What number must you add to complete the square? x2 + 4x = 15 A. 16 B. 4 C. 2 D. 8

Mathematics

1 answer:

Scilla [17]2 years ago

8 0

B. 4 because 4/2=2, 2 squared is 4

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WILL MARK BRAINLIEST!

Artist 52 [7]

Answer:

Following are the responses to the given points:

Step-by-step explanation:

Dilation implies the triangle $\Delta XYZ$ stretched through the factor "2".

$m\angle Y = m\angle C = 90^{\circ} \leftarrow given \\\\$

right triangles:

$\Delta XYZ and \Delta ACB \\\\\angle X \cong \angle A \leftarrow given\\\\$

complementary angles:

$\angle X \ and\ \angle Z$

$m\angle Z = 90^{\circ} - m\angle X \\\\$

complementary angles:

$\angle A \ and\ \angle B$

$m\angle B = 90^{\circ} - m\angle A \\\\\therefore \\\\ \angle Z \cong \angle B \\\\\Delta XYZ \sim \Delta ACB \\\\$

Same triangles: proportional side are corresponding, congruence angles are respective.

$\sin \angle X = \frac{5}{5.59} \leftarrow given \\\\\sin\angle X = \frac{YZ}{XY} \\\\YZ = 5 (units) \rightarrow leg in \Delta XYZ \\\\XZ = 5.59 (units) \rightarrow hypotenuse \ in\ \Delta XYZ\\\\$

Calculating the length of leg XY:

$XY = \sqrt{((5.59)^2 - 52)} \cong 2.4996 (units)\\\\\frac{CB}{YZ} = 2 \leftarrow given \\\\CD = 2YZ = 2 \times 5 = 10 \ (units)\\\\\frac{AC}{XY} = 2 \leftarrow \ given\\\\AC = 2XY \cong 2 \times 2.4996 \cong 4.999\ (units)\\\\$

3 0

2 years ago

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32,

miskamm [114]

The mean deviation of the ratings is 4.12

Explanation

The ratings of the ten experts are: 34, 35, 41, 28, 26, 29, 32, 36, 38 and 40

So, the mean of all ratings $=\frac{34+35+41+28+26+29+32+36+38+40}{10}= \frac{339}{10}=33.9$

The formula for Mean deviation $= \sum \frac{|x_{i}- \mu|}{N}$ , where $x_{i}$ is the given data from $i=1$ to $i=10$ , $\mu$ is the mean of the data and $N$ is the total number of data. So.....

$|x_{1}-\mu |= |34-33.9|=0.1\\ |x_{2}-\mu|=|35-33.9|=1.1\\ |x_{3}-\mu |=|41-33.9|=7.1\\ |x_{4}-\mu |=|28-33.9|=5.9\\ |x_{5}-\mu |=|26-33.9|=7.9\\ |x_{6}-\mu |=|29-33.9|=4.9\\|x_{7}-\mu |=|32-33.9|=1.9\\ |x_{8}-\mu |=|36-33.9|=2.1\\ |x_{9}-\mu |=|38-33.9|=4.1\\ |x_{10}-\mu |=|40-33.9|=6.1$