Mathematics High School

2x+2y
3x+3y

=5
=7

How many solutions does the system of equations above have?

Answers

Answer 1

The system of equations have one solution

How to determine the number of solutions?

The equations are given as:

2x + 2y = 5

3x + 3y = 7

The above equations are distinct linear equations.

This means that they would have one point of intersection, if plotted on a graph

Hence, the system of equations have one solution

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Related Questions

Which table represents a linear function?
X
X
y
1
1
1
2
2
1
2
3
4
34
O
122
1/7/2
O
y
1
121314
X
1
2
3
4
X
1
2
3
14
O
y
7
9
13
21
y
0
6
16
30

Answers

the third one

Step-by-step explanation:

The oblique prism below has an isosceles right triangle
base.
x
(x+2)
(x+3)
Mark this and return
53:21
What expression represents the volume of the prism, in
cubic units?
01/2+2²
028+22²
02 +2
O²+37²2²
Save and Exit
Submit
Next

Answers

The volume of the prism, in cubic units is V = 1/2*x³ + x²

The figure and options are in the figure attached

What is an Oblique Prism ?

An oblique prism is a polyhedron figure , with a rectangular base and triangular side faces .

It is given that

The oblique prism below has an isosceles right triangle base.

In the figure attached, the oblique prism is shown.

The volume of the prism is given by

V = b*h

h is the height and b is the Area of the base

It is given that the base is an isosceles right triangle, its area is:

Area of a Triangle = (1/2) base * height

here the base and height is x

b = 1/2*x²

The height of the prism is (x + 2).

Then, the volume is:

V = 1/2*x²*(x + 2)

V = 1/2*x³ + x² cu. units

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What is the height??

Answers

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, we have given

One isosceles triangle that means the given triangle having two sides equal. The dimensions of the triangle are 21cm, 21 cm and 16 cm.

Consider the given triangle as ABC . In ΔABC, AD acts as a median. It means Angle ADB = 90°

Therefore,

By using Pythagoras theorem,

It states that the sum of the squares of base and perpendicular height is equal to the square of the hypotenuse.

That is,

[tex]\bold{ ( Hypotenuse) ^{2} = (Perpendicular) ^{2} + (base) ^{2}}[/tex]

Subsitute the required values

[tex]\sf{ AC^{2} = AB^{2} + BC^{2}}[/tex]

[tex]\sf{ (21)^{2} = (h) ^{2} + (16)^{2}}[/tex]

[tex]\sf{ 441 = (h)^{2} + 256}[/tex]

[tex]\sf{ (h)^{2} = 441 - 256}[/tex]

[tex]\sf{ h^{2} = 185}[/tex]

[tex]\sf{ h = \sqrt{185}}[/tex]

[tex]\bold{ h = 13.6 \: cm}[/tex]

Hence, The required height of the given isosceles triangle is 13.6 cm.

[ Note :- you can also solve this problem by using Heron's Formula but it's too lengthy to solve that's why I have used simple method ]

Teri was 10 km race she has completed 74% of the way race when the winner crosses to finish there are approximately 2.48 miles in 4 km how many more miles does Terry need to run when the winner crosses the finish line answer to the nearest 10th

Answers

The distance Terry needs to run when the winner crosses the finish line is 1. 6 miles.

How to find the distance Terry needs to run?

The race was a 10 km race and she has completed 74% of the race when the winner crosses the finish line.

Therefore, the number of more miles Terry need to cover can be calculated as follows:

74 / 100 × 10 = 740 / 100 = 7.4 km

He has covered 7.4 km.

The distance remaining to cover = 10 km - 7.4 km = 2.6 km

Therefore,

4km = 2.48 miles

2.6 km = ?

cross multiply

The distance remaining to cover(miles) = 2.6 × 2.48 / 4

The distance remaining to cover(miles) = 6.448 / 4

The distance remaining to cover(miles) = 1.612

The distance remaining to cover(miles) = 1.6 miles

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Which are applications of mathematics in music? Select all that apply.

identifying measurements
calculating beats per minute
calculating the time signature
finding ratios of note frequencies
mapping marching band performances

Answers

Answer:

calculating beats per minute

1. Triangle STU is shown on the coordinate plane below. Triangle STU is transformed using the rule (x, y) -> (x+4, y-2). In the image of the transformation, triangle S'T'U', what is the x-coordinate of S'?

Answers

Using translation concepts, considering S(2,-1), the x-coordinate of S' is given by 6.

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, the rule is given by:

(x, y) -> (x+4, y-2).

Considering S(2,-1), 4 is added to the x-coordinate in the translation, hence:

2 + 4 = 6.

The x-coordinate of S' is given by 6.

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According to the box-and-whisker plot shown above, what are the following:

6. The median?

7. The first quartile?

8. The third quartile?

9. The minimum value?

10. The maximum value?

I need help i put the plot i need help 6 threw 10

Answers

Answer:

6. 80

7. 60

8. 100

9. 40

10. 110

Step-by-step explanation:

A box and whisker plot is a visual representation of the 5-number summary of a data set. The features of the plot are, left-to-right, the minimum, first quartile, median, third quartile, maximum.

