I NEED HELP ASAP Use the Law of Detachment or the Law of Syllogism to draw a conclusion. 3. If Shauna is early for her meeting, she will gain a promotion. If Shauna wakes up early, she will be early for her meeting. Shauna wakes up early.

In a 30-60-90 triangle, the hypotenuse is twice the length of the shortest leg. Hence, if the shortest leg is 4, then the hypotenuse is 8.

In a 30-60-90 triangle, the ratios of the sides are specific and constant. The shortest side, the one opposite the 30-degree angle, is considered to be x. The longest side (hypotenuse), directly across from the 90-degree angle, is 2x, and the remaining side is x√3. In this case, the shortest side (x) is indicated to be 4.

So, in this triangle, the hypotenuse (2x) would be 2*4 = 8.

The Pythagorean theorem, as mentioned in the reference content, will also hold, but in the case of this special triangle, the ratios of the sides simplify the process of determining side lengths.

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The required algebraic expression can be written as [tex](y\div4)-3[/tex].

Given: a statement is [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex].

According to question,

An algebraic expression can be written by use of  [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex].

Here, expression is [tex](y\div4)-3=\frac{y}{4}-3[/tex].

Therefore, the algebraic expression for the statement  [tex]3[/tex] less than the quotient of a number [tex]y[/tex] and [tex]4[/tex] is written as [tex]\frac{y}{4}-3[/tex].

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Answer:

34.49

Step-by-step explanation:

You do it reverse

30.3+4.04=34.34

34.34+0.58=34.92

34.92-0.43=34.49

After 14 years, Jane has accumulated approximately $1587.45, which means her initial investment of $500 has more than tripled due to the power of compound interest at a rate of 8.25%, compounded continuously.

Jane plans to invest $500 at 8.25% interest, compounded continuously. To find out how much money she has accumulated after 14 years, we use the formula for continuous compounding: [tex]A = Pe^{rt}[/tex], where:

For Jane's investment:

P = $500

r = 8.25% or 0.0825 (as a decimal)

t = 14 years

Plugging these values into the formula gets us:

[tex]A = 500e^{0.0825*14}[/tex]

Calculating this gives us:

[tex]A \approx 500e^{1.155} \approx 500 * 3.1749 \approx $1587.45[/tex]

Jane's money has more than tripled in 14 years. It has not quadrupled, but it has significantly grown beyond double the original investment.

Answer:

1.D

2.D

3.B

4.A

5.A

Step-by-step explanation:

1.We are given that two equations

[tex]d+e=15[/tex]

[tex]-d+e=-5[/tex]

Adding two equations then we get

[tex]2 e=10[/tex]

[tex]e=\frac{10}{2}=5[/tex]

Substitute e=5 in equation one then we get

[tex]5+e=15[/tex]

[tex] d=15-5[/tex]

[tex]d=10[/tex]

Hence, the ordered pair as (10, 5).

Therefore,Option D is true.

2.We are given that two equations

Equation S:[tex]y=x+9[/tex]

Equatin T:[tex]y=2x+1[/tex]

Using substitution method

Substitute the value of y from equation one in equation second then we get

[tex]x+9=2x+1[/tex]

Therefore, option D is true.

3.We are given that two equations

Equation C :[tex]y=6x+9[/tex]

Equation D[tex]:y=6x+2[/tex]

The two equations can be written as

[tex]6x-y+9=0[/tex]

[tex]6x-y+2=0[/tex]

[tex]a_1=6,b_1=-1,c_1=9[/tex]

[tex]a_2=6,b_2=-1,c_2=2[/tex]

[tex]\frac{a_1}{a_2}=\frac{6}{6}=1:1[/tex]

[tex]\frac{b_1}{b_2}=\frac{-1}{-1}=1:1[/tex]

[tex]\frac{c_1}{c_2}=\frac{9}{2}[/tex]

[tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}[/tex]

Therefore, system of equations have no solution

Hence, option B is true.

4.We are given that two equations

[tex]2x+y=-4[/tex]

[tex]y=3x+2[/tex]

Using substitution method

Substitute value of y from equation second in equation one

Then we get

[tex]2x+3x=2=-4[/tex]

[tex]5 x=-4-2[/tex]

[tex]5 x=-6[/tex]

[tex]x=-\frac{6}{5}[/tex]

Substitute the value of x in equation second then we get

[tex]y=3\times( -\frac{6}{5})+2[/tex]

[tex]y=\frac{-18+10}{5}[/tex]

[tex]y=-\frac{8}{5}[/tex]

Hence, option A is true.

5.We are given that two equations

[tex]y=-2x+1[/tex]

[tex]6x+2y=22[/tex]

Using substitution method

Substitute value of y from equation one in second equation then we get

[tex]6x+2(-2x+1)=22[/tex]

Hence, option A is true.

Answer:

−(x−1)(x+9)=0

And..

3x2−6x=0

Step-by-step explanation:

Final answer:

The two equations most appropriately solved by using the zero product property are −(x−1)(x+9)=0 and 3x²−6x=0, as they can be directly factored into a product of terms equaling zero.

Explanation:

The question involves finding which two equations would be most appropriately solved by using the zero product property. The zero product property states that if the product of two numbers is zero, then at least one of the multiplicands must be zero. Therefore, equations that can be factored into a product of terms equaling zero can be solved using this property.

The other options, 4x² = 13 and 0.25x²+0.8x−8=0, are not immediately in a form that uses the zero product property without further manipulation or do not directly apply to this property.

Answer:

[tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The slope of a line parallel to b has the exact same slope as b. Therefore, by finding the slope of b, you will find the slope of a line parallel to be as well.

The following formula is used to find m, the slope of the line, using the two given points:

[tex]m=\frac{y_{1}-y_{2} }{x_{1}-x_{2} } \\m=\frac{5--5}{3--1} \\m=\frac{5+5}{3+1} \\m=\frac{10}{4} \\m=\frac{5}{2}[/tex]

The value of x of the triangle is: x = 24 units

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Thus, the length of the base is:

c² = 30² + 40²

c² = 2500

c = √2500

c = 50 units

Using the concept of similarity ratio, we have:

30/50 = x/40

Cross multiply to get:

50x = 1200                      

x = 24 units

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The measure of angle at the tangent of a circle is a right angle.

Start by calculating the measure of angle ABC using the following angle in a triangle theorem

[tex]\angle ABC + 48 + 47 = 180[/tex]

[tex]\angle ABC + 95 = 180[/tex]

Subtract 95 from both sides of the equation

[tex]\angle ABC = 180 - 95[/tex]

[tex]\angle ABC = 85[/tex]

For line BC to be a tangent, then the following must be true

[tex]\angle ABC = 90[/tex]

Hence, the correct statement about BC is (c)

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Answer:

The correct option is C.

Step-by-step explanation:

Given information: AB=20.4, BC=17.7 and ∠ B = 99 °.

It two sides and their inclined angle is given then the area of the triangle is

[tex]A=\frac{1}{2}ab\sin C[/tex]

Where, a and b are two sides of a triangle and C is their inclined angle.

The area of given triangle is

[tex]A=\frac{1}{2}\times 20.4\times 17.7 \sin 99^{\circ}[/tex]

[tex]A=178.317253[/tex]

[tex]A\approx 178.3[/tex]

The area of the triangle ABC is 178.3 square units. Therefore the correct option is C.

Answer:

1. The total score of all three players.

2. Mia's score.

3. 4x-6\

4. -6

The mathematical expression from the scenario represents the total golf scores of Erick, Mia, and Isabelle. The variable represents Mia's score, and the simplified expression is 4x - 6, with -6 being the constant.

From the given scenario, the expression x + x + 10 + 2x - 16 represents the total score of Erick, Mia, and Isabelle. The variable 'x' in this expression represents Mia's golf score, as other scores are dependent on it.

To simplify the expression, we group like terms: x (Mia's score) + x (Erick's score, which is 10 more than Mia's) + 2x (Isabelle's score, which is 16 less than twice Mia's) - 16. Simplifying this, we get 4x - 6. So, the simplified expression is 4x - 6.

The constant in the simplified expression is -6. This is the value that is added or subtracted to the variable's value, irrespective of its value.

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1. f(x)=x²+10x+16

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=1(As, a>0 the parabola is open upward), b=10. by putting the values.

-b/2a = -10/2(1) = -5

f(-b/2a)= f(-5)= (-5)²+10(-5)+16= -9

So, Vertex = (-5, -9)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+16, we get point (0,16).

Now find x-intercept put y=0 in the above equation. 0= x²+10x+16

x²+10x+16=0 ⇒x²+8x+2x+16=0 ⇒x(x+8)+2(x+8)=0 ⇒(x+8)(x+2)=0 ⇒x=-8 , x=-2

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

2. f(x)=−(x−3)(x+1)

By multiplying the factors, the general form is f(x)= -x²+2x+3.

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.

-b/2a = -2/2(-1) = 1

f(-b/2a)= f(1)=-(1)²+2(1)+3= 4

So, Vertex = (1, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point (0, 3).

Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.

-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒x=3 , x=-1

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

3. f(x)= −x²+4

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=0. by putting the values.

-b/2a = -0/2(-1) = 0

f(-b/2a)= f(0)= −(0)²+4 =4

So, Vertex = (0, 4)

Now, find y- intercept put x=0 in the above equation. f(0)= −(0)²+4, we get point (0, 4).

Now find x-intercept put y=0 in the above equation. 0= −x²+4

−x²+4=0 ⇒-(x²-4)=0 ⇒ -(x-2)(x+2)=0 ⇒x=2 , x=-2

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

4. f(x)=2x²+16x+30

Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=2(As, a>0 the parabola is open upward), b=16. by putting the values.

-b/2a = -16/2(2) = -4

f(-b/2a)= f(-4)= 2(-4)²+16(-4)+30 = -2

So, Vertex = (-4, -2)

Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+30, we get point (0, 30).

Now find x-intercept put y=0 in the above equation. 0=2x²+16x+30

2x²+16x+30=0 ⇒2(x²+8x+15)=0 ⇒x²+8x+15=0 ⇒x²+5x+3x+15=0 ⇒x(x+5)+3(x+5)=0 ⇒(x+5)(x+3)=0 ⇒x=-5 , x= -3

From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.

5. y=(x+2)²+4

The general form of parabola is y=a(x-h)²+k , where vertex = (h,k)

if a>0 parabola is opened upward.

if a<0 parabola is opened downward.

Compare the given equation with general form of parabola.

-h=2 ⇒h=-2

k=4

so, vertex= (-2, 4)

As, a=1 which is greater than 0 so parabola is opened upward and the graph has minimum.

The graph is attached below.

Here are a bunch of CORRECT answers, your answer is somewhere in there. For the first CORRECT answer the second point is -5,-9. Don't make the same mistake I did on question 3, but it still shows the correct answer. I love to help.

Answer:

The correct answer is option A, 6 , 7, 8, 9 inches

Step-by-step explanation:

Given the scale of drawing ,

[tex]1 inch = 2 yards\\[/tex]

The size of each side of a quadrilateral when converted as per the scale pf map

[tex]= \frac{12}{2} , \frac{14}{2} , \frac{16}{2} , \frac{18}{2} \\= 6, 7, 8 ,  9 inches\\[/tex]

Chris should construct the enclosure with a width of 5 feet and a length of 10 feet, using her 15 feet of fencing material, which will result in a maximum enclosed area of 50 square feet.

Chris wants to construct an enclosed rectangular area for a mulch pile and use her backyard's corner fence effectively, thereby constructing only two sides of the mulch pile enclosure. She has 15 feet of fencing material to use and wants the length of the rectangular enclosure to be twice the width. To find the dimensions that will produce the maximum area, we can set up an equation.

Let x represent the width (in feet) and 2x represent the length (in feet), since the length is twice the width.

Since Chris is using the corner of the yard, she only needs to construct two sides of the fence.

Therefore, the amount of fencing material she will use (perimeter of two sides) is given by the equation x + 2x = 15, which simplifies to 3x = 15.

Solving for x, we find that x = 5 feet. Thus, the width of the enclosure is 5 feet, and the length is twice that, or 10 feet.

The maximum area that Chris can enclose is therefore 5 ft  imes 10 ft = 50 square feet.

Answer:

I believe its 5.5

Step-by-step explanation: