Which number completes the square? x2 + 18x + _____?

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:

2

Step-by-step explanation:

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]

its the first graph

A

To find the graph of the equation y = 4x + 3, plot the y-intercept at (0,3) and use the slope of 4 to plot additional points. Connect these points to form a straight line that slopes upward to the right, reflecting a positive slope.

The student has asked to identify the graph of the equation y = 4x + 3. This is an equation of a straight line where the slope (m) is 4 and the y-intercept (b) is 3. According to the properties of linear equations, for every increase of 1 on the x-axis, the value of y will increase by the slope value, which is 4 in this case. The graph will intersect the y-axis at 3, which is the y-intercept.

To graph this line, you can start by plotting the y-intercept at (0,3) on the graph. Then, use the slope to determine the next point by moving 4 units up for every 1 unit you move to the right. Repeat this process with several values of x to construct a table, for instance, at x=1, y=7, at x=2, y=11, etc. These points are then plotted and connected with a straight line to represent the graph of the equation.

Referring to Figure 12.4, we can see that the line would match figure (a) which shows a line that slopes upward to the right, because our b value (slope) is greater than 0.

Answer:

The profit for one small cake is £1.31.

Step-by-step explanation:

It is given that that Gina sells 216 cakes in the ratio small:medium:large 5:7:12.

[tex]5+7+12=24[/tex]

Number of small cakes = [tex]216\times \frac{5}{24}=45[/tex]

Number of medium cakes = [tex]216\times \frac{7}{24}=63[/tex]

Number of large cakes = [tex]216\times \frac{12}{24}=108[/tex]

The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake.

Let the profit for one small cake be x. So the profit for one medium and large cake are 2x and 3x respectively.

Her total profit id £648.45.

[tex]45\times x+63\times 2x+108\times 3x=648.45[/tex]

[tex]45x+126x+324x=648.45[/tex]

[tex]496x=648.45[/tex]

Divide both sides 496.

[tex]\frac{496x}{496}=\frac{648.45}{496}[/tex]

[tex]x=1.30735887097[/tex]

[tex]x\approx 1.31[/tex]

Therefore the profit for one small cake is £1.31.

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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Answer:

180 yards on day 21

Step-by-step explanation:

just took on A P E X !!

Answer:

Option A. [tex]43.5\ in^{2}[/tex]  

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=(1/2)(b1+b2)h[/tex]

we have

[tex]b1=1\frac{1}{4}\ ft[/tex]

[tex]b2=14\ in[/tex]

[tex]h=3\ in[/tex]

Convert feet to inches first

Remember that

[tex]1\ ft=12\ in[/tex]

so

[tex]1\frac{1}{4}\ ft=\frac{5}{4}\ ft=12*\frac{5}{4}=15\ in[/tex]

substitute in the formula

[tex]A=(1/2)(15+14)3=43.5\ in^{2}[/tex]  

Answer:

43.5 in^2

Step-by-step explanation:

Answer:

11.15

Step-by-step explanation:

No, Marla is not correct. The correct new equation is 4x + 8y = 20.

No, Marla is not correct. To create a new equation that represents the same system of equations, we need to perform the same mathematical operation on both sides of the equation. In this case, Marla multiplied the left side of the equation by 2, but not the right side. To maintain equality, we need to multiply both sides of the equation by the same constant. Therefore, the correct new equation would be 4x + 8y = 20.

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:

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:

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

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.

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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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:

it is 2;3;5;6

Step-by-step explanation:

Given that z20 = –2 and z 50= –1, which of the following do you know?

The variance is 10.

The standard deviation is 30.

The mean is 80.

The median is 40.

The data point x = 20 is 2 standard deviations from the mean.

The data point x = 50 is 1 standard deviation from the mean.

The data point x = 45 has a z-value of 1.5.

answer2356 on edge

The solution is, it is 2;3;5;6.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

here, we have,

Given that z20 = –2 and z 50= –1, which of the following do you know?

The variance is 10.

The standard deviation is 30.

The mean is 80.

The median is 40.

The data point x = 20 is 2 standard deviations from the mean.

The data point x = 50 is 1 standard deviation from the mean.

The data point x = 45 has a z-value of 1.5.

so, we get,

answer2, 3, 5, 6 on edge.

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The formula of area of triangle is given by

[tex] A= \frac{1}{2} b*h [/tex]

Where b is the base and h is the height .

In the given question, base ,b = 3 feet

Height, h= 6 feet

Substituting the values of b and h in the formula, we will get

[tex] A = \frac{1}{2}*3*6 = 9 ft^2 [/tex]

Correct option is C .

Answer:

9 ft^ 2

Step-by-step explanation:

Answer:

I believe its 5.5

Step-by-step explanation: