Emma needs to find the surface area of a triangular pyramid where the base and all three faces are congruent equilateral triangles.
What is the total surface area?

Answer:

  50°

Step-by-step explanation:

As usual, the diagram is not drawn to scale.

The chord divides the circle into two arcs that have a sum of 360°. If we let "a" represent the measure of the smaller arc, then we have ...

  a + (a+160°) = 360°

  2a = 200° . . . . . . . . . . . subtract 160°

  a = 100°

The measure of the angle at A is 1/2 the measure of the subtended arc:

  acute ∠A = a/2 = (1/2)·100° = 50°

_____

Comment on this geometry

Consider a different inscribed angle, one with vertex V on the circle and subtending the same short arc subtended by chord AB. Then you know that the angle at V is half the measure of arc AB. This is still true as point V approaches (and becomes) point A on the circle. When V becomes A, segment VA becomes tangent line l, and you have the geometry shown here.

Answer:

Equation:  (1 2/3)(2 1/3) = x

Answer:  3 8/9 cups

Step-by-step explanation:

x represents the amount of flour she will need in cups.

To solve, convert the mixed numbers to improper fractions and multiply...

1 2/3 becomes 5/3

2 1/3 becomes 7/3

Now we have

(5/3)(7/3) = x

  35/9 = x

35/9 is 3 8/9 as a mixed number

An equation that represents the number of cups of flour Genise will need​ is (1 2/3 ) × (2 1/3) which gives the value 3 8/9 cups.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Number of cups of flour needed to make 1 batch of cookies = 1 2/3 cups

                                                                                                    = 5/3 cups

We have to calculate the number of cups of flour for 2 1/3 batches.

Number of cups of flour needed to make 2 1/3 batches of cookies is,

(5/3) × (2 1/3)

= (5/3) × (7/3)

= (35/9)

= 3 8/9

Hence the number of cups of flour needed is 3 8/9 cups.

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Answer:

the interest rate is $183.89 =~ $ 184

Step-by-step explanation:

In this question, Antuan deposited $2590 into a 3 year CD (Certificate of Deposit)  at an interest rate of 2.3% compounded quarterly. We need to find the interest account earned after 3 years.

Formula used will be :

[tex] Interest = P ( 1 + r/n) ^ n ^ t - P[/tex]

Where

P= Principal amount

r= interest rate (in decimals)

n= no of times the interest is compounded

t = no of years

Here we are subtracting P because we only need interest amount and not the future value.

Using this formula and finding the value will be:

P= $2590

r = 2.3 % or 0.023

n = 4

t = 3

[tex]Interest = 2590 * ( 1 - 0.023 / 4) ^ 4^ * ^ 3 - 2590[/tex]

[tex]Interest= 2590 (1.071) -2590\\Interest= 2773.89 - 2590\\Interest= 183.89[/tex]

So the interest rate is $183.89 =~ $ 184

Answer:

Step-by-step explanation:

The difference between double the first purchase and the second purchase is $7 and 2 pounds of jelly beans. Hence a pound of jelly beans is $3.50.

  (4t +8j) -2(2t +3j) = (33) -2(13) . . . . . let t and j represent pounds of trail mix and jelly beans, respectively

  2j = 7 . . . . . . . . . . simplify

  j = 7/2 = 3.50

Using that value in the first purchase, we get ...

  2t +3(3.50) = 13

  2t = 13 -10.50

  t = 2.50/2 = 1.25

A pound of trail mix is $1.25.

Answer: 1,340 :)

Step-by-step explanation:

44*13= 572

96*8=768

572+768=1,340

Final answer:

The expression to calculate the total number of beads Lola used to make 13 bracelets and 8 necklaces is 13 × 44 + 8 × 96, with the total being 1340 beads.

Explanation:

To calculate the total number of beads Lola used to make 13 bracelets and 8 necklaces, we need to consider the number of beads used for one bracelet and one necklace individually. For one bracelet, Lola uses 44 beads, and for one necklace, she uses 96 beads.

Now, we add the two quantities together to get the total number of beads used:

572 beads (for bracelets) + 768 beads (for necklaces) = 1340 beads

Therefore, the expression to calculate the total number of beads used is 13 × 44 + 8 × 96.

