Mathematics High School

Can someone please help me?

Answers

Answer 1

Question 4:

2x + 3y = 17 -- equation 1

5x + 6y = 32 -- equation 2

(equation 1) * 2

4x + 6y = 34 -- equation 3

(equation 2) - (equation 3)

x = -2 -- equation 4

plug (equation 4)'s value of x into (equation 1)

2(-2) + 3y = 17

3y - 4 = 17

3y = 21

y = 7

Thus the answer is x = -2 and y = 7

Question 5:

The vertex form of a quadrilateral looks like this:

[tex]y = a(x-h)^2 + k[/tex]

a : coefficient of [tex]x^2\\[/tex](h,k): coordinate of the vertex.

The x-coordinate of the vertex is equal to '-b/2a'. Where b is the

coefficient of x, so:

[tex]h = -\frac{b}{2a} =-\frac{-8}{2*1} =4[/tex]

There is also another formula to find the y-value of the vertex

coordinate, but the easier way to find it is to plug it into the original

equation:

[tex]k=(4)^2-8(4) + 12= 16 -32 + 12 = -16 + 12 = -4[/tex]

Since we know now that h = 4 and k = -4 and that a = 1, lets plug it into

the original equation.

[tex]y = 1*(x-4)^2 - 4 =(x^2-4)-4[/tex]

Thus the answer is [tex]y = (x-4)^2 -4[/tex]

Hope that helps!

Related Questions

please help i am confused

Answers

Answer:

The last answer.

Step-by-step explanation:

Regular means all the side lenghts are the same and all the interior angle measures are the same. Think a stop sign.

Irregular polygons have different side lengths and different interior angle measures.

All interior angles and sides are congruent

Bobby has 58 of a pepperoni pizza in his refrigerator. He eats 14 of this for his lunch. Of the following, which is the best estimate of the fraction of the original pizza left after Bob's lunch?

Answers

Answer:

5/32

Step-by-step explanation:

A circular flower bed is 24m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters. Use 3.14 for pie (round to nearest 10th)

Answers

Answer:

163.3m²

Step-by-step explanation:

area = Pi(r²)

r = d / 2

r = 12

12² = 144

144 x 3.14 = 452.16

diameter of bigger circle = 24 + 4 (2 on each side)

28 / 2 = 14

14² = 196

196 x 3.14 = 615.44

sidewalk = bigger - smaller

sidewalk = 615.44 - 452.16

sidewalk = 163.3

The rectangle shown has a perimeter of 56 cm and the given area. Its length is 8 times more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle.

Answers

Answer:

Dimensions of rectangle = 23 cm x 5 cm

Step-by-step explanation:

Equations we can form

Perimeter of 56 cm

⇒ 2L + 2W = 56

⇒ L + W = 28

Length is 8 more than 3 times its width

⇒ L = 3W + 8

Substitute in previous equation

⇒ 3W + 8 + W = 28

⇒ 4W = 20

⇒ W = 5 cm

⇒ L = 28 - 5 = 23 cm

A farmer has some cows and horses. All the animals are either brown or black. The table shows how many of each
animal is on the farm.

one animal is selected randomly. what is the probability of chowing a horse given that they are brown? round answer to nearest hundredth.

Answers

Answer:

P = 1/5 = 0.20 = (20%)

Step-by-step explanation:

there are 12 horses and 8 cows, in total there are 20 animals

of which 4 horses are brown

Then

[tex]P=\frac{4}{20} =\frac{1}{5}[/tex]

Hope this helps

At what point does the line given by the following equation cross the y-axis? y = (6/9)X + 9

A. (9,0)
B. (0,6/9)
C. (0,9/6)
D. (0,9)

Answers

Answer:

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{6}{9}[/tex] x + 9 ← is in slope- intercept form

with y- intercept c = 9

then the line crosses the y- axis at (0, 9 )

Keiko drove 225 miles using 10 gallons of gas. At this rate, how many gallons of gas would she need to drive 441 miles?

Answers

Answer:

19.6 gallons

Step-by-step explanation:

divide 225 by 10 and you get 22.5 this means you are getting 22.5 miles per gallon so all you have to do is divide 441 by 22.5 and you get 19.6 so you are going to need 19.6 gallons to drive 441 miles

Find a linear equation with two variables that, together with the
equation 10x + 5y = 1, would comprise a system
with one solution

Answers

Answer:

y = x

Step-by-step explanation:

Any equation that describes a different line will be part of a system with exactly one solution. There are an infinite number of possible equations.

Perhaps one of the simplest is ...

y = x

_____

Together with the given equation, this has the solution ...

x = y = 1/15

You need to mark a fifth teen foot beam into five equal segments .how long is each segment ?

Answers

Answer: 3

Step-by-step:

15/5=3

Each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.

Since acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

To find out the length of each segment of a fifteen-foot beam divided into five equal parts, we have to divide the total length of the beam by the number of segments it is being divided into.

We can do this using the division operation as shown below:

15 ÷ 5 = 3

Therefore, we can conclude that each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

Janelle says that lines l and m are skew lines.

Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal.
Is Janelle correct?

Yes, because the lines are not parallel.
Yes, because the lines will intersect.
No, because the lines are in the same plane.
No, because the lines are perpendicular.

Answers

Answer:

C: No, beacause the lines are in the same plane.

Step-by-step explanation:

because skewed lines must lie in different planes.

just trust moi <3

The lines are in the same plane option third "No, because the lines are in the same plane" is correct.

What is a perpendicular line?

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines shown in the picture, line l, and line m.

As we know the skew lines are in different planes and do not intersect.

Thus, the lines are in the same plane option third "No, because the lines are in the same plane" is correct.

Learn more about the perpendicular line here:

brainly.com/question/18271653

#SPJ5

It’s a 4 digit number. The tens are double the ones. The thousands are double the tens. The sum of the digit is 19

URGENT

Answers

Now, the next step is adding all these values and dividing it by ten, since that's how many numbers there are for the data.

Jason's Team MAD: 2.4.

Hannah's Team MAD: 1.6.

Dion's Team MAD: 0.8

As you can see, Jason's Team has the greatest MAD, which is your answer.

Let me know if this is right! :)

Sam rode a bull for 8 seconds.
Maddie rode a bull for 2 fewer seconds than Sam did.
How long did Maddie ride her bull?

Answers

Answer:

is it 7?

Step-by-step explanation:

if he rode for 8 seconds and it says she rode for 2 seconds FEWER are you not subtracting from 8 to get 7?

put the equation below into vertex form.

y=(x+9)(x+25)

Answers

Answer:

Step-by-step explanation:

I need answers asap! | Some blocks are stacked as shown. The face of each block is a square and each block represents one cubic unit, what is the surface area of the figure formed by the blocks?
A. 30 square units
B. 28 square units
C. 24 square units
D. 21 square units

Answers

Answer:

Step-by-step explanation:

n 12. Find the volume of the sphere.

Answers

Answer:

2929 1/3 [tex]\pi[/tex] in^3

Step-by-step explanation:

The equation for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex].

Insert 13 for r. Then, simplify.

Writing linear functions
Use the graph or table to write a linear function that relates y to x

Answers

Step-by-step explanation:

3. Slope is postive

x1=6

x2=3

y1=10

y2=6

m=6-10/3-6

m=4/3

y=mx+b find b

10=4/3*3+b

10=4+b

b=6

y=4/3x+b

4.slope is zero

y=b

Y=3

What is the area of triangle rst? 6 square units 9 square units 12 square units 18 square units

Answers

The area of the considered triangle RST is given by: Option A: 9 sq. units.

How to find the area of a triangle?

If we have:

Length of its base = b unitsIts height = h units long,

Then we get:

Area of a triangle = [tex]\dfrac{b \times h}{2} \: \rm unit^2[/tex]

The missing image is attached below.

If we take the base of the triangle as RS, then as the line UT is perpendicular to RS (as RS is parallel to x axis and UT is parallel to y axis) and touching from the base line RS to T, thus, it can be taken as height.

Thus, we have:

Area of RST = half of length of RS (base) times length of UT (height)

As visible from image, we have:

Length of RS = 6 blocks of unit length = 6 units

Similarly, length of UT = 3 units

Thus, we get:

Area of RST = [tex]\dfrac{6 \times 3}{2} = 9 \: \rm unit^2[/tex]

Thus, the area of the considered triangle RST is given by: Option A: 9 sq. units.

Learn more about area of a triangle here:

https://brainly.com/question/14503701

evaluate 6+4/a + b/3 when a=4 and b=3

Answers

Answer: 31/4 or 7.75

Step-by-step explanation:

it’s the coordinate plan

Solve the equation 3x = 9 Show and justify each step you take to solve the equation

Answers

Hello!

This is a one-step equation, meaning that we can solve it in just 1 step.

This is the step:

Divide both sides by 3

3x=9

x=3

That's the answer; we can easily check it:

3*3=9

Hope everything is clear.

Let me know if you have any questions!

Always Remember: Knowledge Is Power!

