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Show CORRECT WORK and SOLUTION

THE FIRST PIC IS THE QUESTION!!!!

You find the difference in weight by subtacting the weight of the nickel from the weight of the copper.

... (4/5 kg) - (3/5 kg) = (4 -3)/5 kg = 1/5 kg

The piece of copper weighed 1/5 kg more than the piece of nickel.

The point-slope form of a line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 6) and (3, 4). Substitute:

[tex]m=\dfrac{4-6}{3-5}=\dfrac{-2}{-2}=1\\\\y-6=1(x-5)\\\\y-6=x-5\qquad|\text{add 6 to both sides}\\\\y=x+1\qquad|\text{subtract x from both sides}\\\\-x+y=1\qquad|\text{change the signs}\\\\x-y=-1[/tex]

Answer:

slope-intercept form: y = x + 1

point-slope form: y - 6 = 1(x - 5)

standard form: x - y = -1

Hey there!

Given points:

...(5,6) and (3,4)

Slope-intercept form:

... y=mx+b

'm' is the slope and 'b' is the y-intercept.

Slope:

... (y₂-y₁)/(x₂-x₁)

... (4-6)/(3-5)

... -2/-2

...1

:

... y = x + b

... 4 = 3 + b

... b = 1

Slope-intercept form:

... y = x + 1

Hope helps!

Answer:

14

Step-by-step explanation:

"Enlargement" here implies that the two pentagons are similar.  Because of similarity, the following equation of ratios must be true:  7/15 = x/7.  Then 15x=49, and x = 49/15 = 3.27 cm, approximately.

Rounded to the nearest tenth, that comes to 3.3 cm.

Answer:

B

Step-by-step explanation:

given h = 600 - 16t ( add 16t to both sides )

16t + h = 600 ( subtract h from both sides )

16t = 600 - h ( divide both sides by 16 )

t = [tex]\frac{600-h}{16}[/tex]

when h = 400

t = [tex]\frac{600-400}{16}[/tex] = [tex]\frac{200}{16}[/tex] = 12.5 seconds

Answer:

The required time is 3.54 seconds approximately or [tex]\frac{5}{2}\sqrt{2}[/tex] seconds.

Step-by-step explanation:

Consider the provided function.

[tex]h(t) = 600-16t^2[/tex]

Where t represents the time in seconds and h represents the height.

It is given that we need to find the time to reach a height of 400 feet.

Substitute h(t)=400 in the above function.

[tex]400= 600-16t^2[/tex]

[tex]400- 600=-16t^2[/tex]

[tex]-200=-16t^2[/tex]

[tex]200=16t^2[/tex]

[tex]\frac{50}{4}=t^2[/tex]

[tex]t=\sqrt{\frac{50}{4}} \\t=\frac{5}{2}\sqrt{2}[/tex]

Neglect the negative value as time should be a positive number.

Or

[tex]t\approx 3.54[/tex]

Hence, the required time is 3.54 seconds approximately.

The usual rules of addition and multiplication apply to complex numbers as well as to real numbers. The true statements are ...

The true statements after evaluating the expression based on principle of commutativity and associativity are :

x = a + bi

y = c + di

z = f + gi

Recall :

Evaluating the options :

Hence, only 3 of the given statements are true, according to the Commutative or Associative rule.

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We have to write the equation of a line that is perpendicular to the line [tex]x=3[/tex] and that passes through the point [tex](0,-4)[/tex].

The general equation of a line in the slope-intercept form is given by:

[tex]y=mx+b[/tex]

Where, 'm' is the slope and 'b' is the y-intercept.

Now, we need to find the slope first,

The required line is perpendicular to the line [tex]x=3[/tex]. Slope of the line [tex]x=3[/tex] is undefined. A line perpendicular to that must have slope of '0'. That implies, our required line is parallel to the x-axis.

Therefore, m=0

Now that line is passing through the point [tex](0, -4)[/tex].

We can plug in the points to the find the value of y-intercept. After plugging the values, we get:

[tex]y=0 \times 0+(-4)=-4[/tex]

Hence, the equation of the required line is [tex]y=-4[/tex].

Attendance with the higher ticket price is ...

... $1750/$7 = 250

So the percentage change in attendance is ...

... change = (new - original)/original × 100%

... = (250 -300)/300 × 100% = -1/6×100% ≈ -17%

Final answer:

The percentage change in the average number of customers after the movie theater raises ticket prices is approximately -17%.

Explanation:

The movie theater originally charges $5 per ticket and has an average of 300 customers each night. After raising the price to $7, the average nightly ticket sales amount to $1,750. To find the new number of customers, divide the total sales by the price per ticket: $1,750 / $7 = 250 customers.

The change in the number of customers is the new amount minus the original amount, which is 250 - 300 = -50. To find the percentage change, divide the change by the original amount and multiply by 100: (-50 / 300) x 100 = -16.67%. After rounding the decimal, the percentage change is approximately -17%.

2/3 (5/3)(-1) = -10/9

Answer:

-7/9

Step-by-step explanation:

2/3(3 - 1/3)(-1) = (1-2/9)(-1) = -1+2/9 = -7/9

The answer us C. 9/10 minus 3/10 is 6/10 simplified to 3/5 if you need it.

I would say the low I’m just guessing so get it checked

Answer:

the answer is C

Step-by-step explanation:

The low temperatures have the greater range. The range for the highs is 6, the range for the lows is 8.

The first reflection reverses the orientation and alters the direction of the vectors representing the sides of the quadrilateral. The second reflection does the same thing. The end result is that the orientation is unchanged by two reflections, and the direction of the sides of the quadrilateral is changed.

The appropriate choice is ...

... B. The resulting image will be a rotation of the pre-image.

_____

The center of rotation will be the point where the lines cross. (That is the invariant point.)

In the attachment, the green quadrilateral RESP is reflected across the line y=2x+7 (blue) to form the blue quadrilateral R'E'S'P'. That is then reflected across the line y = -12x +5 (orange) to give the orange quadrilateral R"E"S"P", which is a rotation of the pre-image.

The amount of rotation is double the angle between the lines, about 62.7°.

Answer:

$2268

Step-by-step explanation:

Luna's total mortgage payments for the year would be

... (monthly payment)×(number of months in a year)

... = $2100×12 = $25,200

Of that, 9% went to interest, so the interest amount is ...

... $25,200×9% = $2268

_____

About percentages

Your calculator may do percentages directly. If not, it can be helpful to realize that the percent symbol (%) means the same thing as /100 (divided by 100). So, 9% = 9/100 = 0.09

Answer:

$2268

Step-by-step explanation:

did it on apXX

(a) $0.80

(b) 1.25 m

(a) Put 1 where L is, and evaluate the equation.

... p = 0.8·1 = 0.8

The cost for 1 meter of rope is $0.80.

(b) Put 1 where p is and solve for L.

... 1 = 0.8L

... 1/0.8 = L = 1.25

The length of rope that costs $1 is 1.25 meters.

Answer:

a. $ 0.8

b. 1.25 meters.

Step-by-step explanation:

Given equation that represents the price p (in dollars) of a piece of nylon rope having length L meters,

[tex]p=0.8L[/tex]

a. If L = 1 meter,

The cost of the rope would be,

[tex]p=0.8(1) = \$ 0.8[/tex]

b. if p = $ 1.00,

[tex]\implies 1 = 0.8L[/tex]

[tex]\implies L=\frac{1}{0.8}=1.25[/tex]

Thus, the length of the rope would be 1.25 meters.

[tex]4y=2x-10[/tex] and [tex]y=6[/tex]

use the second expression to calculate the left-hand side of the first equation:

[tex]4\cdot 6 = 2x -10\\24 = 2x -10[/tex]

Add 10 to both sides if this equation to get

[tex]34 = 2x[/tex]

and divide both sides by 2

[tex]17 = x[/tex]

this proves that x = 17, give the two initial equations

The least number of gift baskets Jessica can make, given that she has 6 jars of salsa and 4 bags of tortilla chips in each case, is 12. This is calculated by finding the Least Common Multiple of 6 and 4.

Jessica is working with two different quantities: 6 jars of salsa in a case and 4 bags of tortilla chips in a case. In each gift basket, she places 1 jar of salsa and 1 bag of tortilla chips, meaning that she needs the same number of jars and bags for an even number of gift baskets.

Therefore, to find the least number of baskets she can make, we need to find the Least Common Multiple (LCM) of 6 and 4, which the smallest number that both numbers divide evenly into. The LCM of 6 and 4 is 12. Hence, the least number of gift baskets Jessica can make is 12.

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Question 1.) Factor completely [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex]

Since [tex]6[/tex] divides all the three terms of the equation, so we take [tex]6[/tex] common out from the equation.

i.e., [tex]6(2x^{4}+ 1x^{3}+3x^{2})[/tex]

Now, since [tex]x^{2}[/tex] divides all the three terms of the equation, so we take [tex]x^{2}[/tex] common out from the equation.

i.e., [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]

Now, this cannot be factored further as [tex]2x^{2}+ 1x+3[/tex] is a quadratic equation and taking out discriminant of it is:

[tex]D = (1)^2 - 4(2)(3)\\  \ \   = 1- 24\\ \ \ = -23<0[/tex]

Since, the discriminant is less than zero. Therefore, the factored form of the given equation :  [tex]12x^{4}+ 6x^{3}+18x^{2}[/tex]  is : [tex]6x^{2}(2x^{2}+ 1x+3)[/tex]

Question 2.) [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex]

Since [tex]7[/tex] divides all the three terms of the equation, so we take [tex]7[/tex] common out from the equation.

i.e., [tex]7(x^{3}y+ 2x^{2} y^{3} - x^{2}y^{2})[/tex]

Now, since [tex]x^{2}y[/tex] divides all the three terms of the equation, so we take [tex]x^{2}y[/tex] common out from the equation.

i.e., [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]

Therefore, the factored form of the given equation :  [tex]7x^{3}y+ 14x^{2} y^{3} - 7x^{2}y^{2}[/tex]  is : [tex]7x^{2}y(x+ 2y^{2} - y)[/tex]

Question 3.) What is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex] ?

The Greatest Common Factor of two numbers is the biggest number which divides both the given numbers completely.

Now, for the expressions [tex]x^{6}[/tex] and [tex]x^{3}[/tex]:

Since, [tex]x^{3}[/tex] divides both the expressions completely and it is the biggest expression which divides both the expressions.

Therefore, [tex]x^{3}[/tex] is the Greatest Common Factor of [tex]x^{6}[/tex] and [tex]x^{3}[/tex]

Answer:

#2 is definatly B

Step-by-step explanation:

Answer: the angles are if the 30° is in the first quadrant:

30°, 150°, 30°, 150° (from quadrant one to quadrant four)

Step-by-step explanation:

If two lines intersect, and one of the angles that form is 30°, we have that:

Now, suppose that you have only a line, this is the representation of a 180° angle, then if you divide it with a line and one of the angles created is 30°, the other angle must be equal to 150°

and on the other side of the line we will have a mirrored image, right next to the 150° we should see another 30° angle, and after that another 150° angle.

Answer:

<L = 50 degrees

Step-by-step explanation:

B and C are given. There should be a one to one Correspondence. <A should = <L

Since there are 180o in any triangle

<L = <A = 180 - 35 - 95

<L = <A = 50 degrees

Using geometry:

Since M is the origin, point B is the mirror image of point A with respect to the origin. From the origin to point A, you go 5 units left and 4 units up. For the mirror image, start at the origin, and go 5 units right and 4 units down.

Answer: B(5, -4)

Using the midpoint formula:

[tex] x_m = \dfrac{x_1 + x_2}{2}~~~and~~~y_m = \dfrac{y_1 + y_2}{2} [/tex]

[tex] 0 = \dfrac{-5 + x_2}{2}~~~and~~~0 = \dfrac{4 + x_2}{2} [/tex]

[tex] 0 = -5 + x_2~~~and~~~0 = 4 + x_2 [/tex]

[tex] -x_2 = -5~~~and~~~-4 = x_2 [/tex]

[tex] x_2 = 5~~~and~~~x_2 = -4 [/tex]

Answer: B(5, -4)

As you can see, both methods give you the same answer.

a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.

ABCD can be transformed to A'B'C'D' by ...

b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...

SOH CAH TOA tells you

... cos(B) = a/c

... 4/5 = 8/c

... c = 10 . . . . . multiply by 5c/4

By the Pythagorean theorem,

... b = √c² -a²) = √(10² -8²) = √36 = 6

The lengths of the other two sides are: b = 6, c = 10.

_____

You can tell from the value of the cosine that this is a 3-4-5 right triangle. You can tell from the value of "a" that the scale factor is 2. That means the other two sides are 6 and 10.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem and the cosine function. Side a is given as 8 and the cosine of angle B is given as 4/5. Using the cosine function, we can find the length of side b. Then, using the Pythagorean theorem, we can find the length of side c. The lengths of the other two sides are approximately 6.4 and 10.24, respectively.

To find the lengths of the other two sides of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, we are given that side a is opposite angle A and has a length of 8, and we are given the cosine of angle B, which is 4/5. We can use the cosine function to find the length of side b, and then use the Pythagorean theorem to find the length of side c.

Step 1: Use the cosine function to find the length of side b:
cos(B) = 4/5
b/a = cos(B)
b/8 = 4/5
b = (4/5) * 8
b = 32/5
b = 6.4

Step 2: Use the Pythagorean theorem to find the length of side c:
a² + b² = c²
8² + 6.4² = c²
64 + 40.96 = c²
104.96 = c²
c = √104.96
c ≈ 10.24

Therefore, the lengths of the other two sides of the right triangle are approximately 6.4 and 10.24, respectively.

Answer:

cos(A) = 24/25 = 0.96

Step-by-step explanation:

SOH CAH TOA tells you that ...

... cos(A) = AB/AC

We are given AB = 24, but we must calculate AC using the Pythagorean theorem.

... AC² = AB² + BC²

... AC² = 24² + 7² = 576 + 49 = 625

... AC = √625 = 25

Now, we have sufficient information to find cos(A):

... cos(A) = 24/25 = 0.96

The value of cosA is used in trigonometry and physics to calculate the horizontal component of vectors or the angle of right triangles. For example, if we have a vector A, at an angle θ, then Ax = A cos θ, where Ax is the horizontal component of the vector. So in this way, cosA provides a crucial part in vector calculations.

The value of cosA refers to the cosine of angle A. In trigonometry, this is often used in the context of right triangles or in the calculation of vectors. For example, if you have a vector A and an angle θ (theta), the horizontal component of that vector can be found by multiplying the magnitude of the vector (Ax) by cos(θ). This is often denoted as Ax = A cos θ.

To use an example, let's say we have a vector A with a magnitude of 10.3 blocks and an angle of 29.1° from the x-axis. We can find the x-component (Ax) of that vector by calculating (10.3 blocks) * cos(29.1°), which gives us a value of approximately 9.0 blocks.

Therefore, the value of cosA in this context would be used to provide a component part of a vector based on an associated angle.

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Answer:

Given: ∆ABC with the altitudes from vertex B  and C intersect at point M, so that BM = CM.

To prove:∆ABC is isosceles

Proof:-Let the altitudes from vertex B intersects AB at D and from C intersects AC at E( with reference to the figure)

Consider ΔBMC where BM=MC

Then ∠CBM=∠MCB......(1)(Angles opposite to equal sides of a triangle are equal)

Now Consider ΔDMB and ΔCME

∠D=∠E.......(each 90°)

BM=MC...............(given)

∠CME=∠BMD........(vertically opposite angles)

So by ASA congruency criteria

ΔDMB ≅ ΔCME

∴∠DBM=∠MCE........(2)(corresponding parts of a congruent triangle are equal)

Adding (1) and (2),we get

∠DBM+∠CBM=∠MCB+∠MCE

⇒∠DBC=∠BCE

⇒∠B=∠C⇒AB=AC(sides opposite to equal angles of a triangle are equal)⇒∆ABC is an isosceles triangle .

Answer:

m∠MBC = m∠MCB

 by reason: Base Angles

Step-by-step explanation:

:)

The answer to "What is the P(Gate 3 and Gate 4 are both open)?" is

B: 15%

It is because they state that the chance of both gates being open at the same time is 15% and that chance is indeed the probability.

Answer:

B. 80 km/h

Step-by-step explanation:

The graph is linear and goes through the origin, so distance is proportional to time, and the constant of proportionality is speed. The desired answer can be read from the point on the graph at time = 1 hour: 80 km.

Julian's speed is 80 kilometers per hour.

B

speed = [tex]\frac{distance}{time}[/tex]

From the graph the distance travelled = 480 Km

and time taken = 6 hours

speed = [tex]\frac{480}{6}[/tex] = 80 Km / hour

Umm. What is the question?

The design and layout of a Baseball Field Design to the game experience by affecting play flow and ensuring visibility, vital for both players and fans. Elements like the diamond infield and the extensive outfield reflect American sports culture, which emphasizes strategy and skill, and has historically fostered community engagement and identity.

The design and layout of a baseball field significantly impact the experience of the game by determining the flow of play and the visibility of actions, which is crucial for player performance and fan engagement.

Specific elements, such as the diamond shape of the infield and the expansive outfield, align with the American sports culture, which values a balance between strategy and physical skill, offering a variety of play styles from power hitting to meticulous base running.

The historical evolution of professional baseball teams and their ballparks reflects a facet of American identity through sports, as communal spaces like Fenway Park and Forbes Field facilitated a collective civic pride and a space for social interaction among diverse groups including immigrants.

Moreover, participation in sports, even at the informal level of pickup games, represents an integral part of cultural dynamics in American society, aligning with the practice of community building and local support within the cultural geography framework.

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The probable question may be:

How does the design and layout of a baseball field contribute to the overall experience of the game, and what specific elements align with the principles of American sports culture as taught in the curriculum?

24/4 = 6/1

40/5 = 8/1

The answer is 6/1 and 8/1.

Best of luck.

The missing number unit rate of 24/4=?/1 is 6 and 40/5=?/1 is 8.

The missing number of each unit rate is 24/4=?/1 and 40/5=?/1.

Let the missing number be x.

The missing number is determined by cross multiply and then solving for the value of x.

The missing number is,

[tex]\rm \dfrac{24}{4} = \dfrac{x}{1}\\\\24 \times 1 = x \times 4\\\\24 = 4x\\\\x = \dfrac{24}{4}\\\\x = 6[/tex]

And another missing number is,

[tex]\rm \dfrac{40}{5} = \dfrac{x}{1}\\\\40 \times 1 = 5 \times x\\\\40 = 5x\\\\x = \dfrac{40}{5}\\\\x = 8[/tex]

Hence, the missing number unit rate of 24/4=?/1 is 6, and 40/5=?/1 is 8.

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