y−3=2(x+1) Complete the missing value in the solution to the equation. ( -1, _ )

Look at the picture.

We must use the Pythagorean theorem two times.

first time:

[tex]d^2=4^2+6^2\\\\d^2=16+36\\\\d^2=52\to d=\sqrt{52}[/tex]

second time:

[tex]AB^2=1^2+(\sqrt{52})^6\\\\AB^2=1+52\\\\AB^2=53\to AB=\sqrt{53}[/tex]

Answer:

A=6 and B=4.5

Step-by-step explanation:

You are given table

[tex]\begin{array}{cccccc}x&2&4&[A]&7&9\\y&1&2&3&3.5&[B]\end{array}[/tex]

If the paired values are in a proportional relationship, then

[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{[A]}{3}=\dfrac{7}{3.5}=\dfrac{9}{[B]}.[/tex]

Note that

[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{7}{3.5}=2,[/tex]

then

[tex]\dfrac{[A]}{3}=2\Rightarrow [A]=6,\\ \\\dfrac{9}{[B]}=2\Rightarrow [B]=\dfrac{9}{2}=4.5.[/tex]

Answer:

the answer is 6  

Step-by-step explanation: im 100% right this guy is wrong i repeat this guy is wrong!

Answer: $45.00

Step-by-step explanation:

75 x 0.60 = 45

Answer:

$30

Step-by-step explanation:

First, change the percentage into decimal:

60% = 60/100 = 0.6

Multiply 75 with 0.6:

75 * 0.6 = 45

Note that this number 45 (0.6 of 75) is the amount off from the original price (75). Subtract 45 from 75

75 - 45 = 30

$30 is your answer

~

Answer:

Option B is correct.

the value of discriminant is, -7

Step-by-step explanation:

Given the equation: [tex]x^2 + x +2 = 0[/tex]

To find the value of discriminant [tex]b^2-4ac[/tex]

A quadratic equation is of the form [tex]ax^2+bx+c = 0[/tex] where a, b and c are coefficient of the equation.

On comparing with given equation we have;

a  = 1 , b = 1 and c = 2

then;

Discriminant = [tex]b^2-4ac =(1)^2 -4(1)(2) =1 -8 = -7[/tex]

Therefore, the value of discriminant is, -7

[tex]5+8e > 76\qquad\text{subtract 5 from both sides}\\\\8e > 71\qquad\text{divide both sides by 8}\\\\\boxed{e=\dfrac{71}{8}}[/tex]

[tex]e\cdot7<28\qquad\text{divide both sides by 7}\\\\\boxed{e<4}[/tex]

-(-2)^3=-(-8)=8. So the answer is 8. or the fourth answer choice.

Answer:

5h + 2c = 31

5c + 3h = 30

Step-by-step explanation:

Let h = HD video price

Let c = classic video price

Fiona bought 5 HD videos and 2 classic videos for $31

5h + 2c = 31

Iliana bought 5 classic videos and 3 HD videos for $30

5c + 3h = 30

This is the system of equations

5h + 2c = 31

5c + 3h = 30

Answer:

Correct answer on test is D. 5 x + 2 y = 31. 3 x + 5 y = 30.

Step-by-step explanation:

Answer:

= 7.5x-8

Step-by-step explanation:

Total cost = cost per yard * yard of fabric - coupon

total cost = 7.5 x - 8

y = 7.5x-8

Answer:

[tex]y=7.50x+8[/tex]

Step-by-step explanation:

For the equation, the amount of money is [tex]y[/tex], and the number of yards is [tex]x[/tex].

So, the problem says that the persona already have $8, which is constant, it wont' variate, that is, this is the independent term.

Then, it says the the fabric costs $7.50 per yard, and [tex]x[/tex] refer to yards, so this term would be [tex]7.50x[/tex].

Therefore, the equation to model this problem would be:

[tex]y=7.50x+8[/tex]

The point where the line crosses the x-axis is called the [x-intercept]. The [y-intercept] is the point where the line crosses the y-axis.

Y-intercept.

By calculating the separations between two perpendicular lines that pass through a fixed point in Cartesian coordinates, we may find the location of a point P. Assume that O is the fixed point known as the origin and that XOX' and YOY' are the two perpendicular lines that pass through O and are referred to as the Cartesian or Rectangular co-ordinate axes.

given, the graph crosses the y-axis A point having an x-value and a y-value, is a coordinate: (x, y). The origin is the place where the two number lines converge, and it has the following coordinates: (0, 0). The x-value is zero when the graph of a function crosses the y-axis at a value b. As a result, the point is the y-intercept (0, b).

Therefore, A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

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Answer:

First picture:

1)Given

2)Substitution

3) Subtraction Property of Equality

4)if altenate interior angles are equal, then the lines are parallel

Second picture:

1) Given

2)if lines are parallel, then the corresponding angles are equal

3)Substitution

4)if altenate interior angles are equal, then the lines are parallel

Answer: D).-20

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

Answer:

6x^2 - 4y^2 + 2x^2 + 6xy

Step-by-step explanation:

Each of the adjacent sides of the rectangle has a congruent, opposite sides. The perimeter is the sum of the lengths of the 4 sides.

P = 2(3x^2 - 2y^2) + 2(x^2 + 3xy)

P = 6x^2 - 4y^2 + 2x^2 + 6xy

24.

The perimeter of a rectangle l × w is P = 2l + 2w.

We have l = 3x² - 2y² and w = x² + 3xy. Substitute:

P = 2(3x² - 2y²) + 2(x² + 3xy)      use distributive property

P = (2)(3x²) + (2)(-2y²) + (2)(x²) + (2)(3xy)

P = 6x² - 4y² + 2x² + 6xy      combine like terms

keeping in mind that the x-intercept is where the graph touches the x-axis, and when that happens, y = 0, thus

[tex]\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y=-3x+3 \\\\\\ \stackrel{\textit{setting y = 0}}{0=-3x+3}\implies -3=-3x\implies \cfrac{-3}{-3}=x\implies 1=x~\hfill \stackrel{\textit{x-intercept}}{(1,0)} \\\\\\ ~\hspace{34em}[/tex]

Answer: x-intercept = 1

Step-by-step explanation: To solve this problem, we need to remember that the y-intercept is the point where the line crosses the y-axis. So if our line has a y-intercept of 3, it crosses the y-axis up 3 units. So we start this problem by plotting the point (0,3) on y-axis and we can label that point A.

From there, our slope of -3 can be thought of as -3/1 so we go down 3 units and to the right 1 unit and we plot point B. Notice that point B happens to lie on the x-axis at (1,0) and it's important to understand that the x-intercept is the point where the line crosses the x-axis.

Since our line crosses the x-axis at the point (1,0), it as an x-intercept of 1. If you're given a y-intercept and a slope like you are in this problem, you won't always be able to determine the x-intercept but things work out nicely here because point B happens to lie on the x-axis.

I provided an image with the graph and my work as well.

Answer:

B) 2328.50

Step-by-step explanation:

We are given 200 shares at $11.58 per share. By multiplying the number 200 with each share value will get the cost of all shares.

Total shares = 200

Cost per share = $11.58

Cost of 200 shares: Total shares * cost per share

= 200 * 11.58 = 2316

Commission charged = $12.50

Total amount: Cost of 200 shares + Commission charged

                      = 2316 + 12.50

Total amount = 2328.50

Answer:

the answer should be 2,401 were going to St. Ives

Step-by-step explanation:

7 times 7 times 7 times 7 is 2401

Answer:

The answer is B. 7^0 + 7^1 + 7^2 + 7^3

To round 0.1287 to the nearest thousandth, we look at the next place value which here is 7. Since 7 is more than 5, we round up the thousandth place. Hence, 0.1287 becomes 0.129.

To round the number 0.1287 to the nearest thousandth, you need to look at the ten-thousandth place (which is the fourth numeral after the decimal point). In this number, the ten-thousandth place is 7. If this digit is 5 or above, we need to round up. If it is less than 5, we stay with the number as is. Since 7 is bigger than 5, we round up. Therefore, 0.1287 rounded to the nearest thousandth is 0.129.

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Answer:

x = 22.5 and y = 9

Step-by-step explanation:

Since the lines are perpendicular then the angles formed are right, hence

4x = 90 ( divide both sides by 4 )

x = 22.5

and 10y = 90 ( divide both sides by 10 )

y = 9

Answer:

The difference in temperature between a depth of 1200 meters and 3750 meters is 2.55

Step-by-step explanation:

The temperature T of the water in an ocean at depth X below 900 meters is given by:

T= 4500/X

To calculate the difference between a depth of 1200 meters and 3750 meters, it is necessary to calculate the temperature individually.

first, 1200 meters and 3750 meters are below 900 meters, so the equation describe before is applicable.

As a result, for 1200 meters, the temperature (symbolized as T1) is given by:

T1=4500/X

T1=4500/1200

T1=3.75

For 900 meters, the temperature (simbolized as T2) is given by:

T2=4500/X

T2=4500/3750

T2=1.2

The difference between the temperature T1 and T2 is:

Difference in temperature = T1 - T2

Difference in temperature = 3.75 - 1.2

Difference in temperature = 2.55

So, the difference in temperature between a depth of 1200 meters and 3750 meters is 2.55

Answer:

18 kg

Step-by-step explanation:

Recycling rate = 12 kg/6wk

Recycled = 9 × 12/6

Recycled = 9 × 2

Recycled = 18 kg

Answer:

m<S = 45°

Step-by-step explanation:

The sum of the measures of the angles of a triangle equals 180 deg.

m<R + m<S + m<T = 180

3x + 2x + 3x = 180

8x = 180

x = 22.5

m<S = 2x = 2(22.5) = 45

In an isosceles triangle, the sum of the angles must equal 180 degrees. Given the angles labeled as multiples of x, solving for x gives 22.5 degrees, and m∠S is found to be 45 degrees.

The student is asking to find the measure of angle S in an isosceles triangle with vertices labeled R, S, and T, where sides RS and ST are equal, and the angles at R and T are labeled as 3x degrees, and angle S as 2x degrees. Since the sum of angles in any triangle is always 180 degrees, we can set up an equation by adding the angles together: 3x (angle R) + 2x (angle S) + 3x (angle T) = 180. Simplifying the equation gives 8x = 180, and solving for x gives x = 180 / 8 = 22.5 degrees. Finally, to find m∠S, we substitute x back into the expression for angle S: m∠S = 2x = 2(22.5) = 45 degrees.

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Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.

Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.

Given here: Jake reaches 25 inches above the ground in 3 seconds.

The unit rate of Jake's ascend is = 25/3

                                                =8.33 inches/second

If Jake rides the escalator for 15 seconds then we would climb

=8.33×15

=124.95 inches

After 45 seconds Jake would have climbed =45×8.33

                                                                          =374.85 inches

Thus after 45 seconds Jake reaches the top of the escalator.

Hence, Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.

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Answer:

4(x-8)^2 -521

The gradient of the line y= 5-5x is -5 which is the coefficient of 'x'. This connotes a negative slope, meaning the line descends as we move along the positive x-axis.

The equation y = 5 - 5x represents a straight line in the xy-plane. The coefficient of 'x' in the equation represents the slope of the line. Therefore, the gradient of the line is -5. This means for every unit increase in x, y will decrease by 5 units. This negative slope suggests that the line moves downwards as the x-value increases, similar to our reference figure A1 where the slope caused a rise or fall on the vertical axis for every increase of 1 on the horizontal axis.

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Answer:

4 muffins

Step-by-step explanation:

just divide 8 by 2 or see how many times 2 can go into 8.

Answer:

4 muffins per cup of flour

Step-by-step explanation:

To solve this, simplify the ratio as much as possible

8 muffins : 2 cups of flour

You are solving for: x muffins : 1 cup of flour

Simplify. Divide common factors from both the numerator and denominator. In this case, divide 2.

8/2 = 4

2/2 = 1

4 muffins : 1 cups of flour is your simplified version.

4 muffins per cup of flour is your answer

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Answer:

Option 2.

Step-by-step explanation:

You are bisecting angle BAC  with pencil and compass.

Answer:

The angle bisector of a given angle.

Step-by-step explanation:

From the construction, < BAC is the given angle. With any radius, draw arc BC. With any radius and points B and C as the centers consecutively, draw arcs to intersect at O. Join O to A. Line /AO/ is the angle bisector of the given angle <BAC.

The construction illustrated is the angle bisector of a given angle.

5 - 4 + 7x + 1 = 7x + (5 - 4 + 1) = 7x + 2

NO SOLUTIONS:

5 - 4 + 7x + 1 = 7x + a    (a - any real number, except 2)

ONE SOLUTION:

5 - 4 + 7x + 1 = bx + c     (b - any real number, except 7, c - any real number)

INFINITELY MANY SOLUTIONS:

5 - 4 + 7x + 1 = 7x + 2

Examples:

2x + 3 = 2x + 5     subtract 2x from both sides

3 = 5    FALSE      (NO SOLUTIONS)

2x + 3 = x - 4      subtract x from both sides

x + 3 = -4       subtract 3 from both sides

x = -7          (ONE SOLUTION)

2x + 3 = 2x + 3      subtract 2x from both sides

3 = 3     TRUE      (INFINITELY MANY SOLUTIONS)

1) For No Solution

5 - 4 + 7x +1 = 7x

2) For One Solution

5- 4 +7x + 1 = 3

3) For No Solution

5 - 4 + 7x + 1 = 7x + 2

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1) For No Solution

5 - 4 + 7x +1 = 7x

2) For One Solution

5- 4 +7x + 1 = 3

3) For No Solution

5 - 4 + 7x + 1 = 7x + 2

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Answer:

f(-3) =10

Step-by-step explanation:

When given a function f(-3), they want you to substitute x=-3 into the function f(x) and solve

f(x) =|2x+1|+5

Let x=-3

f(-3) =|2 *-3+1|+5

f(-3)=|-6+1|+5

f(-3)=|-5|+5

The absolute value of -5 is positive 5  (absolute values means always positive).

f(-3)=5+5

f(-3) =10

We have three pairs of rectangles:

16ft × 6ft = 96ft²

2ft × 6ft = 12ft²

2ft × 16ft = 32ft²

S.A. = 2 × (96 + 12 + 32) = 2 × 140 = 280ft².

The surface area of a right prism is given by summing the areas of all its faces.

The surface area of a right prism can be calculated by finding the sum of the areas of all its faces.

Let's say the right prism has a rectangular base with length l, width w, and height h.

The surface area of the right prism would then be given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the given values into the formula will give us the surface area of the right prism.

For example, if l = 6ft, w = 8ft, and h = 7ft, the surface area would be:

Surface Area = 2(6)(8) + 2(6)(7) + 2(8)(7) = 192 + 168 + 112 = 472ft²

Therefore, none of the given options match the correct surface area.

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Answer:

= 36000 caps

Step-by-step explanation:

First we need to figure out how many minutes between 8 am and 3:30 pm

There are 7 hours and 30 minutes.

1 hour = 60 minutes

Multiply each by 7

7 hours = 7*60 minutes = 420 minutes

So 7 hours 30 minutes = 420 + 30 = 450 minutes

Bottle caps = rate * minutes

                   = 80 caps/minute * 450 minutes

                    = 36000 caps

The machine can put tops on 36,000 bottles between 8:00 a.m. and 3:30 p.m.

To calculate how many tops can be put on bottles at a factory between 8:00 a.m. and 3:30 p.m. by a machine that works at a rate of 80 bottles per minute, we need to determine the total number of minutes the machine operates between those times and then multiply that number by the rate of the machine.

First, let's find the difference in time from 8:00 a.m. to 3:30 p.m.:

Therefore, the machine operates for a total of 7 hours and 30 minutes. Since 1 hour equals 60 minutes, we have:

7 hours * 60 minutes/hour = 420 minutes

420 minutes + 30 minutes = 450 minutes

Now we multiply the total minutes by the rate of the machine:

450 minutes * 80 bottles/minute = 36,000 bottles

So the machine can put tops on 36,000 bottles between 8:00 a.m. and 3:30 p.m.