solving system by substitution

Answer:

The discount is $0.8d.

Step-by-step explanation:

Given that,

The original cost of Tamara's purchase is d dollars​.

Tamara uses a coupon to save 20% off her purchase at the bookstore.

Discount = 20%

Discount is applied to the original cost.

Discount = d-(20/100)d

Discount = 0.8 d

Hence, the discount is $0.8d.

Answer:y< 3x + 12

y> 5x + 7

Step-by-step explanation:

Answer:

x<5

Step-by-step explanation:

Answer:

160 for each

Step-by-step explanation:

A normal distribution means that mean = median = mode. Furthermore, in a normal distribution, 68% of values are within 1 standard deviation of the mean, 95% of values are within 2 standard deviations, and 99.7% are within 3 standard deviation.

The mean is 150 and the standard deviation is 15. 165 and 135 1 standard deviation away from the mean, so 68% of values are between 135 and 165. This means that 32% of values are not between those values. A normal distributuion is symmetric, so 16% of values are greater than 1 standard distribution and 16% are less. Therefore, 16% of values (160) are less than 135 and 16% of values (160) are greater than 165

Answer:

A. 3

Step-by-step explanation:

Section 1: decrease

Section 2: level, no increase, no decrease

In section 3, the slope is positive. The graph goes up to the right. The level of water increases in section 3.

Section 4: decrease

Section 5: decrease

Answer: A. 3

Answer:

A. 3

Step-by-step explanation:

[tex]\longrightarrow{\blue{ 141x - 8y }}[/tex] 

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex]97x + 58y - 66y + 44x[/tex]

Let us rewrite the expression so that the like terms are next to each other.

[tex] = 97x + 44x+ 58y - 66y[/tex]

Combine the coefficients.

[tex] = (97 + 44)x + (58 - 66)y[/tex]

[tex] = 141x - 8y[/tex]

[tex]\sf\pink{Happy\:learning! }[/tex]

Answer:

range = 10

Step-by-step explanation:

The range is the difference between the largest and smallest values in the data set.

largest value = 12

smallest value = 2

range = 12 - 2 = 10

Answer:

$13.25

Step-by-step explanation:

Given data

Cost of game = $25

Markup= 6%

Let us find the total cost of the game

First, the markup cost

=6/100*25

=0.06*25

=$1.5

Now the total cost is

=25+1.5

=$26.5

So, each is expected to pay

=26.5/2

=$13.25

Given:

Radius of a circle = 21 m

Area of a sector of the circle = 27.72 m²

To find:

The angle at the center of the circle.​

Solution:

The area of a second is:

[tex]A=\pi r^2\times \dfrac{\theta}{360^\circ}[/tex]

Where, r is the radius of the circle and [tex]\theta[/tex] is the central angle.

Putting [tex]\pi=\dfrac{22}{7},\ r=21,\ A=27.72[/tex] in the above formula, we get

[tex]27.72=\dfrac{22}{7}\times (21)^2\times \dfrac{\theta}{360^\circ}[/tex]

[tex]27.72=1386\times \dfrac{\theta}{360^\circ}[/tex]

[tex]27.72=3.85^\circ \times \theta[/tex]

[tex]\dfrac{27.72}{3.85^\circ }=\theta[/tex]

[tex]7.2^\circ=\theta[/tex]

Therefore, the central angle of the sector is [tex]7.2^\circ[/tex].

Answer:

x = -3

Step-by-step explanation:

Okay, the first thing to do is get that 8 away from the fraction. How can we do it? When you have 2³ you have 8, is the same thing, so let's do it:

2³⁰/(2³)⁹ = 2^x

When you have a number with the shape (a^x)^y, you can write it as a^(x•y), so:

(2³)⁹ = 2^3•9 = 2²⁷

Now we have:

2³⁰/2²⁷ = 2^x

When you have a division like this: (a^x)/(a^y), you can write it as a^(x-y), so:

2^(30-27) = 2^x

2^-3 = 2^x

Now you know that x = -3

Answer:

96

Step-by-step explanation:

120/1.25=96

Noah needs to sell 96 slices of pizza to earn $120.

Answer:

a. 5 loaves, b. 14 loaves

Step-by-step explanation:

a.8.50=2.50+1.20x

  6.00=1.20x

  5=x

5 loaves

b.20=2.50+1.20x

   17.50=1.20x

   14.6=x

14 loaves

Answer:

No it cant

Step-by-step explanation:

You have to use the Pythagoras theorem which is a^2 + b^2 = c^2. So 9^2 + 11^2= 202. Then 17 is the hypotenuse so 17^2= 289. They are not equal so they are not.

Answer:

1/6 gallon of water

Step-by-step explanation:

Number of hikers = 3

Quantity of water shared = 1/2 gallon of water

If the water was shared equally among the hikers, then,

Amount of water each hiker drank = Quantity of water shared ÷ Number of hikers

= 1/2 ÷ 3

Multiply 1/6 by the reciprocal of 3

The reciprocal of 3 = 1/3

1/2 ÷ 3

= 1/2 × 1/3

= (1 * 1) / (2 * 3)

= 1/6

Amount of water each hiker drank = 1/6 gallon of water

Answer:

Sample Response: Draw a square and shade half of it. Then draw 2 lines to divide the square into 3 equal parts. There will be one shaded piece in each group, and there are 6 pieces total, so the answer is 1

6

of a gallon.

Step-by-step explanation:

UwU

Answer:

$7,680

$34,240

Step-by-step explanation:

Amount Tessa earns in 2019 = $32000

a. She paid tax of 24% on these earnings. Work out the amount she paid in tax in 2018.

Percent of tax = 24%

Amount of tax paid = 24% of $32,000

= 24/100 * 32,000

= 0.24 * 32,000

= $7,680

Amount of tax paid = $7,680

b. Tessa's earnings increased by 7%. Work out her earnings in 2020.

Percentage increase in earnings = 7%

Amount of increase in earnings = 7% of $32,000

= 7/100 * 32,000

= 0.07 * 32,000

= $2,240

Amount of increase in earnings = $2,240

Total earnings in 2020 = Amount Tessa earns in 2019 + Amount of increase in earnings

= $32,000 + $2,240

= $34,240

Total earnings in 2020 = $34,240

Answer:

x = 72.09555249

Step-by-step explanation:

Since this is a right angle, we can use trig functions

tan x = opp / adj

tan x = 65/21

Taking the inverse tan of each side

tan ^-1 ( tan x) = tan ^-1 ( 65/21)

x = 72.09555249

Answer:

2 and 3

Step-by-step explanation:

Let us start by representing the first consecutive number with x. In a similar sense, the next consecutive number would be x+1. According to the given question, we can write the following equation:

[tex]x+x+1=3x-1[/tex]

Solving for the equation by isolating the term containing x, we have:

[tex]2x+1=3x-1\\2x+2=3x\\\fbox{x=2}[/tex]

Since we have designated x as the first consecutive integer, the other integer we are looking for is x+1, or [tex]\fbox{3}[/tex] .

I hope this helps! Let me know if you have any questionss :)

Step-by-step explanation:

x+2x+8 =200

3x=200-8

3x=192

x = 64

Martha has 64 pence

Peter jas 136 pence

Answer:

8

Step-by-step explanation:

Divide 30 by 3.75 to get 8.

Hope that this helps!

Answer:

we have,AD=x cmBC=AD=x cmAB=2AD=2x cmDC=4 cm+AB=(4+2x)cmPerimeter of the trapezium, p=38 cm

Answer:

250×

Step-by-step explanation:

The ocular lens of the compound microscope is 10×

The objective lens of the compound microscope is 25×

Therefore the total magnification can be calculated as follows

= 10×25

= 250

Hence the total magnification of the compound microscope is 250×

Answer:

20,100

Step-by-step explanation:

hundreds place is the third from the right

Answer:

20,100

Step-by-step explanation:

085 represents 0 hundreds, 8 tens and 5 ones.

That place keeper 0 is rounded  up to a 1 because the following '8' is greater than 5.

Thus, the desired rounded off number is 20,100.

Answer:

Step-by-step explanation:

Since we are finding the x-intercepts, that implies that this is a parabola that opens either up or down as opposed to right or left. It would benefit us to know the equation of the parabola so we could factor it to find the roots (which are also known as the x-intercepts).

Here's what we know:

h = 1, k = 20, x = 0, and y = 20. Filling in the vertex form of a parabola is already halfway to factored, so we'll use that format as opposed to the standard form, which is

[tex]y=ax^2+bx+c[/tex]. The vertex form is

[tex]y=a(x-h)^2+k[/tex] and filling in our values from above:

[tex]16=a(0-1)^2+20[/tex] and

[tex]16=a(1)+20[/tex] and

-4 = a. So the equation for the parabola is

[tex]y=-4(x-1)^2+20[/tex]. Now set it equal to 0 and factor.

[tex]-20=-4(x-1)^2[/tex] and divide both sides by -4 to get:

[tex]5=(x-1)^2[/tex] and take the square root of both sides to get

±[tex]\sqrt{5}=x-1[/tex] and then add 1 to both sides to get the x-intercepts (or roots or solutions or zeros...they're all the same).

x = 1 ±√5 and you're done!

Answer:

Mean: 52.8

Median:52

Mode:54

Step-by-step explanation:

Mean: 54+48+37+55+51+54+42+52+53=476

476/9=52.8

Median: 37,42,48,51,52,53,54,54,55. The middle one is 52.

Mode: Most common one = 54

Hope this helps! Have a nice day!

Answer:

I'm guessing 46 if its actually adding

Answer:

Step-by-step explanation:

not sure if i am right but go off process of elimination

A is a not it to get slope you need to do Y=Mx+b because the slope should be 1.3 and if you get the deciml form of 3 over 9 it would be 0.75

and if you do same process on all of then you will see it is B

Answer:

Second option - 6

Explanation:

Trust! (And the image)

I really ope this helped! :)