Draw AABC with vertices at A(1,6), B(1, 1) and C(5, 1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E = 90°, and
EF = BC.
Paste a picture of your drawing in the answer box.

Highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18

what is greatest integer divisor ?

The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).

For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values

Let gcd(8n + 3, 5n + 4) = d

⟹d|8n+3∧d|5n+4

⟹d|8(5n+4)−5(8n+3)

⟹d|17

Therefore highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18

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Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.

Eva takes to fill an online order at her clothing boutique. = 6 minutes

If Eva and Briana fill an order together = 4 minutes

Briana will take minutes to fill an order alone at her clothing boutique = X minutes.

then the equation will be :

1/6 + 1/x = 1/4

1/x =  1/4 -  1/6

now solve equation by taking LCM

1/x = (6-4)/4x6

1/x = 2/24

1/x = 1/12

x = 12

so the value of x is 12

Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.

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Answer:

10.7a + (−6)

Step-by-step explanation:

If the amount of loan taken in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.

Given that the amount of loan in community college is $2900 and the rate of interest is 6.8%.

We are required to find the amount of interest that will accrue for

loan 1.

Compound interest is the amount of interest that is calculated on the aggregate of principal and interest of previous years.

Compounded amount=P[tex](1+r)^{n}[/tex]

To find out the amount of interest for the loan 1,we have to find the compounded amount after 2 years.

Compounded amount=2600([tex](1+0.068)^{2}[/tex]

=2600*[tex](1.068)^{2}[/tex]

=2600*1.14

=$2964

Interest=2964-2600=$364

Hence if the amount of loan in community college is $2900 and the rate of interest is 6.8% then the amount of interest that will accrue for loan 1 is $364.

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Answer: 40%

Step-by-step explanation:

c=class. m=men. w=women.

c=m+w

40=24+w

40-24=24-24+w

w=16

16/40=

4/10=

4*100%/10=

400%/10=40%

Option a is correct. f(x) has an inverse function because its graph passes the horizontal line test.

An inverse function is a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

From the graph we can see that the horizontal lines intersect less than 2 points, this shows that the f(x) has an inverse.

From the graph, it gets to know.

Hence from the given graph we get to know that f(x) is the inverse function.

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Answer:

40°

Step-by-step explanation:

We know that

[tex]m\angle 2=28^{\circ}+m\angle 1[/tex]

Thus, by the angle addition postulate,

[tex]28+m\angle 1+m\angle 1=108^{\circ} \\ \\ 2m\angle 1=80^{\circ} \\ \\ m\angle 1=40^{\circ}[/tex]

Answer:

I don't know it this question

Step-by-step explanation:

rfhdwhjgdshmfsaghjjdsdbj

Using proportions, it is found that there are 1.125 cups of strawberries in each pie.

A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.

Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.

For this problem, from the ratios, we have that:

The least common multiple of 3 and 4 is 12, hence, multiplying 4 by 3, the ratio is:

Raspberries : Strawberries : Blueberries = 12 : 9 : 4

Meaning that our of 12 + 9 + 4 = 25 cups, we have that:

There amounts are for 8 pies, hence, for a single pie:

9/8 = 1.125 cups.

There are 1.125 cups of strawberries in each pie.

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The probability that a random bird chosen from among these is NOT a duck is 0.67

Given the total number of birds = 262

No of geese = 65

No of ducks = 84

No of robins = 113

We need to find the probability that a random bird chosen from among these is not a duck is

P ( not a duck ) = (total number of birds  - no of ducks) / total number of birds

                         =  262 - 84 / 262

                         =  178 / 262

                          = 0.67

The probability that a random bird chosen from among these is NOT a duck is 0.67.

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The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.

What is a quadratic equation?

In algebra, a quadratic equation is any equation that can be rearranged in standard form as

ax² + b*x + c = 0

The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.

The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side.

A quadratic equation has at most two solutions.

Given,

Initial height h(0) = 3 ft

Initial upward velocity v(0) = 36 ft/sec

Given ball height after 't' seconds is h(t) = 3 + 36t - 16r²

for h= 19 ft

19 = 3 + 36 t - 16 r²

16 r² - 36 t + 16 = 0

4 r² - 9 t + 4 = 0

Quadratic equation for ax² + b*x + c = 0 is x = -b ±√b² - 4ac / 2a

By using the above formula we get

t = 9 ± √9² - 4*4*4 / 2*4

t = 9 ± √81 - 64 / 8

t = 9 ± √17 / 8

t = 9 + √17 / 8              t = 9 - √17 / 8

t = 9 + 0.5                    t = 9 - 0.5

t = 9.5                           t = 8.5

The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.

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Answer:  Continuous at x = 3

The function is only discontinuous at x = 0 since it causes a division by zero error. Everywhere else the function is a continuous curve.

Answer:

  a) the largest angle is 90°, making it a right triangle

  b) the shortest side is 9.5 cm long

Step-by-step explanation:

You want the largest angle and the shortest side in a triangle whose angles are in the ratio 1 : 2 : 3.

Let x represent the smallest angle. Then the other two angles are 2x and 3x. Their sum is ...

  x +2x +3x = 180°

  x = 30° . . . . . divide by 6

  3x = 90° . . . . find the largest angle

The largest angle is 90°, a right angle. So, the triangle is a right-angled triangle.

A triangle with angles of 30°, 60°, and 90° is a "special" right triangle. Its sides are in the ratio 1 : √3 : 2. That is, the shortest side is 1/2 the length of the longest side.

  shortest side = 1/2(19 cm) = 9.5 cm

The length of the shortest side in the triangle is 9.5 cm.

__

Additional comment

In case you're not familiar with the side length ratios of the 30-60-90 special triangle, you can figure the side length from the Law of Sines. That tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

where A, B, C are the angles; and a, b, c are their opposite sides.

The shortest side is opposite the smallest angle, so we have ...

  a/sin(30°) = (19 cm)/sin(90°)

  a = sin(30°)×(19 cm) = 1/2(19 cm) = 9.5 cm

The length of the shortest side is 9.5 cm.

Answer:

-22

Step-by-step explanation:

put the subtraction sign to the side

26 (Gretta's elevation)

-  4 (Hercules' elevation)

22

then re-add the subtraction sign (-22) then you have an answer

Answer: State A has 54 counties and B has 52 counties

Step-by-step explanation: Since the number of counties are even integers, I did a guess and check. Divided 106 by two to get 53. Then realized that if you take away 1 from on of the 53's and add it to the other, they become consecutive even integers 52 and 54

The dimensions of the rectangular traffic sign whose perimeter is 134 inches according to the task content are; 38in by 29in.

It then follows that from the task content that the dimensions of the rectangular traffic sign are to be determined.

Since the perimeter of a rectangle is given by;

P = 2(l+b)

where the length, l = b +9.

So therefore; 134 = 2(b+9 +b)

134 = 4b + 18

4b = 134 - 18

4b = 116

b = 29

In conclusion, the length, l of the traffic sign is; 29 +9

l = 38.

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Answer: 264.6 miles

Step-by-step explanation: Let's put the info we got from the problem into an equation. If the car is rented for three days, we need to multiply 27.95 by 3, which will give us 83.85. Now let's use the equation 150=83.85 + 0.25x, where x represents miles. Subtract 83.85 from both sides and we get 66.15 = 0.25x. Now divide both sides by 0.25 and we get x = 264.6.

Answer:

264 miles

Step-by-step explanation:

y = 27.95x + 0.25n where:

y = budget

x = days rented

n = miles driven

150 = 27.95(3) + 0.25n

150 = 83.85 + 0.25n

150 - 83. 85 = 0.25n

66.15 = 0.25n

66.15 / 0.25 = n

n = 264.6 miles

27.95(3) + 0.25(246.6) = $150

The second matrix in the definition of [tex]f[/tex] is singular, since

[tex]\sin(\pi) = -\cos\left(\dfrac\pi2\right) = \tan(\pi) = 0[/tex]

[tex]\cos\left(\theta+\dfrac\pi4\right) = \sin\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \sin\left(\dfrac\pi4-\theta\right)=-\sin\left(\theta-\dfrac\pi4\right)[/tex]

[tex]\cot\left(\theta+\dfrac\pi4\right) = \tan\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \tan\left(\dfrac\pi4 - \theta\right) = -\tan\left(\theta-\dfrac\pi4\right)[/tex]

[tex]\ln\left(\dfrac4\pi\right) = -\ln\left(\dfrac\pi4\right)[/tex]

In other words, it's antisymmetric; [tex]A^\top=-A[/tex]. It's easy to show that [tex]\det(A)=0[/tex] if [tex]A[/tex] is 3x3 and antisymmetric.

The other determinant reduces to

[tex]\begin{vmatrix}1 & \sin(\theta) & 1 \\ - \sin(\theta) & 1 & \sin(\theta) \\ -1 & -\sin(\theta) & 1 \end{vmatrix} = 2 + 2\sin^2(\theta)[/tex]

Hence

[tex]f(\theta) = 1 + \sin^2(\theta) \implies f\left(\dfrac\pi2\right) = 1 + \cos^2(\theta)[/tex]

With [tex]g[/tex] defined on [tex]\left[0,\frac\pi2\right][/tex], both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are non-negative. So

[tex]g(\theta) = \sqrt{f(\theta)-1} + \sqrt{f\left(\dfrac\pi2-\theta\right)-1} \\\\ ~~~~ = \sqrt{\sin^2(\theta)} + \sqrt{\cos^2(\theta)} \\\\ ~~~~ = |\sin(\theta)| + |\cos(\theta)| \\\\ ~~~~ = \sin(\theta) + \cos(\theta) \\\\ ~~~~ = \sqrt2\,\sin\left(\theta + \dfrac\pi4\right)[/tex]

which is maximized at [tex]t=\frac\pi4[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac\pi2\right)=\sqrt2[/tex], and minimized at [tex]t=0[/tex] and [tex]t=\frac\pi2[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac{3\pi}4\right)=1[/tex].

Edit: The rest of my answer wouldn't fit. Continued in attachment.

Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Before beginning the problem, we have that the symbol # represents a pound, which has 16 ounces.

The remaining fillets weight 4 # 15 oz = 4 pounds + 15/16 of a pound. Hence, considering the cost of $2.74 per pound:

4 x 2.74 + 15/16 x 2.74 = $13.53.

The total value of the remaining fillets is of $13.53.

The price per pound is still the same, of $2.54.

The yield is of 4 pounds + 15/16 of a pound = 4.9375 pounds out of 7 + 6/16 = 7.375 pounds, hence the percentage is:

4.9375/7.375 x 100% = 66.95%.

The salmon’s yield percentage is of 66.95%.

Hence, for 6 + 14/16 = 6.875 pounds, the yield would be of:

0.6695 x 6.875 = 4.6 pounds.

You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.

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Exact Distance = [tex]2\sqrt{5}[/tex] units

Approximate Distance = 4.4721 units

=================================================

Let's use the distance formula

[tex](x_1,y_1) = (3,0) \text{ and } (x_2, y_2) = (-1,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-1))^2 + (0-(-2))^2}\\\\d = \sqrt{(3+1)^2 + (0+2)^2}\\\\d = \sqrt{(4)^2 + (2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.4721\\\\[/tex]

The exact distance is [tex]2\sqrt{5}[/tex] units.

That approximates to about 4.4721 units.

Answer:

Transitive property for equality

Step-by-step explanation:

Answer: I think the answer you are looming for is 80 feet.

Step-by-step explanation:

4 x 10 = 40

To double means to multiply by 2 so

40 x 2 = 80

If angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.

Given that angle BAD=4x° and angle DAC=(3x+8)°.

We are required to find the equation showing the angle BAC.

Angle is basically the figure formed by two rays which is called the sides of the angle and sharing a common endpoint called the vertex of the angle.

∠BAD=4x° and ∠DAC=(3x+8)°

To find the equation showing angle BAC we have to just add the two expressions given in the equation.

∠BAC=∠BAD+∠DAC

∠BAC=4x+3x+8

∠BAC=(7x+8)°

Hence if angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.

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