Which of these statements is correct?

The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.

The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Answer:

The answer is 142°

Step-by-step explanation:

Because 38° and m∠2 are corresponding angles, m∠2 = 38°. Also, m∠2 and m∠5 are supplementary angles, which means the sum of their angles adds up to 180°. We can create the equation 38° + m∠5 = 180°. By subtracting 38° on both sides, we get m∠5 = 142°.

[tex]

L=25,W=105 \\

P=2L+2W=2(L+W)\Rightarrow P=2(25+105) \\

P=2\cdot130=\boxed{260}

[/tex]

Hope this helps.

r3t40

Answer:

the answer is 2 :)

Step-by-step explanation:

lcd 210

1/5=42/210

1/7=30/310

3/21=30/210

42+30+30=102/210

reduced 51/105

The sum of the fractions 1/5, 1/7 and 3/21 is 17/35. This was achieved by finding the least common denominator (LCD), converting the fractions to have the LCD, adding them, and then simplifying the result.

To add or subtract fractions, it's essential to find the least common denominator (LCD). The LCD in this case would be the least common multiple (LCM) of 5, 7, and 21, which is 105. Once we have the LCD, we can rewrite the fractions as an equivalent fraction with the LCD as the denominator:

Now all the fractions have the same denominator, and we can combine the numerators: 21/105 + 15/105 + 15/105 = 51/105. However, this can be simplified to 17/35 by dividing both numerator and denominator by 3.

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ANSWER

[tex](2,-10.75)[/tex]

EXPLANATION

The given function is

[tex]y = {x}^{2} - 4x - 7[/tex]

We rewrite this function to obtain,

[tex](y + 11) = {( x- 2)}^{2} [/tex]

We now compare this function to

[tex](y - k) = 4p {( x- h)}^{2} [/tex]

We have

[tex]4p = 1[/tex]

This implies that,

[tex]p = \frac{1}{4} [/tex]

The vertex is (2,-11).

The focus is

[tex](2,-11+ \frac{1}{4} )[/tex]

[tex](2,- \frac{43}{4} )[/tex]

[tex](2,-10.75)[/tex]

Answer:

95:95:19

Step-by-step explanation:

1.Divide 209 by 11.(209÷19)

2.Multiply 19×5 since 5/11 of the coins are nickels.(19×5=95)

3.Multiply 19×5 again since 5/11 of the coins are dimes.(19×5=95)

4.Multiply 19×1 since there would be 1/11 left of the coins which are quarters. (19×1=19)

5.Check your awnser by adding 95+95+19.(95+95+19=209)

a) x + 5 = 7

x + 5 - 5 = 7 - 5 (Subtract 5 from both sides)

x = 2

b) 2x - 8 = 20

2x - 8 + 8 = 20 + 8 (Add 8 to each side)

2x = 28

2x/2 = 28/2 (Divide each side by 2)

x = 14

c) 4x - 6x = 200

-2x = 200

-2x/-2 = 200/-2 (Divide each side by -2)

x = -100 (Note that a negative number divided by a negative number is positive, whereas a positive number divided by a negative number is negative)

d) x + 1 = 5

x + 1 - 1 = 5 - 1 (Subtract 1 from each side)

x = 4

Answer:

It is just right

Step-by-step explanation:

Kermit's fav = 15 tea bags every 2 liters = 15/2 = 7.5 teabags per liter

Peggy made 90 teabags in 12 liters = 90/12 = 7.5 teabags per leter

Hence peggy used the same teabags per liter than kermit's favorite. It is just right.

edit: calculation error. corrected.

Your answer would be C:Just right.

Because:

2 liters of water = 15 tea bags

15/2 = 7.5 tea bags

Peggy needs to make 12 liters

12 x 7.5 = 90 tea bags

Conclusion:

Peggy's 12-liter batch of iced tea with 90 tea bags is JUST RIGHT.

Hope helps!-Aparri

Answer:

x=8*2

Step-by-step explanation:

Answer:

[tex]8(2)^{x-1}[/tex]

Step-by-step explanation:

Pacey's computer is infected with a virus. The number of files the virus corrupts doubles every 8 minutes.

That means at every 8 minutes interval sequence becomes 8, 8 × 2, 8 × 2 × 2,.....

So the sequence is a geometric sequence.

