Translating Inequalities into Words
Which phrases can be used to represent the inequality? Check all that apply.
One-half + k greater-than 18

The equation to calculate the coordinates of point B is (b) 3 = √(x - 4)²+(y - 2)²

The given parameters are:

A = (4,2)
AB = 3

The distance formula is:

AB = √(x - x1)²+(y - y1)²

So, we have:

3 = √(x - 4)²+(y - 2)²

Hence, the equation to calculate the coordinates of point B is (b) 3 = √(x - 4)²+(y - 2)²

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Answer:

18:12 = A. 3:2

Step-by-step explanation:

Because they are equivalent ratios, they are the same, it also said ratio of strawberries to cherries so I put it in that order.

Can I please have branliest

okay thank you have a good day

Taking into account the definition of a system of linear equations:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The cost of 3 rackets and 2 squash balls is £26.57.

The cost of 5 rackets and 7 squash balls is £52.90.

So, the system of equations to be solved is

[tex]\left \{ {{2x+3y=26.57} \atop {7x+5y=52.90}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable x from the first equation:

[tex]x=\frac{26.57 - 3y}{2}[/tex]

Substituting the expression in the second you get:

[tex]7\frac{26.57 - 3y}{2}+5y=52.90[/tex]

Solving:

[tex]\frac{7}{2}(26.57 - 3y)+5y=52.90[/tex]

[tex]\frac{7}{2}x26.57 - \frac{7}{2}x3y+5y=52.90[/tex]

92.995 - 10.5y +5y= 52.90

92.995 - 5.5y= 52.90

- 5.5y= 52.90 -92.995

- 5.5y= -40.095

y= (-40.095)÷ (-5.5)

y= 7.29

So: [tex]x=\frac{26.57 - 3y}{2}=\frac{26.57 - 3x7.29}{2}[/tex]

x= 2.35

Finally, the cost of a squash ball and a racket are £2.35 and £7.29 respectively.

In this case, a system of linear equations must be proposed taking into account that:

The cost of 4 kg of radishes and 1.5 kg of carrots is £14.80.

The cost of 3 kg of radishes and 2 kg of carrots is £12.50.

So, the system of equations to be solved is

[tex]\left \{ {{4x+1.5y=14.80} \atop {3x+2y=12.50}} \right.[/tex]

You can solve this system using the substitution method. Isolating the variable x from the first equation:

[tex]x=\frac{14.80 - 1.5y}{4}[/tex]

Substituting the expression in the second you get:

[tex]3\frac{14.80 - 1.5y}{4}+2y=12.50[/tex]

Solving:

[tex]\frac{3}{4}(14.80 - 1.5y)+2y=12.50[/tex]

[tex]\frac{3}{4}x14.80 - \frac{3}{4}x1.5y+2y=12.50[/tex]

11.1 - 1.125y +2y= 12.50

- 1.125y +2y= 12.50 - 11.1

0.875y=  1.4

y= 1.4 ÷0.875

y=1.6

So: [tex]x=\frac{14.80 - 1.5y}{4}=\frac{14.80 - 1.5x1.6}{4}[/tex]

x= 3.1

Finally, the cost of 1 kg of radishes and 1 kg of carrots are £3.1 and £1.6 respectively.

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Given

[tex] \text{Base = 4} \\ \text{Perpendicular= 8}[/tex]

To Find

Hypotenuse of the triangle.

Assuming,

[tex] \text{Perpendicular = ‘a’}[/tex]

[tex] \text{Base = ‘b’}[/tex]

[tex] \text{Hypotenuse= ‘c’}[/tex]

[tex] \text{(c)² = (a)² + (b)²} \\ \\ \implies \text{ (c)² = (8)² + (4)²} \\ \\ \implies \text{(c)}^{2} = 64 + 16 \\ \\ \implies \text{(c)}^{2} = 80 \\ \\ \implies \text{(c)} = \sqrt{80} \\ \\ \implies\text{(c)} = 8.94[/tex]

[tex]\text{Rounding it to the nearest tenth = 8.9}[/tex]

[tex]\therefore \text{Hypotenuse of the triangle = 8.9}[/tex]

Option D= 8.9 units is the correct answer

Answer:

The surface area of the regular triangular pyramid is 108 square centimetres.

Step-by-step explanation:

What is a regular triangular pyramid?

A triangular pyramid is a three-dimensional shape that has a triangular base and three triangular faces.

The lateral surface area is the area of all the sides of a 3-dimensional object excluding its base and top.

The surface area of a triangular pyramid is the sum of the areas of the four faces of the pyramid.

What is the surface area?

The area of one face = lateral surface area / 3

81 / 3 = 27

The surface area = 27 x 4 = 108

Answer:

  24

Step-by-step explanation:

Jayla has a couple of options for cutting her original piece of paper.

The greatest number of 3×2 pieces Jayla can cut is 24.

__

The attachments show the different cuts as described above.

if the ordered pair (x,y) is (-3, 4), then the othre ordered pair would (0,0)

Then, you find the slope(m).

So, m = y2 - y1

x2 - x1

if y2 is 4 and y1 is 0

x2 is -3 and y1 is 0

now you subtract to get -4

3

So, m= -4

3

Then, find the y-intercept

So, y=mx+b and substitute the ordered pair (0,0) into y= mx+b

y=mx+ b

0= -4(0) +b

3

0=0+b

-0 -0

b=0

So the equation is y= -4x

3

Answer:

Consider the following statements, Each box of 100 pads of an orange-u happy costs$5 to manufacturer. The variable costs for manufacturing q boxes at 100 pads will be V=5.4

Step-by-step explanation:

The increasing order of the complex numbers is (√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ =  (-1 + √3i)¹² < (√3 - √3i)⁴.

The absolute values of the complex numbers are determined as follows;

(sqrt3-sqrt3i)^4 = (√3 - √3i)⁴

[tex]|z| = \sqrt{(\sqrt{3} )^2 + (\sqrt{3 }\times1 )^2} } \\\\|z| = \sqrt{6}[/tex]

(-1+sqrt3i)^12 = (-1 + √3i)¹²

[tex]|z| = \sqrt{(-1)^2 + (\sqrt{3)^2} } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]

(sqrt 3-i)^6 = (√3 - i)⁶

[tex]|z| = \sqrt{(\sqrt{3})^2 + (-1)^2 } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]

(sqrt2-sqrt2i)^8 = (√2 - √2i)⁸

[tex]|z| = \sqrt{(\sqrt{2} )^2 + (\sqrt{2})^2 } \\\\|z| = 2[/tex]

(sqrt2-i)^6 = (√2 - i)⁶

[tex]|z| = \sqrt{(\sqrt{2})^2 + (-1)^2} } \\\\|z| = \sqrt{3}[/tex]

Increasing order of the complex numbers;

(√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ =  (-1 + √3i)¹² < (√3 - √3i)⁴.

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Answer:

see screenshot below

Step-by-step explanation:

correct on edmentum

Answer:

[tex]x = \dfrac 32, ~ x = -4[/tex]

Step by step explanation:

[tex]~~~~~~~2x^2+5x-12=0\\\\\implies 2x^2 +8x-3x-12=0\\\\\implies 2x(x+4) -3(x+4) = 0\\\\\implies (2x-3)(x+4) = 0\\\\\implies 2x -3 = 0~~~~ \text{or}~~~~~~~~ x +4 = 0\\\\\implies 2x = 3~~~~~~~~~ \text{or}~~~~~~~~x = - 4\\\\\implies x = \dfrac 32~~~~~~~~~~ \text{or}~~~~~~~~x = - 4\\\\\text{Hence,}~ x = \dfrac 32, ~ x = -4[/tex]

Answer:

C

Step-by-step explanation:

If the graph of a relationship is a line or a ray through the origin, then it is proportional.

The line in graph C goes through the origin (0,0)

Answer:

8%

Step-by-step explanation:

Add 2 and 23 together to get 25.

Divide 2 by 25 to get 0.08.

Covert 0.08 into percentage: 8%

Answer:

y=2x+4

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = negative 6 (x minus one-fourth) squared + nineteen-eighths

Step-by-step explanation:

y = –6x^2 + 3x + 2

Divide the first 2 terms of the right side by -6:

y = -6(x^2 - 1/2x) + 2

Now complete the square on the expression in the brackets:

y = -6[(x - 1/4)^2 - 1/16] + 2

y = -6(x - 1/4)^2 + 6/16 + 2

y = -6(x - 1/4)^2 + 38/16

y = -6(x - 1/4)^2 + 19/8

Answer: C

Step-by-step explanation:

Answer: y=0.2

Step-by-step explanation:

y∝(1/x)

this implies that

y=k/x    eq(*)

when y =0.25 when x =4

0.25=k/4

k=1

for y when x=5

y=k/x

y=1/5

y=0.2

[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let [tex]\alpha[/tex] and [tex]\beta[/tex] be the two zeroes of P(x) = [tex]\sf {a}^{2} + bx + c[/tex]

• A polynomial is always equal to it's factors, also the constant "k" is not equal to zero

[tex] \tt \sf {a}^{2} + bx + c = k(x - \alpha )(x - \beta )[/tex]

• Using distributive property

[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} - \beta x - \alpha x + \alpha \beta \bigg)[/tex]

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -k (\beta x )- k(\alpha x )+k( \alpha \beta )[/tex]

• Taking common

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]

• Equating coefficients of like terms

[tex] \sf \: a = k - - (2)[/tex]

[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]

[tex] \sf c = k \alpha \beta - - (4)[/tex]

★ From 3

[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]

★ From 2 we have a = k so we have -

[tex] \sf b = - a( \alpha + \beta ) [/tex]

[tex]\sf - \dfrac{b}{a} = ( \alpha + \beta ) [/tex]

[tex]\sf \therefore \boxed {{ \red{( \alpha + \beta ) = - \dfrac{b}{a} } }}[/tex]

• Sum of zeros = [tex]- \dfrac{b}{a}[/tex]

★ From 4

[tex] \sf c = k \alpha \beta - - (4)[/tex]

★ From 2 we have a = k so we have -

[tex] \sf c = a \: \alpha \: \beta[/tex]

[tex]\sf \dfrac{c}{a} = \alpha \beta[/tex]

[tex]\sf \therefore \boxed {{ \red{( \alpha \beta ) = \dfrac{c}{a} } }}[/tex]

• Product of zeros = [tex] \dfrac{c}{a}[/tex]

Also,

★ From 1

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]

[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( \alpha + \beta ) + ( \alpha \beta \bigg) [/tex]

• Now just put S instead of sum of zeroes and P instead of product of zeroes

[tex] \tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( S ) + ( P \bigg) [/tex]

[tex]\tt \sf{a}^{2} + bx + c = \boxed{ \red{ \sf \tt k \bigg( {x}^{2} - Sx + ( P \bigg ) }}[/tex]

[tex]\rule{280pt}{2pt}[/tex]

Answer:

4x+5y=-12

-2x+3y=-16 ×2

-----------------

eliminate x

4x+5y=-12

-4x+6y=-32

---------------+

11y=-44

y=-44/11

y=-4

y=-4 --->

-2x+3(-4)=-16

-2x-12=-16

-2x=-4

x=-4/-2

x=2

Applying the volume of a rectangular prism, the following are determined:

A & G has a solution of 120.

B & F: 714

C & E: 56

D & H: 9.5

Volume = base area × height of prism = 1/2(bh) × H

A. Volume = 1/2(bh) × H = 1/2(6)(8) × 5 = 120 units³

B. Volume = 1/2(bh) × H = 1/2(6)(14) × 17 = 714 units³

C. Volume = 1/2(bh) × H = 1/2(12)(8) × x = 2,688 units³

48x = 2,688

x = 2,688/48

x = 56 units (height of the prism)

D. Volume = base area × height of prism

Plug in the given values

27.36 = base area × 2.88

27.36/2.88 = area of triangular base

area of triangular base = 9.5 units².

E. Volume = 1/2(bh) × H = 1/2(8)(15) × x = 3,360 units³

60x = 3,360

x = 3,360/60

x = 56 units (height of the prism)

F. Volume = 1/2(bh) × H = 1/2(17)(4) × 21 = 714 units³

G. Volume = 1/2(bh) × H = 1/2(3)(5) × 16 = 120 units³

H. Volume = 1/2(bh) × H = 1/2(1.9)(2) × 5 = 9.5 units³

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Answer

x > 2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that dont contain the variable

Answer:

3

Step-by-step explanation:

Volume of a cone

V = pi x r^2 x h/3

So plug in the values we have

30pi = pi x r^2 x 10/3

30 = r^2 10/3

9 = r^2

3 = r

Step-by-step explanation:

\Given :

x^{3} +x^{2} -20x

Solution:

x^{3} +x^{2} -20x

taking x common from the given polynomial

⇒x(x^{2} +x-20)=0

⇒x(x(x+5)-4(x+5))=0

⇒x(x+5)(x-4)=0

⇒ x=0 , x+5=0 , x-4=0

⇒x = 0 , x = -5 , x = 4

Answer:

0, x = 4, and x = -3.

Step-by-step explanation:

he zeros of the polynomial function f(x) = x3 − x2 − 12x are x = 0, x = 4, and x = -3. To find these, we can factor the polynomial and set each factor equal to zero. Since x = 0 is already given as a zero, we can factor out x from the polynomial to get f(x) = x(x^2 - x - 12) = x(x - 4)(x + 3) = 0. Thus, the other zeros are x = 4 and x = -3.

[tex]f(t) = (t-s)² - q 9

(4-5)² = 9 = 0

(t - 5) ^ 2 = 9

t - 5 = 3or 4-5=-3

(x + 2)(x + 4) = 0

X+26

t=8 or t= 2

f(x) = (x + 2)(x + 4)

vertex: (5,-9) # 1rt = 5

Zeros

y = f(+)

vertex

• line of symmetry[/tex]

Using it's concept, it is found that the functions that have a greater y-intercept than g(x) = |x + 3| + 4 are given as follows:

It is the value of the function when the input is of zero, that is, f(0). An intercept of a rational function is a point where the graph of the rational function intersects the x- or y-axis.

here, we have,

For g(x) = |x + 3| + 4, we have that g(0) = 7. As for the other functions, we have that:

f(x) = -2(x - 8)² -> f(0) = -128.

h(x) = -5|x| + 10 -> f(0) = 10 -> Greater than g(x).

j(x) = -4(x + 2)² + 8 = f(0) = -8.

k(x) = 0.25(x - 4)² + 4 -> f(0) = 8 -> Greater than g(x).

m(x) = 0.25|x - 8| + 6 -> f(0) = 8 -> Greater than g(x).

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Answer:

shade 3 slices

Step-by-step explanation:

9*1/3=3

Answer:

7-4g

Step-by-step explanation:

let the number =g

four times the number = 4×g = 4g

seven decreased br four times the number= 7- 4g

therefore, the answer = 7-4g

========================================================

Explanation:

The circumference is the perimeter of the circle. It's the distance around the circle's edge. Think of it like a fence.

The full circle's perimeter is 6 units. The arc length is a piece of that and it's 1 unit.

1/6 of the full perimeter is the arc length

1/6 of a full 360 degree rotation is (1/6)*360 = 360/6 = 60

The central angle of the arc is 60 degrees.

------------

If you want to use a formula, it would be

[tex]A = \frac{L}{C}*360[/tex]

where,

A = central angle of the arc

L = arc length

C = circumference

You would plug in L = 1 and C = 6 to find that A = 60

Answer:

Point B

Step-by-step explanation:

Let's take your number line from -5 to +5

The point on the number line is -2 1/4

Point A is between -4 and -3, Point B is between -3 and -2, Point C is between -2 and -1, and Point D is between -1 and 0. Because -2 is not between -4 and -3 or -1 and 0, it has to be either Point B or C. Since -2 has a fraction of 1/4, it is  between Point B. It would be Point C if it was -1 1/4 and not -2 1/4. Let me show you on the number line (It is not to scale, sorry haha)

<--------------------------0---------------------------->

-5    -4   -3   -2   -1      1    2    3     4      5

           |     |      |     |

          A    B    C   D

-3 > -2 1/4 > -2

Answer:

B

Step-by-step explanation:

I took the test