Determine which equations below, when combined with the equation 3x-4y=2, will form a system with no solutions. Choose all that apply.
A) 2y = 1.5x - 2
B) 2y = 1.5x - 1
C) 3x + 4y = 2
D) -4y + 3x = -2

Answer:

A. [tex]f(x) = (x-12)^2[/tex]

Step-by-step explanation:

The parent function [tex]f(x) = x^2[/tex] can be shifted 12 units to the right by moving its vertex 12 units to the right. The parent function has a vertex at (0,0) since [tex]f(0) = 0^2=0[/tex]. It will shift to (12,0) so [tex]f(12) =(12-a)^2=0[/tex]. The only value of a which will make it 0 is 12. So the equation is [tex]f(x) = (x-12)^2[/tex]

Answer: -5

Step-by-step explanation:

The slope of a line passing through (a,b) and (c,d) is given by :-

[tex]\text{Slope}=\dfrac{d-b}{c-a}[/tex]

Then the slope of the line AB contains points A (3, −2) and B (1, 8) will be :-

[tex]\text{Slope}=\dfrac{8-(-2)}{1-(3)}\\\\\Rightarrow\text{Slope}=\dfrac{10}{-2}-5[/tex]

Hence, the slope of the line AB contains points A (3, −2) and B (1, 8) = -5

Answer:

To prove the Converse of Pythagorean Theorem:

Step-by-step explanation:

1. Draw a right triangle (Triangle ABC)

2. Draw an altitude from and A to the hypotenuse creating 2 new triangles

3. The part that intersects the hypotenuse will be point D, this makes a right angle

Triangle DBA and triangle ABC both have right angles and share angle B, this means that triangle ABC and triangle DBA are congruent by the AA postulate. Since triangle DAC and triangle ABC both have right angles(angle D and angle A) and they share angle C, triangle DAC and ABC are congruent by the AA postulate as well.

The ratios can be set up as:

AC/BC = DC/AC & AB/BC = DB/BA

Once cross multiplied, the result should be:

(AC)² = (BC)(DC) & (AB)² = (BC)(DB)

Now add both sides together to get:

(AC)² + (AB)² = BC(DC) + (BC)(DB)

To make things easier, factor out the like terms:

(AC)² + (AB)² = BC(DC + DB)

When looking at the triangle(must draw to see), it shows that (DC + DB) is actually side BC. This leaves:

(AC)² + (AB)² = BC(BC) → (AC)² + (AB)² = (BC)²

The Pythagorean theorem says that a² + b² = c². Knowing this, on the original triangle, side AB = a, side AC = b, and side BC = c. Knowing this:

(AC)² + (AB)² = (BC)² → a² + b² = c²

This proves the Converse of the Pythagorean Theorem.

Angela is Saving $12 on the dress.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Original Price of Dress = $60

Discount = 20% off

So, the Price of Dress after discount

= 60-  20% of 60

= 60- 12

= $48

Hence, Angela saving $12.

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Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

[tex]2x>-10---------------------------(1)[/tex]

and

[tex]3x<24------------------------------(2)[/tex]

From eq(1), we have

[tex]\dfrac{2x}{2}>\dfrac{-10}{2}\\\\x>-5[/tex]

From eq(2), we have

[tex]3x<24\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8[/tex]

So, compound inequality becomes

[tex]-5<x<8[/tex]

Hence, Third option is correct.

The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/tex].

Further explanation:

Triangles are congruent when all the corresponding sides and interior angles are equal.

There are four theorems by which we say that the triangles are congruent.

1. Side-Side-Side(SSS)

If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.

2. Angle-Side-Angle(ASA)

If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.

3. Side-Angle-Side(SAS)

If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.

4. Hypotenuse Leg (HL)

If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.

Option (a)

The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.

Both the figures don’t have a single property from the above mentioned properties.

Therefore, option (a) is incorrect.

Option (b)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA.

Thus, option (b) is incorrect.

Option (c)

The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by SAS rule not by ASA rule.

Thus, option (c) is incorrect.

Option (d)

The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.

Both have the same property.

Therefore, the triangles are congruent by ASA rule.

Thus, option (d) is correct.

Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Angles and Triangles

Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.

The pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.

Recall:

The Angle-Side-Angle Congruent Theorem (ASA) states that two triangles are considered congruent if they have two corresponding angles that are congruent and an included side that are congruent to each other.

The included side is the side that is lie between the two congruent angles in each of the triangles.

Thus, form the pairs of angles given, the pair in option d has two corresponding angles and an included side that are congruent to each other in each triangle.

Therefore, the pair of triangles that are congruent by the Angle-Side-Angle Congruent Theorem (ASA) are the pairs that have two corresponding angles and an included side that are congruent to each other which is: Option D.

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The largest size of the square that can be embroidered within the 6 inch hoop is 4.2 inches per side (rounded to the nearest tenth). This is found using geometry principles involving squares and circles.

This question is asking for the side length of a square that will fit within a circle, or in this case, an embroidery hoop, with a certain diameter. This is a concept from geometry that involves the relationship between squares and circles. Essentially, the diameter of the circle becomes the diagonal of the square.

To calculate the side length (x) of the square, we'll use the formula for the diagonal (d) of a square divided by the square root of 2 (d = √2 * x). Since the diameter of the hoop is 6 inches, rearranging the equation gives us x = d / √2 which results in x = 6 / √2 = 4.2 inches (rounded to the nearest tenth)

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The equation x² - 2x - 8 = 0 has two real and distinct roots.

A quadratic equation is an equation of the form ax² + bx + c = 0. In this equation, the coefficient of the x² term is 1, so a = 1, b = -2, and c = -8. We can determine the nature of the roots without solving the equation by looking at the discriminant, which is the term inside the square root of the quadratic formula. The discriminant is given by b² - 4ac. If the discriminant is positive, the equation has two real and distinct roots. If the discriminant is zero, the equation has two real and identical roots. If the discriminant is negative, the equation has two complex roots.

In this case, we have b = -2 and a = 1, so the discriminant is (-2)² - 4(1)(-8) = 4 + 32 = 36. Since the discriminant is positive, the equation has two real and distinct roots.

10 out of 40 said pizza =

divide 10 by 40 = 0.25

0.25 = 25% said pizza

Answer:

b. Jared will get the better deal buying one 32 ounce bottle.

Step-by-step explanation:

Answer:

there's actually 900000

Step-by-step explanation:

lets do the same thing for a smaller number to show where the previous solution went wrong if you take the interval between 255 and 0 (this is the size of one part of an ipv4 we know there is 256 bits because you have the digits 1 to 255 which makes up 255 bits and then if you ad the 0 (lower limit of the interval) you get 256-- the same principle applies here if you just do 999999-100000 you are not counting the lower limit and you are counting the upper limit which is wrong because between may be ambiguous so that it can mean including or excluding the upper and lower limit but it cannot exclude one and include the other thus making the answer 900000 including its limits and 899998 excluding them