The length of the base of an isosceles triangle is x. The length of a leg is 3x + 2. The perimeter of the triangle is 39. Is there enough information to solve for x? if so, find x.

Answer:

53

Step-by-step explanation:

They're vertical angles so they equal the

Answer:

∠ VUX = 53°

Step-by-step explanation:

∠ VUX and ∠ TUS are vertically opposite angles and are congruent, so

∠ VUX = 53°

Answer: y = 2x

Step-by-step explanation:

Write in slope-intercept form,

y = mx + b.

y = 2x

On a graph, the coordinates will be:

(2,4);(4,8) Just like you had said above.

Hope this helped!

The value is x=9, when the points are (x,1), (-3,7), (-5,9), (5,4).

The slope formula is defined as the formula used to calculate the steepness of a line and to determine how much it's inclined. To calculate the slope of the lines, we need the x and y coordinates of the points.

The formula to calculate slope is given as,

m = (y2 - y1)/(x2 - x1)

where m is the slope of the line,

x1, x2 are the coordinates of the x-axis,

y1 and y2 are the coordinates of the y-axis.

Consider the Points as A=(x,1),B=(-3,7),C=(-5,9),D=(5,4)

Now, take two points  C, D to know the m value:

Slope  = y₂ - y₁/ x₂-x₁

m1 = 4 - 9 / 5- [-5]

     = -5 / 5+5  = -5/10 = -1/2

m1 = -1/2

Consider the next two points A, B:

A(x, 1), B(-3,7)

Slope of AB m2 =  7- 1 / -3 - x  

m2= 6/-3-x

As AB  || CD, m2 = m1

6/-3-x=-1/2

6*2=-1 *(-3-x)  {cross multiplication}

12 = (-1 * -3)-x *-1

3+x = 12

x=12-3

x = 9

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a. Yes, the amount of water in the pool is a function of the number of minutes. b. The domain of the function is  0 < x ≤ 588. The domain is continuous c. The required graph has been attached below.

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

a. Yes, the amount of water in the pool is a function of the number of minutes. This is because, for each input value of the number of minutes, there is a unique output value of the amount of water in the pool.

Where the function is y = 17x  

b. The domain of the function is the set of all possible values of the input, which in this case is the number of minutes. The domain is continuous because it includes all possible values within a range (in this case, all possible values of the number of minutes), rather than only a set of specific, discrete values.

Assume that the capacity of the swimming pool with water is 10000 gallons.

So it completed fully fills with water in 588.2 (=10000/17) minutes

Thus, the domain of the functin is 0 < x ≤ 588.

c. Here is a graph of the function using its domain:

Where the vertical axis represents the amount of water in the pool and the horizontal axis represents the number of minutes.

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Answer:

43 inches

Step-by-step explanation:

172 divided by 4

The measures of the angles of the triangles are

m∠1 = 55°

m∠2 = 125°

m∠3 = 35°

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔCDE

And ∠BAC = m∠1

And , ∠CDE = m∠3

Now , from the triangle ΔABC

∠ABC = 180° - 110° ( Angle of a straight line is 180° )

So , the measure of angle ∠ABC = 70°

The sides of the triangle AC and BC are similar

So , The angles of the triangle are = 70° + x + x = 180°

On simplifying the equation , we get

70° + m∠1 + m∠1 = 180°

Subtracting 70° on both sides of the equation , we get

2m∠1 = 110°

Divide by 2 on both sides of the equation , we get

m∠1 = 55° = ∠ACB

And , ∠ACB and m∠2 are on a straight line

So , m∠2 = 180° - 55°

On simplifying the equation , we get

m∠2 = 125°

The triangle ΔCDE is a right triangle with ∠DCE = m∠1 ( vertically opposite angles )

So , the angles of the triangle are = 90° + 55° + m∠3 = 180°

On simplifying the equation , we get

145° + m∠3 = 180°

Subtracting 145° on both sides of the equation , we get

m∠3 = 35°

Hence , the measures of the angles of the triangles are are m∠1 = 55° , m∠2 = 125° , m∠3 = 35°

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The checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.

Given that, Jaquan passed a checkpoint jogging at a constant speed of 9 km/hr.

2 minutes later Odalis passed the same checkpoint.

Odalis runs at a constant speed of 12 km/hr.

