51. The following figures DCBA is parallelogram Find the variables​

Simplifying

2x + 5y = 2

Solving

2x + 5y = 2

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5y' to each side of the equation.

2x + 5y + -5y = 2 + -5y

Combine like terms: 5y + -5y = 0

2x + 0 = 2 + -5y

2x = 2 + -5y

Divide each side by '2'.

x = 1 + -2.5y

Simplifying

x = 1 + -2.5y

Simplifying

5X + 10y = 17

Solving

5X + 10y = 17

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-10y' to each side of the equation.

5X + 10y + -10y = 17 + -10y

Combine like terms: 10y + -10y = 0

5X + 0 = 17 + -10y

5X = 17 + -10y

Divide each side by '5'.

X = 3.4 + -2y

Simplifying

X = 3.4 + -2y

Answer:

6 is your answer i jsut did this its right

Step-by-step explanation:

If Jeff followed the roads, he would have to travel a total of 2 blocks north and 3 blocks east, which would be a distance of 2 * 100 feet + 3 * 100 feet = 500 feet.

What is the Pythagorean theorem in plain English?

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

If he walked diagonally across the field instead, he would be taking a shortcut and the distance he would have to travel would be shorter.

To find the distance Jeff would have to travel if he walked diagonally across the field, you can use the Pythagorean Theorem. The theorem states that in a right 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.

In this case, the length of the hypotenuse (the distance Jeff would have to travel if he walked diagonally across the field) is the quantity we are trying to find. The length of the other two sides are 2 blocks and 3 blocks, which are both 100 feet long.

We can express this relationship as:

hypotenuse^2 = (2 blocks)^2 + (3 blocks)^2

To find the length of the hypotenuse, we can solve the equation for hypotenuse:

hypotenuse = sqrt((2 blocks)^2 + (3 blocks)^2)

Plugging in the values, we get:

hypotenuse = sqrt((2 * 100 feet)^2 + (3 * 100 feet)^2)

hypotenuse = sqrt((200 feet)^2 + (300 feet)^2)

hypotenuse = sqrt(40000 feet^2 + 90000 feet^2)

hypotenuse = sqrt(130000 feet^2)

hypotenuse = sqrt(130000) feet

hypotenuse = 360.54 feet

So the distance Jeff would have to travel if he walked diagonally across the field is 360.54 feet.

To find out how much shorter this distance is compared to the distance he would have to travel if he followed the roads, we can subtract the distance he would have to travel diagonally from the distance he would have to travel if he followed the roads:

500 feet - 360.54 feet = 139.46 feet

So it would be 139.46 feet shorter for Jeff if he walked diagonally across the field instead of following the roads.

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Answer:

The slope of the graph is -3

Step-by-step explanation:

do rise over run.

3 down, 1 right

The amount that one family paid is 25 pound

Here two families had dinner and bill was 100 pound

They used the coupon on which they got 50% off

To find the percentage we have to use percentage formula:

\(=\frac{Value}{Total \ Value} *100\)

\(=\frac{50}{100} *100\)

\(= 50 \ Pounds\)

The remaining bill was 50 pound

Now this amount is divided between the 2 families

\(=\frac{50}{2}\)

\(= 25 \ pound\)

So one family has to pay 25 pounds

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Answer:

in triangle ACD and BCE

AC = EC

angle ACD = angle ECB ( COMMON ANGLE).

CB = CD

BY side and side criteria

triangle ACD is congruent to triangle BCE

so angle a is congruent to angle E

hence, proved

Answer:

Step-by-step explanation:

Geoff is feeling peckish, so he decides to pop into the shop and grab some snacks. He picks up a packet of crisps for 25p, a can of soup for 68p and a watermelon for £1.47. He wonders why the watermelon is so cheap, but he doesn't question it. He goes to the cashier and hands over a £5 note. The customer behind Geoff wonders "how much change does he get back?"

To figure this out, we need to add up the price of the snacks and take it away from the money Geoff gave. We can use a dot to show the pence as parts of a pound. For example, 25p = 0.25 pounds.

The price of the snacks is:

0.25 + 0.68 + 1.47 = 2.40 pounds

The money Geoff gave is:

5.00 pounds

The change is:

5.00 - 2.40 = 2.60 pounds

So, Geoff gets £2.60 in change and a bargain watermelon.

Answer:

Answer:

2.60

Step-by-step explanation:

25+68+147=240

500-240=260

turn into pounds 2.60

Step-by-step explanation:

Answer:

900

Step-by-step explanation:

4500/5

Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent.

In mathematics, the word "graph" has (at least) two distinct meanings. The term "graph" in elementary mathematics refers to a diagram known as a function graph or "function graph." A graph is, in the language of mathematics, a set of points and lines that link a subset (potentially empty) of the points and lines. Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. Bar charts, line charts, histograms, and pie charts are the four types of fundamental statistical charts.

Each bar's height corresponds to the value of the quantity it represents. For comparing numbers and data, bar graphs are excellent. The x and y axes are the names of the vertical and horizontal axes in bar graphs, respectively. A bar graph can be used, for instance, to compare your classmates' heights.

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Answer:

m∠B= 67

m∠C= 23

Step-by-step explanation:

okay so same thing we did before except they will equal 90 not 180

B= 3(c)+2

c+b=90

c+3(c)+2=90

4c+2=90

4c=92

c=23

now input them! or subtract!

90-23=67

m∠C=23

m∠B=67

Answer:

The answer to this is 7.

a+2

5+2

7

Answer:

9

Step-by-step explanation:

Answer:

the bottom one

Step-by-step explanation:

its distributive property. 5x11+5x7

Answer:

36 in²

Step-by-step explanation:

Area of the figure

Answer:

The answer is 36 ft²

Step-by-step explanation:

Let us divide this whole figure into 2 rectangle, a big and a small.

Rectangle 1: (Small)

(Area 1) = l × b

A = 2 × 3 = 6 square ft

Rectangle 2: (Big)

(Area 2) = l × b

A = 6 × 5 = 30 square ft

Now,

Total Area of figure = Area of Rectangle 1 + Area of Rectangle 2.

Total Area = 6 + 30 = 36 square ft.

Thus, The area of the figure is 36 ft².

Answer:

17%

Step-by-step explanation:

Let us say there are 200 people on the JV swim team. That would mean that 110 people do not wear glasses.

Of these 110 people, 30% are in 10th grade. Therefore, 33 people are in 10th grade and do not wear glasses.

This is 33 people ÷ 200 total = 16.5% ≈ 17%

Therefore, there is a 17% probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade

[NOTE] You could also just do 55% × 30% = .55 × .30 = .165 ≈ .17 ⇒ 17%

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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Recall that the product of the slopes of two perpendicular lines is equal to

therefore, if the slope of the green line is 1/7, and x the slope of the blue line we can set the following equation:

Solving for x we get that:

Answer: Option C.

To evaluate the given integral, the most helpful substitution is x = 15 sec θ. The rewritten integral will be dx = 15 sec θ tan θ dθ / (225 + 225 sec² θ)².

In trigonometric substitution, we choose a substitution that simplifies the integral by transforming it into a form that can be easily evaluated using trigonometric identities. In this case, the most helpful substitution is x = 15 sec θ.

To rewrite the integral, we need to express dx in terms of θ. Since x = 15 sec θ, we can differentiate both sides with respect to θ to find dx. The derivative of sec θ is sec θ tan θ, so we have dx = 15 sec θ tan θ dθ.

Substituting this expression for dx and rewriting (225 + x²)² in terms of θ, we obtain:

∫(x² dx) / (225 + x²)² = ∫[(15 sec θ)² (15 sec θ tan θ dθ)] / (225 + (15 sec θ)²)².

Simplifying further, we get:

∫(225 sec² θ tan θ dθ) / (225 + 225 sec² θ)².

This is the rewritten form of the integral using the substitution x = 15 sec θ.

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Answer:

TRUE

Step-by-step explanation:

The probability of committing a type 1 error is called alpha (or the level of statistical significance)

Alpha is the probability of committing a type i error. The statement is True.

Alpha is also known as the level of significance. In hypothesis testing, the level of significance is used to determine the acceptance or rejection of a null hypothesis. It's calculated by dividing the critical value (the value beyond which we can reject the null hypothesis) by the standard deviation of the population. The level of significance is typically set to 0.05 or 0.01. If the p-value (the probability of getting the observed results by chance) is less than the level of significance, we reject the null hypothesis and conclude that the alternative hypothesis is true.

Therefore, it's true that alpha is the probability of committing a type I error, which occurs when we reject a null hypothesis that is actually true. A type I error is also known as a false positive. In other words, we conclude that there is a significant effect or relationship when there isn't one. The level of significance is a measure of how willing we are to make this type of error. If we set a high level of significance, we are more likely to make a type I error.

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Answer:

y = 2/5x + 3

Step-by-step explanation:

The minimum score required for an A grade is approximately 87 when rounded to the nearest whole number.

To find the minimum score required for an A grade, we'll use the given information about the normal distribution and the percentiles associated with each letter grade. Since an A grade is given to the top 8% of scores, we need to find the score that corresponds to the 92nd percentile (100% - 8%). Given the mean of 77.1 and a standard deviation of 7.4, we can use the z-score formula or a z-table to find the score at the 92nd percentile.
The z-score formula is: z = (X - mean) / standard deviation
Using a z-table, we find that the z-score corresponding to the 92nd percentile is approximately 1.41. Now we can use the z-score formula to find the score X:
1.41 = (X - 77.1) / 7.4
Solving for X, we get:
X = (1.41 * 7.4) + 77.1 ≈ 87.4

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The downhill side of the crane base should be raised by approximately 4.53 inches to level the crane on a 2.5° slope.

We can use trigonometry here. Let x be the length (in inches) that the downhill side of the base should be raised. The slope of the ground is given to be 2.5°,

tan(2.5°) ≈ 0.0436

Now, using the equation,

x / 12 = 9tan(2.5°)

Here, we converted the base's width from feet to inches (by dividing by 12) and calculated the crane's required vertical displacement (inches) using the angle's tangent. When we simplify this equation, we obtain,

x = 9tan(2.5°)12

x ≈ 4.53 inches

Therefore, the downhill side of the base should be raised by about 4.53 inches to level the crane.

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Complete question - A crane is being set up on a slope of 2.5 degrees. If the base of the crane is 9.0 ft​ wide, how many inches should the downhill side of the base be raised in order to level the​ crane?

answer:

this is the solution

Answer:

3

Hope this helps!

Step-by-step explanation:

\(\frac{1}{2}\) × 4 × \(\frac{3}{2}\)

1 × 2 × \(\frac{3}{2}\)  ( Simplify 1/2 and 4 )

2 × \(\frac{3}{2}\)

3 ( Simplify 2 and 3/2 )

The exponential function that represents the population is y = 200(1.5)ˣ

An exponential function is given by:

y = abˣ

Let y, x are variables, a is the initial value and b is the multiplication factor.

Where y is the population of the bacteria after x minutes.

From the graph, at the point:

(0, 200):

200 = ab⁰

a = 200

at the point (2, 450):

450 = 200(b²)

b = 1.5

The exponential function that represents the population is y = 200(1.5)ˣ

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Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

Answer:

The last one

Step-by-step explanation: