The side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.
The length of the side of the square and the height will be
6.98 cm and 13.96 cm.
What is a Pyramid ?
Pyramid is a three dimensional Structure ,having square , rectangle , hexagonal base , the faces for a square pyramid and hexagonal pyramid are triangle meeting at one point .
It is given in the question that
A toy is being constructed in the shape of a pyramid.
the maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters.
the height of the toy is double the side length
Let us assume the side length to be x
and therefore the height of the toy is 2x
The surface area of the toy is given = 250 sq.cm
First let us consider for a square base
The surface area of a square pyramid is given by
[tex]\rm A = a^2 + 2 a\sqrt {\dfrac{a^2}{4}+h^2}[/tex]
Here a is the side length which x for us and h = 2x
[tex]\rm 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+(2x)^2}\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{x^2}{4}+4x^2}\\\\\\ 250 = x^2 + 2 x\sqrt {\dfrac{17 x^2}{4}}\\\\\\250 = x^2 + x^2 \sqrt{17}\\\\\\250 = 5.132 x^2\\\\\\48.71 = x^2\\\\\\x = 6.98 cm .[/tex]
Therefore the length of the side of the square and the height will be
6.98 cm and 13.96 cm.
For a hexagonal base
The total surface area is given by
[tex]A =6ah + 3 \sqrt{3}a^2\\\\\\A = 6 \times x \times 2x + 3\sqrt{3} (x)^2\\\\250= 12x^2 + 3\sqrt{3} x^2\\\\\\250 = 17.196 x^2\\\\\\14.54 = x^2\\\\x = 3.81 cm\\\\[/tex]
Therefore the side of the hexagonal pyramid will be 3.81 cm and the height of the toy will be 7.62 cm.
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Enter the solution (x, y) to the system of equations shown.
Answer:
(2, 5 )
Step-by-step explanation:
y = 2x + 1 → (1)
3y = 4x + 7 → (2)
substitute y = 2x + 1 into (2)
3(2x + 1) = 4x + 7 ← distribute parenthesis on left side
6x + 3 = 4x + 7 ( subtract 4x from both sides )
2x + 3 = 7 ( subtract 3 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
substitute x = 2 into (1) for corresponding value of y
y = 2(2) + 1 = 4 + 1 = 5
solution is (2, 5 )
Solve: (6 • 6 + (-3)) ÷ 11
please
Answer:
The correct answer is 3.
Step-by-step explanation:
I'm assuming you need this now so I won't explain it.
Hope this helps:) Goodluck!
What is the value of x in this figure?
O x= 30
O x = 40
O x = 60
O I don't know.
Answer:
i guess you know its 40 now. :p
Step-by-step explanation:
The marked price of a fan is Rs. 1800. If a shopkeeper allows a discount of 10% and still makes a profit of 20%, at what price had the shopkeeper bought the fan?
The shopkeeper had brought the fan at Rs.1350
Billy has been on a diet for
22
weeks. He has averaged a loss of
0.73
pounds each week.
How many total pounds has Billy lost?
Answer:
16.06 lbs
Step-by-step explanation:
I believe, I did~ 0.73x22
In ΔJKL, j = 10 in., k = 7 in., and l = 6.58 in. Find m∠J.
A. 38º
B. 95º
C. 44º
D. 25º
Answer:
B. 95°
Step-by-step explanation:
Given the three sides of a triangle, the Law of Cosines can be used to find any of the angles.
__
j² = k² +l² -2kl·cos(J) . . . . . law of cosines applied to this triangle
J = arccos((k² +l² -k²)/(2kl)) . . . . . solve for angle J
J = arccos((7² +6.58² -10²)/(2·7·6.58)) = arccos(-7.7036/92.12)
J ≈ 94.797° ≈ 95°
The measure of angle J is about 95°.
_____
Additional comment
Angle J is opposite side j, which is the longest side. That means angle J is the largest angle in the triangle. The largest angle of the triangle can never be less than 60°. Only one answer choice qualifies. (No computation is necessary.)
For the quadratic equation 3x^2-18x-21=0, x1 and x2 are the roots. Find:
x1^2+x2^2
|x1-x2|
(x_1+x_2)=-b/a=18/3=6
x_1x_2=c/a=-21/3=-7
So
(x_1+x_2)²-2x_1x_2=x_1^2+x2²x1²+x2²=(6)²-2(-7)=36+14=50(x_1-x_2)²
x1²+x2²-2x_1x250+1464x_1-x_2=8
Answer:
[tex]x{_1}^2+x{_2}^2=50[/tex]
[tex]|x_1-x_2|=8[/tex]
Step-by-step explanation:
Given equation:
[tex]3x^2-18x-21=0[/tex]
Factor to find the roots:
[tex]\implies 3(x^2-6x-7)=0[/tex]
[tex]\implies x^2-6x-7=0[/tex]
[tex]\implies x^2+x-7x-7=0[/tex]
[tex]\implies x(x+1)-7(x+1)=0[/tex]
[tex]\implies (x-7)(x+1)=0[/tex]
Therefore:
[tex]\implies (x-7)=0 \implies x=7[/tex]
[tex]\implies (x+1)=0 \implies x=-1[/tex]
Therefore, the roots of the quadratic equation are:
[tex]x = 7,\quad x = -1[/tex]
Let [tex]x_1 = 7[/tex]
Let [tex]x_2 = -1[/tex]
[tex]\implies x{_1}^2+x{_2}^2=7^2+(-1)^2=50[/tex]
[tex]\implies |x_1-x_2|=|7-(-1)|=8[/tex]
How do I find the difference -6 - (-9)
Pls explain how I can do negatives and positives numbers
Answer:
Step-by-step explanation:
-6 - (-9)
1) Remove parentheses
-6 + 9
2) Simplify
3
See attachted image for rules of positive and negative integers.
Source: YourDictionary
pls give the steps as well
Answer:
-6.4
Step-by-step explanation:
√2(√3×2 - √1×8) = -6.41472901342
Round to the nearest tenth = -6.4
Please help, it’s due tomorrow
Answer:
The largest interger that satisfies the equation is 3
Step-by-step explanation:
If we subtract 10 from each side, we get 7x<=21
Then, we divide 7 on each side to get x<=3.
So the largest interger to satisfy the equation is 3
(Btw, <= means less than or equal to)
Hope this helped you, and have a great day!
Answer:
x<=3
Step-by-step explanation:
minus 10 fom both sides
7x + 10-10<=31-10
restate as
7x<=21
divid both side by same factor
7x/7 and 21/7
restate as
x<=3
Please help thanks!!!!!!
Answer:
See below ~
Step-by-step explanation:
Subpart (e) :
⇒ New volume = 2 x 3 x 2 x 4 x 2 x 5
⇒ New volume = 8 x 60
⇒ New volume = 480 in³
=============================================================
Subpart (f) :
⇒ New volume : Original volume
⇒ 480 : 60
⇒ 1 : 8
=============================================================
Subpart (g) :
Step 1
⇒ SA = 2(6 × 9 + 9 × 11 + 6 × 11)
⇒ SA = 2(54 + 99 + 66)
⇒ SA = 2(219)
⇒ SA = 438 in²
Step 2
⇒ V = 6 × 9 × 11
⇒ V = 54 × 11
⇒ V = 594 in³
Step 3
⇒ New SA = 2 x 438
⇒ New SA = 876 in²
Step 4
⇒ New : Original
⇒ 876 : 438
⇒ 2 : 1
Step 5
⇒ New V = 2³ x 594
⇒ New V = 8 × 594
⇒ New V = 4752 in³
Step 6
⇒ New : Original
⇒ 4752 : 594
⇒ 8 : 1
What is the value of log4 superscript 16?
1
2
4
8
answer ASAP
PPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLEASE Help
Answer:
4cm
Step-by-step explanation:
sin(30) = 2/x (using trigonometry)
rearrange for x to give x = 2/sin(30)
then x = 4cm (using calculator)
SIMILARLY:
You can use 2/cos(60) to also give 4cm
How many days were less than 84°?
Answer:
it has to be 7 days because the other degrees are higher than 84.
