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3 years ago

5) In the figure, triangle ABC is a right triangle at B. If CD = 15, find BC to the nearest tenth.

Mathematics

1 answer:

ycow [4]3 years ago

6 0

Answer:

BC ≈ 4.0

Step-by-step explanation:

∠ DCA = 180° - 70° = 110° ( adjacent angles )

∠ DAC = 180° - (30 + 110)° ← sum of angles in triangle

∠ DAC = 180° - 140° = 40°

Using the Sine rule in Δ ACD to find common side AC

$\frac{AC}{sin30}$ = $\frac{15}{sin40}$ ( cross- multiply )

AC × sin40° = 15 × sin30° ( divide both sides by sin40° )

AC = $\frac{15sin30}{sin40}$ ≈ 11.668

Using the cosine ratio in right triangle ABC

cos70° = $\frac{adjacent}{hypotenuse}$ = $\frac{BC}{AC}$ = $\frac{BC}{11.668}$ ( multiply both sides by 11.668 )

11.668 × cos70° = BC , then

BC ≈ 4.0 ( to the nearest tenth )

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Write an equation of the line, in standard form, containing the points (−6, 19) and (−15, 28).

Rudiy27

The equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13

Recall:

Equation of a line can be written in standard from as Ax + By = C, where Ax and By are all terms of variable x and y, and C is a constant.

The equation of a line in point-slope, $y - y_1 = m(x - x_1)$ , can be rewritten in the standard form.

Slope (m) = $\frac{y_2 - y_1}{x_2 - x_1}$

Given: (−6, 19) and (−15, 28)

Find the slope (m):

$m = \frac{28 - 19}{-15 -(-6)} = \frac{9}{-9} = -1$

Write the equation in point-slope form by substituting m = -1 and $(x_1, y_1) = (-6, 19)$ into $y - y_1 = m(x - x_1)$ .

$y - 19 = -1(x - (-6))\\\\y - 19 = -1(x + 6)$

Rewrite in standard form

$y - 19 = -1(x + 6)\\\\y - 19 = -x - 6\\\\y = -x - 6 + 19\\\\y = -x + 13\\\\\mathbf{x + y = 13}$

Therefore, the equation of the line that contains (−6, 19) and (−15, 28), in standard form, is: x + y = 13

Learn more about equation of a line in standard form on:

brainly.com/question/19169731

7 0

2 years ago

Find the measure of angle x in the figure below: A.) 65° B.) 70° C.) 110° D.) 125°

Grace [21]

Answer: 70ᴼ

Step-by-step explanation:

The triangles are vertical so their angle measures are congruent.

The angles of a triangle add to equal 180ᴼ.

55 + 55 = 110

180 - 110 = 70

7 0

3 years ago

The mark up on an item is $3.75. If the mark up is 35%, what was the original price? Round

oksian1 [2.3K]

Answer:

$10.71

Step-by-step explanation:

$\frac{3.75}{y} =\frac{35}{100}$

y × 35 = 3.75 × 100

35y = 375

35y ÷ 35 = 375 ÷ 35

$y=10\frac{5}{7}$

y = 10.7142857143

10.7142857143 round to 10.71

5 0

3 years ago

Which expressions do you get when you eliminate the negative exponents of .........

kvasek [131]

Answer:

D. 4(a^2)(a^3)/16(b)(b^2)

Step-by-step explanation:

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3 years ago

A coffee company wants to make sure that their coffee is being served at the right temperature. If it is too hot, the customers

Cerrena [4.2K]

Answer:

Null hypothesis: $\mu = 65$

Alternative hypothesis: $\mu \neq 65$

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

For this case the value of $\mu$ represent the parameter associated to the population (True average of cofee temperature)

Step-by-step explanation:

Data given and notation

$\bar X=70.2$ represent the mean height for the sample

$s$ represent the sample standard deviation for the sample

$n=20$ sample size

$\mu_o =765$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean i equal to 70.2, the system of hypothesis would be:

Null hypothesis: $\mu = 65$

Alternative hypothesis: $\mu \neq 65$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

For this case the value of $\mu$ represent the parameter associated to the population (True average of cofee temperature)

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3 years ago