he expression $130-60t$130−60t represents the distance, in miles, the counselor still needs to drive after $t$t hours.

What does the $60$60 in the expression represent?

The solution is:

[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]

Step-by-step explanation:

Given equation is:

[tex]3x^2+3x+5 = 0[/tex]

We will use the quadratic formula for solving the given equation

The quadratic formula is:

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

Here,

a = 3

b = 3

c = 5

[tex]x = \frac{-3+\sqrt{(3)^2-4(3)(5)}}{2(3)}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{(3)^2-4(3)(5)}}{2(3)}\\x = \frac{-3+\sqrt{9-60}}{6}\ \ \ ,\ \ \ x = \frac{-3-\sqrt{9-60}}{6}\\x = \frac{-3+\sqrt{-51}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{-51}}{6}[/tex]

As we know

[tex]i = \sqrt{-1}[/tex]

So,

[tex]x=\frac{-3+\sqrt{51*-1}}{6} \ \ \ , \ \ \ \ x = \frac{-3-\sqrt{51*-1}}{6}\\x=\frac{-3+(\sqrt{51}*\sqrt{-1})}{6} \ \ \ , \ \ \ \ x = \frac{-3-(\sqrt{51}*\sqrt{-1})}{6}\\x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]

Hence,

The solution is:

[tex]x = \frac{-3+\sqrt{51}i}{6}\ \ \ \ AND\ \ \ \ x = \frac{-3-\sqrt{51}i}{6}[/tex]

Keywords: Quadratic equation, quadratic formula

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Answer:

67

Step-by-step explanation:

9*7=63

13*5=65

23*3=69

Answer:

67

Step-by-step explanation:

Only number whose factors are 67 and 1

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Answer:

22

Step-by-step explanation:

21.6 would round up because 6 is closer to 10 than it is 0

The number 21.6 rounded to the nearest whole number is 22.

Rounding off of a number is defined as the simplification of the number by keeping the value of the number same but is made closer to the next number.

Rounding can be done for whole numbers as well as decimals.

Given a number 21.6.

We have to round the number.

Here the first digit after the decimal place is 6, which is greater than 5.

So we have to add 1 to the last digit in the whole part.

So 21.6 is rounded to 22 to the nearest whole number.

Hence the correct number is 22.

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Answer:

The area would be 111.41 unit² ( approx )

Step-by-step explanation:

Given,

KLMN is a trapezoid,

In which KL=MN, KM=15, m∠MKN=49°,

Suppose O and P are point in the segment LM, ( shown below )

Such that,

KN = OP,

In triangle MKO,

m∠KMO = 49° ( ∵ KM ║ LM, using alternative interior angle theorem ),

KM = 15 unit ( given )

[tex]\sin 49^{\circ} = \frac{KO}{KM}[/tex]

[tex]\implies KO = KM \sin 49^{\circ}=15 \sin 49^{\circ}[/tex]

i.e. height of the trapezoid KLMN is 15 sin 49°,

Again,

[tex]\cos 49^{\circ} = \frac{OM}{KM}[/tex]

[tex]\implies OM = KM \cos 49^{\circ}=15 \cos 49^{\circ}[/tex]

[tex]OP + PM = 15 \cos 49^{\circ}[/tex]

[tex]\implies KN + PM = 15 \cos 49^{\circ}----(1)[/tex]

Now, in right triangles KOL and NPM,

KL = MN,

OK = NP

By HL postulate of congruence,

Δ KOL ≅ Δ NPM

By CPCTC,

LO = PM,

⇒ LM = LO + OP + PM = PM + OP + PM = OP + 2PM = KN + 2PM-----(2),

Thus, the area of the trapezoid KLMN,

= 1/2 × height × sum of opposite parallel sides

[tex]=\frac{1}{2}\times KO\times (KN+LM)[/tex]

[tex]=\frac{1}{2}\times KO\times (KN+KN + 2PM)[/tex]

[tex]=\frac{1}{2}\times KO\times (2KN+2PM)[/tex]

[tex]=KO\times (KN+PM)[/tex]

[tex]=15 \sin 49^{\circ}\times 15 \cos 49^{\circ}[/tex]

[tex]=111.405157734[/tex]

[tex]\approx 111.41\text{ square unit }[/tex]

The area of a triangle can be found using the formula 1/2 x base x height. For a base of 166 mm and height of 930 mm, the area is 77.19 cm². However, for trapezoid KLMN, additional information is needed to calculate its area.

To find the area of a trapezoid, especially when it has special properties like equal non-parallel sides (as trapezoid KLMN does with KL equal to MN), we often need to break it down into simpler shapes such as triangles and rectangles. However, with the information given, it's not straightforward to calculate the area of the trapezoid without additional height or angle information. The area of a triangle can be calculated using the formula ½ × base × height. For example, if you have a triangle with a base of 166 mm and height of 930.0 mm, the area is calculated as ½ × 166 mm × 930.0 mm which equals 77190 mm² or 77.19 cm² when converted to square centimeters, maintaining the proper number of significant figures.

Answer:

93 h

Step-by-step explanation:

P = 4300eᵏᵗ

1. Calculate the value of k

lnP = ln4300 + kt

ln5800 = ln4300 + k(40 h)

8.666 = 8.366 + 40k h

8.666 - 8.366 = 40k h

0.299 = 40 k h

k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹

2. Calculate the time for the population to double

2 × 4300 = 4300eᵏᵗ

2 = eᵏᵗ

ln2 = kt

t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h

It takes 93 h for the population to double.

Answer:

The x-coordinate gives the solution of the original equation.

Step-by-step explanation:

Let us assume that the original equation is 2x = x + 5 ........... (1) and the solution that this equation has will be x = 5.

But, if we solve the equation by graphing each side as a separate line i.e. y = 2x and y = x + 5, then solving those two equations we get the solution x = 5 and y = 10.

Therefore, the x-coordinate i.e. x = 5 gives the solution of the original equation (1). (Answer)

Answer:

D

Step-by-step explanation:

edge

Answer:

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.

Step-by-step explanation:

Given:

[tex]y=3x+6[/tex]

Solution:

The Given Equation is in Slope - Point Form i.e

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

Where,

[tex]m=slope\\\\c=y-intercept[/tex]

On Comparing the given equation with above we get

[tex]slope=m=3\\\\y-intercept =6[/tex]

Now we Know that

Intercepts:

The line which intersect on x-axis and y-axis are called intercepts.

There are two intercepts:

y-intercept: The line which intersect at y-axis. So when the line intersect at y-axis X coordinate is zero.

x-intercept: The line which intersect at x-axis. So when the line intersect at x-axis Y coordinate is zero.

For x-intercept

Put y = 0 in

[tex]y=3(x+2)[/tex]

[tex]0=3x+6\\\\3x=-6\\\\\therefore x=\dfrac{-6}{3}=-2[/tex]

∴ x-intercept of

[tex]y=3x+6[/tex]

x-intercept = -2

The equivalent equation is correctly matched with a key feature of the graph is

y = 3(x + 2) highlights that the x-intercept is at -2.

Answer:

  The slopes of the lines are different.

Step-by-step explanation:

If you do convert the standard form equation to slope-intercept form, you get ...

  y = -x +5

You see that the slope of this line is -1, whereas the slope of the other line is +1. Both lines have a y-intercept of 5. It is the slopes that are different.

_____

You can determine this to be the case without converting the form of the equation if you have some practice with the various forms of the equation of a line.

In standard form, if the variable signs are the same, the slope is negative. Of course, in slope-intercept form, the sign of the slope is the sign of the coefficient of x.

The y-coordinate of point A is -22

Step-by-step explanation:

Given

B = (24,16)

P = (4,-3)

The formula for mid-point of AB will be given by:

[tex]P = (\frac{x_A+x_B}{2} , \frac{y_A+y_B}{2})[/tex]

As we already know the y-coordinate of midpoint

We can put the formula's y coordinate equal to the given value

[tex]\frac{y_A+y_B}{2} = -3\\\frac{y_A + 16}{2 } = -3\\y_A+16 = -3 * 2\\y_A +16 = -6\\y_A = -6-16\\y_A = -22[/tex]

Hence,

The y-coordinate of point A is -22

Keywords: Mid-point, coordinate geometry

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Answer: base a=2ft

               height hₐ=5ft

Step-by-step explanation:

use equation for area of triengle

A=a*hₐ/2

hₐ-height of tringle

a-base of triangle

hₐ=a+3

A=a(a+3)/2

2A=a²+3a

A=5ft

2*5=a²+3a

a²+3a-10=0

a=(-3±√9+40)/2

a=(-3±7)/2

a=-5ft

a=2 ft

hₐ=2+3=5ft

Answer:

[tex]\frac{1}{20}[/tex]

Step-by-step explanation:

First, we need to look at the # of chips. There are a total of 25, 6 of which are blue.

This means that the chance of getting the first blue chip would be [tex]\frac{6}{25}[/tex]

As there is no replacement, the total number of chips is 24 and there are only 5 blue left. This gives us the chance of [tex]\frac{5}{24}[/tex]

Now all we need to do is mulitply these two and then simplify

[tex]\frac{6}{25} *\frac{5}{24} =\frac{30}{600} =\frac{1}{20}[/tex]

Answer:

1/20

Step-by-step explanatio

pick without replacement must mean pick it two times without put back the first chip

6/25 x 5/24 = 1/20

Answer:

C,D,A

Step-by-step explanation:

Answer:
Was it factory or dealer-installed?
Are there charges for documents like taxes and tags?

Is there a dealer advertising fee?

Step-by-step explanation:

''Step two involves preparing a list of suitable questions for the dealers you wish to visit. For example, if you want rustproofing, was it factory-installed or dealer-installed? Are there charges for documents like taxes and tags? Is there a dealer advertising fee? These charges won't appear on a factory invoice, but you will pay for them.''

All the information is in the problem you just have to format it into an equation.

Point slope form: [tex]y_{2}-y_{2}=m(x_{2}-x_{1})[/tex] where "m" is the slope.

The equation would look like...

y+6=[tex]\frac{1}{5}[/tex](x+4)

Answer:

Step-by-step explanation:

If 2 pounds costs $4, then 1 pound costs $2.  That's why the equation is y = 2x and x is the number of pounds you buy.  If you buy 2.5 pounds, then the cost is y = 2(2.5) so

y = $5

Final answer:

Leah can make 46 full bags of toy cars to sell at the flea market when placing 6 toys in each bag out of her 280 toy cars, with 4 toys remaining unsold.

Explanation:

Leah has 280 toy cars and wants to sell them in gift bags, with 6 toys in each bag. To find out how many full bags she can sell, we need to divide the total number of toy cars by the number of toys per bag.

The calculation would be 280 ÷ 6 = 46 R4. This means Leah can make 46 full bags of toys and there will be 4 toys left over. Since she only sells full bags, the 4 extra toys will not be sold.

Answer:

12.5 centimeters per minute

Step-by-step explanation:

From the graph, the rate at which the diameter increasing would be inthe units of cm/min

The rate is basically the slope of the line. The slope (m) has formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where

[tex](x_1,y_1)[/tex]  is any point from the graph

and

[tex](x_2,y_2)[/tex]  is another point from the graph

Let's take the origin (0,0) as the first point and (4,50) as the second point. Now lets calculate the slope:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\m=\frac{50-0}{4-0}\\m=\frac{50}{4}\\m=12.5[/tex]

Thus, we can say:

The diameter of the hot air balloon is increasing at a rate of 12.5 centimeters per minute

Solve for x.

20% × x = 35

0.2x=35

x=175

answer: 175

Answer: 175

Step-by-step explanation: We can change this problem to mean the same thing but it will say 20% of what number is 35.

To answer the question 20% of what number is 35, we translate the question into an equation. First we have 20% which we need to write as a decimal and remember to write 20% as a decimal, we move the decimal point 2 places to the left and we get 0.20.

Next we have "of what number" that's times x, "is 35" = 35. Now we have the equation (.20)(x) = 35.

Not to solve for x, since x is being multiplied by .20, we need to divide by .20 on both sides of the equation. On the left side of the equation the .20's cancel and we have x. On the right side of the equation we have 35 divided by .20 which is 175.

This means that 20% of 175 is 35.

Answer:

Step-by-step explanation:

9×3 = 27

9×4 = 36

9×5 = 45

HOPE IT HELPS

Answer : 9,18,27,36,45,54,63,72,81,90,99,108,117,126,135,144,153,162,171,180,189,198,207,216,225,234,243,252,261,270,279,288,297,306,315,324,333,342,351,360,369,378,387,396,405,414,423,432,441

Answer:

option C. and D.

Step-by-step explanation:

For two quantities with inverse variation, as one quantity increases, the other quantity decreases. For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases.An inverse variation can be represented by the equation xy=k or y=kx .

Answer:

The measure of the angle is 64 degree.

The measure of the supplement is 116 degree.

Step-by-step explanation:

Let the measure of the angle be 'x'.

Given:

Supplement of the angle is 12 less than twice the measure of the angle.

Twice the angle means 2 times of the angle which is [tex]2x[/tex] and 12 less means 12 is subtracted from [tex]2x[/tex].

So, supplement of the angle = [tex]2x-12[/tex]

Now, by definition of supplementary angles, if two angles are supplement of one another, then their sum is 180 degrees.

Therefore, the sum of the given angles = 180°

⇒ [tex]x+2x-12=180[/tex]

⇒ [tex]3x-12=180[/tex]

⇒ [tex]3x=180+12[/tex]

⇒ [tex]3x=192[/tex]

⇒ [tex]x=\frac{192}{3}=64\°[/tex]

The measure of the supplement = [tex]2(64)-12=128-12=116[/tex]

The measure of the angle is 64 degree.

The measure of the supplement is 116 degree.

Answer: 2/3

Step-by-step explanation:

7/9 - 2/8 =x 4/9

= 48/72

However, they are asking for the answer in SIMPLEST FORM.

48/72 in simplest form is 2/3.

Answer:

A) [tex]\frac{x+y+z}{3}[/tex]

Step-by-step explanation:

the formula for average is the sum of the digits, then divide that sum by the number of digits.

for example: let x = 1, let y = 2, let z = 3

so 1+2+3 is 6

then divided by the number of digits: 3

6/3=2

the average is 2

Answer:

The length of A'B' is 15 units

Step-by-step explanation:

As line segment AB has end points

The distance formula to calculate the distance between two points is given by:

[tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}}[/tex]

[tex]{\displaystyle d={\sqrt {(20-4)^{2}+(4-16)^{2}}}}[/tex]

[tex]d=\sqrt{16^2+(-12)^2}[/tex]

[tex]d=\sqrt{256+144}[/tex]

[tex]d=\sqrt{400}[/tex]

[tex]d=20[/tex]

[tex]d=20[/tex] is also the length of the line segment AB.

As segment will be dilated with a scale factor of 3/4 and a center at the origin to create A'B'.

So,

The length of A'B' can be obtained by multiplying the length of AB by 3/4

Therefore,

The length of A'B' = 3/4 × 20 = 15

So, the length of A'B' is 15 units.

Keywords: dilation, distance formula, length, line segment

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Final answer:

Each apple costs 41 cents when a dozen apples are bought for $4.92, determined by dividing the total cost by the number of apples.

Explanation:

The question asks to find the cost per apple when a dozen apples are purchased for $4.92. To find the cost per individual apple, you divide the total cost by the number of apples. There are 12 apples in a dozen, so:

$4.92 ÷ 12 apples = $0.41 per apple

So, each apple costs 41 cents. This exercise of finding the individual cost from a total is an example of a ratio used in basic arithmetic, often taught in middle school mathematics.

Step-by-step explanation:

Solve the bracket first. starting with multiplication and then subtraction

0.00035 + (4.2 x 10-5)

0.00035 + (42-5)

0.00035 + 37

0.01295

Answer:

100+10

Step-by-step explanation:

Answer:

5184

Step-by-step explanation:

first of all we sove multiplication of terms then addition

2592+1296+1296

5184 ans

Answer:

27k-20n

Step-by-step explanation:

3(9k-4)-4(5n-3)

27k-12-20n+12

27k-20n-12+12

27k-20n

Answer:

11/10

Step-by-step explanation:

4/5-(-3/10)=4/5+3/10=8/10+3/10=11/10

Answer: Yes, it does, because each input value has an unique output value.

Step-by-step explanation:

First, you need to know when a relation is considered a function.

By definition, a relation is a function if an only if each input value has one and only one output value.

It is important to remember that the input values are the values of "x" and the output values are the values of "y".

Then, in this case, you can observe in the graph attached ( which shows the data for Camille’s puppy), that each x-value (Weeks) has an unique y-value (Weight in pounds).

Therefore, based on this and keeping on mind the explained before, you can conclude that the data for Camille’s puppy shows a function.

Answer:

Yes it does

Step-by-step explanation:

Because it passes the vertical line test and it only touches 1 unit point in the line no need for big explanations you cant understand