Step-by-step explanation:
80 - 82 = 7 days
Reciprocal of 1/y where y not equals to 0
Answer:
y (y/1)
Step-by-step explanation:
the reciprocal of a number is basically what it needs to multiply to to equal to one
so basically you flip the numbers
1/y s reciprocal would be y/1 which is also just y
Answer: y
Step-by-step explanation:
In a pet store there are a total of 25 animals 15 of the animals are dogs term is the ratio of animals that are not dogs to the total animals in the store explain the reasoning
for your answer
Answer:
25.15
Step-by-step explanation:
the 25 comes before the 18 in the sentence. super easy
Determine the following probabilites based on a standard deck of cards
1) Pblack or heart)=
2) Pired or 10) =
3) P(Q or 6) =
4) P(5 or club) =
5) P(picture card or 4) =
6) P(black 9 or red) =
There are 52 cards total.
Hearts and diamonds are red.
Clubs and spades are black
LQ and K are called picture cards.
Answer & Step-by-step explanations:
I assume they want probability as a decimal as opposed to a fraction. I will do two questions for you, apply the same logic to all the rest.
P(Black or heart):
There are 26 black cards in a deck, and 13 (red) hearts.
26 + 13 out of 52 cards.
39 / 52 as a decimal is 0.75
P(Black or heart) = 0.75 or 75%
If wanted as a fraction, simplify your fraction down
39/52 has a common factor of 13, divide both numbers by 13
P(Black or heart) = 3/4
P(Red or 10):
There are 26 red cards and four 10's in a deck. Two of these 10's are red, so we will not double count them.
26 + 2 out of 52 cards.
28 / 52 as a decimal is about 0.54 or 54%
P(Red or 10) = 0.54 or 54%
If wanted as a fraction, simplify your fraction down
28/52 has a common factor of 4, divide both numbers by 4
P(Red or 10) = 7/13
PLS HELP I WILL GIVE BRAINIEST If triangle BCD were rotated over the y-axis from point (0, 0), what would be the coordinates of the new triangle's vertices?
A. (0, -1) , (-4, -3), (-2, -1)
B. (-1, 0), (-5, -2), (-3, 4)
C. (1, 0), (5, 2), (3, 0)
D. (1, 0), (1, -2), (-3, -4)
The coordinates of the new triangle's vertices are (0, -1), (-4, -3), and
(-2, -1). Hence option A is true.
Used the rule of a point (x, y) when rotated over the y-axis of 90° clockwise rotation from point (0, 0),
(x, y) → (y, - x)
Given that the triangle BCD is shown in the image.
Here, the coordinates of the vertices of BCD are,
B = (1, 0)
C = (3, - 4)
D = (1, - 2)
Now apply the rotation rule, the coordinates of the new triangle's vertices are;
B' = (0, - 1)
C' = (- 4, - 3)
D' = (- 2, - 1)
Therefore, the option A is true.
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Alicia found $1.90 on the beach. Her brother found three times as much money. How much money did Alicia and her brother find in total? $5.70 $7.60 $9.60 $11.40
Answer:
$7.60
Step-by-step explanation:
If you multiply 19.0 by 4 then you get $7.60
HELP!!!
Jay borrows $8,000 at a rate of 1.9% interest per year. What is the amount due at the end of 6 years if the interest is compounded continuously?
I'm confused.
$8,966.02 is your answer
Identify the equations of ellipses whose major axis lengths are twice their minor axis lengths.
The equations of ellipses whose major axis lengths are twice their minor axis lengths are
(x - h)²/4b² + (y - k)²/b² = 1 and (x - h)²/b² + (y - k)²/4b² = 1To answer the question, we need to know what an ellipse is.
What is an ellipse?An ellipse is part of a conic section.
The equation of the ellipseThe equation of an ellipse centered at (h,k) with major axis on the x-axis and major axis length, 2a and minor axis length 2b is
(x - h)²/a² + (y - k)²/b = 1
The equation of ellipse with major axis x-axis
The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the x-axis. Since the major axis is twice the length of the minor axis, a = 2b.
So, (x - h)²/a² + (y - k)²/b² = 1
(x - h)²/(2b)² + (y - k)²/b² = 1
(x - h)²/4b² + (y - k)²/b² = 1
The equation of ellipse with major axis y-axis
The equations of ellipses whose major axis lengths are twice their minor axis lengths with ellipse centered at (h,k) with major axis on the y-axis. Since the major axis is twice the length of the minor axis, a = 2b.
So, (x - h)²/b² + (y - k)²/a² = 1
(x - h)²/b² + (y - k)²/(2b)² = 1
(x - h)²/b² + (y - k)²/4b² = 1
So, the equations of ellipses whose major axis lengths are twice their minor axis lengths are
(x - h)²/4b² + (y - k)²/b² = 1 and (x - h)²/b² + (y - k)²/4b² = 1Learn more about ellipse here:
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Question 1 GIVING BRAINLIESTT!!!!!!!!
Give the MOST specific name for the figure shown. A) parallelogram B) quadrilateral C) rhombus Eliminate D) trapezoid
Answer: C
Step-by-step explanation:
Because there are two pairs of opposite parallel sides, it is a parallelogram.
Since the diagonals intersect at a right angle, the parallelogram is also a rhombus.
HELP ME PLEASEEEEE
Answer:
x = 4
Step-by-step explanation:
x(x + 8) = 48
x² + 8x = 48
x² + 8x - 48 = 0
times into -48
add into 8
(x - 4)(x + 12) = 0
x - 4 = 0
x = 4
or
x + 12 = 0
x = -12
A length cannot be a negative number therefore x = 4
The coordinates of the vertices of are E (-4, 5), F (-1, 1), and G (3, 4). Determine whether EFG is a right triangle and support your decision. Show all work.
Answer:
No, it will not be a right triangle
Step-by-step explanation:
Since E (-4, 5) and F (-1, 1) are both in-plane one and G (3, 4) in-plane two
The x's are wrong for E and F which would be a cause for not a right triangle
And the y for G is not either 5 or 1 which would help make the triangle a right triangle.
So the triangle ends up being an scalene triangle and not a right triangle
Hopes this helps :)
A triangle has sides with lengths of 30 millimeters, 40 millimeters, and 48 millimeters. Is it a
right triangle?
yes
no
Answer:
No, because a right angle must not have the least 90°/. degrees c
For function f(x), which pair of limits would verify the existence of a vertical asymptote at x = –1?
This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:
[tex]\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)[/tex]
Limit of a functionFor the limit of a function to be continuous at a point x = a, the left hand limit of the function must be equal to the right hand limit.
Mathematically, the expression below must be true
[tex]\lim_{x \to a^+} a_n = \lim_{x \to a^-} a_n =f(c)[/tex]
This shows that for the function f(x), the pair of limits that would verify the existence of a vertical asymptote at x = –1 is expressed as:
[tex]\lim_{x \to -1^+} a_n = \lim_{x \to -1^-} a_n =f(c)[/tex]
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express 5x - 2y - 12 = 0 in y=mx + b form and state the slope and y-intercept
Answer:
Step-by-step explanation:
5x-2y-12=0
5x-2y+12-12=0+12
5x-2y=12
5x-5x-2y=12-5x
-2y=12-5x
(-2y)/-2=(12-5x)/-2
y=5/2x-6
slope= 5/2x up 5 over 2
y-intercept is -6
Keisha collects vintage glass marbles. Her favorite marbles have a diameter of 2.5 centimeters each. She keeps 66 of her favorite marbles in a pouch. One cubic centimeter of glass has a mass of 2.6 grams. What is the mass of the marbles in Keisha’s pouch rounded to the nearest gram? Use 3.14 for π
Answer:
Im pretty sure the guy above me is right
Step-by-step explanation:
if 110% of a number is 528, then the number is:
a) 475.2
b) 52.8
c) 480
d) 580.8
e) 475
Answer:
c) 480
Step-by-step explanation:
Any percentage can be converted to a number ratio by dividing by 100%.
E.g. 100%/100% = 1
Following this concept, we can find the equivalent of 110% :
110%/100% = 1.1
Since 528 is 1.1 times the number we are looking for, we just need to divide 528 by 1.1 to find our number. This is because 1.1/1.1 = 1
528/1.1 = 480
Hope this helped!
