A blueprint of a house shows a dining room with
an area of 7 square inches. If the blueprint's
scale is 1 inch: 6 feet, what would be the actual
area of the dining room?
A = 7 in.²
Actual Area = [?] ft²

To eliminate the y terms and solve for x in the fewest steps, you can multiply the equations by appropriate constants so that the coefficients of the y terms in Both equations have the same magnitude but opposing signs. So to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x

In this instance, you can do the following steps:

Start with the original equations:

Equation 1: 2x + 3y = 8

Equation 2: 3x - 2y = 4

To eliminate the y terms, multiply Equation 1 by 2 and Equation 2 by 3:

Multiply Equation 1 by 2:

2(2x + 3y) = 2(8)

4x + 6y = 16

Multiply Equation 2 by 3:

3(3x - 2y) = 3(4)

9x - 6y = 12

Now, add the two modified equations together to eliminate the y terms:

(4x + 6y) + (9x - 6y) = 16 + 12

4x + 9x + 6y - 6y = 28

13x = 28

Finally, solve for x by dividing both sides of the equation by 13:

x = 28/13

Therefore, to eliminate the y terms and solve for x in the fewest steps, you should multiply the first equation by 2 and the second equation by 3x

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The probable question may be:

To eliminate the y terms and solve for x in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? The first equation should be multiplied by 2 and the second equation by 3. x.

m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

An equation is an expression that shows the relationship between two or more numbers and variables.

m∠ZAB + m∠CAB = 180° by the angle addition postulate

m∠CAB + m∠ACB + m∠CBA = 180° because of the triangle angle sum theorem

m∠ZAB = m∠ACB + m∠CBA using the subtraction property

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Answer:

We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition.

We know that m∠ZAB + m∠CAB = 180° by the

✔ angle addition postulate

.

We also know m∠CAB + m∠ACB + m∠CBA = 180° because

✔ of the triangle angle sum theorem

.

Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA.

Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the

✔ subtraction property

.

Step-by-step explanation:

Answer:

×=11

Step-by-step explanation:

2×-4×+27-5=0

-2×+22=0

-2×=-22

×=11

Answer:

Question 1: A. Replace one equation with a multiple of the other equation

Question 2: B. No

Step-by-step explanation:

1) How can we get System B from System A?

Choose 1 answer:

A. Replace one equation with a multiple of the other equation

B. Replace one equation with a multiple of itself

C. Swap the left-hand sides of both equations

D. Swap the order of the equations

2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution?

Choose 1 answer:

A. Yes

B. No

The answer to both questions is in bold and in the "Answer" section.

Hope this helps!

If not, I am sorry.

Answer:

0.74

Step-by-step explanation:

A tree diagram is a visual way of showing combinations of two or more events. The outcome of each branch is labelled at the end of the branch line and its probability is written alongside the branch.

To calculate the probabilities of each combination, follow the branches and multiply the probabilities together.

There are two possible combinations to get a final outcome of D:

Therefore, the probability of D is:

⇒ P(D) = P(A and D) OR P(B and D):

⇒ P(D) = 0.42 + 0.32

⇒ P(D) = 0.74

The measure of angle XYZ in the parallelogram is: 71°.

In a parallelogram, the angles that are opposite each other are congruent.

Find m∠XWZ using the triangle sum theorem:

m∠XWZ = 180 - m∠WXZ - m∠WZX

m∠XWZ = 180 - 81 - 28

m∠XWZ = 71°

m∠XWZ = m∠XYZ [opposite angles are congruent]

m∠XYZ = 71°

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Answer:

71°

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 Star and a Thanks :)

The function g(x) gets shifted toward right by 6 units. Then the correct option is C.

The complete question is attached below.

Let b is the base and x is the power of the exponent function and a is the leading coefficient. The exponent is given as

y = a(b)ˣ

The function f(x) is given below.

f(x) = 10ˣ

And the function g(x) is given as

g(x) = f(x – 6)

Then the function can be written as

[tex]\rm g(x) = 10^{x - 6}[/tex]

The function g(x) gets shifted toward right by 6 units.

Then the correct option is C.

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The measure of arc BEC is 134°. The correct option is the first option 134°

From the question, we are to determine the measure of arc BEC

In the given diagram,

Measure of angle C = 1/2 (measure of arc AB)

Reason: The measure of an inscribed angle is half the measure of the intercepted arc

∴ Measure of angle C = 1/2 (76°)

Measure of angle C = 38°

m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)

m∠A + 75° + 38° = 180°

m∠A + 113° = 180°

m∠A = 180° - 113°

m∠A = 67°

Measure of arc BEC = 2 × m∠A (Angle at the center is twice the angle at the circumference)

Measure of arc BEC = 2 × 67°

Measure of arc BEC = 134°

Hence, the measure of arc BEC is 134°. The correct option is the first option 134°

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The total area of the given composite figure is 84.8 ft²

We are given;

Area of Triangle = 5.6 ft²

Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²

Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)

Area of rectangles = 14.4 + 16 + 43.2

Area of rectangles = 73.6 ft²

Total area of composite figure = 73.6 ft² + 11.2 ft²

Total area of composite figure = 84.8 ft²

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Answer:

D:  -5 ≤ x < 1

R:  -4 ≤ y < 7

Step-by-step explanation:

The x values go between -5 and 1. The closed circle on -5 means it is included. The open circle on 1 means it is not included.

The y values go between -4 and 7. The closed circle means -4 is included, the open circle means the 7 is not included.

Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x    where r is the growth rate (interest rate)

So the equation can be written as

[tex]m= P(1.04)^t[/tex]    where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

[tex]I = P(1.04)^t-P[/tex]  where I represents the interest paid.

plug the values into the equation

[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]

The number of hours that students have to work on homework will be 1/3 hours.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

Mr. K's maths class is 1 and 1/4 hours long.

After working problems on the board for 55 minutes  or 11 / 12 hour.

He gave the students the rest of the class period to work on homework.

Then the number of hours that students have to work on homework will be

⇒ 1 + 1/4 - 11/12

⇒ 5 / 4 - 11/ 12

⇒ (15 - 11) / 12

⇒ 4/12

⇒ 1/3 hours

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Answer:

well by using the formulae a²+b²=c² with "a" being the opposite "b" being the adjacent and "c" being hypotenuse

Answer:

BY LEARNING  Pythagorean Theorem Formula Proof using Similar Triangles

Step-by-step explanation:

In a right-angled triangle, the Pythagoras Theorem Formula is expressed as:

c2 = a2 + b2

Where,

'c' = hypotenuse of the right triangle

'a' and 'b' are the other two legs.

Answer:

258 km

Step-by-step explanation:

We can calculate the speed of the boat with (333km/7 hours) = 47.57 km/hr.

Assuming the same speed, the boat would travel (47.57 km/hr)*(6 hr) = 258 km

Answer:

Given -

5x - y = (-1)

-5x + 3y = 25

To find - Summation of this

5x - y = (-1)

+ (-5x) + 3y = 25

adding both the equation we get,

5x +(-5x) - y + 3y = (-1) + 25

0 + 2y = 24

2y = 24.

Answer:

2y = 24

Step-by-step explanation:

5x – y = -1

+ - 5x + 3y = 25

2y = 24

Hence, A. 2y = 24 is the right answer.

Answer: 55[tex]m^{2}[/tex]

Step-by-step explanation:

First find the area of the trapezoid: [tex]\frac{b1 +b2}{2}[/tex](h) : (base 1 + base 2) ÷ 2 x height

base 1 is 5m and we know the other base is parallel to the base of the rectangle so base 2 is 9m.

Since the total height is 7 m and the height of the rectangle is 5 m, subtract to get the height of the trapezoid: 7m - 5m = 2m

put the three values into the equation and solve:

(5m + 9m) ÷ 2 x 2m

(14m) ÷ 2 x 2m

7m x 2m

14[tex]m^{2}[/tex]

Find area of the rectangle which is just base x height

Which is 9m x 5m = 45[tex]m^{2}[/tex]

To find the total area, add the area of the trapezoid and the area of the rectangle. 14[tex]m^{2}[/tex] + 45[tex]m^{2}[/tex] = 55[tex]m^{2}[/tex]

Hope this helps

Answer:

21% of 456 = 0.21 x 400 + 0.21 x 50 + 0.21 x 6 = 95.76

Step-by-step explanation:

Answer:

  4/3

Step-by-step explanation:

The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...

  tan(θ) = y/x

__

For the given point on the terminal side, the tangent is ...

  tan(θ) = (-4)/(-3) = 4/3

_____

Additional comment

There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:

  (x, y) = (r·cos(θ), r·sin(θ))

Then the ratio y/x is ...

  y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)

The correct answer is option D which is ASA ( Angle - Side - Angle).

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In triangles ABC and ADC,

Angles BCA and DAC are congruent (from the diagram);

Angles BAC and DCA are congruent (from the diagram);

AC is congruent AC (by reflexive property).

So, the triangles ABC and CDA are congruent with the ASA postulate.

ASA (Angle-Side-Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Therefore the correct answer is option D which is ASA ( Angle - Side - Angle).

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The value of x in the triangle is 117.2 units

The missing image is attached with the answer.

An equation is formed when two expression is equated by an equal sign to a constant , variable or an expression.

Cosine rule of Triangles is used and is given by

c² = a² + b² - 2ab cos C

Where a, b, c are the sides and C is the angle opposite side c.

from the given data in the figure

c = 63

a = 61 and

angle B is 142 degree

x² = 63² + 61² - 2(63)(61) * cos(142)

On solving

x = 117.2

The value of x in the triangle is 117.2 units

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Answer:

111 cm^2

Step-by-step explanation:

h = 11.4

d = 5  so  r (radius) = 2.5

Surface Area of a Cone Formula: πr^2 + πrs

s represents the slant height of the cone, lets represent this with a drawing.

We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.

a^2 + b^2 = c^2

These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.

s = √(11.4^2 + 2.5^2)   so  s = 11.67

now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs

π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2

The surface area of the solid cone requiring paint will be 111 square cm.

Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.

Then the lateral surface area of the cone will be

SA = πrl + πr²

Then the slant height is given as

l² = r² + h²

The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.

Then the radius of the base circle will be

r = 5 / 2

r = 2.5 cm

The length of the slant height will be

l² = 11.4² + 2.5²

l² = 136.21

 l = 11.67

Then the surface area of the solid cone requiring paint will be

SA = π × 2.5 × 11.67 + π × 2.5²

SA = 29.18π + 6.25π

SA = 35.43π

SA = 111.3

SA ≈ 111 square cm

The surface area of the solid cone requiring paint will be 111 square cm.

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Two pairs of corresponding angles are congruent, so the triangles are similar.

The correct option is (A).

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

As, the measurement of two angles are equal.

So, the angles are congruent.

Hence, by AA criteria the triangles are similar.

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Answer:

A

Step-by-step explanation:

Answer:

A.) 132.3 mm Hg

B.) 49 years old

Step-by-step explanation:

[tex]P= 0.006y^{2} -0.01y+119[/tex]

P = blood pressure

y = age in years

A.) Solution

To find: P

Given: y = 48

[tex]P= 0.006y^{2} -0.01y+119[/tex]

P = 0.006 x 48 x 48 - 0.01 x 48 + 119

P = 0.006 x 2,304 - 0.48 + 119

P = 13.824 - 0.48 + 119

P = 132.344 ⇒ 132.3

B.) Solution

To find: y

Given: P = 132.92

[tex]P= 0.006y^{2} -0.01y+119[/tex]

[tex]132.92= 0.006y^{2} -0.01y+119[/tex]

[tex]0.006y^{2} -0.01y-13.92[/tex]

.......................................................

Answer: 49 years old

The value of (x,y) is  (1.2 , -4.7) , Option D is the right answer.

The complete question is

On a coordinate plane, a line is drawn from point a to point b. point a is at (7, negative 2) and point b is at (negative 8, negative 9). what are the x- and y-coordinates of point c, which partitions the directed line segment from a to b into the ratio 5:8? round to the nearest tenth, if necessary. x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (–2.2, –6.3) (–2.4, –6.4) (2.7, –0.7) (1.2, –4.7)

Coordinates are the location of a point in an (x,y) plot.

The given data is

Coordinates of

A = (7,-2)

B = (-8,-9)

m:n = 5:8

The coordinates of partition has to be determined

The formula used is

[tex]\rm (x,y) = \dfrac{1}{m+n} *(nx_1 + mx_2 , ny_1+ny_2)\\\\\\\rm (x,y) = \dfrac{1}{5+8} *(5*-8 + 8*7 , 5*-9+8*-2)[/tex]

(x,y ) = (1.2 , -4.7)

Therefore Option D is the correct answer.

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To factor an expression, we can identify common factors between each terms, and take them out.

117n + 90

Both terms have the common factor of 9. Factor this out:

= 9(13n + 10)

13 and 10 do not have a common factor. Therefore, this is the final factored expression.

9(13n + 10)

Answer:

n = -5

Step-by-step explanation:

Given:

  [tex]\dfrac{y^4 \cdot y^n}{y^2}=y^{-3}[/tex]

Multiply both sides by y²:

[tex]\implies \dfrac{y^4 \cdot y^n}{\diagup \!\!\!\!\!y^2} \cdot \diagup \!\!\!\!\!y^2=y^{-3}\cdot y^2[/tex]

[tex]\implies y^4 \cdot y^n=y^{-3} \cdot y^2[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies y^{4+n}=y^{-3+2}[/tex]

[tex]\implies y^{4+n}=y^{-1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies 4+n=-1[/tex]

Solve for n by subtracting 4 from both sides:

[tex]\implies 4+n-4=-1-4[/tex]

[tex]\implies n=-5[/tex]

Answer:

===========

Given equation:

Solve it for n:

===========

Used properties:

The length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The area of a rectangle is represented by the expression [tex]6x^3y^5[/tex].

The area of the rectangle = [tex]2x^2y^2 \times 3xy^3[/tex]

                                          = [tex]6x^3y^5[/tex]

So, the length and width of the rectangle are: [tex]2x^2y^2 , 3xy^3[/tex]

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