Seven subtracted from the product of three and a number is 23. What is the number?

Bob had 50 pencils in the beginning.

A fractional number is expressed in the form -

x/y    {where y ≠ 0)

Given is that Bob gave four - fifths of his pencils to Barbara, then he gave two - thirds of the remaining pencils to bonnie.

Assume that he had {x} pencils in the beginning. We can write -

4x/5 + 2/3(x - 4x/5) = 10

4x/5 + 2x/3 - 8x/15 = 10

x(4/5 + 2/3 - 8/15) = 10

x = 10/0.93

x = 50

Therefore, Bob had 50 pencils in the beginning.

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{QUESTION IN ENGLISH -

Bob gave four fifths of his pencils to Barbara, then he gave two thirds of the remaining pencils to bonnie, if he ended up with 10 pencils for himself... how many pencils did bob have at the beginning?}

Answer:

its 5.11 grms because of the phto sintises

Step-by-step explanation:

Answer: AB> AC> BC

Step-by-step explanation:

A+B= 134

A+C= 124

B+C= 102

Therefore, the sides from greatest to least are AB>AC>BC.

That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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Answer:

7.5

Step-by-step explanation:

The actual fraction is 15/2, which is equivlent to 7.5

Im pretty sure its infinite solutions

The radical form is  \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

Given,

In the question:

Write 5x^2/3 in radical form​.

Let's Know,

What is Radical Form?

An expression that uses a root, such as a square root, cube root is known as a radical notation. Therefore, 33/2 in radical form is √33 = √27. ​​​​Example 2: Solve the radical: 3√x = 8 using the radical formula. Therefore, Thus, the value of x for 3√x x 3 = 8 is 512.

Now, According to the question:

\((5x)^\frac{2}{3}\)

Convert in Radical form:

Apply the rule :

\(x^\frac{m}{n} = \sqrt[n]{x^m}\)

To rewrite the exponential as a radical .

=> \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

Hence, The radical form is  \((5x)^\frac{2}{3}=\sqrt[3]{(5x)^2}\)

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Step-by-step explanation:

perimeter means to add all sides

SO

perimeter of triangle is

QR+QP+RP

SO

= 63+70+47

=180

Answer:

perimeter= 180

Step-by-step explanation:

Add 63+70+47=180

63

70

47

+

---------

  180

Answer:

0 < A < 90

0 < C < 90

Step-by-step explanation:

If B is the right angle of the triangle, then the sum of the other angles, A and C, must equate 90° since all angles in a triangle sum to 180°:

A + C = 90

A and C could both be anything between 0 and 90, but they must satisfy the equation above:

0 < A < 90

0 < C < 90

The coordinates of the image if triangle ABC is translated 4 units down would be: A′(1, -6), B′(9, -6), C′(5, -2)

To translate the triangle 4 units down, we need to subtract 4 from the y-coordinate of each vertex.

Vertex A has coordinates (1, -2), so its image A' after the translation is (1, -2 - 4) = (1, -6).

Vertex B has coordinates (9, -2), so its image B' after the translation is (9, -2 - 4) = (9, -6).

Vertex C has coordinates (5, 2), so its image C' after the translation is (5, 2 - 4) = (5, -2).

Therefore, the coordinates of the vertices of triangle ABC after it is translated 4 units down are A′(1, −6), B′(9, −6), and C′(5, −2).

So, the answer is option A: A′(1, −6), B′(9, −6), C′(5, −2)..

How can you use the coordinates of the vertices of a figure to determine its image after a translation?

To determine the image of a figure after a translation, you can add or subtract the same amount from the x- and/or y-coordinates of each vertex, depending on the direction and distance of the translation.

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The image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

A dilation with a center of (0,0) and a scale factor of 7 means that every point in the plane will be multiplied by a factor of 7 from the origin.

To find the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7, we can simply multiply the coordinates of L by the scale factor.

The coordinates of the image point L' will be:

L' = (-4 × 7, 0 × 7) = (-28, 0)

Therefore, the image of the point L(-4,0) after a dilation with a center of (0,0) and a scale factor of 7 is the point L'(-28,0).

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Answer:

Step-by-step explanation:

1 white 1 green 1 blue + 2 reds = 5 balls

5 seen as a percentage

5%

Answer:

D. 2, 4

Step-by-step explanation:

6x+8y=44

5y = 20

y = 4

6x = 12

x = 2

Answer:

(0,5)

Step-by-step explanation:

f(x) = x^2 + 3x + 5

The y intercept is when x =0

f(0) = 0 + 3*0 + 5

f(0) = 5

(0,5)

9514 1404 393

Answer:

  the correct choice is marked

Step-by-step explanation:

The denominators of the two fractions must be the same. To make that happen, Juan can multiply the second fraction by (x-2)/(x-2) -- the marked answer choice -- and multiply the first fraction by 3/3. These operations can be done in some order.

The offered choices suggest that treating the second fraction first is Juan's preferred choice.

Answer:

Step-by-step explanation:

\(\\\begin{array}{|c|c|c||c|c|c|}x&y&\Delta y&x&y&\Delta y\\---&---&---&---&---&---\\0&-6&-1.5&0&6.1&-4\\1&-4.5&-1.5&1&6.1&-4\\2&-3&-1.5&2&-1.9&-4\\3&1.5&-1.5&3&-5.9&-4\\---&---&---&---&---&---\\\end {array}\\\\Tables\ representent\ lines\\\\First\ line: \ passing\ through\ (0,-6)\ and\ (2,-3)\:\\\\y+6=\dfrac{3} {2} (x-0) \ or\ y=\dfrac{3} {2} x-6\\\\\\Second \ line: \ passing\ through\ (0,6.1)\ and\ (1,2.1\:\\\\y-6.1=-4(x-0) \ or\ y=-4x+6.1\\\\Solution\ of\ the\ system\\\\\)

\(\Bigg\{\begin{array}{ccc}y&=&\dfrac{3}{2}x-6 \\y&=&-4x+6.1\\\end {array} \right.\\\\\\\Bigg\{\begin{array}{ccc}y&=&-4x+6.1\\\dfrac{3}{2}x-6&=&-4x+6.1 \\\end {array} \right.\\\\\\\Bigg\{\begin{array}{ccc}x&=&2.2\\y&=&-2.7 \\\end {array} \right.\\\\\)

An equation that could be used to determine M, the unknown side length of the logo is X = (36/5) x M

Let's assume that the unknown side length of the logo is 'M'. The logo is a rectangle, and the area of a rectangle is given by multiplying its length and width. Since we know the length of the logo is 7(1)/(5) feet, we can write the equation:

A = L x W

where A is the area of the logo, L is the length of the logo, and W is the width of the logo.

Substituting the given values, we get:

A = (7(1)/(5)) x M

or

A = (36/5) x M

Now, we know that the area of the logo is exactly the maximum area allowed by the building owner. Let's assume this maximum area is 'X'. So, we can write another equation:

A = X

Combining both equations, we get:

X = (36/5) x M

This is the required equation that could be used to determine the unknown side length 'M' of the logo if we know the maximum area allowed by the building owner 'X'.

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Answer: The answer is 6

Step-by-step explanation: I know this because there are 4 months and in a total of those months she read 24 total books which you divide by 4 which is 6

Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8

Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;

Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);

When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;

Given:

Hannah makes 5 out of 8 attempted free-throws.

Now,

The average waiting time of hannah to make her first basket is 5/8

The probability of hannah making basket at her last attempt is 1/8

The probability of hannah making basket before her last attempt is 2/8

Hence, the probabilty will be 1/8 and 2/8;

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Answer:

7 tens

Step-by-step explanation:

the value of the first half of the statement is 83 and the value of the second one is 13 (without the tens) so that mean it has 70 left over to make it 7 tens.

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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Answer:

35

Step-by-step explanation:

You can easily graph this in desmos for a visual understanding.

The slope of a line is received by (y2-y1)/(x2-x1). Assuming that Days is X and the cost is Y, we get (160-90)/(4-2), and it makes 70/2, which equates out to 35. Because the prices become more and more expensive, the slope is positive 35.

Answer:

-----------------

Find the differences in the sequence  -11, -7, -3, 1, ...

The difference is common, so the sequence is an AP.

The nth term is:

Find the 52nd term:

Find the 52nd term using the given formula:

Find the previous term:

Find the common difference:

Answer:

\(\begin{aligned}\textsf{34)} \quad d&=4\\a_n&=4n-15\\a_{52}&=193\end{aligned}\)

\(\begin{aligned}\textsf{35)} \quad d&=-4\\a_{52}&=-238\end{aligned}\)

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Given sequence:

To determine if the given sequence is arithmetic, calculate the differences between consecutive terms.

