========================================================
Explanation:
Consecutive even integers are things like 2,4,6,8 or 20,22,24,26
Each number is even and the numbers follow one after another.
Let x be the first even number. The next even number is x+2
Based on the fact that "five times the first equals four times the second", we can then write the equation of 5x = 4(x+2)
Let's solve for x.
5x = 4(x+2)
5x = 4x+8
5x-4x = 8
x = 8 is the first even number
x+2 = 8+2 = 10 is the second even number
------------
Check:
5*(first) = 4*(second)
5*8 = 4*10
40 = 40
The answers work out.
Two consecutive even integers such that five times the first equals four times the second are 8 and 10.
Let us suppose the first integer as a,
Then the second consecutive even integer would be a+2
from the question, it is evitable that,
5a = 4(a+2)
5a = 4a + 8
a = 8
Therefore first even integer is 8.
The second even integer will be,
a+2
8+2 = 10
Cross verifying:
5 × 8 = 40
4 × 10 = 40
Hence the two consecutive even integers such that five times the first equals four times the second are 8 and 10.
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Find the length of AC¯¯¯¯¯¯¯¯A. 33.13B. 377.19C. 378.63D. 2.89
The trigonometry ratios are
[tex]\begin{gathered} SinD=\frac{AK}{KD} \\ \\ tanD=\frac{AK}{AD} \\ \\ tanK=\frac{AD}{AK} \\ \\ cosK=\frac{AD}{KD} \end{gathered}[/tex]AD = 31
AK = 24
Since we do not have the length of KD, then
The value of sinD and cosK are wrong
Let us find tanD and tanK to check which one is right
[tex]tanD=\frac{24}{31}[/tex]But the given value is 31/24, then tanD is wrong
[tex]tanK=\frac{31}{24}[/tex]It is the same with the given value
The correct option is C
The owners of a house want to knock down the wall between the kitchen and the family room.
The area of the family room is x² + 10 + 24 and the area of the kitchen is x² + 7x + 12. Write an
expression that represents the area of the new combined space.
Answer:
[tex]2x^2+7x+46[/tex]
Step-by-step explanation:
[tex](x^2+10+24)+(x^2+7x+12) \\ \\ =x^2+34+x^2+7x+12 \\ \\ =2x^2+7x+46[/tex]
fing the square root of 225 with process class 5
The Square root of 225 is 15
What is division ?The act of repeatedly subtracting is called division. It functions in the opposite way to how multiplication works. Forming equal groups is how it is described. When dividing numbers, we split a larger number into smaller ones so that the product of the multiplication of those smaller numbers equals the larger number that was divided. As an illustration, 4 2 = 2. This knowledge can be expressed as the multiplication 2 x 2 = 4.
Given that :Square root of 225
225 = 3 × 75
225 = 3 × 3 ×25
225 = 3 ×3 × 5 ×5
225 = 3² × 5²
225 = (3 × 5)²
225 = 15²
√225 = 15
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in
ABC, ABC is a right angle AB=3 units, and BC=2 units &ABC is dilated by a scale factor of 0.5 with point 8 as the center of dilation, resulting
in the image AABC. Which statement about AB is true?
OA AB is 15 units long but lies on a different line than AB
OB AB is 3 units long but lies on a different line than AB
OC AB is 3 units long and lies on the same line as AB
OD. AB is 1.5 units long and lies on the same line as AB?
Answer:
A'B' is 1.5 units long and lies on the same line as AB.
Step-by-step explanation:
If AB = 3 units, BC = 2 units and a scale factor of 0.5 is applied, then A'B = 3*0.5 = 1.5 and B'C = 2* 0.5 = 1. Given that the point B is taken as the center of dilation then, segments A'B lies on the same line as AB and B'C lies on the same line as BC.
provide the correct reason for the statement in line 3. (please help)
The property that completes the proof is the segment addition postulate
How to determine the statement that represents the reason in the proof?The given parameters in the question are:
The point C is the midpoint of AE
BC = CD
The above implies that
AC = CE
And it also means that:
The line segment BC and the line segment CD have equal lengths
Using the above as a guide, we have the following equations
AB + BC = AC
CD + DE = CE
The above equations are true because of the segment addition postulate
This postulate states that:
For any two points (A and C) located on a line segment and a third point (b) between the initial points. The lengths between the points can be represented as AB + BC = AC
Hence, the statement that represents the reason 3 in the proof is (b) segment addition postulate
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A candy company developed a new consumer product that is expected to earn $3,000 in profit each year if consumer demand is low, $19,000 per
year if consumer demand is moderate, and $31,000 per year if consumer demand is high. The probability of low, moderate, and high demand is
35%, 45%, and 20%, respectively. Determine the expected monetary value (EMV) for the new product.
The most appropriate choice for probability and profit will be given by:
Expected monetary value is $15800
What is probability and profit?
Probability of an event is the chance of occurance of that event.
Probability can be obtained by Number of favourable outcomes divided by the total number of outcomes
Probability varies from 0 to 1.
If the selling price of an item is more than its cost price, difference between the selling price and the cost price gives the profit.
Profit if consumer demand is low = $3000
Profit if consumer demand is moderate = $19000
Profit if consumer demand is high = $31000
Probability of low demand = 35%
Probability of moderate demand = 45%
Probability of high demand = 20%
Expected monetary value = $([tex]3000 \times \frac{35}{100}+19000 \times \frac{45}{100}+ 31000 \times \frac{20}{100}\\[/tex])
= $([tex]1050 + 8550+6200[/tex])
= $[tex]15800[/tex]
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If 2 tan x 1- tan2 x 1 V3 then x can equal: + MT B. X= A. x=112 x- 7 C. X = ST D. X=
Solve for x
[tex]\frac{2\tan (x)}{1-tan^2(x)}=\frac{1}{\sqrt[]{3}}[/tex]Step 1: Let tan(x) represent y
[tex]\begin{gathered} \frac{2y}{1-y^2}=\frac{1}{\sqrt[]{3}} \\ \text{cross multiply} \\ 1-y^2=2\sqrt[]{3}y \\ y^2+2\sqrt[]{3}y-1=0 \end{gathered}[/tex]Step 2: Using quadratic equation solve for y
[tex]\begin{gathered} y^2+2\sqrt[]{3}y-1=0 \\ y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ a=1,b=2\sqrt[]{3},c=-1 \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{(2\sqrt[]{3})^2-4(1)(-1)}}{2(1)} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{12+4}}{2} \\ y=\frac{-2\sqrt[]{3}\pm\sqrt[]{16}}{2} \\ y=\frac{2(-\sqrt[]{3}\pm2)}{2} \\ y=-\sqrt[]{3}\pm2 \end{gathered}[/tex]Since the y represents tan x
[tex]\begin{gathered} \tan \mleft(x\mright)=-\sqrt{3}-2,\: \tan \mleft(x\mright)=2-\sqrt{3} \\ x=\arctan \mleft(-\sqrt{3}-2\mright)+\pi n,\: x=\arctan \mleft(2-\sqrt{3}\mright)+\pi n \\ x\text{ in degrees} \\ \: x=-75^{\circ\: }+180^{\circ\: }n,\: x=15^{\circ\: }+180^{\circ\: }n \\ \: x=15^{\circ\: }+180^{\circ\: }n \end{gathered}[/tex]Therefore the correct answer is
[tex]x=\frac{\pi}{12}+n\pi[/tex]Hence the correct answer is Option B
Which equation represents this graph?
In the picture there is a graph with one line. The equation of the line is x+2y=1.
Given that,
In the picture there is a graph with one line.
We have to find the equation of the line in the graph.
The points on line are (2,1) and (0,3).
The slope of the line formula is
m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(3-2)/(0-2)
m=1/(-2)
m=-1/2
The equation of the line formula is y=mx+b
Take point (2,1) as (x,y).
2=(-1/2)1+b
1=-1/2+b
b=1-1/2
b=2-1/2
b=1/2
The equation of the line is y=-1/2x+1/2
2y=-x+1
x+2y=1
Therefore, the equation of the line is x+2y=1.
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12 eggs cost 3 dollers how much is one egg
Work Shown:
12 eggs = 3 dollars
12/12 eggs = 3/12 dollars
1 egg = 0.25 dollars
1 egg = 25 cents
Answer:
.25 cents
Step-by-step explanation:
3/12= .25
.25 x 12= 4.00
Question
Two sides of a right triangle have lengths of 5 inches and 12 inches. Which of the following could be the
length, in inches, of the third side of the triangle?
A 3
B 8
C 13
D 17
How do u determine the value of the ratio?
Answer:
Step-by-step explanation:
Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.
You drive 2 hours to the lake. Driving home on the same route, you decrease your speed by 25
miles per hour, increasing your drive time by 2 hours. Write and solve an equation to find how
fast you were driving to the lake.
Equation:
Solution:
Velocity differs from speed. Distance divided by time is the dimension of speed.
The speed of the vehicle while driving from home to the lake was 50 miles per hour.
What is Speed?The speed of an object, sometimes known as "v" in daily speech and kinematics, is a scalar quantity that measures how much its position changes over time or how much it changes per unit of time. The distance traveled by an object during a time interval is equal to the duration of the interval divided by the object's speed, with the instantaneous speed being the upper limit of the average speed as the interval's duration becomes closer to zero. Velocity differs from speed. Distance divided by time is the dimension of speed. The meter per second (m/s) is the SI unit of speed, although the kilometer per hour (km/h) or, in the US and UK, miles per hour, is the most widely used measure in daily life (mph). The knot is a popular choice for air and sea travel.From Home to Lake,
Let the speed of driving be 'x' miles per hour,
Time taken = 2 hours
Speed = Distance/Time
⇒ Distance = Speed x Time = 2x ..................(1)
From Lake to Home,
Distance will be the same (as the same route is taken),
Speed = (x-25) miles per hour
Time = 2 + 2 = 4 hours
So, Distance = Speed x Time = 4(x-25) ....................(2)
On equating (1) and (2),
2x = 4(x-25)
simplifying the above equation, we get
⇒ 2x = 4x - 100
⇒ 4x - 2x = 100
⇒ 2x = 100
⇒ x = 100/2
⇒ x = 50
Therefore, the speed of the vehicle while driving from home to the lake was 50 miles per hour.
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heyyyyyyyyyyyyyyyyyyy
The statement says that Kristen read a total of 18 books over 3 months.
And then ask us to calculate the numbers of books that he will read in a period of 5 months.
In order to calculate that, we must determine first how many books Kristen read in a month.
# of books that Kristen read in a month = 18 books / 3 months = 6 books / month
So, in order to calculate the number of books that Kristen read in 5 month, we just multiply:
5 months * 6 books/month = 30 books (answer)
I WILL GIVE YOU BRAINLIEST PLEASE HELPPPP
What is the sign of (-2)³? What is the sign of (-3)²? Justify your answers.
Based on the given bases with powers, the sign of (-2)³ is negative.
The sign of (-3)² can be found to be positive.
The justification for the signs can be found below.
How to find the sign?When multiplying two negative numbers, the result would be a positive number. When multiplying positive number by a negative number, the result would be negative.
(-2)³ is the same as -2 x -2 x -2 which is:
= -2 x -2 x -2
= 4 x -2
= -8
4 became positive but then became negative when multiplied by another -2.
(-3)² is 3 x 3:
= 3 x 3
= 9
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Find the LCD for:
2/x²-x-12, 1/x² - 16
The LCD for the expressions is (x + 3)(x² - 16)
How to calculate the LCD for the expressions?The expressions are given as
2/x² - x - 12 and 1/x² - 16
Write out the denominator of the expressions
This is represented as
x² - x - 12 and x² - 16
Factorize the above denominators
This gives
x² - x - 12 = (x+3)(x-4)
x² - 16 = (x-4)(x+4)
Multiply the common factors without repetition
LCD = (x+3)(x-4)(x+4)
Evaluate the products
LCD = (x + 3)(x² - 16)
Hence, the LCD in this case is (x + 3)(x² - 16)
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The parent function f(x)=3√x is transformed to g(x)=f(x+2)-4 which is the graph of g
What is the rate of return when 10 shares of Stock
A, purchased for $30/share, are sold for $380? The
commission on the sale is $6.
Rate of Return = [?] %
Give your answer as a percent rounded to the
nearest tenth.
Answer:
24.7%
Step-by-step explanation:
You want to know the rate of return if 10 shares of stock purchased at $30 per share are sold for $380 with a commission on the sale of $6.
ReturnThe net proceeds from the sale will be ...
$380 -6 = $374
Rate of returnThe percentage change in stock value is ...
% change = (proceeds/cost -1) × 100%
% change = (374/300 -1) × 100% ≈ 24.7%
The rate of return on the stock is about 24.7%.
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What is the area, in square inches, of a square whose perimeter is 44 inches?
The area is 121 square inches
Explanation:The perimeter of a square is given as:
P = 4l
where l is the length of its sides
Given that the perimeter is 44 inches, we have:
44 = 4l
l = 44/4 = 11
The length of it's sides is 11 inches.
The area is given as:
[tex]\begin{gathered} A=l^2 \\ \\ =11^2 \\ =121 \end{gathered}[/tex]The area is 121 square inches.
Answer:121 square inches.
Step-by-step explanation:
Help please!!!!!!!!!!!!!
Answer the question.
A juice drink contains 24% real fruit juice. Find the amount of real fruit juice in 8 ounces of the drink. (Include units in your answer. More information.)
Answer:
i think it is 24.76% of real jucie
Step-by-step explanation:
because the rest is not real jucie
PLS HELP I NEED IT IM GOING TO GET AGRDE ON THIS PLE HELP
Answer: The answer is 6 presents
Step-by-step explanation: Here is the math: He used 25 cm of tape to wrap 5 presents, so that is 25/5= 5 cm of tape per present. Now you take 30 cm of tape and divide it by 5 = 6 presents wrapped with 30 cm of tape.
What’s the correct answer answer now for brainlist
the answer to this would be D
−5x≤−15 or 7x−17≥32 please help me!!! This is due tonight and I need to get my grade up because I have under 60% in math class!! :(
Answer:1. x≥3 2. x≥7
Step-by-step explanation:
Lin drew the following dilation of triangle AED and she made triangle ABC
What is The center of dilation is ?
The Scale factor for triangle AED to triangle ABC is?
1. A, as A is the shared vertex of both triangles. and 2. The original is ABC, and the dilated version is AED. as triangle ABC's half is represented by triangle AED.
How do you calculate a triangle's dilation?The following is a basic formula to determine a dilated figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.
What is the triangle's center of dilation?A fixed point in the plane around which all points are enlarged or contracted is the center of a dilation.
The center, which may be found within, outside, or on a figure, is the only invariant (constant) point under a dilation (k 1).
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If 37% of high school students said that they exercise regularly, find the probability that 5 randomly selected high school students will say that they exercise regularly. Would you consider this event likely or unlikely to occur?
Very unlikely to occur
1) In this problem, let's find the binomial probability of that event to take place.
[tex]\begin{gathered} P(X=5)=\binom{5}{5}(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=1\cdot(0.37)^5(1-0.37)^{5-5}= \\ P(X=5)=0.37^5\mleft(0.63\mright)^{5-5} \\ P(X=5)=0.0069343957 \end{gathered}[/tex]2) Note the binomial probability of that event happening is very very low.
3) So we can state that this event is very unlikely to occur
Question 1 (1 point)
write an equation (slope-intercept form) of the line
passing through the point (-20, 4)
that is perpendicular to the line
2x + 5y = 10.
y =
Blank 1:
The an equation (slope-intercept form) of the line is 2y = 5x + 108.
What is described as the slope-intercept form?A line's equation can be written in a variety of ways, each of which is valid. The slope-intercept form of such a line is a way of writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, and the y-intercept is the point where line intersects the y-axis.For the given question;
The equation of the perpendicular line is given as 2x + 5y = 10.
The passing points of the line (-20, 4)
(x₁, y₁) = (-20, 4)
The equation of line in slope-intercept form is given as; y = mx + c.
Where, c is the y intercept and m is the slope.
The relation of the slope of two perpendicular lines are-
m₁ x m₂ = -1
The equation of line is-
2x + 5y = 10; find m₁
5y = -2x + 10
y = (-2/5)x + 10
Comparing with standard form.
m₁ = (-2/5)
Then, m₁ x m₂ = -1
(-2/5) x m₂ = -1
m₂ = 5/2
Put in the equation of line;
y - y₁ = m(x - x₁)
Put the values;
y - 4 = (5/2) (x + 20)
Solving;
2y - 8 = 5x + 100
2y = 5x + 108
Thus, the an equation (slope-intercept form) of the line is 2y = 5x + 108.
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This graph shows a proportional relationship.500450400350300Words2502001501005023455670010Time (minutes)What is the unit rate shown by the graph?75 minutes per word1.25 minutes per word1.25 words per minute75 words per minute
In the graph we can see that the person wrote 300 words after 4 minutes. so the rate is:
[tex]\frac{300}{4}=75[/tex]75 words per minute
The value of the 1 digit in 13,089 is how much greater that the value of the digit one in 30,124
For 13,089 - the value of the digit 1 is ten thousand or 10,000
For 30,124 - the value of the digit 1 is one hundred or 100
Therefore:
[tex]\frac{10000}{100}=100[/tex]Answer: the value of the digit 1 in 13,089 is 100 times greater than the value of the digit 1 in 30,124
What is the reason for each step in the solution of the equation?
4x−1=−2(x+1)