Daisy wants to buy a car battery that has a full price of $85 plus a 6% sales tax, which is the better offer, a 20%-off sale or a $15 coupon?

[tex]\left\{\begin{array}{ccc}y=6x+2&(*)\\y=x+17&(**)\end{array}\right\\\\\text{Substitute}\ (*)\ \text{to}\ (**):\\\\6x+2=x+17\qquad\text{subtract 2 from both sides}\\6x=x+15\qquad\text{subtract x from both sides}\\5x=15\qquad\text{divide both sides by 5}\\\boxed{x=3}\\\\\text{Put the value of x to the second equation}:\\\\y=3+17\\\boxed{y=20}\\\\Answer:\ \boxed{D.\ (3,\ 20)}[/tex]

Answer:

D ( 3, 20 )   For A pex

Step-by-step explanation:

Answer: choice A. 40 liters

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

Explanation:

x = number of liters of the 50% alcohol solution

If we have x liters of 50% alcohol, then we have 0.50*x liters of pure alcohol. This is added to 0.90*40 = 36 liters of pure alcohol (from the 90% solution).

So far we have 0.50*x + 36. This expression represents the total amount of pure alcohol. We want a 70% solution, so we want 70% of the total 40+x meaning 0.50*x + 36 is to be set equal to 0.70*(40+x) and we solve for x as shown below

0.50*x + 36 = 0.70*(40+x)

0.50*x + 36 = 0.70*(40)+0.70*(x)

0.50*x + 36 = 28+0.70*x

36 - 28 = 0.70*x - 0.50x

8 = 0.20x

0.20x = 8

x = 8/0.20

x = 40

So that is why the answer is choice A. 40 liters

Answer: 6

The remainder theorem says that if we divide p(x) over x-k, then the remainder is r = p(k)

In this case, we have p(x) = x^2+5 and x-k = x+1 = x-(-1). So k = -1 is plugged into p(x) to get

p(x) = x^2+5

p(-1) = (-1)^2+5

p(-1) = 1+5

p(-1) = 6

That is why the remainder is 6. You can use polynomial long division or synthetic division to confirm this answer.

Answer:

The remainder would be 6.

Step-by-step explanation:

the answer is 9x(to the power of 2)−42x+49

Answer:

1st)  geometric

2nd)  arithmetic

3rd)  arithmetic

Step-by-step explanation:

Geometric = you multiply or divide to get the next term

Arithmetic = you add or subtract to get the next term

1st)  you times by 3 to get next term = geometric

2nd)  you add one to get next terms = arithmetic

3rd) you add 4 to get next term = arithmetic

Answer:

Answer in simplified form is:

(sinФ - cosФ)² + (sinФ + cosФ)² = 2

Step-by-step explanation:

Given,

(sinФ - cosФ)² + (sinФ + cosФ)²

This can be simplified as:

(sin²Ф + cos²Ф - 2sinФcosФ) + (sin²Ф + cos²Ф +2sinФcosФ)

We know that : sin²Ф + cos²Ф = 1

So,

( 1 - 2sinФcosФ) + (1 + 2sinФcosФ)

or 1 + 1 -2sinФcosФ + 2sinФcosФ

or 2

Hence we got  (sinФ - cosФ)² + (sinФ + cosФ)² = 2

Answer:

32

Step-by-step explanation:

XY means x times y

and x = 8 or x is 8

and y = 4 or y is 4

so 4 times 8 is 32

so

XY = 32

Answer:

x = 15

Step-by-step explanation:

The segment that is x units long is the midsegment of the largest triangle. The midsegment is half as long as the line parallel to the midsegment. It is half as long as the 30 unit long segment.

Note how the vertical sides (marked with the double tickmarks) are congruent to one another. The smaller pieces are both the same length, so they combine to something twice as big. Go in reverse: one segment with a pair of double tickmarks is exactly half as long as the entire vertical side. The same can be said about the horizontal sides as well.

Answer: Alternate Interior Angles Theorem (choice B)

If you have two parallel lines, and cut them with a third line, then you'll form two pairs of alternate interior angles. Alternate interior angles are angles that that are on the inside of the parallel "train tracks", but they are on opposite sides of the transversal line.

[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\\text{We have}\ f(x)=x+7\ \text{and}\ g(x)=\dfrac{1}{x-13}.\\\\\text{Substitute}\\\\(f\cdot g)(x)=(x+7)\cdot\dfrac{1}{x-13}=\dfrac{x+7}{x-13}\\\\\text{The domain:}\\\\x-13\neq0\qquad\text{add 13 to both sides}\\\\x\neq13\\\\Answer:\ \boxed{x\in\mathbb{R}-\{13\}}\to\boxed{\text{All real numbers except 13}}[/tex]

Answer:

I do believe the radius of P is PN

Question

What is radius of circle P?

Answer:

Step-by-step explanation:

MN is the diameter, so half diameter is the radius, PN is your answer (remember that PM is also a radius)

Answer:

-1.5, -1.6, -1.7, -1.8, -1.9

Step-by-step explanation:

A rational number is a number that can be written as the ratio of two integers.

-1.5 is a rational number between -2 and -1

-1.5  can be written as -15/10

-1.6  is a rational number between -2 and -1

-1.6 can be written as -16/10

1.7  is a rational number between -2 and -1

-1.7 can be written as -17/10

1.8  is a rational number between -2 and -1

-1.8 can be written as -18/10

1.9  is a rational number between -2 and -1

-1.9 can be written as -19/10

Final answer:

The unit rate of 2134 meters in 212 hours is approximately 10.063 meters per hour. This calculation involves dividing the total distance by the total amount of time.

Explanation:

To find the unit rate of 2134 meters in 212 hours, we need to calculate how many meters are covered in one hour. The unit rate is computed by dividing the total distance by the total time.

The calculation is as follows:

Unit rate = Total distance / Total time

Unit rate = 2134 meters / 212 hours

Calculating this gives us a unit rate of approximately 10.063 meters per hour. It's important to make sure that the result is reasonable. If you travel a certain distance in a given number of hours, dividing the distance by the time should give you how many meters you travel in one hour, which in this case, it does.

9.915 mi and that's all and that helped friend me please thanks stay pretty

Answer:

9.91 miles

Step-by-step explanation:

Refer the attached figure

Forest Ranger at point A observes the fire at angle of 41° north of east i.e.∠CAB = 41°

The distance between the two rangers is 15 miles i.e. AB = 15 miles

Forest Ranger at point B observes the fire at at 56° north of west. i.e.∠CBA= 56°

Now we are supposed to find who is closest to the fire

So, we are supposed to find the length of AC and BC

So, first calculate ∠ACB

We will use angle sum property of triangle

Angle  sum property of triangle  : Sum of all angles of triangle is 180°

So, ∠CBA+∠ACB+∠CAB =180°

56°+∠ACB+41° =180°

97°+∠ACB =180°

∠ACB =180°-97°

∠ACB =83°

Now to find  AC and BC we will use law of sines

[tex]\frac{a}{sin A}=\frac{b}{Sin B}=\frac{c}{SinC}[/tex]

Refer the attached figure

[tex]\frac{AC}{sin 56}=\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

So, [tex]\frac{BC}{Sin 41}=\frac{15}{Sin83}[/tex]

[tex]BC=\frac{15}{Sin83} \times Sin 41[/tex]

[tex]BC=9.91478[/tex]

[tex]\frac{AC}{sin 56}=\frac{15}{Sin83}[/tex]

[tex]AC=\frac{15}{Sin83} \times sin 56[/tex]

[tex]AC=12.5289[/tex]

So, BC< AC

So, the ranger who is closest to fire is at a distance of 9.91 miles .

So, Option 1 is true

Answer:

the answer is:

b

d

e

Functions are used to show relationships between variables. The true statements are:

I've added as an attachment, the table of values of f(x)

Next, we test the given options

(a) f(x) > 0 over the interval ([tex]-\infty[/tex], 3).

Using the table of f(x), the values in ([tex]-\infty[/tex], 3) are values less than 3; i.e. -3 to 2.

If f(2) = 0, then f(x) > 0 is not true

(b) f(x) ≤ 0 over the interval [0, 2].

The values in [0, 2] are values from 0 to 2; i.e. 0, 1 and 2.

If f(0) = 0, f(1) = -3 and f(2) = 0

Then, f(x) ≤ 0

(c) f(x) < 0 over the interval (−1, 1).

Using the table of f(x), the values in (-1, 1) are values between -1 and 1; i.e. 0

If f(0) = 0, then f(x) < 0 is not true

(d) f(x) > 0 over the interval (–2, 0).

Using the table of f(x), the values in (-2, 0) are values between -2 and 0; i.e. -1

If f(-1) = 3, then f(x) > 0 is true

(e) f(x) ≥ 0 over the interval [2, [tex]\infty[/tex])

Using the table of f(x), the values in [2, [tex]\infty[/tex]) are values from 2; i.e. 2 and 3

If f(2) = 0 and f(3) = 15, then f(x) ≥ 0  is true

Hence, the true statements are:

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Answer: slope is 5 and y-intercept is 15

Step-by-step explanation:

you pay 5 dollars each hour or whatever the time is and have to pay $15 to get in the cab. So the $15 is a must pay.

Answer:

You pay $5\time and must pay $15 to ride in it.

Answer:

51869 ft

Step-by-step explanation:

If he climbed both mountains, then we add the heights together

22834 + 29035

51869 ft

Answer:

51,869 ft

Step-by-step explanation:

Add the two heights.

22,834 ft + 29,035 ft = 51,869 ft

Answer:

First of all, I expect you fulfill your word and give what you promise... ha ha just kidding, I already solved a question like this one, please see below explanation.

1. Tessellation is the covering of a surface with pattern(s) of flat shapes so that there are no overlaps or gaps. It is also called Tiling.

2. Triangles, Squares, and Hexagons are regular polygons.

3. Previous three shapes create a regular tessellation pattern because all their sides and all their angles are the same. the intersection point of the interior angles is called "Vertex". For a regular tessellation, the pattern is identical at each Vertex.

Unlike the triangle and quadrilateral case, the Pentagon's angle sum of 540° is not helpful when trying to fit a bunch of Pentagons around a vertex. Therefore, even though the Pentagon is a regular polygon, it cannot tessellate.

4. See attached screenshot of 3 tessellations created with Tessellation Artist Software online.

Answer: 320

Step-by-step explanation:

[tex]a_n=a_1(r)^{n-1}\quad \text{where}\ a_1\ \text{is the first term, r is the ratio, n is the term}[/tex]

[tex]a_7=5(2)^{7-1}[/tex]

   [tex]=5(2)^{6}[/tex]

   [tex]=5(64)}[/tex]

   [tex]=320[/tex]

Answer:

The 7th term in Geometric Sequence is 320

Step-by-step explanation:

Given : the geometric sequence whose first term is 5 and whose common ratio is 2.

To Find : 7th term

Solution :

Using the formula of Geometric Sequence :

[tex]a_{n} =a_{1} *r^{n-1}[/tex]    --(A)

Since,

[tex]a_{1}=5[/tex]

r =2

n = 7 (term no. need to calculate)

Putting these values in ---(A)

⇒[tex]a_{7} = 5*2^{7-1}[/tex]

⇒[tex]a_{7} = 5*2^{6}[/tex]

⇒[tex]a_{7} = 5*64[/tex]

⇒[tex]a_{7} =320[/tex]

Hence the 7th term in Geometric Sequence is 320

Answer:

The period is [tex]2\pi[/tex] and the amplitude is 3.

Step-by-step explanation:

The period goes from one peak to the next (or from any point to the next matching point). The amplitude is the height from the center line to the peak.

The period of the function [tex]y=a\sin (bx)[/tex] is [tex]T=\dfrac{2\pi }{b}[/tex] and the amplitude is [tex]|a|.[/tex]

Consider the function [tex]f(t)=-3\sin t.[/tex]

The period for the function [tex]f(t)[/tex] is

[tex]T=\dfrac{2\pi}{1}=2\pi[/tex]

and the amplitude is 3.

Answer:

B & D

Step-by-step explanation:

The quadratic formula can be used to solve for x for any quadratic. Recall a quadratic is any function whose highest exponent known as degree is 2. Looking at the answer selections, A has one term with exponent 3. This isn't possible in the formula. Looking at answer C, the term with exponent 2 has the same coefficient on each side of the equal sign. When it is rearranged these will cancel out no exponent of 2 will be in the equation anymore. Only B & D work after being rearranged and simplified

The two equations after simplifying will give quadratic equations are:-

x ²-6x-7=2x² and 5x²-3x+10=2x².

The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.

Solving for the quadratic equation:-

Option B:-

x ² -   6x   -   7  =   2x²

- 2x²   +   x ² -   6x   -   7  =  0

x ²  +  6x  +  7  =  0

Option D:-

5x²   -   3x   +   10  =    2x².

5x²  -  2x². -   3x   +   10  =   0

3x²  -   3x  +  10  =  0

Therefore two equations after simplifying will give quadratic equations are- x ²-6x-7=2x² and 5x²-3x+10=2x².

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Answer:

(a)

system of equations are

[tex]s+k=425[/tex]

[tex]k-s=25[/tex]

(b)

Graph is attached

(c)

Sam earned =$200

Kevin earned =$225

Step-by-step explanation:

Let's assume

's' for the amount Sam earned

'k' for the amount Kevin earned

(a)

Together they earned a total of $425

so, we get

[tex]s+k=425[/tex]

Kevin earned $25 more than Sam

so, we get

[tex]k=s+25[/tex]

so, system of equations are

[tex]s+k=425[/tex]

[tex]k-s=25[/tex]

(b)

now, we can draw graph

(c)

intersection point will be our solution

and we got intersection point as

(200, 225)

so,

s=200

k=225

(a) The system of equations for the situation is s + k = 425 and k = s + 25.

(b) Graph these equations to find their point of intersection.

(c) Using the graph, estimate that Sam earned around $200, and Kevin earned around $225.

(a) To write a system of equations for this situation, we can use the information provided:

1. Sam and Kevin earned a total of $425, which can be expressed as:

  s + k = 425

2. Kevin earned $25 more than Sam:

  k = s + 25

So, the system of equations is:

1. s + k = 425

2. k = s + 25

(b) To graph these equations, you can rearrange them into slope-intercept form (y = mx + b), where y represents one of the variables (s or k) and x represents the other variable.

From equation 2, we can rewrite it as k = s + 25, which can be expressed as k = 1s + 25.

Now, the system is represented as:

1. s + k = 425

2. k = s + 25

You can graph these equations on a coordinate plane.

(c) Once you graph the equations, you can look for the point of intersection, which represents the solution to the system and gives you the values of s and k. The point where the two lines intersect will provide estimates for how much Sam and Kevin earned. Using the graph, estimate that Sam earned around $200, and Kevin earned around $225.

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Answer:

£120

Step-by-step explanation:

First calculate 25% of £160 then subtract this from the £160.

25% of 160 = 25/100  * 160

= 1/4 * 160 = £40.

£160 - £40  = £120  (answer).

Answer:

The answer is $120

Step-by-step explanation:

First you must find 25% of $160

First, I found out what is 25% of 16

Next, made 25% = 1/4

Then, 1/4 of 16 is also 16 divided 4 and you will get 4

Then, you add the zero on the back and make it $40

Finally, subtract 40 from 160 and that will be your answer

160 - 40 = $120

Answer:

12/24

Step-by-step explanation:

A ratio is a comparison of two quantities and can be written in several forms including fractions. It is most commonly written in fraction form or a:b.

To write a ratio, we count the number of each quantity we are comparing. The number of shaded squares is 12. While the total number of squares is 24. We write the ratio as shaded : total.

12:24 or

[tex]\frac{12}{24}[/tex] or

0.5 as a decimal.

Answer:

D, which is 7.

Step-by-step explanation:

if you notice that -2+4= 2, and 4+14= 18, you can make an educated guess.

The missing number in the given synthetic division problem is 7 hence, option (D) is correct.

The synthetic division used to divide a polynomial by any expression in that expression should be the leading coefficient as one.

Given that in problem first term has written as it is.

Then multiply 2 with 2 and add 4 with -2.

Again multiply 2 by 2 and add with 3 which gives 7.

Hence 7 will be the missing number in the given problem.

For more information about synthetic division.

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Answer: 56

Step-by-step explanation: The pattern is 8 x 3.5 = 28, 10 x 3.5 = 35, 12 x 3.5 = 42... so 16 x 3.5 = 56

Answer:

56

Step-by-step explanation:

Answer:

The equation of the line would be y = -15/24x + 6

Step-by-step explanation:

In order to find the equation of the line, you need to start by using the slope formula with the points given. This will give you the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (11 - 7/2)/(-8 - 4)

m = (15/2)/-12

m = 15/-24

m = -15/24

Now that we have the slope, we can use that and either point to find the equation in point-slope form.

y - y1 = m(x - x1)

y - 11 = -15/24(x + 8)

y - 11 = -15/24x - 5

y = -15/24x + 6

Answer:The answer on ed is y= -5/8x + 6

Step-by-step explanation:

Answer:

Associative Property of Addition.

Step-by-step explanation:

It states that no matter how the numbers are ordered, the result will be the same. Feel free to look it up on google for more information :)

Answer:

The answer is Associative Property of Addition. Hope I helped!

Answer:

the x-coordinate

Step-by-step explanation:

The slope intercept form is: y = mx + c

where m⇒ slope

          c ⇒ y-intercept

          (x,y) is a point on the graph the  satisfy the equation representing that graph.

∴ x is the x-coordinate of a point on the line.  

Answer:

25

Step-by-step explanation:

Formula

2xy + 1

Givens

x = 3

y = 4

Solve

2*(3)*(4) + 1

24 + 1

25