Explicit formula of geometric sequence is

[tex]A_{x}=A_{0}(r)^{x-1}[/tex]

When[tex] A_{x}[/tex] = xth term

[tex]A_{0}[/tex] = first term

x = number of term

and r = common ratio

Here [tex]A_{0}[/tex] = 8 and r = [tex]\frac{8\times2}{8}[/tex] = 2

So expression representing the number of files corrupted will be [tex]A_{x}[/tex] = [tex]8(2)^{x-1}[/tex]

Answer:

C≈1256.64in

Step-by-step explanation:

C=πd=π·400≈1256.63706in

Hope this helps!

Answer:

odd

Step-by-step explanation:

Just so you know there are shortcuts for determining if a polynomial function is even or odd. You just to make sure you use that x=x^1 and if you have a constant, write it as constant*x^0 (since x^0=1)

THEN!

If all of your exponents are odd then the function is odd

If all of your exponents are even then the function is even

Now you have -4x^3+4x^1

3 and 1 are odd it is an odd function

This a short cut not the legit algebra way

let me show you that now:

For it to be even you have f(-x)=f(x)

For it be odd you have f(-x)=-f(x)

If you don't have either of those cases you say it is neither

So let's check

plug in -x  -4(-x)^3+4(-x)=-4*-x^3+-4x=-4x^3+-4x

that's not the same so not even

with if we factor out -1 .... well if we do that we get -(4x^3+4x)=-f(x)

so it is odd.

[tex]\bf \cfrac{2}{5}\div\cfrac{7}{9}=N\implies \cfrac{2}{5}\cdot \cfrac{9}{7}=N\implies \cfrac{18}{35}=N\implies 0.514\approx N \\\\[-0.35em] ~\dotfill\\\\ \boxed{0}\rule[0.35em]{10em}{0.25pt}\stackrel{N}{0.514}\rule[0.35em]{9em}{0.25pt}\boxed{1}[/tex]

Answer:

Part 1) The amount invested in the first account at 7% was $4,400

Part 2) The amount invested in the second account at 12% was $4,200

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x------> the amount invested in the first account at 7%

(8,600-x) -----> the amount invested in the second account at 12%

in this problem we have

[tex]t=1\ year\\ P1=\$x\\ P2=\$8,600-x\\ I=\$812\\r1=0.07\\r2=0.12[/tex]

substitute in the formula above

[tex]812=x(0.07*1)+(8,600-x)(0.12*1)[/tex]

[tex]812=0.07x+1,032-0.12x[/tex]

[tex]0.12x-0.07x=1,032-812[/tex]

[tex]0.05x=220[/tex]

[tex]x=\$4,400[/tex]

so

[tex]8,600-x=\$8,600-\$4,400=\$4,200[/tex]

therefore

The amount invested in the first account at 7% was $4,400

The amount invested in the second account at 12% was $4,200

Answer:

$4,400 at 7%

$4,200 at 12%

Step-by-step explanation:

Let the amount invested in 7% be x, so,

amount invested in 12% would be "8600 - x"

We can now write an equation and solve for x:

[tex]0.07(x)+0.12(8600-x)=812\\0.07x+1032-0.12x=812\\-0.05x=-220\\x=\frac{-220}{-0.05}=4400[/tex]

Thus, the amount invested in 12% is  8600 - 4400 = 4200

So,

$4,400 at 7%

$4,200 at 12%

Answer: x = 2

Step-by-step explanation:

3x2 - 6 = 10 - x2

       +6   +6

3x2 = 16 - x2

+x2         +x2

4x2 = 16

4/4     16/4

x2 = 4

√x2 = √4

x = 2

(pls mark me brainliest)

Answer:

The inputs to this formula are:

The equation of this line in point-slope form will be:

[tex]y - 4 = -2(x +11)[/tex].

Step-by-step explanation:

The general form of a 2D line in its point-slope form is:

[tex]l:\; y - y_0 = m(x - x_0)[/tex].

This form of the equation of a line takes two pieces of information:

For this line, the point [tex](x_0, y_0)[/tex] is [tex](-11, 4)[/tex].

The slope of this line is [tex]-2[/tex]. In other words,

Apply the point-slope formula for a 2D line:

[tex]l:\; y - 4 = -2 (x - (-11))[/tex].

[tex]l:\; y - 4 = -2 (x +11 )[/tex].

Answer:

well it's 9/25 or 0.36% or (36%) only

Step-by-step explanation:

So you add all the numbers up it would be 25, divide the numerator by the denominator and get 0.36%, i can't remember if you divide .36 by 100 or not but anyway you get 36%.

But I hope i have helped you in anyway.

Answer:

Step-by-step explanation:

The angle adjacent to the 106 degree angle is 180 degrees - 106 degrees, or 74 degrees.  Next, the adjacent angle to the 145 degree angle is 35 degrees; in other words, the two bottom angles of this triangle are 35 degrees and 35 degrees.  That means that a 35 degree angle is vertical angle to x, and so x is also 35 degrees.

The sum of the three interior angles is 35 degrees + 74 degrees and

Check the picture below.

let's recall that vertical angles, angles across a junction, are equal, namely the angle across the "x" is also "x".

Answer:

The y-intercept of this line: -4

Step-by-step explanation:

A line passes through the points (8, –1) and (–4, 2).

Slope = (-1 - 2)/(8 + 4) = -3/4

Equation in slope intercept form:

y = mx + b where m = slope and b = y-intercept

Substitute m = -3/4 into the equation to find y-intercept

y = -3/4 x + b

Plug in one of those coordinate points above to find b. In this case, I'm using  (–4, 2)

y = -3/4 x + b

2= -3/4 (-4) + b

-1 = 3 + b

b = -4

Answer:

THE ANSWER IS -4

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

It could be equal because what if the proportions are something like 2/3=3/2

In this case the product of both sides is 6.

B. False

When I say that the proportion is 2 ratios that are equal to each other, It mean this in the sense of 2 fractions being equal to each other.

Proportions could be written as equivalent fractions and as = ratios. When we  can say that the ratios in the proportion are =, we mean that we could multiply and divide 1 ratio by some constant to result in the other.

It can be equal because what if the proportions are something such as

2/3=3/2

In this case the product of both sides is 6.

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Answer:

[tex]-\frac{3}{4}[/tex]  meters

Step-by-step explanation:

From the answer choices, we basically need to find which of them is between   [tex]-\frac{1}{2}[/tex]  and  [tex]-1\frac{2}{3}[/tex]

Converting all of them to decimals would make it really easier:

So we need to find number between -0.5  and -1.67

Answer choice A is -2.33

Answer choice B is  -0.75

Answer choice C is  -0.25

Answer chioce D is  -1.83

So which number, from the choices, is between -0.5 & -1.67?

Clearly, it is -0.75, or,  [tex]-\frac{3}{4}[/tex]  meters

Answer:

table d is the proportional relationship

Step-by-step explanation:

Answer:

[tex]2x^2+7x-4[/tex]

Answer:

2x² + 7x - 4

Step-by-step explanation:

Each term in the second factor is multiplied by each term in the first factor, that is

2x(x + 4) - 1(x + 4) ← distribute both parenthesis

= 2x² + 8x - x - 8 ← collect like terms

= 2x² + 7x - 8

The index of a radical is the number indicating what root of a given number should be taken. In the expression '4 radical 8', '4' is the index of the radical, meaning the expression represents the fourth root of 8.

In the expression '4 radical 8', '4' is referred to as the index of the radical. The index of a radical is the number that denotes what root of the number is to be taken. For example, an index of 2 (which is often not written) refers to a square root, an index of 3 refers to a cube root, and so on. In this case, since the expression is '4 radical 8', it means we are looking at the fourth root of 8.

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In 4 radical 8, the given index of the radical 4, means we are looking for a number that, when raised to the power of 4, gives us 8.

The index of a radical is the number that is written just above and to the left of the radical symbol. In your problem, 4 radical 8, the number 4 is the index of the radical. So, the index of the radical in 4 radical 8 is 4. This means that we are looking for a number that, when raised to the power of 4, gives us 8.

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Answer:

Step-by-step explanation: 5 times 4 then that times 3 then that times 2.

120

5! = 120.

5! equals 5 x 4 x 3 x 2 x 1 which is equal to 120.

The exclamation mark denotes a factorial, which is the product of all positive integers up to that number.

Answer:

-1/2 , 0 , 3/2

Step-by-step explanation:

Given equation is:

[tex]4x^3-5x = |4x|[/tex]

We know that [tex]|x|=a\\The\ solution\ will\ be:\\x=a\ and\ x=-a\\[/tex]

So, from given equation,we will get two solutions:

[tex]4x^3-5x = 4x\\4x^3-5x-4x=0\\4x^3-9x=0\\x(4x^2-9) = 0\\x = 0\\and\\4x^2-9 = 0\\4x^2=9\\x^2 = \frac{9}{4} \\\sqrt{x^2}=\sqrt{\frac{9}{4} }\\[/tex]

x= ±√3/2 , 0

and

[tex]4x^3-5x = -4x\\4x^3-5x+4x=0\\4x^3-x=0\\x(4x^2-1) = 0\\x = 0\\and\\4x^2-1 = 0\\4x^2=1\\x^2 = \frac{1}{4} \\\sqrt{x^2}=\sqrt{\frac{1}{4} }[/tex]

x= ±1/2 , 0

We can check that 1/2 and -3/2 do not satisfy the given equation.

[tex]4x^3-5x = |4x|\\Put\ x=1/2\\4(\frac{1}{2})^3 - 5(\frac{1}{2}) = |4 * \frac{1}{2}|\\   4 * (\frac{1}{8)} - \frac{5}{2} = |2|\\ -2 = 2\\Put\ x=-\frac{3}{2} \\4(\frac{-3}{2})^3 - 5(\frac{-3}{2}) = |4 * \frac{-3}{2}|\\-6 = 6\\[/tex]

So, 1/2 and -3/2 will not be the part of the solution ..

So, the solutions in increasing order are:

-1/2 , 0 , 3/2 ..

Answer:

[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]

Step-by-step explanation:

We are given that an equation

[tex]4x^3-5x=\mid x\mid[/tex]

We have to find the solution of given equation and arrange the solution in increasing order.

[tex]4x^3-5x=4x[/tex]  when x >0

and [tex]4x^3-5x=-4x[/tex] when x < 0

because [tex]\mid x\mid =x when x > 0 [/tex]

                                     =-x when x < 0

[tex]4x^3-5x-4x=0[/tex]

[tex]4x^3-9x=0[/tex]

[tex]x(4x^2-9)=0[/tex]

[tex]x(2x+3)(2x-3)=0[/tex]

Using identity [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]x=0,2x+3=0,2x-3=0[/tex]

[tex]2x=3\implies x=\frac{3}{2}=1.5[/tex]

[tex]2x=-3 \implies x=-\frac{3}{2}=-1.5[/tex]

[tex]4x^3-5x=-4x=0[/tex]

[tex]4x^3-5x+4x=0[/tex]

[tex]4x^3-x=0[/tex]

[tex]x(4x^2-1)=0[/tex]

[tex]x(2x+1)(2x-1)=0[/tex]

[tex]x=0,2x+1=0[/tex]

[tex]2x-1=0[/tex]

[tex]2x-1=0[/tex]

[tex]2x=1 \ilmplies x=\frac{1}{2}=0.5[/tex]

[tex]2x+1=0[/tex]

[tex]2x=-1 \implies x=-\frac{1}{2}=-0.5[/tex]

When we substitute x=[tex]\frac{1}{2}[/tex]

[tex]4(\frac{1}{2})^3-\frac{5}{2}=\frac{1}{2}-\frac{5}{2}=\frac{1-5}{2}=-2[/tex]

[tex]\mid 4(\frac{1}{2})\mid=2[/tex]

[tex]-2\neq 2[/tex]

Hence, [tex]\frac{1}{2}[/tex] is a not solution of given equation.

When substitute [tex]x=\frac{-3}{2}[/tex]

[tex]4(\frac{-3}{2})^3+\frac{15}{2}=\frac{-27}{2}+\frac{15}{2}=\frac{-27+15}{2}=-6[/tex]

[tex]\mid 4(-\frac{3}{2}\mid=6[/tex]

[tex]-6\neq 6[/tex]

Hence, [tex]\frac{-3}{2}[/tex] is not  a solution of given equation.

Substitute x=[tex]-\frac{1}{2}[/tex] in the given equation

[tex]4(-\frac{1}{2})^3+\frac{5}{2}=-\frac{1}{2}+\frac{5}{2}=2[/tex]

[tex]\mid 4(-\frac{1}{2})\mid=2[/tex]

[tex]2=2[/tex]

Hence, [tex]-\frac{1}{2}[/tex] is   a solution of given equation.

Substitute [tex]x=\frac{3}{2}[/tex] in the given equation

[tex]4(\frac{3}{2})^3-\frac{15}{2}=\frac{27-15}{2}=6[/tex]

[tex]\mid 4(\frac{3}{2})\mid =6[/tex]

[tex]6=6[/tex]

Hence, [tex]\frac{3}{2}[/tex] is a solution of given equation.

Answer:[tex]-\frac{1}{2},0,\frac{3}{2}[/tex]

Answer:

Option C is correct.

Step-by-step explanation:

Let x be the original width

then x+2 will be the length (consecutive odd integer)

if length is increased by 5 feet , length will be: (x+2)+5 = x+7

Area = 60 square ft.

Area = length * width

60 = (x+7) *x

60 = x^2 +7x

Rearranging

x^2 + 7x -60 = 0

Solving quadratic equation to find the value of x

using Quadratic formula

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a=1, b =7, c=-60

[tex]x=\frac{-7\pm\sqrt{(7)^2-4(1)(-60)}}{2(1)}\\x=\frac{-7\pm\sqrt{49+240}}{2}\\x=\frac{-7\pm\sqrt{289}}{2}\\x=\frac{-7\pm17}{2}\\x=5 \,\, and \,\, x = -12\\[/tex]

Since width can be positive so x=5

length of original rectangle = x+2 = 5+2 =7

Area of original rectangle = Length * Width

Area of original rectangle = 5 * 7

Area of original rectangle = 35 ft^2

So, Option C is correct.

Final answer:

The width of the original rectangle is 5 feet, and the length is 7 feet, making the area 35 square feet. We determined this by setting up an equation for the area of the enlarged rectangle and solving for the odd integer width.

Explanation:

We are given that a rectangle has dimensions of consecutive odd integers and if the length is increased by 5 feet, the resulting area is 60 square feet. Let's denote the width as w feet (an odd integer) and the length as w + 2 feet (the next consecutive odd integer), since consecutive odd integers are two units apart.

After increasing the length by 5 feet, the new dimensions are w feet and w + 7 feet. The area can be calculated as the product of these dimensions:

w × (w + 7) = 60

Solving this quadratic equation: w² + 7w = 60

Subtracting 60 from both sides gives: w² + 7w - 60 = 0. Factoring this, we get: (w + 12)(w - 5) = 0

Considering the positive value that fits the condition of being an odd integer, we find that w = 5 feet. This makes the width 5 feet and the length 7 feet (5 + 2) for the original rectangle.

Thus, the area of the original rectangle is 5 feet × 7 feet = 35 square feet.

Therefore, the correct answer is C. 35 ft².

Answer:

6

Step-by-step explanation:

2+6=8

8+6=14

14+6=20

20+6=26

Answer:

[tex]\displaystyle \frac{25}{2}\pi \approx 39.3[/tex] inches.

Step-by-step explanation:

The question gives the central angle and radius of an arc and is asking for the length.

An arc is part of a circle. What is the circumference of a circle with a radius 15 inches?

[tex]\text{Circumference} = \pi \times \text{Diameter} = 2\pi \times \text{Radius} = 30\pi[/tex] inches.

However, this wiper traveled only a fraction of the circle. A full circle is [tex]360^{\circ}[/tex]. The central angle of this arc is only [tex]150^{\circ}[/tex]. As a result,

[tex]\displaystyle \frac{\text{Length of this arc}}{\text{Circumference of the circle}} = \frac{150^{\circ}}{360^{\circ}} = \frac{5}{12}[/tex].

The length of the arc will thus be

[tex]\displaystyle \frac{5}{12} \times 30\pi = \frac{25}{2}\pi \approx 39.3[/tex].

In other words, the windshield wiper traveled approximately 39.3 inches.

To find the distance traveled by the end of the windshield wiper making a 150° arc, calculate the circumference of the circle swept and apply the formula to determine the distance traveled.

Distance traveled by the end of the windshield wiper:

Calculate the circumference of the circle swept by the windshield wiper: Circumference = 2πr = 2π(15 in).

Convert the circumference to inches: Multiply the circumference by the angle traversed (150°/360°) to find the distance traveled by the wiper's end.

Distance traveled = Circumference x (150/360) = 15π/2 inches or 23.56 inches.

Using the Pythagorean theorem a^2 + b^2 = c^2, where a and b are the sides and c is the hypotenuse, we can find the length needed.

6^2 + 8^2 = c^2

Simplify:

36 + 64 = c^2

100 =c^2

Take the square root of both sides:

c = √100

c = 10

The hypotenuse is 10 meters.