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3 years ago

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Mathematics

1 answer:

lidiya [134]3 years ago

6 0

Answer:

$4\frac{3}{8}$ yards of wood

Step-by-step explanation:

The correct question is Hakim is making birdhouses. Each birdhouse uses 7 /8 yard of wood. What is the total length of wood Hakim will need to build 5 birdhouses?

Answer: Given that the amount of wood need to produce one bird house is 7/8 yard, for 5 birdhouse, the amount of wood needed would be 5 times the number needed for one birdhouse. It is given by:

Amount of wood needed for 5 birdhouse = 5 × amount of wood for 1 birdhouse

Amount of wood needed for 5 birdhouse = 5 × 7/8 yards = 35/8 = $4\frac{3}{8}$ yards of wood

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Give statements and reasons

PolarNik [594]

Answer:

A two column proof is presented as follows;

Statement ${}$ Reason

1. AB ║ DE, BD bisects AE ${}$ Given

2. ∠BAE = ∠AED, ∠ABD = ∠BDA ${}$ Alternate ∠s are equal

3. $\overline {AC}$ = $\overline {EC}$ , $\overline {BC}$ = $\overline {CD}$ ${}$ ${}$ By definition of bisection of line AE by BD

4. ΔABC ≅ ΔEDC ${}$ By SAA, rule of congruency

Step-by-step explanation:

Step 1. AB ║ DE, BD bisects AE ${}$ Given

Step 2. ∠BAE , ∠AED, and ∠ABD, ∠BDA ${}$ are pairs of alternate angles formed by the parallel lines, AB and DE and are therefore, equal

Step 3. $\overline {AC}$ = $\overline {EC}$ , $\overline {BC}$ = $\overline {CD}$ The bisection of line gives two lines of equal length. The bisection of AE by BD gives, $\overline {AC}$ and $\overline {EC}$ where $\overline {AC}$ = $\overline {EC}$

Similarly, the bisection of BD by AE gives, $\overline {BC}$ and $\overline {CD}$ , where $\overline {BC}$ = $\overline {CD}$

Step 4. ΔABC ≅ ΔEDC ${}$ By the Side-Angle-Angle (SAA), rule of congruency, which states that two triangles having two angles and the corresponding non included sides of each triangle equal to the other, the two triangles are congruent.

6 0

3 years ago

Solve for the variable x.

inna [77]

Answer:

Step-by-step explanation:

Equating the terms :

x + 3 = 2x - 2

Add 2 on both sides :

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

Subtract x from both sides :

x + 5 - x = 2x - x
<u>x = 5</u>

3 0

2 years ago

The ratio of the cost of a shirt to the cost of a jacket is 2:5. If the jacket cost $240 more than the shirt,

IrinaVladis [17]

Given:

The ratio of the cost of a shirt to the cost of a jacket is 2:5.

The jacket cost $240 more than the shirt.

To find:

The cost of the shirt and the cost of the jacket.

Solution:

Let x be the cost of the shirt.

The jacket cost $240 more than the shirt. So, the cost of Jacket is (x+240).

The ratio of the cost of a shirt to the cost of a jacket is 2:5. So,

$\dfrac{x}{x+240}=\dfrac{2}{5}$

$5x=2(x+240)$

$5x=2x+480$

Subtract 2x from both sides.

$5x-2x=480$

$3x=480$

Divide both sides by 3.

$x=\dfrac{480}{3}$

$x=160$

So, the cost of shirt is $160.

Now, the cost of jacket is:

$160+240=400$

Therefore, the cost of shirt is $160 and the cost of jacket is $400.

6 0

2 years ago

Calculate the coefficient of x4y18 in the expansion of (x − y)22

Oksana_A [137]

Binomial theorem:

$(x-y)^n=\displaystyle\sum_{k=0}^n\binom nkx^k(-y)^{n-k}$

The term with $x^4y^{18}$ corresponds to $n=18+4=22$ and $k=4$ (or $k=18$ , since $\dbinom nk=\dbinom n{n-k}$ ).

So, the coefficient of this term is

$\dbinom{22}4(-1)^{18}=\dbinom{22}4=\dfrac{22!}{4!(22-4)!}=7315$

4 0

3 years ago

I am a little confused: One method you can use to determine whether a triangle is a right triangle, given three side lengths, is

Vsevolod [243]

Trigonometric ratios are sine, cosine, and tangent (opposite side over hypotenuse, adjacent side over hypotenuse, and opposite side over adjacent side, respectively); if you wanted to prove that one of the angles of the triangle is 90º, then the cosine of that angle would be 0, the sine would be 1, and the tangent would be undefined.

7 0

3 years ago

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