Man I gotta get smarter I wish my kindergarten brain was in my 5th grade brain :,(

The values of the unknown angles are ∠1 = 92°, ∠2 = 24°, ∠3 = 64°, ∠4 = 35°, ∠5 = 81°

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal). For example, in the below-given figure, angle p and angle w are the corresponding angles.

∠1 + 88 = 180°( angles on a straight line)

∠1 = 180 - 88 which is 92°

∠3 = 64°( corresponding angles are equal)

∠2 + ∠1 + ∠3 = 180( sum of angles in a triangle)

∠2 + 92° + 64° = 180

∠2 = 180 - 92 - 64

∠2 = 24°

∠4 + 81 + ∠3 = 180 ( angles on a straight line)

∠4 + 81 + 64 = 180

∠4 = 180 - 64 -81

∠4 = 35°

∠5 = 81°( alternate angles are equal)

In conclusion the values of ∠1, ∠2, ∠3, ∠4, ∠5 are 92°, 24°, 64°, 35° and 81° respectively.

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Answer:

\( {b}^{2} - 4ac = 0 \\ { ( - k - 2)}^{2} - 4(1)(4) = 0\\ {k}^{2} + 4k + 4 - 4 = 0 \\ {k}^{2} + 4k = 0 \\ k(k + 4) = 0 \\ \therefore \: k = 0 \: or \: k = - 4\)

The value of x is equal to 8.

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

In the similar triangles, TRS similar to DBC

TS/ SR = DC/ CB

70 / (11x - 4) = 50 / 60

Using cross products

70 (60) = 50 (11x - 4)

Distribute

4200 = 550x - 200

550x = 4200 + 200

550x = 4400

x = 8

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The function is continuous in the domain x ≥ 3/4

Here we have a root function:

f(x) = ⁴√(4x - 3)

This is an even degree root function, so we have problems when the argument is negative.

Then the allowed values (where the function is defined, and thus, continuous) are:

4x - 3 ≥ 0

4x ≥ 3

x ≥ 3/4

There the function is continuous.

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Answer:

×7

Step-by-step explanation:

\(84 \div 12 = 7\)

The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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Answer:

Step-by-step explanation:

multiply length x width times hight

If the cards are placed upside down, this makes the choice made whenever a card is drawn a random probability.

There are 4 different cards in the arrangement and only 1 card with a heart on it.

Therefore, the probability of picking a heart is:

Now the probability of not picking a heart is:

Therefore, the final answer is 3/4

4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.

5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.

In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;

RU ║ ST

Slope of side RU = Slope of side ST

Slope of RU = (y₂ - y₁)/(x₂ - x₁)

Slope of RU = (1 + 3)/(5 + 3)

Slope of RU = 4/8

Slope of RU = 0.5.

Slope of RS = (y₂ - y₁)/(x₂ - x₁)

Slope of RS = (-9 + 3)/(-4 + 3)

Slope of RS = -6/-1

Slope of RS = 6.

Slope of ST = (y₂ - y₁)/(x₂ - x₁)

Slope of ST = (-2 - 1)/(10 - 5)

Slope of ST = -3/5

Slope of ST = -0.6.

Slope of UT = (y₂ - y₁)/(x₂ - x₁)

Slope of UT = (-2 + 9)/(10 + 4)

Slope of UT = 7/14

Slope of UT = 0.5.

Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.

Question 5.

In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance RT = √[(-2 + 3)² + (10 + 3)²]

Distance RT = √170 units.

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance US = √[(5 + 4)² + (1 + 9)²]

Distance US = √181 units.

Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.

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Answer:

h(x)=1/4x

Step-by-step explanation:

function×inverse=-1

4x=-1

Answer:

h(x) = 1/4x

Step-by-step explanation:

y = 4x

x = 4y

1/4 x = y

The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Answer:The First one 65 R2

Step-by-step explanation:

Answer:

2. $2.4

3. $3.6

4. $4.8

5. $6

The expression representing the perimeter of the polygon is given as follows:

7mn³/3 + 4m² + 3mn².

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

Hence the perimeter for the polygon in this problem is given as follows:

mn³(1/3 + 2) + m²(1 + 3) + mn²(1 + 2) = 7mn³/3 + 4m² + 3mn².

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Answer:

(3) 48 meters in 3 seconds

Answer:

12 inches

Step-by-step explanation:

120/10 * 1 = 12 inches

Answer:

12 inches

Step-by-step explanation:

This question is asking for us to find the amount of inches that is represented to the amount of miles given (120 miles). In order to do this, let's divide the amount of miles that we need to find out for inches, over what information we already have. By dividing 120 over 10, that will give us the amount of inches that 120 miles represents. So:

120 miles / 10 miles = 12 inches.

This is true, because fractions are basically like division. As our example shows, 120 ÷ 10 = 12, which is true.

I hope that this helps.

Answer:

27.75₁₀

Step-by-step explanation:

Convert binary 11011.110 to base 10

11011.110 = 1*2^4 + 1*2^3+0*2^2 + 1*2^1 + 1* 2^0 + 1*2^-1 + 1* 2^-2 + 0

11011.110 = 16+8+0+2+1+1/2+1/4

11011.110 =27 + 3/4

11011.110  = 27.75₁₀

Hence the binary number to base 10 is 27.75₁₀

Answer:

the second to last one!!!

Step-by-step explanation:

hope this helps

Answer:

  $1,021,337.13

Step-by-step explanation:

The sum of present values of medical expenses is ...

  30,000/1.05 +30,000(1.0513)/1.05^2 +30,000(1.0513^2)/1.05^3 +...

So, the series has an initial value of 30,000/1.05 and a common ratio of 1.0513/1.05. Its sum is given by ...

  S = a(r^n -1)/(r -1)

where a = 30,000/1.05, n = 35, r = 1.0513/1.05.

Filling in these values and doing the arithmetic, we get ...

  S = $1,021,337.13

You need an initial deposit of $1,021,337.13 to cover rising expenses for 35 years.

Using the combination formula, it is found that:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:

\(C_{28,7} = \frac{28!}{7!21!} = 1,184,040\)

For two defective tablets, the selections are given as follows:

Hence the number of selections is calculated as follows:

\(C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490\)

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The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.

The future values of the savings account are calculated in two installments.

The first installment is for 10 years when the account earns 6% compounded semiannually.

Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.

Future values can be determined using the future value formula or an online finance calculator, as follows:

N (# of periods) = 20 (10 years x 2)

I/Y (Interest per year) = 6%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $3,612.22

Total Interest $1,612.22

N (# of periods) = 32 (8 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)

PMT (Periodic Payment) = $0

Results:

FV = $5,816.85

Total Interest $2,204.63

Thus, the value of the account after 18 years was $5,816.85.

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The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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Answer:

75%

Step-by-step explanation:

The polynomial which is equivalent to fog(x) is 2/x + 1.

A polynomial is a type of expression. An expression is a mathematical statement without an equal-to sign (=).

Here,

given functions are;

f(x) = x + 1   ;     g(x) =  2/x

Now, we need to compose fog(x) from the given function;

fog(x)  =   f ( g(x) )

          =  f( 2/x)

          = 2/x + 1

Thus, the polynomial which is equivalent to fog(x) is 2/x + 1.

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Answer:

0.65A = X

Step-by-step explanation:

Given that an item that regularly sells for A dollars is on sale for 35% off its regular price, to write an expression that shows the price in dollars after the discount the following equation must be proposed:

100 - 35 = 65

0.65A = Discount price

Therefore, if the regular price were $ 50, this equation would work as follows:

0.65 x 50 = X

32.5 = X

Answer:

The value of z = -3 or z = 9

Step-by-step explanation:

Given equation => z² – 6z – 27 = 0

=> z² - 9z + 3z - 27 = 0

=> z(z -9 ) +3 (z - 9 ) = 0

=> (z + 3) (z - 9)

=> z = -3 or z = 9

Answer:z = –3 or z = 9

Step-by-step explanation:

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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