Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Explain.

Answer: [tex]5y - x = -25[/tex]

Step-by-step explanation:

The formula for calculating equation of line when a point and a slope is gives is :

[tex]y - y_{1} = m ( x - x_{1})[/tex]

[tex]x_{1} = 10[/tex]

[tex]y_{1} = -3[/tex]

[tex]m = \frac{1}{5}[/tex]

substituting into the formula , we have

[tex]y - (-3) = \frac{1}{5}(x - 10 )[/tex]

[tex]y + 3 = \frac{1}{5}(x - 10 )[/tex]

multiply through by 5 ,

[tex]5 (y+ 3 ) = x - 10[/tex]

[tex]5y + 15 = x - 10[/tex]

in standard from , we have

[tex]5y - x = -10 - 15[/tex]

[tex]5y - x = -25[/tex]

Answer:

Step-by-step explanation:

A i think sorry if it is wrong

The only ordered pair that can be added to make the relation a function, without repeating an x-value, is option B. (-1,-1).

The question is asking which ordered pair (x,y) makes the given set of ordered pairs a function. A function is defined as a relation where every x-value (input) is associated with exactly one y-value (output). We already have the points (2,3), (–2,5), (4,4), and (-4,5) in our set. To maintain the definition of a function, the x-value of the ordered pair we are going to add cannot be the same as any x-value already present in the set. Looking at our options:

Therefore, the only ordered pair that makes the relation a function is option B. (-1,-1).

Answer:

can you be more clear

Step-by-step explanation:

Answer:

distance is the dependent variable because it depends on the time hiked.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Do 25 ^ 2 = 625

Do 20 ^ 2 = 400

Because you're finding something that's nor the hypotenuse you subtract

So you do 625 - 400 = 225

Then you do the square root of 225 to get the answer

Which is 15

Answer:

15

Step-by-step explanation:

Let 'l' be the length of the other leg

Using pythagoras theorem,

25² = 20² + l²

625 = 400 + l²

225 = l²

l = 15

Answer:

2.19

Step-by-step equation:

Answer:

(0,9) for y-intercept

perp.: (-1/2)= m

y - 9 = (-1/2)x - 0

y = (-1/2)x + 9

Step-by-step explanation:

Yo sup??

we know that the sum of all the angles of a triangle is 180

therefore

11x+7x+90=180

18x=90

x=5

exterior angle formed on the ground=180-11x

=180-55

=125

Hope this helps

Answer:

According to the dictionary, it is any of a large group of organic compounds occurring in foods and living tissues and including sugars, starch, and cellulose.

The simplified form of the given expression is 6x+3.

The given expression is x+3+5x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be simplified as follows

Now, x+3+5x

Add like terms

(x+5x)+3

= 6x+3

Therefore, the simplified form of the given expression is 6x+3.

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Answer:

←

Step-by-step explanation:

less than as 4.567 is less than 4.576

The correct symbol to use between 4.567 and 4.576 is '<', since 4.567 is less than 4.576.

The question is asking to choose the correct mathematical symbol that makes the given number sentence true. The two numbers are 4.567 and 4.576. In this case,  since 4.576 is greater than 4.567, the correct symbol would be less than ('<'). Thus, the correct number sentence is 4.567 < 4.576.

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Answer:

Ricky hits 1202 base

Pedro hits = 1485 base

Step-by-step explanation:

Pedro + Ricky = 2687 hits

Let Ricky hits = x

So the Pedro hits will be = x + 283

( x + 283 ) + x = 2687

2 x + 283 = 2687

2 x = 2687 - 283

2 x = 2404

x = 1202

So the Ricky hits 1202 base

Pedro hits (1202 + 283) = 1485 base

Final answer:

To determine the number of hits Ricky and Pedro had, a system of equations was set up and solved. Ricky had 1202 hits, while Pedro had 1485 hits last season.

Explanation:

To solve the problem involving teammates Pedro and Ricky's base hits, we need to set up a system of equations based on the information given:

Pedro and Ricky's hits together total 2687.

Pedro had 283 more hits than Ricky.

Let's denote Ricky's hits as R and Pedro's hits as P. The two equations representing the situation are:

R + P = 2687

P = R + 283

To find the number of hits Ricky had, we can substitute the second equation into the first:

R + (R + 283) = 2687

2R + 283 = 2687

2R = 2687 - 283

2R = 2404

R = 2404 / 2

R = 1202

Now that we have Ricky's hits, we can find Pedro's hits by adding 283 to Ricky's total:

P = R + 283

P = 1202 + 283

P = 1485

Therefore, Ricky had 1202 hits, and Pedro had 1485 hits last season.

Answer:   [tex]\sqrt{20}[/tex]

Work Shown:

[tex]2\sqrt{5} = \sqrt{4}*\sqrt{5}\\\\2\sqrt{5} =\sqrt{4*5} \text{ use the rule } \sqrt{x}*\sqrt{y} = \sqrt{x*y}\\\\2\sqrt{5} = \sqrt{20}[/tex]

Answer:

528

Step-by-step explanation:

because each class has 22 students and there are 24 classes you multiply them

Answer: 528 children

Step-by-step explanation: 22 children in each class. 24 total classes.

22•24=528

Answer:

Steps. (6x - 3) - (2x -2)= 6x - 3 - 2x + 2. = (6x - 2x) + (-3 + 2) = 4x + (-1 ) 4x - 1 ---> Answer.

Answer:

The least number of people that share a birthday is 1, no matter what the size of the population is.

Step-by-step explanation:

Tricky Question

Suppose there is one person that has their birthday on Feb 02. It's perfectly possible that no one else in the city has their birthday on the same day, i.e. their birthdays are any time except Feb 02. So that person will be the only one who has that as a birthday. It's even possible that no one has a birthday on Feb 02, so the answer will be zero, but it's not possible to talk about sharing if no one is doing it, so the answer is

The least number of people that share a birthday is 1, no matter what the size of the population is.

Note: If this question is talking about probability calculations, then the matter is totally different.

Answer:

sum was 300000

Step-by-step explanation:

let sum of money is placed  is x rs

Term T = 3 years, rate R = 10%

Then simple interest for for 3 years is

[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]

Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie

[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]

Sum was 300000

At the simple interest rate, the rate is applied only to the initial sum, while

at the compound interest, the rate is applied to the amount in the account.

Reasons:

Let P represent the sum of money invested, we have;

Where;

P = The initial sum invested

r = The simple and compound interest rate applied = 10% = 0.1

t₁ = The number of years the money is placed at simple interest = 3 years

t₂ = The number of years the money is placed at compound interest = 2 years

Therefore;

[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]

Which gives;

[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]

[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]

The sum of money invested, P ≈ Rs 355,847.466

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Answer:x-1

Step-by-step explanation:

Answer:

Right angle triangle hypotenuse formula

c = √a²+b²

a=11

b=60

c = √11² + 60²

c = 3611

Step-by-step explanation:

I hope this helps!

(1) The numbers are 8 and 16.

(2) John have 12 nickels and 6 dimes.

Solution:

(1) Let x and y be the two numbers.

Sum of two numbers = 24

⇒ x + y = 24 – – – – (1)

One number = Other number – 8

⇒ x = y – 8 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ y – 8 + y = 24

⇒ 2y – 8 = 24

Add 8 on both side of the equation, we get

⇒ 2y = 32

Divide by 2 on both sides.

⇒ y = 16

Substitute y = 16 in equation (2)

⇒ x = 16 – 8

⇒ x = 8

Hence the numbers are 8 and 16.

(2) Let n and d be the nickels and dimes respectively.

Nickels + Dimes = 18

⇒ n + d = 18 – – – – (1)

Nickles = Dimes + 6

⇒ n = d + 6 – – – – (2)

Substitute equation (2) in equation (1), we get

⇒ d + 6 + d = 18

⇒ 2d + 6 = 18

Subtract 6 from both side of the equation.

⇒ 2d = 12

Divide by 2 on both side of the equation, we get

⇒ d = 6

Substitute d = 6 in equation (1), we get

⇒ n = 6 + 6

⇒ n = 12

Hence John have 12 nickels and 6 dimes.

Answer:

$67.15

Step-by-step explanation:

79*(1-.15)

= $67.15

Angle 3 and angle 4 are supplementary angles and when added together need to equal 180 degrees.

To find angle 4 subtract angle 3 from 180.

Angle 4 = 180 - 101 = 79 degrees.

Answer:

your answer is correct

Step-by-step explanation: because each angle equals the same thing

Answer:

The height of the rectangle is 4 cm.

Step-by-step explanation:

You find area by multiplying base and height.

The formula is  A=bh

so 100=25h

25 times 4 is 100

100=25*4

4cm is your answer

Final answer:

The expression given is factored to identify common factors of 30 and 44. By identifying factors like 3, 5 (for 30) and 2, 11 (for 44), it's shown that the expression is indeed divisible by both 30 and 44.

Explanation:

The student asked to prove that the value of the expression: (518−258)(164−213−45) is divisible by 30 and 44. To approach this proof, we will simplify and factor the expression where possible to find common factors of 30 (2*3*5) and 44 (4 × 11).

First, let's factor each part of the expression:

518 = (52)9 = 259

258 = (52)8 = 516

164 = (24)4 = 216

213 remains the same

45 = (22)5 = 210

Now, we rewrite the original expression with these factors:

(259 − 516)(216 − 213 − 210)

Looking at the first parenthesis, we see that 259 and 516 have a common factor of 516, so we can factor it out:

516(25−1)(216−213−210)

Recognizing that 25−1 = 24, and that 24 is divisible by both 3 and 8 (and thus 4), we have a clear division by 30.

For the second parenthesis, we can see that 210 is a common factor:

210(26−23−1)

Again, noticing that 26−23−1 leaves us with numbers of the form 2n − 2n-k − 1, we can confirm divisibility by 2 and potentially by 4 depending on the value of n. Checking the values, 26 − 23 − 1 equals 57, which is also divisible by 3.

So the original expression has factors that include 2, 3, 5, and 11, thereby confirming that the expression is divisible by both 30 and 44.

Answer: Associative Property of Multiplication

It states that a(b*c) is the same as (a*b)*c

Hope this helped!

Answer: a 3,-2

Step-by-step explanation:

When a point is rotated, it must be rotated around a center.

The coordinate of the image of (-2,-3) is (3,-2)

The point is given as:

[tex](x,y) = (-2,-3)[/tex]

The rule of 90 degrees counterclockwise rotation is:

[tex](x,y) \to (-y,x)[/tex]

So, we have:

[tex](-2,-3) \to (3,-2)[/tex]

Hence, the coordinate of the image of (-2,-3) is (a) (3,-2)

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Answer:

5x+10

Step-by-step explanation:

you will add 7x_2x=5x

then 4+6=10

5(x-2)-3x+7

5x-10-3x+7

2x-10+7

2x-3

Hope this step by step process helped

Answer:

length=8+w........1

area=84square feet........2

area of rectangle =length x width

area=(8+w)x W

area=8w+w^2

84=8w+w^2

w^2+8w+(4^2)=84+(4^2)

(w+4)^2=84+16

(w+4)^2=100

√(w+4)^2=√100

w+4=±100

w+4=100 or w+4=-100

w=96 or w=-104

the answer is 96

Answer:

900

Step-by-step explanation:

You first split it up with 12x10x25 for the smaller one and you do 20x12x25 for the other

I hope this helps if you need the work i can give it to you

Answer:

3.16227766017

Step-by-step explanation:

I think so