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3 years ago

What is the converse of the following conditional statement? If x = –10, then x2 = 100

1 answer:

8 0

The converse would be If x² = 100 then x = -10

So essentially if the conditional statement is p → q then the converse is q → p (In essence, the converse of a conditional statement is formed by interchanging the hypothesis and the conclusion.)

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Evaluate f (x) = 2 x for x = -4, 0, and 5.

aleksklad [387]

The function f(x) is defined in to different ways depending on the value of X. When x is < 5, use the expression 2x - 1 to evaluate the function When x is ≥ 5, use the expression x2 - 3 for example f(1) = 2(1) - 1 = 1 f(10) = (10)2 - 3 = 97

8 0

3 years ago

If the measure of DAC is x and the measure of CAB is (2x – 30), what is the value of x? (HINT** remember how we label angles, th

Scorpion4ik [409]

Answer:

Step-by-step explanation:

∠ BAD = 90° and

∠ DAC + ∠ CAB = ∠ BAD, that is

x + 2x - 30 = 90

3x - 30 = 90 ( add 30 to both sides )

3x = 120 ( divide both sides by 3 )

x = 40 → b

6 0

3 years ago

A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of

cestrela7 [59]

The amount of gas consumed by first and second car were 20 gallons and 15 gallons respectively.

Explanation

Suppose, $x$ gallons of gas were consumed by the first car.

As the total gas consumption in one week is 35 gallons, so the amount of gas consumed by second car will be: $(35-x)$ gallons.

The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas.

So, the distance traveled by the first car in $x$ gallons of gas $=35x$ miles and the distance traveled by the second car in $(35-x)$ gallons of gas $=15(35-x)$ miles.

Given that, the two cars went a combined total of 925 miles. So, the equation will be.....

$35x+15(35-x)=925\\ \\ 35x+525-15x=925\\ \\ 20x=925-525=400\\ \\ x=\frac{400}{20}=20$

So, the amount of gas consumed by the first car is 20 gallons and the amount of gas consumed by the second car is: (35 - 20) = 15 gallons.

3 0

3 years ago

The numbers of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance,

tensa zangetsu [6.8K]

We have the following data set:

2,7,15,3,12,9,15,8,3,10

The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.

2,3,3,7,8,9,10,12,15,15

Then,

$\begin{gathered} \text{Range}=15-2 \\ \text{Range}=13 \end{gathered}$

Mean is represented by the following expression:

$\text{Mean}=\frac{\text{Sum of all data points}}{Number\text{ of data po}ints}$ $\text{Mean}=\frac{84}{10}=8.4$

Population variance formula looks like this:

$\begin{gathered} \sigma^2=\frac{\sum^{}_{}(x-\mu)^2}{N} \\ \text{where,} \\ \sigma^2=\text{population variance} \\ \sum ^{}_{}=addition\text{ of} \\ x=\text{each value} \\ \mu=population\text{ mean} \\ N=\text{ number of values in the population} \end{gathered}$

Then, substituting:

$\begin{gathered} \sigma^2=\frac{(2-14)^2+(3-14)^2+\cdots+(15-14)^2}{10} \\ \sigma^2=20.44 \end{gathered}$

For the standard deviation:

$\begin{gathered} s=\sqrt[]{\frac{\sum ^{}_{}(x-\mu)^2}{N}} \\ s=4.521 \end{gathered}$

5 0

1 year ago

What is the area of the figure below? 6 in. 5 in. 4 in.

uysha [10]

120
6x5x4=120
hope this helps

4 0

3 years ago