Distance traveled 342 miles with an average speed of 40 mph. What is the travel time of the trip?

Answer:

2 real solutions

Step-by-step explanation:

To determine the nature of the solutions use the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real solutions

• If b² - 4ac = 0 the 2 real and equal solutions

• If b² - 4ac < 0 then no real solutions

Given

x² + 9x + 20 = 0 ← in standard form

with a = 1, b = 9, c = 20, then

b² - 4ac

= 9² - (4 × 1 × 20 ) = 81 - 80 = 1

Since b² - 4ac > 0 then there are 2 real solutions

Answer:

x=102

Step-by-step explanation:

[tex]\frac{1}{5}[/tex](x-2)=20 (multiply both sides by 5)

x-2=100 (move the -2 to the right)

x=100+2 (add)

x=102

hope this helps :)

Step-by-step explanation:

1/5(x-2) =20

multiply both sides by 5

=> (x-2) = 100

make x the subject of the formula...

x = 100 + 2

x = 102

Answer:

y= 1/2 x +6

Step-by-step explanation:

y-8= 1/2 (x-4)

y-8= 1/2 *x - 1/2*4

y= 1/2 *x - 1/2*4 +8

y= 1/2 *x - 2 +8

y= 1/2 *x +6

Answer:

A. 7 red candles, 1 silver candle

Step-by-step explanation:

6 red candles * $3 each = $18

2 silver candles * $7 each = $14

$18 + $14 = $32 (the total cost)

Answer:

B. 6 red candles, 2 silver candle

Step-by-step explanation:

Answer:

B y=55

Step-by-step explanation:

The sum of the angles of a triangle a 180 degrees

40 + y + (y+30) = 180

Combine like terms

70 + 2y = 180

Subtract 70 from each side

70-70 +2y = 180-70

2y = 110

Divide by 2

2y/2 = 110/2

y = 55

The angle at B is 1/2 the angle at O

Angle B = 54

B +C = 54 + 29 = 83

Angle A + B + C = O

A + 54 + 29 = 108

A = 108 - 83

A = 25

X = 25

Answer:

B

Step-by-step explanation:

It is rational because it is terminal (meaning it ends and doesn't go on forever) it is also under 0 because it is negative. It is an integer because it is not a fraction or decimal.

-5 is an integer, a category of whole numbers that includes positive, negative, and zero. Specifically, -5 is a negative integer.

The number -5 in mathematics is classified as an integer. An integer is any whole number found on the number line that can either be positive, negative, or zero. Therefore, the number -5, being a whole number and negative, fits into the category of integers. -5 is also an example of a negative integer.

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Answer:

6 units²

Step-by-step explanation:

The area (A) of a triangle is

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 3 and h = 4, hence

A = 0.5 × 3 × 4 = 0.5 × 12 = 6

Answer:

4 ml of the 63% milk drink

Step-by-step explanation:

Multiplying 15 ml by 0.15 results in 2.25 ml, the amount of whole milk in the drink.  Let m represent the number of ml of a drink that is 63% milk.

The final amount of milk drink that is to be 45% milk will be 15 ml + m, and the amount of whole milk contained in this drink will be 0.45(15 + m).

Then:

0.15(15 ml) + 0.63(m) = 0.45(15 + m), where m is to be in milliliters.

2.25 + 0.63m = 6.75 + 0.45m

First:  consolidate the m terms on the left.  0.63m less 0.45m yields 18 m; then we have:

2.25 + 18m = 6.75, or

18 m = 4.50, or m = 4 ml.

In conclusion:  adding 4 ml of that 63% milk drink to the initial 15 ml of 15% milk will result in (15 ml + 4 ml) of a 45% milk drink.            

Answer:

From top to bottom:

3

7

6

12

Step-by-step explanation:

You just simply add the number in the top row and the number in the column together.

2 + 1 = 3

4 + 3 = 7

2 + 4 = 6

6 + 6 = 12

Answer:

m∠A=90°, m∠B=60°, m∠C=30°

Step-by-step explanation:

step 1

Verify if the triangle ABC is a right triangle

Applying the Pythagoras theorem

[tex]12^{2}=6^{2}+(6\sqrt{3})^{2}[/tex]

[tex]144=144[/tex] ----> is true

therefore

Is a right triangle

m∠A=90°

Find the measure of angle C

sin(C)=AB/BC

substitute

sin(C)=6/12=1/2

so

m∠C=30°

Find the measure of angle B

we know that

m∠C+m∠B=90°------> by complementary angles

so

m∠B=90°-30°=60°

Answer:

17.1

Step-by-step explanation:

The standard deviation of the miles Henry hiked is 17.1

The standard deviation of the miles henry biked to the nearest tenth will be 17.08.

It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.

The standard deviation is given as,

[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]

Henry recorded the number of miles he biked each day for a week. The data is given below.

25, 40, 35, 25, 40, 60, 75

Then the mean of the data is given as,

μ = (25 + 40 + 35 + 25 + 40 + 60 + 75) / 7

μ = 300/7

μ = 42.857

Then the standard deviation is given as,

[tex]\sigma = \sqrt{\dfrac{(25 - 42.857)^2 + (40- 42.857)^2 + ......+(75- 42.857)^2}{7}}[/tex]

Simplify the equation, then we have

σ = √(2042.857 / 7)

σ = √291.837

σ = 17.08

More about the standard deviation link is given below.

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The length of h in the given composite figure will be 4, i.e. option B.

Composite geometric figures are made from two or more geometric figures.

We have,

A composite figure,

Now,

From the figure -- (dash) marked lines are equal , and all dashed marked lines are equal to 1.

Now,

h of the given composite figure consists of two dashed marked lines and 2m.

i.e.

h = 1 + 1 + 2

So,

h = 4 m

So,

The length of h is 4m.

Hence, we can say that the length of h in the given composite figure will be 4, i.e. option B.

To know more about composite figure click here

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Ans.

7/12 , 2/3 , 5/6

Why:

If we give all the fractions the same denominator then the fractions are, 8/12 , 10/12 , 7/12. We then can easily see what is the order. Once ordered correctly, just simplifiy.

Answer:

7/12 , 2/3 , 5/6

Step-by-step explanation:

Firstly, give them a common denominator.

What do 3,6 and 12 all have in common? 12

So what we do to the bottom, we do to the top.

Multiply the 2/3 by 4 (3x4=12) to make 8/12.

Multiply the 5/6 by 2 (2x6=12) to make 10/12

7/12 already has 12 as the denominator.

Now order them.

7/12 , 8/12, 10/12.

Change them back to the original sums.

7/12 , 2/3 , 5/6

Given line: y =3x - 7

Slope-intercept form is y = mx + b where m is slope and b is the y intercept

To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)

the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]

This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]

This is the current formula you found:

[tex]y=\frac{-1}{3} x + b[/tex]

To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b

-1 = [tex]\frac{-1}{3}[/tex](2) + b

-1 = [tex]\frac{-2}{3}[/tex] + b

[tex]\frac{-1}{3}[/tex] = b

That means that the equation perpendicular to y = 3x - 7 is...

y = [tex]\frac{-1}{3} x - \frac{1}{3}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

y =3x - 7

Step-by-step explanation:

Answer:

x<11

Step-by-step explanation:

To solve this inequality, we must isolate the x. To do that, we divide both sides by 5. This gives us x<11. So all numbers less than eleven belong to the solution set of the inequality.

Answer:

All number less than 11.

Step-by-step explanation:

5x < 55

We just isolate x by dividing both sides by 5:

5x / 5 < 55/5

x < 11.

Answer:

D

Step-by-step explanation:

If two secants intersect to form the vertex of an angle outside a circle and the sides of the angle intercept arcs on the circle, then the measure of the angle is equal to one-half the difference of the measures of the arcs intercepted by the sides of the angle.

So

[tex]85-25=60[/tex]

[tex]\frac{60}{2}=30[/tex]

Answer:  14.6

Step-by-step explanation:

Draw a right triangle such that the building is perpendicular to the ground (which is where the shadow is cast).

Use Pythagorean Theorem to find the length of the shadow (x):

x² + 34² = 37²

x²          = 37² - 34²

x²          = 213

√x²       = √213

x          = 14.59

Answer:

g(4) = 12

Step-by-step explanation:

We need to find the value the function g(x) when x = 4, that is;

g(4)

In the first definition of the function, the value of x is strictly less than 4. Consequently, we shall use the second definition of the function to evaluate g(4)

In the second definition, g(x) is given as;

Q(x) = 0.5x + 10

plug in x = 4 and simplify;

Q(4) = 0.5(4) + 10

Q(4) = 12

Answer:

any real number

Step-by-step explanation:

Answer when simplified gives 0 = 0

This indicates that any real value of x is a solution.

Usually because the equations on both sides are equal.

That is 2x + 10 = 2x + 10 leading to 0 = 0

Answer:

Step-by-step explanation:

[tex]-\dfrac{1}{2}(2n-4)+6=-9+4(2n+1)\qquad\text{use the distributive property}\\\\\left(-\dfrac{1}{2}\right)(2n)+\left(-\dfrac{1}{2}\right)(-4)+6=-9+(4)(2n)+(4)(1)\\\\-n-2+6=-9+8n+4\qquad\text{combine like terms}\\\\-n+(-2+6)=8n+(-9+4)\\\\-n+4=8n-5\qquad\text{subtract 4 from both sides}\\\\-n=8n-9\qquad\text{subtract}\ 8n\ \text{from both sides}\\\\-9n=-9\qquad\text{divide both sides by (-9)}\\\\n=1[/tex]

Tomas should subtract 2x from both sides of the equation, not add 6.

In the given question, Tomas is buying granola and walnuts and he can spend a total of $12 on the ingredients.

He buys 3 pounds of granola that costs $2.00 per pound, and the walnuts cost $6 per pound.

The equation he uses to represent the total cost is: y = 12 - 2x, where x represents the number of pounds of granola and y represents the number of pounds of walnuts.

To solve the equation for y, Tomas should subtract 2x from both sides, not add.

This will give the correct equation for the number of pounds of walnuts he can buy.

Therefore, the correct equation is: y = 12 - 2x.

Answer:

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

Step-by-step explanation:

It is given that the matrix below represents the distance in miles between three cities. A row label represents the city traveled from. A column label represents a city traveled to.

[tex]\begin{bmatrix}0 & 5 & 15\\ 5 & 0 & 35\\ 15 & 35 &0 \end{bmatrix}[/tex]

Here first element of first row represents the distance in miles from city 1 to city 1.

[tex]C_1\Rightarrow C_1=0[/tex]

Second element of first row represents the distance in miles from city 1 to city 2.

[tex]C_1\Rightarrow C_2=5[/tex]

Third element of first row represents the distance in miles from city 1 to city 3.

[tex]C_1\Rightarrow C_3=15[/tex]

The round trip distance in miles from city 1 to city 3 is 15. Therefore the correct option is 1.

Answer:

x=20

Step-by-step explanation:

Since this is a right angle, it is equal to 90 degrees

x + 3x+10 = 90

Combine like terms

4x+10 = 90

Subtract 10 from each side

4x+10-10 =90-10

4x=80

Divide by 4

4x/4=80/4

x = 20

If we are given the equation y = -27x + 577 and that

x = weeks

y = money left in account

Then you must replace 145 (the money) for y and solve for x (the weeks)

145 = -27x + 577

145 - 577 = -27x + 577 - 577

-432 = -27x

-432/-27 = -27x/-27

16 = x

This means that after 16 weeks Alma will have $145 left in her account

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

b

Step-by-step explanation:

Answer: 10 bags

Step-by-step explanation:

First we must calculate the field area. Assuming it is a rectangle then its area equals the product of its length times its width

[tex]A =360*160\\\\A = 57600 ft^2[/tex]

You use 8 pounds of fertilizer per 1,000 square feet

So the amount of fertilizer you should use is:

[tex]57,600 ft^2 * \frac{8\ pounds}{1,000\ ft^2} = 460.8\ pounds[/tex]

As the fertilizer comes in bags of 50 pound then you need

[tex]460.8\ pounds * \frac{1\ bag}{50\ pounds} = 9.2\ bags[/tex]

Since you can not buy 9.2 bags then we round up to the next whole number.

Finally you need 10 bags of fertilizer

For this case we must find an equation equivalent to:

[tex]\sqrt {x ^ 2 + 81} = x + 10[/tex]

We square both sides of the equation to eliminate the root:

[tex]x ^ 2 + 81 = (x + 10) ^ 2[/tex]

We have by definition that:

[tex](a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2[/tex]

So, rewriting the right side of the equation we have:

[tex]x ^ 2 + 81 = x ^ 2 + 2 * 10 * x + 10 ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x + 100[/tex]

ANswer:

Option D