Each cell in the crossnumber below contain a single non-zero digit. The answer
two-digit number.
What is the value of x?
A 1
21 UK Mathematics Trust
Clues
ACROSS
1. A square
3. An odd square
B 3
Down
1. A square
2. A square
C 5
www.ukmt.org.uk
1
3
D 7
2
X

Answer:

30.7

Step-by-step explanation:

sin(71) = 29/x

x = 29/sin71

≈ 30.7

The coordinates of triangle XYZ are X(-2,-2), Y(2,4), and Z(-4,8).

In mathematics, a transformation refers to a change or modification of an object's position, shape, size, or orientation in a coordinate plane or space. Transformations can be described as functions that map the points or vertices of an object to new positions in the plane or space.

Common transformations include:

Translation: a transformation that moves an object without changing its size, shape, or orientation. Translation involves shifting all points of the object by the same distance in the same direction.

Rotation: a transformation that turns an object about a fixed point or axis by a certain angle. Rotation preserves the size and shape of the object, but changes its orientation.

Scaling: a transformation that changes the size of an object by multiplying the coordinates of each point by a fixed factor. Scaling can either enlarge or reduce an object.

Since the transformation function is not provided, I'll assume that D2(ABC) means dilating the triangle ABC with center at the origin and a scale factor of 2.

To find the coordinates of the new triangle XYZ, we can apply the dilation transformation to each vertex of the original triangle:

For vertex A(-1,-1), we multiply its coordinates by the scale factor 2, giving us point X(-2,-2).

For vertex B(1,2), we multiply its coordinates by the scale factor 2, giving us point Y(2,4).

For vertex C(-2,4), we multiply its coordinates by the scale factor 2, giving us point Z(-4,8).

Therefore, the coordinates of triangle XYZ are X(-2,-2), Y(2,4), and Z(-4,8), as shown below:

To know more about triangle visit:

https://brainly.com/question/29196380

#SPJ1

Step-by-step explanation:

The equation 2x − 15 = 185 represents the relationship between Sam's and Martha's heights. We can solve for x, which represents Martha's height, by isolating x on one side of the equation:

2x − 15 = 185

Add 15 to both sides of the equation:

2x = 200

Divide both sides of the equation by 2:

x = 100

Therefore, Martha's height is 100 centimeters.

Answer:

The formation of a linear programming model involves the following steps:

1. Define the objective: Determine what you want to optimize or minimize, such as maximizing profit or minimizing costs.

2. Identify the decision variables: Identify the variables that affect the objective, such as the number of units produced.

3. Formulate the constraints: Establish the limitations that the model needs to operate within, such as production capacity, labor availability, or budget constraints.

4. Write the mathematical equations: Use the identified decision variables, constraints and objective function to write a set of linear equations.

5. Test and solve the model: Test the model by solving the linear equations using mathematical techniques such as simplex method or graphical method.

6. Interpret the results: Analyze the results of the model to gain insights into the optimization of your objective and how changes in variables or constraints can affect the outcome.

Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

The expression that completes the equation the result of 30/100 + 9/10 is 1.2.

The typical form for linear equations with two variables is Ax+By=C. For instance, the linear equation 2x+3y=5 is in standard form. When attempting to solve problems containing two linear equations, this form is also quite helpful.

We must multiply the values of 30 and 100, then add the resulting product to the resulting product of the values of 9 and 10 in order to complete the equation 30 100 + 9 10.

The result of multiplying 30 by 100 is:

30 x 100 = 3000

The result of adding 9 and 10 is:

9 x 10 = 90

Thus, we must combine these two items to finish the equation:

3000 + 90 = 3090

30100 + 910 = 3090, which is the expression that completes the equation.

To know more about Equation visit:

brainly.com/question/29538993

#SPJ1

the complete question is:

complete the equation

[tex]\frac{30}{100}+\frac{9}{10}[/tex]

Answer:

The answer is 39/100

Step-by-step explanation: Nothing more.

A 90 degree clockwise rotation about the point (0,0), the new coordinates of Point B are (3, -1) and the new coordinates of Point C are (1, -2).

A quadrilateral can be proven to be a rectangle in a number different ways. Here are the three simplest methods: 1. Establish that all angles are 90 degrees; 2. Establish that two opposed angles are 90 degrees; and 3. Establish that the diagonals are equally long and intersect one another.

The following transformation matrix can be used to rotate a point (x,y) 90 degrees clockwise with respect to the origin (0,0):

|0 1|\s|-1 0|

This transformation matrix can be applied to each point to determine its new coordinates upon rotation.

Point B is the first point, and its initial coordinates are (-1, 3). The transformation matrix in use:

|0 1| |-1| |3|

|-1 0| x |3| = |-1|

After rotating Point B 90 degrees clockwise, the new coordinates are: (3, -1).

The transformation matrix is then applied to Point C, whose initial coordinates are (2, 1):

|0 1| |2| |1|

|-1 0| x |1| = |-2|

After rotating in a clockwise direction by 90 degrees, Point C's new coordinates are (1, -2).

As a result, after rotating 90 degrees in a clockwise direction around Point 0, Point B's new coordinates are (3, -1), while Point C's new coordinates are (1, -2).

To know more about Quadrilateral Graph visit:

https://brainly.com/question/12518144

#SPJ1

Answer:

Step-by-step explanation:

This question's answer is 'c'. In the first function here we put the value of x=0, then y =3 but in the second function if we put the value of x=0 then y  =2. so c is the correct answer.

Answer:

50% chance

ur welcome-ssq

Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).

Formula to find the area of a rectangle is given by-

[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]

On substituting the values-

[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]

[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]

Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.

Therefore , the solution of the given problem of angles comes out to be  M∠R measured at 45.4 degrees, to the closest tenth.

The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.

Here,

To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:

=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)

=>  cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)

=>  cos(R) = 0.6960917

When we calculate the inverse cosine of both sides, we obtain:

=>  R = cos⁻¹(0.6960917)

=>  R equals 45.4 degrees

Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.

To know more about angles visit:

brainly.com/question/14569348

#SPJ1

Yes, this is an example of bias, specifically, response bias.

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain. Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is an important concept in many fields, including mathematics, statistics, physics, and engineering, and is used to make predictions, analyze data, and make decisions under uncertainty.

Here,

Response bias occurs when the answers given by respondents in a survey do not accurately reflect their true opinions or beliefs. In this case, the question asked by the soft drink company is leading and suggestive, and it suggests that the company's product is superior to its rival's product. By framing the question in this way, the soft drink company is more likely to receive a positive response from respondents, even if they do not actually believe that the company's product is better than its rival's product.

To know more about probability,

https://brainly.com/question/30034780

#SPJ1

According to the solving the area of the sidewalk is 138.16 square meters.

Size of a location on a surface is expressed in terms of area. As opposed to surface area, which refers to the area of an open surface or the border of a three-dimensional object, plane region or plane size refers to the area of a shape or planar lamina.

The width of the circular sidewalk is 2 m, which means that the radius of the entire area, including the flower bed and the sidewalk, is 10 m + 2 m = 12 m.

To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the larger circle.

Area of larger circle = πr²

= 3.14 x 12²

= 452.16 square meters (rounded to two decimal places)

Area of flower bed = πr²

= 3.14 x 10²

= 314 square meters

Area of the sidewalk = Area of larger circle - Area of flower bed

= 452.16 - 314

= 138.16 square meters (rounded to two decimal places)

Therefore, the area of the sidewalk is 138.16 square meters.

To know more about area visit:

https://brainly.com/question/27683633

#SPJ9

The average allowance for each student is $9.25.

To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.

Adding up the allowances:

$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74

There are 8 students, so we divide the total allowance by 8 to get:

$74 / 8 = $9.25

Therefore, the average allowance for each student is $9.25.

Read more about mean at

https://brainly.com/question/987944

#SPJ1

The values of r and s, considering that the system has an infinite number of solutions, are given as follows:

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The number of solutions of a system of two linear functions is given as follows:

For this problem, the system has an infinite number of solutions, meaning that the equations are multiples, thus the values of r and s are given as follows:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

B

Step-by-step explanation:

The correct answer is B. The total number of people on the field trip must be a multiple of 9 (1 adult and 8 students).

A is not true because if there were only 9 people, there could not be both an adult and 8 students, and the ratio would not be 1:8.

C is not necessarily true. It is possible that there were more adults than students on the field trip, or that the ratio was not an exact 1:8.

D is not true because if there were 8 times as many students as adults, the ratio would be 1:64, not 1:8

The area should the base of the new container must have option D that is, A = 2m-10.

In mathematics, area is a measurement of the size of a two-dimensional surface or shape, usually measured in square units such as square meters, square centimeters, or square feet. It is the amount of space inside the boundary of a flat object or shape.

Here,

To calculate the area of the base of the new container, we need to find the radius of the container first. Since the diameter is given as 10 cm, the radius would be half of that, which is 5 cm. The formula for the area of a circle is A = πr², where A is the area and r is the radius. So, substituting the values, we get:

A = π(5 cm)²

A = π(25 cm²)

A = 25π cm²

However, the answer choices are not in this format. To simplify the answer, we can use the value of π as approximately 3.14 (rounded to two decimal places). So, the area of the base would be:

A = 25π cm²

A ≈ 25(3.14) cm²

A ≈ 78.5 cm²

Now, we need to choose the answer option that represents this area in terms of variables. The only option that matches is:

d. A = 2m-10

To know more about area of circle,

https://brainly.com/question/28642423

#SPJ1

Complete question:

Question 6. One of the bases of a container for storing gasoline has broken and it is necessary to buy a new one. The diameter of the container is 10 cm. What area should the base of the new container have?

a. A = -10²

b. A = 2m-5

c. A = -5²

d. A = 2m-10

To simplify the expression 5^2 + 9^2, we can evaluate the squares of 5 and 9 and then add the results:

5^2 = 5 x 5 = 25

9^2 = 9 x 9 = 81

So, 5^2 + 9^2 = 25 + 81 = 106

Therefore, the simplified form of the expression 5^2 + 9^2 is 106.

The proof that ΔABC ≅ ΔDCB (congruent) in a parallelogram is because they are alternate interior angles.

If AABC is a parallelogram, then AB and AC are parallel. Therefore, angle BAC is equal to angle BDC since they are alternate interior angles.

Similarly, angle ABC is equal to angle ADC since they are also alternate interior angles.

Now, using the angle-angle-side (AAS) postulate to show that ΔABC and ΔDCB are congruent.

Since angle BAC = angle BDC and angle ABC = angle ADC, angle A = angle D, angle B = angle C, and side AB = side DC.

Therefore, ΔABC ≅ ΔDCB.

Find out more on alternate interior angles here: https://brainly.com/question/24839702

#SPJ1

Image transcribed:

8. Prove ΔABC≅ΔDCB (parallelogram)

Barbie should build a roof support that is 4√7 inches high to fit the slanted roof perfectly on her dream house.

The Pythagorean theorem is a fundamental theorem in mathematics that describes the relationship between the three sides of a right-angled triangle. It is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.

The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, this can be expressed as:

a² + b² = c²

where a and b are the lengths of the two shorter sides of the triangle (called the legs), and c is the length of the hypotenuse.

The Pythagorean theorem has important implications in geometry, trigonometry, and other branches of mathematics. It is also widely used in a variety of real-world applications, such as architecture, engineering, and physics. For example, it can be used to calculate the distance between two points in a two-dimensional plane, the height of a building or a tree, or the length of a diagonal in a rectangle or a square.

To solve this problem, we need to use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse (the longest side).

In this case, the two legs of the right triangle are the height of the roof and half the width of the house (since the roof slants down from the center of the house). The hypotenuse is the length of the roof, which is 16 inches on both sides.

So, we can set up the equation:

(height)² + (12)² = (16)²

Simplifying and solving for the height:

(height)² = (16)² - (12)²

(height)² = 256 - 144

(height)² = 112

height = √112

Using a calculator or simplifying by hand, we find that:

height = 4√7 inches

Therefore, Barbie should build a roof support that is 4√7 inches high to fit the slanted roof perfectly on her dream house.

To know more about length visit:

https://brainly.com/question/26388230

#SPJ1

Where m is the distance from A to P and n is the distance from P to B.

Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches. Length is also used to measure the amount of time it takes for something to occur, such as the length of a movie or a song.
Therefore, if the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2), the x- and y- coordinates of point P would be:

x= [2/3(x2 -x1) +x1
y = [2/3](y2 - y1) +y1

This equation can be used to calculate the coordinates of any point P on a directed line segment from A to B such that P is a fraction of the length of the line segment from A to B. By setting the fraction equal to 2/3, we can calculate the coordinates of point P that is 2/3 the length of the line segment from A to B. This can be useful in a variety of applications, such as computer graphics, game design, and engineering. For example, this equation could be used to calculate the coordinates of a point on a line segment that is an exact distance from the two endpoints, or to calculate the coordinates of a point that is a certain percentage of the distance between the two endpoints.

To know more about length click-
https://brainly.com/question/25292087
#SPJ1

The coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).

Length is a measure of distance or size. It is the measurement of the longest dimension of an object, such as a line, segment, or plane. It is commonly used to measure the physical size of objects, as well as the space between them. Length can be measured in many different units, such as meters, feet, or inches.

Given the coordinates of the points A, B and P, we can calculate the x- and y- coordinates of point P such that it is 2/3 the length of the line segment from A to B.
To do this, we need to use the following formula: x = [m/m+n](x2 -x1) +x1, y = [m/m+n](y2 - y1) +y1, where m is 2/3, n is 1/3, x1 and y1 are the x- and y-coordinates of point A, and x2 and y2 are the x- and y-coordinates of point B.
In this case, m = 2/3, n = 1/3, x1 = 2, y1 = -1, x2 = 4, y2 = -3.
Therefore, plugging these values into the formula we get:
x = [2/3](4 -2) +2 = 4
y = [2/3](-3 - (-1)) + (-1) = -2
Therefore, the coordinates of point P such that it is 2/3 the length of the line segment from A to B are (4, -2). Therefore, the correct option is d-(3,-2).

