ABC is similar to LMN. Also, side AB measures 5 cm, side AC measures 7 cm, and
side LM measures 35 cm.
What is the measure of side LN?

Answer:

y=-3x+5

Step-by-step explanation:

y-y1=m(x-x1)

y-5=-3(x-0)

y-5=-3(x)

y-5=-3x

y=-3x+5

Answer:

641

Step-by-step explanation:

24,358 ÷ 38=641

Hope this helps!!

24,358 / 38 = 641

Use long division to find the answer :)

Hope this helps!

Answer:

x = -5 + 5i, -5 - 5i

Step-by-step explanation:

Answer: 14ft > 4 1/2 yd

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

Divide both sides by 3/4 to solve for x.

－24/1*4/3 = -96/3

－96/3=－32

Answer:

Rock phosphate, insoluble phosphates in bone deposits, and dissolved phosphates available to plants

The solution to the given equation (-20+5) (58-65) is 105. This is calculated by first simplifying the expressions within the brackets and then multiplying the resulting numbers.

The student's question relates to the calculations and simplifying of expressions in mathematics. This type of operation can be found in basic algebra, and its mastery is an essential part of succeeding in mathematics.

To solve the equation given, which is (-20+5) (58-65), we'll need to separate it into two steps. First, simplify the expressions in the brackets. Therefore, -20+5 equals -15 and 58-65 equals -7. Now, substitute these values back into the equation getting -15 * -7. Multiplying these two values will give a product of 105. That is the final answer. The provided list of numbers following the initial problem statement seems to be irrelevant to this specific calculation.

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Answer: 12 girls

Step-by-step explanation: Our first step in this problem is to write down the unit ratio that is involved. In this case, it's girls/boys.

Next, we set up our proportion. We know that at a movie there are 3 girls for every 8 boys so we have 3/8 and we are asked how many girls are at the movie if 32 boys are the movie so that's x/32.

Now we have the proportion 3/8 = x/32.

Notice that the 32 boys must go on the bottom of the second ratio because our unit ratio tells us that we put girls/boys.

Solving from here, we use the means-extremes property to get 3 times 32 to get 96 = 8 times x or 8x. So we have 96 = 8x.

Dividing both sides by 8, we find that 12 = x.

This means that 12 girls are at the movie when 32 boys are at the movie.

Answer: H-7

Step-by-step explanation: I got it right on test!  have a great day! :)

Final answer:

C paid Rs. 127,050 for the car.

Explanation:

To find out what C paid for the car, we need to consider the gains made by A and B. A bought the car for Rs.100,000 and spent Rs. 10,000 on repairs. This means A's total cost is Rs. 110,000. A then sells the car to B at a gain of 10%, which means B buys the car for 110% of Rs. 110,000, or Rs. 121,000.

Now, B sells the car to C at a gain of 5%. To find out what C paid, we need to calculate 105% of Rs. 121,000, which gives us Rs. 127,050. Therefore, C paid Rs. 127,050 for the car.

Answer:

see explanation

Step-by-step explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b)

(x - 1)² - 25 ← is a difference of squares

with a = x - 1 and b = 5, thus

(x - 1)² - 25

=(x - 1 - 5)(x - 1 + 5) = (x - 6)(x + 4), then

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

Solutions are x = - 4, x = 6

Final answer:

The new balance in the checkbook register is $114.04.

Explanation:

To find the new balance in a checkbook register after a deposit and a check are processed, you need to add the deposit to the current balance and then subtract the amount of the check.

Initially, the checkbook register has a balance of $158.

A deposit of $35 is made, and a check for $78.96 is written.

Calculating the new balance involves the following steps:

After completing these steps, the new balance in the register would be $193 - $78.96 = $114.04.

Balancing your checkbook regularly is essential to manage your money efficiently and to avoid fees associated with overdrafts or insufficient funds.

a. She pays $100 for 5 sheets

b. 25+15x dollars for x sheets

c. 8 sheets

Step-by-step explanation:

Given

Sitting cost = $25

Per sheet picture cost = $15

Let p be the number of sheets of pictures

Then the cost can be written as a function of p

[tex]c(p) = 25+15p[/tex]

Now,

a. How much does she pay for 5 sheets of pictures?!

Putting p = 5 in the function

[tex]c(5) = 25 + 15(5)\\= 25+75\\=100[/tex]

She will pay $100 for 5 sheets of pictures

b. How much does she pay for "x" sheets?

Putting x in place of p

[tex]c(x) = 25+15x[/tex]

c. How many sheets can she buy for $145?

We know the cost now, we have to find p so,

[tex]145 = 25+15p\\145-25 = 25+15p-25\\120 = 15p[/tex]

Dividing both sides by 15

[tex]\frac{15p}{15} = \frac{120}{15}\\p = 8[/tex]

Hence,

She can buy 8 sheets for $145

Keywords: Linear equation, Algebraic functions

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Answer:

This number line

shows the numbers

between 95 and 101.

Step-by-step explanation:

96, 97, 98, 99, and 100 all fall between 95 and 101.