Answer:

  [550, 1250] miles ([minimum, maximum] miles)

  700 miles (difference between minimum and maximum)

Step-by-step explanation:

"Range" has different meanings in different contexts with respect to a list of numbers and/or ordered pairs.

For a function, characterized by ordered pairs, the range is often specified by the interval between the minimum and the maximum. That is, the range of the function ...

  (Jan, 914), (Feb, 740), (Mar, 815), (Apr, 550), (May, 815), (Jun, 1250), (Jul, 740)

can be specified either as the list of dependent variable values:

  {550, 740, 815, 914, 1250}

or as the interval between the minimum and the maximum:

  [550, 1250]

___

If you're plotting these values or creating a histogram, the "range" you're interested in is often the difference between the minimum and maximum:

  1250 -550 = 700

The widths of bins of a histogram are defined by dividing this range into a suitable number of smaller intervals.

Answer:

-3x^2 -6x -7

Step-by-step explanation:

See the attachment for the synthetic division. Of course, polynomial long division will give the same result. Make sure you deal with the signs and the powers of x properly.

Answer:

the exterior angles of a polygon sum to 360

so the number of sides is 360/45

-PlushDna

Answer:

The difference in number of sides from one park to the next is 7

Step-by-step explanation:

For all polygon's the exterior angles combine to measure to 360 degrees. So to find the number of sides of each gazebo, we simply divide 360 by the measure of each individual exterior angle. We'll start with Logan Park.

360/22.5 = 16 sides

Now we can do the same with Cerro Park.

360/15.65 = 23 sides

Therefore, the difference in sides would be 7

23 - 16 = 7

Answer:

V =64 cm^3

Step-by-step explanation:

The volume of a cube is given by

V =s^3

We know the side length is s=4

V =4^3

V =64 cm^3

V = 64 cm ^ 3

V = s 3   x

s = 4

V = 4 ^ 3

V = 64 cm x  3

Answer:

  y ≈ 240.3 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between an angle and the sides adjacent and opposite is ...

  Tan = Opposite/Adjacent

In this triangle, the interior angle at lower right is the same as the one marked at upper left: 31°. y is the side opposite that angle, and 400 ft is the side adjacent. Then the relation is ...

  tan(31°) = y/(400 ft)

Multiplying by 400 ft gives ...

  y = (400 ft)·tan(31°) ≈ 240.3 ft

_____

The triangle interior angle at lower right and the angle marked 31° are "alternate interior angles" relative to the transversal marked x and the (parallel) horizontal lines in the figure. Alternate interior angles always have the same measure.

In geometry problems like this one, it means the angle of elevation (above the horizontal) is equal to the angle of depression (below the horizontal).

(x + 3) divided by 2

third option

Answer:

(x + 3) divided by 2

third optionStep-by-step explanation:

The answer is C. His gross pay is $974.00.

Answer:

Step-by-step explanation:

Weekly Salary = 844 dollars.

Commision Rate = 4% = 0.04

Last week Sales = 3250 dollars.

Last week commission on sales = 0.04 x 3250 = 130 dollars.

Gross pay = Weekly Salary + Commission amount.

Gross pay = 844 + 130 = 974 dollars.

Hence, option C is correct i.e. 974.00 dollars.

Answer:

Parallel line = Same m value (same slope)

Perpendicular line = The reciprocal m value (x/y = y/x).

Going through a point = First, find the slope of the line (perpendicular or parallel), then plug in the point (4,10) to find the y intercept.

Answer:

See below.

Step-by-step explanation:

Parallel

y = -1/2x + b

The slope is the same for any set of parallel lines. The point determines the y intercept.

x = 4

y = 10

Solve for b

10 = -1/2(4) + b

10 = - 2 + b

b = 10 + 2

b = 12

Equation: y = - 1/2 x + 12

Perpendicular

Here you actually have to solve for the slope.

Equation

m1 * m2 = - 1

m1 is the given slope of - 1/2 which I will chance to -0.5. Substitute for m1.

-0.5 * m2 = - 1                          Divide by -0.5

m2 = -1/-0.5

m2 = 2

Now what you have is

y = 2x + b

x = 4

y = 10

10 = 2*4 + b

10 = 8 + b

10 - 8 = b

b = 2

Equation: y = 2x + 2

Answer:

  length: 10 ft; width: 7 ft.

Step-by-step explanation:

Factorizations of 70 are ...

  70 = 1·70 = 2·35 = 5·14 = 7·10

The last pair of numbers has the relation that 2·7 -10 = 4, so the numbers 7 and 10 can be used for width and length.

The length is 10 ft; the width is 7 ft.

Answer:

Step-by-step explanation:

The graph a.) is the best draw that represents a line with positive rate of change.

Best regards

Answer:

1.85 gallons

Step-by-step explanation:

1 gallon = 3.785 liters

(7 liters)/(3.785 liters/gallon) = 1.85 gallons

Answer:

1.8492

Step-by-step explanation:

for an approximate result, divide the volume value by 3.785

Answer:

  A.) 0.9cm, 1.2cm, 1.5cm

Step-by-step explanation:

The side ratios of the offered answers are ...

  A — 3:4:5 . . . . . . obviously a right triangle

  B — 3:5:5 . . . . . . isosceles, but not a right triangle

  C — 3:4:6 . . . . . . an obtuse triangle

  D — 3:2:5 . . . . . . not even a triangle (just a line segment)

_____

Comment on 3:4:5

This set of small integers appears often in problems involving right triangles. It is the smallest "Pythagorean triple" — a set of integers that satisfies the relationship of the Pythagorean theorem — and it is the only Pythagorean triple that is an arithmetic sequence (differences between the numbers are the same).

When you see a triangle with sides in these ratios, you know it is a right triangle. When you see a right triangle with two of the sides having a ratio of 3:4, 3:5, or 4:5 (where "5" is the hypotenuse), then you know the length of the remaining side.

Answer:

1,080 Pennies

Step-by-step explanation:

This question is fairly simple, you just have to simplify it. You are starting at already half-full, so you can keep that 1/2 in mind. Then, she adds 360 pennies to get 5/6. If you convert 1/2 into 3/6, you can see that 360 pennies fills 2/6 of the piggy bank. So now you can solve two different ways. The first, you can take 360 and multiply it by 3 to get the amount that can fit in the piggy bank, because 2 * 3 = 6 and that would make it 6/6, or 1. The other way would be to divide 360 by 2 to get 1/6 of the piggy bank, or 180. Then you can multiply 180 by 6 to get the entire amount.

Hope this helped ^-^

By setting up a proportion, we can find that the total capacity of Amy's penny bank is 1440 pennies.

The subject of this problem is mathematics. We know that after adding 360 pennies, Amy's penny bank was 5/6 full. Before she added those pennies, it was 1/2 full. So, those 360 pennies represent the difference between 5/6 and 1/2 of the capacity of the penny bank.

To find the total capacity of the penny bank, we can set up a proportion as follows:

360 pennies / (5/6 - 1/2) = x pennies / 1

Therefore, x = 360 * (1 / (5/6 - 1/2))

By simplifying this, we find that the total capacity of Amy's penny bank is 1440 pennies.

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Answer:

51°

Step-by-step explanation:

The sum of all exterior angles of any polygon is always 360°.

To find the measure of one of these angles, divide 360° by the number of sides of the polygon

In this case, we have 7 sides, so

m = 360°/7 = 51.42°, or 51° rounded to the nearest degree

Answer:

for ape x its 51

Step-by-step explanation:

Answer:

either of Step 3 or Step 4

Step-by-step explanation:

At Step 3, -1 is added to both sides of the equation. Technically, this is correct (not an error), but it does not lead to a solution to the equation (so, could be considered to be an error). Adding +1 to both sides of the equation would lead more directly to a solution.

__

At Step 4, x -1 -1 is simplified to x. This is an error, as the correct simplification is x-2, so the equation after this step should read x-2 = 5. If Step 3 had been executed by adding +1 to both sides of the equation, then the simplification here would be x=7.

_____

Answering "why" someone does something is always tricky. One can project one's own interpretation onto the actions of others, but one never really knows whether that is accurate or not.

The "why" in this case could go back to the motivation of the problem's author, which may be to see if the student can recognize that the opposite of -1 is +1, or that the sum -1-1 is not zero.

___

My guess is that Step 3 is considered to be the erroneous step, and that choosing Step 4 will get you into a losing argument with your grader.

Answer:

The value of 55th term a₅₅  = 161

Step-by-step explanation:

It is given that,

aₙ = −1 + 3(n − 1)

To find 55th term

To find the 55th term we have to substitute 55 instead of n in the expression of an.

aₙ = −1 + 3(n − 1)

a₅₅ = −1 + 3(n − 1) = -1 + 3( 55 - 1)

  = -1 + 3 * 54 = -1 + 162

  = 161

Therefore the value of 55th term a₅₅  = 161

Answer:

2.  22/35

3a. 0.24

3b. 0.84

3c. 0.54

3d. 0.73

Step-by-step explanation:

2. There are 22 songs on albums 1 and 2, and 35 total songs. Thus the probability of randomly choosing a song from albums 1 or 2 is 22/35.

__

3. The sum of the probabilities of all possible mutually exclusive events is 1, so ...

a. p(blue) = 1 - p(any other color) = 1 - 0.76 = 0.24

b. p(not green) = 1 - p(green) = 1 - 0.16 = 0.84

c. p(green+yellow+blue) = p(green) +p(yellow) +p(blue) = 0.16 +0.14 +0.24 = 0.54

d. p(not(yellow+red)) = 1 - p(yellow+red) = 1 - 0.27 = 0.73

Answer:

46 packages

Step-by-step explanation:

2 7/8= 23/8= 46/16...THUS SINCE SHE IS MAKING 1/16 POUND PACKAGES, SHE CAN MAKE 46 PACKAGES

Answer:

a = 102.05

b = 393.76

B = 93°

Step-by-step explanation:

The law of sines tells you ...

a/sin(A) = b/sin(B) = c/sin(C)

Since the sum of angles in a triangle is 180°, angle B must be ...

B = 180° -72° -15° = 93°

and the unknown sides must be ...

a = c/sin(C)·sin(A) = 375·sin(15°)/sin(72°) ≈ 102.05192

B = 93°

b = 375·sin(93°)/sin(72°) ≈ 393.75796

_____

The rounding requirement got cut out of your picture, so we can't help you with that.

The distance from the center of the circle at (-1,2) to the point (2,-2) is 5 units and he did not calculate the distance correctly

The distance of a line between 2 points is always positive and given by the formula

Let the first point be A ( x₁ , y₁ ) and the second point be B ( x₂ , y₂ )

The distance between A and B is D , and the distance D is

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Given data ,

Let the first point be P = P ( -1 , 2 )

Let the second point be Q = Q ( 2 , -2 )

To find the distance from the center of the circle at (-1,2) to the point (2,-2), we can use the distance formula:

Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²

Distance D = √[(2 - (-1))² + (-2 - 2)²]

Distance D = √[3² + (-4)²]

D = √[9 + 16]

D = √25 = 5 units

Therefore, the point (2,-2) does lie on the circle.

However, Amit's work does not account for the fact that the center of the circle is not at the origin, but rather at (-1,2). This means that the distance from (-1,2) to (2,-2) must be used to determine if the point is on the circle, not the radius of the circle.

No, he should have used the center of the circle at (-1,2) to calculate the distance.

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Answer:

• 2/3|2 -x| = 1/15

• |2 -x| = 1/10

• 1/5 +|4/3 -2/3x| = 4/15

Step-by-step explanation:

Starting with the given equation, subtract 1/5 = 3/15.

(2/3)|2 -x| = 4/15 - 3/15

(2/3)|2 -x| = 1/15 . . . . . . . . matches the first choice

Now, multiply by 3/2.

|2 -x| = 3/30

|2 -x| = 1/10 . . . . . . . . . . . . matches the third choice

___

If you decide to distribute the coefficient 2/3 instead, you have

1/5 + |2·2/3 -x·2/3| = 4/15

1/5 + |4/3 -2/3x| = 4/15 . . . . matches the selected choice

Answer:

The answer is A and C

Step-by-step explanation:

I just did the work

Good luck

Answer:

D p^2 +3p -10

Step-by-step explanation:

(p+5) (p-2)

FOIL

First  p*p = p^2

Outer  -2*p = -2p

Inner  5*p = 5p

Last  -2 *5= -10

Add them together

p^2 -2p+5p -10

p^2 +3p -10

Answer:

Their answer is correct.

Step-by-step explanation:

Answer:

1. g

2. a

3. d

4. b

Step-by-step explanation:

If you can't do these in you head or on a graph, you can always let your calculator do it.

When adding vectors put the tail of one at the nose of the other. When subtracting, add the opposite. When adding or subtracting a multiple, just do the repeated addition or subtraction.