To know more about length click-
brainly.com/question/25292087
#SPJ1

Answer:

52500

Step-by-step explanation:

first do 5*105 to get 525 then mutiply by 100 to get 52500

The correct answer is (d) No, quadrilaterals LMNO and PQRS are not similar because their corresponding sides are not proportional.

A quadrilateral is a geometric shape with four sides and four corners.

To be classified as a quadrilateral, its shape must be a closed figure with four straight sides and four interior angles. 

To determine quadrilaterals are similar, we need to check if corresponding angles are congruent and corresponding sides are proportional.

Checking corresponding angles are congruent:

∠ L  to ∠P.

∠M  to ∠Q.

∠ N  to ∠ R.

∠O  to ∠S.

All corresponding angles are congruent. Therefore, quadrilaterals have the same shape.

Check if corresponding sides are proportional.

LM =√((-1 - (-2))² + (4 - 2)²) = √(2² + 2²) = 2√2

MN = √((3 - (-1))² + (4 - 4)²) = √(4²) = 4

NO = √((4 - 3)² + (2 - 4)²) = √(2² + 2²) = 2√(2)

OL = √((-2 - 4)² + (2 - (-6))²) = √(6² + 8²) = 10

PQ = √((4 - 2)² + (-2 - (-6))²) = √(2² + 4²) = 2√5

QR = √((12 - 4)² + (-2 - (-2))²) = √(8²) = 8

RS = √((15 - 12)² + (-6 - (-2))²) = √(3² + 4²) = 5

SP = √((2 - 15)² + (-6 - (-6))²) = √(13²) = 13

LM / PQ = (2√2) / (2√5) = √(8/5)

MN / QR = 4 / 8 = 1/2

NO / RS = (2√(2)) / 5√(1) = (2/5)√(2)

OL / SP = 10 / 13

The corresponding sides are not proportional because they are not all equal or proportional to each other. Therefore, we can conclude that the quadrilaterals LMNO and PQRS are not similar.

To know more about corresponding angles visit:

https://brainly.com/question/17038219

#SPJ1

Answer:

Let's denote the duration of each episode of Lola's podcast by "L" and the duration of each episode of Franco's podcast by "F".

From the information given, we can write two equations based on the total duration of content for the two years:

17L + 43F = 5,645 (equation 1)

36L + 43F = 6,956 (equation 2)

To solve for L and F, we can eliminate F by subtracting equation 1 from equation 2:

(36L + 43F) - (17L + 43F) = 6,956 - 5,645

Simplifying, we get:

19L = 1,311

Therefore, the duration of each episode of Lola's podcast (L) is:

L = 1,311 / 19

L ≈ 69.0 minutes

To find the duration of each episode of Franco's podcast (F), we can substitute the value of L into either equation 1 or 2:

17L + 43F = 5,645

17(69.0) + 43F = 5,645

1,173 + 43F = 5,645

43F = 4,472

F = 4,472 / 43

F ≈ 104.0 minutes

Therefore, each episode of Lola's podcast is approximately 69.0 minutes long, and each episode of Franco's podcast is approximately 104.0 minutes long.

Answer:

This should be a permutation

Step-by-step explanation:

P (n, r) = n!/(n-r)!

P (12,5) = 12!/(12-5)!

P (12,5) = 12!/7!

P(12,5) = 95040

Answer:

Step-by-step explanation:

Para convertir 44 semanas a meses, debemos saber cuántas semanas hay en un mes. El número de semanas en un mes no es exacto, pero generalmente se considera que hay alrededor de 4.33 semanas en un mes (ya que el año tiene aproximadamente 52 semanas y 12 meses).

Entonces, para calcular cuántos meses hay en 44 semanas, podemos dividir 44 por 4.33:

44 semanas / 4.33 semanas por mes = 10.16 meses (aproximadamente)

Por lo tanto, 44 semanas equivalen aproximadamente a 10.16 meses.

A) The completed table is given as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

B) the graph is attached accordingly.

C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.

We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.

D(L) = ceil(L/6)

Using this formula, we can complete the table as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).

b) The graph is attached.

c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.

So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.

In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

Learn more about Graph at:

https://brainly.com/question/17267403

#SPJ1

Answer:

$12.00

Step-by-step explanation:

We know that 1 pound = 16 oz.  Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:

[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]

Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:

40 * 0.30 = $12.00