In January Jennifer was allowed to use 150 text messages. If she is allowed to use the same amount of text messages every month. How many text messages would she have used in all by the month of August?

Answer:

2x + 2(x - 5) = 78

x + x - 5 = 39

2x = 44

x = 22

Rate of the slower cyclist = 17 mph

Rate of the faster cyclist = 22 mph

Answer:

4

Step-by-step explanation:

36 / 9 = 4

4 x 9 = 36

Answer: c) 1 unit

Step-by-step explanation: Because if u take the scale factor and multiply it by 3

Answer:

C:  1 unit

Step-by-step explanation:

(3 units) times scale factor (1/3) comes out to (1/3)(3 units), or 1 unit.

The correct answer is C:  1 unit.

The set of equations x = t and y = 3t could be parametric equations ⇒ 3rd answer

Step-by-step explanation:

Lets explain the meaning of parametric equations

A parametric equation is where the x and y coordinates are both written in terms of another letter

Examples:

Let us find the set of the parametric equations from the answer

Fist answer:

∵ y = x and y = 3x

∴ It is a set of linear equations

Second answer:

∵ y = x + 1 and y = 3x²

∴ It is a set of linear and quadratic equations

Third answer:

∵ x = t and y = 3t

∵ x and y are represented in terms of t

∴ It is a set of parametric equations

Fourth answer:

∵ x = 3y and y = x + 1

∴ It is a set of linear equations

The set of equations x = t and y = 3t could be parametric equations

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Answer:

30

Step-by-step explanation:

Simplify from left to right

6-3+15-1+8+11-6

=3+15-1+8+11-6

=18-1+8+11-6

=17+8+11-6

=25+11-6

=36-6

=30

Answer:

6 lunch tables

Step-by-step explanation:

Since one lunch table can hold 10 students and 60 students are needed to hold,

60 ÷ 10 = 6 lunch tables

Answer:

6

Step-by-step explanation:

1 table is 10

60 divided by 10= 6

Answer:

x=2, y=0. (2, 0).

Step-by-step explanation:

x-y=2

2.5x+y=5

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

x=y+2

2.5(y+2)+y=5

2.5y+5+y=5

3.5y=5-5

3.5y=0

y=0/3.5

y=0

x=0+2=2

Answer:   (x-7)/(x-5)

The (x+1) terms divide and cancel out due to the rule that x/x = 1, when x is nonzero. In that rule, we can replace 'x' with any algebraic expression we want.

To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can expand and simplify the expression to -x²+4x-4, which is always negative.

To prove that 3(x+1)(x+7)-(2x+5)² is never positive, we can use algebraic manipulation and properties of quadratic equations. Let's expand and simplify the expression:

3(x+1)(x+7)-(2x+5)² = 3(x²+8x+7)-(4x²+20x+25) = 3x²+24x+21-4x²-20x-25 = -x²+4x-4

Since the leading coefficient of the quadratic term is negative (-1), the graph of this equation will be a downward-opening parabola. Therefore, the quadratic expression is never positive.

The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x.

Step 1

To prove that [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, we can simplify the expression and analyze its sign.

Expanding the expression:

[tex]\[3(x+1)(x+7)-(2x+5)^2 = 3(x^2 + 8x + 7) - (4x^2 + 20x + 25)\][/tex]

[tex]\[= 3x^2 + 24x + 21 - 4x^2 - 20x - 25\][/tex]

[tex]\[= -x^2 + 4x - 4\][/tex]

Step 2

Now, we have a quadratic expression [tex]\( -x^2 + 4x - 4\)[/tex]. The coefficient of [tex]\(x^2\)[/tex] is negative, indicating a downward-opening parabola. Therefore, the maximum value of the expression occurs at the vertex, which lies at [tex]\(x = \frac{-b}{2a} = \frac{-4}{2(-1)} = 2\)[/tex].

Substituting x = 2 into the expression, we get:

[tex]\[ -2^2 + 4(2) - 4 = -4 + 8 - 4 = 0 \][/tex]

Since the maximum value is 0, the expression is always non-positive.

The expression [tex]\(3(x+1)(x+7)-(2x+5)^2\)[/tex] is never positive for all real values of x, as proven by its maximum value of 0.

Answer:

24(x+2)

Step-by-step explanation:

24 can be pulled from both 24 and 48

Answer:

b = 8 your welcome

Answer:

k = -5

Step-by-step explanation:

2(7k + 1) - 5(3k + 3) = 1 - 2k + 6 + 5k

At first, we will break the parenthesis by multiplying by the adjacent number. As we know, (+) x (-) = (-) and (-) x (-) = (+) [Algebraic operation]

or, (2*7k) + (2*1) - (5*3k) - (5*3) = (1 + 6) + 5k - 2k

or, 14k + 2 - 15k - 15 = 7 + 3k

Interchanging the values, we can get,

or, 14k - 15k - 3k = 7 + 15 - 2

or, 14k - 18k = 22 - 2

or, -4k = 20

or, k = 20/(-4)

or, k = -5

Therefore, the answer is -5

Answer:

both are a minimum

Step-by-step explanation:

Given a quadratic function in vertex form

y = a(x - h)² + k

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here

f(x) = (x + 4)² + 2 ← with a = 1 > 0 ⇒ minimum vertex

g(x) = (x - 2)² - 2 ← with a = 1 > 0 ⇒ minimum vertex

Answer:

193 packets

Step-by-step explanation:

Each morning they order with a shipping fee of $10 daily.

Considering they order all 7 days of the week, so the total shipping fee for the week would be:

7 * $10 = $70

Their budget for the week is $554, out of which $70 is for shipping for the week, so remaining balance would be:

554 - 70 = $484

This 484 dollars are for coffee packets that cost $2.50 each, so the number of packets would be:

484/2.50 = 193.6

You can't order fractional packets so 193 packets is the max in this budget

Answer:

Step-by-step explanation:

Yeah it right thank sweetheart

The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.

Finding Original Dimensions of a Rectangle

Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.

The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:

w(w + 10) - (w - 2)(w + 8) = 48

Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:

[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48

w2 + 10w - w2 - 6w + 16 = 48

4w + 16 = 48

4w = 32

w = 8 cm.

Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).

Answer:

36 cm

Step-by-step explanation:

We know that the perimeter is 2 l + 2 w.

In this case, the equation is 36 + 2 w = 108

2 w = 72

w = 36

Final answer:

To find the milliliters of acid in the solution, multiply the total volume of the solution by the acid percentage.

Explanation:

To find the milliliters of acid in the solution, we first need to calculate the volume of acid. We know that 13.2% of the solution is acid, so we can calculate the volume of acid by multiplying the total volume of the solution by the acid percentage:

Volume of acid = 357 mL * 0.132 = 47.124 mL

Rounding to the nearest tenth, we get:

Volume of acid = 47.1 mL

Answer:

3 months

Explanation:

Amount saved in Gina’s saving account= 250

Amount Gina puts  in her account each month= 4% of 3100

=[tex]\frac{4}{100} \times 3100[/tex]

= 4 × 31

= 124

Hence total amount  added in each month =124

Therefore money credited x months

= 250 + 124 x

Amount saved in Rodger’s account = 350

Amount Rodger puts in his account each month = 3% of 2900

=[tex]\frac{3}{100} \times 290[/tex]

=87

Hence total amount added in each month = 87

Therefore money credited x months

=350 + 87 x

Now to calculate the nearest month when Gina have more in her account than Rodger does

=Amount of money credited in x months in Gina’s account ≥  Amount of money credited in x months in Rodger’s account

=250+124 x ≥ 350+87 x

=37 x≥100

= x≥2.78

=3

Answer:

this threw me off ,i got the same question:(

Step-by-step explanation:

Answer:

When Sum of square of two Sides is equal to square of third side of triangle.

Step-by-step explanation:

Given:

Three side length of triangle are given we need find the which value to substitute for a, b, c in Pythagoras theorem.

First we will find the squares of all length, then we will check which two square of side are equal to square of third side as per Pythagoras theorem.

Hence the two side would according be a and b and third side will become c.

For example if length of triangle  is given as 6 cm, 8 cm and 10 cm.

We will first take square of all

[tex]6^2=36\\8^2=64\\10^2=100[/tex]

Now we can see that

[tex]36+64=100\\6^2+8^2=10^2[/tex]

Now by Pythagoras theorem.

[tex]a^2+b^2=c^2[/tex]

Hence we can say a = 6 cm, b = 8 cm, c= 10 cm  

The Pythagorean Theorem is specifically applicable to right-angled triangles and states that:

[tex]\[a^2 + b^2 = c^2\][/tex]

Theorem, follow these steps:

1. Identify the longest side: The hypotenuse  c is always the longest side in a right-angled triangle.

2. Assign the longest side to c : Among the three given side lengths, the one with the greatest value should be assigned to c .

Example

Suppose you are given three side lengths: 5, 12, and 13. To determine which lengths correspond to  a ,  b , and c :

1. Identify the longest side: Among 5, 12, and 13, the longest side is 13.

2. Assign the longest side to c : So, c = 13 .

3. Assign the remaining sides to  a  and  b: Thus,  a and  b can be 5 and 12, respectively (or vice versa).

Verify using the Pythagorean Theorem:

[tex]a^2 + b^2 = c^2[/tex]

[tex]5^2 + 12^2 = 13^2[/tex]

25 + 144 = 169

169 = 169

Since the equation holds true, the side lengths 5, 12, and 13 do indeed form a right-angled triangle, with 13 being the hypotenuse.

General Case

When given any three side lengths x ,  y , and z :

1. Determine the longest side and assign it to c .

2. The remaining two sides are a  and b

3. Check if [tex]\( a^2 + b^2 = c^2 \)[/tex] to verify if the triangle is a right-angled triangle.

By following this process, you can correctly identify the sides to substitute into the Pythagorean Theorem.

Answer:

A

Step-by-step explanation:

United states is too broad and too many different conditions for the land. You do not base weather on the date either.

Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today best describes the most likely way the probability was determined. Thus option A is correct.

The mathematical discipline known as probability specializes with determining the possibility of an event occurring. Composite reliabilities vary from 0 to 1, with 1 representing certainty and 0 representing hesitation.

Probability, which expresses the probability of a risk, is calculated by dividing the total possible combinations by the frequency of favorable events. Mornings with weather levels comparable to today's, precipitation has fallen 10% of the time. The Weather Forecast estimates there remains a 10% chance of snowfall around his region today.

Therefore, option A is the correct option.

Learn more about probability, Here:

https://brainly.com/question/11234923

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Answer:

The area of the given figure is [tex]66.5\ cm^2[/tex].

Step-by-step explanation:

To find out the area we should have to redraw the figure having nomenclature ABCDE and join BD. Thus we have a rectangle ABDE and a triangle BCD.

The new figure is in the attachment.

Given,

Length of AE = 7 cm

Length of DE = 8 cm

Length of CF = 11 cm

Solution,

Area of rectangle ABDE = [tex]length\times breadth=length\ of AE\timeslength\ of DE[/tex]

Area of ABDE = [tex]7\times8=56\ cm^2[/tex]

Now for triangle BCD,

Length of BD = length of AE = 7 cm

Length of GF = Length of DE = 8 cm

∴ Length of CG = Length of CF-Length of GF = [tex]11-8=3\ cm[/tex]

Area of triangle BCD = [tex]\frac{1}{2}\times base\times height}=\frac{1}{2}\times length\ of\ BD\times length\ of\ GF[/tex]

Area of BCD =  [tex]\frac{1}{2}\times7\times3=\frac{21}{2}=10.5\ cm^2[/tex]

Area of ABCDE = Area of ABDE + Area of BCD = [tex]56+10.5=66.5\ cm^2[/tex]

Thus the area of the given figure is [tex]66.5\ cm^2[/tex].

Answer:

The margin of error is 1.85 cm to 1.95 cm.

Step-by-step explanation:

Given:

Will measured the diameter of a penny as 1.9 cm using the ruler.

We need to find the margin error.

Now, as we know that the margin of error is a statistic expressing the amount of random sampling error in a survey's results.

It is an amount (usually small) that is allowed for in case of miscalculation or change of circumstances.

Now, we have the margin of error to be:

1.85 cm to 1.95 cm.

As, the value of change to the left and right of 19 is same and is small it is 0.05.

So, 1.9-0.05 = 1.85 cm

and 1.9+0.05 = 1.95 cm .

Hence, the margin of error is: ± 0.05.

Therefore, the margin of error is 1.85 cm to 1.95 cm.

Answer: -39

Step-by-step explanation:

9 x -4 -3 = -39

Answer:

it's 18 if your talking about multiplication

It's 42 if your talking about the powers

Step-by-step explanation:

Multiplication-(6•0)+(6•1)+(6•2)= 18

The powers-(6^0)+(6^1)+(6^2)=42

Answer:

the answer is 43

Step-by-step explanation:

For this case we must multiply the following expression:

[tex](6a ^ 3-5) (4a ^ 3-11a) =[/tex]

We apply distributive property considering that:

[tex]+ * + = +\\+ * - = -\\- * - = +[/tex]

So:

[tex]6a ^ 3 * 4a ^ 3-6a ^ 3 * 11a-5 * 4a ^ 3 + 5 * 11a =[/tex]

To multiply powers of the same base, we place the same base and add the exponents.

[tex]24a^ {3 + 3} -66a^ {3 + 1} -20a ^ 3 + 55a =\\24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]

Answer:

[tex]24a ^ 6-66a ^ 4-20a ^ 3 + 55a[/tex]

Answer:

slope = - 2, y- intercept = - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 6x + 3y = - 3 into this form by subtracting 6x from both sides

3y = - 6x - 3 ( divide all terms by 3 )

y = - 2x - 1 ← in slope- intercept form

with slope m = - 2 and y- intercept c = - 1

Answer:

20 cups

Step-by-step explanation:

16 ounces = 1 pound

8 ounces = 1 cup

16 ounces = 2 cups

1 pound = 2 cups

10 pounds = 20 cups

Answer:

20 cups

Step-by-step explanation:

Think

1 pound is 16 oz

So each cup has 8 oz

This you have to convert the 10 pound into ounces

Which then equals 160 ounces

Now divide 160 ounces by 8 and you get..

You get 20

So, 10 pounds of apples fit into 20 cups

Answer:

x = ±√y

Step-by-step explanation:

y = x²

±√y=√x²

±√y = x