97, 98, 99, and 100 are all greater than 96, so option 2 is incorrect.

96 is less than 97, so option 3 is incorrect.

Answer:

V ≈ 63.4

Step-by-step explanation:

The arc length of the segment becomes the circumference of the cone's base.  Therefore, we can find the radius of the cone:

s = C

(90/360) 2π (10) = 2π r

r = 2.5

The radius of the segment is the slant length of the cone.  So we can use Pythagorean theorem to find the cone's height.

l² = r² + h²

10² = 2.5² + h²

h = √93.75

The volume of the cone is:

V = π/3 r² h

V = π/3 (2.5)² √93.75

V ≈ 63.4

I believe that the answer is 7 because it is in the tens place.

Sorry misunderstood the Question the other user is correct

originally had a 2

Answer:

7 because it is in the 0.1 (1/10 or tenth) place of the number

Answer:

[tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

Step-by-step explanation:

Given the arithmetic sequence in recursive formula.

f(0) = 30 and f(n + 1) = f(n) + 7 ......... (1)

Therefore, putting n = 0 in equation (1) we get f(1) = f(0) + 7 = 30 + 7 = 37 {Since, f(0) is given to be 30}

Again, putting n = 1 in equation (1) we get f(2) = f(1) + 7 = 37 + 7 = 44

And, putting n = 2 in equation (1) we get f(3) = f(2) + 7 = 44 + 7 = 51

and so on.

Therefore, the arithmetic sequence is 30, 37, 44, 51, .......

Therefore, the linear equation of this sequence is given by [tex]t_{n}  = 30 + 7n[/tex], where, n = 0, 1, 2, 3, 4, .........

(Answer)

Answer:

Step-by-step explanation:

the amount of mark up = 23% of 80

= [tex]\frac{23*80}{100}[/tex]

= 23 * 0.8 = $18.4

Answer:

Step-by-step explanation:

P = Q - 7.......Q is the quantity of baskets....and he makes 15 baskets....so sub in 15 for Q and solve for P, the price

P = 15 - 7

P = 8 <====

Answer:

D.$8

Step-by-step explanation:

Firstly, you replace Q with 15. Then you solve the equation.

P=15-7

P=8

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

By definition, if two lines are perpendicular then the product of their slopes is -1.

We have the following equation of the line:

[tex]y = 2x-5[/tex]

Then [tex]m_ {1} = 2[/tex]

We find [tex]m_ {2}:[/tex]

[tex]m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = \frac {-1} {2}\\m_ {2} = - \frac {1} {2}[/tex]

Thus, the perpendicular line will be of the form:

[tex]y = - \frac {1} {2} x + b[/tex]

We substitute the given point and find "b":

[tex]-2 = - \frac {1} {2} (8) + b[/tex]

[tex]-2 = -4 + b\\-2 + 4 = b\\b = 2[/tex]

Finally, the equation is of the form:

[tex]y = - \frac {1} {2} x + 2[/tex]

ANswer:

[tex]y = - \frac {1} {2} x + 2[/tex]

Answer:

9.

Step-by-step explanation:

It's given that A = 16. It shows that B = A-7, so that would mean B is 16-7, which is 9.

Answer:

The answer is 5 years ago.

Step-by-step explanation:

5 years ago the age of the mother was 5 times the daughter's age.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Suppose the current age of the daughter is D while the mother is M.

As per the given, The daughter is 36 years younger than her mother.

D = M - 36

And , M = 50

D = 50 - 36 = 14

Let's say x year age the mother was 5 times the daughter's age.

(M - x) = 5(D - x)

(50 - x) = 5(14 - x)

50 - x = 70 - 5x

-x + 5x = 70 - 50

4x = 20

x = 5

Hence "5 years ago the age of the mother was 5 times the daughter's age".

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Answer:

Question 1:

Draw a line that crosses the largest number of dots. Then use the line to check the best prediction of the number of baseballs that will be used if 275 pitches are thrown.

Question 2:

A). y = 1.2x - 6

Question 3:

J). y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

F). f(n) = -3n + 24 *Although it doesn't work when f(n) = 6 and n = 6*

Step-by-step explanation:

Question 2:

The line passes throught point (5, 0) and is parallel to the line whose equation is y = 1.2x + 3.8

For parallel lines, their values of slope is the same.

So our line, that passes through point (5, 0), also has a slope of 1.2

Taking another point (x, y) on our line;

Slope = change in y ÷ change in x

1.2 = [tex]\frac{y - 0}{x - 5}[/tex]

y = 1.2x - 1.2(5)

y = 1.2x - 6

Question 3:

The line passes x-axis at point (36, 0)

The line is perpendicular to another line whose equation is y = -[tex]\frac{4}{9}x[/tex] + 5

For perpendicular lines, the product of their slopes = -1

Let's say the slope of our unknown line is a ;

Given: The slope of our second line is -4/9

So,

a × -4/9 = -1

a = -1 × -9/4 = 9/4

Taking another point (x, y) on our unknown line;

Slope = change in y ÷ change in x

9/4 = [tex]\frac{y - 0}{x - 36}[/tex]

Cross-multiplying that you get;

y = [tex]\frac{9}{4}x - 81[/tex]

Question 4:

The function that model that situation is f(n) = -3n + 24 though it doesn't work when f(n) = 6 and n = 6

Answer:

x = 65

Step-by-step explanation:

The triangle has 2 congruent sides and is therefore isosceles.

The base angles are congruent, both 25°

Subtract the sum of the base angles from 180° for vertex angle

vertex angle = 180° - (25 + 25)° = 180° - 50° = 130°

Hence x = 130° ÷ 2 = 65

Answer:

Triangle ABC is dilated is dilated with a scale factor of ⅓ with the center of dilation at the point (3,4) resulting in triangle DEC

Step-by-step explanation:

From triangle ABC,

|AC|=3 units

From triangle DEC,

|EC|= 1 unit

Since the two triangles are similar, we can find the scale factor using the ratio of the image length over the corresponding object length.

[tex]scale \: factor = \frac{ |EC| }{ |AC| } [/tex]

Let us substitute the values to get:

[tex]scale \: factor = \frac{1}{3 } [/tex]

When we trace through AD and EB, they will meet at C. Hence C(3,4) is the center of dilation.

Answer:

$2,480

Step-by-step explanation:

Let $x be next year tuition. Aiden will pay $2,400, that is 75% of $x.

$x - 100%

$2,400 - 75%

Write a proportion:

[tex]\dfrac{x}{2,400}=\dfrac{100}{75}\\ \\75x=2,400\cdot 100\\ \\75x=240,000\\ \\x=3,200[/tex]

Next year’s tuition will be $720 more than this year’s, then this year tuition is

[tex]\$3,200-\$720=\$2,480[/tex]

Answer:

The answer should be C. 1 1/4

Step-by-step explanation:

Eliminate A and B because none of them work

Eliminate E because we are using 1/4s

Eliminate D because we aren't using decimals

You can also think of a clock with adding 1/4s: 0.75 + 1/4= 1

1 + 1/4 = 1 1/4

(you can divide 1/2 into 2 one fourths)

The answer is 1 1/4 option C.

What is the sum of 1/2 and 0.75?

Simply add these two terms i.e:

1/2 + 0.75

Write 0.75 as a 75/100 and take lcm and lcm is 100.

1/2 + 75/100

On solving we get,

= ( 50 + 75 )/100

= 125/100

= 5/4

= 1 1/4

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Answer:

The ordered pair is not a solution of the system of inequalities

Step-by-step explanation:

we know that

If a ordered pair is a solution of a system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

we have the system

[tex]x+5y < 16[/tex] ----> inequality A

[tex]x< 8[/tex] ----> inequality B

substitute the value of x and the value of y of the ordered pair in each inequality

ordered pair (6,2)

Verify inequality A

For x=6, y=2

[tex]6+5(2) < 16[/tex]

[tex]16 < 16[/tex] ----> is not true

so

The ordered pair not satisfy the inequality A

therefore

The ordered pair is not a solution of the system of inequalities

Final answer:

The quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Explanation:

To find the quotient when 4x^3 + 2x + 7 is divided by x + 3, we can use long division. Divide the first term, 4x^3, by x which gives 4x^2. Multiply x + 3 by 4x^2 to get 4x^3 + 12x^2. Subtract this from the original expression to get -10x^2 + 2x + 7. Then, divide -10x^2 by x which gives -10x. Multiply x + 3 by -10x to get -10x^2 - 30x. Subtract this from the previous result to get 32x + 7. Finally, divide 32x by x which gives 32. Multiply x + 3 by 32 to get 32x + 96. Subtract this from the previous result to get -89. Therefore, the quotient when 4x^3 + 2x + 7 is divided by x + 3 is 4x^2 - 10x + 32 with a remainder of -89.

Time taken by stone in air is 7 seconds and time taken by stone in water is 5 seconds

Solution:

Let "x" represents the time taken by stone in the air

Given that the stone's entire fall took 12 seconds

Thus, the total time taken by it in both air and water = 12 seconds

time taken by stone in the air = x

time taken by stone in water = 12 - x

In the air, it had an average speed of 16 m/s

average speed in air = 16 m/s

We know that,

distance = speed x time

distance covered by it in air = [tex]16 \times x = 16x[/tex]

distance covered in air = 16x

It had an average speed of 3 m/s before hitting the seabed

average speed in water = 3 m/s

distance covered by it in water = [tex]3 \times (12 - x) = 36 - 3x[/tex]

distance covered in water = 36 - 3x

Then,

Total distance covered = distance covered in air + distance covered in water

Total distance covered = 16x + 36 - 3x = 13x + 36

But, the total distance covered by it = 127 meters ( Given )

Therefore,

13x + 36 = 127

13x = 127 - 36

13x = 91

x = 7

Hence, the time taken by stone in air = x seconds = 7 seconds,

And, the time taken by it in water = 12 - x = 12 - 7 = 5 seconds