Can anyone please solve these two questions

Answer:

Total Money = $ 75.00

Step-by-step explanation:

Let X be the Total Money

Amount Spent for Shopping = 2/3 of X = 2X/3

Money Lost = 3/5 of (X -2X/3) = 3/5 of (3X-2X)/3 = 3X/15 = X/5

Balance in hand = $ 10.00

is X - 2X/3 - X/5 = $ 10.00

LCM of 3 and 5 = 15

ie (15X - 10X - 3X)/15 = $ 10.00

(15X - 10X - 3X) = 150.00

2X = $ 150.00

X = $ 150.00/2

X = $ 75.00

A variable is a place where values are kept. The number of students in Shawn's school with at least one sibling is 367.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A variable is a symbol and a stand-in for any mathematical object in mathematics. A variable can specifically denote a number, a vector, a matrix, a function, its argument, a set, or one of its elements.

Let the number of students be x, then

25/32 = x/470

simplifying the above equation, we get

25(470) = 32x

32x = 11750

Dividing both sides of the equation by 32, we get

32x / 32 = 11750 / 32

x = 367

The value of x = 367.

Therefore, at least one sibling is present among 367 kids at his school.

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Answer:

It would be b. and c. and d.

Step-by-step explanation:

The area of the circular shaded area is of 116.113 cm².

The area of a circle of radius r is given by pi multiplied by the radius squared, as follows:

A = πr²

For this problem, the shaded area is the area of the larger circle subtracted by the area of the smaller circle. We have that:

Hence the area of the larger circle is given by:

Al = π(6.5)² = 132.732 cm².

The area of the smaller circle is given by:

As = π(2.3)² = 16.619 cm².

Hence the shaded area is given by:

A = Al - As = 132.732 - 16.619 = 116.113.

The shaded area is of 116.113 cm².

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To ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

We are given that:

For 27 liters of petrol, we can drive a car for 95 km.

SO, by using the unitary method, we get that:

for 1 km of journey, the liters of petrol that we need is = 27 / 95 liters.

1 km = 27 / 95 liters

For 185 km, we get that:

185 km = 27 / 95 × 185 liters

185 km = 52.58 liters.

Therefore, to ensure that the car has enough petrol of a trip, we get that it should have 52.58 liters of petrol.

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Answer:

V = E - F + 2.

Step-by-step explanation:

V − E + F = 2

Add E to both sides

V + F = E + 2

Subtract F from both sides:

V = E - F + 2.

Answer:120 plus 80 plus 17 equals 217

Step-by-step explanation:

Answer:

Step-by-step explanation:

217

 In the equation of the given parabola the values of the vertex, focus and directrix are as follows:

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

  In this case we have an expression given by:

x = - 4y²

   We must find the canonical equation:

-4(y - 0)² = 1(x - 0)

(x - 0) = -4 (y - 0)²

has the form

(y - k)² = 4p(x - h)

  This means that the vertex of this parabola is

v = (h, k)

v = (0,0)

  To know the focus we must know the value of "p".

4p = -1/4

p = -1/16

f = (0, -1/16)

d = x = 1/16

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The slope is -A/B and y-intercept is C/B in the line (A/D)x + (B/D)y = C/D

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x.

We also refer to this tan as the line's slope

We know that the equation for slope(m) and y - intercept(c) of a line is given by :

y = mx + c

Here the equation is give as (A/D)x + (B/D)y = C/D, lets simply

⇒ (A/D)x + (B/D)y = C/D

⇒ B(y)/D = C/D -(A/D)x

⇒ [tex]\frac{B(y)}{D}[/tex] = [tex]\frac{C -A(x)}{D}[/tex]

⇒ B(y) = C - A(x)

⇒ y = [tex]\frac{C -A(x)}{B}[/tex]

⇒ y = [tex]\frac{ -A}{B}x + \frac{C }{B}[/tex]

Here, slope is -A/B and y-intercept is C/B

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Using the given information, the equation of the circle with center located at point (1 , -2) and passes through the point (0 , 1) is (x - 1)^2 + (y + 2)^2 = 10.

Using the distance formula, get the radius of the circle by solving for the distance between the center (1 , -2) and the point (0 , 1).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(0 - 1)^2 + (1 - -2)^2

radius= √1 + 9

radius = √10

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (1 , -2)

r = √10

(x - 1)^2 + (y - -2)^2 = (√10)^2

(x - 1)^2 + (y + 2)^2 = 10

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The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given [tex]$m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is [tex]m*2=-1[/tex]  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.[tex]m*-1=-1[/tex] i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. [tex]3=-1/2*3+b[/tex]  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

[tex]y=-x/2+9/2[/tex]

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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$34.52 is the function for the given number of minutes.

What is a formula for linear equations?

The function is

long- distance cell phone calling fee = Monthly service fee + Rate*Minutes used

long- distance cell phone calling fee = $4.52 + $0.12*250 = $34.52

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The expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

The correct answer options is option B and C

Algebra is a system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.

The expression to represent one of the sections = Quantity of decorative fence border ÷ Number of sections

= 12 ÷ 4

= 12 / 4

Therefore, the expressions which does not represent one of the section is 4 ÷ 12 and 4 × 12

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Answer:

(1,12)

Step-by-step explanation:

in a graph we know that 5 is equal to 10 so the answer is 1,12

The monthly payment for Jake borrowing $41,000 for 5 years at a 3% APR is $736.72.

Monthly payments are equal periodic payments made to offset an outstanding liability.

The monthly payments are the compounded principal (Principal + Compound Interest amount) divided by the number of periods.

The  monthly payments can be computed using an online finance calculator as follows:

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 3%

PV (Present Value) = $41,000

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $736.72

Sum of all periodic payments= $44,203.20

Total Interest = $3,203.20

Thus, Jake who borrowed $41,000 for 5 years at a 3% APR needs to make a monthly payment of $736.72 to settle the principal and the compounded interest.

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The solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is; $15

Let the cost of roses be x

Let the cost of carnations be y

Let the cost of Daisies be z

Thus, we have the three simultaneous equations as;

12x + 8y + 8z = 42   ------(1)

8x + 6y + 10z = 34.5   ------(2)

10x + 10y + 6z = 37.5    ------(3)

Using online simultaneous equation calculator gives us the values as;

x = 2; y = 1; z = 1.25

Thus, the solution of the system as an ordered triple (x, y, z) is; (2, 1, 1.25).

The cost of a bouquet of 12 daisies is;

Cost = 12 * 1.25 = $15

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Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

A ratio can be defined as the comparison of two numbers or elements indicating their sizes in relation to each other.

It also explains how many times a number contains another.

From the information given, we have;

To determine the distance Jupiter is from the sun than Neptune, we have to divide the distance for Jupiter by Neptune

= 7. 78 × 10^8/ 4. 5 × 10^9

= 0. 173

= 17. 3 × 10^ -2 kilometers

Thus, Jupiter is closer to the sun with 17. 3 × 10^ -2 kilometers

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Answer:4

Step-by-step explanation: 2x2 = 4 just as u said

The number of green and yellow balls is 24 and 36 respectively.

Given that,
Masha bought red, green, and yellow balloons for a party.
red balloons =  40 .
The number of green balloons Masha purchased = 3/5 of the red balloons.
The number of green balloons is again = 2/3 of yellow balloons.

Fraction is described as the number of compositions that comprise the Whole.

Here,
according to the question
Number of red ballons = 40
The number of green balloons Masha bought is 3/5 of the number of red balloons = 40 * 3/5
               = 8* 3
               = 24
The number of green balloons is also 2/3 of the number of yellow balloons.
= 3/2 * 24
= 36

Thus, the number of green and yellow balls is 24 and 36 respectively.

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The output is always an even integer for every input. Odd numbers end in the digits 1, 3, 5, 7 while even numbers conclude in the numerals 0, 2, 4, 6, 8.

Let us consider an input = number (n) × even number.

So, the output is definitely an even number.

The output is always an even integer for every input. Odd numbers end in the digits 1, 3, 5, 7 while even numbers conclude in the numerals 0, 2, 4, 6, 8. In this instance, we can multiply any x number by any even integer to obtain an even number.

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Answer: the circle is not a function

the square is a function

Step-by-step explanation:

The egg production in 2000 is predicted to be 64.6 billions eggs

y = mx + c

m = ( y2 - y1 ) / ( x2 - x1 )

m = (60.3 - 51.7 ) / ( 4 - 0 )

m = 8.6 / 4

m = 2.15

y - y1 = m ( x - x1 )

y - 51.7 = 2.15 ( x - 0 )

y - 51.7 = 2.15

y = 2.15x + 51.7

year 2000 is equivalent to x = 6

y = mx + c

plugging in x = 6 gives

y =  2.15 * 6 + 51.7

y = 64.6 billions eggs

The egg production in 2000 is predicted to be 64.6 billions eggs

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The diameter of a circle is defined as being twice the length of its radius.

If SU = 16.2 centimeters then the value of RT = 8.1 cm.

The diameter of a circle is defined as being twice the length of its radius. The radius of a circle is measured from the center to one of the circle's endpoints, whereas the diameter is measured from one end of the circle to another end of the circle, passing through the center.

In geometry, a circle's diameter is any straight line segment that passes through the center of the circle and has endpoints on the circle. It is also referred to as the circle's longest chord. Both definitions apply to a sphere's diameter.

The diameter is twice the radius because the greatest distance between two points on a circle must be a line segment through the center of the circle.

Here, SU is the diameter and RT is the radius.

Radius of the circle = 1/2 d

Where d = 16.2 then

substitute the value of d in the above equation, and we get

Radius of the circle  = 1/2 (16.2)

Radius of the circle = 8.1

Therefore, the value of RT = 8.1 cm.

The complete question is:

If SU = 16.2 centimeters, what is RT?

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The hypothesis is the phrase following the word if = " 2 x+6=10"

The conclusion is the phrase following the word then = " x=2"

A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.

Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).

The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.

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Answer:

greater for the data set 1.

The  triangle formed by joining three points on the graph is isosceles triangle

To find out the type we need to find the length of each side which can be found out with distance formula =√[tex](x2-x1)^{2}[/tex]+[tex](y2-y1)\^{2}[/tex] ) provided in the coordinate geometry

so, the length of side PQ of triangle PQR = √[tex](4-2)^{2}[/tex])+[tex](2-5) ^{2}[/tex])

   = √[tex]2^{2}[/tex] +[tex](-3)^{2}[/tex]

                          = √4+9

                           = √13 units

So, the length of side QR of triangle PQR =  √[tex](7-4)^{2}[/tex]+[tex](4-2)^{2}[/tex] )

   = √[tex]3^{2}[/tex] + [tex]2^{2}[/tex]

                          = √(9+4)

                           = √13 units

So, the length of side PR of triangle PQR = √([tex](7-2)^{2}[/tex]+[tex](4-5)^{2}[/tex] )

   = √([tex]5^{2}[/tex] + [tex](-1)^{2}[/tex] )

                          = √(25+1)

                           = √26 units

As the two sides of triangle are equal so this triangle formed by joining three points on the graph is isosceles triangle

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   The equation that defines the parabola with vertex at the origin and directrix at x = -5/2 is

x = y²/10

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v = (0, 0)

d = (-2.5, 0) them the focus is on the right so the parabola is of the form X = Y².

(y - 0)² = 4p(x - 0)

If the directrix is x = -5/2 then the focus will be:

f = (0 + p, 0)

0 + p = 2.5

p = 0 + 2.5

p= 2.5

(y - 0)² = 4*2.5(x - 0)

(Y)² = 10(X)

x = y²/10

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