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Papessa [141]
4 years ago
15

Find all real numbers t such that (2/3)t - 1 < t + 7 ≤ -2t + 15. Give your answer as an interval.

Mathematics
1 answer:
Andrews [41]4 years ago
8 0
Break up chain with AND statement:

(2/3)t - 1 < t + 7 AND <span>t + 7 ≤ -2t + 15

left side, we solve for t
</span>
<span>(2/3)t - 1 < t + 7
(2/3)t - t < 7 + 1
(-1/3)t < 8
t > -24

right side, we solve for t</span>
<span>t + 7 ≤ -2t + 15
t + 2t </span><span>≤ 15 - 7
3t </span><span>≤ 8
t </span><span>≤ 8/3

So our answer would be </span>
t > -24 AND t <span>≤ 8/3

as an interval, this is
</span>-24 < t <span>≤ 8/3
or in interval notation
(-24, 8/3]</span>
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PLZ HELP! ASAP!!! I WILL GIVE BRAINLIEST
Ira Lisetskai [31]

Answer:

see explanation

Step-by-step explanation:

Using cross- products, that is

\frac{a}{b} = \frac{c}{d} then ad = bc

Given the ratios

\frac{4}{14} and \frac{6}{21}

Then equating and using cross- products

If both sides equate then the ratios are equivalent

\frac{4}{14} = \frac{6}{21}, then

4 × 21 = 6 × 14 ⇒ 84 = 84

Both sides are equal thus the ratios are equivalent

8 0
3 years ago
A tin has asquare base whose sides measures 32 cm .the vertical sides are 50cm high.cake mixture is poured into the tin and leve
zepelin [54]

Answer:

(a) V = 51200 cubic cm

(b) V' = 38912 cubic cm

(c) V'' = V - V' = 12288 cubic cm

Step-by-step explanation:

side of the square base, s = 32 cm

height, h = 50 cm

height of cake mixture, h' = 38 cm

(a) The capacity of the tin is the volume.  

Capacity of tin, V =  s x s x h = 32 x 32 x 50 = 51200 cubic cm

(b) The volume of the cake mixture is

V' =  s x s x h'

V' = 32 x 32 x 38 = 38912 cubic cm

(c) Volume of unoccupied space is

V'' = V - V' = 51200 - 38912 = 12288 cubic cm

6 0
3 years ago
A right triangle has legs measuring 6 and 7 inches. What is the length of the hypotenuse?
Alchen [17]

Answer:

5

Step-by-step explanation:

8 0
3 years ago
Consider this right triangle.<br> 21<br> 29<br> 20<br> Enter the ratio equivalent to s
AleksAgata [21]

Answer:

Part 1) sin(B)=\frac{21}{29}

Part 2) csc(A)=\frac{29}{20}

Part 3) cot(A)=\frac{21}{20}

Step-by-step explanation:

<u><em>The complete question is</em></u>

Consider this right triangle. 21 29 20 Write the ratio equivalent to: Sin B - CscA- Cot B

The picture of the question in the attached figure

Part 1) Write the ratio equivalent to: Sin B

we know that

In the right triangle ABC

sin(B)=\frac{AC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(B)=\frac{21}{29}

Part 2) Write the ratio equivalent to: Csc A

we know that

In the right triangle ABC

csc(A)=\frac{1}{sin(A)}

sin(A)=\frac{BC}{AB} -----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(A)=\frac{20}{29}

therefore

csc(A)=\frac{29}{20}

Part 3) Write the ratio equivalent to: Cot A

we know that

In the right triangle ABC

cot(A)=\frac{1}{tan(A)}

tan(A)=\frac{BC}{AC} -----> by TOA (opposite side divided by the adjacent side)

substitute the values

tan(A)=\frac{20}{21}

therefore

cot(A)=\frac{21}{20}

4 0
3 years ago
Can a triangle have two obtuse angles? please Justify your answer.
Scrat [10]

Answer:

No, a triangle cannot have 2 obtuse angles. The definition of an obtuse angle is an angle with a measure that is greater than 90°.

Step-by-step explanation:

8 0
3 years ago
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