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anzhelika [568]

2 years ago

13

the sides of a triangle, in centimetres,are x,2x-3 and 2x+5. The perimeter of the triangle is 57 cm.a)write down an equation for

x. b)work out the lengths of three sides of the triangle

2 answers:

soldier1979 [14.2K]2 years ago

6 0

Answer:

11 cm, 19 cm, 27 cm

Step-by-step explanation:

Triangles have 3 sides and perimeter is the sum of all side lengths. So the equation is x + (2x-3) + (2x+5) = 57.

x + (2x-3) + (2x+5) = 57

x + 2x - 3 + 2x + 5 = 57

x + 2x + 2x - 3 + 5 = 57

5x + 2 = 57

5x = 57 -2

5x = 55

x = 11

Now that we know the value of x, we can figure out the side lengths. The first side (x) is 11 cm long, the second side (2x - 3) is 19 cm, and the third side (2x + 5) is 27 cm long.

Agata [3.3K]2 years ago

6 0

<u>Answer with step by step explanation</u>

The perimeter of a triangle is the sum of the sides.

There fore,

<h3>a) x + 2x - 3 + 2x + 5 = 57</h3>

Now, let us solve the above equation and find the value of x.

Let us solve.

x + 2x - 3 + 2x + 5 = 57

Combine like terms.

5x -3 + 5 = 57

5x + 2 = 57

5x = 57 - 2

5x = 55

Divide both sides by 5.

x = 11

And now they've asked us to write the lengths of three sides.

Let us write now.

<h3>b) x = <u>11 cm</u></h3><h3> ( 2x - 3 ) ⇒ ( 2 × 11 - 3 ) ⇒ ( 22 - 3 ) ⇒ <u>19 cm</u></h3><h3>( 2x + 5 ) ⇒ ( 2 × 11 + 5 ) ⇒ ( 22 + 5 ) ⇒ <u>27 cm</u></h3>

Let me know if you have any other questions. :)

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Advocard [28]

Answer: (-2, -2)

Step-by-step explanation:

Reflection over the x-axis: (x, y) → (x, -y)

(-2, 2) → (-2, -2)

x would remain the same but the y would turn negative since we're reflecting over the x-axis. The x never changes in this situation but since we're flipping it over the x-axis, they y has to be negative.

Hope this helps!

8 0

3 years ago

In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A

Marina86 [1]

Answer:

(a) 0.94

(b) 0.20

(c) 90.53%

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let $p_1$ be the probability that a bearing meets the specification.

So, $p_1=0.9$

Sample size, $n_1=500$ , is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: $\mu_1=n_1p_1=500\times0.9=450$

Variance: $\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45$

$\Rightarrow \sigma_1 =\sqrt{45}=6.71$

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, $X\geq 440.$

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56$ .

So, the probability that a given shipment is acceptable is

$P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062$

Hence, the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by $p_2$ .

$p_2=0.94$

The total number of shipment, i.e sample size, $n_2= 300$

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, $\mu_2$ , and variance, $\sigma_2^2$ .

Mean: $\mu_2=n_2p_2=300\times0.94=282$

Variance: $\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92$

$\Rightarrow \sigma_2=\sqrt(16.92}=4.11$ .

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

$z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85$ .

So, the probability that a given shipment is acceptable is

$P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977$

Hence, the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, $\alpha$ be the required probability of acceptance of one shipment.

So,

$-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}$

On solving

$\alpha= 0.977896$

Again, the probability of acceptance of one shipment, $\alpha$ , depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let $p$ be the probability that one bearing meets the specification. So

$-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}$

On solving

$p=0.9053$

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

8 0

3 years ago

A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area (A=lw), how long is the rectangl

Lynna [10]

----------------------------------------------------------------------------------------
Formula
----------------------------------------------------------------------------------------
Area of rectangle = Length x Width

----------------------------------------------------------------------------------------
Find Length
----------------------------------------------------------------------------------------
357 = Length x 17

----------------------------------------------------------------------------------------
Divide by 17 through
----------------------------------------------------------------------------------------
Length = 357 ÷ 7
Length = 51 inches

----------------------------------------------------------------------------------------
Answer: The length of the rectangle is 51 inches
----------------------------------------------------------------------------------------

7 0

3 years ago

A 32 foot tall tree casts a shadow that is 48 feet long. How far away from the tree is a

sveticcg [70]

Answer:

39 feet

Step-by-step explanation:

take the tree as AB , the distance between the man and the tree as BC, the distance between the man and the tip of the shadow CD and the point intersecting the hypotenuse CE

since CE parallel to AB we can BPT

CE/AB = CD/BD

6/32= CD/48

CD = 9 feet

since CD is feet

BC is 48-9 = 39 feet

3 0

2 years ago

In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while

I am Lyosha [343]

Answer:

See Below.

Step-by-step explanation:

We are given that:

$\angle ABC \cong \angle DEC\text{ and } \angle GFE \cong \angle DCE$

By vertical angles:

$\displaystyle \angle DEC\cong \angle GEF\text{ and } \angle DCE\cong \angle ACB$

Hence, by substitution:

$\displaystyle \angle ABC\cong \angle GEF\text{ and } \angle GFE\cong \angle ACB$

Then by Angle-Angle Similarity:

$\Delta ABC \sim \Delta GEF$

8 0

3 years ago