\(a_4-a_3=1-(-3)=4\)

\(a_3-a_2=-3-(-7)=4\)

\(a_2-a_1=-7-(-11)=4\)

As the differences are constant, the sequence is arithmetic, with common difference, d = 4.

The explicit formula for an arithmetic sequence is:

\(\boxed{a_n=a+(n-1)d}\)

where:

To find the explicit formula for the given sequence, substitute a = -11 and d = 4 into the formula:

\(\begin{aligned}a_n&=-11+(n-1)4\\&=-11+4n-4\\&=4n-15\end{aligned}\)

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=4(52)-15\\&=208-15\\&=193\end{aligned}\)

Therefore, the 52nd term is a₅₂ = 193.

\(\hrulefill\)

Given explicit formula for an arithmetic sequence:

\(a_n=-30-4n\)

To find the common difference, we need to compare it with the explicit formula for the nth term:

\(\begin{aligned}a_n&=a+(n-1)d\\&=a+dn-d\\&=a-d+dn\end{aligned}\)

The coefficient of the n-term is -4, therefore, the common difference is d = -4.

To find the 52nd term, simply substitute n = 52 into the formula:

\(\begin{aligned}a_{52}&=-30-4(52)\\&=-30-208\\&=-238\end{aligned}\)

Therefore, the 52nd term is a₅₂ = -238.

The Function  f(g(x)) = g(f(x)) = x + 8.

The functions are: f(x) = x + 4 and g(x) = x + 4. We can find f(g(x)) by substituting g(x) in place of x in f(x).

f(g(x)) = f(x + 4) = (x + 4) + 4 = x + 8

Similarly, we can find g(f(x)) by substituting f(x) in place of x in g(x).g(f(x)) = g(x + 4) = (x + 4) + 4 = x + 8

Thus, we can see that f(g(x)) and g(f(x)) are equal to each other,

which is x + 8.

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The volume of the clay brick is 2.25 cubic inches and the weight of the clay brick is 0.1575 pounds

The volume of the clay brick, we need to use the dimensions provided. The length of the brick is 1 inch and the width is 2 \(\frac{1}{4}\) inches. We can assume the height of the brick is also 1 inch since it is not specified.

The formula for the volume of a rectangular object is

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

Using the given dimensions, we can calculate the volume of the brick:

V = (1 inch) x (2 \(\frac{1}{4}\) inches) x (1 inch)

V = (1 inch) x (2.25 inches) x (1 inch)

V = 2.25 cubic inches

V = 2.25 inches³

Since the density of the clay is given as 0.07 pounds per cubic inch, we can find the weight of the brick using the formula:

Weight = Volume x Density

Weight = 2.25 inches³ x 0.07 pounds/inches³

Weight = 0.1575 pounds

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How would you describe the difference between the graphs of f(x) = 2x² and g(x) = -2x²: D. g(x) is a reflection of f(x) over the x-axis.

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

In this context, we can reasonably infer and logically deduce that a graph of transformed function g(x) = -2x² would be created by applying a reflection over or across the x-axis to the graph of the parent function f(x) = 2x² as shown in the image attached below.

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Answer:

57

Step-by-step explanation:

Given:

x = 4

y = 5

w = -3

Work:

3xy + w

3(4)(5) + (-3)

12(5) - 3

60 - 3

57

Answer:

\(25\)

Step-by-step explanation:

\(2x-1=x+4\\2x=x+5\\x=5\\\text{Check:}\\2(5)-1=5+4\\10-1=9\\9=9\\9\cdot 2 +7=18+7=25\)

Answer:25 ft

Step-by-step explanation:

This triangle is an isosceles triangle (2 sides are congruent), we see this because is two angles of a triangle is congruent, then the two opposite sides are congruent.

From this information, we can say that 2x-1 = x+4

Add 1 on both sides to get 2x=x+5

Then minus x on both sides to get x=5

Next, plus x into the two equations separately.

1) 2 times 5-1

2 times 5 is 10

10-1=9

2) 5+4=9

Finally, add the sides together to get the answer.

9+9+7=25ft

Hope this helped!