expand expression (3x-7)(2x+7), without using long multiplication find 53×47
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By using the properties of rectangle, it can be calculated that-

Value of z is 31°

What is a rectangle?

Rectangle is a four sided two dimensional figure which satisfies the properties of a parallelogram and whose every angle is 90°

FH = 2z + 8

EG = 2z + 8 [Diagonals of a rectangle are equal]

EI = 35

EG = [tex]35 \times 2 = 70[/tex] [Diagonals of rectangle bisect each other]

So,

2z + 8 = 70

2z = 70 - 8

2z = 62

z = [tex]\frac{62}{2}[/tex]

z = 31

Value of z is 31°

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x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.

What is the quadratic equation?

A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers, with a 0.

We have,

Amelia has 2 sheets of construction paper with length x centimeters.

One piece of construction paper has a width of x+4.5 centimeters, and the other has a width of x+6.25 centimeters.

expression to represent the area the 2 pieces of construction paper will cover.

To find the area(A) of a paper:

multiply its height by its width:

A = (x + 4.5) * (x + 6.25)

A = x² + 6.25x + 4.5x + (4.5) * (6.25)

A =  x² + 6.25x + 4.5x + 28.125

hence, x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.

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The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangles are said to be congruent if two points and the contained side among one triangle match two angles and the contained side of another triangle.

In triangles ΔADB and ΔCDB, then we have

∠BAD = ∠BCD          (Given)

∠BDA = ∠BDC          (Given)

    AD = AD               (Common side)

The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.

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Answer:

Part A: 2 Part B: 2- and 4-Part C: 8 The graph shows at 8 seconds the slope starts to decrease rapidly. Part D: I believe at 14 seconds the water balloon would be o the ground.

Step-by-step explanation:

Answer:29,921.25

Conner and Darian made a profit of $40,021.50 on the first day of their hot chocolate sale. They donated $10,050.25 of that money to their school, which leaves them with $40,021.50 - $10,050.25 = $29,971.25.

Conner and Darian each gave their dad $25.00, which means they gave a total of $25.00 * 2 = $<<25*2=50.00>>50.00 to their dads.

This means that Conner and Darian had $29,971.25 - $50.00 = $29,921.25 left to invest in their hot chocolate shop.

The true statement about the graph include:

1. The y-intercept represents the orders for hot chocolate on a day when the outside temperature was 52°F.

2. Sheryl gets 160 orders for hot chocolate on a day when the outside temperature is 52°F.

It is clearly mentioned on graph above 52 degrees fahrenheit. So y-intercept represents the orders for hot chocolate when the outside temparature was 52 F.

For every 16° increase in temparature above 52°F there is a decrease of 32 orders. Therefore for each degree increase above 52°F decrease in order = 32/16 => 2

So Sheryl gets 2 few orders for each degree decrease in temperature above 52°F. The slope of the line represents the decrease in numbers of order per degree increase in temparature.

As graph starts with 52oF and the number of orders on it is 160; So, Sheryl gets 160 orders when outside temparature is 52°F.

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Answer:

The answer for the above question is:

b)2

When solving a word problem using a system of equations with two unknowns, you must create two equations. So, correct option is B.

The reason is that each unknown in the problem requires an equation to represent its relationship with the other variables.

For example, let's say you have two unknowns, x and y. You need two equations to define the relationships between these variables. These equations can be represented as:

Equation 1: x + y = 10 (This equation represents the relationship between x and y based on the given information in the problem.)

Equation 2: 2x - y = 4 (This equation represents another relationship between x and y based on additional information provided in the problem.)

With a system of two equations involving two unknowns, you can use algebraic methods such as substitution or elimination to solve for the values of x and y.

Having only one equation would not be enough to determine unique values for both x and y, as there would be an infinite number of possible solutions. On the other hand, having more than two equations might lead to over-determining the system, making it inconsistent or redundant.

Therefore, two equations are the minimum required to solve for two unknowns effectively. So, correct option is B.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer: B

Step-by-step explanation:

Substitution method

solve the equation for Y by putting the variable on the left. -3 = y - 2x would become y = 2x - 3

Plug Y into the top equation. 2(2x - 3) + 6 =4x

4x - 6 + 6 = 4x

Combine like terms

4x - 0 = 4x

4x = 4x

Infinite Solutions

Answer:

you would times them both so 4x543 =2172

Step-by-step explanation:

543 cubic centimeters has 0.543 L approximate displacement.

Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.

Basic formula to calculate engine displacement is =

V = π/4 x D² x H x N

Where :

D = Bore Diameter

H = Length of Stroke

N = Number of Cylinder

Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.

First, we state what is known. It is the displacement at cubic centimeter.

Cubic centimeter = 543 cc

Next, we change the unit of cubic centimeter (cc) into liter (L)

Displacement = cc / 1000 L

= 543 / 1000 L = 0.543 L

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1/2 is the slope of the following when you simplify

1) The base rate for the empty bus is $120.

2) The variable cost (slope) for each person on board the bus is $2.

3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.

The total charge for taking 30 people aboard = $180

The total charge for taking 50 people on board = $220

The differences in the number of people and charges are 20 and $40, respectively.

Let x = the number of people boarding the bus and n = the fixed rate per bus.

30x + n = 180 ... Equation 1

50x + n = $220  ... Equation 2

Subtract Equation 1 from Equation 2:

20x = $40

x = $2 ($40/20)

The variable cost per person = $2 ($40/20)

The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.

= 60 + n = $180

n = $120

OR:

50(2) + n = $220

100 + n = $220

n = $120

The equation for the cost, c, of a bus with x number of people:

C = 120 + 2x

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Answer:

Step-by-step explanation:

17 hours multiplied by 60 (60 seconds in 1 minute) = 1020 minutes + 38 minutes = 1058 minutes.

Miles per hour = distance/time

1163/1058 = 1.10 miles per hour

Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.

y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).

We need to check by substituting value of y in every equation to check correct option.

(a) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 3x= 3×3=9

L.H.S≠R.H.S

So, it is not a correct option.

(b) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x-3= 3-3=0

L.H.S≠R.H.S

So, it is not a correct option.

(c) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = x+2= 3+3=5

L.H.S≠R.H.S

So, it is not a correct option.

(d) Substituting y=6 and x=3 in function

L.H.S = 6

R.H.S = 2x= 2×3=6

L.H.S=R.H.S

So, it is correct option.

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Answer:

1)x=2

2)4<x

3)x<4/5

4)1<x

The relation between variables is represented by an equation ; y = 2.5x+15

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

Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5

We can represent the relationship as ;

y = 2.5x+15

Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.

Hence, the relation is described as y = 2.5x+15

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The process by which people are separated from social participation is known as social exclusion.

This term refers to the process in which people or groups are separated or not allowed to participate.

Exclusion is considered a negative process or phenomenon, since:

In this sense, what must be done is to fight to eliminate exclusion and promote inclusion.

¡Hope this helped!

A fraction of the students who have brown hair is equal to 1/7.

You should shade only one (1) section on the pie chart to show the number of students with brown hair.

In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.

Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;

Number of brown hair = 1 brown hair.

Number of blonde hair = 4 blonde hair.

Number of black hair = 2 black hair.

Therefore, the total number of hairs is equal to 7 hairs.

For the fraction of students with brown hair, we have;

Fraction = 1/7.

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The value of d for the given angles will be equal to d = 13. The correct option is B.

The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.

Complementary angles are formed when the sum of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.

Given that one angle measures 18° and another angle measures (6d − 6)°.

The value of d will be calculated as,

18 + 6d - 6 = 90

6d + 12 = 90

6d = 90 - 18

6d = 78

d = 78 / 6

d = 13

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The correct answer is D. A 95% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.

The width of a confidence interval reflects the degree of uncertainty about the estimate of the population parameter. A wider interval indicates a higher degree of uncertainty, while a narrower interval indicates a lower degree of uncertainty.

The confidence level of a confidence interval is the probability that the interval contains the true population parameter. For example, a 95% confidence interval means that there is a 95% probability that the interval contains the true population parameter. Similarly, an 80% confidence interval means that there is an 80% probability that the interval contains the true population parameter

Since a 95% confidence interval is more confident that it captures the true value of the population parameter than an 80% confidence interval, the 95% confidence interval must be wider in order to capture the true value with a higher degree of confidence.

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Answer:

Step-by-step explanation:

first things first go back in the lesson or your notes if you wrote down some and if not go right some down and in the notes there would be the answer between pages 1-5 or maybe  6 IDR ( i dont remember )  but look thru those  pages and you will find the answer hope this helped. please mark me brainiest please.

The amount of time required for an assembly line worker to complete a repetitive task is measured using a time and motion study.

According to the data, the average time it takes to move apart from the bin to its place on a car's chassis is 11 seconds, while the standard deviation is 2 seconds.

If XX and YY are independent, the property mean and variance are as follows: X 1 = 11; sigma_X_1 = 2, X 1 = 2, mu_X_2 = 20, X 2 = 20, sigma_X_2 = 4, and X 2 = 4.

aX+bY = a X + b Y; sigma_aX+bY = a X + b Y; aX+bY 2 = a 2 X 2 + b 2 Y 2; and finally, we have the following results:

X 1 + X 2 = X 1 + X 2 = 11+20=31 sigma_X_1+X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_1+

The value reduced by the mean and divided by the standard deviation is the z-score:

z=\dfrac{x-\mu} {\sigma} =\dfrac{30-4.4721} \approx - 0.22

z=σx−μ =4.472130−31

≈−0.22

Decide the relating esteem utilizing table A:

P (X_1+X_2 30) = P(Z-0.22) = 0.4129 P (X 1 30) = P(Z-0.22) = 0.4129

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The option that shows the estimation that Bradley’s change is reasonable is A. Add 11 and 5 and 3 to get $19; $20-$19=$1, which is very close to the amount of change received by Bradley

Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose even when the input data is incomplete, uncertain, or unstable. Nonetheless, the value is usable because it is based on the best available information.

In this situation, Henri paid $10.75 for a calculator, $4.98 for copier paper, and $3.21 for folders. He paid with a $20 bill and got $1.06 in change.

The correct estimation is option A.

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Answer:

y = 1/3x + 6

Step-by-step explanation:

Answer: D

Step-by-step explanation:

(4,16)

The rate of change of the table of values is calculated as: A. 1/5.

Given the table above, the rate of change can be calculated using the formula below:

Rate of change (m) = change in y / change in x.

Using two pairs of values from the table, (10, 2) and (20, 4):

Change in y = 4 - 2 = 2

Change in x = 20 - 10 = 10

Therefore:

Rate of change (m) = 2/10

m = 1/5

Therefore, the rate of change is determined as: A. 1/5.

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Length of each Plan A workout: 4 hours and Length of each Plan B workout: 8 hours.

To find the length of each workout plan, we need to know the total amount of time that Deshaun spent on each plan. We can find this by adding up the number of clients who did each plan on Friday and Saturday and then multiplying by the total amount of time that Deshaun spent training his clients on each day.

On Friday, Deshaun had 4 clients who did Plan A and 8 who did Plan B, for a total of 4 + 8 = 12 clients.

On Saturday, Deshaun had 2 clients who did Plan A and 3 who did Plan B, for a total of 2 + 3 = 5 clients.

In total, Deshaun had 12 + 5 = 17 clients who did his workout plans.

Since Deshaun trained his Friday clients for a total of 17 hours and his Saturday clients for a total of 7 hours, the total amount of time that he spent on Plan A was 4 × 17 = 68 hours.

The total amount of time that he spent on Plan B was 8 × 17 = 136 hours.

Since there were 17 clients in total, the length of each Plan A workout is 68 / 17 = 4 hours.

The length of each Plan B workout is 136 / 17 = 8 hours.

Thus, the length of each Plan A workout is 4 hours, and the length of each Plan B workout is 8 hours.

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Answer:

To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:

1 1/2%/100 = 15/of

Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:

(1 1/2%/100) * 100 = (15/of) * 100

of = (15/1 1/2%) * 100

Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:

of = (15/1.5%) * 100

of = (15/0.015) * 100

of = 1000

Therefore, the number we are trying to find is 1000.

In summary, the proportion that represents the given word problem is:

1 1/2%/100 = 15/1000

Answer:

[tex]\textsf{Proportion}: \quad \sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

[tex]\textsf{Solution}: \quad \sf x=1000[/tex]

Step-by-step explanation:

Given proportion formula:

[tex]\sf \dfrac{\%}{100}=\dfrac{is}{of}[/tex]

Given word problem:

Let the unknown number be x.

Therefore:

Substitute these into the proportion formula to create a proportion to represent the given word problem:

[tex]\sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]

To solve the proportion, cross multiply:

[tex]\implies \sf 1.5x=15 \cdot 100[/tex]

[tex]\implies \sf 1.5x=1500[/tex]

Divide both sides by 1.5:

[tex]\implies \sf \dfrac{1.5x}{1.5}=\dfrac{1500}{1.5}[/tex]

[tex]\implies \sf x=1000[/tex]

The percentage increase is about 16.66%.

What is a percentage increase?

The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.

The initial amount was $18 and the final amount is $21.60.

By using the percentage increase formula, we can write

        Percentage increase = (final value - initial value)/|Final value| * 100

                                            = ((21.60 - 18)/21.60)*100

                                            = 16.66%

Hence, the percentage increase is about 16.66%.

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The correct answer is (D) 2 + 3 = 6. If an organism is homozygous for 3 genes and heterozygous for 2 genes, it can produce a total of 2 + 3 = 5 different gametes.

When an organism is homozygous for a gene, it means that it carries two copies of the same allele for that gene. When an organism is heterozygous for a gene, it means that it carries two different alleles for that gene.

In this case, the organism is homozygous for 3 genes, which means that all its gametes will carry the same alleles for these 3 genes. It is also heterozygous for 2 genes, which means that it can produce gametes that carry either one of the two alleles for these 2 genes.

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