which of exercises 14-19 could you solve mentally​

Answer:

a) yes

b) yes

c)  days

d) equation: 18 - 0.8x =1.2

solution: 21

e)inequality: equation: 18 - 0.8x [tex]\geq[/tex]1.2

solution: x < 21. This means that if he drives for less than 21 days the warning sign won't turn on.

Step-by-step explanation:

a) 18 - 15*0.8 = 6 so yes

b) 18 - 20*0.8 = 18 - 16 = 2

d) 18 - 0.8x =1.2

0.8x = 16.8

x = 16.8/0.8 = 21

Final answer:

a. No, the car cannot go 15 days without the warning light turning on. b. No, the car cannot drive 20 days without the light coming on. c. 'T' in the expression 18 - 0.8t stands for the number of days of fuel usage. d. Diego's car can go 21 days before the warning light turns on. e. The inequality 18 - 0.8t > 1.2 represents the situation.

Explanation:

a. To determine if Diego's car can go 15 days without the warning light turning on, we need to find out how much fuel will be left after 15 days of usage. Each day the car uses 0.8 gallons of fuel, so after 15 days, the car will have used 15 * 0.8 = 12 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 15 days will be 18 - 12 = 6 gallons. Since the warning light comes on if the remaining fuel is 1.2 gallons or less, Diego's car will not be able to go 15 days without the warning light turning on.

b. To determine if Diego's car can drive 20 days without the light coming on, we follow the same steps as in part a. After 20 days, the car will have used 20 * 0.8 = 16 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 20 days will be 18 - 16 = 2 gallons. Since the remaining fuel is less than 1.2 gallons, the warning light will turn on before 20 days.

c. In the expression 18 - 0.8t, 't' represents the number of days of fuel usage.

d. To determine the number of days Diego's car can go before the warning light turns on, we need to solve the equation 18 - 0.8t = 1.2. Rearranging the equation, we have 0.8t = 18 - 1.2, which simplifies to 0.8t = 16.8. Dividing both sides by 0.8, we get t = 21. So Diego's car can go 21 days before the warning light turns on.

e. To write an inequality that represents this situation, we can say that the remaining fuel after t days should be greater than 1.2 gallons. This can be expressed as 18 - 0.8t > 1.2. Solving this inequality, we get t < 21. This means that Diego's car can go up to 20 days before the warning light turns on, but on the 21st day, the warning light will turn on.

Ken earned $128 from his part-time job and spent 25% of it, leaving him with $96. He then donated 1/6 of the remaining money to charity, which equals $16.

This problem is about percentages and fractions. Ken earned $128 from his part-time job and spent 25% of it on games, which equals <$128 * 25/100 = $32>. So after buying games, Ken is left with <$128 - $32 = $96>. Ken then decides to donate a fraction, 1/6 of the remaining money to charity. To figure out how much he donates, we multiply $96 by 1/6, which is <$96 * 1/6 = $16>. So, Ken donates $16 to charity from his summer job earnings.

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The answer is:

The area of the shape is: [tex]10units^{2}[/tex]

[tex]TotalArea=10units^{2}[/tex]

To solve the problem, we must consider that the shape is formed by two right triangles and a square, so, to calculate its area, we need to calculate the areas of the two triangles and square, and then, add them.

So, we are given the following information:

Smallest triangle:

[tex]base=2units\\height=2units[/tex]

Square:

[tex]base=2units\\height=2units[/tex]

Largest triangle:

[tex]base=4\\height=2[/tex]

Smallest triangle:

We can calculate the area of a triangle using the following formula:

[tex]A=\frac{base*height}{2}[/tex]

So, substituting, we have:

[tex]A=\frac{2units*2units}{2}=2units^{2}[/tex]

Square:

We can calculate the area of a square using the following formula:

[tex]A=base*height[/tex]

So, substituting, we have:

[tex]A=2units*2units=4units^{2}[/tex]

Largest triangle:

We can calculate the area of a triangle using the following formula:

[tex]A=\frac{base*height}{2}[/tex]

So, substituting, we have:

[tex]A=\frac{4units*2units}{2}=4units^{2}[/tex]

Now, calculating the area of the entire shape, we have:

[tex]TotalArea=SmallestTriangleArea+SquareArea+LargestTriangleArea\\\\TotalArea=2units^{2} +4units^{2} +4units^{2} =10units^{2}[/tex]

Hence, the area of the shape is: [tex]10units^{2}[/tex]

[tex]TotalArea=10units^{2}[/tex]

Have a nice day!

Answer:56

Step-by-step explanation:

Answer: 0.31

Step-by-step explanation:

7ab3

To find the GCF, find the number(s) that that have the highest multiple factor in common. The first numbers can all be divided by 7, there's 1 a in common, and 3 b's in common. Combine them since you have variables and numerical values to get 7ab3 .

The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,

⇒ 7ab³

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

We have to given that;

The numbers are,

⇒ 42a⁵b³, 35a³b⁴, and 42ab⁴

Now, We can formulate;

⇒ GCD {42, 35, 42 } = 7

⇒ GCD {a⁵, a³, a } = a

⇒ GCD {b³ , b⁴, b⁴} = b³

Thus, The greatest common factor of 42a⁵b³, 35a³b⁴, and 42ab⁴ is,

⇒ 7ab³

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[tex]\frac{21}{5}[/tex]

Start with your equation: [tex]\frac{(8 * 7) - 35}{3 + 2}[/tex]

Now, simplify the multiplication: [tex]\frac{56 - 35}{3 + 2}[/tex]

Then, simplify the addition and subtraction: [tex]\frac{21}{5}[/tex]

This fraction cannot be simplified further, so it is the answer.

Answer:

[tex]\frac{\left(\left(8x\cdot \:7\right)\right)-35}{3+2}=\frac{56x-35}{5}[/tex]

[tex]\frac{8x\cdot \:7-35}{3+2}\\\mathrm{Multiply\:the\:numbers:}\:8\cdot \:7=56; =\frac{56x-35}{3+2}\\\mathrm{Add\:the\:numbers:}\:3+2=5; =\frac{56x-35}{5}[/tex]

Hope this helps and have a great day!!!

[tex]Sofia[/tex]

Answer: [tex]68ft^2[/tex]

Step-by-step explanation:

The formula for calculate the surface area of a rectangular prism is:

[tex]SA=2lw+2lh+ 2wh[/tex]

Where "l" is the lenght, "w" is the width and "h" is the height.

In this case, you know that the top of the flower box is opened, then, the formula changes to:

[tex]SA=lw+2lh+2wh[/tex]

You can identify that the dimensions of the box are:

[tex]l=10ft\\w=2ft\\h=2ft[/tex]

Then you must substitute these values into the formula [tex]SA=lw+2lh+2wh[/tex].

 Finally, you get that the surface area of the open-top flower box is:

[tex]SA=lw+2lh+ 2wh\\SA=(10ft)(2ft)+(2)(10ft)(2ft)+(2)(2ft)(2ft)]\\SA=68ft^2[/tex]

Answer:

The surface area of box =  64 ft²

Step-by-step explanation:

From the figure we can see that a cuboid with length = 10 ft, width = 2 ft and height = 2 ft

To find the surface area of cuboid

Surface area = 2(lb + bh +  lh) - lh

  = [2(10 * 2) + (2 * 2) + (10 * 2)] - (10 * 2)

  = [2( 20 + 4 + 20)] - 20

  = 2 * 44 - 20 = 84 - 20 = 64 ft²

The correct answer is surface area of box =  64 ft²

Answer:

The correct option is C.

Step-by-step explanation:

The general exponential function is

[tex]f(x)=ab^x[/tex]

Where, a is initial value and b is growth factor.

The given function is

[tex]f(x)=(\frac{1}{2})^x[/tex]

Here [tex]b=\frac{1}{2}<1[/tex], therefore it is a decay function. In other words, the given function always decreases.

The given function is defined for all real numbers, therefore the domain of the function is all real number.

Put x=0, to find the y-intercept.

[tex]f(x)=(\frac{1}{2})^0=1[/tex]

The y-intercept of the function is at (0,1). Therefore option C is correct.

[tex](\frac{1}{2})^x>0[/tex]

[tex]f(x)>0[/tex]

Therefore the range of the function is y>0.

Answer:

The correct answer is C: The y-intercept is (0,1).

Answer: It is correctly simplified form.

Step-by-step explanation:

Since we have given that

[tex]-3m-[2x+(5-m)]+7[/tex]

We need to simplify the above expression:

[tex]-3m-2m-5+m+7\\\\=-5m+m+2(\text{gather the like terms})\\\\=-4m+2\\\\=2-4m[/tex]

So, [tex]-3m-[2x+(5-m)]+7=2-4m[/tex]

Hence, it is correctly simplified form.

Answer:

6 & 2

21 & 9

8 & 12

18 & 6

Step-by-step explanation:

Answer:

A. AB and EF

B. AC, CB, and EF

D. AD, DB, and EF

Step-by-step explanation:

The lengths would help  you to calculate the volume of the oblique pyramid are:

An oblique pyramid is known to be a type of shape that is often known as 'right pyramid'.

Note that its shape is one that has the ap.ex "is shaped" to one side and as such the options that can best explain the volume of the oblique pyramid is the ones written above.

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ANSWER

[tex]d = 3 \sqrt{13} [/tex]

EXPLANATION

We use the distance formula to find distance between two points.

[tex]d = \sqrt{(x_2-x_1)^2 +(y_2-y_1)^2} [/tex]

The two points are R(-1, 0) and S(8, 6).

We substitute the points into the formula to get:

[tex]d = \sqrt{(8 - - 1)^2 +(6-0)^2} [/tex]

[tex]d = \sqrt{(9)^2 +(6)^2} [/tex]

[tex]d = \sqrt{81+36} [/tex]

[tex]d = \sqrt{117} [/tex]

[tex]d = 3 \sqrt{13} [/tex]

Therefore the distance between the two points is [tex]3 \sqrt{13} [/tex] units.

Answer:

The distance between these points = 3√13

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

It is given two points R(-1, 0) and  S(8, 6)

To find the distance

Here, (x1, y1)  = (-1, 0) and (x2, y2) = (8, 6)

Distance = √[(x2 - x1)² + (y2 - y1)²]

= √[(8 - -1)² + (6 - 0)²]

= √[(8+1)² + (6)²]

 =√[(9)² + (6)²]

 = √[(81 + 36)]

 =√117 = √(3 * 3 * 13)

 = 3√13

The distance between these points = 3√13

Answer:

C. The number of runners in a race

Step-by-step explanation:

Variables can be widely be classified as either discrete or continuous. A continuous variable is a variable which can take on any value within its domain. A continuous variable can take on fraction of units. Examples of continuous variables include;

time to finish a race - it can be 10.5 sec or 35.56 sec

temperature at start of race - the temperature could be 25.5 K, or 45.57 K

length of race in kilometers - the length could be 20 km, 22.45 km or 38.8 km

All the above variables can be measured in fraction of units and are thus continuous in nature.

On the other hand, a variable is said to be discrete if it can take on only integer values. An example in this case would be ;

the number of runners in a race. We can only have, 10, 45, 600, 565 and so on runners but never a fraction of a runner.

Answer:

Step-by-step explanation:

Use the order of operations.

First multiplication next addition and subtraction (from left to right).

4 + (-3) - 2 × (-6)

= 4 - 3 + 12

= 1 + 12

= 13

(-)(-) = (+)

(+)(-) = (-)(+) = (-)

(+)(+) = (+)

Answer:

13

Step-by-step explanation:

12x+1 = 13

Answer:

C. 1 and 3

Step-by-step explanation:

You are right, now here's why.

You are looking for two equations that have the same constant of proportionality.  That means they behave the same, that if you enter a X value in one, you'll get the same effect as if you enter it in another.

If you look at all four equations, you'll see that 1 and 3 are essentially the same thing, just that the first one is simplified (4y = 3x) while the other isn't (8y = 6x).  But for each time you enter a X value, the Y value will be 33% (1/3) bigger.

we are required to demonstrate that we understand what represents a function and what does not represent a function by writing a paragraph which can be given as:

We know that functions are mathematical entities that assign unique outputs to given inputs. In other words, a function can't have repeated values in the input repeated x-value.

For example consider the relation {(1,4), (1,5), (2,6), (3,7), (4,8), (5,9)}.

We see that above relation has repeated x-value "1" which is assigned to two different output values 4 and 5. So by definition of function, above relation can't be a function.

Answer:

18 smaller bags

Step-by-step explanation:

Each one pound bag becomes 3 one-third pound bags.

So 6 one pound bags will become 6×3=18 one-third pound bags.

Answer:

18 smaller bags

Step-by-step explanation:

Answer:

When the range is wide

Step-by-step explanation:

The mean is the most useful in describing a set of data when range is wide.

Simply dividing the total number of values in a data set by the sum of all of the values yields it.

The mean can be used to provide a broad overview or overall impression of the data set. The optimal situation for using mean is when the data set's values are closely spaced.

When your data distribution is continuous and symmetrical, such as when your data are normally distributed, the mean is typically the best measure of central tendency to utilise.

Also, when the range is wide because it has high variability.

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Answer:

Step-by-step explanation:

X+2x-5= 40

3x-5=40

+5=+5

3x=45

3x/3=45/3

X=15

Answer:

Step-by-step explanation:

The sum of two number is 40 would be:

[tex]x+y=40[/tex]

The second number is 5 less than twice the first number would be:

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

Now, we can find the value by solving this system of equations, we will isolate x in the first equation, then we replace it in the second equation:

[tex]x=40-y[/tex]

[tex]y=2(40-y)-5\\y=80-2y-5\\y+2y=75\\3y=75\\y=\frac{75}{3}=25[/tex]

Then, we replace this value in one equation of find the other variable:

[tex]x+25=40\\x=40-25\\x=15[/tex]

Therefore, the value of the first number is 15 and the second number is 25.

the answer would be d because it goes down 2 and over 1

The answer is d because of the y intercept is -1 and the slope is -2 according to y=mx+b

[tex] \frac{15t}{5} = \frac{2t + 3}{6} \\ 90t = 10t + 15 \\ 80t = 15 \\ t = 0.1875[/tex]

Answer:

(6,10)

Step-by-step explanation:

Used a calculator

Answer:  x7

 x7

Step by step solution :

Step  1  :

           x14

Simplify   ———

           x7  

Dividing exponential expressions :

1.1    x14 divided by x7 = x(14 - 7) = x7

Answer:

x7

Step-by-step explanation:

Answer: Wow! That's a tough one, but x = 5 is the only possibility

Step-by-step explanation:

Answer:

12cm.

Step-by-step explanation:

The radius is half of a circe.

6 * 2 = 12.

Answer:

37.68 cm

Step-by-step explanation:

the circumference of a circle  is :   P = 2π r

P= 2×3.14×6 =37.68 cm

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

m = 116 and a = 105

Step-by-step explanation:

The angle m and 64 are supplementary angles because line of a straight line separated by another straight line. This means that m + 64 = 180, or m = 116.

The sum of all the angles in a quadralateral like this one is 360. So angle a = 360 - 89 - 50 - 116, or a =105.

Answer:

m=116  a=105

Step-by-step explanation:

there is 360 degrees inside a square, i found M by subtracting 180 - 64, because there is a 180 degree angle on a flat line and it showed the other side has 64 degrees, and since we know that m is 180-64=116, we can find A. take the total of degree of the inside of the square which is 360, and subtract all the other angle degrees from it to find the missing number. 360-89-50-116=A. A= 105 degrees.

im sorry if this made your problem more confusing, its hard to explain with words alone

ANSWER

See explanation

EXPLANATION

Question 1:

The third term of the arithmetic sequence is :

14=a+2d...(1)

The twelveth term is

59=a+11d...(2)

Subtract equation (1) from (2)

45=9d

This implies that

d=5

a=14-2(5)=4

The explicit rule is;

[tex]a_{n}=4 + 5(n - 1)[/tex]

[tex]a_{n}=4 + 5n -5[/tex]

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

Recursive formula:

[tex]a_{n}=a_{n - 1} + 5[/tex]

Question 2

The geometric sequence has the fourth term to be 2 and the common ratio to be r=⅓

This implies that,

[tex]a {( \frac{1}{3} })^{3} = 2[/tex]

This implies that,

[tex] \frac{a}{27} = 2[/tex]

[tex]a = 54[/tex]

The explicit rule:

[tex]a_n=54 {( \frac{1}{3} })^{n - 1} [/tex]

The recursive rule is

[tex]a_n=( \frac{1}{3} )a_{n-1}[/tex]

where,

[tex]a_1 = 54[/tex]

Answer:

I'm having trouble with this type of math to so your not alone

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

First, determine how many dogs are at the boarding service:

2+8+22+12 = 44

Then:

# of Dobermans          12

--------------------------  =  ------- = 6/22 or 3/ 11

     total # of dogs         44

The desired ratio is 3/11.

Answer:

 c • (15c2 + 14)

Step-by-step explanation:

14c +  (3•5c3)

3.1     Pull out like factors :

  15c3 + 14c  =   c • (15c2 + 14)

Answer:

c ( 1 4 c + 1 5 )

Step-by-step explanation:

1 4 c ² + 1 5 c

Factor out c

c ( 1 4 c + 1 5 )