You are being asked to identify the numerical value associated with each of these features.

The left whisker extends to the minimum of 40.

The left end of the box identifies the first quartile as 60.

The line in the middle of the box is the median, 80.

The right end of the box identifies the third quartile as 100.

The right whisker extends to the maximum of 110.

Additional comment

We hope you can rearrange the order of these numbers to suit the order in which the questions ask for them.

The original price of a hat is $35. The sale price is $19.95. What is the percent of discount?

Answers

Answer:

43%

Step-by-step explanation:

19.95 ÷ 35 = .57 or 57%

100 - 57 = 43

Sid has a water dispenser in his refrigerator as shown in the figure.
PLS HELP!

A prism has a length of 4 inches, height of 14 inches, and width of 8 inches.

Sid would like to have three water dispensers in his refrigerator. How much cubic space will all three dispensers take up in Sid’s refrigerator?

448 in.3

896 in.3

1,200 in.3

1,344 in.3

Answers

Answer:

c. I'm sorry if I'm wrong

Step-by-step explanation:

Write the equation for g(x)

Answers

The equation of the function, g(x) from the task content is; g(x) = -x/25 + 203/25.

What is the equation of the function g(x)?

From observation of the function, f(x), it follows that the slope of f(x) is 25. Hence, it follows that the slope of g(x) is; -1/25 since both functions are perpendicular to each other.

Therefore, the equation for g(x) is;

-1/25 = (y-8)/(x-3)

25y -200 = -x +3

Hence, y = -x/25 + 203/25.

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Mr Ellis invests £800 into an account that pays 3.4% compound interest per year how much will be in the account after two years

Answers

The amount after 2 years will be 855.3248

What is Interest?

Interest, in its most simple form, is calculated as a percent of the principal.

Given:

P= £800 , r= 3.4%, t= 2 year

For, compounded annually

=800*(0.034+1)²

=800* 1.034*1.034

=800* 1.069156

=855.3248

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K is an example of.
O an equation
O a formula
O a constant
O a variable

Answers

the answer is (a variable)

Answer:

a variable.

Step-by-step explanation:

I know this because I had a test today that I studied for but I of course failed it…

It was for math.

a negative number raised to an odd power is ____ negative ?

Answers

Answer:

always negative?

Step-by-step explanation:

-2^3=-8

Answer:

It is negative

Step-by-step explanation:

since you are multiplying the negative no. by itself an odd no. of times, your answer will be negative, b/c a negative no. multiplied an odd no. of times will be negative, and if it is multiplied an even no. of times it will be positive.

what type of function is this?

Answers

Answer:

It's a sech x function

Step-by-step explanation:

Explanation is in attached file

it is a sech x function

13) Circle O is shown with point A, B, C, and D on Circle O.

If x = 50, what is the value of y and the angle measurement of angle AOB?

y = _____

m
(25) (50) (100) (not enough information)

Answers

The value of y is 50

The angle measurement of angle AOB is 100°

Circle Geometry

From the question, we are to determine the value of y and the measure of angle AOB

From one the circle theorems, we have that

Angles in the same segment are equal

In the given diagram, x° and y° are angles in the same segment

∴ x° = y°

From the given information,

x = 50

∴ y = 50

Hence, the value of y is 50

Also, from another circle theorem,

Angle at the center is twice the angle at the circumference

∴ ∠AOB = 2x° = 2y°

Then,

∠AOB = 2×50°

∠AOB = 100°

Hence, the angle measurement of angle AOB is 100°

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For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form

Answers

Answer: 3

Step-by-step explanation:

The required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]

For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.

What is a complex number?

The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi

[tex]z = 5\sqrt{3}/4 - 5/4i[/tex]
the polar form complex numbner can be given as
[tex]z = rcos\theta +rsin\theta i[/tex] - - - - - -(1)
where r = [tex]\sqrt{a^2+b^2}[/tex]
and [tex]\theta=tan^-\frac{b}{a}[/tex]

Since a = 5√3/4 and b = -5/4
[tex]r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}[/tex]
r = 10/4
r = 5/2
Now,
[tex]\theta=tan^-\frac{b}{a}[/tex]
[tex]\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30[/tex]

Now the polar form is given by substituting the values of r and [tex]\theta[/tex] in equation 1
Here,
[tex]z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i[/tex]

Thus, the required polar form of the equation is [tex]Z = 5/2cos30 - 5/2sin30i.[/tex]

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A parabola opens upward. The parabola goes through the point (3, -1), and the vertex is at (2, -2). write the equation of the parabola

Answers

The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)

What is a Parabola ?

A parabola is a u shaped curve. It is a plane curve whose all points are at a fixed distance form a point called focus.

(x-h)² = 4a(y-k)

It is given that the parabola goes through the point (3, -1), and the vertex is at (2, -2).

Therefore
(x -2)² = 4a(y +2)

The parabola passes through the point (3,-1)

(3-2)² = 4*a(-1+2)

1 = 4 a

a = 1/4

The equation of the parabola is

(x-2)² = (y+2)

Therefore The value of a is 1/4 and the equation of the parabola is (x-2)² = (y+2)

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. Here is a table that shows the ratio of flour to water in an art paste. Complete the table with values in equivalent ratios.

Answers

You can’t see the table

make r the subject of the formula in V= ⅓π r²h

Answers

Answer:

switch the position

1/3πr²h=v

multiply all through by 3

3•1/3πr²h=3•v

3 will cancel out 3

πr²h=3v

divide both sides by πh

r²=3v/πh

root both sides

r=±√3v/πh

four students are trying to determine what number must replace the question (x^2)^7=x^4*x^8 in order to make it true
Joe said the answer is 6. Sam said it is impossible to answer.
Peter said the answer is 32. Alex said the answer is 16.
Who is correct? Explain why.

Answers

Let's solve ourselves instead of believing anyone

[tex]\\ \rm\Rrightarrow (x^2)^7=x^4x^8[/tex]

a^m+a^n=a^m+n

[tex]\\ \rm\Rrightarrow x^{14}=x^{4+8}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}=x^{12}[/tex]

[tex]\\ \rm\Rrightarrow x^{14}-x^{12}=0[/tex]

[tex]\\ \rm\Rrightarrow x^{12}(x^2-1)=0[/tex]

[tex]\\ \rm\Rrightarrow x^2-1=0[/tex]

[tex]\\ \rm\Rrightarrow x^2=1[/tex]

[tex]\\ \rm\Rrightarrow x=\pm 1[/tex]

0 is also a solution

Answer:

Joe is correct

Step-by-step explanation:

Given equation:

[tex](x^2)^?=x^4 \cdot x^8[/tex]

The exponent outside the bracket is a question mark and the students are trying to determine the value of the question mark.

For ease of answering, let y be the unknown number (question mark):

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

First, simplify the equation by applying exponent rules to either side of the equation:

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}\quad\textsf{to the left side}:[/tex]

[tex]\implies (x^2)^y=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c} \quad \textsf{to the right side}:[/tex]

[tex]\implies x^{2y}=x^4 \cdot x^8[/tex]

[tex]\implies x^{2y}=x^{4+8}[/tex]

[tex]\implies x^{2y}=x^{12}[/tex]

Now, apply the exponent rule:

[tex]x^{f(x)}=x^{g(x)} \implies f(x)=g(x)[/tex]

Therefore,

[tex]x^{2y}=x^{12}\implies 2y=12[/tex]

Finally, solve for y:

[tex]\implies 2y=12[/tex]

[tex]\implies 2y \div 2 = 12 \div 2[/tex]

[tex]\implies y=6[/tex]

Therefore, Joe is correct as the unknown number is 6.

answer this question asap

Answers

Answer:

the first option

Step-by-step explanation:

f(c)= 1/3p + 5/3

The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.

(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.

(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas

Answers

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be

How to calculate the values?

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:

= (1520 - 1232)/1232

= 288/1232

= 0.234

The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:

= (1448 - 1333)/1333

= 115/1333

= 0.086

The regional governing board that should receive the new board member is Salinas.

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50% if £80 pls helppp

Answers

Answer:

50%×€80

50/100×80

€40

Step-by-step explanation:

please mark me as brainlest

Answer:

£40

Step-by-step explanation:

▪︎ Method I:

£80 - 100%

£x - 50%

x = (£80 * 50%) / 100% = £40

▪︎ Method II:

50% is one half

Therefore, 50% of £80 is £80 / 2 = £40

This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes. cubes boxes number of cubes 1 n 5 625 8 1,000 what is the unknown value representing the unit rate? 8 125 140 156

Answers

The unknown value representing the unit rate is 125.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

This table represents the proportional relationship between the number of boxes and the number of magnetic cubes held by the boxes.

Cubes boxes number of cubes

1 5

n 625

8 1,000

If the unit cube box has 5 number of cubes.

then,

n cubes boxes = 625/5

= 125

The unknown value representing the unit rate is 125.

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Answer:

125

Step-by-step explanation:

What is the solution for x in the equation?
-2x+14+ 10x=34
OA. x = 6
OB. x = 5/2
OC. x = 1/8
OD. x = 2/5

Answers

Answer:

B. x = 5/2

Step-by-step explanation:

-2x+14+ 10x=34

-2x+10x=34-14

8x=20

x=20/8 =5/2

HELP MEE ,20 POINTS !!!!
Celina says that each of the following expressions is actually a binomial in disguise:
5abc-2a^2+6abc
5x^3∙2x^2-10x^4+3x^5+3x∙(-2) x^4
(t+2)^2-4t
5(a-1)-10(a-1)+100(a-1)
(2πr-πr^2 )r-(2πr-πr^2)∙2r

Answers

Celina says true that each of the following expressions is actually a binomial expression.

What is binomial?

The binomial is a polynomial of two-term only. For example, x + 5 where x and 5 are the two separate terms.

Celina says that each of the following expressions is actually a binomial in disguise:

a. 5abc - 2a² + 6abc = 11abc - 2a²