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5 days ago

What additional information could you use to show that ΔSTU ≅ ΔVTU using SAS? Check all that apply.

Mathematics

2 answers:

zzz [12.3K]5 days ago

6 0

I think the correct solutions are: UV = 14 ft and m∠TUV = 45°; ST = 20 ft, UV = 14 ft, and m∠UST = 98°. In other words, Options A and D.

AnnZ [12.3K]5 days ago

6 0

The initial and fourth pieces of information can serve as supplemental details to demonstrate that ΔSTU ≅ ΔVTU using SAS. To explain, in ΔSTU and ΔVTU, we have SU=14ft, VT=20 ft, m∠SUT=45°, and m∠TUV=98°. The additional information provided is: 1. UV = 14 ft and m∠TUV = 45°, thus SU=UV = 14 ft [given], and m∠TUV = m∠SUT = 45° [given]. The length TU is the same in both triangles due to the Reflexive property, resulting in ΔSTU ≅ ΔVTU via the SAS congruence postulate. 2. TU = 26 ft, which does not provide sufficient information to establish triangle congruence. 3. m∠STU = 37° and m∠VTU = 37°, meaning we also need additional data to confirm their congruency. 4. ST = 20 ft, UV = 14 ft, and m∠UST = 98° leads to ST = 20 ft=TV [given], and the reflexive property shows TU=TU, thus establishing ΔSTU ≅ ΔVTU under the SAS postulate. 5. m∠UST = 98° alongside m∠TUV = 45° also supports ΔSTU ≅ ΔVTU through the AAS congruence theorem. Therefore, the first and fourth pieces of information can indeed serve to demonstrate that ΔSTU ≅ ΔVTU using SAS.

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Which property does each equation demonstrate? x2 + 2x = 2x + x2 (3z4 + 2z3) – (2z4 + z3) = z4 + z3 (2x2 + 7x) + (2y2 + 6y) = (2

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1. Closure

2. Distributive

3. Closure

Detailed explanation:

In this scenario, we are examining the properties that each equation demonstrates.

The first equation shows the closure property.

This indicates that whether we add in one direction or the other, the result remains unchanged. Therefore, we conclude that addition conforms to the closure property in this case.

The third equation also shows the closure property. Regardless of how we approach the addition for this equation, the outcome remains consistent.

The second equation displays the distributive property.

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Mindy, a local artist, sells a piece of art at the pizza shop for $15, and the shop takes 15 percent commission. Instead of rece

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To tackle this problem, we first need to ascertain the commission taken by the pizza shop and how much money belongs to Mindy. We know that Mindy sells her artwork for $15, and the pizza shop retains a 15% commission. Therefore, the commission is calculated as (15/100) * 15, which equals 2.25 dollars. This means the pizza shop deducts $2.25 from each art sale made by Mindy. Consequently, the amount Mindy receives is (15 - 2.25), resulting in $12.75. Since Mindy opts not for cash but instead chooses a pizza valued at $12, including a 5% sales tax, it seems she benefits by $0.75 plus the pizza worth $12. Therefore, this arrangement appears fair for Mindy. Meanwhile, the pizza shop also makes an additional $2.25 from this transaction, making it equitable for both Mindy and the shop owner.

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The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1. On a coordinate plane, a parabola, labeled f of x, opens up. I

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Answer:

The correct option is:

On the coordinate plane, there is a parabola that opens upwards, passing through the points (2, 10), having its vertex at (5, 1), and intersecting (8, 10).

Step-by-step explanation:

Initially, we must understand the translation rules

1) {f(x) + a} signifies f(x) moved up by (a) units

2) {f(x) – a} means f(x) moved down by (a) units

3) {f(x + a)} represents f(x) moved left by (a) units.

4) {f(x – a)} indicates f(x) moved right by (a) units.

Given information:

f(x) = x²

g(x) = (x-5)² + 1

By comparing the transformation from f(x) to g(x) with the translation rules

It can be concluded that g(x) represents f(x) through a translation of 5 units to the right and 1 unit upwards (rules 1 and 4)

Refer to the attached image, which illustrates the graphs of both f(x) and g(x)

As depicted, g(x) intersects (2, 10), has a vertex at (5, 1), and crosses through (8, 10)

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For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second

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Let’s define x as the amount invested by Sam in the first year.
Here are the corresponding expressions derived from the provided descriptions for Sam's investments.

For Sam:
2nd year: investment = 5x/2 - 2000
3rd year: investment = x/5 + 1000

The total Sam invested is:
x + (5x/2 - 2000) + (x/5 + 1000)

Next, we can form the expressions for Sally’s investments.
For Sally
1st year: investment = 3x/2 - 1000
2nd year: investment = 2x - 1500
3rd year: investment = x/4 + 1400

Thus, Sally's total investment is,
total = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Setting both totals equal gives us:
(x) + (5x/2 - 2000) + (x/5 + 1000) = (3x/2 - 1000) + (2x - 1500) + (x/4 + 1400)

Solving for x,
x = 2000
For Sally's investment for the third year:
investment = x/4 + 1400 = (2000/4 + 1400) = 1900

RESULTS:
Sam's first year = $2000
Sally's third year = $1900

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