale rating of the scale

In this case, n = 8.4.

So, we have:

log(x) = 8.4

Express as an exponent

x = 10^8.4

Evaluate the exponent

x = 251188643.151

Hence, the value of x when the richter scale rating scale is 8.4 is 251188643.151

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Answer:

vertex : (-5/2, -53/4)

solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)

Step-by-step explanation:

1.The vertex of the function is (-5/2, -53/4).

2.We have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.

1. Vertex:

The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:

x = -b / (2a)

y = f(x) = ax^2 + bx + c

Given: a = 1, b = 5, c = -7

x = -5 / (2 * 1) = -5 / 2

Now, substitute the value of x into the equation to find y:

y = (-5/2)^2 + 5 * (-5/2) - 7

y = 25/4 - 25/2 - 7

y = 25/4 - 50/4 - 7

y = (25 - 50 - 28) / 4

y = -53 / 4

So, the vertex of the function is (-5/2, -53/4).

2. Solutions (or roots or x-intercepts):

To find the solutions (x-intercepts) of the function, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Given: a = 1, b = 5, c = -7

x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1

x = (-5 ± √(25 + 28)) / 2

x = (-5 ± √53) / 2

Now, we have two solutions:

x = (-5 + √53) / 2 ≈ 0.73

x = (-5 - √53) / 2 ≈ -5.73

So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.

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Answer:

60.

100 (total) - 40 (amount in the library Saturday morning) = 60.

Type: Percentages / Fractions

The correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

Given a function f(x)=[tex]a^{x+g} +k[/tex].

We are told to find the domain and range of the function.

The domain is basically the values which we enters in a function.

The range is basically the values which we are getting by entering some values in the function.

An exponential function is given in the function which has no restrictions hence the domain is  (-∞,∞).The range depends on the vertical shift given by k. Hence the range of function is (k,∞).

Hence the correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).

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Answer:

$20

Step-by-step explanation:

$5.00 = 10miles

$0.25(40) = 40 miles

Remaining miles: 100 - (10 + 40) = 50

0.10(50) = 50 miles

5.00 + 0.25(40) + 0.10(50)

5.00 + 10.00 + 5.00

$20.00 for 100 miles

To find the missing numbers in the sequence, we must identify the rule by which they change.

The sequence starts at 8 and then decreases by 1, therefore, the second term is 7. The third term increases by 4 units with respect to the second, going from 7 to 11, and the fourth decreases again by 1, now remaining at 10.

The fifth term increases again by 4 units, from 10 to 14. This already gives us a clear idea of the rule that the sequence follows.

                                                  ₊₄              ₊₄

                                            ⁻¹             ⁻¹               ⁻¹  

In this way, the sixth element must decrease by 1, that is 13 and the seventh must increase by 4, that is 17.

8, 7, 11, 10, 14, 13, 17,…

The next numbers that the numerical sequence are 13 and 17, to complete. ✅

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

From the question, we are to write a polynomial that has a GCF of 7m

That is,

We are to write a polynomial that has a greatest common factor of 7m

Writing the polynomial

14mn - 21m + 49m²n + 7mn²

The  polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms

We are to write a polynomial with a GCF of 2ab²

Writing the polynomial

6a²b² - 8ab³ + 4a³b² + 2a³b³

The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms

Hence,

The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²

The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³

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At the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

Here, the initial population is [tex]P=1.23\times 10[/tex] and the growth rate is [tex]r=6.7\%[/tex].

So the population after [tex]t=4[/tex] years will be:

[tex]A=P(1+\frac{r}{100})^t\\\Longrightarrow A=1.23\times 10\times(1+\frac{6.7}{100})^4\\\Longrightarrow A=1.23\times 10\times(1.067)^4[/tex]

Therefore, at the growth rate of [tex]6.7\%[/tex], the population of the town after 4 years can be represented by the equation, [tex]A=1.23\times 10\times(1.067)^4[/tex].

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Answer:

x = 46 degrees

Step-by-step explanation:

180 - 134 = 46

Answer:

46°

Step-by-step explanation:

134 + x   add to a straight line angle = 180

134+x = 180

x = 46

The behavior of the graph of I and what it means in context can be explained below:

Sound intensity, serves as the  power that is been carried by sound waves per unit area and this is usually in the direction perpendicular to that area.

we were given the  function [tex]I = \frac{P}{4pir^2}[/tex]

r  represent the Distance from the source of sound

P represent the Power of the sound

when there is increase in the  distance from the source the intensity moves to zero.

we can see that there is is an inverse proportion between the Intensity and the distance r  which implies that The intensity decreases  when the distance increases.

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The gallons of the first brand of antifreeze should be 60 gallons.

The gallons of the second brand of antifreeze should be 90 gallons.

0.2f + 0.45s = 52.50 (0.35 x 150) equation 1

f + s = 150  equation 2

Where:

how many gallons of each brand of antifreeze must be used?

Multiply equation 2 by 0.2

0.2f + 0.2s = 30 equation 3

Subtract equation 3 from equation 2

0.25s = 22.50

s = 22.50 / 0.25

s = 90

f = 150 - 90 = 60 gallons

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Answer:

m=8

Step-by-step explanation:

-5m=-40

divide both side by -5

-5m=-40

-5=-5 answer is m=8

Step-by-step explanation:

(52900 ÷ 28.7) × 100 = 184320 ( rounded to nearest whole number, since you cannot have half humans)

By critically observing the number lines, the intersection of both (-∞, 6) and (-∞, 9) is (6, 9) because this is the point where they overlap. Also, the union of both (-∞, 6) and (-∞, 9) on a number line is (-∞, 9).

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Given the following intervals:

On a number line, the first interval would comprise the following numerical values -∞,..........-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6.

On a number line, the second interval would comprise the following numerical values -∞,..........-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

By critically observing the number lines, we can logically deduce that intersection of both (-∞, 6) and (-∞, 9) is (6, 9) because this is the point where they overlap.

Also, the union of both (-∞, 6) and (-∞, 9) on a number line is (-∞, 9).

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Answer: [tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Step-by-step explanation:

Given the requirement of function form

Point-slope form: y - y₁ = m (x - x₁)

Given information

Slope (m) = -6/5

Y-intercept (x₁, y₁) = 2 = (0, 2)

Substitute values into the required form

y - y₁ = m (x - x₁)

y - (2) = (-6/5) (x - 0)

[tex]\Large\boxed{y-2=-\frac{6}{5} (x-0)}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

an angle bisector

Step-by-step explanation:

This is showing the construction of the bisector of ∠LNM

Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.

The steps involved in inscribing a square in a circle include;

Alicia deductions were;

Draws two diameters and connects the points where the diameters intersect the circle, in order, around the circle

Benjamin's deductions;

The diameters must be perpendicular to each other. Then connect the points, in order, around the circle

Caleb's deduction;

No need to draw the second diameter. A triangle when inscribed in a semicircle is a right triangle, forms semicircles, one in each semicircle. Together the two triangles will make a square.

It can be concluded from their different postulations that Benjamin is correct because the diameter must be perpendicular to each other and the points connected around the circle to form a square.

Thus, Benjamin is correct about the diameter being perpendicular to each other and the points connected around the circle.

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The value of the rate of change of the function is 14a + 7h

The rate of change of function is also known as the slope expressed according to the equation shown below;

f'(x) = f(a+h)-f(a)/h

Given the function below expressed as:

f(x) =1 + 7x^2

Determine the function f(a)

To determine the function, simply replace x with 'a" to have:

f(a) =1 + 7a^2

Determine the function f(a+h)

f(a+h) = 1 + 7(a+h)^2

f(a + h) = 1 + 7(a^2+2ah+h^2)

f(a + h) = 1 + 7a^2 + 14ah + 7h^2

To determine the rate of change

f'(x) = f(a+h)-f(a)/h

f'(x) = 1 + 7a^2 + 14ah + 7h^2 - 1 - 7a^2/h
f'(x) =  + 14ah + 7h^2/h

f'(x) = 14a + 7h

Hence the value of the rate of change of the function is 14a + 7h

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The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.

This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.

For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:

(k + m)u = ku + mu

Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."

Given the following vector:

k(x, y, z) = {k²x, k²y, k²z}

If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].

If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):

x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0

x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].

In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").

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Complete Question:

Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.

The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

Step-by-step explanation:

Let x = amount of 30% solution.

Let y = amount of 60% solution.

Equation of amounts of solutions.

x + y = 60

Equation of amounts of alcohol in the solutions.

0.3x + 0.6y = 0.4 × 60

x = 60 - y

0.3(60 - y) + 0.6y = 24

18 - 0.3y + 0.6y = 24

0.3y = 6

y = 20

x + y = 60

x + 20 = 60

x = 40

Answer:

40 liters of 30% solution.

20 liters of 60% solution.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Let 30% solution = m

Let 60% solution = n

Now,

A scientist needs 60 liters of a 40% solution of alcohol.

He has a 30% solution and a 60% solution available.

This means,

m + n = 60 _____(1)

30% of m + 60% of n = 40% of 60

0.30m + 0.60n = 0.40 x 60

0.30m + 0.60n = 24 ____(2)

From (1) and (2) we get,

m + n = 60

m = 60 - n _____(3)

Putting (3) in (2) we get,

0.30m + 0.60n = 24

0.30(60 - n) + 0.60n = 24

18 - 0.30n + 0.60n = 24

18 + 0.30n = 24

0.30n = 24 - 18

0.30n = 6

n = 6/0.30

n = 20

Putting n = 20 in (3) we get,

m = 60 - 20

m = 40

Now,

The number of liters of the 30% solution is 40.

The number of liters of the 60% solution is 20.

Thus,

The number of liters of the 30% solution and the number of liters of the 60% solution to mix to make the 40% solution is 40 liters and 20 liters.

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Last box

As it's 7:2

Difference between x and y must increase in big number as x and y increases

Option D is correct in that manner

Let's double check

Answer:

b = 5

Step-by-step explanation:

All quadratic equations are formed in the format of [tex]a^{2}[/tex] + bx + c = 0

Using this formula, we can re-arrange the equation to fit the given format.

[tex]3x^{2}[/tex] - 2 = -5x
[tex]3x^{2}[/tex] + 5x - 2 = 0

5 is plugged in for "b" in this equation, therefore b = 5.

Answer:

963 hours

Step-by-step explanation:

I subtracted 20 from the 981

The correct answer for the hours elaine spend attending classes is  [tex]817.5[/tex]  hours.

Given,

The time spent doing homework was 20% less than the time she spent attending class.

Assume the time Elaine spent attending class is "x" hours.

So, the time spent on these activities is 0.2 * x hours.

Now, the total time  spent attending class, doing homework, or  in extracurricular activities is 981 hours.

The equation representing the total time is:

[tex]x + 0.2x = 981[/tex]

solve for "x":

[tex]1.2x = 981[/tex]

[tex]x= \dfrac{981}{1.2}[/tex]

[tex]x= 817.5[/tex]

Elaine spent approximately [tex]817.5[/tex] hours attending class.

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The new curriculum significantly affects the earning potential.

According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.

The probability level is given to be 5%.

When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.

A probability level of 0.05 means that the new curriculum significantly affects the earning potential.

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Answer:

you better give me brainliest

Step-by-step explanation:

2x +5x+2 = 7x+2