Solve the simultaneous equations using an algebraic method.
x + 2y = 13
3x + y = 24

Answer:

-5y - 8.3xy

General Formulas and Concepts:

Pre-Algebra

Step-by-step explanation:

Step 1: Define

y(-5 - 8.3x)

Step 2: Expand

Answer:

26 becouse if you just add it together and then add the other as well and x mean 4

The slope of the parent function f(x) determines how steep the line is at any given point on the graph.

The slope is defined as the change in y divided by the change in x, or the rise over run. The parent function is a basic or fundamental function that is used as a starting point for creating more complex functions.

In general, the slope of the parent function is constant, meaning it does not change as x increases or decreases. However, the slope of any transformed function, or function that has been shifted or stretched, will be different.

Understanding the slope of the parent function is important in calculus and other mathematical applications, as it helps determine rates of change and other important variables.

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Answer:

needa pictureeeeeeee plss

Answer:

Php 210

Step-by-step explanation:

Basic pizza = Php 150

each additional slice of meat topping = Php 5

y = 150 + 5x

Where,

y = Total cost of pizza

x = number of additional meat topping

How much will the pizza cost if it has a dozen slices of meat

toppings?

A dozen slices of meat

toppings = 12 slices of meat

toppings

y = 150 + 5x

= 150 + 5(12)

= 150 + 60

= 210

y = Php 210

Using a linear function, it is found that the pizza will cost Php 210.

A linear equation has the following format:

\(y = mx + b\)

In which:

In this problem:

Then:

\(y = 5x + 150\)

The cost if it has a dozen slices of meat  toppings is y when x = 12, thus:

\(y = 5(12) + 150 = 210\)

The pizza will cost Php 210.

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Given,

5(2)+15v=00

where v is the number of vans.

Solving,

15v=90

v=6

Thus the correct answer is 6 vans are needed to transport students.

Answer:

C. 12

Step-by-step explanation:

16 divided by 4 is 4 which means 1/4 of 16 equals 4. If you want 3/4 of 16, you multiply 4 by 3 which is 12.

Answer: it would take 5 weeks

the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

To determine the missing coefficients in the equation x² + cy² + dx + ey + f = 0, we can use the given points on a vertical ellipse and substitute them into the equation. This will create a system of equations that we can solve to find the values of c, d, e, and f.

Let's substitute the given points into the equation:

For the point (3.75, 0):

(3.75)² + c(0)² + d(3.75) + e(0) + f = 0

14.06 + 3.75d + f = 0            -- Equation 1

For the point (0, 2.71):

(0)² + c(2.71)² + d(0) + e(2.71) + f = 0

7.35c + 2.71e + f = 0            -- Equation 2

For the point (1, -7):

(1)² + c(-7)² + d(1) + e(-7) + f = 0

1 + 49c + d - 7e + f = 0        -- Equation 3

For the point (-1, -5.725):

(-1)² + c(-5.725)² + d(-1) + e(-5.725) + f = 0

1 + 32.86c - d - 5.725e + f = 0 -- Equation 4

We now have a system of equations with four variables (c, d, e, f). By solving this system, we can find the missing coefficients.

Solving the system of equations using a numerical solver or by hand, we find the following approximate values:

c ≈ 0.5

d ≈ 0.7

e ≈ -1.6

f ≈ -9.9

Therefore, the missing coefficients are approximately c = 0.5, d = 0.7, e = -1.6, and f = -9.9.

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e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.

A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).

The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).

The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.

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Ms. Wamboldt ruler will not fit in the envelope .

In the question ,

it is given that

Ms. Wamboldt ruler length is = 30cm

the length of the envelope is = 26 cm

the width of the envelope is = 14 cm

to make the ruler fit into the envelope , we need to find the diagonal of the envelope first ,

since the side of the envelope form a right triangle ,

so by using Pythagoras theorem , we get

length² + width² = diagonal²

26² + 14² = diagonal²

diagonal² = 676 + 196

diagonal² = 872

diagonal = √872 = 29.52

since 29.52 < 30 , the ruler will not fit in the envelope .

Therefore , Ms. Wamboldt ruler will not fit in the envelope .

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Step-by-step explanation:

Total number of students taking Geometry

74 + 47 + 112 + 51 = 284

12th grade students taking Geometry = 51

Answer : 51/284 = 0.18

The solution to the equation 12 + 5x + 7 = 0 is x = -19/5.

To solve the equation 12 + 5x + 7 = 0, we can follow these steps:

Combine like terms:

12 + 5x + 7 = 0

19 + 5x = 0

Move the constant term to the other side of the equation by subtracting 19 from both sides:

19 + 5x - 19 = 0 - 19

5x = -19

Solve for x by dividing both sides of the equation by 5:

5x/5 = -19/5

x = -19/5

As a result, x = -19/5 is the answer to the equation 12 + 5x + 7 = 0.

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Answer: the answer is 0.51

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

N = 34

Step-by-step explanation:

METHOD I

(hit and trial)

The given two ratios have to be equal.

This means, 24 : N must break down to 12 : 17 after dividing it by some common factor.

The common factor here is 2.

Since,

12 × 2 = 24

17 × 2 = 34

\( \boxed{\mathsf{ \underline{N \: must \: be \: 34}}}\)

(after dividing the first ratio by 2(common factor) we get the second ratio. Meaning that they become equivalent as required by the question).

METHOD II

(mathematical approach)

Ratios can be written in form of fractions as:

\( \boxed{ \mathsf{ \frac{24}{N} = \frac{12}{17} }}\)

Cross multiplying:

\( \implies \mathsf{24 \times 17 = 12 \times N }\)

taking 12 to the denominator:

\( \implies \mathsf{ \frac{24 \times 17 }{12} = N }\)

24 and 12 gets canceled and 2 takes up their spot

(why?

=> 24 ÷ 12 = 2)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{2 \times 17 = N } \)

\( \implies \mathsf{ N = 34 } \)

\( \implies \mathsf{ N = 34} \)

Answer:

Step-by-step explanation:

This problem bothers on the mensuration of solids, cube

Step one:

The volume of the tanks will hold 60L of water

hence the volume of the tank is 60L

we know that the expression for the

volume of cube = L*L*L

Volume of cube = L^3

60= L^3

L=  √60

L= 7.7459

To the nearest 0.01m we have  L= 7.75 m

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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The vertex and range are (-2, -3) and y >= -3 respectively

The equation is given as:

y = |x +2| - 3

The above equation is an absolute value equation

An absolute value equation is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-2, -3)

Also, we have

a = 1

Since a is positive, then the vertex is a minimum

Hence, the vertex and range are (-2, -3) and y >= -3 respectively

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Answer:

It is a function because it doesn't have 2 inputs (do vertical line test)

Step-by-step explanation:

A function only has one input.

TIP: make sure no points connect. If they do, it's not a function.

Answer:

B

Step-by-step explanation:

A=1/2bh=1/2(8)(6)=24

4 × 24 = 96 sq cm

(x^2 + 43x + 10) - (-10x^2 - 5x + 10) = 11x^2 + 48x

Given polynomial (x^2 + 43x + 10) and (-10x^2 - 5x + 10)

We have to subtract the given polynomials.

Consider  (x^2 + 43x + 10) and (-10x^2 - 5x + 10)

Subtract (1) - (2) , we have,

(x^2 + 43 + 10) - (-10x^2 - 5x + 10)

x^2 + 43x + 10 + 10x^2 - 5x + 10

x^2 + 10x^2 + 48x + 5x + 10 - 10

Add similar elements : 43x + 5x = 48x

= x^2 + 10x^2 + 48x + 10 - 10

Add similar elements : x^2 + 10x^2 =  11x^2

= 11x^2 + 48x + 10 - 10

Solving , we get,

= 11x^2 + 48x

Thus, (x^2 + 43 + 10) - (-10x^2 - 5x + 10) = 11x^2 + 48x

Answer:

Exact Form:

11/6

Decimal Form:

1.83

Mixed Number Form:

1 5/6

Step-by-step explanation:

Convert the mixed numbers to improper fractions, then find the LCD and combine.

P(-1.32 < z < -0.45) is approximately 0.233. To find the probability P(-1.32 < z < -0.45) for a standard normal distribution, we need to use a standard normal distribution table or a statistical calculator.

Using a standard normal distribution table, we can look up the values for -1.32 and -0.45. The table provides the area under the curve to the left of a given z-value.

Looking up -1.32 in the table, we find the corresponding area to be 0.0934. Looking up -0.45, we find the corresponding area to be 0.3264.

To find the probability between -1.32 and -0.45, we subtract the area to the left of -0.45 from the area to the left of -1.32:

P(-1.32 < z < -0.45) = 0.3264 - 0.0934 = 0.233

Therefore, P(-1.32 < z < -0.45) is approximately 0.233.

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Answer:

Step-by-step explanation:

the first one your missing 3cm and the second one your missing 1cm.

Answer:

3. PR=51

4. FE=28

Step-by-step explanation:

3. since the two triangles are similar, set up a proportion:

x+8/3x-9=24/28

*cross multiply*:

28(x+8)=24(3x-9)

28x+224=72x-216

44x=440

x=20

to find PR:

PR=3x-9

PR=3(20)-9

PR=51

4. same here:

39/4x+2=42/5x-2

39(5x-2)=42(4x+2)

195x-78=168x+84

27x=162

x=6

to find FE:

FE=5x-2

FE=5(6)-2

FE=28

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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It will take 11 posts for the number of followers to be equal

They will have 255 folllowers each on the 11th post

Here, we want to get the number of posts that would make them both have the same number of followers

For the first person, her number of followers after n post will be;

For the second person, her number of follwers after n post will be;

Since we have that, after n posts, the number of followers will be equal; we simply go on to equate the two

Thus, we have this as;

So after 11 posts, the number of follwers they each have will be the same

Now, we want to calculate the number of followes they have at the 11th post

We just need to substitute for n in any of the equations

Thus, we have that, the number of followers is';