How many solutions does the following equation have?
-14(z-5) = -14z +70
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions

Answer: (-1, 3)

Step-by-step explanation:

Midpoint formula: ((x1 + x2) / 2, (y1+y2) / 2)

((-5+7)/2, (4+2) / 2))

((-2/2), (6/2))

(-1, 3)

Answer:

45

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

AB = 20 - 12 = 8

BC = 8 : 2 = 4

CD = 4 + 12 = 16

Answer:

CD = 16

Step-by-step explanation:

Check the image for the steps

On dividing 1658 by 25 , the quotient is equal to 66.32.

As given in the question,

Dividend is equal to 1,658

Divisor is equal to 25

Unit place value of 1658 is equal to 8.

25 is not a factor of 1658

Smallest number to 1658 divisible by 25 is 1650

Divide 1658 by 25 we get remainder

Dividend = ( Divisor × quotient) + remainder

1658 = 1650 + 8

        = ( 25 × 66 ) + 8

Remainder is equal to 8

Quotient is equal to 66

In decimal form

1658 ÷ 25

= 66.32 is quotient.

Therefore, the quotient of dividing 1658 by 25 is equal to 66.32.

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Answer:

check this one

Step-by-step explanation:

this is the answer

Answer: 12/7

Step-by-step explanation:  The answer is 12/7 because here is what we know: A group of friends collected toys to donate to children in need. After sorting the toys into boxes, that's what we know,  we also know that they found they had 6/7 of a box of stuffed animals, and we also know that they found 5/7 of a box of board games and

1/7 of a box of doll. What they want to know is  In total, how many boxes of toys did the friends collect?  so you take 6/7 from the box stuffed animals they found + 5/7 from the box of board games they found which equals 11/7 then you add the 11/7 with the 1/7 the box of dolls they found.  In total the friends collect 12/7 boxes. Hope this helps!

The density of  a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is  0.003 kg / m³.

Density of the matter means space taken by matter.

To find the density, density = mass of matter / volume of mass.

Given that mass of the pumpkin 2.0 kg and a volume of 0.0060 m³.

Now the density from the formula;

Density = mass of pumpkin / volume of pumpkin

Density = 2.0 / 0.0060

Multiply by 10000,

Density = 20000 / 60

Density = 2000 / 6

Density = 1000 / 3

Density = 0.003 kg / m³

Therefore, the density of  a pumpkin with a mass of 2.0 kg and a volume of 0.0060m³ is  0.003 kg / m³

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The temperature on Sunday was 20° C

The equations representing the number and value of coins are n + q = 12  and 5n + 25q = 2.20 respectively.

A system of linear equations is a group of  equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

The given problem can be solved as follows,

Suppose the number of nickel and quarter coins are n amd q respectively.

Then, the equation for the total number of coins can be written as,

n + q = 12                  (1)

And, the equation for their value is given as,

5n + 25q = 2.20       (2)

Hence, the two equations that can be used to represent the given case are n + q = 12  and 5n + 25q = 2.20 respectively.

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The number 1.1 * 10⁴ in standard form is 11000

From the question, we have the following parameters that can be used in our computation:

Number = 1.1\times 10^{4}1.1×104

Rewrite the given number properly

So, we have the following representation

Number = 1.1 * 10⁴

Solving further, we need to apply the law of indices to expand the exponents

Using the above as a guide, we have the following:

Number = 1.1 * 10 * 10 * 10 * 10

Evaluate the product of the 10's

So, we have the following representation

Number = 1.1 * 10000

Evaluate the products of the 1.1 and 10's

So, we have the following representation

Number = 11000

Hence, the number is 11000

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On solving the provided question, we got by the help of Slope formula - [tex]= 5x - y + 5 = 0[/tex]

A line's slope can be calculated as the ratio of how much y rises when x rises by a specific amount. A line's slope, or how much y increases as x increases, is indicated by the word "slope." Along the straight line, the slope is constant (equal) everywhere.

From the figure we got that,

X1 = 0, Y1 = 5

X2 = -1, Y2 = 0

(0,5) and (-1,0)

By the of slope formula

[tex]\frac{y - y1}{x - x1} = (\frac{y2 - y2}{x2 - x1} )(\frac{x - x1}{y - y1} )[/tex]

[tex]{y - 5} = (\frac{0-5}{-1-0} )({x - 0 )\\\\\\[/tex]

[tex]= > 5x - y + 5 = 0[/tex]

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In parallelogram lonm, om is 34.

What is parallelogram?

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of equal size.

A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

First we have OQ =QM,

So 2x+3=3x-4,

x =7.

Hence OM =2(17)=34.

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Answer: D) 34

Step-by-step explanation:

edge 2023

To obtain a score of 85% on a test worth 135 points, one needs to get 115 points. By using proportions, we get the required value.

A proportion is defined as an equality between two ratios.

Consider two ratios a:b and c:d. Then, the proportion we can write,

a: b = c : d

Then, the simplification we have for this proportion is

a/b = c/d or ad = bc

It is given that, a certain test is worth 135 points.

One to get 85% on this test, he/she needs to get X number of points.

So, we can write the proportions as

X : 135 = 85 : 100

⇒ X/135 = 85/100

⇒ X = 85/100 × 135

∴ X = 114.75 ≅ 115 points

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Answer:

x=4/3, 8/3

Step-by-step explanation:

We will solve this in two steps, one where the right hand side is 2, one where it is -2. This is because the equation is satisfied either way when [tex]|6-3x|[/tex] is equal to either of those values.

Let's start with 2. We have [tex]6-3x=2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 4/3. This is the first value.

Now, we solve for when it equals -2. We have [tex]6-3x=-2[/tex]. Subtracting 6 from both sides and then dividing by 3 gives us that x = 8/3. This is the second value.

Feel free to contact me with any questions about my answer. I hope this helps!

Answer:

.5l means that you are going to add 1/2 cups of lemon juice for every bath that you make.  If you made one batch, you would use  1/2 of lemon juice. If you made 2 batches you will add 1 cup of lemon juice and so on.

2s means that you will add 2 cups of sugar for each batch.  If you made one batch, you would add 2 cups of sugar, if you made 2 batches you would add 4 cups nd so on.

Step-by-step explanation:

Step-by-step explanation:

always remember Pythagoras for right-angled triangles (90°) :

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90° angle), a and b are the legs.

so, in our case

ramp² = 11² + 60² = 121 + 3600 = 3721

ramp = sqrt(3721) = 61 ft

Answer:

61 feet

Step-by-step explanation:

Because the triangle is a right triangle we can use the Pythagorean theorem to solve for the length of the ramp.

The Pythagorean theorem is a² + b² = c²

Where, a and b = leg lengths and c = hypotenuse (longest side)

Here, the length of the ramp represents the hypotenuse as it is the longest side. We are also given the length of the legs. The lengths being 60 ft and 11 ft.

This means that a and b = 11 and 60

We can plug these lengths in and then solve for c or the length of the ramp

a² + b² = c²

==> plug in a = 11 and b = 60

11² + 60² = c²

==> simplify exponents

121 + 3600 = c²

==> add 121 and 3600

3721 = c²

==> take the square root of both sides

61 = c

So the length of the ramp is 61 feet

Answer:

Your answer is [tex]x = -1[/tex] and [tex]y = -2[/tex]

Step-by-step explanation:

(attached)

Answer:

smaller = 25, bigger = 65

Step-by-step explanation:

x = smaller

y = bigger

2x + 15 + x = 90

3x + 15 = 90

3x = 75

x = 25

y + x = 90

y + 25 = 90

y = 65

The resulting triangle is 7/10 the original triangle.

The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).

Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 7/10,

Then changed triangle is  A'B'C'

So, relation between them is A'B'C' = 7/10(ABC)

Thus, the resulting triangle is 9/5 multiple of triangle ABC.

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The value of the exponent illustrated as 27^1/3 is 3.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this situation, it should be noted that 27^1/3 simply means the cube root of 27. This will give a value of 3.

Check: 3 × 3 × 3 = 27.

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1

substitute 9 as x because 9 is in the brackets

then follow bidmas

brackets first so -10 + 9 = -1

now indices so square -1 which is 1.

therefore you answer is 1

Therefore the solution of this question is ratio length =  every 1 inch of toy car represents 1.5 feet of actual car

In mathematics, a ratio shows how two numbers are multiplied together. In a bowl of fruit, for instance, the proportion of oranges to lemons is eight to six if there are eight oranges and six lemons. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.

Here,

A toy Jeep measures 12 1/2 inches.

Before calculating the ratio, let's first convert each size into the same unit of measure and decimal points:

=>12 ½ = 25/2  

=> 12.5 inches;

=> 18 ¾ = 75/4

=> 18.75 feet .

The actual length of a jeep is 18.75 feet.

The ratio can now be determined by converting feet to inches.

1 inch of a toy car equals 1.5 feet of an actual car because

=> 1 foot = 12 inches

=>  12.5 inches : 225 inches

 => 225 / 12.5

=> 18 inches

Therefore, every 1 inch of toy car represents 1.5 feet of actual car.

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Answer:

20:50 or 2:5

Step-by-step explanation:

30 dogs

20 cats

50 total animals

Part to whole relationship:

20:50

Answer:

Step-by-step explanation:

5

It is possible to calculate the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our question-

The likelihood that responses to fewer than two of the final six questions were right can be calculated using the procedure below:

There are 6 questions with a total of 4 possible answers, hence the value of p is:

The following formula provides the probability:

The following formula is used to calculate the likelihood that Ira would properly answer exactly 1 of the final 6 questions:

P(X = 1) = 0.35595

P(X = 0) = 0.17797 gives the likelihood that Ira will correctly answer 0 out of the final 6 questions.

 Accordingly, the likelihood that the last 6 questions' answers contain fewer than 2 valid responses is: P = 0.17797 + 0.35595.

P = 0.53392

P = 53.392%

Hence, the probability that in the last 6 questions, there were fewer than 2 right answers, which is 53.392%.

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Your first step of simplifying is to distribute the "–" or "–1" in front of the second set of parentheses through that second set of parentheses.  The –1 must be distributed to every term in the second set:

    [tex]\begin{aligned}(4x^2-5x)-(4x^2-4x-8)&=(4x^2-5x)\boldsymbol{{}-1}(4x^2-4x-8)\\[0.5em]&=4x^2-5x\boldsymbol{{}-1(4x^2)-1(-4x)-1(-8)}\\[0.5em]&=4x^2-5x\boldsymbol{{}-4x^2+4x+8}\\[0.5em]&=-x+8\\\end{aligned}[/tex]

That's what changes the sign on every term in the second set of parentheses, making that –8 become +8.

The area of the given circle is 95 cm².

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, we know that the diameter of the circle is 11 cm.

Radius = Diameter/2

11/2

5.5 cm

Area of circle: πr²

3.14(5.5)²

3.14*30.25

94.985

Rounding off: 95 cm²

Therefore, the area of the given circle is 95 cm².

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The equation of line in slope-intercept form is,

a.) y = -6x - 47

b.) y = x/6 - 8/3

What is Equation of line ?

A straight line's general equation is y = mx + b, where m denotes the gradient and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.

We know, slope-intercept form is

y = mx + b

The given equation is in point slope form,

a.) y + 5 = -6 (x + 7)

b.)  y + 2 = 1/6 (x-4)

Now, let's write each equation in slope-intercept form,

a.) y + 5 = -6 (x + 7)

y + 5 = -6x - 42

y = -6x - 42 - 5

y = -6x - 47            [which is slope-intercept form]

b.) y + 2 = 1/6 (x-4)

y + 2 = 1/6 * x - 1/6 * 4

y + 2 = x/6 - 2/3

y = x/6 - 2/3 - 2

y = x/6 - [2/3 + 2]

y = x/6 - [(2 + 6) / 3 ]

y = x/6 - 8/3            [which is slope-intercept form]

Hence, the equation of line in slope-intercept form is y = -6x - 47 and y = x/6 - 8/3  

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The mean weight of 7 grapefruits will be 7 pounds and the standard deviation will be 0.84 pounds.

The mean weight of R will be 3 pounds and the standard deviation will be 0.36 pounds.

The mean weight of Q will be 4 pounds and the standard deviation will be 0.48 pounds.

a. The mean and standard deviation of 7 grapefruits will be 7 times the mean and standard deviation of a single grapefruit, respectively.

b. If G represents the weight of a single grapefruit, then

R = G + G + G

= 3G.

The mean and standard deviation of R will therefore be 3 times the mean and standard deviation of a single grapefruit, respectively.

c. If T represents the total weight of all 7 grapefruits, then

Q = T - R

= 7G - 3G

= 4G.

The mean and standard deviation of Q will be 4 times the mean and standard deviation of a single grapefruit, respectively.

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