Mathematics High School

What is the distance between -3.1 and -5.7 on a number line?

Answers

Answer 1

-3.1-(-5.7)=2.6
so your answer should be either -2.6 or 2.6

Answer 2

The distance between -3.1 and -5.7 on the number line is 2.6 units.

The distance between two points on the number line is the absolute difference between those two points.

So, the distance between -3.1 and -5.7 is:

[tex]|-3.1 - (-5.7)| = |-3.1 + 5.7| = |2.6| = 2.6[/tex]

Therefore, the distance between -3.1 and -5.7 on the number line is 2.6 units.

Related Questions

Of 100 clock radios with digital tuners and / or CD players sold recently in a department store, 70 had digital; tuners and 90 and CD players. How many radios had both digital tuners and CD players? ...?

Answers

The answer is 60.

Let A be the number of radios with digital tuners and let B be the number of radios with CD players.
The total number of radios is A∪B. It consists of both A radios and B radios, but however, radios with both digital tuners and CD players (A∩B) must be excluded from that number (either way they will be counted twice):
A∪B = A + B - A∩B

A∪B = 100
A = 70
B = 90
A∩B = ?

100 = 70 + 90 - A∩B
100 = 160 - A∩B
A∩B = 160 - 100
A∩B = 60

Final answer:

To determine the number of radios with both digital tuners and CD players, we use the principle of inclusion-exclusion. With 70 radios featuring digital tuners and 90 featuring CD players out of 100, the calculation reveals that 60 radios had both features.

Explanation:

The question asks how many radios sold recently in a department store had both digital tuners and CD players, given that 70 had digital tuners and 90 had CD players out of a total of 100 clock radios. To find the number of radios that had both features, we can use the principle of inclusion-exclusion. The formula for this principle is: Total = A + B - (A and B), where A and B are the two groups, and (A and B) is the intersection of the two groups. In this case, A is the number of radios with digital tuners, and B is the number of radios with CD players.

Substituting the given values: 100 = 70 + 90 - (A and B). Solving for (A and B), which represents the radios with both features, we get: (A and B) = 70 + 90 - 100 = 160 - 100 = 60.

Therefore, 60 radios had both digital tuners and CD players.

For the table below, determine the function rule, and find each of the missing y-values.

Function Rule: ?
x y
1 4
3 6
4 7
5 ?
7 10
10 ?

Answers

The answer is 8 and 13

y = ax + b
y = 4, x = 1 ⇒ 4 = a + b
y = 6, x = 3 ⇒ 6 = 3a + b

Solve the system of equation:
a + b = 4
3a + b = 6
______
b = 4 - a
3a + b = 6
______
3a + 4 - a = 6
2a + 4 = 6
2a = 6 - 4
2a = 2
a = 2/2 = 1
b = 4 - a = 4 - 1 = 3

So, the function rule is: y = x + 3

Thus, if x = 7, then y = 7 + 3 = 10
If x = 10, then y = 10 + 3 = 13

x y
1 4
3 6
4 7
5 8
7 10
10 13

The box plots show student grades on the most recent exam compared to overall grades in the class.

Which of the following best describes the information about the medians?

A. The class and exam medians are almost the same.

B. The exam median is much higher than the class median.

C. The class and exam Qv3 are the same, but the exam has the lowest median.

D. The low outlier on exams pulls the median lower.

Answers

A median is a line that separates 2 halfs of data. Higher and lower. In this case median is represented by a line inside the box. Median doesnt have to be in exactly the midle of the box. That is very important to know.

We can see that in both boxes medians are practicaly the same. Which means that the correct answer is A

Answer:

A. The class and exam medians are almost the same.

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?

Answers

number of x intercepts in this equation is 2 because max power in the function is 2. number of x intercepts is determined by "highest power".

let x1 represent first x intercept and
let x2 represent second x intercept

Formula for finding average of x intercepts is logicaly:
Avg = (x1 + x2)/2

we want to find x1 and x2
4x^2 - 24x + 20 = 0
x^2 - 6x + 5 = 0

[tex]x = \frac{6 +- \sqrt{6^2 - 4*1*5} }{2*1} [/tex]
x1 = 5
x2 = 1

Avg = 3

Answer:

Step-by-step explanation:

Find the percent of tip:
Cost of meal $18.50, Tip $2.59

13%

14%

15%

16%

Answers

The answer is 14%

Cost of meal is 100%: $18.50 is 100%
Tip is x%: $2.59 is x

Make a proportion:
$18.50 : 100% = $2.59 : x
x = 100% * $2.59 : $18.50
x = 14%

A machine make 24 items in 8 minutes how many can it make in 14

Answers

To get from 8 minutes to 14 minutes, you divide by 4 and multiply by 7. Therefore, if you divide 24 by 4 (6) and multiply by 7 (42), then you get the answer of 42 items in 14 minutes. Hope this helps!

6 gallons and 3 quarts equal

Answers

False, 6 gallons is 24 quarts or 3 quarts is 0.75 of a gallon

Group A consists of X students and their total age is 221 and their average age is an integer.When group A is merged with Group B with twice the number of students (the number of students between 30 and 40) average age of B is reduced by 1.What is the original average age of B?
...?

Answers

mean = sum / count

Group A
m = 221 / c
221 = c x m
221 = 17 x 13 (as it is a whole number under 20)

Group B
m = s / 34

(221 + x) / 51 = x /34 - 1

544/ 34 = 16

16

Answer:

16 years

Step-by-step explanation:

Given,

Number of students in group A = X,

Sum of their ages = 221,

So, the average age of students in group A = [tex]\frac{\text{Sum of ages}}{\text{Total students}}[/tex]

[tex]=\frac{221}{X}[/tex]

According to the question,

[tex]\frac{221}{X}=\text{Integer}[/tex]

∴ X must be a factor of 221,

∵ 221 = 13 × 17,

Now, If X = 13,

Then the number of students in group B = 26 ( NOT POSSIBLE )

If X = 17,

Then the number of students in group B = 34

Which is between 30 and 40,

Now, Let S be the sum of ages of students in group B,

So, the average age in group B = [tex]\frac{S}{34}[/tex]

Again according to the question,

[tex]\frac{S+221}{17+34}=\frac{S}{34}-1[/tex]

[tex]\frac{S+221}{51}=\frac{S-34}{34}[/tex]

[tex]34S+7514 = 51S - 1734[/tex]

[tex]34S - 51S = -1734 - 7514[/tex]

[tex]17S = 9248[/tex]

[tex]\implies S = 544[/tex]

Therefore, the average age of B = [tex]\frac{544}{34}[/tex] = 16 years.

2x plus 4 in vertex form

Answers

Vertex form only applies to quadratics. A quadratic is a polynomial with 2 being the largest exponent. I don't see any x^2 term here. Please check the problem to make sure that it's typed correctly.

A card is drawn from a deck of 52. Find the probability of drawing a king or a heart. Enter your answer in simplified fraction form; example: 3/20. ...?

Answers

The solution to the problem is as follows:

A heart or a king: P(H or K) = P(H)+P(K)-P(H and K)
There are 13 hearts out of 52 cards, so P(H) = 13/52 = 1/4
There are 4 kings out of 52 cards, so P(K) = 4/52 = 1/13

There is 1 card which is a heart and a king (the king of hearts), so P(H and K) = 1/52, so P(H or K) = P(H)+P(K)-P(H and K) = 1/4+1/13-1/52 = 13/52+4/52-1/52 = 16/52 = 4/13

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

whats 358 divided by 3 useing compatible numbers

Answers

The answer is 119.333333333

What is the equation of the following graph in vertex form?

parabolic function going down from the left and turning at the point negative one comma zero and going up through the point zero comma one and continuing towards infinity
Courtesy of Texas Instruments

y = (x − 1)2
y = (x − 1)2 + 1
y = (x + 1)2 − 1
y = (x + 1)2

Answers

Correct answer is D.

Graph passes through the point (-1, 0).
Therefore, x = -1 and y = 0.

[tex]y=(x+1)^2 \\0=(-1+1)^2 \\0=0^2 \\0=0 \;\; \text{T}[/tex]

This is the only equation which is true for x = -1 and y = 0.
Therefore, the solution is [tex]y=(x+1)^2[/tex]

Answer:

y = (x + 1)^2

Step-by-step explanation:

I used desmos and put each answer choice into the graphing calculator and answer choice D was the only one that matched with the image in the question.

make h the subject of the formula

t=gh/10

Answers

given t=gh/10
gh=10t
h=10t/g

Final answer:

To make 'h' the subject of the formula, multiply both sides by 10 to get the equation 10t = gh. Then divide both sides by 'g' to get h = 10t/g.

Explanation:

The formula given in the question is t = gh/10. To make h the subject of the formula, we'll need to isolate it. To do this, you should start off by multiplying both sides of the equation by 10, thus removing the divide by 10 part. This will give you 10t = gh. Finally, divide both sides of the equation by g. So, your revised formula would be h = 10t/g. This formula now clearly places h as the subject.

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Three friends agree to save money for a graduation road trip. They decide that each of them will put $0.25 in the fund on the first day of May, $0.50 on the second day, $0.75 on the third day, and so on. At the end of May, there will be $_____ in their fund. (Hint: There are 31 days in May.)

Answers

Answer: At the end of May, there will be $372.

Explanation:

Since we have given that

On the first day of May, each one save =$0.25

Number of friends = 3

Total save on the first day of May is given by

[tex]0.25\times 3=\$0.75[/tex]

Similarly,

On the second day of May, each one save =$0.25

Total save on the second day of May is given by

[tex]0.50\times 3=\$1.5[/tex]

Similarly,

On the third day of May, each one save =$0.25

Total save on the third day of May is given by

[tex]0.75\times 3=\$2.25[/tex]

This series becomes arithmetic progression,

[tex]0.75,1.5,2.25......[/tex]

Here, a = 0.75

d=common difference is given by

[tex]d=a_2-a_1=1.5-0.75=0.75\\d=a_3-a_2=2.25-1.5=0.75[/tex]

Since there are 31 days in the month of May,

So, n=31

We need to calculate the sum of 31 terms to get our answer,

[tex]S_n=\frac{n}{2}(2a+(n-1)d)\\\\S_{31}=\frac{31}{2}(2\times 0.75+(31-1)\times 0.75)\\\\=\frac{31}{2}(1.5+30\times 0.75)\\\\=\frac{31}{2}(24)\\\\=31\times 12\\\\=\$372[/tex]

Hence, at the end of May, there will be $372.

Final answer:

The total amount in the fund at the end of May is 239.25.

Explanation:

To find the total amount of money in the fund at the end of May, we need to calculate the sum of the money put into the fund on each day. The students decide to put 0.25 on the first day, 0.50 on the second day, 0.75 on the third day, and so on. This is an arithmetic sequence, where the first term (a) is 0.25 and the common difference (d) is 0.25. The formula to find the sum of an arithmetic sequence is:

S = (n/2)(2a + (n-1)d)

In this case, n = 31 (since there are 31 days in May), a = 0.25, and d = 0.25. Plugging these values into the formula, we get:

S = (31/2)(2 * 0.25 + (31-1) * 0.25) = 239.25

Therefore, at the end of May, there will be 239.25 in their fund.

Convert 41,650,000 to scientific notation.

Answers

Hi , the answer is 4.165x10*7.

In scientific notation, the whole number is between 1 to 10. So the number will be 4.165 and then we multiply by the appropriate power of 10.
4.165 x 10⁷

Given the following:

29 day billing cycle
4/17 Billing date previous balance $1,100
4/27 Payment 700
4/29 Charge 300
5/7 Payment 60

The average daily balance is:
$910.34
$755.17
$810.43
$755.71
None of these

Answers

Final answer:

The average daily balance for the given billing cycle is calculated by summing the product of each daily balance and the length of time it was held, and then dividing by the number of days in the billing cycle. After doing this, the average daily balance comes out to be $755.17.

Explanation:

The subject of this question is finance and it involves calculating the average daily balance for a billing cycle. In this method, the daily outstanding balances are added together and then divided by the total number of days in the billing period.

Here, the billing cycle lasts for 29 days, from 4/17 to 5/17.

From 4/17 to 4/26 (10 days), the balance was $1,100.From 4/27 to 4/28 (2 days), the balance was reduced by $700, therefore, it was $400.From 4/29 to 5/6 (8 days), the balance increased by $300, so became $700.From 5/7 to 5/17 (11 days), the balance was reduced by $60, therefore, it was $640.

Like this, you calculate the balance for each portion of the billing cycle, then multiply each by the number of days that balance was held, add those up, and finally, divide by the number of days in the billing cycle:

((1100*10) + (400*2) + (700*8) + (640*11)) / 29 = $755.17

Therefore, the average daily balance is $755.17.

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Select all ratios equivalent to 21:14.
14:10, 8:4, 9:6, 12:21

Answers

the ratio 21:14 when divided by 7 on each side, is the smallest ratio that has the same value as 21:14. this becomes 3:2

then multiply both sides by a few different numbers on both sides each ,

for example, 3:2 is the same as
6:4 (3:2 times 2)
9:6 (3:2 times 3)
12:8 (3:2 times 4)
15:10 (3:2 times 5) and so on
the ratio of the right number I
divided by the left on all of them is 1.5

so,
14/10 equals 1.4 (nope)
8/4 equals 2 (nope)
9/6 equals 1.5 (yay)
12/21 equals 0.57 (Lol)

So your answer is 9:6

Point M is the midpoint of segment QR. If QM = 16 + x and MR = 2(x + 2), find the length of QM.

Answers

just add them
QM+MR=QR
16+x+2(x+2)=QR
16+x+2x+4=QR
20+3x=QR

7x-5y=20 in slope intercept form

Answers

slope inercept
solve for y

mnus 7x both sides

-5y=-7x+20
divide both sides by -5
y=7/5x-4

Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y-7x)= 7x^2-10y^2-2x What error did Marcus make?

A: He combined the terms 5x and –7x incorrectly.
B: He combined the terms 3x^2 and 4x^2 incorrectly.
C: He combined the terms –2y^2 and 12y^2 incorrectly.
D: He subtracted the polynomials instead of adding.

Answers

we have

[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)[/tex]

Combine like terms

[tex](3x^{2} -2y^{2}+5x)+(4 x^{2}+12y^{2}-7x)\\=(3x^{2}+4x^{2})+(-2y^{2}+12y^{2})+(5x-7x)\\=7x^{2} +10y^{2}-2x[/tex]

therefore

the answer is the option C

He combined the terms [tex]-2y^{2}[/tex] and [tex]12y^{2}[/tex] incorrectly

Solve logarithm Equation: 3 log5 x-log5 4= log5 16

Answers

Final answer:

To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we use logarithmic properties to combine terms and then solve for x, finding that x = 4.

Explanation:

To solve the logarithmic equation 3 log5 x - log5 4 = log5 16, we can use the properties of logarithms.

First, we rewrite the equation using the property that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us:

log5 x^3 - log5 4 = log5 16.

Next, we utilize the property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. So we can combine the left side of the equation into a single logarithm:

log5 (x^3 / 4) = log5 16.

Now, since the bases of the logarithms are the same, we can equate the arguments of the logarithms:

x^3 / 4 = 16

Solving for x, we multiply both sides by 4 and then take the cube root:

x^3 = 64

Therefore, x = 4, since 4 cubed equals 64.

The complete question is: Solve logarithm Equation: 3 log5 x-log5 4= log5 16 is:

Final answer:

To solve the logarithmic equation, apply the properties of logarithms to simplify and solve for x.

Explanation:

To solve the logarithmic equation, we can use the properties of logarithms. First, let's apply the property that states the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers. This gives us: 3 log5 x - log5 4 = log5 16. Next, we can apply the property that states the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number. This gives us: log5 x3 - log5 4 = log5 16. We can simplify the equation by combining the logarithms and solving for x.

x3 / 4 = 16

x3 = 64

x = 4

Please help me understand how to do this!

In ΔRST shown below, segment SU is an altitude:

What property or definition is needed to prove that ΔRUS is similar to ΔSUT?

Answers

it would be answer choice 3

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that in ΔRST , segment SU is an altitude. It means the angle SUR and angle SUT are right angles.

It triangle RST and SUT,

[tex]\angle RST=\angle SUT=90^{\circ}[/tex] (Definition of altitude)

[tex]\angle STR=\angle UTS[/tex] (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

[tex]\triangle RST\sim \triangle SUT[/tex] .... (1)

It triangle RST and RUS,

[tex]\angle RST=\angle SUR=90^{\circ}[/tex] (Definition of altitude)

[tex]\angle SRT=\angle URS[/tex] (Common angle)

Two corresponding angles are equal. So by AA property of similarity,

[tex]\triangle RST\sim \triangle RUS[/tex] .... (2)

According to transitive property of equality,

if a=b and b=c, then a=c.

From (1) and (2), we get

[tex]\triangle RUS\sim \triangle SUT[/tex] ( Transitive property of equality)

Therefore the correct option is 1.

4n³·2n²=?
Simplify your answer.

Answers

8 to the 5th multiply and just add the exponents. I could not write the exponent but you get what i mean.

All real numbers that are greater than or equal to -1.5 and less than 9.2

Answers

-5.2 is yo answer hope i helped

lets write condition after condition and than merge them.

All real number greater or equal to -1.5
let x be some real number

we write:
x[tex] \geq [/tex]-1.5

all real numbers less than 9.2

x < 9.2

if we merge them together we can write:
[tex]-1.5 \leq x\ \textless \ 9.2[/tex]

which equation in standard form has a graph that passes through the point (-4 , 2) and has a slope of 9/2?
A. 9x-2y=36
B. 9x-2y=26
C. 9x-2y=-40
D. 9x-2y=-10

Answers

answer is C. 9x-2y=-40

hope that helps

because y = 9/2x +20 then 2y = 9x + 40 so 9x -2y = -40

The equation in standard form passing through (-4, 2) with a slope of 9/2 is 9x - 2y = -10.

Since the equation is in standard form, rearrange it to slope-intercept form y = mx + b.

Given slope m = 9/2 and point (-4, 2), substitute these values to find the correct equation.

After substitution, the equation is 9x - 2y = -10.

A scale on a blueprint is 1 inch = 5 feet. What is the length of an object that is 8 1/2 inches long on the blueprint

Answers

Final answer:

To find the actual length of the object, multiply the length on the blueprint by the scale factor of 5 feet/inch. The length of the object in actual size is 42 feet 6 inches.

Explanation:

To find the actual length of the object represented on the blueprint, we can use the scale factor provided. The scale on the blueprint is 1 inch = 5 feet. So, if the object is 8 1/2 inches long on the blueprint, we can multiply it by the scale factor to find the actual length.

Step 1:

Convert 8 1/2 inches into a mixed number fraction by adding 1 to the whole number.
8 1/2 inches = 8 + 1/2 = 17/2 inches

Step 2:

Multiply the length on the blueprint by the scale factor:
17/2 inches * 5 feet/inch = 85/2 feet

Step 3:

Simplify the fraction if possible:
85/2 feet = 42 feet 6 inches

Therefore, the length of the object in actual size is 42 feet 6 inches.

Final answer:

To find the actual length of an object that is 8 1/2 inches long on a blueprint with a scale of 1 inch = 5 feet, you multiply 8.5 by 5, resulting in an actual length of 42.5 feet.

Explanation:

If the scale on a blueprint is 1 inch = 5 feet, then to determine the actual length of an object that is 8 1/2 inches long on the blueprint, we simply multiply the length on the blueprint by the scale factor.

So, for every inch on the blueprint, there are 5 feet in reality. Therefore, we calculate the actual length as follows:

Multiply 8 1/2 inches by the scale factor, which is 5 feet per inch.8.5 inches * 5 feet/inch = 42.5 feet.

Thus, the actual length of the object is 42.5 feet.

Write a quadritic equation in standard form that has the roots of 5 and -2

Answers

We'll generalize the situation. Imagine that you want a quadratic equation that has the roots a and b. Then, your equation will be in the form: [tex]A(x-a)(x-b)=0[/tex], where [tex]A\neq0[/tex] is a constant.
Notice that if x=a or x=b the equation is true. To simplify, we'll choose A=1. In that problem, a=5 and b=-2. Hence:

[tex]1(x-5)(x-(-2))=0\iff (x-5)(x+2)=0\iff\\\\x^2-3x-10=0[/tex]

Final answer:

To find the quadratic equation with roots 5 and -2, we can use the quadratic formula. Substituting the values of the roots into the formula, we get the equation (x - 5)(x + 2) = 0.

Explanation:

A quadratic equation in standard form is written as ax² + bx + c = 0, where a, b, and c are constants. To find the equation with roots 5 and -2, we can use the fact that the solutions of a quadratic equation are given by the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values of the roots into the quadratic formula, we have:

x = (-b ± √(b² - 4ac)) / (2a)

For the first root, x = 5:

5 = (-b ± √(b² - 4ac)) / (2a)

Substituting a = 1, b = -7, and c = 10, we get:

5 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))

Simplifying further:

5 = (7 ± √(49 - 40)) / 2

5 = (7 ± √9) / 2

5 = (7 ± 3) / 2

So, the first root gives us the equation:

x = 5, which translates to x - 5 = 0.

For the second root, x = -2:

-2 = (-b ± √(b² - 4ac)) / (2a)

Substituting a = 1, b = -7, and c = 10, we get:

-2 = (-(-7) ± √((-7)² - 4(1)(10))) / (2(1))

Simplifying further:

-2 = (7 ± √(49 - 40)) / 2

-2 = (7 ± √9) / 2

-2 = (7 ± 3) / 2

So, the second root gives us the equation:

x = -2, which translates to x + 2 = 0.

Therefore, the quadratic equation in standard form with roots 5 and -2 is:

(x - 5)(x + 2) = 0

In the figure below what is the name of the angle formed by two rays QR and QP? What is the common. endpoint,for this angle?

Answers

The common endpoint is Q. The angle is: angle RQP, angle PQR, or just angle Q

over the course of a lifetime about how much more does a college graduate earn than someone who does not have a college degree

a. $450,000
b. $600,000
c. $750,000
d. $900,000

Answers

C or 750,000 because lol thats just what it is, you can look it up

Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2

Answers

Well knowing that the terminal arm of the standard position angle is in quadrant 2, we can determine the reference angle, in quadrant 2, by simply taking the difference between 180 and whatever the angle is.

So ø reference = 180 - ø in standard position.

Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.

Solve for adjacent side using Pythagoras theorem.

A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.

Then write the cos ratio using the new side.

Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.

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