the vertex of this parabola is at (5,-4). which of the following could be its equation?

Answer:

  d.  x-intercept: (-15/7,0); y-intercept: (0, -15)

Step-by-step explanation:

I find it convenient to start with the equation in standard form:

  7x + y = -15 . . . . . . use y = g(x); add 7x to both sides

Now, you can ...

  → find the x-intercept by setting y to zero and dividing by the x-coefficient.

  x = -15/7

  → find the y-intercept by setting x to zero and dividing by the y-coefficient.

  y = -15

The x- and y-intercepts for the function g(x) are (-15/7, 0) and (0, -15).

Answer:

Step-by-step explanation:

x-intercept is for y = 0

y-intercept is for x = 0

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

We have G(x) = -7x - 15 → y = -7x - 15

x-intercept:

-7x - 15 = 0      add 15 to both sides

-7x = 15      divide both sides by (-7)

x = - 15/7 → (- 15/7, 0)

y-intercept:

y = -7(0) - 15

y = 0 - 15

y = -15 → (-15, 0)

Answer:

Her total run is 0.81 miles.

Step-by-step explanation:

Consider the provided information.

The provided information can be visualized by the figure 1.

The path she covers represent a right angle triangle, where the length of two legs are given as 0.19 and 0.28.

Use the Pythagorean theorem to find the length of missing side.

[tex]a^2+b^2=c^2[/tex]

Where, a and b are the legs and c is the hypotenuse of the right angle triangle.

The provided lengths are 0.19 and 0.28.

Now, calculate the missing side.

[tex](0.19)^2+(0.28)^2=(c)^2[/tex]

[tex]0.0361+0.784=(c)^2[/tex]

[tex]0.1145=c^2[/tex]

[tex]\sqrt{0.1145}=c[/tex]

[tex]c\approx{0.34}[/tex]

Thus, the total distance is:

0.34 + 0.19 + 0.28 = 0.81

Therefore, her total run is 0.81 miles.

Answer:

about 0.81 miles

Step-by-step explanation:

Alyssa's route can be considered a right triangle with legs of length 19 and 28 (hundredths). The Pythagorean theorem tells us the hypotenuse (x) will satisfy ...

x^2 = 19^2 +28^2

x^2 = 1145

x = √1145 ≈ 34 . . . . hundredths of a mile

Then Alyssa's total route is ...

0.19 + 0.28 + 0.34 = 0.81 . . . . miles

Answer:

This conduit fill table is used to determine how many wires can be safely put in conduit tubing.The rows going across is the size of the conduit and the type. The columns going down shows the gauge of wire that is being used. The results are the numbers of wires of that gauge, that can be run through that size, of that kind of conduit such as EMT, IMC, and galvanized pipe. This chart is based on the 2017 NEC code.

Step-by-step explanation:

Answer:

The correct answer option is B. 1/5.

Step-by-step explanation:

We are given four fractions in the answer options and we are to determine whether which one of them has terminating decimal as its decimal expansion.

Terminating decimal means a decimal value which has a finite amount of numbers and has an end to it.

[tex]\frac{1}{3} = 0.333333333[/tex]

[tex]\frac{1}{5} = 0.2[/tex]

[tex]\frac{1}{7} = 0.142357142[/tex]

[tex]\frac{1}{9} = 0.111111111[/tex]

Therefore, the correct answer is 1/5.

Answer:

C and D

Step-by-step explanation:

The quadratic formula is

x= (-b±√b²-4ac)/2a

The formula uses the numerical coefficients in the quadratic equation.

The general quadratic equation is ax²+bx+c where a, b and c are the numerical coefficients

So, lets try and see;

A.

[tex]5x+4=3x^4-2\\\\=3x^4-5x-2-4\\=3x^4-5x-6\\a=3,b=-5,c=-6[/tex]

But due to the fact that  in this equation you have x⁴, the equation is not a quadratic equation thus can not be solved using this formula

B

[tex]-x^2+4x+7=-x^2-9\\\\\\=-x^2+x^2+4x+7+9\\=4x+16[/tex]

C

[tex]9x+3x^2=14+x-1\\\\\\=3x^2+9x-x-14+1\\\\=3x^2+8x-13\\\\\\a=3,b=8,c=-13\\[/tex]

D.

[tex]2x^2+x^2+x=30\\\\\\=3x^2+x-30\\\\\\a=3,b=1,c=-30[/tex]

From the checking above, the equations will be C and D

Answer:

Option C and D

Step-by-step explanation:

To find : After being rearranged and simplified, which of the following equations could  be solved using the quadratic formula? Check all that apply.

Solution :

Quadratic equation is [tex]ax^2+bx+c=0[/tex] with solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

A. [tex]5x+4=3x^4-2[/tex]

Simplifying the equation,

[tex]3x^4-2-5x-4=0[/tex]

[tex]3x^4-5x-6=0[/tex]

It is not a quadratic equation.

B. [tex]-x^2+4x+7=-x^2-9[/tex]

Simplifying the equation,

[tex]-x^2+4x+7+x^2+9=0[/tex]

[tex]4x+16=0[/tex]

It is not a quadratic equation.

C. [tex]9x + 3x^2 = 14 + x-1[/tex]

Simplifying the equation,

[tex]3x^2+9x-x-14+1=0[/tex]

[tex]3x^2+8x-13=0[/tex]

It is a quadratic equation where a=3, b=8 and c=-13.

[tex]x=\frac{-8\pm\sqrt{8^2-4(3)(-13)}}{2(3)}[/tex]

[tex]x=\frac{-8\pm\sqrt{220}}{6}[/tex]

[tex]x=\frac{-8+\sqrt{220}}{6},\frac{-8-\sqrt{220}}{6}[/tex]

[tex]x=1.13,-3.80[/tex]

D. [tex]2x^2+x^2+x=30[/tex]

Simplifying the equation,

[tex]3x^2+x-30=0[/tex]

It is a quadratic equation where a=3, b=1 and c=-30.

[tex]x=\frac{-1\pm\sqrt{1^2-4(3)(-30)}}{2(3)}[/tex]

[tex]x=\frac{-1\pm\sqrt{361}}{6}[/tex]

[tex]x=\frac{-1+19}{6},\frac{-1-19}{6}[/tex]

[tex]x=3,-3.3[/tex]

Therefore, option C and D are correct.

Check the picture below.

the first one is simply a serie, using the previous term - 3 times the one after it.

the second one is just an arithmetic sequence, where you add the previous term plus the ordinal position.

the third one is also an arithmetic sequence, simply adding the previous term with 1.4.

recall that an arithmetic sequence is adding up, a geometric sequence is multiplying about.

Answer:

[tex]t=0.444\ seconds [/tex]

Step-by-step explanation:

Let

x -----> the number of objects

t ----> the time in seconds

we have

[tex]t=0.003x^{2}+0.001x[/tex]

For x=12 objects

substitute in the formula and solve for t

[tex]t=0.003(12)^{2}+0.001(12)[/tex]

[tex]t=0.444\ seconds [/tex]

To find the time to sort 12 objects, we plug x = 12 into the equation t=0.003x^2 + 0.001x to get t = 0.444 seconds.

The student has asked for the time it will take for a computer to sort 12 objects, according to the function t=0.003x^2 + 0.001x.

Step 1: Plug in the value

The first step is to plug the value x = 12 into the given equation.

t = 0.003(12)^2 + 0.001(12)

Step 2: Calculate squares and products

We calculate (12)^2 which is 144, then multiply it by 0.003, which equals 0.432.

Next, we calculate 0.001 times 12, which equals 0.012.

Step 3: Solve for t

Finally, we sum the two products: t = 0.432 + 0.012, resulting in t = 0.444 seconds.

Answer:

2.04 seconds

Step-by-step explanation:

Falling objects near the surface of the earth have an acceleration of -9.81 m/s².

Acceleration is the change in velocity over change in time:

a = (v − v₀) / t

-9.81 = (-30.0 − (-10.0)) / t

-9.81 = -20.0 / t

t = 2.04

It takes 2.04 seconds.

