Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 26.47 units²
B. 28.53 units²
C. 33.08 units²
D. 27.28 units²

Answer:

[tex]\large\boxed{x=-6\pm\sqrt{30}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+12x+6=0\qquad\text{subtract 6 from both sides}\\\\x^2+2(x)(6)=-6\qquad\text{add}\ 6^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(6)+6^2}_{(*)}=-6+6^2\\\\(x+6)^2=-6+36\\\\(x+6)^2=30\Rightarrow x+6=\pm\sqrt{30}\qquad\text{subtract 6 from both sides}\\\\x=-6\pm\sqrt{30}[/tex]

C. 112.5

The Angles of Intersecting Chords Theorem  states:

"If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle"

So, the arc intercepted by the angle ∠5 is:

360° - 50° - 115° - 85° = 110°

On the other hand, the arc intercepted by its vertical angle is:

115°

Therefore:

[tex]\angle 5 = \frac{1}{2}(110^{\circ}+115^{\circ}) \\ \\ \boxed{\angle 5 = 112.5^{\circ}}[/tex]

Answer:

40 ft

Step-by-step explanation:

We can use ratios to solve this problem.  Put the scale over the actual size

1/4 inch           2 inches

-------------- = ----------------

5 ft                  x ft

Using cross products

1/4 x = 2 *5

1/4 x = 10

Multiply each side by 4

4*1/4 x = 4 * 10

x = 40

The wall is 40 ft

Answer: D: 672

Step-by-step explanation:

use the equation C = 2πR, where C is circumference and R is radius

re-write the equation with 107 instead of R

C=2*π*107

then solve (use 3.14 for pi and round up)

3.14*2=6.28

6.28*107=671.96

then round up to get 672

I hope this helps!

The circumference of a circular park with a radius of 107 m, calculated with the formula Circumference = 2 * π * radius, is approximately 672 m.

The circumference of a circle is calculated by using the formula: Circumference = 2 * π * radius. In this case, the radius of the circular park is given as 107 m. Substituting the radius into the formula, we obtain: Circumference = 2 * 3.14 * 107 which equals approximately 672 m. So, to the nearest meter, the circumference of the park is 672 m.

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Answer:

3 gallons per mile, slope of 3

Step-by-step explanation:

To find out how many gallons the train uses per mile, look at the point (50,150). If you know that the train used 150 gallons to travel 50 miles, do 150/50 to get an answer of 3 gallons per mile.

For the second part, you know that as x increases by 1 (miles traveled) y (gallons) increases by 3, so therefore the slope is 3. You can also check this value by plugging in the points (150,450) and (50,150) into the [tex]m=\frac{x_{2}  - x_{1}}{y_{2}  - y_{1}}[/tex]

Answer:

[tex]x=-5/7[/tex]

Step-by-step explanation:

we have

[tex]f(x)=7x+5[/tex] ----> The degree of this polynomial is 1 (linear equation)

Remember that

The zero of the polynomial is the value of x when the value of f(x) is zero

so

For f(x)=0

[tex]0=7x+5[/tex]

solve for x

[tex]x=-5/7[/tex] ----> the zero of the polynomial or x-intercept

Answer:

see below

Step-by-step explanation:

395.2

Step-by-step explanation:

Area of a trapezoid is:

A = ½ (a + b) h

where a and b are the top and bottom lengths and h is the height.

If 7.6 refers to the entire side length, then the area is:

A = ½ (2.6 + 7.6) (4)

A = 20.4

If 7.6 refers only to the length right of the right angle, we can use Pythagorean theorem to find the length on the left:

x² + 4² = 5²

x = 3

So the whole side length is 3 + 7.6 = 10.6.  That means the area is:

A = ½ (2.6 + 10.6) (4)

A = 26.4

Answer:

3^9 * 11^9

Step-by-step explanation:

33^9 =

We know that (ab)^c = a^c * b^c

(33)^9 = (3*11)^9 = 3^9 * 11^9

Answer:

5

Step-by-step explanation:

[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]

Answer:

y^2+12-7y

Step-by-step explanation:

(y-3)(y-4)

I will split it up for us

y*y= y^2

-3*y= -3y. \

y*-4= -4y. / -7y

-3*-4= 12

y^2+12-7y

The product of (y-3)(y-4), is y^2 - 7y + 12.

To find the product of (y-3)(y-4), we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials.

First: Multiply the first terms of each binomial: y × y = y^2.

Outer: Multiply the outer terms: y × -4 = -4y.

Inner: Multiply the inner terms: -3 × y = -3y.

Last: Multiply the last terms of each binomial: -3 × -4 = 12.

Adding these products together, we get: y^2 - 4y - 3y + 12. Simplifying by combining like terms, the final product is: y^2 - 7y + 12.

Final answer:

The equation of the line through (7, -4) and (-1, 3) has a slope of -7/8. It can be written in a point-slope form as y + 4 = -7/8(x - 7), and in slope-intercept form as y = -7/8x + 25/8.

Explanation:

To write the equation of the line that passes through the points (7, –4) and (–1, 3), the first step is to find the slope of the line. The slope (m) is given by the rise over run, which is the change in y divided by the change in x:

Now that we have the slope, we can use the point-slope form which is given by the formula:

We can choose one of the points for x1 and y1; let's use (7, -4):

Therefore, the point-slope form of the line is:

Now, to convert this into the slope-intercept form (y = mx + b), we just solve for y:

After simplifying the constant term:

The slope-intercept form is y = -7/8x + 25/8, where -7/8 is the slope and 25/8 is the y-intercept.

Answer:

The correct option is 10....

Step-by-step explanation:

The formula of circumference of the circle is:

C = 2πr

where C is the circumference of the circle

r = radius

In this question we have given the circumference and we have to find out the radius:

Thus substitute the values in the formula:

C = 2πr

20π= 2πr

Move 2π to the L.H.S.

20π/2π = r

Cancel out π by π and 20/2 by the table of 2

Therefore we have:

10=r

Thus the correct option is 10....

Answer is provided in the image attached.

Answer:

Here's one way to do it.

Step-by-step explanation:

-24 ÷ (-4)

-24 is the final number on the number line

-4 means you count by 4s on the number line moving backwards.

Answer: +6 (The sign is + because you are still facing forward).

After modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

" Number line is defined as a straight line which represents the number at the equal interval on it on the both the side of zero."

According to the question,

Given division,

[tex](-24)[/tex] by [tex](-4)[/tex]

As shown on the model of  number line the given division we have,

Hence, after modeling the division of [tex]-24[/tex] by [tex]-4[/tex] on the number line, we reach to zero after [tex]6[/tex] steps.

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Answer:

I am sure it is D

Answer:

7 high priced speakers

21 Low priced speakers

Step-by-step explanation:

170x7 =1190

90x21=1890

1890+1190=3080

90’s are the low speaker docks, and 170’s are the high speaker docks.

3 times 90 is 270, plus 170 is 440

3080 divided by 440 is 7, the number of 170’s they sold. 7 times 3 is 21, the number of 90’s they sold.

Answer:

The answer should become clearer once we convert everything to a common denominator:

14/15,12/15,10/15,8/15

We can now see we have an arithmetic sequence with common difference 2/5. The next term is thus

6/15=2/5

2/5 is the answer

Answer:

2/5

Step-by-step explanation:

because I someone didn't let me solve it the way I normally do;

you need to convert all of them to a common denominator;

making them [tex]\frac{14}{15}[/tex], [tex]\frac{12}{15}[/tex], [tex]\frac{10}{15}[/tex], [tex]\frac{8}{15}[/tex]

making the next one [tex]\frac{6}{15}[/tex] or [tex]\frac{2}{5}[/tex]

Answer:

D. 113°, Consecutive interior angles theorem.

Step-by-step explanation:

We use the interior angle theorem which states that when 2 lines are parallel and are intersected by a transversal, the interior angles on one side add up to 180°

67° and angle 2 are therefore supplementary angles.

67+ angle2=180°

angle2= 180-67 =113°

Answer:

2 is the only even prime number.

Step-by-step explanation:

Two is the only even prime number. It's the only even number that can be divided by only itself (2) and one.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The number is 80

Step-by-step explanation:

The question in English is

The excess of one number over 20 equals three quarters of the same number. What is the number?

Let

x ------> the number

we know that

The linear equation that represent this situation is

[tex]x-20=\frac{3}{4}x[/tex]

Solve for x

[tex]x-\frac{3}{4}x=20[/tex]

[tex]\frac{1}{4}x=20[/tex]

[tex]x=80[/tex]

therefore

The number is 80

Answer:

Option D (4, -5)

Step-by-step explanation:

This question can be solved by various methods. I will be using the hit and trial method. I will plug in all the options in the both the given equations and see if they  balance simultaneously.

Checking Option 1 by plugging (-4, -5) in the first equation:

-2(-4) + 6(-5) = -38 implies 8 - 30 = -38 (not true).

Checking Option 2 by plugging (-5, 4) in the first equation:

-2(-5) + 6(4) = -38 implies 10 + 24 = -38 (not true).

Checking Option 3 by plugging (1, -6) in the second equation:

3(1) - 4(-6) = 32 implies 3 + 24 = 32 (not true).

Since all the options except Option 4 have been ruled out, therefore, (4,-5) is the correct answer!!!

Answer:

Step-by-step explanation:

the curve is representing the projectile. at t=0, the projectile is on the ground.  at t=6, the projectile has finished its journey and is back on the ground.  In between t=0 and t=6 will be the projectile's peak altitude.  the point between t=0 and t=6 is t=3.  So plug in t=3 and solve for s(t), and you get 36ft.  gg

In the given Angles and Rays question, Based on the given diagram descriptions, the correct answers are ray AB, ∠DCE, and ray CE.  Therefore, the correct options are: B. ∠DCE, C. ray AB, D. ray CE.

The given question seems to be talking about geometric figures involving rays and angles. From the description, we know that there are two diagrams. The first diagram contains a ray namely AB and the second diagram contains two rays namely CD and CE forming angle DCE at common point C.

Based on the given information, Ray AB is correct because it's mentioned explicitly in first diagram. Angle DCE, represented as ∠DCE, is also correct as it has been stated to exist in the problem description within the second diagram. Lastly, ray CE is a legitimate answer as it is a fundamental part of the second figure forming an angle with ray CD at point C.

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Answer:

Step-by-step explanation:

14n+6p-8n=18p

6n=12p

n=2p

Answer:

Step-by-step explanation:

[tex]14n+6p-8n=18p\qquad\text{combine like terms}\\\\(14n-8n)+6p=18p\qquad\text{subtract}\ 6p\ \text{from both sides}\\\\6n=12p\qquad\text{divide both sides by 6}\\\\n=2p[/tex]

The hexagon is made up of two trapezoids, each having the following dimensions:

[tex]a=12\text{ m}\\b=5\text{ m}\\h=4\text{ m}[/tex]

So, its total area is the sum of the areas of those two trapezoids.

[tex]A_h=2A_t=2\cdot\dfrac{1}{2}(a+b)h=(a+b)h\\A_h=(12+5)\cdot 4=68\text{ m}^2[/tex]

The value of x = -1

The value of y = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be A

The value of A is

y = 3x - 2   be equation (1)

Let the second equation be B

The value of B is

x - y = 4   be equation (2)

On simplifying equation (2) , we get

Adding y on both sides of the equation , we get

x = y + 4   be equation (3)

Substituting the value of x in equation (1) , we get

y = 3x - 2

y = 3 ( y + 4 ) - 2

y = 3y + 12 - 2

y = 3y + 10

Subtracting y on both sides of the equation , we get

2y + 10 = 0

Subtracting 10 on both sides of the equation , we get

2y = -10

Divide by 2 on both sides of the equation , we get

y = -5

Substitute the value of y in equation (3) , we get

x = y + 4

x = -5 + 4

x = -1

Therefore , the value of x is -1 and the value of y is -5

Hence , The value of x = -1

The value of y = -5

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Final answer:

To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.

Explanation:

To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.

Step 1: Isolate y in the first equation.

We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.

Step 2: Substitute y into the second equation.

Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.

Step 3: Solve for x.

Now, we simplify and solve for x:

x - 3x + 2 = 4

-2x + 2 = 4

-2x = 4 - 2

-2x = 2

x = -1

Step 4: Substitute x back into the first equation to solve for y.

Using x = -1 in the first equation y = 3x - 2, we get:

y = 3(-1) - 2

y = -3 - 2

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

53.06°

Step-by-step explanation:

In triangle ABC, since ∠CAB is 90 degree, therefore consider AB to be the opposite and AC be the adjacent.

Now to find the angle, ∠ACB using trigonometry,

tan θ = opposite / adjacent

tan θ = AB / AC

given AC = 6 and AB = 8

tan θ = 8 / 6

tan θ = 1.33

therefore, θ = [tex]tan^{-1}[/tex] 1.33

                 θ = 53.06°

Therefore, the bearing from post C to post B is 53.06°

Answer:

28

Step-by-step explanation:

Substitute 8 for x in g(x) = 5x - 12:

g(8) = 5(8) - 12 = 28

By using PEDMAS rule, g(8) = 28

PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.

Given

g(x) = 5x - 12

Substitute x = 8

g(8) = [tex]5\times 8-12[/tex]

Calculate the product

g(8) = [tex]40-12[/tex]

Calculate the sum or difference

g(8) = 28

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Answer:

15.1792 or 15.18

Step-by-step explanation:

14.32 timex 6% or .06 is 0.8592. You add .8592 to 14.32 and get 15.1792 or 15.18 :)

Answer:

$15.18

Step-by-step explanation:

To find the sales tax, you would multiply $14.32 by 6%.

6% = 0.06

0.06*14.32 =  0.8592

Then add the sales tax to the original price to find how much the total costs.

0.8592 + $14.32 = $15.1792

Round $15.1792 to the nearest cent since its money.

So its $15.18

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

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

[tex]y\leq-2x+10[/tex]

Draw the solid line [tex]y=-2x+10[/tex].

Shade region below the line.

for x = 5

[tex]y=-2(5)+10=-10+10=0\to(5,\ 0)[/tex]

for x = 0

[tex]y=-2(0)+10=0+10=10\to(0,\ 10)[/tex]

[tex]y>\dfrac{1}{2}x-2[/tex]

Draw the dotted line [tex]y=\dfrac{1}{2}x-2[/tex]

Shade region above the line.

for x = 0

[tex]y=\dfrac{1}{2}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 4

[tex]y=\dfrac{1}{2}(4)-2=2-2=0\to(4,\ 0)[/tex]

Look at the picture

The solutions: A, C, D, K

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{6}{ h},\stackrel{-1}{ k})\qquad \qquad radius=\stackrel{4}{ r} \\\\[-0.35em] ~\dotfill\\[1em] [x-6]^2+[y-(-1)]^2=4^2\implies (x-6)^2+(y+1)^2=16 \\\\\\ \stackrel{\mathbb{F~O~I~L}}{(x^2-12x+36)}+\stackrel{\mathbb{F~O~I~L}}{(y^2+2y+1)}=16\implies x^2+y^2-12x+2y+37=16 \\\\\\ x^2+y^2-12x+2y+37-16=0\implies x^2+y^2-12x+2y+21=0[/tex]

ANSWER

Option A

EXPLANATION

When a circle has it's center at (h,k) and and radius r units, then its equation in standard form is

[tex] {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]

The given circle has its center at (6,-1) and its radius is r=4 units.

We plug in these values to get

[tex]{(x - 6)}^{2} + {(y - - 1)}^{2} = {4}^{2} [/tex]

[tex]{(x - 6)}^{2} + {(y + 1)}^{2} =16[/tex]

We now expand to obtain

[tex] {x}^{2} - 12x + 36 + {y}^{2} + 2y + 1 = 16[/tex]

[tex] {x}^{2} + {y}^{2} - 12x +2 y + 36 + 1 - 16 = 0[/tex]

[tex]{x}^{2} + {y}^{2} - 12x +2 y + 21 = 0[/tex]

This is the equation in general form of the circle.