In △ABC , line AB is extended up to point E and line BC is extended up to D . The measure of some of the angles is given as; ∠BAC=70° and ∠EBC=120° .
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Answer:

Step-by-step explanation:

Given that the functions f and g are defined by

[tex]f(x)=2x^2+x-3[/tex] and [tex]g(x)=x-1[/tex]

To find (f-g)(x)

Substitute the values of the functions we get

[tex](f-g)(x)=f(x)-g(x)=2x^2+x-3-(x-1)[/tex]

[tex]=2x^2+x-3-1(x)-1(-1)[/tex]

[tex]=2x^2+x-3-x+1[/tex]

[tex]=2x^2-2[/tex] ( by adding the like terms )

The value of (f-g)(x) is [tex]2x^2-2[/tex]. Thus, the correct option is (D)

Two different functions are given that are as follow:

[tex]f(x)=2x^2+x-3[/tex]

[tex]g(x)=x-1[/tex]

We need to determine the value of the composite function that is (f-g)(x).

Now, by using the property of the composite function (f-g)(x) can also be written as:

[tex](f-g)(x)=f(x)-g(x)[/tex]

Substitute the values of both the functions and solve it further for (f-g)(x).

[tex]\begin{aligned}(f-g)(x)&=(2x^2+x-3)-(x-1)\\&=2x^2+x-3-x+1\\&=2x^2-2\\&=2(x^2-1)\end{aligned}[/tex]

Thus, the value of (f-g)(x) is [tex]2x^2-2[/tex]. Thus, the correct option is (D)

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Answer:

D)M(x)=70x

Step-by-step explanation:

The function that represents the remaining distance after x hours is M(x) = 617 - 70x (option C).

The question asks about the function that represents the number of remaining miles, M(x), Kyle has to travel after x hours at a speed of 70 miles per hour. To calculate the remaining distance, we subtract the distance traveled (70 miles per hour times x hours) from the total distance of the trip, which is 617 miles. Therefore, the correct function is M(x) = 617 - 70x, which corresponds to option C.

To further illustrate this with an example, if Kyle drives for 1 hour at 70 miles per hour, he would have traveled 70 miles, so the remaining distance would be M(1) = 617 - 70(1) = 547 miles.

The equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]

Explanation:

The equation of the line is perpendicular to [tex]y=-14 x-8[/tex]

The equation is of the form [tex]y=mx+b[/tex] where m=-14

Slope:

The slope of the perpendicular line can be determined using the formula,

[tex]m_1 \cdot m_2=-1[/tex]

[tex]-14 \cdot m_2=-1[/tex]

       [tex]m_2=\frac{1}{14}[/tex]

Thus, the slope of the line is [tex]m=\frac{1}{14}[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the slope [tex]m=\frac{1}{14}[/tex] and the point (2,-4), we get,

[tex]y+4=\frac{1}{14}(x-2)[/tex]

Simplifying, we get,

[tex]y+4=\frac{1}{14}x-\frac{1}{7}[/tex]

     [tex]y=\frac{1}{14}x-\frac{1}{7}-4[/tex]

     [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]

Thus, the equation of the line is [tex]y=\frac{1}{4}x-\frac{29}{7}[/tex]

Answer:

53°

Step-by-step explanation:

x + (2x + 21) = 180

(Corresponding angles &

Supplementary angles)

3x + 21 = 180

3x = 159

x = 53°

Answer:

A square has 4 sides. 4 squares have 16 sides.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the midpoint of segment AB is (4, 2). The coordinates of point A is (2, 7).

[tex]4=\frac{2+x_2}{2}[/tex]                    [tex]2=\frac{7+y_2}{2}[/tex]

Multiply by 2 we get                             Multiply by 2 we get  

[tex]4(2)=2+x_2[/tex]                                           [tex]2(2)=7+y_2[/tex]

[tex]8=2+x_2[/tex]                                                [tex]4=7+y_2[/tex]

Subtracting 2 on both

the sides                                    Subtracting 7 on both the sides

[tex]8-2=2+x_2-2[/tex]                                [tex]4-7=7+y_2-7[/tex]

[tex]6=x_2[/tex]                                                       [tex]-3=y_2[/tex]

Rewritting the above equation      Rewritting the equation

[tex]x_2=6[/tex]                                                      [tex]y_2=-3[/tex]

Lenny's hourly rate is calculated by dividing his gross pay of $196.90 by the total number of hours worked, which is 22 hours. The calculation gives an hourly rate of $8.95.

The question is asking to calculate Lenny's hourly rate based on his gross pay for work done over three days. To find this rate, we will add the total number of hours worked and divide the total gross pay by this number.

Therefore, Lenny's hourly rate is $8.95.

Answer:

There are many fractions that are equivalent to 8/12. But if you are looking for the most simplified fraction, then the answer would be 2/3. Because you divide 8 and 12 both by 2. 8 divided by 2 equals 4, and 12 divided by 2 equals 6. Then you would do it again, since both can be divided by 2 again. 4 divided by 2 equals 2, and 6 divided by 2 equals 3. You cannot divide 3 by 2, so your answer would be 2/3.

Answer:

d > -5

Step-by-step explanation:

Step 1:  Subtract 15 from both sides

15 + d > 10

15 + d - 15 > 10 - 15

d > -5

Answer:  d > -5

Miss C weight before she started her diet is 80 kg.

Solution:

Weight before diet = x

Weight loss percent = 8%

Present weight of Miss C = 73.6 kg

[tex]$ x-x\times \ 8 \% =73.6[/tex]

[tex]$ x-x\times \frac{8}{100} =73.6[/tex]

The denominators must be same to add/subtract the fractions.

LCM of 1 and 100 = 100

Multiply first term by [tex]\frac{100}{100}[/tex] and 73.6 by [tex]\frac{100}{100}[/tex] to make the denominator same.

[tex]$ \frac{100x}{100} - \frac{8x}{100} =\frac{7360}{100}[/tex]

[tex]$ \frac{100x-8x}{100} =\frac{7360}{100}[/tex]

Multiply by 100 on both sides, we get

100x - 8x = 7360

92x = 7360

Divide by 92 on both sides, we get

x = 80

Miss C weight before she started her diet is 80 kg.

great someone deleted all my answers again

A convex polygon with n + 2 sides has the sum of its interior angles equal to 2160 degrees, which is 360 degrees more than a polygon with n sides that has 1800 degrees.

The degree measure of the sum of the interior angles of a convex polygon with n sides, given as 1800 degrees, follows the formula (n - 2) times 180 degrees. For a convex polygon with n + 2 sides, we can apply the same formula: ((n + 2) - 2) times 180 = (n times 180) + (2 times 180).

Therefore, the degree measure of the sum of the interior angles of a convex polygon with n + 2 sides is 1800 degrees plus 360 degrees, giving us a total of 2160 degrees.

Answer:

x=-1

x=-2

Step-by-step explanation:

4x2 + 12x + 8

To solve a quadratic equation, factorisation Method, formulae method or completing the square method can be used. But for the purpose of this question, the formulae method will be used.

(-b±√(b²-4ac))2a

Where a=4, b=12 and c=8

(-12±√(12²-4(4)(8))/2(4)

(-12±√(144-128)/8

(-12±√16)/8

(-12±4)/8

(-12+4)/8 or (-12-4)/8

-8/8 or -16/8

-1 or -2

There was a minor mistake in the second step. The sum should be 2/3 + 4/9, not 2/9 + 4/9. After finding the common denominator and converting the fractions, we add the numerators to get 10/9, which simplifies to 1 1/9.

The process Rodrigo followed is correct, but there was a small mistake in the second step. Here, the problem should be 2/3 + 4/9, not 2/9 + 4/9. To add fractions like this, it's critical to ensure they have common denominators. The lowest common denominator (LCD) of 3 and 9 is 9.

So, the fraction 2/3 should be converted to its equivalent fraction with 9 as the denominator. Multiplying both the numerator and the denominator of 2/3 by 3, we get 6/9. So now our problem becomes 6/9 + 4/9.

Now, we can add them by combining their numerators: 6+4 = 10. So, the answer would be 10/9. But in simplest form, we would write this as 1 1/9. Hence, the sum of 2/3 and 4/9 in simplest terms is 1 1/9.

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To find what percent 9 is of 20, you divide 9 by 20 and multiply the result by 100. The answer is 45%.

To determine what percent 9 is of 20, you'd set up an equation based on the mathematical definition of percentage:

p = (part/whole) * 100%

Here, our part is 9 and our whole is 20. So you arrange the numbers in the given formula:

p = (9/20) * 100%

Solving the equation gives us 45%

Therefore, 9 is 45% of 20.

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To find out what percent 9 is of 20, we can use the formula part/whole = percent/100. Using this equation, we can solve for p and find that 9 is 45% of 20.

To find out what percent 9 is of 20, we can set up an equation using the formula:

part/whole = percent/100

In this case, the part is 9, the whole is 20, and we want to find the percent. So the equation becomes:

9/20 = p/100

To solve for p, we can cross multiply:

9 * 100 = 20 * p

Dividing both sides of the equation by 20 gives us:

900 = 20p

Finally, dividing both sides by 20 gives us the value of p:

p = 900/20 = 45

Therefore, 9 is 45% of 20.

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Answer:

100

Step-by-step explanation:

1. 100 divided by 5 = 20

2. 20 x 100 = 2000

3. Final Answer = 100

A company plans to ship 2,000 packages of chocolate, the number of packages is  X=100. This is further explained below.

Generally, the number of packages is given as

X=(No Packages* incorrect weight)/ random selections

Therefore

X=2000*5/100

X=100

In conclusion, the number of packages predicted to have an incorrect weight is

X=100

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Answer:

3 nights

Step-by-step explanation:

Set up an equation that represents the problem:

y = 1.25x + 3.95

Where y is the total cost and x is the number of additional nights you rent the movie

Substitute:

7.70 = 1.25x + 3.95

Subtract 3.95 on both sides:

7.70 = 1.25x + 3.95

-3.95              -3.95

3.75 = 1.25x

Divide by 1.25 on both sides:

3.75 = 1.25x

/1.25    /1.25

3 = x

Therefore, you kept the movie for 3 additional nights.

Answer:

3

Step-by-step explanation:

Answer:

3/10

mark brainliest

Step-by-step explanation:

Answer:

x=2 and y= -3

Step-by-step explanation:

This is a simultaneous equation. To solve this type of equation, there are three methods; substitution, Elimination and Graphical.

But here, we would be using the substitution method.

3x-y=9 Equation 1

2x-y=7. Equation 2

Getting y from equation 2, we have

-y= 7-2x

Multiply both sides by -

y= 2x-7 Equation 3

Substituting y for 2x-7 in equation 1, we have

3x- (2x-7)=9

3x-2x+7=9

x+7=9

x=9-7

x=2

Substituting x as 2 in equation 3

y=2x-7

y= 2(2)-7

y= 4-7

y= -3

Answer:

220.5

Step-by-step explanation:

:3

Answer:

220.5 lb

Step-by-step explanation:

1 kg = 2.20462262185 lb

100 kg = 100×2.20462262185 lb

100 kg = 220.462 lb

100 kg = 220.5 lb

Here in question, the table is not given to complete the table with ordered pairs. So, in general, found the possible integer ordered pairs to create the table as in attached figure are [tex](x,y) =(0,3), (12,0),(4,2),(8,1)[/tex].

Step-by-step explanation:

We have the following given linear equation : [tex]x+4y = 12[/tex].Let's find out ordered pairs that satisfies this linear equation .

At x=0 ,

[tex]0 + 4y = 12 \\4y=12\\y=3[/tex]

So, one pair is [tex](x,y) = (0,3)[/tex].

Similarly, At y=0,

[tex]x +4.0 = 12\\x=12[/tex]

SO, another pair is [tex](x,y) = (12,0)[/tex].

At x=4,

[tex]4+4y=12\\4y=8\\y=2[/tex]

Pair is [tex](x,y) = (4,2)[/tex].

At x=8,

[tex]8+4y=12\\4y=4\\y=1[/tex]

Pair is [tex](x,y) = (8,1)[/tex].

Therefore all the possible integer ordered pairs are [tex](x,y) =(0,3), (12,0),(4,2),(8,1)[/tex].

Answer:

The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = 25 blocks.

Step-by-step explanation:

Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.

So, Reyna's house, the school, and the Shaquille's house form a right triangle and the shortest distance from Shaquille's house to Reyna's house is the hypotenuse of the right triangle.

So, the shortest distance that Shaquille could walk on his way to school when he walks with Reyna is = [tex]\sqrt{12^{2} + 5^{2}} + 12 = 13 + 12 = 25[/tex] blocks. (Answer)

The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.

Since Reyna's house is 12 blocks due west of the school. Shaquille's house is 5 blocks due north of the school.

So, here the shortest distance is

[tex]= \sqrt{(12)^2 + (5)^2}+ 12\\\\[/tex]

= 13 + 12

= 25

Hence, The shortest distance that Shaquille could walk on his way to school when he walks with Reyna is 25 blocks.

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About 32.9 minutes have gone by.

To find this answer you take your percent and make it a decimal by dividing it by 100. In doing so, you'll get 0.53. Then multiply 0.53 by 62 to get 32.86. Since you have to round to the nearest tenth, you look at the hundredths place to see whether you round up (5-9) or round down (1-4). In this case, you round up making your answer 32.9 minutes.

I hope this helps!

Answer/Step-by-step explanation:

About 32.9 minutes have gone by.

To find this answer you take your percent and make it a decimal by dividing it by 100. In doing so, you'll get 0.53. Then multiply 0.53 by 62 to get 32.86. Since you have to round to the nearest tenth, you look at the hundredths place to see whether you round up (5-9) or round down (1-4). In this case, you round up making your answer 32.9 minutes.

I hope this helps!

Answer: 24

Step-by-step explanation:

2^3 + 4^2

(2×2×2) + (4×4)

8+16 = 24

d ≤ 6

The solution set is {6, 5, 4, 3, 2, 1, 0, –1, –2, ....}

Solution:

Given expression is the inequality.

The inequality is [tex]\frac{d}{3}\leq 2[/tex].

To solve this inequality:

[tex]$\frac{d}{3}\leq 2[/tex]

Multiply by 3 on both sides of the inequality, we get

[tex]$\frac{d}{3}\times 3\leq 2 \times 3[/tex]

[tex]$d\leq 6[/tex]

That is the value of d is 6, 5, 4, 3, 2, 1, 0, –1, –2, ....

The solution set is {6, 5, 4, 3, 2, 1, 0, –1, –2, ....}

Hence d ≤ 6.

Answer:

Ninety and four one hundredths

Step-by-step explanation:

The word form of the number is Ninety and four hundredths.

We have,

To write 90.04 in word form, you can express it as "ninety and four hundredths."

Here's an explanation:

The whole number part, 90, is read as "ninety."

The decimal part, 0.04, is read as "four hundredths."

Combining these two parts, we say "ninety and four hundredths" to represent the decimal number 90.04 in word form.

Thus,

The word form of the number is Ninety and four hundredths.

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Answer:

The intersection is (1,-2) I am really sure.

The measure of angle B is 65°

Explanation:

Given that ∠A and ∠B are supplementary angles.

The measures are ∠A = (3x - 17)° and ∠B = (2x-23)°

The value of x:

Since, supplementary angles add up to 180°, then we have,

[tex]\angle A+ \angle B=180^{\circ}[/tex]

Substituting the values, we have,

[tex]3x-17+2x-23=180[/tex]

               [tex]5x-40=180[/tex]

                       [tex]5x=220[/tex]

                        [tex]x=44[/tex]

Thus, the value of x is 44

Measure of angle B:

Let us determine the measure of angle B by substituting the value of x in ∠B = (2x-23)°

Thus, we have,

[tex]\angle B=(2(44)-23)^{\circ}[/tex]

[tex]\angle B=(88-23)^{\circ}[/tex]

[tex]\angle B=65^{\circ}[/tex]

Thus, the measure of angle B is 65°