given: line 1 passes through (-3, -7) and (5,3)
Line 2 passes through (-4, -2) and is perpendicular to line 1

the equation representing amount paid by Peggy and Daniel for songs is

the cost per download for members and for non-members

from the question the following information can deduced

Daniel is not a member of the club and downloaded 85 at rate of $0.35

total amount paid by Daniel

= 85 * 0.35

= 29.75

Peggy is a member and downloaded 105 songs at a rate of $x

Total amount paid by Peggy

= 105 * $x

= 105x

equating both amounts

105x = 29.75

cost of downloading a song for members, x0.28

105x = 29.75

x = 29.5 / 105

x = 0.28

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(98 × 100) ÷ 70

= 140%

or

[(98 - 70) × 100] ÷ 70

2800 ÷ 70

40%

basically, 40% increase

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

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

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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Answer:

No

Step-by-step explanation:

Total money = €150

1 pair of sunglasses = €70

3 pairs of shorts = €15 × 3 = €45

then, Total = €70 + €45 + x

€150 = €115 + x

x = €150 - €115

x = €35

Which means Eddie got only €35 left on him which is not enough for him to buy the trainers

The required positive number whose product is 25 and whose sum is minimum is 5, 5

Sum of two numbers means adding two same or different number together

Let two positive numbers xy = 25

Divide both side by x

y  = [tex]\frac{25}{x}[/tex]  ----------Equation (1)

Sum of two positive numbers s = x + y  -------Equation (2)

Substitute equation (1) into equation (2)

S = x + [tex]\frac{25}{x}[/tex]

differentiate with respect to x

[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]

[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex]  ---------- Equation (3)

[tex]\frac{ds}{dx} = 0[/tex]

[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0  ⇒ [tex]x^{2}[/tex] = 25

x = 5

Differentiate equation (3) again

[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]

hence, at point x = 5,   [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex]  [tex]= \frac{50}{25} = 2[/tex]

Value of s minimum at point x = 5.

substitute the value of x into equation (1)

[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]

Therefore the required positive numbers are 5, 5.

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Answer:

A and C

Step-by-step explanation:

For every x value, there should be at most 1 y value.

B and D violate that constraint.

Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

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Solution

From given equation

Slope = -2

and y-intercept is (0,0)

Therefore,

if we put x= 0

then y = -2*0 = 0

if we put x = 1

then y = -2*1 = -2

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Answer:

expanded: x^2+8x+15

Step-by-step explanation:

(x+3)(x+5)

x^2+5x+3x+15

Answer:

5

Step-by-step explanation:

Distribute 1st

-3 x 8 +232 /8

Multiply -3 and 8

-24 +232 /8

Divide 232 and 8

-24+29

Add -24 and 29

5

Answer:

Let the age of brother be x and that of a sister be y.

(x+y) =16

(x) ×(y) =63

Using the substitution method, x=16-y

Substitute in equation 2

(16-y)(y)=63

16y-y^2=63

Y^2-16y+63=0

P=63

Sum= -16

Factor=(y-7),(y-9)

(y-7)(y-9)=0

Therefore y=7 or y=9

Therefore age of brother = 16-7 =9 0r 16-9=7

Therefore their ages are 9 years and 7 years

Answer:

x = 9

Step-by-step explanation:

According to the question,

Perimeter of an isosceles triangle = 37

Length of the base = x

Length of one leg = 4x - 4

As it is an isosceles triangle so length of the other leg will also be 4x - 4.

Perimeter of triangle is equal to sum of all the lengths of the triangle.

[tex] \therefore [/tex]

[tex] \rm \implies Length \: of \: base + Length \: of \: one \: leg + Length \: of \: other \: leg = 37

\\ \\ \rm \implies x + 4x - 4 + 4x - 4 = 37

\\ \\ \rm \implies 9x - 8 = 37 \\ \\ \rm \implies 9x = 37 + 8 \\ \\ \rm \implies 9x = 45 \\ \\ \rm \implies x = \frac{45}{9} \\ \\ \rm \implies x = 5

[/tex]

Answer:45

Step-by-step explanation:

75*3/5

Answer:

f(f(x)) = [tex]x^{4}[/tex] + 2x² + 2

Step-by-step explanation:

to evaluate f(f(x)), substitute x = f(x) into f(x)

f(f(x))

= f(x² + 1)

= (x² + 1)² + 1 ← expand factor using FOIL

= [tex]x^{4}[/tex] + 2x² + 1 + 1

= [tex]x^{4}[/tex] + 2x² + 2

Answer:

[tex]f[f(x)]=x^4+2x^2+2[/tex]

Step-by-step explanation:

Given function:

[tex]f(x)=x^2+1[/tex]

To find the composite function f[f(x)], substitute the function f(x) in place of the x in function f(x):

[tex]\begin{aligned}\implies f[f(x)]&=f(x^2+1)\\&=(x^2+1)^2+1\\&=(x^2+1)(x^2+1)+1\\&=x^4+x^2+x^2+1+1\\&=x^4+2x^2+2\end{aligned}[/tex]

Answer:

Completely satisfied with their car:  60.00%

Step-by-step explanation:

I'll assume that "180 percent of people not satisfied . ." is meant to read "180 people not satisfied . . ."

Add the people in the groups to find a total.  Then divide the numeber of people in each group by the total.  This will provide a decimal number which can be multiplies by 100% to give the breakdown requested.

   Group              Count   Percent(%)

Not S.                      180        7.20

Somewhat S.          820      32.80

Completely S.       1500       60.00

Total People:       2500      100.00%

The linear function with f values f(0) = -3 and f(7) = 11 is f(x) = 2x - 3

linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line. In case, if the function contains more variables, then the variables should be constant, or it might be the known variables for the function to remain it in the same linear function condition.

if f(0) = -3, it means at x = 0, f(x) = -3

and if f(7) = 11, it means at x = 7, f(x) = 11

So the Linear equation that will yield these results is f(x) = 2x - 3

In conclusion, the Linear function is f(x) = 2x - 3

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Step-by-step explanation:

x/y = y/z = z/x

x = y²/z = zy/x and y = z²/x

x = y²/z

putting this into the 3rd part of the original equation :

z/x = z/ y²/z = z²/y²

now using the y identity of the second part there :

y = z²/x

z²/y² = z² / z⁴/x² = x²/z² (= z/x per previous equation)

so,

x²/z² = z/x

x³/z³ = 1

x/z = 1

x = z

then

y/z = y/x = z/x (= 1)

and therefore,

y/x = z/x meaning

y = z (and therefore = x)

so,

x = y = z

Veremos que originalmente tenias $300, y el valor de la compra fue de $90

Definamos X como la cantidad original de dinero. Ahora trabajaremos con porcentajes.

Sabemos que tu gastaste 30% de esto, entonces lo que te sobra es:

0.7*X

Sabemso qe si hubieras gastado el 40% (en este caso te sobra 0.6*X), te sobrarian 30 dolares menos, entonces podemos escribir:

0.7*X = 0.6*X + $30

Resolviendo para X

0.7*X - 0.6*X = $30

0.1*X = $30

X = $30/0.1 = $300

Originalmente tenias $300 dolares, y gastaste:

$300*0.3 = $90

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The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.

Equivalent ratios can be described as ratios that have the same values when compared to each other. For example, 8/16, 4/8 and 1/2 re equivalent ratios because:

8/16 = 1/2

4/8 = 1/2

Therefore, 8:16 = 4:8 = 1:2.

Given the table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, the ratio is: 3:4.

This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.

Therefore:

6/8 = 3/4

9/12 = 3/4

6/8 = 9/12 = 3/4

This implies that 6:8, 9:12 and 3:4 are all equivalent ratios.

Therefore, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.

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Answer:

your answer is 16

Step-by-step explanation:

So, to solve (1 + 3)²

first add 1 and 3

then you will get 4

and your equation would be (4)²

then you just square 4.

(4)² > 4x4 = 16

hope this helps (can you mark as brainiest pls)

By using the concept of translation, it can be inferred that

The graph of the equation is translated 3 units to the left and 4 units down

What is translation?

Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.

The given equation is

[tex]y = (x +3)^2 + 4[/tex]

This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.

So the first option is correct.

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The probability of the value of  (0.21) distribution using the normal distribution table is: 0.3166

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

In the question, we have

Probability of (0.21 < z <1.28)

= P(z < 1.28) - P(z < 0.21)

Probability of value for z

= 1.28 using z table is 0.8997

=> P(z < 1.28)

= 0.8997

probability of value for z = 0.21

Now, find the value of the probability using the normal distribution table:

using the z table of 0.21; we get:

The value of z is: 0.5832

=> P(z < 0.21) = 0.5832;

The value of  Probability of (0.21 < z <1.28)

= Probability of (z < 1.28) - Probability of (z < 0.21)

= 0.8997 - 0.5832

= 0.3165

~ 0.3166

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Answer:

$53.8.

Step-by-step explanation:

10% of $538 is like saying 538 times .10. After you multiply, you get $53.8 as the fee that Monica had to pay.

Answer:

400 minutes

Step-by-step explanation:

25 % *4 =100 %

100*4=400 minutes

The correct option is A) There is a x-intercept at (0, -2).

What is x-intercept and y-intercept ?

   The graph's intercept is the location where the line or curve crosses the axis. The term "x-intercept" refers to a point that crosses the x-axis. The y-intercept is the location where a point crosses the y-axis. The x- or y-axis intersection point is what is meant by an intercept for a line. Typically, the y-axis is taken into account if the axis is not stated. It is typically represented by the letter "b."

The y-axis will always be crossed by that line, even if it is far from the top or bottom of the chart, because it is precisely vertical.

The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.

Here in the given graph x axis crossed the line at (-2,0) and y axis crossed the line at ( 0 ,-3) .

Hence the correct option is A) There is a x-intercept at (0, -2).

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Proportionality denotes a linear relationship between two quantities or variables.

A.  Table is mentioned below.

B. Yes, it is a proportional relation.

C. y = 1/24 x

Therefore,

Part C : We know that,

1 day = 24 hours,

⇒ 1 hour = 1/24 day

As a result, the number of days in x hours (say y) = hours number of days in each hour

⇒ y = 1/24 x

Which is an equation of line.

Part A :

Hours       1              2           3           4          5      

Days       1/24       1/12        1/8         1/6       5/24

Part B :

∵ a line passes through the origin always shows a proportional relation,

Since, for (0, 0),

0 = 1/24 (0) ( True )

i.e. there is a proportional relation between number of days and number of hours.

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Answer:

Can't be solved

Step-by-step explanation:

Using Pythagoras theorem,

H2= O2 + A2 (where, H= Hypotenuse,O=Opposite,A=Adjacent)

The hypotenuse,H=7feet long

If the opposite side of the triangle is 4 feet longer than the adjacent side, then;

O=A+4

while, A=A

,then using H^2= O^2 + A^2(The 2 are power,that is square)

7^2 = (A+4)^2 + A^2

49= (A+4)(A+4) + A^2

49=A^2 +4A+4A+16 + A^2

49=A^2+8A+16+A^2

(collect like terms)

49-16=A^2+A^2+8A

33=2A^2+8A

Then a quadratic equation,

2A^2+8A=33

2A^2+8A-33=0,

using (-b+/-√4ac) /2a

where b=8, a=2, c=-33

[-8 +/-√4*2*(-33) ]/2(2)

-8 +/-

The algebra properties associated to each case are listed below:

Case 1: Distributive property

Case 3: Associative property (multiplication)

Case 5: Existence of inverse (addition)

In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:

Now we proceed to determine the property associated to corresponding operation:

Case 1

9 · (x + y) = 9 · x + 9 · y → Distributive property

Case 3

[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)

Case 5

(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)

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The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.

A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.

The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;

d² = (x₂ - x₁)² + (y₂ - y₁)²

The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;

[tex]\overline{AB}^2[/tex] = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2

[tex]\overline{AC}^2[/tex] = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2

[tex]\overline{BC}^2[/tex] = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)

72 + 32 = 104

Therefore; [tex]\overline{AB}^2[/tex] + [tex]\overline{AC}^2[/tex] = [tex]\overline{BC}^2[/tex]

ΔABC is a right triangle

The slopes of the equation of the lines of the sides of the triangle are;

Slope of side AB = (5 - (-1))/(6 - 0) = 1

Slope of side BC = (3 - 5)/(-4 - 6) = 0.2

Slope of side AC = (3 - (-1))/(-4 - 0) = -1

Therefore;

[tex]\overline{AB}[/tex] ⊥ [tex]\overline{AC}[/tex]

Which gives;

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The perimeter of the composite figure would be = 21 (to the nearest tenth).

Perimeter is defined as the quantity that is used to evaluate the total length of the sides of an object.

From the given diagram, the composite figure is made up of 6 sides. The addition of these sides is the figures perimeter.

The sides of the composite figure are:

a = 6; b = 12; c = 9; d = 9; e = -9; f = -6.

The perimeter = a + b + c + d + e + f.

= 6 + 12 + 9 +9+ (-9) + (-6)

= 27 - 6

= 21 ( to the nearest tenth)

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