We know that, 1 hour = 60 minutes

So, 2 minutes = [tex]\frac{2}{60}[/tex] hour

= [tex]\frac{1}{30}[/tex] hour

So, the distance = [tex]9\times\frac{1}{30}[/tex]

= [tex]\frac{3}{10}[/tex] km

When the speed is 12 km/hr, we get

Distance = [tex]12\times\frac{1}{30}[/tex]

= [tex]\frac{2}{5}[/tex] km

Now, [tex]\frac{2}{5} - \frac{3}{10}[/tex]

= [tex]\frac{4}{10} - \frac{3}{10}[/tex]

= [tex]\frac{1}{10}[/tex] km

= 0.1 km

Therefore, the checkpoint Odalis will be when they catch up to Jaquan is 0.1 km.

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Answer:

1.2

Step-by-step explanation:

none

Answer:

[tex]\huge\boxed{\sf Perimeter = 42\ cm}[/tex]

Step-by-step explanation:

Here,

Perimeter = 7 cm + 7 cm + 7 cm + 7 cm + 7 cm + 7 cm

[tex]\rule[225]{225}{2}[/tex]

Percentage error in the area is 79.84 %

Percentage error is defined by the difference between actual value and estimated value while comparing to the actual value and expressed in percentage.

given, sides of a rectangle are 6.2 cm and 4.8 cm.

actual length = 6.2 cm

actual width = 4.8 cm

hence, area of rectangle = length × width

                                       = 6.2 cm x 4.8 cm

actual area = 29. 76 square centimeters.

measured length = 2 cm

measured width = 3 cm

measured area = 2 x 3 = 6 square cm

percentage error in the area = (actual area - measured area) / actual area ×100

                                                      =(29.76 - 6) / 29.76 × 100

                           percentage         error               = 79.84 %

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The inequality between -4 and 6 is; -4<x<6

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions

Let X represents the numbers between -4 and 6

X is between -4 and 6  means -4 and 6 is not included in the series of number. That is they are the boundaries

The numbers between -4 and 6 are; -3, -2, -1, 0, 1, 2, 3, 4, 5.

To find the inequality look the series of numbers. We notice that the numbers ( -3, -2, -1, ) are greater than -4  (the numbers are greater than -4 because they are nearer  to 0 on the left hand side of the number line) and the numbers (1, 2, 3, 4, and 5) are smaller than 6

Therefore, the inequality is; -4 < X < 6

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The diameter is twice the radius, so it is decreasing at a rate of [tex]$2(1.26 \times 10^{-2} \ \text{cm}/\text{hr}) = \boxed{2.52 \times 10^{-2} \ \text{cm}/\text{hr}}$[/tex]

The volume of the grindstone is [tex]$\pi r^2 h = \pi \cdot 100^2 \cdot 10 = 3141600 \ \text{cm}^3$[/tex], so the rate at which it is wearing away is  [tex]$\frac{50}{3141600} = 1.59 \times 10^{-4} \ \text{cm}^3/\text{hr}$[/tex]

The grindstone is a cylinder, so its volume is proportional to its radius squared. Therefore, the radius is decreasing at a rate proportional to [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].

The diameter is twice the radius, so it is decreasing at a rate of [tex]$\sqrt{1.59 \times 10^{-4}} = 1.26 \times 10^{-2} \ \text{cm}/\text{hr}$[/tex].

A diameter is a line segment that passes through the centre of a circle or other curved shape and has its ends at the circumference. The length of a diameter is twice the length of the radius of the circle. A radius is a line segment joining the centre of a circle or other curved shape to any point on its circumference. The length of a radius is half the length of the diameter of the circle. Both the diameter and radius are fundamental measurements in determining the size and shape of a circle or other curved shape.

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The diameter of the grindstone is decreasing at a rate of 5/(πr) cm/hr.

Therefore the answer is b) 5/ (πr) cm/hr.

The grindstone is losing material at a rate of 50 cm³/hr, and since it is a cylinder, we can use the formula for the volume of a cylinder to find the rate at which its diameter is decreasing.

The volume of a cylinder is given by:

[tex]V= \frac{ \pi D^{2} h}{4}[/tex]

where V is the volume, d is the diameter and h is the height (in this case the thickness of the grindstone).

We know that the grindstone is losing material at a rate of 50 cm³/hr, and that the grindstone's thickness is 10 cm. To find the rate at which the diameter is decreasing, we need to find the rate at which the radius is decreasing, which we can find by differentiating the volume equation with respect to time.

So

[tex]\frac{dV}{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{d(\frac{\pi\\D^{2}h }{4}) }{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{2}{4}\pi Dh\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]

Substitute the known values,

[tex]\frac{2}{4}\pi *(D)*(10cm)\frac{dD}{dt} = -50\ cm^{3}/hr[/tex]

[tex]\frac{dD}{dt}= (-50 cm^3/hr)*\frac{4}{2\pi *(D cm)*(10 cm)}[/tex]

[tex]\frac{dD}{dt}= \frac{-10}{\pi D}cm/hr[/tex]

We know D = 2r

[tex]\frac{dD}{dt}= \frac{-10}{\pi*(2r)}cm/hr[/tex]

[tex]\frac{dD}{dt}= \frac{-5}{\pi r}cm/hr[/tex]

--The question is incomplete, answering to the question below--

"A 10 cm thick grindstone is initially 200 cm in diameter, and it is wearing away at a rate of 50 cm³/hr. At what rate is it's diameter decreasing?

a. 5/ (2πr) cm/hr

b. 5/ (πr) cm/hr

c. 5/ (2π) cm/hr

d. 5/ π cm/hr"

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Answer: $180 for 4 shirts and 360 for 8 shirts (this includes the 10% discount for both answers)

Step-by-step explanation: First, we have to multiply 50 by 4, since each shirt is $50 and there are 4 shirts to purchase. The answer is $200, but you have a 10% discount to consider. 10% of 200 is 20, so subtract $20 from 200, and you get $180 for 4 shirts. To find out the amount of money it costs to pay for 8 shirts, you can simply add 180 and 180 together and it'll give you 360.  This way, the 10% discount will not be left out.

Let me know if this is right! :)

Answer:

  (a)  $1049.15

Step-by-step explanation:

You want to know the interest earned by an account that pays 3.2% interest compounded semiannually if the balance is $6049.15 after 6 years.

The formula for the balance of an account earning compound interest is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.

We have ...

  6049.15 = P(1 +0.032/2)^(2·6) = P(1.016^12)

The amount of interest earned is the difference between the account balance and the principal:

  interest = 6049.15 -(6049.15/1.016^12) ≈ 1049.15

The total amount of interest earned is $1049.15.

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The age of Kate will be 16 years.

The age of Leo will be 20 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Kate is 4 years younger than Leo.

And, Twice Kate's age minus 3 is the same as Leo's age plus 9.

Now,

Let the age of Leo = x

So, The age of Kate = x - 4

Here, Twice Kate's age minus 3 is the same as Leo's age plus 9.

Hence, We can formulate;

⇒ 2 (x - 4) - 3 = x + 9

Solve for x as;

⇒ 2x - 8 - 3 = x + 9

⇒ 2x - x = 9 + 11

⇒ x = 20 years

Thus, The age of Leo = x

                                 = 20 years

So, The age of Kate = x - 4

                               = 20 - 4

                               = 16 years

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Answer: Its y-intercept is obtained when the x coordinate is 0, so that the function crosses the y-axis. Therefore, it means that x=0 . Note that the y value that corresponds to this intercept is y=f(0) y = f ( 0 ) . Thus, an ordered pair that represents the y-intercept is (0,f(0)) ( 0 , f ( 0 ) )

Step-by-step explanation:

The statement must be true about p(x): "The remainder when p(x) is divided by x - 2 is -5". which is the correct answer that would be an option (D).

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

For a polynomial p(x), the value of p(2) is -5.

The remainder when p(x) is divided by x - 2 is -5.

This statement must be true because, by definition, the remainder of a polynomial division is the value of the polynomial when it is evaluated at the divisor. In this case, the divisor is x - 2, so the remainder when p(x) is divided by x - 2 is p(2). Since the value of p(2) is given as -5, it follows that the remainder when p(x) is divided by x - 2 must be -5.

None of the other statements are necessarily true based on the information given.

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The values of a, b and c are a= 2, b = 3, c = -10

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We have been given an Cos Ф = 1/8

Cos Ф = 4x/y

Cos Ф = 4x/y = 1/8

x/y = 1/32

We need to write given expression in the form y² = ax² +bx+c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with expression where a, b and c are numbers.

a = 2, b = 3 and c = -10

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The probability of selecting a heart and flipping a coin and landing on heads is the product of these two probabilities, or approximately 0.12.

To find the probability, We have given:

There are 13 hearts in a standard pack of playing cards, and there are 52 cards total. The probability of selecting a heart is 13/52, or approximately 0.25. The probability of flipping a coin and landing on heads is 1/2, or approximately 0.50.

The probability of selecting a heart and flipping a coin and landing on heads is the product of these two probabilities, or approximately 0.12. This can be written as P(heart) * P(heads) = (13/52) * (1/2) = 0.12.

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The probability of selecting a heart and the coin landing on heads = 1.25

In this question we have been given a  card is drawn at random from a standard pack of playing cards then a fair coin is flipped.

We need to find the probability of selecting a heart and the coin landing on heads.

We know that there are 13 hearts in a standard deck of playing cards, and there are 52 cards total.

So, the probability of selecting a heart would be,

P1 = 13/52

P1 = 1/4

P1 = 0.25

We know that the probability of flipping a coin and landing on heads is 1/2

P2 = 1/2

P2 = 0.50

The probability of both occurring is the product of the two probabilities,

P = P1 * P2

P = 0.25 * 0.50

P =1.25

So, the required probability is 1.25

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I will have 11 cookies remaining.

The expression will be; Y = 33 - X

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on.

For the first batch

Total = 36 - 33 (collected by dad)

Total = 33

Second batch

Let remainder = Y

Y = 33 - X

where X = teachers part

To find the remainder, X = 2/3 x Total

X = 2/3 x 33

X = 22

Therefore;

Y = 33 - 22

Y = 11

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By evaluating the quadratic equations we will get:

3c(a-4)+3d(a+5) =  3*(a^3 - 8a^2 + 102a + 22)

Here we have two quadratic functions:

c(x)=x^3-2x and d(x)=4x^2-6x+8

And we want to find the value of the expression:

3c(a-4)+3d(a+5)

First, let's evaluate the functions in these values:

3*c(a - 4) = 3*[ (a - 4)^3 - 2*(a - 4)] = 3*(a - 4)*[ (a - 4)^2 - 2]

               = 3*(a -4)*(a^2 - 8a + 16 - 2)

               = 3*(a - 4)*(a^2 - 8a + 14)

               = 3*(a^3 - 12a^2 + 46a - 56)

3*d(a + 5) = 3*[ 4*(a + 5)^2 - 6*(a + 5) + 8]

                = 3*[ 4a^2 + 40a + 100  -6a - 30 + 8]

                = 3*[4a^2 + 36a + 78]

Then the expression is:

3c(a-4)+3d(a+5) = 3*(a^3 - 12a^2 + 46a - 56) + 3*[4a^2 + 36a + 78]

                           = 3*(a^3 - 12a^2 + 46a - 56 + 4a^2 + 36a + 78)

                           = 3*(a^3 - 8a^2 + 102a + 22)

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The maximum number of boxes in each pack is 9, and:

To find the greatest number of boxes in each pack, we need to find the largest common factor between the given numbers.

We know that:

We can decompose these numbers as a product between their prime factors, we will get:

18 = 2*3*3

36 = 2*2*3*3

45 = 5*3*3

You can see that the largest common factor is 3*3 = 9

So the maximum number of boxes that each pack can have is 9 boxes.

In that case:

Garth bought 18/9 = 2 packs.

Rico bougth 36/9 = 4 packs.

Mia bought 45/9 = 5 packs.

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Answer: Jacob will be 16 (16.5) years old, which is half of Todd's age, in 4 years.

I respect the Todoroki profile pic :)

Step-by-step explanation:

33 ÷ 2 = 16.5

1/2 of Todd's age = 16.5 (16)

16 - 12 = 4 years (4.5 years to be specific)

Answer:

9z square+49+42z

Step-by-step explanation:

right!

Answer:

414 t

Step-by-step explanation:

If the problem is 72 fluid ounces and "t" is teaspoons (?), then the conversion is:

(72 oz)(5.751669 t/oz) = 414 t

**this also assumes the fluid is water

Answer:1. Let  a = 1  and  b = 1 .

2. Now this means that  a = b .

3. If we multiply both sides by  a  we get  a^{2} = ab .

4. If we then subtract  b^{2}  from both sides we would have  a^{2} - b^{2} = ab - b^{2} .

5. We can then factorise both sides to get  (a + b)(a - b) = b(a - b) .

6. Dividing both sides by  (a - b)  would give us  a + b = b .

7. Substituting back the values of  a = 1  and  b = 1  would give us that  1 + 1 = 1 .

8. So this "proves" that  1 + 1 = 1  not  2 .

Except that in step 6, when we are dividing by  a - b , we are in fact dividing by zero. This is a violation of the rules of mathematics :/ soo... Um lol...

Step-by-step explanation: this is what happens when you dont do math correct

Yes, because 225 minutes is greater than 205 minutes.

In this question answer is

Yes, because 225 minutes is greater than 205 minutes.

This can be determined by using the outlier rule

which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.

The IQR is calculated as Q3 - Q1,

which in this case is

110 - 15 = 95. Therefore,

1.5 times the IQR is 95 x 1.5 = 142.5.

The upper quartile (Q3) is 110,

so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.

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Yes, because 225 minutes is greater than 205 minutes.

Outlier rules, also known as outlier detection algorithms, are algorithms designed to detect the presence of outliers in a dataset.

Outliers are data points that are significantly different from the rest of the data, and can be caused by measurement error, experimental error, or some other anomaly.

Outlier rules are used to identify and remove outliers from data sets in order to improve the accuracy of data analysis and modeling.

Outlier rules typically use some combination of statistical measures, such as mean, median, and standard deviation, to detect the presence of outliers in the data.

In this question answer is

Yes, because 225 minutes is greater than 205 minutes.

This can be determined by using the outlier rule

which states that any data point that is more than 1.5 times the interquartile range (IQR) away from the upper quartile (Q3) is considered an outlier.

The IQR is calculated as Q3 - Q1,

which in this case is

110 - 15 = 95. Therefore,

1.5 times the IQR is 95 x 1.5 = 142.5.

The upper quartile (Q3) is 110,

so any data point more than 205 (110 + 142.5) is considered an outlier, including 225.

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Answer:

-3.5,-3,-2[tex]\frac{1}{2}[/tex], -2,2.5

Step-by-step explanation:

For numbers that are negative, the larger the number is the lesser the value is. For numbers that are positive, the larger the number is the larger is value is. Positive numbers are always greater than negative numbers.

Answer:

-3.5 | -3 | -2[tex]\frac{1}{2}[/tex] | -2 | 2.5 |

Step-by-step explanation:

Negative number are smaller than positive numbers so 2.5 is the largest number. Negative numbers are kind of opposite of positive numbers. The larger the negative number is, the smaller it is. With positive numbers, the larger the number, the larger the value is.

The equation of the circular flower garden represented on the blueprint is (x-5)²+(y-15)² = 4

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Fencing encloses a rectangular backyard that measures 200 feet by 600 feet. A blueprint of the backyard is drawn on the coordinate

plane so that the rectangle has vertices (0,0), (0, 30), (10, 30), and (10, 0).

A circular flower garden is dug to be exactly in the centre of the backyard, with a radius of 40 feet. This garden is represented of on the blueprint.

Since, the rectangle has vertices (0,0), (0, 30), (10, 30), and (10, 0) therefore, it will form a rectangle with width 10 units and height 30 units.

In this situation, the centre of the rectangle is at (5, 15) (Half of the width in the first coordinate and half of the height in the second one)

Since, we know that the equation of the circle is given by;

(x-a)²+(y-b)² = R²

Where, (a, b) is the centre point and R is the radius,

Therefore, the equation of the flower garden will be;

(x-5)²+(y-15)² = R²

Now, solving for R,

We know that the rectangular backyard width is 200 feet and this is represented with a rectangle in the blueprint with width 10 units

10 units = 200 ft

Therefore, 40 ft = 2 units

Therefore, The radius of 40 feet is represented with 2 units in the blueprint.

Now we replace R = 2 in the equation :

(x-5)²+(y-15)² = 2²

(x-5)²+(y-15)² = 4

Hence, the required equation is (x-5)²+(y-15)² = 4

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Answer:

The second one is your answer!!

Step-by-step explanation: