Choose the number sentence that shows the distributive property of multiplication over addition.
A.
4 × (7 + 6) = (4 × 7) + 6
B.
4 × (7 + 6) = (4 × 7) + (4 × 6)
C.
4 × (7 + 6) = (4 + 7) × (4 + 6)

y=-1/4x+3/4

Pq Slope * Vt Slope should equal -1

4 * -1/4 = -1 Yes they are perpendicular.

The slope for the first equation is 4, and after transforming the second equation into slope-intercept form the slope is -0.25. Since these slopes are negative reciprocals of each other, the lines pq and vt are perpendicular.

The given equations are y=4x+3 (equation of line pq), and 2x+8y=6 (equation of line vt). To find out if these lines are perpendicular, we need to rewrite the second equation in slope-intercept form (y=mx+b). You can achieve this by isolating y.

Here are the steps:

At this point, you can see that the slope of this line is -0.25.

Line pq has a slope of 4, and line vt has a slope of -0.25. Two lines are perpendicular if their slopes are negative reciprocals of each other. The negative reciprocal of 4 is -0.25, so we can conclude that lines pq and vt are perpendicular.

https://brainly.com/question/18271653

#SPJ12

To determine the approximate number of workers hired during the seventh year based on the quadratic model, we need more information about the model and the values of a, b, and c.

To approximate the number of workers hired during the seventh year based on the quadratic model, we need more information about the model. Quadratic models are typically of the form y = ax^2 + bx + c, where x represents the time and y represents the number of workers hired. Without knowing the values of a, b, and c, we cannot determine the exact number of workers hired in the seventh year. However, if we have the values of a, b, and c, we can substitute x = 7 into the equation to find the approximate number of workers hired during the seventh year.

I would travel 40hours.  16 times two is 32 plus 8 is 40.

Answer:

Given: [tex]m\angle 1 = m\angle 3[/tex] and [tex]m\angle 2 = m\angle 3[/tex]

To prove that:

[tex]l || m[/tex]

1. [tex]m\angle 1 = m\angle 3[/tex]          [Given]

[tex]m\angle 2 = m\angle 3[/tex]

Substitution property of equality says that:

If x = y, then x can be substituted in y, or y can be substituted in x.

2 [tex]m\angle 1 = m\angle 2[/tex]          [ By Substitution Property]

Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.

3. [tex]\angle 1[/tex] and  [tex]\angle 2[/tex] are alternate interior angles  [By definition Alternate interior angle].

Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.

4. [tex]l || m[/tex] ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1. [tex]m\angle 1 = m\angle 3[/tex]          [Given]

 [tex]m\angle 2 = m\angle 3[/tex]

2. [tex]m\angle 1 = m\angle 2[/tex]          [Substitution]

3. [tex]\angle 1[/tex] and  [tex]\angle 2[/tex] are alternate interior angle       [By definition of alternate interior angles ]

4. [tex]l || m[/tex] the lines are parallel  [If alternate interior angles are equal]

The question involves a geometrical proof where measurements of angles are given and a conclusion regarding parallel lines need to be derived. The steps of proof are matched with relevant geometric concepts. The matching involves principles like substitution, definition of alternate interior angles, and a theorem about alternate interior angles and parallel lines.

In the context of the given problem, the matching would be as follows:

https://brainly.com/question/31408211

#SPJ2

Polygon A: 20 ft x 60 ft

           P = 2(20) + 2(60)

              =   40    +  120

              =         160

Polygon B: 3 ft x 9 ft

          P = 2(3) + 2(9)

             =   6   +   18

             =       24

Ratio of Perimeters: [tex]\frac{160}{24} = \frac{20}{3}[/tex]  = 20:3      

B. 0.6 seconds

Because they want you to round to the nearest 10th and 0 is the ground.

Answer:

Option B. 0.6 seconds

Step-by-step explanation:

As given in the table at time t = 0 the maximum height of the penny is 2 meters.

In simpler way we can say the penny has been throw from a height of 2 meters.

Now this process can be represented by the equation of motion

[tex]h=ut+\frac{1}{2}gt^{2}[/tex]

For free fall u = 0

So [tex]h=\frac{1}{2}gt^{2}[/tex]

where h = 2 meters

and g = 9.81 m/sec²

By putting these values in the equation

[tex]2=\frac{1}{2}(9.81)(t)^{2}=4.905t^{2}[/tex]

[tex]t^{2}=\frac{2}{4.905}=0.4077[/tex]

t = √0.4077 = 0.6385 seconds

or t = 0.6 seconds

Answer is option B. 0.6 seconds

(c) multiply by 0.4

given [tex]\frac{x}{0.4}[/tex] = 10

multiply both sides by 0.4 to eliminate the fraction

x = 0.4 × 10 = 4

and [tex]\frac{4}{0.4}[/tex] = 10

I believe the answer is 9.8

Hope this helps :)

Answer:

1, -4, 2 + 5i, 2 - 5i

Step-by-step explanation:

First, I factor x^2 + 3x - 4

==> I get: (x - 1) (x +4)

Then, I factor (x^2 - 4x + 29)

==> And I get (2 + 5i) (2 - 5i)

You can use the quadratic formula to factor or use the "X" to solve them.

Hope this help!

Applying the factor theorem, it is found that the roots of the equation are:

[tex]x = 1, x = -4, x = 2 + 5i, x = 2 - 5i[/tex]

The factor theorem states that if [tex]x_1, x_2, ..., x_n[/tex] are roots of a polynomial, it can be written as:

[tex](x - x_1)(x - x_2)...(x - x_n)[/tex]

In this problem:

[tex](x^2 + 3x - 4)(x^2 - 4x + 29) = 0[/tex]

Thus, the roots are the values of x for which either:

[tex]x^2 + 3x - 4 = 0[/tex]

Or

[tex]x^2 - 4x + 29 = 0[/tex]

First, [tex]x^2 + 3x - 4 = 0[/tex]

Which is a quadratic equation with [tex]a = 1, b = 3, c = -4[/tex], thus:

[tex]\Delta = 3^{2} - 4(1)(-4) = 25[/tex]

[tex]x_{1} = \frac{-3 + \sqrt{25}}{2} = 1[/tex]

[tex]x_{2} = \frac{-3 - \sqrt{25}}{2} = -4[/tex]  

Thus, [tex]x = 1[/tex] and [tex]x = -4[/tex] are roots.

Then, we solve [tex]x^2 - 4x + 29 = 0[/tex].

The coefficients are [tex]a = 1, b = -4, c = 29[/tex], so:

[tex]\Delta = (-4)^{2} - 4(1)(29) = -100[/tex]

[tex]x_{1} = \frac{-(-4) + \sqrt{100}}{2} = 2 + 5i[/tex]

[tex]x_{2} = \frac{-(-4) - \sqrt{100}}{2} = 2 - 5i[/tex]

Thus, [tex]x = 2 + 5i[/tex] and [tex]x = 2 - 5i[/tex] are also roots.

A similar problem is given at https://brainly.com/question/24380382

Your answer is 5/2.

Steps:

Convert element to fraction

Multiply fractions

Cancel the common factor (1)

--

Hope this helped!

This is how you would graph your function.

A container holds 62 cups of water how much is this in a gallon

Answer: We are given that a container contains 62 cups of water.

We are required to find how much water is contained in the container in terms of gallons.

We know that:

[tex]1[/tex] gallon [tex]=16[/tex] cups

[tex]\therefore 62[/tex] cups [tex]=\frac{62}{16}[/tex] gallons

                 [tex]=3.875[/tex] gallons

Therefore, a container contains 3.875 gallons of water.

Final answer:

To convert cups to gallons, divide the number of cups by 16 (since 1 gallon = 16 cups). For 62 cups, the conversion is 62 cups ÷ 16 cups/gallon = 3.875 gallons.

Explanation:

To convert cups to gallons, we must first know the conversion factors between these units. Using the provided reference information, we know that 1 gallon is equal to 16 cups since there are 4 quarts in a gallon and each quart is equivalent to 4 cups. Therefore, to convert from cups to gallons, we would divide the number of cups by 16.

Converting 62 cups to gallons:

So, the container holds 3.875 gallons of water.

The pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.

To find the dimensions of the pen that will give the maximum area, we can use the fact that for a given perimeter, a square has the maximum area. Since one side of the pen is formed by a wall, we have 36 meters of fencing for the other three sides. Let's denote the length of the pen as [tex]\( l \)[/tex] and the width. The perimeter  of the three sides that need fencing is given by:

[tex]\[ P = l + 2w \][/tex]

 We know that the total length of the fencing available for these three sides is 36 meters, so:

 [tex]\[ l + 2w = 36 \][/tex]

To maximize the area, we want [tex]\( l \)[/tex] to be as close to [tex]\( w \)[/tex] as possible, which means we want to divide the 36 meters of fencing equally among the three sides. If we let \( w = w \), then the equation becomes:

[tex]\[ l + 2l = 36 \][/tex]

[tex]\[ 3l = 36 \][/tex]

[tex]\[ l = \frac{36}{3} \][/tex]

[tex]\[ l = 12 \][/tex]

However, this would mean that there is no fencing left for the width, as all 36 meters would be used for the length. To avoid this, we need to distribute the fencing so that two of the sides (the widths) are equal and the remaining side (the length) is the third side. To find the maximum area, we set [tex]\( l = 2w \)[/tex], which gives us:

[tex]\[ 2w + 2w = 36 \][/tex]

[tex]\[ 4w = 36 \][/tex]

[tex]\[ w = \frac{36}{4} \][/tex]

[tex]\[ w = 9 \][/tex]

 Now, we can find the length [tex]\( l \):[/tex]

[tex]\[ l = 2w \][/tex]

[tex]\[ l = 2 \times 9 \][/tex]

[tex]\[ l = 18 \][/tex]

However, since we initially assumed[tex]\( l = 2w \)[/tex] to find the width, we need to adjust the length to account for the actual fencing used. We have two widths and one length, so the correct equation is:

[tex]\[ l + 2w = 36 \][/tex]

[tex]\[ 18 + 2 \times 9 = 36 \][/tex]

[tex]\[ 18 + 18 = 36 \][/tex]

[tex]\[ 36 = 36 \][/tex]

Therefore, the dimensions of the pen are 9 meters by 6 meters, with the wall forming the side of 18 meters.

 The final answer is that the pen should be built with dimensions of 9 meters by 6 meters, with the wall forming one of the 9-meter sides.

its d. i know for sure had the same question promise no lie

Answer:

As you know that Additive inverse of any number

 A = - A  , For example additive inverse of 2 is -2

or additive inverse of (-2) is 2.

Now, According to the question given

Emily has fixed monthly expenses that are taken directly out of her bank account.

As she wants to know,  how much money she must deposit in her account each month to cover these expenses.

So, Expenses are Additive inverse of Deposit or Deposit are additive inverse of Expenses.

Out of the given Options Option D which is, Emily can add (–48) + (–12) + (–44) to find her total expenses. The additive inverse of this number is the amount Emily must deposit each month. is correct.

Answer:

d

Step-by-step explanation:

[tex]-67\geq5+3n-21\\\\-67\geq3n+(5-21)\\\\-67\geq3n-16\ \ \ \ |+16\\\\-51\geq3n\ \ \ \ |:3\\\\-17\geq n\to n\leq-17\\\\Answer:\ \boxed{B.\ n\leq-17}[/tex]

Answer:

1)  a=12 , b=-9 , c=4

2)  a=-1 , b=-10 , c=2

3)  a=5 , b=-1 , c=9

4)  a=1 , b=-8 , c=16

Step-by-step explanation:

(1) y = 12x² - 9x + 4 no real solutions.

(2) 10x + y = -x² + 2, two real solutions.

(3) 4y - 7 = 5x² - x + 2 + 3y, no real solution.

(4) y = (-x + 4)², one real solution.

The number of real solutions for each quadratic equation is determined using discriminant.

The discriminant, denoted as Δ, is used to determine the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.

Δ = b² - 4ac

From the given equations;

y = 12x² - 9x + 4

a = 12, b = -9, c = 4

Δ = (-9)² - 4(12)(4)

Δ = 81 - 192

Δ = -111

Since the discriminant Δ is negative (-111), this quadratic equation has no real solutions.

10x + y = -x² + 2

y = -x² - 10x + 2

a = -1, b = -10, c = 2

Δ = (-10)² - 4(-1)(2)

Δ = 100 + 8

Δ = 108

Since the Δ is positive and greater than zero, the equation has two real solutions.

4y - 7 = 5x² - x + 2 + 3y

4y - 3y = 5x² - x + 2 + 7

y = 5x² - x + 9

a = 5, b = -1, c = 9

Δ = (-1)² - 4(5)(9)

Δ = 1 - 20(9)

Δ = 1 - 180 = -179

No real solution.

y = (-x + 4)²

when y = 0

0 = -x + 4 or

0 = -x + 4

x = 4

The equation has one real solution.

Learn more about solutions of quadratic equations here: https://brainly.com/question/1214333

#SPJ4

The slope-intercept form of a line:

y = mx + b

m - slope

b - y-intercept

We have

[tex]y=\dfrac{2}{3}x+2[/tex]

therefore the y-intercept is 2

C is the correct answer

HAVE smart phones + do NOT have smart phones = 125

Have smart phones

[tex]\frac{3}{5} *125 = \frac{3(125)}{5} = 3(25) = 75[/tex]

HAVE + NOT = 125

 75     + NOT  = 125

-75                     -75

             NOT = 50

Answer: 50 people do not have a smart phone

Yuri will have 1/7 of a bag of carrots left. This is because half of 2 is 1.

600,000 would be your answer

vote on my answer pplz

He has:

45 red tiles

90 blue tiles

75 yellow tiles

Greatest number of stones Marco can make is the GCF of the three numbers above which is 3 × 5 = 15 (Solution attached below)

This is your answer thanks!

Answer:

they are perpendicular to each other

Step-by-step explanation:

Final answer:

The smallest power of 10 that exceeds 999,999,999,991 is 10¹² because 999,999,999,991 is just one less than 1,000,000,000,000, which can be expressed as 10¹² in exponential form.

Explanation:

The question asks for the smallest power of 10 that would exceed 999,999,999,991. Understanding how to convert numbers into their exponential form plays a crucial role here. For a power of 10, the exponent tells you how many zeros you'd add to the digit 1 to express that number in long form. For example, 10² is 100, which is a 1 followed by 2 zeros. In the case of 999,999,999,991, we need to find a power of 10 that is just larger than this number.

Observing the number 999,999,999,991, it is just one less than 1,000,000,000,000. If we were to express 1,000,000,000,000 in exponential form, it would be 10¹², because it is a 1 followed by 12 zeros. Therefore, the smallest power of 10 that exceeds 999,999,999,991 is 10¹². This example illustrates how understanding integer powers and exponential notation is essential in solving problems of this nature effectively.