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2 years ago

Marco and Elaine are building a stand like the one shown to display trophies.

Mathematics

2 answers:

rodikova [14]2 years ago

7 0

Answer:

68 square feet is the total surface area of the stand.

Step-by-step explanation:

Since both the parts of the stand are in the shape of prism.

Therefore surface area of the stand = surface area of horizontal prism + surface area of vertical prism

Since the formula of surface area of prism = 2(lw + lh + hw)

where l = length, w = width, h = height

Now for horizontal prism

l = 7 ft. , w = 1 ft. , h = 2 ft

Therefore area of horizontal prism = 2(7×1 + 7×2 + 2×1) = 2×23 = 46 square feet

Now dimensions of the vertical prism

l = 3 ft. , w = 2 ft. , h = 1 ft.

and area = 2(3×2 + 3×1 + 1×2) = 2(11) = 22 square feet.

Now the area of whole structure will be = 46 + 22 = 68 square feet.

zloy xaker [14]2 years ago

5 0

The surface area is basically the sum of all the exposed area of the figure given in the pictures. Since all sides are rectangular, the area can be calculated through the equation,
Area = length x width
The total surface area of the figure is 58 ft².

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a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers; b) A series is divergent if it is not convergent. A convergent series is a series for which lim n → ∞ an exists.

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A sequence is a pattern; it is an ordered list of numbers. A series, however, is the sum of a sequence.

A convergent series is a series for which the sequence of its partial sums tends to a limit; this means the limit exists. A divergent series is a series that is not convergent.

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2 years ago

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JulsSmile [24]

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2 years ago

Unit 7 polygons & quadrilaterals homework 3: rectangles Gina Wilson answer key

Irina-Kira [14]

Answer:

In the image attached you can find the Unit 7 homework.

We need to findt he missing measures of each figure.

Notice that the first figure is a rectangle, which means opposite sides are congruent so,

VY = 19

WX = 19

YX = 31

VW = 31

To find the diagonals we need to use Pythagorean's Theorem, where the diagonals are hypothenuses.

$VX^{2}=19^{2}+31^{2}\\ VX=\sqrt{361+961}=\sqrt{1322} \\VX \approx 36.36$

Also, $YW \approx 36.36$ , beacuse rectangles have congruent diagonals, which intercect equally.

That means, $ZX = \frac{VX}{2} \approx \frac{36.36}{2}\approx 18.18$

Figure number two is also a rectangle.

If GH = 14, that means diagonal GE = 28, because diagonals intersect in equal parts.

Now, GF = 11, because rectangles have opposite sides congruent.

DF = 28, because in a reactangle, diagonals are congruent.

HF = 14, because its half of a diagonal.

To find side DG, we need to use Pythagorean's Theorem, where GE is hypothenuse

$GE ^{2}=11^{2}+DG^{2}\\28^{2}-11^{2}=DG^{2}\\DG=\sqrt{784-121}=\sqrt{663}\\ DG \approx 25.75$

This figure is also a rectangle, which means all four interior angles are right, that is, equal to 90°, which means angle 11 and the 59° angle are complementary, so

$\angle 11 +59\°=90\°\\\angle 11=90\°-59\°\\\angle 11=31\°$

Now, angles 11 and 4 are alternate interior angles which are congruent, because a rectangle has opposite congruent and parallel sides.

$\angle 4 = 31\°$

Which means $\angle 3 = 59\°$ , beacuse it's the complement for angle 4.

Now, $\angle 6 = 59\°$ , because it's a base angle of a isosceles triangle. Remember that in a rectangle, diagonals are congruent, and they intersect equally, which creates isosceles triangles.

$\angle 9=180-59-59=62$ , by interior angles theorem.

$\angle 8 =62$ , by vertical angles theorem.

$\angle 10 = 180- \angle 9=180-62=118\°$ , by supplementary angles.

$\angle 7 = 118\°$ , by vertical angles theorem.

$\angle 5=90-59=31$ , by complementary angles.

$\angle 2 = \angle 5 = 31\°$ , by alternate interior angles.

$\angle 1 = 59\°$ , by complementary angles.

$m\angle BCD=90\°$ , because it's one of the four interior angles of a rectangle, which by deifnition are equal to 90°.

$m\angle ABD = 6\° = m\angle BDC$ , by alternate interior angles and by given. $m\angle CBE=90-6=84$ , by complementary angles.

$m\angle ADE=90-6=84$ , by complementary angles.

$m\angle AEB=180-6-6=168\°$ , by interior angles theorem.

$m\angle DEA=180-168=12$ , by supplementary angles.

$m\angle JMK=180-126=54$ , by supplementary angles.

$m\angle JKH=\frac{180-54}{2}=\frac{126}{2}=63$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle HLK=90\°$ , by definition of rectangle.

$m\angle HJL=\frac{180-126}{2}=27$ , by interior angles theorem, and by isosceles triangle theorem.

$m\angle LHK=90-27=63$ , by complementary angles.

$m\angle = JLK= m\angle HJL=27$ , by alternate interior angles.

The figure is a rectangle, which means its opposite sides are equal, so

$WZ=XY\\7x-6=3x+14\\7x-3x=14+6\\4x=20\\x=\frac{20}{4}\\ x=5$

Then, we replace this value in the expression of side WZ

$WZ=7x-6=7(5)-6=35-6=29$

Therefore, side WZ is 29 units long.

We know that the diagonals of a rectangle are congruent, so

$SQ=PR\\11x-26=5x+28\\11x-5x=28+26\\6x=54\\x=\frac{54}{6}\\ x=9$

Then,

$PR=5x+28=5(9)+28=45+28=73$

Therefore, side PR is 73 units long.

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2 years ago

A business buys invoice forms at a cost of $4.45 a box for the first 20 boxes, $4.00 a box for the next 25 boxes, and $3.75 a bo

Sergio039 [100]

So the first 20 boxes at 4.45 a piece will total 89.
The next 25 at 4 each will be 100.
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45/3.75 = 12 .
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2 years ago

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Leto [7]

Answer:

Step-by-step explanation:

The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.

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(1/2) ÷ (1/4) = (1/2) × (4/1) = 2

That doesn’t help you answer this particular question, though.

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1 year ago