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3 years ago

Given:

Mathematics

1 answer:

Fynjy0 [20]3 years ago

5 0

Answer:

Option B is correct.

$\triangle RST \cong \triangle TUR$

Step-by-step explanation:

Given: RSTU is a parallelogram.

By definition of parallelogram, two pairs of opposite sides are congruent in length.

⇒ $TU \cong RS$ and $TS \cong RU$

In triangle RST and triangle TUR

$RS \cong TU$ [Side]

$TS \cong RU$ [Side]

$RT \cong RT$ [Common side]

SSS(Side-Side-Side) postulates states that if three sides of one triangle are congruent to three sides of other triangle, then the triangles are congruent.

then, by SSS postulates we have;

$\triangle RST \cong \triangle TUR$

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For questions 1-2 identify the zeros of the function

Ipatiy [6.2K]

Answer:

Step-by-step explanation:

The zeros of a function are where it crosses the x axis, so just find the coordinates for the x intercepts.

$(2,0)$ and $(-1,0)$

$(3,0)$ and $(-3,0)$

8 0

3 years ago

John took all his money from his savings account. He spent $110 on a radio and 4/11 of what was left on presents for his friend

svp [43]

Answer:

$1210

Step-by-step explanation:

Let x be total amount

First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with

$\frac{7}{11}(x-110)=\frac{7}{11}x-70$

Then he put 2/5 of his remaining money into a checking account

$\frac{3}{5}\left(\frac{7}{11}x-70\right)$

Rest he donated to charity

$420=\frac{3}{5}\left(\frac{7}{11}x-70\right)\\\Rightarrow \left(\frac{7}{11}x-70\right)=\frac{2100}{3}\\\Rightarrow \frac{7}{11}x-70=700\\\Rightarrow \frac{7}{11}x=770\\\Rightarrow x=1210$

Hence total amount of money John originally had was $1210

8 0

3 years ago

Im really confused can somebody explain this?

vovikov84 [41]

Given:

The given ratio is $16 : 12$

We need to determine three ratios that are equivalent to the given ratio.

Option A: $8:6$

The given ratio is $16 : 12$

Let us divide the given ratio $16 : 12$ by 2.

Thus, we have;

$8:6$

Hence, the expression $8:6$ is equivalent to $16 : 12$

Thus, Option A is the correct answer.

Option B: $32:24$

The number 32 goes by 16 in 2 times and the number 24 goes by 12 in 2 times.

Thus, multiplying the ratio $16 : 12$ by 2, we get;

$32:24$

Thus, the expression $32:24$ is equivalent to $16 : 12$

Hence, Option B is the correct answer.

Option C: $4:3$

Let us divide the given ratio $16 : 12$ by 4.

Thus, we have;

$4:3$

Thus, the expression $4:3$ is equivalent to $16 : 12$

Hence, Option C is the correct answer.

Option D: $12:8$

The number 12 goes by 16 in $\frac{3}{4}$ times and the number 8 goes by 12 in $\frac{2}{3}$ times.

The ratios are multiplied by different numbers.

Thus, the expression $12:8$ is not equivalent to $16 : 12$

Hence, Option D is not the correct answer.

Option E: $24:16$

The number 24 goes by 16 in 1.5 times and the number 16 goes by 12 in 0.75 times.

The ratios are multiplied by different numbers.

Thus, the expression $24:16$ is not equivalent to $16 : 12$

Hence, Option E is not the correct answer.

Therefore, the equivalent ratios are Option A, B and C

5 0

3 years ago

What is the value of x, the acid concentration of the first solution?

bezimeni [28]

Answer:

A) 0.05

Step-by-step explanation:

Let's summarize into an equation the information we can get from that table.

We have 4 liters of an acid of an unknown concentration, let's call it (4x).

We have 10 liters of an acid with known concentration of 0.40.

And we have a total of 14 liters overall with a concentration of 0.3o.

That's like a weighted average formula: 4x + 10 y = 14z

Let's replace the concentration values we know and solve this:

4x + 10 (0.4) = 14 * 0.3

4x + 4 = 4.2

4x = 0.2

x = 0.05

So, the concentration of the 4 liters of acid on concentration X are in fact of concentration of 0.05.

6 0

3 years ago

Read 2 more answers

Maria is draining her hot tub at a rate of 5.5 gallons per minute. Is the amount of water left in the pool a function of the amo

AleksandrR [38]

The amount of water in the pool after t minutes is modeled by the linear function $V(t) = V(0) - 5t$ , hence it is a function of time.

A linear function for the amount of water in the pool, considering that it is drained at a rate of a gallons per minute, is modeled by:

$V(t) = V(0) - at$

In which V(0) is the initial volume.

In this problem, draining her hot tub at a rate of 5.5 gallons per minute, hence $a = 5.5$ , and:

$V(t) = V(0) = 5.5t$

Which is a function of time.

To learn more about linear functions, you can take a look at brainly.com/question/13488309

8 0

2 years ago