Solve the system of equation using the solution method:
y=3x+2
2x-3y=8

Answer:

y - 8 = 7(x - 5)

y - 8 = 7x - 35

y = 7x - 27

Step-by-step explanation:

Answer:

Angela eats more cake

Angela ate 1/8 more cake

1/4 of the chocolate

3/8 of the Vanilla

no more Strawberry

Step-by-step explanation:

Angela: 4/8 + 2/8 + 4/8 = 10/8 = 1 1/4

David: 2/8 + 3/8 +4/8 = 9/8 = 1 1/8

Chocolate: 4/8 + 2/8 = 6/8,  8/8 - 6/8 = 2/8 or 1/4

Vanilla: 2/8 + 3/8 = 5/8, 8/8 - 5/8 = 3/8

Strawberry: 4/8 + 4/8 = 8/8, 8/8 - 8/8 = 0

Final answer:

Angela ate more cake than David by 0.125 of a cake after calculating fractions consumed by each. The remaining amounts of cake are 1/4 of chocolate, 3/8 of vanilla, and none of the strawberry cake is left.

Explanation:

To find out who eats more cake, Angela or David, we need to calculate the fractions of each cake they consumed. Firstly, we can simplify the fractions of the cake Angela and David ate by converting them to have the same denominator or to represent them as decimals. The total amount of each cake consumed needs to be added up individually for Angela and David.

Angela's Cake Consumption:

Chocolate Cake: 4/8 (simplified to 1/2 or 0.5)

Vanilla Cake: 2/8 (simplified to 1/4 or 0.25)

Strawberry Cake: 2/4 (simplified to 1/2 or 0.5)

Total cake eaten by Angela = 0.5 (chocolate) + 0.25 (vanilla) + 0.5 (strawberry) = 1.25

David's Cake Consumption:

Chocolate Cake: 1/4 (or 0.25)

Vanilla Cake: 3/8 (simplified to 0.375)

Strawberry Cake: 1/2 (or 0.5)

Total cake eaten by David = 0.25 (chocolate) + 0.375 (vanilla) + 0.5 (strawberry) = 1.125

Angela ate more cake than David by 0.125 of a cake.

Amount of Each Cake Left:

Chocolate Cake: 1 - (0.5 + 0.25) = 1/4 or 0.25 left

Vanilla Cake: 1 - (0.25 + 0.375) = 3/8 or 0.375 left

Strawberry Cake: 1 - (0.5 + 0.5) = 0 left

The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.

Step-by-step explanation:

Diagonals of the kite = 16 inches and 18 inches

Area of the kite = (16 x 18) /2

= 144 square inches

Area of 3 kites = 3 x 144

= 432 square inches.

The material needed to make 1 kite is 144 square inches and for 3 kites she need 432 square inches of the material.

Answer:

the first one is 144 and the second one is 432

Step-by-step explanation:

Answer:

D

1.collect like terms (-11x and 6x) which equal -5

2. rewrite equation (-5x-30=0)

3. Move constant to the right hand side and change its sign.(-5x=30)

4. Divide both sides by -5 (30 divided by -5 equal s -6)

Answer:

y = 5/3 x + 5

Step-by-step explanation:

5x - 3y = -15

Subtract 5x from each side

5x-5x - 3y = -15-5x

-3y = -5x-15

Divide each side by -3

-3y/-3 = -5x/-3 -15/-3

y = 5/3 x + 5

To solve 5x - 3y = -15 for y, you need to isolate y, by adding 5x to both sides and then dividing by -3, yielding the solution y = -5x/3 + 5.

To solve the equation 5x - 3y = -15 for y, we need to isolate y on one side of the equation. Here's a step-by-step process:

Using this method, we can solve any linear equation in two variables for one of the variables. In this case, we have expressed y as a function of x.

Answer:

Trapezoid

Step-by-step explanation:

Trapezoid is a type of parallelogram that consist of two obtuse angles and two acute angles

EK=6, KF=6

By the Pythagorean theorem

[tex]6^2+6^2=EF^2\\EF=\sqrt{36+36} \\EF=\sqrt{72}[/tex]

EF≈8,48≈8

Answer: 8 units

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P.S. Hello from Russia :^)

Hello there, to answer your question....

The diameter and radius of a circle with an 18 inch circumference is

I hope the information I have provided helps. :)

The approximate diameter of the circle is 5.73 inches, and the approximate radius is 2.86 inches.

To discover the diameter and radius of a circle with a given circumference, ready to utilize the taking after equations:

Circumference = π * Diameter

Diameter = Circumference / π

Given that the circumference of the circle is 18 inches, able to calculate the diameter as follows:

Diameter = 18 inches / π

To discover the radius, we will utilize the equation:

Radius = Diameter / 2

Let's calculate the values:

Diameter = 18 inches / π ≈ 5.73 inches

Radius = 5.73 inches / 2 ≈ 2.86 inches

Hence,  the approximate diameter of the circle is 5.73 inches, and the approximate span is 2.86 inches.

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Answer:

Yes

A parallelogram with opposite sides equal to 6 units and 3 units and each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex]

Step-by-step explanation:

Given: A rectangle has side lengths of 6 units and 3 units

To check: If a quadrilateral can be made that is not identical to the given rectangle using the same four side lengths

Solution:

A parallelogram with opposite sides equal to 6 units and 3 units can be made.

Take each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex]

This parallelogram is not identical to rectangle as each of the angle of the rectangle is equal to [tex]90^{\circ}[/tex] but here each of the pair of opposite angles as equal to [tex]50^{\circ}\,,\,130^{\circ}[/tex].

Yes, one can construct another quadrilateral, such as a parallelogram, using the same side lengths of 3 units and 6 units. While both a rectangle and parallelogram are quadrilaterals, a parallelogram is not identical to a rectangle as not all angles in a parallelogram are right angles.

Yes, it is possible to make another quadrilateral with the same side lengths that are not identical to the rectangle.

One of the ways is to make a parallelogram using side lengths of 3 units and 6 units. While a rectangle is a type of parallelogram, the noticeable difference is that not all angles in a parallelogram are right angles. In a rectangle, all angles are right angles, making it a special case of a parallelogram.

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The line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.

What is the slope intercept form of a line ?

The equation of line that can be written as y = mx + c, where m is the slope and c is the line's y-intercept, is known as a slope intercept form.

The equation of a line is given which is 3x – 2y = 12.

This can be also written as :

3x - 2y - 12 = 0

We know that general equation of a line is given by ax + b + c = 0.

So , the given equation is :

3x – 2y = 12

dividing by 12 on both sides we get "

[tex]\frac{3x}{12}[/tex] - [tex]\frac{2y}{12}[/tex] = [tex]\frac{12}{12}[/tex]

[tex]\frac{x}{4}[/tex] - [tex]\frac{y}{6}[/tex] = 1

or

[tex]\frac{x}{4}[/tex] + (- [tex]\frac{y}{6}[/tex]) = 1

This is the slope intercept form of the given equation.

So , using the slope intercept form of line ,

y = mx + c

y = [tex]\frac{3}{2}[/tex] x - 6

If we compare : we get

c = y intercept = -6

and

Slope (m) = [tex]\frac{3}{2}[/tex]

Therefore , the line with equation 3x – 2y = 12 has the value of slope (m) equal to [tex]\frac{3}{2}[/tex] and y - intercept equal to -6.

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Final answer:

The line 3x – 2y = 12 has a slope of 3/2 and a y-intercept of -6, corresponding to choice A.

Explanation:

The equation of the line is given as 3x – 2y = 12. To find the slope and the y-intercept, we should rewrite this equation in slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. To do this, solve the given equation for y:

So, we have the slope (m) as 3/2 and the y-intercept (b) as -6, which corresponds to choice A.

Answer:

x = 6, x = -8

Step-by-step explanation:

Since the Pythagorean Theorem is L^2 + L^2 = H^2, all we have to do is substitute each variable and its equation for our L's.

(x + 2)^2 + (x)^2 = 100

2x^2 + 4x + 4 = 100

2x^2 + 4x - 96 = 0

Using quadratics, sorry, there was no other way, we get:

x = 6 or x = -8.

Check:

6 + 2 = 8^2 = 64

6^2 = 36

64 + 36 = 100 = 10.

-8 works as well.

Therefore, x = 6, x = -8 are correct.

Answer: a= -6 or 8

b=6 or -8

Step-by-step explanation:

From the result in the diagram

X=6 or -8

Remember

A=x+2

Substitute for x=6

A=6+2=8 or

A= -8+2= -6

So how answer for

A= -6 or 8

B=6 or -8

Each angle is 40 degrees because a straight line is 180 and there is a 100 so just subtract 100 from 180 then divide 80 by 2 and you're left with 40

Answer:

A = 1.75

Step-by-step explanation:

A = (a+b )/2h

A = (3 + 4) / 2 *2 =

= 7/4 = 1.75

Hey there!

In order for you to find the one that is equivalent to the given expression is to COMBINE YOUR LIKE TERMS then work from there!

12q + q^2 - 8 + q = ?

(q^2) + (12q + q) + (-8)

q^2 = q^2 since it doesn't have any like term(s)

12q + q = 12q + 1q = 13q

-8 = -8 since it doesn't have any like term(s)

Put all the numbers we solved for in An equation and Thats your answer!

If you did it correctly you should have: q^2 + 13q - 8

Answer: q^2 + 13q - 8 ✅

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

Y=h(x)

Y=k(h)

Because they are on positive

The functions y = h(x) and y = k(x) depict exponential growth.

A rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay. Over time, exponential functions monitor constant growth. Examples from the actual world include radioactive decay, compound interest, and bacterial proliferation.

The standard form of an exponential equation is y = a(b)ˣ  

where a is the initial value

b is the rate

Exponential decay is where the final value (y) is less than the initial value (a). An example would be the decrease of bacteria in a person

Exponential growth is where the final value (y) is greater than the initial value (a). An example would be the spreading of a rumor.

A graph that is flat in the beginning and instantaneously grows in the vertical direction over a period of time

therefore, y = h(x) and y = k(x) are the functions represent exponential growth.

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Answer:

The dot plot that is most strongly skewed right is the first example

This is because the numbers 4 and 5 are to the right of the graph, and the numbers 4 and 5 in this example are the highest compared to the others.

For example, in this first example, 4 has 7 dots and 5 has 6 dots.

In the rest of the examples, the highest numbers for 4 and 5 are 4 dots and 3 dots

I hope this helps :)

Answer:

C

Step-by-step explanation:

all real values of x where 1 < x < 4

All real values of x where 1 < x < 4.

The graph of a function f is the set of all points inside the aircraft of the shape (x, f(x)). We can also define the graph of f to be the graph of the equation y = f(x). So, the graph of a character is a unique case of the graph of an equation.

For graphing functions, we need to plot its asymptotes, its x and y-intercepts, holes, and some factors on it by means of building a desk of values. Then simply join the factor by not touching the asymptotes and maintaining a observation of the area and range of the characteristic.

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Answer:

x=3

Step-by-step explanation:

First, subtract 12 on both sides

36x + 12 = 120

36x=108

Divide by 36 on both sides

x=3

Hope this helps! :)

Answer:

A. 210 ft

Step-by-step explanation:

Answer:

#7 : 6

#8 : 12

#9 : ?

#10 : 110

#12 : ?

Answer:

The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].

Step-by-step explanation:

The center-radius form for a circle is:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.

Compare:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x+4)^2+(y-5)^2=121[/tex]

[tex]-h=4[/tex] implies [tex]h=-4[/tex].

[tex]-k=-5[/tex] implies [tex]k=5[/tex]

[tex]r^2=121[/tex] implies [tex]r=\sqrt{121}=11[/tex].

The center is [tex](-4,5)[/tex] and the radius is [tex]11[/tex].

The center is (-4.5) and the radius is 11.

The center-radius form for a circle is:

⇒ (x-h)²+(y-k)² = r²

where (h,k) is the center and r is the radius.

Compare:

(x-h)²+(y-k)²

(x+4)+(-5)² = 121

-h = 4 implies h = -4.

-k = -5 implies k = 5

r² = 121 implies r = √121= 11,

The center is (-4.5) and the radius is 11.

The center is a fixed point in the middle of the circle; usually given the general coordinates (h, k). The fixed distance from the center to any point on the circle is called the radius.

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Answer: Sales tax would be $5.40

Step-by-step explanation: The sales value itself of the dress (that is, without tax) is $65.49.

The amount charged as sales tax in Pearland is given as 8.25% (or 0.0825).

Hence if she is shopping in Pearland, the AMOUNT OF SALES TAX she would pay can be calculated as,

Sales tax = Sales price x 0.0825

Sales tax = 65.49 x 0.0825

Sales tax = 5.402925

Approximately to two decimal places, the sales tax becomes $5.40

Answer:

[tex]x = 5.625[/tex]

Step-by-step explanation:

Step 1:  Make an expression

[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]

Step 2:  Cross Multiply

[tex]\frac{3}{4} = \frac{x}{7.5}[/tex]

[tex]4 * x = 7.5 * 3[/tex]

[tex]4x = 22.5[/tex]

Step 3:  Divide both sides by 4

[tex]4x / 4 = 22.5 / 4[/tex]

[tex]x = 5.625[/tex]

Answer:  [tex]x = 5.625[/tex]

Answer:

The original price was reduced 35%

Step-by-step explanation:

we know that

Jeans are reduced from $28.00 to $18.20

In this problem

The original price of 28.00 represent 100%

so

using proportion

Find out what percentage represent the difference between the original price and the new price

[tex]\frac{28}{100}=\frac{28-18.20}{x}\\\\x=100(9.8)/28\\\\x=35\%[/tex]

therefore

The original price was reduced 35%

Answer:

3 > x

Step-by-step explanation:

0>3x-3-6

Combine like terms

0>3x-9

Add 9 to each side

0+9>3x-9+9

9 > 3x

Divide each side by 3

9/3 > 3x/3

3 > x

62.5%...? Taking division into account, the number between 61 and 64 is 62.5 (dont trust me)

Answer:

The answer is B

Step-by-step explanation:

I just took the test got a 100 on it and that is the right answer

Answer: it is b

Step-by-step explanation:

i just took the test on this and i 100 on it

Answer:

Sales amount = $ 300.08

Step-by-step explanation:

Sale amount = selling price + sales tax

Here selling price = $300

sales tax = 8 %

sale amount = 300 + 8%

          = 300 + 8/100

           =( 300 ×100 + 8 )÷100

         = (30000 + 8 ) ÷ 100

          = 30008 ÷ 100

           =$ 300.08

Sales amount = $ 300.08

Answer:

I think   D but not to sure