Which number is a solution of the inequality 8 – 14b ≥ 27?

Mathematics

2 answers:

Katarina [22]3 years ago

6 0

Answer:

2d + 3 ≤ –11

Step-by-step explanation:

Tamiku [17]3 years ago

4 0

8 - 14b equal to or greater than 27

__________________________________

b equal to or greater than -1.1875

So, the answer must be bigger, or equal to, -1.1875. 140 is the only number that fits this description.

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In the figure shown, r || s. If the measure of ∠ 2 = 146°, what is the measure of ∠ 7

borishaifa [10]

Answer:

34°

Step-by-step explanation:

1. First, let's find the measure of ∠1 because since r || s, that means ∠1 = ∠7 because they're both alternate exterior angles. Alternate exterior angles are congruent.

2. (Solving for ∠1)

$146 + x = 180$
$146 + x - 146 = 180 - 146$
$x = 34$

3. Now, since we know ∠1 = ∠7, ∠7 = 34°.

3 0

2 years ago

ABCD is a rectangle. The measure of angle BCE is 4x-23 and the angle measure of angle DCE is 5+5x. Find the measure of angle BEC

Temka [501]

<h2>Explanation:</h2><h2></h2>

The diagram for this problem is shown below. Point E is the intersection of the two diagonals and we know that:

$\angle BCE=\beta \\ \\ \angle DCE=\theta$

Every internal angle of any rectangle measures 90 degrees, so:

$\beta +\alpha=90 \\ \\ (4x-23)+(5+5x)=90 \\ \\ \\ Isolating \ x: \\ \\ (4x+5x)+(5-23)=90 \\ \\ 9x-18=90 \\ \\ 9x=108 \\ \\ x=\frac{108}{9}=12$

So:

$\beta=4x-23=4(12)-23=25^{\circ}$

So the measure of angle BEC can be found as follows:

We know that triangle ΔCEB is an isosceles triangle because the diagonals of any rectangle measure the same. So

$\angle EBC=\beta$

The sum of internal angles of any triangle add up to 180 degrees, so:

$\beta + \beta+\angle BEC=180^{\circ} \\ \\ 2\beta+\angle BEC=180^{\circ} \\ \\ \angle BEC=180^{\circ}-2\beta \\ \\ \angle BEC=180^{\circ}-2(25^{\circ}) \\ \\ \angle BEC=180^{\circ}-50^{\circ} \\ \\ \boxed{\angle BEC=130^{\circ}}}$