Answer:
- False
- True
- false
Step-by-step explanation:
- The variable that changes is the price
- 30 is the slope and 6 is the y-int
- 30(.75) + 6 = 28.5
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer.
It is proven that "the sum of the squares of four consecutive integers is an even integer" is the solution part.
To prove that the sum of the squares of four consecutive integers is an even integer, we need to show that it can be expressed as twice another integer.
Let's assume the four consecutive integers are n, n+1, n+2, and n+3.
The sum of their squares can be expressed as:
[tex]n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2[/tex]
Expanding the squares, we have:
[tex]n^2 + (n^2 + 2n + 1) + (n^2 + 4n + 4) + (n^2 + 6n + 9)[/tex]
Combining like terms, we simplify this expression to:
[tex]4n^2 + 12n + 14[/tex]
Now, let's consider this expression [tex]4n^2 + 12n + 14[/tex].
We can factor out 2 from each term, resulting in:
[tex]2(2n^2 + 6n + 7)[/tex]
Since [tex]2n^2 + 6n + 7[/tex] is an integer, let's denote it as k, where k is an integer.
Therefore, the expression becomes:
2k.
We have successfully expressed the sum of the squares of four consecutive integers as twice another integer (2k), which proves that it is an even integer.
Hence, the sum of the squares of four consecutive integers is an even integer.
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In the equation A = bh,
СС
what does each of the
variables stand for?
Answer:
A= Area
B= Base of the figure
H= Height of the figure
B and H are multiplied together to find the area
Step-by-step explanation:
(-9,-13) , [7 1/2, 3 1/2], (5,1), (4,0), (0,__)
what is the next number?
Answer:
56
Step-by-step explanation:
Nearly two out of ten American women end their childbearing years without having borne a child. What percent of American women end their childbearing years without having borne a child?
Answer:
20%
Step-by-step explanation:
Turn 2 out of 10 into a percentage.
[tex]\frac{2}{10}[/tex] × [tex]\frac{10}{10}[/tex] = [tex]\frac{20}{100}[/tex] → 20%
If m∠NLO = 41° and m∠NLM = 88°, what is m∠OLM? 47° 44° 129° 23°
Answer:
∠ OLM = 47°
Step-by-step explanation:
Given:
∠ NLO = 41°
∠ NLM = 88°
Find:
∠ OLM
Computation:
⇒ ∠ NLM = ∠ NLO + ∠ OLM
⇒ 88° = 41° + ∠ OLM
⇒ ∠ OLM = 88° - 41°
⇒ ∠ OLM = 47°
Answer:
47
Step-by-step explanation:
Solve for m.
5m + 3m - 8 = 64
a m = 9
b m = 2
c m = -2
d m = 5
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 9}}}}}[/tex]
Option A is the correct option
Step-by-step explanation:
[tex] \sf{5m + 3m - 8 = 64}[/tex]
Collect like terms
⇒[tex] \sf{8m - 8 = 64}[/tex]
Move 8 to right hand side and change it's sign
⇒[tex] \sf{8m = 64 + 8}[/tex]
Add the numbers
⇒[tex] \sf{8m = 72}[/tex]
Divide both sides of the equation by 8
⇒[tex] \sf{ \frac{8m}{8} = \frac{72}{8} }[/tex]
Calculate
⇒[tex] \sf{m = 9}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex]\Huge \boxed{m=9}[/tex]
Step-by-step explanation:
[tex]5m + 3m - 8 = 64[/tex]
Combining like terms.
[tex]8m - 8 = 64[/tex]
Adding 8 to both sides.
[tex]8m=72[/tex]
Dividing both sides by 8.
[tex]m=9[/tex]
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°
x°=
(x+5)°=
5X°=
Answer:
[tex] \boxed{ \bold{ \sf{x = 25°}}}[/tex]
[tex] \boxed{ \bold{ \sf{(x + 5) = 30°}}}[/tex]
[tex] \boxed{ \bold{ \sf{5x = 125°}}}[/tex]
Step-by-step explanation:
We know that sum of angle of triangle adds up to 180°
Finding the value of x
[tex] \sf{5x + x + x + 5 = 180°}[/tex]
Collect like terms
⇒[tex] \sf{7x + 5 = 180}[/tex]
Move 5 to right hand side and change its sign
⇒[tex] \sf{7x = 180 - 5}[/tex]
Subtract 5 from 180
⇒[tex] \sf{7x = 175}[/tex]
Divide both sides of the equation by 7
⇒[tex] \sf{ \frac{7x}{7} = \frac{175}{7} }[/tex]
Calculate
⇒[tex] \sf{x = 25°}[/tex]
Finding the value of ( x + 5 )°
[tex] \sf{x + 5}[/tex]
plug the value of x
⇒[tex] \sf{25 + 5}[/tex]
Add the numbers
⇒[tex] \sf{30°}[/tex]
Finding the value of 5x
[tex] \sf{5 \times 25}[/tex]
Multiply the numbers
⇒[tex] \sf{125°}[/tex]
Hope I helped!
Best regards!!
Answer:
x° = 25°
(x + 5)° = 30°
5x° = 125°
Step-by-step explanation:
total angle inside the triangle = 180 = x + (x+5) + 5x
180 = x + x + 5 + 5x
group like terms
7x + 5 = 180
subtract 5 each sides
7x = 175
x = 175/7
x = 25°
solve for : (x + 5)°
(x + 5)° = 25 + 5
(x + 5)° = 30°
solve for 5x°
5x° = 5 * 25
5x° = 125
check
180 = x + (x+5) + 5x
180 = 25 + (25+5) + (5*25)
180 = 25 + 30 + 125
180 = 180
Which number line can you use to simplify 2 + (–8)?
Answer:
D
Step-by-step explanation:
The question has 2 + (-8), and in the timeline, your starting point has to be in positive 2. As for the -8, the negative goes to the left, and therefore your answer is D, as that is the only timeline that follows the instructions of the question,
Answer:
[tex]\Huge \boxed{\mathrm{D}}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
2 + ( -8 )
2 is on the number line.
When -8 is added to 2, the value decreases, and it moves 8 units to the left side.
The result is -6.
[tex]\rule[225]{225}{2}[/tex]
Two brown and 8 red birds are flying. What is the probability that two brown sit together?
The probability that two brown sit together is 0.2.
What is the meaning of arrangements?
the act of putting things in order
Here, it is given that ;
there are Two brown and 8 red birds.
Total number of ways 10 distinct birds can sit = 10!
Now,
When out of total arrangement the number of ways in which two brown birds and 8 red birds can sit is :
¹⁰C₂ = 10!/ (2! x 8!)
¹⁰C₂ = 45 ways
Now, consider two brown birds as one bird then the number of arrangement will be :
⁹C₁ = 9!/1! = 9
The probability that two brown sit together will be :
9/45 = 0.2
Therefore, the probability that two brown sit together is 0.2.
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six times a number x squared
Answer:
6x^2
Step-by-step explanation:
Because we are multiplying 6 and a number x squared, we know that x will have an exponent of 2. Then, multiplying that by 6 and using conventional algebraic techniques, we can combine the two terms together.
6 * x^2
6x^2
Answer:
[tex]\displaystyle \rm \longmapsto 6 \times x {}^{2} [/tex]
[tex]\displaystyle \rm \longmapsto {6x}^{2} [/tex]
The hypotenuse of a right triangle is 15cm long. One of the triangle’s legs is two times the length of the other leg. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth. 1
Step-by-step explanation:
Given that,
The hypotenuse of a right triangle is 15 cm
Let x is the length of the other leg. So, the length of the first leg is 2x.
Using Pythagoras theorem for the right angle triangle such that,
hypotenuse² = base²+height²
Let base is x and height is 2x
So,
[tex]15^2=x^2+(2x)^2\\\\225=x^2+4x^2\\\\225=5x^2\\\\x^2=45\\\\x=3\sqrt{5} \ cm[/tex]
Hence,
Base = [tex]3\sqrt{5} \ cm[/tex]
Height = [tex]2\times 3\sqrt{5} \ cm=6\sqrt5\ cm[/tex]
Hyoptenuse = 15 cm (given)
Find an equation of the line passing through the point (−6,−5) that is parallel to the line y=4/3x−5
Answer:
y = [tex]\frac{4}{3}[/tex] x + 3
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 )
y = [tex]\frac{4}{3}[/tex] x - 5 ← is in slope- intercept form
with slope m = [tex]\frac{4}{3}[/tex]
Parallel lines have equal slopes, thus
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (- 6, - 5) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = [tex]\frac{4}{3}[/tex] x + 3 ← equation of parallel line
Type the correct answer in the box. The motion of a clock pendulum is modeled by this graph. The function describing this graph is a transformation of the parent cosine function, y = cos x . Find the range, period, and maximum of the transformed function, D(t).
Answer:
The range of the function is -10, 10.
The period of the function is 1.2 seconds.
The maximum of the function is 10 centimeters.
Step-by-step explanation:
The range of a cosine function is the set of output values. In this situation, the range is the distance the pendulum covers, which is represented on the D(t) axis. The graph shows that the range of the function D(t) is [-10, 10].
The period is the length of a cycle. The graph shows that the cycle repeats every 1.2 seconds.
The maximum is the y-value of the highest point on the graph. The graph shows the maximum of the function is 10 centimeters.
If cde is a straight angle, de bisects gdh, m gde = (8x-1), m edh = (6x+15), and m cdf= 43, find each measure.
Answer:
GDE = 63
EDH = 63
GDH = 126
FDG = 74
FDH = 200
FDE = 137
Step-by-step explanation:
It is stated that DE bisects <GDH. Since bisecting means halving into equal parts, <GDE = <EDH
from the question,
<GDE = (8x-1)
<EDH = (6x+15)
Since <GDE = <EDH,
(8x-1) = (6x+15), if we collect like terms
8x - 6x = 15 + 1
2x = 16
x = 8°
Again, from the diagram, we see that
<GDH = <GDE + <EDH, thus
<GDH = (8x-1) + (6x+15)
<GDH = 8x -1 + 6x + 15
<GDH = 14x + 14, substitute for x
<GDH = 14*7 + 14
<GDH = 112 + 14
<GDH = 126°
<FDG = 180 - <CDF - <GDE
<FDG = 180 - 43 - 63
<FDG = 74°
<FDH = <FDG + <GDE + <EDH
<FDH = <FDG + <GDH
<FDH = 74 + 126
<FDH = 200°
<FDE = <FDG + <GDE
<FDE = 74 + 63
<FDE = 137°
The measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
The straight angle ∠CDE, DE bisects GDH, m∠GDE=(8x-1)°, m∠EDH=(6x+15)° and m∠CDF=43°.
Here, m∠GDE+m∠EDH+m∠CDF = 180°
So, (8x-1)°+(6x+15)°+43°=180°
14x+57°=180°
14x=180°-57°
14x=123
x=123/14
x=8.8°
m∠GDE=8x-1
= 71.4°
m∠EDH= 65.6°
Hence, the measure of angle m∠GDE is 71.4° and the measure of angle m∠EDH is 65.6° on straight angle ∠CDE.
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ABCD. If AB=5x and CD=3x + 10, find CD
A. 25
B. 2
C. 5
D. 20
Answer:
c
Step-by-step explanation:
Answer:
A.25
Step-by-step explanation:
set up a skeletal profit and loss statement in boss dollars and percentage if your year-end profit is 7800, the profit percentage is 3.9%, and the yearly cost of your goods sold is 120000
ne s o
Step-by-step explanation:
Seven less than the product of 8 and a number is equal to 5.
Answer:
8n - 7 = 5
Step-by-step explanation:
number - n
product of 8 and a number - 8n
Seven less than the product of 8 and a number - 8n - 7.
Seven less than the product of 8 and a number is equal to 5.
8n - 7 = 5
Answer:
8n-7=5
you can do this
i cand do explaination
solve for x
pleaseee answer and explain <333
Hello! :)
Answer:
[tex]\huge\boxed{x = (\frac{b}{a})(P+c)}[/tex]
[tex]\frac{a}{b}x - c = P[/tex]
Solve for x:
Begin isolating the variable by adding "c" to both sides:
[tex]\frac{a}{b}x - c + c= P + c[/tex]
[tex]\frac{a}{b}x = P+ c[/tex]
Divide both sides by a/b, or multiply by the reciprocal (b/a)
[tex](\frac{b}{a}) \frac{a}{b}x = (\frac{b}{a})(P + c)[/tex]
Therefore:
[tex]x = (\frac{b}{a})(P + c)[/tex]
In a behavioral field study, my colleagues and I found that teams of three
students exercised more than everyone else in the study.
True
False
Answer:
False
Step-by-step explanation:
The given statement is false because behavioral field study deals with the cognitive processes during field study or task.
In the given statement only the physical strength of the students is measured while behavioral field study measures or explores human behavior and how or what techniques are students using to perform the field task.
Hence, the correct option is "False".
A truck leaves Pensacola heading east at 50 mph. One hour later, a second
truck leaves Pensacola heading east at 65 mph. How long will it take the
second truck to overtake the first truck?
Answer:
The answer is 10/3.
Step-by-step explanation:
Think of position. After one hour just as the fast truck starts, the slow truck is at a position 50 miles. Let's see where they aree at time t hours after the fast truck begins his trip: Slow Truck: 50 miles + (50 miles/hour)×t Fast Truck: (65 miles per hour)×t .
What is t when their positions are the same?
50 + 50t = 65t
50 = 65t - 50t
50 = 15t
50/15 = t
10/3 = t
t = 10/3.
This the actual full picture of the question.
Answer:
Center: (4, -6)
Radius: 2
Step-by-step explanation:
Circle Equation: (x - h)² + (y - k)² = r²
(h, k) is center
r = radius
Step 1: Write out equation
(x - 4)² + (y + 6)³ = 4
Step 2: Identify variables
h = 4
k = -6
r² = 4
Step 3: Find answers
Center = (4, -6)
√r² = √4
r = 2
-5, 4, -26, -48, 12 least to greatest
Answer:
hey!
Your answer is ...
-48 , -26 , -5 , 4 , `12
Step-by-step explanation:
HOPE THIS HELPED!
:)
Suppose that a factory worker turns 62 years old and retires from her job. Which statistic is not affected
Answer:
The question is not complete, below is the complete question:
Suppose that a factory worker turns 62 years old and retires from her job. Which statistic is not affected? A. number of unemployed B. unemployment rate C. labor force D. labor-force participation rate
Answer:
The correct andwer is:
number of unemployed (A.)
Step-by-step explanation:
The terms highlighted in the options of the question refer to terms associated with the labour force of an economy. Let us take a look at each of them and justify why we chose the option A
1. Number of unemployed: The number of unemployed in an economy refers to the number of people who are without employement, while actively searching for employment, willing to work and have actively sought for employment in the past four weeks. In this example, a factory worker retiring at 62 is not actively looking for work anymore, hence this transition does not affect the number of unemployed individuals in an economy
2. unemployment rate: The unemployment rate refers to the percentage of labor force that is jobless. Mathematically, it is represented as:
[tex]Unemployment\ rate\ =\ \frac{umemployed}{Labour\ force} \times\ 100[/tex]
In this example, a factory worker retiring at 62, reduces the labor force (number fit to work) in a population, and since the unemployment rate is in turn affected by the labour force (inversely), the unemployment rte is affected by the retiring of the factory worker
3. Labor force: The labor force in an economy are all the individuals who are fit and able to work. It inclues all those who are actively employed and those who are unemployed. A retired factory worker is not part of the labor force, because retirement age disqualifies him/her from being fit to work, hence the retirement reduces the labor force.
4. Labor-force participation rate: This is the coolective numbere of civilians or non-institutional people 16 years or older, who are working or actively looking for work. Retirement reduces the labor-force participation rate
3 to the power of negative 2 is equivalent to what 1/9 1/6 -6 -9
Answer:
1/9
Step-by-step explanation:
You have 3 to the power of -2.You must take that and turn it into 1/3 to the power of 2, so now the exponent is no longer negative and therefore can be solved.After solving the exponent, you are left with 1/9 as your answer.Pls help me with this!!!
Answer:
30.39in^2 (^2 means squared)
Step-by-step explanation:
3 x 3 = 9in^2
3.1 x 6.9 =21.39in^2
9 + 21.39 = 30.39in^2
The tallest man in medical history was Robert Wadlow. He was 12 4/5times as tall as he appears in a Book of Reords photograph. He is 7 1/2 inches tall in the photograph. How tall was Robert Wadlow?
Write an equation in slope-intercept form for the line described. Slope 4, passes through (6,9)
Answer:
y= 4x -15
Step-by-step explanation:
Please see attached picture for full solution.
Mr. Hobbs has 10 blue markers, 6 black markers, and 8 red markers
on his desk. What fraction of black markers can be found on Mr.
Hobbs' desk? thats the question if you could answer that that'd be great.
Answer: 1/4
Step-by-step explanation:
If there are 6 black markers and they are a total combination of 24 difference colored markers.
The the fraction will be 6/24 which reduces to 1/4
please help// geometry question pt.3
Answer:
Last one - CD with a line over it with arrowheads.
Step-by-step explanation:
Last one - CD with a line over it with arrowheads.
How do I find the exact angle for b?
Answer:
107° 30'
Step-by-step explanation:
As in part (a), the hour hand moves 30° per hour, so at 1:25, it has moved ...
(1 25/60)(30°) = 42.5°
from the vertical at noon.
Similarly, the minute hand moves 6° per minute, so at 1:25, it has moved ...
(25)(6°) = 150° from the vertical at 1 o'clock.
The exact angle difference is ...
150° -42.5° = 107.5° = 107° 30'