Solve the following equation:
(d - 3) tan 37°
17
Give your answer to 1 d.p.
-

Transformation is a process in which the size and/or orientation of a given figure are/is adjusted. The appropriate answers are:

i. equal to

ii. congruent to

iii. the same distance to

Transformation is the process required to either increase or decrease the size of a given shape, or change the orientation of a given shape. The methods of transformation are dilation, reflection, rotation, and translation.

Thus the required statements to complete the reflection across a line as required in the question are:

i. equal to

ii. congruent to

iii. the same distance to

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In accordance with the definitions of rigid transformation and translation, the correct rule for the translation is defined by (x, y) → (x - 3, y + 4). (Right choice: A)

Mathematically speaking, transformations are rigid transformations that are modelled according to the following formula:

P'(x, y) = P(x, y) + (h, k)     (1)

Where:

Hence, a leftward translation indicates that h < 0. The correct rule for the translation is defined by (x, y) → (x - 3, y + 4).

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Answer:

a

Step-by-step explanation:

the picture

Answer: X = 12.1 units

Step-by-step explanation:

Solving the side x of the triangle just requires the Pythagorean theorem.

x^2 + 7^2 = 14^2

x^2 + 49 = 196

subtract 49 on both sides, to cancel the 49 on the left side.

x^2 = 147 units

extract the square root of each side.

X = 12.1 units

Hope I Helped!

Answer:

32°, 58°

Step-by-step explanation:

Let one acute angle measure x.

The other acute angle measures 2x - 6.

The sum of the measures of the acute angles of a right triangle is 90.

x + 2x - 6 = 90

3x - 6 = 90

3x = 96

x = 32

2x - 6 = 2(32) - 6 = 58

Answer: 32°, 58°

Answer:

can't see anything in this photo because this photo is not clear

Answer:

7 ÷ 15 = 0.46666666666667

Step-by-step explanation:

Answer:

0.47

Step-by-step explanation:

To turn any fraction into a decimal, we must simply divide the numerator by the denominator. 7 divided by 15 is equal to 0.466666...

If we round this number to the nearest hundredth, we get 0.47.

The number of steps that Julissa walked each hour is 3409.6 steps per hour.

According to this question, Julissa works in the warehouse of a large online retailer. She walked 20,458 steps on Tuesday from 9:00 a.m. to 3:00 p.m.

9:00 a.m to 3:00pm is 6 hours difference. This means that Julissa walked 20,458 steps in 6 hours.

Therefore, Julissa walked 20,458 steps ÷ 6 = 3409.6 steps per hour.

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Answer:

it's A

Step-by-step explanation:

The sum of the expression (–x² + x) and (x² – 3x – 1) will be –2x – 1. Then the correct option is D.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression can be written as

(–x² + x) and (x² – 3x – 1)

Then the sum of the expression (–x² + x) and (x² – 3x – 1) will be

(–x² + x) + (x² – 3x – 1) = –2x – 1

Then the correct option is D.

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Answer:

B) [tex]-5\leq y\leq -1[/tex]

Step-by-step explanation:

The range is the lowest point to the highest point on the graph.

Remember this:

1. domain (x-axis) LEFT –> RIGHT

2. range BOTTOM (y-axis) –> TOP

when this equation is graphed over the domain, it limits the range to being (8,–5) and (–8,–1) and since with range you only look at the y-coordinates that means that the range is [–5,–1]

Answer:

(a) x = 0

(b) g(2) = -5

Step-by-step explanation:

Another way of representing g(x) is with the variable "y". In other words, the value of g(x) is the value on the y-axis (vertical axis).

(a) The question is asking you to give the "x" value when the line crosses y = -4. The only value which satisfies this is x = 0.

(b) When 2 is placed inside the parentheses of g(x), it is asking you to find the "y" value of the line at x = 2. The only value which satisfies this is y = -5.

The value of x would be 35.

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

In order to calculate the value of x in the parallelogram, we have to find the following;

Let ∠m = 2x - 10

∠n = 2x + 50

So, ∠m + ∠n = 180

2x-10 + 2x+50 = 180

4x + 40 = 180

4x = 180 - 40

4x = 140

x = 35

Hence, the value of x is 35.

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The equation for the ellipse centered at the origin is C. x²/4 + y²/49 = 1.

Let the equation of the ellipse be:

x²/b² + y²/a² = 1

The co vertices are at (2, 0) and (-2, 0). The major axis is 14 units. Therefore, 2a = 14. This implies that a = 7 and a² = 7 × 7 = 49.

Therefore, since x²/b² + y²/a² = 1, this will be x²/4 + y²/49 = 1.

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The value of discriminant [tex]b^{2} -4ac[/tex] of the equation [tex]-2x^{2} -3x+8=0[/tex] is equal to 73.

Given equation [tex]-2x^{2} -3x+8=0[/tex] and we have to find the value of determinant and the number of roots of the equation.

Determinant is the quantity that depends on the coefficients of variables.

To find out the value of determinant we have to put the values in [tex]b^{2} -4ac[/tex] in which b=-3, a=-2 and c=8

[tex]b^{2} -4ac[/tex]=[tex]-3^{2} -4*(-2)*8[/tex]

=9+8*8

=9+64

=73

And because the value of discriminant is one so the number of real solution that [tex]-2x^{2} -3x+8=0[/tex] is 2. If the discriminant is equal to zero then there is exactly one real root.

Hence the value of determinant of the equation [tex]-2x^{2} -3x+8=0[/tex] is 73.

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Ly has 15 dimes, 12 nickels and 30 quarters given that he has 3 more dime than nickels and twice as many quarters than dimes and the value of these coins is $9.60. This can be obtained by giving variables to each represent the number of each coin and adding the values to equate with the total value of coins.

Let number of dimes be y

Given that,

3 more dime than nickels ⇒ Number of nickel = y - 3

twice as many quarters than dimes ⇒ Number of quarters = 2y

9.60 = 0.1y + 0.05(y-3) + 0.25(2y)

9.60 = 0.1y + 0.05y - 0.15 + 0.5y  

9.60 = 0.1y + 0.05y - 0.15 + 0.5y  

9.60 + 0.15 = 0.65y

y = 9.75/0.65 = 15

y = 15

Therefore the number of each coin,

Hence Ly has 15 dimes, 12 nickels and 30 quarters given that he has 3 more dime than nickels and twice as many quarters than dimes and the value of these coins is $9.60.

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This shows that the food will only last 1 1/3 meals

Fractions are written as a ratio of two integers. Given the following

Total pounds of food bought = 24 pounds

Amount fed each per meal = 3/4 * 24 pounds = 18 pounds

Remains = 24 - 18

Remaining = 6 pounds

This shows that the food will only last 1 1/3 meals

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Answer:

approximately 8.5

Step-by-step explanation:

So you can use the distance formula: [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\[/tex] which is derived from the Pythagorean theorem because normally x2-x1 would kind of give the distance length between x2 and x1 except sometimes it would be negative which wouldn't make much sense right? but it doesn't matter because it's being squared so the value ultimately becomes positive, and the same thing goes for the y-value. the distance between x2 - x1 really represents the base and y2-y1 represents the height and then adding them together gives the hypotenuse squared which is why you take the square root over the entire thing to find the distance, since the hypotenuse is the shortest distance between two points

Now all you have to do is plug the values in to get

[tex]\sqrt{(-7 - (-4))^2 + (-8 - 0)^2}\\\sqrt{(-3)^2 + (-8)^2}\\\sqrt{9 + 64}\\\sqrt{73}\\distance \approx 8.5[/tex]

Answer: y = -2/3x+23/3

Step-by-step explanation:

Parallel is the key point here. They gave points (7,3), 7 is the x value, 3 is the y value.

Take your equation

y = -2/3x+3 and substitute the 7 for the x value and 3 for the y value.

Like this...

3 = -2/3(7)+b

3 = -14/3 +b

Add 14/3 to 3

The answer is 23/3

So y = -2/3x+ 23/3

***Don't change -2/3 because it's asking for parallel***

***If 2 lines are parallel their slopes are equal***

The solution will be a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

Inequalities are equations that are separated by an equal sign. Given the inequality expression

3(8 – 4x) < 6(x – 5)

Expand

3(8) - 3(4x) < 6x - 6(5)

24 - 12x < 6x - 30

Collect the like terms

-12x - 6x < -30 - 24

-18x < -54

x > 3

Hence the solution will be a number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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The two inside angles add up to the external angle's total. The m∠1 will be 69°. Option D is correct.

An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).

From the exterior angle property, the sum of the exterior angle is the sum of the two interior angles.

The m∠1 will be 69°.

Hence, option D is correct.

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Yosef's average weekly fuel cost would be $2537.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Yosef drove 12,900 miles last year. His truck's fuel efficiency averages 15 mpg.

Karla used 12900/15 = 860 gallons to drive 12900 miles.

The average cost of gas last year was $2.95 per gallon.

Therefore, Yosef's average weekly fuel cost would be

2.95 x 860 = $2537

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Answer:

3. Increase

Step-by-step explanation:

If more people are being born compared to the number of deaths, then you have population growth.

Answer:

3. increase

Explanation:

When birth rate is higher than the death rate, it is called natural increase.

The formula for natural increase is:

[tex]natural \space\ increase = \frac{Crude \space\ Birth \space\ Rate \space\ - \space\ Crude \space\ Death \space\ Rate}{100}[/tex]

The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form

An equation is an expression that shows the relationship between two or more variables and numbers.

A fraction in its simplest terms is given as a/b, where a is the numerator and b is the denominator.

Hence:

0.7 / 8 = 7 / 80

The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form

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Answer:

19

Step-by-step explanation:

Given:

To find how many full bags of sweets the machine can fill, divide the total number of sweets by the number of sweets per full bag:

⇒ 4275 ÷ 28 = 152.6785714...

Therefore, the machine can fill 152 full bags.

To calculate how many sweets are left, subtract the product of the number of full bags and the number of sweets per bag from the total number of sweets:

⇒ 4275 - (152 · 28)

⇒ 4275 - 4256

⇒ 19

Therefore, there are 19 sweets left after the machine has filled as many bags as possible.

Answer:

x = - [tex]\frac{5}{p}[/tex]

Step-by-step explanation:

px + 17 = 12 ( subtract 17 from both sides )

px = - 5 ( isolate x by dividing both sides by p )

x = [tex]\frac{-5}{p}[/tex] = - [tex]\frac{5}{p}[/tex]

Simplified value of  subtraction of 7x+27x+2 from -5x^2-2x−5x 2 −2x. is [tex]-10x^{2} -38x-2[/tex].

Given Expressions  7x+27x+2 and  -5x^2-2x−5x 2 −2x.

Expressions refers to the combination of numbers, variables and symbols. It represents the relationship between variables. They are solved for finding out the value of variables. It is mainly not in equal to form. Subtraction is possible when subtracting the coefficients of same variable.

We have to subtract 7x+27x+2 from -5x^2-2x−5x 2 −2x. and to do this we need to first solve the expressions itself.

7x+27x+2=34x+2------------------1

[tex]-5x^{2} -2x-5x^{2} -2x[/tex]=[tex]-10x^{2} -7x-2x[/tex]--------------------2

Now subtract 1 from 2

=[tex]-10x^{2} -7x-2x[/tex]-34x+2

=[tex]-10x^{2} -38x-2[/tex].

Hence the simplified value of subtraction is [tex]-10x^{2} -38x-2[/tex].

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