What are the angle measures?

Step-by-step explanation:

4(3-U)+U = 22+2U

12-4U+U = 22 + 2U

12-5U= 22+2U

10=3U

U = 10/3

U= 3.3

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

Angle between HB and FG = 90°

Therefore, HB and FG are perpendicular segments.

HB ⊥ FG

Similarly, angle between HB and AC = 90°

Therefore, both the segments HB and AC will be perpendicular.

HB ⊥ AC

Since FG and AC are both perpendicular to HB.

Therefore, FG║AC.

Option (2) will be the correct option.

The required magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24 is   | 6   |   8    | 10 |

                  | 13  | 15    | 17  |

                  | 20 | 22   | 24 |.

A magic square is a square grid of numbers, typically integers, where the numbers in each row, column, and diagonal add up to the same constant value.

Here,
To create a magic square using the numbers 6, 8, 10, 13, 15, 17, 20, 22, and 24, we can follow these steps,

Start by placing the number 15 in the center square of the grid.

Place the number 6 in one corner of the grid. We'll choose the top left corner for this example.

Place the number 24 in the opposite corner. We'll choose the bottom right corner for this example.

Place the remaining numbers in the empty squares of the grid, following these rules:

a. If a square is already occupied, move to the next square in the same direction.

b. If you reach the edge of the grid, wrap around to the other side.

c. If you reach a square that is diagonally adjacent to a previously filled square, move to the next empty square in a clockwise direction.

Using these rules, we can fill in the rest of the grid as follows:

| 6   |   8    | 10 |

| 13  | 15    | 17  |

| 20 | 22   | 24 |

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Answer:

when say your expenses are $400 a month but your income is only $350 a month that is -$50 every month so in that case you aren't getting a positive cash flow (which would be making more money than your expenses) So you must be getting a negative cash flow in which you are losing money and going into debt.

Hope this Helps :)

Answer:

Annie walked 1 11/12 miles

Step-by-step explanation:

Trail= 4 1/2 miles

Annie ran the first 2/3 miles

Remaining miles= Total miles - Miles covered first

= 4 1/2 - 2/3

= 9/2 - 2/3

= 27-4 / 6

= 23/6 miles

Remaining miles = 23/6 miles

Annie walked for 1/2 of the remaining distance

1/2 of the remaining miles= 1/2 × 23/6

=23 / 12

= 1 11/12

Annie walked 1 11/12 miles

Answer:

-18

Step-by-step explanation:

So we have the expression:

[tex]a-6y[/tex]

And we want to evaluate it when y=2 and a=-6.

Substitute in these values:

[tex]=(-6)-6(2)[/tex]

Multiply:

[tex]=(-6)-12[/tex]

Subtract:

[tex]=-18[/tex]

Answer:

-18

Step-by-step explanation:

We are given the expression:

[tex]a-6y[/tex]

and asked to evaluate when a= -6 and y=2.

Therefore, we must substitute -6 in for a and 2 in for y.

[tex]a-6y , a=-6, y=2[/tex]

[tex](-6)-6(2)[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.

Multiply 6 and 2.

[tex](-6)-(6*2)[/tex]

[tex](-6)-(12)[/tex]

[tex](-6)-12[/tex]

Subtract 12 from -6.

[tex](-6-12)[/tex]

[tex]-18[/tex]

The expression a-6y when evaluated for a=-6 and y=2 is equal to -18.

Answer:

a = 60°

Step-by-step explanation:

Formula used:

[tex] \red{\boxed {\bold {\tan \: \theta = \cot \: (90\degree - \theta)}}} [/tex]

[tex] \tan \: 30 \degree = \cot \: a \\ \cot \: (90 \degree - 30 \degree) = \cot \: a \\ cot \: 60 \degree = \cot \: a \\ 60 \degree = a \\ \huge \red{ \boxed{ a = 60 \degree}}[/tex]

Divide the number Janine did by the number Craig did:

36/9 = 4

Janine did 4 times as many as Craig

Answer:

4 times

Step-by-step explanation:

Because 36 divided by 9 = 4

So your answer is 4 times the number of problems.

Answer:

5.25 or 21/4 or 5 1/4

Step-by-step explanation:

hope this helps

Hello, Please consider the following.

Fibonacci numbers are defined as

[tex]u_0=1\\\\u_1=1\\\\u_{n+2}=u_{n+1}+u_{n} \ for \ n\geq 0[/tex]

Step 1 - The proposition is true for n = 1

[tex]GCD(u_2,u_1) ?\\[/tex]

Let's apply Euclidean algorithm

[tex]u_1=1, u_2=2\\\\u_2=2\times u_1+0 = 2 \times 1 +0[/tex]

This is exactly 1 step and [tex]GCD(u_2,u_1) =1[/tex]

Step 2 - We assume that this is true for k, meaning that the Euclidean algorithm takes precisely k steps to prove that [tex]GCD(u_{k+1},u_{k})=1[/tex]

[tex]u_{k+2}=u_{k+1}+u_k \ and \ 0 < u_k < u_{k+1}[/tex]

So, the first step of the algorithm is

[tex]u_{k+2}=u_{k+1}\times 1 +u_{k}[/tex]

And from now, we need to find [tex]GCD(u_{k+1},u_k)[/tex] which is 1 and takes k steps, by induction Hypothesis. Therefore, it takes k + 1 steps to find [tex]GCD(u_{k+2},u_{k+1})=1[/tex]

Step 3 - Conclusion

We have just proved that the Euclidean algorithm takes precisely n steps to prove that [tex]GCD(u_{n+1},u_{n})=1[/tex]

Thanks

Step-by-step explanation:

Answer:30. hope this helps

Answer:

30

Step-by-step explanation:

9+(5x10)+1-(15x2)

Multiply the numbers

9+(50)+1-(30)

9+50+1-30

30

Multiply the cost per bottle by the number of bottles and add that to the cost of ice.

Answer : C = 0.75b + 3.78

Answer:

C = 0.75b + 3.78

Answer:

Center: (3, - 4)

Step-by-step explanation:

We can start to solve this problem by converting this equation into standard form. In other words, by completing the square --- (1)

Subtract " 10 " from either side of the equation x² + y² - 6x + 8y + 10 = 0

x² + y² - 6x + 8y = - 10

Step 1: Complete the square for the expression " x² - 6x "

Using the quadratic equation ax² + bx + c we know that a = 1, b = - 6, c = 0. Assume that d = b / 2a. We have...

d = - 6 / 2(1) = - 6 / 2 = - 3

Now let's assume that e = c - (b²) / 4a...

e = 0 - (-6)² / 4(1) = 0 - 36 / 4 = 0 - 9 = 9 (Substitute values d and e)

(x - 3)² - 9

Step 2: Respectively we can complete the square for the remaining expression " y² + 8y "

Here a = 1, b = 8, c = 0

d = 8 / 2(1) = 8 / 2 = 4

e = 0 - (8)² / 4(1) = 0 - 64 / 4 = 0 - 16 = - 16 (Substitute values)

(y + 4)² - 16

This leaves us with the expression " (x - 3)² - 9 + (y + 4)² - 16 = - 10. " If we simplify this a bit further it leaves us with the following circle equation. Using this we can identify the center of the circle as well --- (2)

[tex]\mathrm{Standard}\:\mathrm{Circle}\:\mathrm{Equation} : (x - 3)^2 + (y +4)^2 = 15,\\\mathrm{General}\:\mathrm{Form} : (x - h)^2 + (y +k)^2 = r^2,\\\mathrm{Properties} : \mathrm{Center} = (3, - 4), \mathrm{Radius} = \sqrt{15}[/tex]

As you can see our center here is (3, - 4)

Answer:

Domain: {XS, Red, Yellow, 45, A}

Range: {Size, Color, Number, Letter}

Step-by-step explanation:

The domain of the function shown in the mapping above are all variables that fall under "A word", while the range consists of all variables under "category".

The mapping shows that the relation represents a function, because each domain variable has exactly one range variable. No single domain variable is mapped to two different range variable.

The correct answer is:

Domain: {XS, Red, Yellow, 45, A}

Range: {Size, Color, Number, Letter}

Answer: B

Step-by-step explanation: (3, 4) is 4 units above the x-axis

Answer:

C($)= (x²/2 +11x)5.75

Step-by-step explanation:

Let's assume the height= x

The base= x+22

Area= 1/2(base*height).

Area= 1/2((x+22)(x))

Area= x²/2 +11x

Cost per ft= $5.75

Cost for painting the triangular mural C

C($)= (x²/2 +11x)5.75

Answer:

C. selling a car and making a profit of $3,000

Step-by-step explanation:

An example of earning income from capital gains is selling a car and making a profit of $3,000 which the correct answer would be an option (C).

Gross capital formation for a unit or sector is calculated using the total value of gross fixed capital growth, changes in inventories, and asset acquisitions with fewer asset disposals.

As we know, from the meaning of capital gain:

When a capital asset is sold, the rise in value is known as a capital gain.

Selling a car and getting $3,000 in profit is one example of making money through capital gains.

An example of earning income from capital gains is selling a car and making a profit of $3,000

Hence, the answer would be option (C).

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Answer:

(-17+7)-13 or -17-13+7

Step-by-step explanation:

Answer:

Step-by-step explanation: -17+7=10-13=-2

Answer:

We need to evaluate this: [(-16)+4] / [(-2)+5]

First, we do the brackets:

[(-16)+4] = -16 + 4 = -12

[(-2) + 5] = -2 + 5 = 3

Now, we only need to divide, as we have calculated both brackets:

-12/3 = -4

(Remember that when dividing a negative number by a positive one, we always obtain a negative)

So the result is -4

Answer:

Larger angle= 153°

Smaller angle= 27°

Step-by-step explanation:

Supplementary angles are two angles that add up to 180°

Let the smaller angle= x

Let the larger angle= y

X+y= 180... equation one

Y-126= x..... equation two

(Y-126) +y = 180

2y= 180+126

2y= 306

Y= 153°

Y-126= x.

153-126= x

27°=x

The solution (with steps) and answer are included in the images below.

Best of Luck!

Answer:

-0.4 = −2/5

Step-by-step explanation:

Rewrite the decimal number as a fraction.

-0.4/1

Multiply to remove 1 decimal places.

-0.4/1 x 10/10 =4/10

Find the GCF.

4 ÷ 2/10 ÷ 2 = 2/5

x = 2/5

-2/5

Answer:

Length = X + 3

Step-by-step explanation:

Examples for the length width relationship would go as follows:

Width    Length

1              4

2             5

3             6

4             7

Hope this helps!

-TheBusinessMan

Answer:

Length = x + 3

Step-by-step explanation:

Width = x

Length = 3 + Width

So, Length = 3 + x

So, if Width as a number, then Length will be 3 more than that number.

Answer:

[tex] t = 4x [/tex]

Step-by-step explanation:

We are given that in 1 month, Jessica takes 4 business trips. Take 4 as our coefficient or constant.

Let t be the total number of business trips Jessica has taken.

For 1 month, 4 trips are taken.

For x months, total business trips taken will be expressed as,

[tex] t = 4x [/tex]

Let's say for example, we have 5 months in a row, i.e. x = 5. Total business trips taken by Jessica can be gotten by simply plugging in the value of x.

[tex] t = 4(5) = 20 trips [/tex]

In 5 months in a row, Jessica takes 20 business trips.

Answer:

There is no sufficient evidence to support  the claim that the boards are either too long or too short

Step-by-step explanation:

From the question we are told that

   The  population mean is [tex]\mu = 2599.0[/tex]

    The sample size is  [tex]n = 23[/tex]

     The  sample mean is  [tex]\= x = 2600.3 \ mm[/tex]

    The  standard deviation is  [tex]\sigma = 13.0[/tex]

     The  level of significance is  [tex]\alpha = 0.05[/tex]

The  null hypothesis  is  [tex]H_o : \mu = 2599.0[/tex]

  The  alternative  hypothesis is [tex]H_a : \mu \ne 2599.0[/tex]

Generally the test statistics is mathematically represented as

            [tex]t = \frac{ \= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]

=>          [tex]t = \frac{ 2600.3 - 2599.0 }{ \frac{13}{ \sqrt{ 23} } }[/tex]

=>            [tex]t = 0.3689[/tex]

Now from the normal distribution table  the critical value  of  [tex]\alpha[/tex] is  

    [tex]Z_{\alpha } = 1.645[/tex]

Hence from the evaluated and obtained value we see that

    [tex]t < Z_{\alpha }[/tex]

Hence we fail to reject the null hypothesis  

  Thus we can conclude that there is no sufficient evidence to support  the claim that the boards are either too long or too short

Answer:

in my opition is 2x(-7)

Step-by-step explanation:

hope it help

Answer:

1.5

Step-by-step explanation:

Answer:  y=-8x -12

Step-by-step explanation:

-8x - y =12      to solve for y add -8x to both sides

+8x    +8x

 -y = 12 +8x   Now divide each side by -1

  y = -8x -12

Answer:

Rs0.83

Step-by-step explanation:

i hope it helped you.