Manuel's bus ride to school is 9/10 of a mile and Jessica's bus ride is 3/10 of a mile. How much longer is Manuel's bus ride than Jessica's?
A)
6
0
of a mile
Eliminate
B)
12
0
of a mile
C)
6
10
of a mile
D)
12
20
of a mile

To solve the given operation firat we take LCM for both terms.

As denominator of first term is 3 and second term is [tex] 12x-8 [/tex]

Therefore, the Lcm is [tex]3(12x-8) [/tex]

Now solving and making same denominator for each term

[tex]\frac{7}{3} [/tex] [tex]\times [/tex] [tex] \frac{12x-8}{12x-8} [/tex]

On multiplying we get

[tex]\frac{7(12x-8)}{3(12x-8)} [/tex] [tex]=\frac{84x-56}{3(12x-8)} [/tex]

Now solving other term

[tex]\frac{8}{12x-8} [/tex] [tex]\times [/tex] [tex]\frac{3}{3} [/tex]

On multiplying we get

[tex]\frac{24}{3(12x-8)} [/tex]

Now solving the expression by putting the values

[tex]\frac{84x-56-24}{3(12x-8)} [/tex]

[tex]\frac{84x-80}{12(3x-2)} [/tex]

[tex]\frac{4(21x-20)}{12(3x-2)} [/tex]

On solving we get

[tex]\frac{21x-20}{3(3x-2)} [/tex]

There denominator of the expression is

[tex]9x-6 [/tex]

Hope this will help

"Alternate" angles are on opposite sides off the transversal.

"Interior" angles are between the lines the transversal is crossing.

The appropriate choice for alternate interior angles is ...

... 5 and 3

Answer:

The pair of angles the are alternate interior angles are 5 and 3. Or C.

Step-by-step explanation:

Multiplication was invented to reduce the work involved in repeated addition.

... 88 + 88 + 88 + 88 = 4×88 = 352

352 passengers are carried to the island each day.

_____

Some questions must be answered before we can give a definite answer.

1. If the same person rides twice, are they counted twice?

2. Are passengers on the return trips (from the island) counted?

3. If return trip passengers are counted, is the ferry full on those trips?

4. Does every passenger to the island return the same day?

5. Does any passenger go to the island more than once per day?

Direct variation is a relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first. If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).

Given the equation [tex]2x-4y=0,[/tex] you can see that

[tex]4y=2x,\\\\y=\dfrac{2}{4}x=\dfrac{1}{2}x.[/tex]

Then the constant [tex]k=\dfrac{1}{2}.[/tex]

Answer: correct choice is C.

x = [tex]\frac{3}{2}[/tex] ± [tex]\frac{1}{2}[/tex]i

the equation has no real zeros but instead has 2 complex zeros

the discriminant = b² - 4ac

with a = 2, b= - 6, c = 5

b² - 4ac = (-6)² - (4 × 2 × 5 ) = -4

since b² - 4ac < 0  there are no real zeros

using the quadratic formula

x = ( 6 ± √(- 4 ) )/4 = ( 6 ± 2i ) / 4

x = [tex]\frac{6}{4}[/tex] ± [tex]\frac{2}{4}[/tex] i

  = [tex]\frac{3}{2}[/tex] ± [tex]\frac{1}{2}[/tex] i

Answer: x=3+i/2 or x=3-i/2

APEX

Answer:

Step-by-step explanation:

a) There are 16 ounces in a pound, so 10 ounces is 10/16 = 5/8 lb. The total weight of the pigs is their number multiplied by their average weight:

... weight of pigs = 30 × 95 5/8 lb = ((30·95) + (30·5/8)) lb

... = (2850 + 150/8) lb = (2850 +18 3/4) lb = 2868 lb 12 oz

b) The truck tare weight is the gross weight less the weight of the pigs.

... truck tare = truck gross - truck load

... = (8×2000 lb) + (1123 lb) + (6/16 lb) - (2868 3/4 lb)

... = 17123 3/8 lb - 2868 3/4 lb = (17123 -2868) lb +(3/8 -3/4) lb

... = 14255 lb - 3/8 lb

... = 14254 5/8 lb

... = 14000 lb + 254 lb + 5/8 lb

... truck tare weight = 7 tons 254 lbs 10 oz

_____

Many graphing calculators will handle calculations with fractions very nicely.

answer:

128

step-by-step explanation:

1. recognize how we get to each number in the pattern

to get from 2 to 8 we can either add 6 or multiply by 4

2. lets see if either of those match up with the rest of the numbers in the pattern

0.125 + 6 = 6.125

our next value is .5 not 6.125

0.125 × 4 = .5

that works! so lets see if it works with the rest of our pattern -

0.5 × 4 = 2

it works! so our pattern is multiplying each value by 4

3. use our pattern on the value of 8

8 × 4 = 32

32 is our 5th value but we are looking for our 6th value

4. use on pattern on the 5th value (32)

32 × 4 = 128

The 6th number in the pattern is calculated by identifying the rule that each number is being multiplied by 4 to get the next one. By continuously applying this rule, we find that the 6th number is 128.

The subject of this question involves the identification and continuation of a numerical pattern. The given pattern is 0.125, 0.5, 2, 8. To recognize this pattern, observe the relationship between consecutive numbers. It seems like each number is being multiplied by 4 to obtain the next one. We can apply the same rule to find the 6th number in the sequence:

Therefore, the 6th number in the given pattern should be 128.

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C

given the 2 equations

8(a + b) + 3z = - 9 → (1)

(a + b) + z = 2 → (2)

multiply (2) by 3 so that the coefficients of z are equal

3(a + b) + 3z = 6 → (3)

subtract (1) - (3) to eliminate term in z

5(a + b) = - 15 ( divide both sides by 5 )

(a + b) = - 3 → C

30%

3/10

0.3

I think these are the right answers if I am understanding you correctly. :)

30%  ✔

3/10  ✔

1/3  ✖

0.3  ✔

0.03  ✖

Hope i Helped ❤

3z = 5

To isolate the variable ( solve for z), you need to divide both sides by 3.

The answer is D.

Let's make the mysterious, original price not-so-mysterious by calling it x. 245.97 is 3/5 of x.

We can equation this.

245.97 = 3/5x

x = 245.97 / (3/5)

x = 409.95

The answer, I believe, is $409.95. Hope this helps!

The original price of the laptop that Tom bought is calculated using the formula for the value of a part. This leads us to an equation, $245.97 / 0.6, resulting in the original price of the laptop being $409.95.

The subject of this question is basic mathematics, predominantly fraction and ratio. The problem states that Tom paid $245.97, which was 3/5 of the original price of the laptop. To find the original price, we can apply the formula for the value of a part, which states that the whole is equal to the part divided by the ratio representing the part. In this case, this gives us the equation $245.97 / (3/5) = Original Price.

To make this easier, we can convert the fraction 3/5 to its decimal form, which is 0.6. So, we will then have $245.97 / 0.6 = Original Price, which should give us the original price of the laptop. Completing the math, we find that the original price of the laptop is $409.95.

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Try this option (see the attachment, the answers are marked by red colour), note, the value of the left angle in not visible (task no. 3) >> solution not given.

Ask google if you still can't get the answer.

remainder = - 1

6x² + 11x - 3 ÷ (x + 2 ) = 6x - 1 - [tex]\frac{1}{x+2}[/tex]

Answer:  The required remainder is 1.

Step-by-step explanation:  We are given to find the remainder when the following polynomial is divided by (x + 2) :

[tex]p(x)=6x^2+11x-3.[/tex]

Remainder Theorem :  If a polynomial f(x) is divided by (x - a), then the remainder is f(a).

So, for the given polynomial p(x), the remainder will be equal to p(-2).

We have

[tex]p(-2)\\\\=6(-2)^2+11(-2)-3\\\\=24-22-3\\\\=-1.[/tex]

Thus, the required remainder is -1.

It would equal 0.75 and as a fraction it is 3/4

Hi!

[tex]\frac{9}{34}* \frac{17}{6}[/tex]

[tex]\frac{9*17}{34*6}[/tex]

[tex]\frac{153}{34*6}[/tex]

[tex]\frac{153}{204}[/tex]

[tex]Answer---->\frac{3}{4}[/tex]

Explanation: First multiply by the fraction 9*17/34*6. Then multiply by the numbers 9*17=153, with 153/34*6. Next you can also multiply by 34*6=204, with 153/204 as a fraction. You can also cancel the common factor 51, and the answer is 3/4 is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. And have a great day! -Charlie

Answer:

1/27

Step-by-step explanation:

Its 1/27 because you have to multiply (3)-3,

3 times 3 times 3

that will give you positive 27 so if your on usatestprep its positive  1/27

The number (3)⁻³ equals 1/27, which is the result of taking the reciprocal of 3 raised to the third power.

The question asks which number equals (3)⁻³. The notation (3)-3 indicates that we are dealing with an exponentiation operation, specifically raising the number 3 to the power of -3. To solve this, we'll use the rule that any number raised to a negative exponent is equal to 1 divided by that number raised to the positive exponent. Therefore, (3)⁻³ is equal to 1/(3³).

Now we'll calculate the exponent 3³, which is 3 multiplied by itself three times: 3 x 3 x 3 = 27. So, 1/(3³) is 1/27.

The final answer is therefore (3)⁻³ = 1/27.

the first number line

given | x + 4 | = 2

removing the bars from the absolute value gives

x + 4 = 2 or x + 4 = - 2

x = 2 - 4 or x = - 2 - 4

x = - 2 and x = - 6 ← solutions

these are indicated on the number line by a solid circle at - 2, - 6

Answer:

The solution is represented by  the first number line, wich has the solutions x=-6 and x=-2.

Step-by-step explanation:

We have an absolute value function for the equation. This means that we should have two differents solution in the real number line. As the equation is

[tex]|x+4|=2[/tex]

when we clear out the absolute value, we will have two possible solutions:

[tex]x+4=2[/tex]

and

[tex]-(x+4)=2[/tex]

now we clear x from both equations

[tex]x+4=2 \Leftrightarrow x=2-4 \Leftrightarrow x=-2[/tex]

[tex]-(x+4)=2 \Leftrightarrow -x-4=2 \Leftrightarrow -2-4=x \Leftrightarrow x=-6[/tex]

Then, we have that x=-2 and x=-4 are the solutions for the equation, and therefore the number line that represents the solution is the first one, where the points -6 and -2 are highlighted.

Solution-

The original or cost price of the good = $21.00

Then, it is marked up 78.7%, i.e the price is 78.7% more than the initial price, which in this case is $21.

The new price is,

[tex]21+(21\times \frac{78.7}{100})=\$37.527[/tex]

Then, 10% profit must be earned after selling the good. Hence, the list price must be 10% more of 37.527,

So, the selling or list price is

[tex]37.527+(37.527\times \frac{10}{100})=\$41.279 \approx \$41.28[/tex]

∴ $41.28 is the selling price of the good and this is how you got it.

Answer:

The equation of [tex]C_{1}[/tex] is:  [tex]x^2+y^2=4[/tex]

and the equation of [tex]C_{2}[/tex] is:  [tex]x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]

Step-by-step explanation:

The standard form of circle equation: [tex](x-h)^2+(y-k)^2 = r^2[/tex] , where [tex](h,k)[/tex] is the center and  [tex]r[/tex] is the radius of the circle.

The center of the circle [tex]C_{1}[/tex] is at origin or at (0, 0)  and has radius of 2.

So, the equation of the circle [tex]C_{1}[/tex] will be........

[tex](x-0)^2+(y-0)^2=(2)^2\\ \\ x^2+y^2=4 ..........................................(1)[/tex]

Now, the center of [tex]C_{2}[/tex] is the point in the first quadrant, where the line [tex]y=x[/tex] intersects [tex]C_{1}[/tex]

Solving the equations  [tex]x^2+y^2=4[/tex] and [tex]y=x[/tex] , we will get......

[tex]x^2+x^2= 4[/tex]  (Substituting [tex]y[/tex] as [tex]x[/tex])

[tex]2x^2= 4\\ \\ x^2=2\\ \\ x=\pm \sqrt{2}[/tex]

So,  [tex]y=x = \pm \sqrt{2}[/tex]

Thus, the center of the circle [tex]C_{2}[/tex] will be at  [tex](\sqrt{2},\sqrt{2})[/tex]  (Negative value is ignored as the point is in first quadrant)

Now, the distance between the center of [tex]C_{2}[/tex] and the x-axis is [tex]\sqrt{2}[/tex] and the circle touches the x-axis only at one point.

That means, the radius of the circle [tex]C_{2}[/tex] will be also [tex]\sqrt{2}[/tex]

So, the equation of the circle [tex]C_{2}[/tex] will be......

[tex](x-\sqrt{2})^2+(y-\sqrt{2})^2= (\sqrt{2})^2\\ \\ x^2-2\sqrt{2}x+2+y^2-2\sqrt{2}y+2=2\\ \\ x^2+y^2-2\sqrt{2}x-2\sqrt{2}y+2=0[/tex]

Earl is incorrect

let x be the number of discount tickets sold

then the number of regular tickets sold is 6x

the total tickets sold is 1456, thus

x + 6x = 1456

7x = 1456 ( divide both sides by 7 )

x = 208

number of discount tickets sold = 208

[tex]\frac{1456}{6}[/tex] ≠ 208

but [tex]\frac{1456}{7}[/tex] = 208

Earl is incorrect , dividing by 7 gives the amount sold

A cell phone company sold 450 cell phones in three hour

450 is 30% of the number of phones sold that day

30% of number of phones = 450

We need to find the number of phones for 100%

Let x be the number of cell phones sold that day

30% of x is 450

[tex]\frac{30}{100} * x= 450[/tex]

multiply by 100 on both sides

30 * x = 45000

Divide by 30

x = 1500

So 1500 cell phones are sold that day

To find the total number of cell phones sold by the company in a day, set up a proportion using the given information and solve for the total number of cell phones sold. In this case, the company sold 15,000 cell phones that day.

A cell phone company sold 450 cell phones in three hours, which was 30% of the phones sold that day. To find the total number of cell phones sold that day, we can set up a proportion:

Let x be the total number of cell phones sold that day.

450/3 = x/100

450 × 100 = 3x

45000 = 3x

x = 15000

Therefore, the cell phone company sold 15,000 cell phones that day.

Answer: Domain (-∞,∞) ; range: (0,∞)

Step-by-step explanation:

1. The exponential functions with the form [tex]f(x)=ab^{x}[/tex] has domain of all real numbers, becaure there is no values in the set of real number for which the value of [tex]x[/tex] is not define. When [tex]x[/tex] approches to ∞, the function approches to ∞.

2. When [tex]x[/tex] approches to -∞, the function approches to 0 but never touches it. This means  that [tex]y[/tex] is always greater than zero ([tex]y>0[/tex]). Therefore, the range of the function is (0,∞).

Answer:

Lesson 1 unit 5 exponential, logarithmic, pricewise functions

Step-by-step explanation:

1. A and D

2. C

3. B

4.c

Answer:

      -4 - 2

m= --------- (over)

      -1 - 2

Step-by-step explanation:

2x - y = 2

obtain the equation of the line in slope-intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (- 1, - 4) ← 2 points on the line

m = [tex]\frac{-4-2}{-1-2}[/tex] = [tex]\frac{-6}{-3}[/tex] = 2

the line crosses the y-axis at (0, - 2 ) ⇒ c = - 2

y = 2x - 2 ← in point-slope form

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

rearrange y = 2x - 2 into this form

subtract y from both sides

0 = 2x - y - 2 ( add 2 to both sides )

2x - y = 2 ← in standard form

The missing number can be shown as the variable x.

6 + 10 - 2 = 11 + x  

So, you need to figure out what x is by getting it by itself. First, combine everything on the left side of the equation.

16 - 2 = 11 + x

14 = 11 + x  

Now, what you do to one side of an equation, you have to do to the other. Subtract 11 from both sides

14 - 11 = 11 - 11 + x   Cancel out the 11s and solve the left side.

3 = x  

There's your answer! Now you can check your work by trying the 3 in your original problem.

6 + 10 - 2 = 11 + 3

14 = 14

Your missing number is 3.

Given expression is [tex]7 \sqrt{50x^{15}y^{21}}[/tex] where x and y are non negative.

Now we have to simplify this to find the correct matching choice.

[tex]7 \sqrt{50x^{15}y^{21}}[/tex]

[tex]=7 \sqrt{25*2x^{15}y^{21}}[/tex]

[tex]=7 \sqrt{25*2x^{14}*xy^{20}*y}[/tex]

[tex]=7*5x^{7}y^{10} \sqrt{2*x*y}[/tex]

[tex]=35x^{7}y^{10} \sqrt{2xy}[/tex]

Which best matches with choice D.

Hence final answer is [tex]35x^{7}y^{10} \sqrt{2xy}[/tex] .

Answer:

B

Step-by-step explanation:

I also got 35x^7y^10√2xy

:)

y - 2

You get 2 less than a value when you subtract 2 from that value.

The solution follows the sequence ...

The problem is in the first step, where parentheses are eliminated. One of the multiplications is done incorrectly, and the error is propagated through the rest of the solution.

0.15(y -0.2) = 0.15y - 0.03 . . . . not 0.15y - 0.3

If you carry forward the value 0.03 instead of 0.30, you find the answer is

... -153/35 = y

______

Some of the other steps should be ...

.15y -.03 = 2 - .5 + .5y

15y -3 = 150 +50y

-153 = 35y

3 + 6i

multiply the numerator/ denominator by the conjugate of 2 + i

the conjugate of 2 + i = 2 - i

[tex]\frac{15(2-i)}{(2+i)(2-i)}[/tex]

= ( 30i - 15i² ) / (4 - i² ) → ( i² = (√-1 )² = -1 )

= [tex]\frac{30i+15}{5}[/tex] = 6i + 3

Answer:

3+6i

Step-by-step explanation:

[tex]\frac{15i}{2+i}[/tex]

To divide we multiply by the conjugate of denominator

conjugate of 2+i is 2-i

Multiply top and bottom by 2-i

[tex]\frac{(15i)(2-i)}{(2+i)(2-i)}[/tex]

Apply FOIL method to multiply. value of i^2 = -1

(15i)(2-i) = 30i - 15i^2 = 30i +15(-1)= 30i+15

(2+i)(2-i)= 4 - i^2 = 4+1= 5

[tex]\frac{30i+15)}{5}[/tex]

Divide each term by 5

6i+3

so its 3+6i