Consider the following system of equations:
Equation 1: 3x + y = 5
Equation 2:5x – 4y = -3
What is the solution to this system?
(To answer this question, we need to know the value of y.)
O (1.8)
O (1,2)
O (1,1)
O (1.3)

Answer:

The numbers are 165 and 113

Step-by-step explanation:

Let

x ----> one number

y ----> the other number

we know that

[tex]x+y=278[/tex] ----> equation A

[tex]x=y+52[/tex] ----> equation B

substitute equation B in equation A

[tex](y+52)+y=278[/tex]

solve for y

[tex]2y=278-52[/tex]

[tex]2y=226[/tex]

[tex]y=113[/tex]

Find the value of x

[tex]x=y+52[/tex]

[tex]x=113+52=165[/tex]

therefore

The numbers are 165 and 113

Answer:

1.997 x 10²

Step-by-step explanation:

The number with the highest exponent is the greatest value.

10² is bigger than 10⁻⁶ and 10⁻⁸, so 1.997 x 10² is your answer.

The slope is -4/5

Step-by-step explanation:

We have to observe the graph to find two points to find slope.

The graph has two points

(-5,0) and (0, -4)

The formula for slope is given by:

[tex]m = \frac{y_2-y_1}{x_2-x_1}\\[/tex]

Here

(x1,y1) = (-5,0)

(x2,y2) = (0,-4)

Putting the values

[tex]m = \frac{-4-0}{0+5}\\=-\frac{4}{5}[/tex]

Hence,

The slope is -4/5

Keywords: slope, steepness

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Final answer:

The Peace of Augsburg allowed rulers to establish either Lutheranism or Roman Catholicism as the official religion in their lands, giving birth to the principle 'whose realm, their religion' but excluded other religious groups such as Calvinists and Anabaptists.

Explanation:

The religious settlement reached with the Peace of Augsburg in 1555 allowed rulers within the Holy Roman Empire to choose either Lutheranism or Roman Catholicism as the official religion of their territories. This principle, known as cuius regio, eius religio ('whose realm, their religion'), meant that a ruler's subjects were obliged to follow the same religion.

The Peace of Augsburg formally recognized the division between Catholics and Protestants, mainly Lutherans, and ended the religious conflict within the empire at that time. However, other religious groups, such as Calvinists and Anabaptists, were not accommodated, and the agreement failed to resolve underlying tensions leading to future wars, including the devastating Thirty Years' War.

Answer:

Step-by-step explanation:

Answer:

[tex]\displaystyle 2x - 3y = 6\:OR\:y = \frac{2}{3}x - 2 \\ \\ 3x - 2y = 40\:OR\:y = \frac{3}{2}x - 20[/tex]

Step-by-step explanation:

2 = ⅔[6] + b

4

[tex]\displaystyle -2 = b \\ \\ y = \frac{2}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅔x - 2

- ⅔x - ⅔x

_________

−⅔x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid it.]

−3[−⅔x + y = −2]

[tex]\displaystyle 2x - 3y = 6[/tex]

_______________________________________________

−5 = 3⁄2[10] + b

15

[tex]\displaystyle -20 = b \\ \\ y = \frac{3}{2}x - 20[/tex]

If you want it in Standard Form:

y = 3⁄2x - 20

- 3⁄2x - 3⁄2x

__________

−3⁄2x + y = −20 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−2[−3⁄2x + y = −20]

[tex]\displaystyle 3x - 2y = 40[/tex]

* Parallel Lines have SIMILAR RATE OF CHANGES [SLOPES], so ⅔ and 3⁄2 remain the way they are.

I am joyous to assist you anytime.

Answer:

Length of the base = 8

Step-by-step explanation:

Area of a triangle = 1/2(h*b)

h = height

b = base

52 = 1/2 (13 * b)

Rearrange the equation to get b on it's own

52 * 2 = 13 * b

104 = 13 * b

104/13 = b

b = 8

A = 1/2(bh)

in this case, b = 2a/h. plug in the values:

steps

b = 2a/h

b = 2(52)/13

b = 104/13

b = 8 meters

Answer:

y = 3

Step-by-step explanation:

Step-by-step explanation:

Given the equation

[tex]3x^3\:+10x^2-x-12=0[/tex]

Steps

[tex]3x^3+10x^2-x-12[/tex]

Rational Root Theorem definition

[tex]\mathrm{For\:a\:polynomial\:equation\:with\:integer\:coefficients:\quad }a_nx^n+a_{n-1}x^{n-1}+\ldots +a_0[/tex]

[tex]\mathrm{If\:}a_0\mathrm{\:and\:}a_n\mathrm{\:are\:integers,\:then\:if\:there\:is\:a\:rational\:solution}[/tex]

[tex]it\:could\:be\:found\:by\:checking\:all\:the\:numbers\:produced\:for\:\pm \frac{dividers\:of\:a_0}{dividers\:of\:a_n}[/tex]

[tex]a_0=12,\:\quad a_n=3[/tex]

[tex]\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:3,\:4,\:6,\:12,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1,\:3[/tex]

[tex]\mathrm{The\:following\:rational\:numbers\:are\:candidate\:roots:}\quad \pm \frac{1,\:2,\:3,\:4,\:6,\:12}{1,\:3}[/tex]

Plugging x = -1 is False

[tex]3\left(-1\right)^3+10\left(-1\right)^2-\left(-1\right)-12=0[/tex]

[tex]-4=0[/tex]    ∵L.H.S ≠ R.H.S

Plugging x = 1 is True

[tex]3\cdot \:1^3+10\cdot \:1^2-1-12=0[/tex]

[tex]0=0[/tex]      ∵ L.H.S = R.H.S

Similarly,

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-3\right)^3+10\left(-3\right)^2-\left(-3\right)-12=0[/tex]

[tex]0=0[/tex]       ∵ L.H.S = R.H.S

x = 3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -6 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 12 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 1/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4/3 satisfies the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

As

[tex]3\left(-\frac{4}{3}\right)^3+10\left(-\frac{4}{3}\right)^2-\left(-\frac{4}{3}\right)-12=0[/tex]      ∵ L.H.S = R.H.S  

x = 4/3 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 2 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = -4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

x = 4 does not satisfy the equation [tex]3x^3\:+10x^2-x-12=0[/tex].

Hence, out of all the mentioned rational roots of the equation [tex]3x^3\:+10x^2-x-12=0[/tex], the rational roots which validate the equation are [tex]x=-\frac{4}{3},\:x=1,\:x=-3[/tex].

Keywords: rational roots, rational root theorem

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Answer:

the most it could cost would be $83 dollars

Step-by-step explanation:

2000-1500=500

500/3=83.33

Final answer:

The fraction of a 3-gallon container filled with 1/3 gallon of water is 1/9. This is found by dividing the amount of water by the total capacity of the container. It can be represented through multiplication and division, both yielding the result 1/9.

Explanation:

The question asks what fraction of a container is filled if there is 1/3 gallon of water in a 3-gallon container. To represent this situation, we can simply realize that the fraction filled is equal to the amount of water in the container (1/3 gallon) divided by the container's total capacity (3 gallons).

So, 1/9 of the container is filled with water.

To set up a multiplication and division equation to represent the situation:

These representations show how to derive the fraction of the container that is filled using multiplication and division.

Answer:

30%

Step-by-step explanation:

Use formula to find percent decrease

[tex]\text{Percent Decrease}=\dfrac{\text{Old Value}-\text{New Value}}{\text{Old Value}}\cdot 100\%[/tex]

In your case,

Old Value = 2.5 pounds

New Value = 1.75 pounds

Hence,

[tex]\text{Percent Decrease}=\dfrac{2.5-1.75}{2.5}\cdot 100\%\\ \\=\dfrac{0.75}{2.5}\cdot 100\%\\ \\=\dfrac{75}{250}\cdot 100\%\\ \\=\dfrac{3}{10}\cdot 100\%\\ \\=30\%[/tex]

(gof)(0) cannot be evaluated

Solution:

Given that,

[tex]f(x) = \frac{1}{x}\\\\g(x) = x - 4[/tex]

A composite function is denoted by (g o f) (x) = g (f(x)).

The notation g o f is read as “g of f”

Therefore, let us find whether (gof)(0) can be evaluated or not

To find (gof)(0):

(g o f) (x) = g (f(x))

Now substitute the given value of f(x)

[tex](g o f) (x) = g(\frac{1}{x})[/tex]

[tex]\text{ Substitute } x = \frac{1}{x} \text{ in } g(x) = x - 4[/tex]

[tex](g o f) (x) = \frac{1}{x} - 4[/tex]

Now to find (gof)(0), substitute x = 0

[tex](g o f) (x) = \frac{1}{0} - 4[/tex]

Since 1 divided by 0 is undefined, because any number divided by 0 is undefined

(gof)(0) cannot be evaluated

Answer:

You must evaluate the function f first.

Division by 0 is undefined.

The composition cannot be evaluated.

Step-by-step explanation:

Answer: x = 12

Step-by-step explanation:

[tex]\frac{6}{x}[/tex] = [tex]\frac{4}{8}[/tex]

cross multiply

4x = 6 × 8

4x = 48

divide through by 4

x = 12

Answer:

26.4 ft^2 (1 d.p.)

Step-by-step explanation:

[tex]area \: of \: circle = \pi {r}^{2} [/tex]

Since it is given that r, the radius of the circle, is 2.9 ft,

area of circle= π(2.9)^2= 8.41π= 26.4 ft^2 (1 d.p.)

Answer: point, line, and plane.

Step-by-step explanation:

Answer:

Hope it helps In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined.  A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.

Step-by-step explanation:

Answer:

[tex]6 \frac{5}{9} [/tex]

is greater than

[tex]6 \frac{15}{28} [/tex]

Answer:6 5/9 is greater than 6 15/28

Step-by-step explanation: positive proper fractions: 15/28, 5/9;

1 positive integer number: 6; Any positive proper fraction is smaller than

any positive integer number Sort the positive proper fractions:

15/28 and 5/9 15/28 already reduced to the lowest terms;

the numerator and the denominator have no common prime factors:

15 = 3 × 5;

28 = 22 × 7;

5/9 already reduced to the lowest terms;

the numerator and the denominator have no common prime factors:

5 is a prime number;

9 = 32; 15 = 3 × 5;

5 is a prime number;

Multiply all the unique prime factors, by the largest exponents:

LCM (15, 5) = 3 × 5 = 15 Divide LCM by the numerator of each fraction:

For fraction: 15/28 is 15 ÷ 15 = (3 × 5) ÷ (3 × 5) = 1;

For fraction: 5/9 is 15 ÷ 5 = (3 × 5) ÷ 5 = 3;  Build up all the fractions to the same numerator (which is LCM).

Multiply the numerators and the denominators by their expanding number:

15/28 = (1 × 15)/(1 × 28) = 15/28;

5/9 = (3 × 5)/(3 × 9) = 15/27;

Answer:

B. 28 degrees

Step-by-step explanation:

ok so,

the starting temperature is 35 degrees then the temperature dropped 4 degrees. making the temp 31 degrees. next the temperature rose 2 degrees, making it 33 degrees. lastly, the temperature dropped another 5 degrees making it 28 degrees out on wednesday.  

so the number line showing this would be B.

Final answer:

After a cold front caused the temperature to drop by 40 degrees from the initial 35 degrees Fahrenheit, the resulting temperature would be -5 degrees Fahrenheit on the number line for Wednesday morning at 8:00am.

Explanation:

The student originally observed a temperature of 35 degrees Fahrenheit on Sunday morning. If we suppose a cold front blows in and drops the temperature by 40.0 Fahrenheit degrees, the temperature change can be calculated by subtracting 40 from the initial temperature:

35 °F - 40 °F = -5 °F

Therefore, the number line that shows the temperature on Wednesday morning at 8:00am should have a point at -5 degrees Fahrenheit, representing the new temperature after the cold front.

Answer:

OPTION A: [tex]$ \frac{12}{1 + 8x} $[/tex], where [tex]$ x \ne - \frac{1}{8} $[/tex].

Step-by-step explanation:

Given: [tex]$ \frac{- 12x^4}{x^4 + 8x^5} $[/tex]

Taking [tex]$ x^4 $[/tex] common outside in the denominator, we get:

[tex]$ = \frac{-12x^4}{(x^4)(1 + 8x)} $[/tex]

[tex]$ x^4 $[/tex] will get cancelled on the numerator and denominator, we get:

[tex]$ = \frac{-12}{1 + 8x} $[/tex]

we know that the denominator can not be zero.

That means, 1 + 8x [tex]$ \ne $[/tex] 0.

[tex]$ \implies 8x \ne -1 $[/tex]

[tex]$ \implies x \ne \frac{-1}{8} $[/tex]

So, the answer is: [tex]$ \frac{-12}{1 + 8x} $[/tex], where [tex]$ x \ne \frac{-1}{8} $[/tex].

Answer:

AY = 10 cm.

Step-by-step explanation:

Given that, ΔABC is similar to ΔAXY

and [tex]\frac{AB}{AX }  = \frac{5}{3}[/tex]

⇒  [tex]\frac{AC}{AY }  =  [tex]\frac{BC}{XY } = \frac{5}{3}[/tex]

⇒ BC = XY× \frac{5}{3}[/tex] =  \frac{20}{3}[/tex] (as XY = 4 cm given)

Now, check the attached figure,

given, BY bisects ∠XYC

let ∠XYB = ∠BYC = x

⇒ ∠AYX = 180-2x (angle on a straight line)

and also ∠AYX = ACB (similar triangle properties)

⇒ ∠ACB = 180-2x

Now, sum of angles in ΔBYC = 180°

⇒ ∠YBC = x

⇒ BC = YC (as two sides of equal angles are equal in a triangle)

⇒ YC =  \frac{20}{3}[/tex]

And also [tex]\frac{AC}{AY }  = \frac{5}{3}[/tex]

AC = AY + YC

⇒ [tex]\frac{AY+YC}{AY }  = \frac{5}{3}[/tex]

⇒ [tex]\frac{AY+\frac{20}{3}[/tex]}{AY }  = \frac{5}{3}[/tex]

⇒ 5AY = 3AY + 20

⇒ AY = 10 cm

Answer:

par value of the TIPS is $1034.05

Step-by-step explanation:

Given:

-  original reference CPI = 182.1

- current CPI = 188.3

Assume face value of tips = $1000

par value of the TIPS = [tex]face\ value\ of\ tips\times \frac{current\ CPI}{original\ reference\ CPI}[/tex]

par value of the TIPS = [tex]1000\times \frac{188.3}{182.1}\approx $1034.05[/tex]

Final answer:

The par value of a TIPS adjusts with the CPI's inflation rate. To find the adjusted par value of a 4.15% TIPS, multiply the original par value by 1 plus the inflation rate, which is determined by the percentage increase from the original to the current CPI.

Explanation:

A student asked about the par value of a Treasury Inflation-Protected Security (TIPS) given an original reference Consumer Price Index (CPI) of 182.1 and a current CPI of 188.3. The par value of TIPS adjusts with inflation to protect investors, with the adjustment based on the change in the CPI.

First, we need to calculate the percentage increase in the CPI by using the formula:

(Current CPI - Original CPI) ÷ Original CPI x 100%.

Plugging in the given CPI values:

(188.3 - 182.1) ÷ 182.1 = 0.0340 or 3.40%

This percentage tells us how much the CPI has increased since the TIPS was issued. To find the adjusted par value, you would multiply the original par value of the TIPS (which is typically $1,000) by 1 plus the inflation rate. Since we do not have the original par value, we can only provide the formula for its calculation.

The adjusted par value would be:

Original Par Value x (1 + Inflation Rate).

Answer:

x-intercept

= 7/6

= 1.16667

Answer:

The width of the sandbox is 4 feet

Step-by-step explanation:

Area = Length x Width

Fill in known values

26 sq ft = 6.5 ft x w

Divide by 6.5 on both sides

4 ft = w

Width = 4 ft

:)

Answer:

[tex]\angle a=35^o[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

An isosceles triangle has two equal sides and two equal interior angles

The angles opposite to the equal sides of an isosceles triangle are equal.

[tex]\angle b=\angle c[/tex]

we have

[tex]\angle c=55^o[/tex] -----> given problem

so

[tex]\angle b=55^o[/tex]

Remember that

The sum of the interior angles in any triangle must be equal to 180 degrees

[tex]\angle b+\angle c+2\angle a=180^o[/tex]

substitute the given values

[tex]55^o+55^o+2\angle a=180^o[/tex]

[tex]110^o+2\angle a=180^o[/tex]

[tex]2\angle a=180^o-110^o[/tex]

[tex]2\angle a=70^o[/tex]

[tex]\angle a=35^o[/tex]

The probability of drawing the 8 of spades from a deck of cards is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.

The probability of drawing the 8 of spades from a deck of cards is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, there is only 1 8 of spades card in the deck, and there are a total of 52 cards. Therefore, the probability is 1/52, or approximately 0.0192, which can also be expressed as 1.92%.

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Answer:

Option C) 24 < x < 54

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Let

x ----> the measure of the third side

Applying the triangle inequality theorem

1) [tex]15+39 > x[/tex]

[tex]54 > x[/tex]

Rewrite

[tex]x < 54\ units[/tex]

2) [tex]x+15> 39[/tex]

[tex]x > 39-15[/tex]

[tex]x > 24\ units[/tex]

therefore

The range of possible measures for the third side is the interval (24,54)

Answer:

They are not equal? I don't get what you're trying to ask.

Answer:

Step-by-step explanation:

X=-1/2

Hope this helps mark me as brainiest pls

Yes, -1/2 will be the x-coordinate for the solution. We can also find the y-coordinate by subbing in -1/2 for x in the equation y=4x+7.

y=4(-1/2)+7

y=-2+7

y=5

The intersection point would be (-1/2,5).