Solve the equation for x

Answers

Answer:

5x-18=4x+7 ( vertical opposite angle)

5x-4x=7+18

x=25

If sin(0)=24/26 what are the other two trigonomic ratios

Answers

Answer:

[tex]\begin{aligned}{&\cos \theta=\frac{10}{26} \\\bf{&\tan \theta=\frac{24}{10}}\end{aligned}[/tex]

Step-by-step explanation:

Since the angle is in the first quadrant, the values of all trigonometric functions are positive. Also. the formulas for the trigonometric functions we need to find from the problem are shown below:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\\tan \theta &=\frac{y}{x}\end{aligned}[/tex]

Based on the formulas listed, the value of y and r are y = 24 and r = 26 respectively. This means that in order to determine the value of the other functions, we need In compute for the value of x using the Pythagorean Theorem:

[tex]\begin{aligned}r^{2} &=x^{2}+y^{2} \\r^{2}-y^{2} &=x^{2}+y^{2}-y^{2} \quad\left[\text { \text{Subtracting \ both \ sides \ of \ the \ equation\ by} } y^{2}\right] \\r^{2}-y^{2} &=x^{2} \\\sqrt{r^{2}-y^{2}} &=\sqrt{x^{2}} \\\sqrt{r^{2}-y^{2}} &=x \\\sqrt{26^{2}-24^{2}} &=x \\10 &=x\end{aligned}[/tex]Then, substituting this to the formula to determine the answers yields:

[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\&=\frac{10}{26} \\\tan \theta &=\frac{y}{x} \\&=\frac{24}{10}\end{aligned}[/tex]

Therefore, the answers are:

[tex]\begin{aligned}&\cos \theta=\frac{10}{26} \\&\tan \theta=\frac{24}{10}\end{aligned}[/tex]

Answer:

See below

Step-by-step explanation:

We are here given that ,

[tex]\longrightarrow \sin\theta =\dfrac{24}{26}[/tex]

And we would like to find out other trigonometric ratios ( since it is not mentioned about which two I will find out all 6 ) . As we know that ,

[tex]\longrightarrow \sin\theta =\dfrac{perpendicular}{hypotenuse} =\dfrac{p}{h}[/tex]

So that ,

[tex]\longrightarrow \dfrac{p}{h} =\dfrac{24}{26}[/tex]

Let us assume the given ratio to be 24x : 26x .

So we can say that ,

hypotenuse = 26xperpendicular = 24x

Now let's find out the value of base , so that we can find out the other ratios .

By Pythagoras Theorem ,

[tex]\longrightarrow (perpendicular) ^2+(base)^2=(hypotenuse) ^2[/tex]

Substitute the respective values ,

[tex]\longrightarrow (26x)^2=(24x)^2+b^2\\[/tex]

[tex]\longrightarrow 676x^2 = 576x^2+b^2\\ [/tex]

[tex]\longrightarrow b^2=100x^2\\[/tex]

[tex]\longrightarrow b =\sqrt{100x^2}\\[/tex]

[tex]\longrightarrow \boldsymbol{ b = 10x } [/tex]

Now we may find the other ratios as ,

[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{10x}{26x}=\boxed{\boldsymbol{\dfrac{5}{13}}}\\[/tex]

[tex]\longrightarrow \tan\theta =\dfrac{perpendicular}{base}=\dfrac{24x}{10x}=\boxed{\boldsymbol{\dfrac{12}{5}}}\\[/tex]

[tex]\longrightarrow \cosec\theta =\dfrac{hypotenuse}{perpendicular}=\dfrac{26x}{24x}=\boxed{\boldsymbol{\dfrac{13}{12}}}\\ [/tex]

[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{26x}{10x}=\boxed{\boldsymbol{\dfrac{13}{5}}} \\[/tex]

[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{10x}{24x}=\boxed{\boldsymbol{\dfrac{5}{12}}} [/tex]

And we are done !

consider the equation 21= m +14 1/6 which which step will help to solve this equation

Answers

Answer:

m = 41/6

Step-by-step explanation:

21 = m + 14 1/6

Convert everything into improper fractions with a denominator of 6.

21 = m + 14 1/6126/6 = 6m/6 + 85/6126 = 6m + 856m = 126 - 856m = 41m = 41/6

Ariana started a savings account with $240. She deposits $30 into her account at the end of each month. She wants to know how many months it will take for her account to have a balance greater than $500.

Answers

Answer:

9 months

Step-by-step explanation:

$500 - $240 = $260

$260/$30 = 8.67(3s.f.) ≈ 9 months

Recheck:

Balance after 9 months = 240 + (30×9) = 240 + 270 = $510

∴ $510 > $500

which of the following statements is true?

Answers

Answer:

D. In an axiomatic system, every statement, either its capable of being proven true or false.

Step-by-step explanation:

I'm sure.

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