A truck driver drove 120 miles in 1 3/4 hours. What is the speed of the truvk in miles per hour? work shown

Steps:

[tex]x=\frac{-8+\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1}: -4+2i[/tex]

[tex]x=\frac{-8-\sqrt{8^2-4\cdot \:1\cdot \:20}}{2\cdot \:1} -4-2i[/tex]

=\frac{-8-\sqrt{16}i}{2\cdot \:1}[tex]=-8-\sqrt{16}i[/tex]

[tex]=\frac{-8-\sqrt{16}i}{2}[/tex]

[tex]=\frac{-8-4i}{2}[/tex]

[tex]=-2\left(2+i\right)[/tex]

[tex]=-4-2i[/tex]

[tex]x=-4+2i,\:x=-4-2i[/tex]

Answer:you can use the quadratic formula but if you have to factor do the following:

x^2+8x+20=0

add -4 to both sides of the equation to complete the square

x^2+8x+20+(-4)=0+(-4)

x^2+8x+16=-4

(x+4)^2=-4

take the square root of both sides

x+4=+sqrt(-4)

x+4=+sqrt[(4)(-1)]

x+4=+2sqrt(-1) where sqrt(-1)=i, a complex number

x+4=+2i

x=-4+2i

x=-4+2i and x=-4-2i

you would get the same answer using the quadratic formula

Step-by-step explanation:

Answer-

The coordinates of the solution to the system of equations is (4, -3)

Solution-

According to the graph the equations are,

[tex]y=-\frac{1}{2}x-1\\\\y=\frac{1}{4}x-4[/tex]

We can get the coordinates of the solution to the system of equations, by substitution.

[tex]\Rightarrow y=\frac{1}{4}x-4[/tex]

Putting the value of y in first equation,

[tex]\Rightarrow \frac{1}{4}x-4=-\frac{1}{2}x-1[/tex]

[tex]\Rightarrow \frac{1}{4}x+\frac{1}{2}x=-1+4[/tex]

[tex]\Rightarrow \frac{3}{4}x=3[/tex]

[tex]\Rightarrow x=3\times \frac{4}{3}[/tex]

[tex]\Rightarrow x=4[/tex]

Putting the value of x in the first equation,

[tex]y=-\frac{1}{2}\times 4-1=-2-1=-3[/tex]

Therefore, the coordinates of the solution to the system of equations is (4, -3)

If you look at clue #2 first then you see that if you know one of the numbers then the other number is 3 less than it, so if I let one of the numbers be x then the other is

x - 3. Now clue # 1 says the sum of the two numbers is 21 so

x + (x - 3) = 21

12+9=21 because 12-3=9 and 9+12 is 21

Since one piece is four time the length x, we can represent that as 4x.

Thus making the equation:

4x+x=275

5x=275

x=55

4(55)=220

220+55=275

So, the length of the longer piece is 220 inches, and the length of the shorter piece is 55 inches.

In order to find the length of the shorter piece of pipe, we can set up and solve the equation x + 4x = 275. When simplified, we get 5x = 275, and by dividing both sides of the equation by 5, we find that x = 55. This tells us that the length of the shorter piece is 55 inches.

To solve this problem, let's denote the shorter piece as x. Because the other piece is four times the length of the shorter one, it can be denoted as 4x. We know that these two pieces put together make the total length of the initial pipe, which is 275 inches. Therefore, we can set up the equation: x + 4x = 275.

Simplifying this equation, we get 5x = 275. To get the value of x, we need to divide both sides of this equation by 5, resulting in x = 55. Hence, the length of the shorter piece is 55 inches.

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To represent 8.2 using base 10 blocks, you need 8 one blocks and 2 tenth blocks, where one blocks represent 1 and tenth blocks represent 0.1. This method is effective for visualizing numbers in base 10.

To represent the number 8.2 using base 10 blocks, we use different sizes of blocks to represent different place values in base 10.

Each size block is worth a different value based on its place in the number.

To represent 8.2, we would need:

This method of representation helps in visualizing and understanding the value of numbers in the base 10 system. It's particularly useful in educational settings for explaining the concept of place values and decimals.

3/5(30) = 18.

60% of the days in April it rained.

It rained 18 days in April.

Best of luck.

60% of it rained cause 3/5 is equaled to 60% so 18 Yeah.

Let cost of Emma's phone = x

Given that cost of Sophie's phone = 640

Then ratio of their phones cost will be x:640 or x/640

Given that ratio of their phones cost is 7:8 or 7/8

So both ratios will be equal.

[tex]\frac{x}{640}=\frac{7}{8}[/tex]

[tex]x=\frac{7}{8}*640[/tex]

x=560

So the new ratio of the cost of their phones will be 560:640

Now we have to find about how much should the prices of their phones decrease in order to have a ratio of 9:11.

So let that decreased amount is k then we will get equation :

[tex]\frac{560-k}{640-k}=\frac{9}{11}[/tex]

11(560-k)=9(640-k)

6160-11k=5760-9k

6160-5760=11k-9k

400=2k

200=k

Hence final answer is prices of their phones should decrease by 200 in order to have a ratio of 9:11.

Answer:

For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364

Step-by-step explanation:

To answer this question, call x on Emma's phone and z on Sophie's phone.

We know that the price relationship between x and z is 7: 8

This means that:

[tex]\frac{7}{8} =\frac{x}{z}[/tex]

We know that the price of Sophie's phone is $ 640

Entoces z = 640  

Now we clear x

[tex]\frac{7}{8} =\frac{x}{640}\\ x =640}\frac{7}{8}=560\\ x = 560[/tex]

Then, if the new relationship is 9:11 then:

[tex]\frac{9}{11} =\frac{x}{640}[/tex]

x = $523,636

For the ratio between the price of the phones to be 9:11, the price of Emma's phone must decrease from $ 560 to $ 523.66. That is, the price of Emma's phone should decrease $ 36,364

78 - 19 = 59

If you're looking for the number of boxes that are left, its 59, but if you are looking for how many DVDs are left then you would proceed to do:

116 · 59 = 6844

6844 would be the number of DVDs that are left in the remaining boxes.

t<-3 should be the answer. I hope this helps

[tex]6\cdot32=6(30+2)=(6)(30)+(6)(2)=180+12=192\\\\7\cdot29=7(30-1)=(7)(30)-(7)(1)=210-7=203[/tex]

Answer:

Step-by-step explanation:

We are given number of miles the 3 bike trips they took last month = 45.7, 40.9, and 38 miles.

Sam and Bruno were computing how many kilometers.

Also one kilometer equals 0.621 miles.

From this we can see than 1 kilometer is smaller unit and a mile is a larger unit.

In order to convert number of miles into kilometers, we need to divide each number of mile by 0.621 miles.

We always divide a larger value by a smaller value to get the smaller unit.

Therefore,

8 + 5n = -27

5n = -35

n = -7

You would first try to round the numbers to the nearest 10 and then multiply for a reasonable estimate. In other words, 40x70=2800

We are given the  volume of a spherical tank =  790.272 π cubic feet.

We need to find the diameter of the container .

We know formula for volume of a sphere.

[tex]V=\frac{3}{4}(r^{3}\pi)[/tex]

Where r is the radius.

Plugging V= 790.272 π  in the above formula, we get

[tex]790.272\pi =\frac{3}{4}(r^{3}\pi)[/tex]

Dividing both sides by π, we get

790.272 =[tex]\frac{4}{3}(r^{3})[/tex]

Multiplying both sides by 3, we get

2370.816 = [tex]4r^3[/tex]

Dividing both sides by 4, we get

592.704 = [tex]r^3[/tex]

Taking cube root on both sides, we get

r=8.4.

Diamater is 2 times of radius, that is 2 × 8.4 = 16.8

Therefore, the diameter of the container = 16.8 feet.

3 3/4 miles as a decimal is 3.75 miles. He rode for one hour. Average speed within an interval is (distance made) / (interval duration). So the average speed = 3.75 miles / 1 hour, or 3.75 mph.

k=-5/6 would be your answer

The answer you are looking for is K = -5/6.

To find this, you must get K by itself. First, subtract 8k from both sides to get 12k + 11 = 1. Next, subtract 11 from both sides to get 12k = -10. Finally, divide both sides by 12 to get K = -10/12, which simplified, is -5/6. Thus making -5/6 the answer.

I hope this helps!

Henrieta's work is incorrect. The correct answer is 0.04.

No, Henrieta's work is not correct. To divide 0.80 by 20, we need to divide the numerator (0.80) by the denominator (20).

Dividing 0.80 by 20, we get 0.04.

Therefore, the correct answer is 0.04.

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To find the X and Y intercepts from a slope intercept equation, first understand the equation structure (y = mx + b). The 'm' signifies the slope, and the 'b' indicates the y-intercept. To find the x-intercept, set y to zero and solve for x. To find the y-intercept, look at the 'b' value.

In a slope intercept equation written in the form y = mx + b, the x-intercept and y-intercept are determined by values of y and x when they equal zero respectively. The 'm' signifies the slope of the line, indicating the rise over run on the graph, and the 'b' indicates the y-intercept, which is the point at which the line intersects the y axis.

To find the y-intercept from a slope-intercept equation, you consider the 'b' in the equation. For instance, in the line graph, the y-intercept is 9, meaning the line crosses the y-axis at the point (0,9).

To find the x-intercept (the point where the line crosses the x-axis), you set y equal to zero and solve for x. If 'y' is equal to '0', then the equation becomes 0 = mx + b. Solving for 'x' in this equation will give the x-intercept.

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let x represent the number of apples and y represent the number of oranges.

TOTAL: x + y = 112  

                  y = 112 - x

PEELED: [tex]\frac{3}{8}x = \frac{1}{2}y[/tex]

[tex](8)\frac{3}{8}x = (8)\frac{1}{2}y[/tex]

3x = 4y

3x = 4(112 - x)

3x = 448 - 4x

7x = 448

x = 64

y = 112 - x

  = 112 - 64

  = 48

a) There are 64 apples and 48 oranges

Peeled apples: [tex]\frac{3}{8}x = \frac{3}{8}(64)[/tex]= 3(8) = 24

Unpeeled apples: 64 - 24 = 40

Unpeeled - Peeled: 40 - 24 - 16

b) there are 16 more unpeeled apples than peeled apples

264. Is another way once you multiply it.

1 lb = 16 ounces

11.3 lb x 16 oz = 180.8 ounces

11.3 lb equals 180.8 oz

Answer: 180.8 ounces

Step-by-step explanation: To convert 11.3 pounds to ounces, first find the conversion factor for pounds and ounces.

Conversion factor → 16 ounces = 1 pound

Next, notice that we are going from a larger unit "pounds" to a smaller unit "ounces." When we go from a larger unit to a smaller unit we multiply.

Larger ⇒ smaller multiply

In this case, we multiply 11.3 pounds by our conversion factor which is 16 ounces.

11.3 × 16 = 180.8 oz.

This means that 11.3 pounds is equal to 180.8 ounces.

It is $600. Hope i helped

g(x):

flip f(x) over x-axist and next translate 2 units down.

Look at the picture.

Translations

y = f (x) + m up m units

y = f (x) - m down m units

y = f (x + m) left m units

y = f (x - m) right m units

Stretches/Shrinks

y = n · f (x) stretch vertically by a factor of n

y = 1/n · f (x) shrink vertically by a factor of m (stretch by 1/n)

y = f (1/n x) stretch horizonally by a factor of n

y = f (nx) shrink horizontally by a factor of n (stretch by 1/n)

Reflections

y = - f (x) reflect over x-axis (over line y = 0)

y = f (- x) reflect over y-axis (over line x = 0)

x = f (y) reflect over line y = x

2 11/32 / 1 1/2 = 25/16 hope this helps you

Answer:

A) y=mx+b

Step-by-step explanation:

The slope-intercept form is simply the way of writing the equation of a line so that the slope (steepness) and y-intercept (where the line crosses the vertical y-axis) are immediately apparent. Often, this form is called y = mx + b form.

Answer:

88

Step-by-step explanation:

You are just adding 82+6=88