Answer:

117 miles

Step-by-step explanation:

First we need an equation for the situation.  The number of miles is our unknown, x.  If she is charged 18 cents per mile, that can be expressed as .18x.  The flat rate, what she is charged regardless of how many miles she drives, is 18.95.  In other words, even if she drives 0 miles, she is still charged 18.95 for the rental of the car.  C(x) is the amount she will pay after the flat rate plus the number of miles she drives.  Therefore, our equation is:

C(x) = .18x + 18.95

If she can only spend 40, then we replace C(x) with 40 and solve for x, the number of miles:

40 = .18x + 18.95

Begin by subtracting 18.95 from both sides to get:

21.05 = .18x

Now divide both sides by .18 to get that

x = 116.9 miles

Rounding, we have that she can drive

117 miles

with the amount of money she has to spend on a rental car.

The maximum number of miles Meredith can drive without exceeding her $40 budget is 117 miles.

Total budget of Meredith on car rental = $40.

Initial charges: $18.95

Remaining budget for mileage charges: $40 - $18.95 = $21.05

Maximum number of miles = $21.05 / $0.18 per mile = 116.94 miles ≈ 117 miles

For this case we have that by definition, if two lines are parallel their slopes are equal.

The line given for the following points:

(0,3) and (3, -1). Then the slope is:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1-3} {3-0} = \frac {-4} {3} = - \frac {4} {3}[/tex]

Then, the requested line will be of the form:

[tex]y = - \frac {4} {3} x + b[/tex]

To find "b" we substitute the given point:

[tex]2 = - \frac {4} {3} (- 3) + b\\2 = 4 + b\\2-4 = b\\b = -2[/tex]

Finally, the line is:

[tex]y = - \frac {4} {3} x-2[/tex]

By manipulating algebraically we have:

[tex]y + 2 = - \frac {4} {3} x\\3 (y + 2) = - 4x\\3y + 6 = -4x\\4x + 3y = -6[/tex]

Answer:

Option D

Answer: last option.

Step-by-step explanation:

 The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

Knowing that the given line passes through the points (0,3) and (3,-1), we can find the slope:

[tex]m=\frac{-1-3}{3-0}=-\frac{4}{3}[/tex]

Since the other line is parallel to this line, its slope must  be equal:

 [tex]m=-\frac{4}{3}[/tex]

Substitute the slope and the point (-3, 2) into [tex]y=mx+b[/tex] and solve for "b":

 [tex]2=-\frac{4}{3}(-3)+b\\\\2-4=b\\\\b=-2[/tex]

Then, the equation of the other line in Slope-Intercept form is:

[tex]y=-\frac{4}{3}x-2[/tex]

Rewriting it in Standard form, you get:

[tex]y+2=-\frac{4}{3}x\\\\-3(y+2)=4x\\\\-3y-6=4x\\\\4x+3y=-6[/tex]

Answer:

My proof is in the explanation.  

Step-by-step explanation:

This is a two-column proof.

One column for statements and the other for the reason for that statement.

Hopefully it shows up well on your screen. Let me know if it doesn't.

Statement                                          |        Reason

1) CD is the perpendicular                   1) Given

bisector of AB

2) AD=DB                                              2) Definition of bisector

3) CD=CD                                              3) Reflexive property

4) mAngleCDA=90                               4) Definition of perpendicular

5) mAngleCDB=90                               5) Definition of perpendicular

6) mAngleCDA=mAngleCDB               6) Substitution property

7) Corresponding parts of each           7)  SAS

triangle are congruent                                (side-angle-side)

8) AC=CB                                               8) The two triangles are ............................................................................congruent so

                                                                   the corresponding parts ............................................................................are

                                                                   congruent.

Answer:

4x - 8

Step-by-step explanation:

Cost of producing x soccer balls = h(x) = 5x + 6 in thousands of dollars

Revenue generated from x soccer balls = k(x) = 9x - 2 in thousands of dollars

We need to calculate the profit for x soccer balls.

Profit = p (x) = Revenue - Cost

p(x) = (9x - 2) - (5x + 6)

p(x) = 9x -2 - 5x- 6

p(x) = 4x - 8

Thus the profit from x soccer balls in thousands of dollars would be 4x - 8.

Answer:4x-8

Step-by-step explanation:

Answer:

Arc length is  [tex]\frac{14\pi}{3}[/tex] ,  or,  14.7

Step-by-step explanation:

AB is an arc intercepted by 140 degree angle. The formula for length of an arc is given by

[tex]AL=\frac{\theta}{360}*2\pi r[/tex]

Where

AL is the arc length

[tex]\theta[/tex]  is the angle (in our case, 140)

r is the radius of the circle (which is 6)

Substituting, we get:

[tex]AL=\frac{\theta}{360}*2\pi r\\AL=\frac{140}{360}*2\pi (6)\\AL=\frac{7}{18}*12\pi\\AL=\frac{14\pi}{3}[/tex]

In decimal (rounded to tenths) -  14.7

Answer:

X=5, X=9

Step-by-step explanation:

The first one has two sides that are equal length, so the angles opposite of those sides are equal. This means that there are 2 73 degree angles. A triangle only had 180 degrees, so the last angle is equal to 34 degrees. When you set 6x+4=34, x is equal to 5.

The second triangle is an equilateral triangle, so every angle is equal to 60 degrees. We can set 7x-3=60. Add 3 to isolate x. 7x=63. Divide by 7 to solve for x. x=9.

Answer:

Give Zdomi Brainliest now <3

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

It doesn't make sense for either x or y to be negative because we are talking about x representing the number of acres and y representing another number of acres and that they should add up to no more than 400.

So I'm not going to look at A or C.

B looks good 250+150=400

D almost looks good 1+400=401; the problem with this answer is that is more than 400

Option B (250, 150) is the only viable solution as it adheres to the constraints of the problem, summing to exactly 400 acres with both variables being non-negative.

The farmer has set a constraint for planting peas and carrots where the total acres used for planting both cannot exceed 400 acres.

Thus, we are looking for a solution where the sum of x (acres of peas) and y (acres of carrots) must be equal to or less than 400. The solution should also satisfy the requirement that both x and y must be non-negative since you cannot plant crops on a negative amount of land.

Among the options provided, option B (250, 150) is the viable solution. Here's why:

A.) (−125, 500): We cannot have negative acres for crops, so x cannot be negative. Also, y exceeds 400 acres on its own, violating the total area constraint.

B.) (250, 150): This solution sums up to 400 acres exactly, fitting within the constraint and with both x and y being non-negative.

C.) (400, −10): y cannot be negative, representing a nonsensical scenario for planting.

D.) (1, 400): The total acreage here is 401, which exceeds the maximum allowable acreage.

Answer:

The correct answer option is b) 1.95.

Step-by-step explanation:

We are to evaluate [tex] ln 7 [/tex].

For this, we can either log in the value directly in a scientific calculator for the the given value [tex] ln 7 [/tex] and get the answer in decimals.

Another way can be to rewrite the expression as:

log to the base [tex] e [/tex] or [tex] 7 [/tex] = x

or [tex] e ^ x = 7 [/tex]

which gives x = 1.95

Answer:

30 and 150

Step-by-step explanation:

Whether these are same side interior or same side exterior, the sum of them is 180 when the angles are on the same side of a transversal that cuts a pair of parallel lines.  Let's call the angles A and B.  If angle A is 5 times smaller than angle B, then angle B is 5 times larger than angle A.  So the angles are x and 5x.  They are supplementary so

x + 5x = 180 and

6x = 180 so

x = 30 and 5(30) = 150

Answer:

140

Step-by-step explanation:

Rewording the problem will make it easier to write the equation you need to solve this. Think of it in simpler terms: "7 is 5% of how many?". "7" is just a 7; the word "is" means =; "5%" is expressed as its decimal equivalency (.05); the word "of" means to multiply; and "how many" is our unknown (x). Putting that all together in one equation looks like this:

7 = .05x

Solve for x by dividing both sides by .05 to see that

x = 140

Answer:

