It cost Angel $6.75 to send 75 text messages. How much does it cost to send one text?​

The diagram of the number line is shown below

Thus, the distance CD which is the distance between point D and point C is

13 - 11 = 2

CD = 2

The cost of the present is $20.67

Given,

The cost of the present = x

Amount given by cousin = $13.78

Amount given by cousin is 2/3 of x.

That is,

13.78 = 2/3 of x

Lets find x

13.78 = 2/3 × x

13.28 = 2x/3

Multiply with 3 on both sides

13.78 × 3 = (2x/3) × 3

We get,

41.34 = 2x

Divide 2 on both sides

That is,

41.34/2 = 2x/2

We get,

x = 20.67

Here, x is the cost of the present

Therefore, the cost of the present is $20.67

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1) Let's solve that exponential equation

Converting the bases:

2) Since we are on the same base let's just calculate the exponents.

3) Blake has committed a mistake when He didn't apply the distributive property properly. He didn't multiply the 7 by 4. He subtracted the x variables wrongly and added -7 to -5.

When He started operating the exponents.

Answer:

-1, 1

Step-by-step explanation:

The translation is 1 unit left and 1 unit up.

Answer:

[tex]y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]

Step-by-step explanation:

Intercept form of a quadratic equation

[tex]y=a(x-p)(x-q)[/tex]  

where:

Given:

Substitute the given values into the formula and solve for a:

[tex]\begin{aligned} y&=a(x-p)(x-q)\\\\\implies-6&=a(5-(-7))(5-3)\\-6&=a(12)(2)\\-6&=24a\\a&=\dfrac{-6}{24}\\\implies a&=-\dfrac{1}{4}\end{aligned}[/tex]

Substitute the given x-intercepts and the found value of a into the formula:

[tex]\implies y=-\dfrac{1}{4}(x+7)(x-3)[/tex]

Expand to standard form:

[tex]\implies y=-\dfrac{1}{4}(x^2-3x+7x-21)[/tex]

[tex]\implies y=-\dfrac{1}{4}(x^2+4x-21)[/tex]

[tex]\implies y=-\dfrac{1}{4}x^2-x+\dfrac{21}{4}[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{3}{4} -\frac{1}{2} p > \frac{5}{4} \\\frac{3}{4}(4)-\frac{1}{2} p(4) > \frac{5}{4} (4)\\3-2p > 5\\-2p > 5-3\\-2p > 2\\\frac{-2p}{-2} > \frac{2}{-2} \\p < -1[/tex]

when you divide or multiply by a negative number the signs <> change directions.

An equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) = 72.2 .

As given in the question,

Pierce is making a rectangular frame for a photo collage.

Perimeter of a rectangular frame is equal to 72.2 inches.

Length of the rectangular frame is equal to 20.3 inches

Perimeter of the rectangle = 2(length + width) __(1)

Let x inches be the width of the frame

Equation with x width of the frame is given

2(20.3 + x) = 72.2

Therefore, an equation to find the width of a rectangular frame with perimeter 72.2inches and length 20.3 inches is given by 2( 20.3 + x ) =72.2.

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The difference between the depths in February and July is D. 13 feet.

From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.

Therefore, it should be noted that the depth in July is -18.

Therefore, the difference between the depths in February and July will be:

= -5 - (-18)

= -5 + 18

= 13

Therefore, the difference is 13 feet.

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(-4,5)

4 to the left on the axis is neg. 5 units up on the y axis makes it positive.

Answer:

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The liters of 80% material is 2/3 liters.

The liters of the 50% solution is 1/3 liters.

Based on the information, the scientist is working with two different concentrations of hydrochloric acid (HCI).

Let x = volume of 80%

Let 1 -x =volume of 50%

Therefore, the expression to illustrate the information will be:

80x + 50 × (1 - x) = 70

80x + 50 - 50x = 70

30x = 70 - 50

30x = 20

Divide

x = 20/30

x = 2/3

Therefore there are 2/3 liters of 80% material

The liters for the 50% solution will be 2/3 subtracted from 1. The 2/3 implies that for the 80% material. This will be:

= 1 - 2/3

= 1/3

There are also 1/3 liters of 50% material.

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The value of k given that both points lie on a line passing through the origin is 48.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Since both points lie on a line which passes through the origin, we can logically deduce the following points:

Point (x, y) = (0, 0)

Substituting the given points into the formula, we have;

Slope, m = Δy/Δx

Slope, m = (-2 - 0)/(-12 - 0)

Slope, m = -2/-12

Slope, m = 1/6

At point (-12, -2) and (k, 8), we have:

1/6 = (8 - (-2))/(k - (-12))

1/6 = (8 + 2)/(k + 12)

1/6 = 10/(k + 12)

k + 12 = 10(6)

k + 12 = 60

k = 60 - 12

k = 48

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Steve's new credit card balance at the end of the month and after making the minimum monthly payment will be $519.39.

A credit card balance is an amount the cardholder owes to the credit card issuer at the end of a credit period.

The credit card balance consists of purchases, finance charges, and repayments.

Credit card's APR = 11.99%

Credit limit = $1,800

Minimum monthly payment = 6.5%

Purchase at the beginning of the month = $550

Credit card interest for the month = $5.50 ($550 x 11.99% x 1/12)

New balance = $555.50

Minimum payment = $36.11 ($555.50 x 6.5%)

Balance after the minimum payment = $519.39 ($555.50 - $36.11)

Thus, If he buys $550 in school supplies at the beginning of the month, Steve’s new balance at the end of the month is $555.50, which he can reduce to $519.39 by making the required minimum monthly payment.

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The given expression is

3.4 - 2.8d + 2.8d - 1.3

By collecting like terms, we have

- 2.8d + 2.8d + 3.4 - 1.3

= 0 + 2.1

= 2.1

The equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Here, we are given a circle with center D and equation as-

[tex]x^{2}+ y^{2}+2x -8y + 8 =0[/tex]

Comparing this to the general form of equation of a circle which is  [tex]x^{2}[/tex] + [tex]y^{2}[/tex]+ 2gx + 2fy + c = 0, we get-

g = 1, f = -4 and c = 8

thus, the center of the circle is (-1,4) and radius =[tex]\sqrt{ (1+16-8)}[/tex] = 3

Now, since PT is a tangent to the circle, DP will e perpendicular to PT.

We can find the length of PD using the distance formula as we know P(4,6) and D(-1,4)

= [tex]\sqrt{(4+1)^{2} +(6-4)^{2} }[/tex]

= [tex]\sqrt{(5)^{2} +(2)^{2} }[/tex]

= [tex]\sqrt{25 +4 }[/tex]

=[tex]\sqrt{29}[/tex]

Thus, in triangle, PDT by using Pythagoras theorem, we will have-

[tex]PT^{2} + DT^{2} = PD^{2}[/tex]

since DT is the radius of the circle, DT = 3

⇒ [tex]PT^{2} + 3^{2} = (\sqrt{29}) ^{2}[/tex]

[tex]PT^{2} + 9 = 29[/tex]

[tex]PT^{2} = 29 - 9[/tex]

[tex]PT^{2} = 20[/tex]

[tex]PT = \sqrt{20}[/tex]

Thus, we've proved that the length of PT is [tex]\sqrt{20}[/tex] units.

Now, the circle with center P, passing through T will have radius = [tex]\sqrt{20}[/tex]

so r = [tex]\sqrt{20}[/tex] and (h,k) = (4,6)

Thus, the equation of the circle will be-

[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = (\sqrt{20}) ^{2}[/tex]

[tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

Thus, the equation of the circle center P which passes through the point T is [tex](x-4)^{2} + (y-6)^{2} = 20[/tex]

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Answer:2 choice

Step-by-step explanation:you use the rise over run technique with 2 points, it should give you rise 1 run 4 since the line is decreasing its a negative. For the y-int its the point where the line crosses Y int which is (0,-2) answer is -2

Using the z-distribution to test the hypothesis, we have that:

a) The null hypothesis is [tex]H_0: \mu = 50[/tex].

b) The p-value of the test is greater than 0.05, hence we do not reject the null hypothesis, meaning that the supplements did not have the intended effect.

At the null hypothesis, it is tested if there is not enough evidence that the mean was different, hence:

[tex]H_0: \mu = 50[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean was different, hence:

[tex]H_1: \mu \neq 50[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

In the context of this test, the parameters are given as follows:

[tex]\overline{x} = 54, \mu = 50, \sigma = 12, n = 16[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{54 - 50}{\frac{12}{\sqrt{16}}}[/tex]

z = 1.33.

Considering a two-tailed test, as we are testing if the mean is different of a value, with z = 1.33, the p-value of the test is of 0.1835, which is greater than 0.05, meaning that we do not reject the null hypothesis and the supplement did not change the mean.

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Answer:900

Step-by-step explanation: 1. set up an equation

x= (p * n)/100 when x= the answer p= the percentage and n= the total number

2. plug in the numbers

x= (30 * 3000)/100

3.solve

x= (30*3000)/100

x= (90000)/100

x= 900

Check the picture below.

let's bear in mind that the standard deviation measures deviation in a dataset, so is a measure of how much the data fluctuates, so a dataset of 3 , 1000, will have a much higher deviation value than a same total of 450 , 553.

The three Points that  lie on the given line 2x=6y+4 are  (5,1) , (8,2) and (11,3).

The given equation of line is given below,

2x=6y+4                              equation 1

We need to find the points that lie on the given line.

Point 1 :

Put x = 5 in equation 1

2(5) = 6y + 4

6y = 6

y=1

So, Point (5,1) lie on the given line.

Point2:

Put x = 8 in equation 1

2(8) = 6y + 4

6y = 12

y=2

So, Point (8,2) lie on the given line.

Point 3 :

Put x = 11 in equation 1

2(11) = 6y + 4

6y = 18

y=3

So, Point (11,3) lie on the given line.

Thus, Points (5,1) , (8,2) and (11,3) lie on the line 2x=6y+4 .    

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Answer: B. (5√3)

Step-by-step explanation: In a 60-30-90 triangle, the hypotenuse is 2x, and the long is x√3. Solve for x by setting 2x=10, which you would get 5. Then, you can plug 5 for x in x√3 to get 5√3.

The most appropriate choice for linear equation will be given by-

The cost of bench is $375

What is linear equation?

A one degree equation is called a linear equation.

Here,

Let the cost of the bench be $x

cost of garden table = $(x + 80)

Total cost of bench and garden table= $(x + x + 80)

                                                              = $(2x + 80)

By the problem,

                           2x + 80 = 830

                            2x = 830 - 80

                             2x = 750

                                x = [tex]\frac{750}{2}[/tex]

                                x  = $375
So,

The cost of bench is $375

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Step 1: Concept

To convert km to meters you will multiply with 1000.

To convert minute to hour you will divide by 60

Step 2: Convert

Step 3: Final answer

Option B and D

Total expenses = $289 + $361 + $433 + $217 = $1300

Percentage of money spent on rent:

(Money spent on rent)/(Total expenses) = $361/$1300 = 0.2777 ≈ 28%

Therefore 28% of total expenses are for rent

Answer:

26, 27, 28

Step-by-step explanation:

Let the 3 integers be: x, x+1, x+2

x+x+1+x+2 = 81

3x+3 = 81

3x = 78

x = 26

x+1 = 27

x+2 = 28