The tape diagram represents an equation. 7 Write an equation to represent the image. + Report a problem​

The expression included parentheses as 21+m/7, the division inside the parentheses takes priority and we divide 28 by 7 first before adding 21.

An expression is a mathematical phrase that combines numbers, variables, and operations, but does not have an equal sign or equation.

According to the given information:

To evaluate 21+m/7 for m=28, we substitute the value of m=28 into the expression and simplify according to the order of operations, which is:

1) Perform any calculations inside the parentheses, if there are any.

2) Evaluate any exponents or roots, from left to right.

3) Perform multiplication and division, from left to right.

4) Perform addition and subtraction, from left to right.

Applying this order of operations, we get:

21 + m/7

= 21 + 28/7 [Substitute m=28]

= 21 + 4 [Divide 28 by 7 to get 4]

= 25 [Add 21 and 4]

Therefore, 21+m/7 for m=28 equals 25.

Note that if the expression had been written without parentheses as 21 + m ÷ 7, the order of operations would have required us to perform the division before the addition, which would have given us:

21 + m ÷ 7

= 21 + 28 ÷ 7 [Substitute m=28]

= 21 + 4 [Divide 28 by 7 to get 4]

= 25 [Add 21 and 4]

However, since the expression included parentheses as 21+m/7, the division inside the parentheses takes priority and we divide 28 by 7 first before adding 21.

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The expression included parentheses as 21+m/7, the division inside the parentheses takes priority and we divide 28 by 7 first before adding 21.

What is expression?

An expression is a mathematical phrase that combines numbers, variables, and operations, but does not have an equal sign or equation.

According to the given information:

To evaluate 21+m/7 for m=28, we substitute the value of m=28 into the expression and simplify according to the order of operations, which is:

1) Perform any calculations inside the parentheses, if there are any.

2) Evaluate any exponents or roots, from left to right.

3) Perform multiplication and division, from left to right.

4) Perform addition and subtraction, from left to right.

Applying this order of operations, we get:

21 + m/7

= 21 + 28/7 [Substitute m=28]

= 21 + 4 [Divide 28 by 7 to get 4]

= 25 [Add 21 and 4]

Therefore, 21+m/7 for m=28 equals 25.

Note that if the expression had been written without parentheses as 21 + m ÷ 7, the order of operations would have required us to perform the division before the addition, which would have given us:

21 + m ÷ 7

= 21 + 28 ÷ 7 [Substitute m=28]

= 21 + 4 [Divide 28 by 7 to get 4]

= 25 [Add 21 and 4]

However, since the expression included parentheses as 21+m/7, the division inside the parentheses takes priority and we divide 28 by 7 first before adding 21.

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From the question,

Rohan bought an almirah for =Rs.13600= cost price

Transportation cost =Rs.400

The total cost price of almirah =Rs.(13600+400)

The total cost price of almirah =Rs.(13600+400)=Rs.14000

He sold it for =Rs.16800= selling price

By comparing SP and CP=SP>CP, so there is a gain

Gain=SP−CP

=16800−14000

=Rs.2800

Gain %={(gain/CP)×100}

={(2800/14000)×100}

={2800/140}

=20%

Recall that for two vector x and y making an angle θ with each,

x • y = ||x|| ||y|| cos(θ)

If we replace y with x, we see that

x • x = ||x|| ||x|| cos(0) = ||x||²   ⇒   ||x|| = √(x • x)

Using the last identity, the magnitude of w is

||w|| = √(w • w)

but since w = u + v, we have

w • w = (u + v) • (u + v)

The dot product distributes over sums and is commutative, so

w • w = (u • u) + (u • v) + (v • u) + (v • v)

… = ||u||² + 2 (u • v) + ||v||²

… = ||u||² + 2 ||u|| ||v|| cos(θ) + ||v||²

If u has a direction of 45° with the positive x-axis, v has a direction of 150°, then the angle between u and v is |45° - 150°| = 105°. So,

||w|| = √(||u||² + 2 ||u|| ||v|| cos(150°) + ||v||²)

… = √(10² + 2 • 10 • 13 cos(150°) + 13²)

… ≈ 14.2

Using the parallelogram rule for vector addition (see attached sketch), the sum of the angle between w and u and 45° is equal to the direction of w.

If φ is the angle between w and u, then

w • u = ||w|| ||u|| cos(φ)

… = 14.2 • 10 • cos(φ)

but we also have

w • u = (u + v) • u

… = (u • u) + (v • u)

… = ||u||² + ||u|| ||v|| cos(105°)

… = 10² + 10 • 13 • cos(105°)

… ≈ 66.4

Then

14.2 • 10 • cos(φ) ≈ 66.4

cos(φ) ≈ 0.467

φ ≈ 62.1°

and so the direction of w is 62.1° + 45° ≈ 107.1°.

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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9514 1404 393

Answer:

  (b)  -3

Step-by-step explanation:

It can work well to rewrite the equation as powers of 2.

  \(4^x=\left(\dfrac{1}{8}\right)^{x+5}\\\\(2^2)^x=(2^{-3})^{x+5}\qquad\text{as powers of 2}\\\\2x=-3(x+5)\qquad\text{equate exponents}\\\\5x=-15\qquad\text{add $3x$}\\\\\boxed{x=-3}\qquad\text{divide by 5}\)

__

Check

  4^-3 = (1/8)^(-3+5)   ⇒   1/64 = (1/8)^2 . . . . true

The completed statements and reasons, which can be used to complete the two column table to prove that the triangles ΔRSU and ΔTQU are congruent can be presented as follows;

Statement \({}\)                            Reasons

U is the midpoint of \(\overline{QS}\)      \({}\)    Given

U is the midpoint of \(\overline{QS}\)    \({}\)      Given

\(\overline{QT}\) ≅ \(\overline{RS}\)  \({}\)                                Given

\(\overline{TU}\) ≅ \(\overline{RU}\) \({}\)                                 Definition of midpoint

\(\overline{QU}\) ≅ \(\overline{SU}\)        \({}\)                          Definition of midpoint

ΔRSU ≅ ΔTQU \({}\)                        SSS

Congruent triangles are triangles that have the same shape and size.

The details of the reasons used to prove that the two triangles are congruent can be presented as follows;

Definition of midpoint;

The midpoint of a line is the point that splits the line into two segments that have the same length.

SSS;

The SSS (Side-Side-Side) congruence theorem states that two triangles are congruent if the length of the three sides of one triangle are congruent to the three sides of the other triangle.

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Normal distribution curve is symmetric around the mean, it shows that values close to the mean happen more frequently than those distant from the mean.

A bell-shaped (symmetric) curve, the normal probability distribution or the normal curve. The mean of it is represented by and the standard deviation by σ.

In this example, the mean and median are both equal and lie in the center of the distribution; they are 64, and the standard deviation is 7, with 68% of the values falling within the first standard deviation, 95% within the second standard deviation, and 99.7% within the third. Once more, variance is equal to the standard deviation squared.

According to the normal distribution curve:

"the percent of women whose heights are between 64 and 69.5 inches" represents the values within 2 standard deviation.

Area from a value (Use to compute p from Z)

Value from an area (Use to compute Z for confidence intervals)

Let the parameters be

Mean 64

Standard deviation 2.75

Above 1.96

Below 1.96

Between 64 and 69.5

Outside -1.96 and 1.96

Area (probability) 0.4772

And that value is 95 % of the whole data

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Answer:

12.57

Step-by-step explanation:

A = πr^2

3.14 x 2 x 2 = 12.57 meters ^2

ANSWER: approximately 18.84 meters  

Step-by-step explanation:

The most commonly used equation for circumference is C=2πr.  Where c is the circumference, π is pi (or 3.14159...), and r is the radius.

In your equation, you are given diameter.  Remember that the radius is half of the diameter.  So, in this case, the radius, r, is half of 6, or 3 meters.

Now, substitute the radius into the equation for circumference, and you get:

C= 2π(3)

=approximately 18.84 meters

What you know have found is the distance around the circle.

We will have the following:

*First: We test the expressions:

1)

2)

3)

4)

So, the only rational number would be in option 3:

Answer: Part A: 1/26 or 0.38

Part B: 1/59 or 0.017

Step-by-step explanation:

Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

Step-by-step explanation:

Answer:

x=15/4 or x=3.75

Step-by-step explanation:

4/5*x=3

4/5=0.8

0.8*3.75=3

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

The area of a circle is expressed as; A = πr²

Given that;

A = πr²

A = 3.14 × (3yd)²

A = 3.14 × 9yd²

A = 28.36 yd²

Given the diameter of the circular garden, the area of the garden is 28.36 yd².

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Answer:

3r =15

Step-by-step explanation:

r=20-15

r=5

3r=3×5

3r=15

pls follow

Answer:

r = 5

Step-by-step explanation:

20 - r = 15

     + r    + r

20 = 15 + r

-15    -15

5 = r

Answer:

letter c the BD= 10

Step-by-step explanation:

Answer:

BD=10

Step-by-step explanation:

1. BAD=BCD=60

Therefore

BA = BC (sides opposite to equal angles are equal)

BA=20

Therefore BC=20

2.BAC+BCA+ABC=180(sum of the interior angles of a triangle is 180)

60+60+ABC=180

ABC=180-120

ABC=60

ABC=BAC=BCA

Therefore ABC is an equilateral triangle

AC=20

4. AC=AD+DC

AD=DC (BD is a perpendicular bisector)

Therefore

AC=2×AD

AC=20

20=2×AD

AD=20÷2

AD=10

Hope this helps!

We have two expressions and we have to compare them.

We don't need to calculate the exact value of each expression. We can left them as products of 250.

Then, expression A is already 5/6 of 250.

We can rearrange expression B as:

Expression B is also 5/6 of 250, so the two expressions are equal.

Answer: expression A is equal to expression B.

The shaded region of the rectangle is 242.9 cm² and the shaded region of the sector is 7.1 square units.

Question 17) is a figure of a rectangle and two inscribed circles.

The area of a rectangle is expressed as: A = length × width

The area of a circle is expressed as: A = πr²

Where r is the radius.

To determine the area of the shaded region, we simply subtract the areas of the two circles from the area of the rectangle.

Area = ( Length × width ) - 2( πr² )

Area = ( 40 × 10 ) - 2( π × 5² )

Area = ( 400 ) - 2( 25π )

Area = 400- 50π

Area = 242.9 cm²

Area of the shaded region is 242.9 squared centimeters.

Question 18) is the a figure a sector of a circle and a right triangle.

The area of a sector is expressed as: A = (θ/360º) × πr²

The area of a triangle  is expressed as: A = 1/2 × base × height

To determine the area of the shaded region, we simply subtract the areas of the triangle from the area of the sector.

Hence:

Area = ( (θ/360º) × πr² ) - ( 1/2 × base × height )

Plug in the values:

Area = ( (90/360º) × π × 5² ) - ( 1/2 × 5 × 5 )

Area = 25π/4 - 12.5

Area = 7.1

Therefore, the area of the shaded region is 7.1 square units.

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Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

the sale price is $827.70.

Step-by-step explanation:

11% of 930 is 102.3

930-102.3=827.70

Answer:

A reduction of 450ml

Step-by-step explanation:

Given

\(V_1 = 200ml\) -- To glass 1

\(V_2 = 250ml\) --- To glass 2

Required

The final change to the carton

To do this, we simply add V1 and V2

So, we have:

\(Total = V_1 + V_2\)

\(Total = 200ml + 250ml\)

\(Total = 450ml\)

This implies that the changes is a reduction of 450ml

Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

In general, given two points on a line, we can find its equation by using the formula below

Therefore, in our case,

Thus, the answer is 3x+y=33, option C.

Answer:

4x² + 22x - 12

Step-by-step explanation:

A = bh/2

A = (4x - 2)(2x + 12)/2

A = (8x² + 48x - 4x - 24)/2

A = (8x² + 44x - 24)/2

A = 4x² + 22x - 12

The difference between their ages one year ago was 2 years.

Difference in maths, the result of one of the important mathematical operations, which is obtained by subtracting two numbers.

Given that, Jack is 2 years older than Bob,

Let Bob's age be x then, Jack's age will be (x+2)

Their ages before 1 year was =

Bob's = x-1

Jack's = (x+1)

Difference = x + 1 - x + 1 = 2

Hence, The difference between their ages one year ago was 2 years.

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The volume of the rectangular pyramid is 900 cubic yards.

The standard formula of the volume of the rectangular pyramid is written as

V = 1/3s²h

where s refers the base edge and h refers the height.

Here we have given that the square base has side lengths 15 yards and the height is 12 yards.

Now, we have to find the volume of the rectangular pyramid

As we know the the value of base edge is 15 yard and the height is 12 yards.

Now, we have to apply the values on the formula then we get,

=> V = 1/3 x 15² x 12

It can be simplified as,

=> V = 4 x 225

When we do the appropriate arithmetic operation, then we get,

=> V = 900 cubic yard.

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Traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Earth to Mars is compared to traveling from Earth to the moon, we need to calculate the difference between the distances.

The distance from Earth to the moon is approximately 3.74 x 10^5 km.

The distance from Earth to Mars is approximately 9.25 x 10^7 km.

To find the difference, we subtract the distance to the moon from the distance to Mars:

9.25 x 10^7 km - 3.74 x 10^5 km

To subtract these numbers, we need to make sure the exponents are the same. We can rewrite the distance to the moon in scientific notation with the same exponent as the distance to Mars:

3.74 x 10^5 km = 0.374 x 10^6 km (since 0.374 = 3.74 x 10^5 / 10^6)

Now we can perform the subtraction:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 km - 0.374 x 10^6 km

To subtract, we subtract the coefficients and keep the same exponent:

9.25 x 10^7 km - 0.374 x 10^6 km = 9.25 x 10^7 - 0.374 x 10^6 km

Simplifying the subtraction:

9.25 x 10^7 - 0.374 x 10^6 km = 9.249626 x 10^7 km

Therefore, traveling from Earth to Mars is approximately 9.249626 x 10^7 km farther than traveling from Earth to the moon.

Scientific notation is a convenient way to express very large or very small numbers. It consists of a coefficient (a number between 1 and 10) multiplied by a power of 10 (exponent). It allows us to write and manipulate such numbers in a compact and standardized form.

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Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.

Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.

The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.

To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.

Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.

The payment for raw materials purchases in July (35% of X pounds) will be:

0.35 * X pounds

The payment for raw materials purchases in August (65% of X pounds) will be:

0.65 * X pounds

Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:

Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July

X pounds - 0.35 * X pounds = 9,500 pounds

Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.

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