(x - 3)²/3² - (y + 4)²/2² = 1 ⇒ (0 , -4) , (6 , -4)

(x - 4)²/7² - (y + 6)²/5² = 1 ⇒ (-3 , -6) , (11 , -6)

(y + 5)²/5² - (x - 4)²/8² = 1 ⇒ (4 , 0) , (4 , -10)

(y + 7)²/7² - (x + 2)²/4² = 1 ⇒ (-2 , 0) , (-2 , -14)

(x + 1)²/9² - (y - 1)²/11² = 1 ⇒ (8 , 1) , (-10 , 1)

Step-by-step explanation:

* Lets revise the standard form of the equations of the hyperbola

- The standard form of the equation of a hyperbola with  center (h , k)

 and transverse axis parallel to the x-axis is  (x - h)²/a² - (y - k)²/b² = 1

- The coordinates of the vertices are (h ± a , k)

- The standard form of the equation of a hyperbola with center (h , k)

 and transverse axis parallel to the y-axis is  (y - k)²/a² - (x - h)²/b² = 1

- The coordinates of the vertices are (h , k ± a)

* Lets solve the problem

# (x - 3)²/3² - (y + 4)²/2² = 1

∵ (x - h)²/a² - (y - k)²/b² = 1

∴ a = 3 , b = 2 , h = 3 , k = -4

∵ The coordinates of the vertices are (h ± a , k)

∴ The coordinates of the vertices are (3 - 3 , -4) , (3 + 3 , -4)

∴ The coordinates of the vertices are (0 , -4) , (6 , -4)

* (x - 3)²/3² - (y + 4)²/2² = 1 ⇒ (0 , -4) , (6 , -4)

# (y - 1)²/2² - (x - 7)²/6² = 1

∵ (y - k)²/a² - (x - h)²/b² = 1

∴ a = 2 , b = 6 , h = 7 , k = 1

∵ The coordinates of the vertices are (h , k ± a)

∴ The coordinates of the vertices are (7 , 1 - 2) , (7 , 1 + 2)

∴ The coordinates of the vertices are (7 , -1) , (7 , 3)

* No answer for this equation

# (x - 4)²/7² - (y + 6)²/5² = 1

∵ (x - h)²/a² - (y - k)²/b² = 1

∴ a = 7 , b = 5 , h = 4 , k = -6

∵ The coordinates of the vertices are (h ± a , k)

∴ The coordinates of the vertices are (4 - 7 , -6) , (4 + 7 , -6)

∴ The coordinates of the vertices are (-3 , -6) , (11 , -6)

* (x - 4)²/7² - (y + 6)²/5² = 1 ⇒ (-3 , -6) , (11 , -6)

# (y + 5)²/5² - (x - 4)²/8² = 1

∵ (y - k)²/a² - (x - h)²/b² = 1

∴ a = 5 , b = 8 , h = 4 , k = -5

∵ The coordinates of the vertices are (h , k ± a)

∴ The coordinates of the vertices are (4 , -5 + 5) , (4 , -5 - 5)

∴ The coordinates of the vertices are (4 , 0) , (4 , -10)

* (y + 5)²/5² - (x - 4)²/8² = 1 ⇒ (4 , 0) , (4 , -10)

# (y + 7)²/7² - (x + 2)²/4² = 1

∵ (y - k)²/a² - (x - h)²/b² = 1

∴ a = 7 , b = 4 , h = -2 , k = -7

∵ The coordinates of the vertices are (h , k ± a)

∴ The coordinates of the vertices are (-2 , -7 + 7) , (-2 , -7 - 7)

∴ The coordinates of the vertices are (-2 , 0) , (-2 , -14)

* (y + 7)²/7² - (x + 2)²/4² = 1 ⇒ (-2 , 0) , (-2 , -14)

# (x + 1)²/9² - (y - 1)²/11² = 1

∵ (x - h)²/a² - (y - k)²/b² = 1

∴ a = 9 , b = 11 , h = -1 , k = 1

∵ The coordinates of the vertices are (h ± a , k)

∴ The coordinates of the vertices are (-1 + 9 , 1) , (-1 - 9 , 1)

∴ The coordinates of the vertices are (8 , 1) , (-10 , 1)

* (x + 1)²/9² - (y - 1)²/11² = 1 ⇒ (8 , 1) , (-10 , 1)

Answer:

(x - 3)²/3² - (y + 4)²/2² = 1 ⇒ (0 , -4) , (6 , -4)

(x - 4)²/7² - (y + 6)²/5² = 1 ⇒ (-3 , -6) , (11 , -6)

(y + 5)²/5² - (x - 4)²/8² = 1 ⇒ (4 , 0) , (4 , -10)

(y + 7)²/7² - (x + 2)²/4² = 1 ⇒ (-2 , 0) , (-2 , -14)

(x + 1)²/9² - (y - 1)²/11² = 1 ⇒ (8 , 1) , (-10 , 1)

The price per pound of apples and cherries can be calculated using a system of linear equations. This is based on the given information about how much Frederick and Wilhelmina spent on these fruits at the farmers' market.

In order to find the price per pound of apples and cherries at the farmers' market, we will use a system of linear equations. We can assume the price per pound of apples is A and the price per pound of cherries is C. Frederick's purchases can be represented as 4A + 15C = 36.93 and Wilhelmina's purchases can be represented as 12A + 9C = 30.51. By using these equations, we can solve for A and C using any method you are comfortable with, such as substitution or elimination.

Note: The information regarding fruit consumption in 2001 and the cost calculation methodology is not directly relevant to the main question, but it provides a context of fun facts.

https://brainly.com/question/34783456

#SPJ2

Answer:

Quadratic formula:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

Step-by-step explanation:

If you want to solve something that looks like [tex]ax^2+bx+c=0[/tex], the answer will have this form [tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].

This is called the quadratic formula.

Answer:

The length of this altitude is 5 cm.

Step-by-step explanation:

The length of the altitude = ?

Given the diagonal forms the altitude of the parallelogram. The figure is shown in image.

Given

The perimeter of the parallelogram = 50 cm

The length of one side is 1 cm longer than the length of the other.

Thus,

Let one side (a) is x cm, The other side (b) be (x + 1) cm

Perimeter of parallelogram = 2(a + b) = 2(x +(x + 1)) = 4x + 2 = 50 cm

Thus,

x = AB = CD = 12 cm

x + 1 = BC = AD = 13 cm

Using Pythagorean theorem to find the length of the altitude as:

ΔABC is a right angle triangle.

AB² + AC² = BC²

AC² = 13² - 12² = 5 cm

The length of this altitude is 5 cm.

To solve the problem we will substitute the value of x and C in the given function.

Given to us

The cost​ C, in​ dollars, of renting a moving truck for a day C(x)=0.20x+45,

To find the cost if a person drives x=160 ​miles, simply substitute the value of x in the function of cost c,

[tex]C(x)=0.20x+45\\\\C(160)=0.20(160)+45\\\\C(160)=77[/tex]

Hence, the cost of the moving truck if a person drives x=160 ​miles is $77.

To solve the problem substitute the value of C as 120 in the given function,

[tex]C(x)=0.20x+45\\\\120 = 0.20x+45\\\\x = 375\rm\ miles[/tex]

Hence, If the cost of renting the moving truck is ​$120​, the person​ drives 375 miles.

To solve the problem substitute the value of C as 200 in the given function,

[tex]C(x)=0.20x+45\\\\200 = 0.20x+45\\\\x = 775\rm\ miles[/tex]

Hence, if a person wants the cost to be no more than ​$200. The maximum number of miles a person can​ drive is 775.

Implied Domain is the value of C for which it is defined, since even if the truck is not moving a single mile it will still be costing $45, to a person, therefore, the domain of C is [45, +∞].

If we look at the function it is a function of line therefore, the comparing the two equations,

[tex]y = mx+c\\C=0.20x+45[/tex]

we know that m is the slope of the function,

m = 0.20

therefore, the slope of the function is 0.20.

We know that the intercept of y is the value of y at which it intersect the y axis.

when we put the value of x=0, we get the value of y as 45, therefore, the intercept of y is 45.

Hence, the intercept of y is 45.

Learn more about Line:

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Answer:

=49.15 cm²

Step-by-step explanation:

To find the area of the triangle we use the sine formula

A= 1/2ab Sin∅

where A is the area a and b are the lengths of two sides that intersect at a point and ∅ is the angle between them.

a=10 cm

b= 12 cm

∅=55°

A= 1/2×10×12×Sin 55

=49.15 cm²

ANSWER

[tex]Area =49.1 {cm}^{2} [/tex]

EXPLANATION

The area of triangle given included angle and length of two sides can be calculated using the formula:

[tex]Area = \frac{1}{2} ab \sin(C) [/tex]

Where C=55° is the included angle and a=12 cm , b=10cm are the known sides.

We plug in these values into the formula to get,

[tex]Area = \frac{1}{2} \times 12 \times 10 \sin(55 \degree) [/tex]

[tex]Area =49 .14912266[/tex]

Rounding to the nearest tenth, the area is

[tex]Area =49.1 {cm}^{2} [/tex]

Answer:

[tex]4^x-5=6[/tex] gives the solution [tex]x=\frac{\log(11)}{\log(4)}[/tex].

[tex]4^{x-5}=6[/tex] gives the solution [tex]x=\frac{\log(6)}{\log(4)}+5[/tex].

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is [tex]4^{x}-5=6[/tex], then the following is the process:

[tex]4^x-5=6[/tex]

Add 5 on both sides:

[tex]4^x=6+5[/tex]

Simplify:

[tex]4^x=11[/tex]

Now write an equivalent logarithm form:

[tex]\log_4(11)=x[/tex]

[tex]x=\log_4(11)[/tex]

Now using the change of base:

[tex]x=\frac{\log(11)}{\log(4)}[/tex].

If we assume the equation is [tex]4^{x-5}=6[/tex], then we use the following process:

[tex]4^{x-5}=6[/tex]

Write an equivalent logarithm form:

[tex]\log_4(6)=x-5[/tex]

[tex]x-5=\log_4(6)[/tex]

Add 5 on both sides:

[tex]x=\log_4(6)+5[/tex]

Use change of base formula:

[tex]x=\frac{\log(6)}{\log(4)}+5[/tex]

Answer:

6.292

Step-by-step explanation:

I got it right on the test.

Answer:

The loan will cost you 2000 dollars more.

Step-by-step explanation:

If you pay 200 per month for 60 months, then you are paying 200(60) after the 60 months.

200(60)=12000.

So the loan will cost you 12000.

The difference between paying 12000 and 10000 is 2000.

The loan will cost you 2000 dollars more.

Answer:

D. 6

Step-by-step explanation:

The result of 20 rolls in given in the statement we have to find how many times did the roll resulted in a result greater than the average number. So first we have to find the average of the 20 rolls.

The formula for the average is:

[tex]\frac{\text{Sum of observations}}{\text{Total number of observations}}[/tex]

So, the formula for the given case will be:

[tex]Average = \frac{\text{Sum of results of 20 rolls}}{20}\\\\ = \frac{60}{20}\\\\ =3[/tex]

Thus, the average result from the 20 rolls is 3. Now we have to look for values greater than 3 in the rolls. These are:

6, 4, 5, 4, 5, 6

So, 6 values in total are greater than 3.

Hence, Gabe rolled 6 times above average.

Answer:

the coordinates of C' = (2,1)

Step-by-step explanation:

The coordinates of point C can be found by looking at the graph.

Coordinates of C are C= (6,3)

If ABCD is dilated by a factor of 1/3 then the coordinates of C' can be found by multiplying the coordinates of C by 1/3

C = (6,3)

C' =(1/3*6,1/3*3)

C' = (2,1)

So, the coordinates of C' = (2,1)

Answer:

1/258 *(t^28)

= t^28 / 4^4

= t^28 4^-4

= (t^-7 * 4)^-4

= (4t^-7)^-4

Step-by-step explanation:

Answer:

so the answer is d

Step-by-step explanation: