Step-by-step explanation:
[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ [/tex]
[tex] \because \: time \times speed = distance \\ \therefore \: 4(t + 3) \times 10(t + 3) = 810 \\ \therefore \: 4(t + 3)^{2} = 81 \\ \therefore \: \{2(t + 3) \}^{2} = {9}^{2} \\ \therefore \: \{2(t + 3) \} = {9} \\ \therefore \: t + 3 = \frac{9}{2} \\ \therefore \: t = \frac{9}{2} - 3 \\ \therefore \: t = \frac{9 - 6}{2} \\ \therefore \: t = \frac{3}{2} \\ \therefore \: t = 1.5 \: hrs \\ speed \: of \: car = 10(t + 3) \\ \hspace{60 pt} = 10(1.5 + 3) \\ \hspace{60 pt}= 10 \times 4.5 \\ \red{ \boxed{ \bold{ \therefore \: speed \: of \: car = 45 \:km/ h}}} \\ [/tex]
Why is x = 4 a solution to the proportion StartFraction 14 over x EndFraction = StartFraction 56 over 16 EndFraction?
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{14}{x}[/tex] = [tex]\frac{56}{16}[/tex] ( cross- multiply )
56x = 14 × 16 = 224 ( divide both sides by 56 )
x = 4
Select the correct answer
Psychologists have identified four stages of personality growth. In which stage does a person develop life skills and learn to take initiative?
A
infancy
childhood
B.
c. adolescence
D. adulthood
Reset
Next
Answer:
adolescence
Step-by-step explanation:
The speed limit on a road is 45 miles per hour. What is this rate in miles per minute?
Answer:
0.7499 miles per minute
Step-by-step explanation:
Google "what is 45 mph to minutes"
Answer:
0.7499
Step-by-step explanation:
45 miles per hour
this equals 45/60 miles per minute
which then equals 0.7499
in order to be admitted for a certain ride a an amusement park, a child must be greater than or equal to 36 inches tall and less than 48 inches tall. Draw a number line to represent the following information
Step-by-step explanation:
this one is easy to graph your answer on a number line draw a filled in circle on the number 36 and an open circle on the number 48 then you shaed between the two numbers
The required number line has been attached which represents the given information.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
We have been given that a child must be greater than or equal to 36 inches tall and less than 48 inches tall.
Let the height of the child would be x
According to the given situation, we can write the inequality would be as:
⇒ 36 ≤ x < 48
As per the above inequality, we can draw the required number line.
Thus, the required number line has been attached which represents the given information.
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2. Evelyn has $7. Liz gives her one $5 bill
and two $1 bills. How much money does
Evelyn have now?
Answer:
14 dollars.. hope it helps!
Step-by-step explanation:
7+5+1+1=14
Final answer:
Evelyn initially has $7, and after Liz gives her a $5 bill and two $1 bills, Evelyn's total money becomes $14.
Explanation:
The question asks us to calculate how much money Evelyn has after Liz gives her additional cash. Initially, Evelyn has $7. Liz gives her one $5 bill and two $1 bills. To find out the total amount of money Evelyn has now, we simply need to add the amounts together:
Original amount Evelyn has: $7
Liz gives her: 1 x $5 bill = $5
Plus: 2 x $1 bills = $2
Total amount after receiving money from Liz: $7 + $5 + $2 = $14
Therefore, Evelyn now has a total of $14.
The graph of a proportional relationship passes through (4, 32) and (1, y). Find y.
Answer:
[tex]y = \frac{32}{4} = 8[/tex]
What is the solution set for this inequality?
−8x + 40 > −16
A) x > 7
B) x < 7
C) x > -3
D) x < -3
Answer:
B) x < 7
Step-by-step explanation:
−8x + 40 > −16
Subtract 40 from each side
−8x + 40-40 > −16-40
-8x > -56
Divide each side by -8, remembering to flip the inequality
-8x/-8 < -56/-8
x <7
Jen has 3 times as many stamps Jacks does. Together they have 36 stamps. How many stamps does Jen have
Answer:
Jen has 12 stamps.
Step-by-step explanation:
Answer: Jen has 27 stamps
Step-by-step explanation:
Let the number of stamps Jack has be y.
Since Jen has 3times of Jack stamps, Jack's stamp is 3×y which is 3y.
Jack's stamp+Jen's stamp= 36
y+3y = 36
4y = 36
y = 9
So Jack has 9 stamps and Jen has 9×3 which is 27 stamps.
Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?
Answer:
h = S - 2πr² /2πr
Step-by-step explanation:
Marta is solving the equation S = 2πrh + 2πr2 for h. Which should be the result?
To solve;
S = 2πrh + 2πr²
The first thing to do is to subtract 2πr² from both-side of the equation
S - 2πr² = 2πrh + 2πr² - 2πr²
S - 2πr² = 2πrh
Then next is to divide both-side of the equation by 2πr
S - 2πr² / 2πr = 2πrh /2πr
On the right-hand side of the equation 2πr at the numerator will cancel-out 2πr at the denominator, leaving us with just h while on the left-hand side of the equation S-2πr² will be divided by 2πr)
S - 2πr² / 2πr = h
Therefore the result should be h = S - 2πr² / 2πr
Answer:
A) [tex]h =\frac{s}{2\pi r} -r[/tex]
Step-by-step explanation:
[tex]s = 2\pi rh + 2\pi r^2[/tex]
[tex]s = 2\pi r (h + r)\\h + r =\frac{s}{2\pi r} \\h =\frac{s}{2\pi r} -r[/tex]
The difference of a number and six is seven. Find the number.
Answer 13-6=7
Step-by-step explanation:
The given expression indicates a difference of six and an unknown number equals to seven. To solve, we isolate the unknown number by adding six to both sides of the equation. Thus, the unknown number is 13.
Explanation:The question states that 'The difference of a number and six is seven.' To find out the number, we can set up the following equation where x represents our unknown number:
x - 6 = 7
To solve for x, we can add 6 to both sides of the equation, which balances it rendering the final result:
x = 7 + 6
Finally, adding 7 and 6, we find that x = 13. The number we are seeking is 13.
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Which is the equation of a line that has a slope of One-half and passes through point (2, –3)?
y = one-half x minus 4
y = one-half x minus 2
y = one-half x + 2
y = one-half x + 3
Answer:
The Answer is (A).
Step-by-step explanation:
hope this helps chu :)
Answer:
Its A
Step-by-step explanation:
I did the test! Hope this helps<3
find the difference in length between a walking stick and a bumblebee PLS HELP HURRY
Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.
Solution:
Given data represents the length of the insects.
Length of the walking stick = 4 in
Length of the bumble bee = [tex]\frac{5}{8}[/tex] in
Difference between their length
[tex]$=4-\frac{5}{8}[/tex]
[tex]$=\frac{4}{1} -\frac{5}{8}[/tex]
To make the denominator same, multiply and divide the first term by 8.
[tex]$=\frac{32}{8} -\frac{5}{8}[/tex]
[tex]$=\frac{32-5}{8}[/tex]
[tex]$=\frac{27}{8}[/tex]
Now, change improper fraction into mixed fraction, we get
[tex]$=3\frac{4}{8}[/tex]
Difference between the lengths of walking stick and lengths of bumble bee is [tex]3\frac{4}{8}[/tex] inch.
Angle x measures 42°. Find the measure of angle y.
42°
48°
138°
148°
1. Calculate the average speed of a car that travels 600m in 60 seconds.
2. Calculate the average speed of a cyclist who travels 100m in 5 seconds.
3. Calculate the average speed of a train that travels 4000m in 80 seconds.
4. Calculate the average speed of a bus that travels 2500m in 500 seconds.
5. Calculate the average speed of a rocket that travels 3000m in 2 seconds.
Answer:
1-10m/s
2-20m/s
3-5/m/s
4-5m/s
5-1500m/s
Step-by-step explanation:
using formula of speed i.e. speed=distance/time or v=s/t. solve for all five cases.
we get,
1- v=s/t=600/60 =10m/s
2- v=s/t=100/5 =20m/s
3- v=s/t =400/80=5m/s
4-v=s/t=2500/500=5m/s
5-v=s/t=3000/2=1500m/s
1. The average speed of a car that travels 600m in 60 seconds is 10 m/s
2. he average speed of a cyclist who travels 100m in 5 seconds is 20 m/s
3. The average speed of a train that travels 4000m in 80 seconds is 50 m/s
4. The average speed of a bus that travels 2500m in 500 seconds is 5 m/s
5. The average speed of a bus that travels 2500m in 500 seconds is 1500 m/s.
To calculate the average speed, we use the following formula:
Average speed = Distance / Time
1. Average speed of a car that travels 600m in 60 seconds:
Average speed = 600m / 60s = 10 m/s
2. Average speed of a cyclist who travels 100m in 5 seconds:
Average speed = 100m / 5s = 20 m/s
3. Average speed of a train that travels 4000m in 80 seconds:
Average speed = 4000m / 80s = 50 m/s
4. Average speed of a bus that travels 2500m in 500 seconds:
Average speed = 2500m / 500s = 5 m/s
5. Average speed of a rocket that travels 3000m in 2 seconds:
Average speed = 3000m / 2s = 1500 m/s
Please note that the unit of speed can vary depending on the context. For example, we can express speed in meters per second (m/s), kilometers per hour (km/h), or miles per hour (mph).
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2.3.5.9.17
How does each term relate to the previous term?
Add 1.
Multiply by 3 and stract 3.
Multiply by 2 and subtract 1.
Multiply by 2 and subtract 3.
Answer:
Multiply by 2 and subtract 1
Step-by-step explanation:
If we consider the sequence term by term
n = 2 → 2(2) - 1 = 4 - 1 = 3 ← the second term
n = 3 → 3(2) - 1 = 6 - 1 = 5 ← the third term
n = 5 → 5(2) - 1 = 10 - 1 = 9 ← the fourth term
n = 9 → 9(2) - 1 = 18 - 1 = 17 ← the fifth term
Answer:
C. Multiply by 2 and subtract 1.
Step-by-step explanation:
2 × 2 = 4. 4 - 1 = 3
3 × 2 = 6. 6 - 1 = 5
5 × 2 = 10. 10 - 1 = 9
9 × 2 = 18. 18 - 1 = 17
what is the range of 8,9,9,8,8,5,8
Answer:
The range is 4
Step-by-step explanation:
To find the range, you subtract the lowest number from the highest number.
Example: If the set was: 1, 2, 6, 6, 8, 10
What is the highest number: 10
What is the lowest number: 1
You will do this -> 10 - 1 = 9
Problem: 8, 9, 9, 8, 8, 5, 8
What is the highest number: 9
What is the lowest number: 5
9 - 5 = 4
Answer: The range is 4
How long is the minor axis for the ellipse shown below?
(x+3)^2/64 + (y-7)^2/4=1
A. 16
B. 4
C. 8
D. 64
Imagine is shown above.
The length of the minor axis is 4
Step-by-step explanation:
Step 1 :
The given equation is [tex]\frac{(x-3)^{2}}{64} + \frac{(y-7)^{2}}{4} = 1[/tex]
Here we see the denominator below the variable x is greater than below y. Hence the ellipse's major axis and the minor axis are parallel to x-axis and y-axis respectively
Step 2 :
The square of the semi minor axis will be the denominator of the y variable. So in the given ellipse ,
the square of the semi minor axis = 4
Hence the length of the semi minor axis = [tex]\sqrt{4}[/tex] = 2
Step 3 :
The length of the minor axis = 2 times the length of the semi minor axis
= 2 × 2 = 4
Answer :
The length of the minor axis is 4
Final answer:
The length of the minor axis of the given ellipse is 4 units, as the semi-minor axis length is derived from the square root of the denominator of the y-term in the ellipse equation. The correct option is B.
Explanation:
The minor axis of an ellipse is the shortest diameter of the ellipse, and it runs perpendicular to the major axis. In the given equation of the ellipse, (x+3)²/64 + (y-7)²/4=1, the denominators of the fractions correspond to the squares of the semi-axes lengths. Therefore, the length of the semi-minor axis 'b' is the square root of 4, which is 2. Since the minor axis is twice the length of the semi-minor axis, we must multiply 2 by 2 to get the length of the minor axis, which is 4.
So the correct answer for the length of the minor axis for the given ellipse is 4 units, which corresponds to option B.
Which equation represents the graphed function?
y=-3x + 3
y= 3x - 3
y= 3x - 1
y=-x+3
Answer:
y= 3x + 1
Step-by-step explanation:
For Plato
Using the following diagram, tick the correct angles which are congruent to the angles given in the first column.
(20 points)
Answer:
Step-by-step explanation:
Angle 1 = 1, 3, 5, 7
Angle 3 = 1, 3, 5, 7
Angle 4 = 2, 4, 6, 8
Pretty much just look at the congruent symbols and you can figure it out.
Which best explains why a hot air balloon rises into the air?
A. As the air is cooled, it becomes more dense and the balloon rises.
B. As the air is cooled, it becomes less dense and the balloon rises.
C. As the air is heated, it becomes less dense and the balloon rises.
Answer:
C. As the air is heated, it becomes less dense and the balloon rises.
Step-by-step explanation:
A is wrong. The denser cold air would cause the balloon to drop.
B is wrong. As the air is cooled, it becomes less dense.
A bottle filled with water weighs 9.6 kilograms. If the
water by itself weighs 5 times as much as the bottle,
what is the weight of the bottle?
Answer:
1.92
Step-by-step explanation:
9.6 divided by 5 = 1.92
A napkin is 37 centimeters long.How many millimeters is this?
Answer:
370 millimeters
Step-by-step explanation:
Have a nice day :)
Step-by-step explanation:
1 cm = 1 millimeters
[tex] \therefore \: 37 \: cm \: = 37 \times 10 = 370 \: mm[/tex]
What is the solution to log Subscript 2 Baseline (9 x) minus log Subscript 2 Baseline 3 = 3 x = three-eighths x = eight-thirds x = 3 x = 9
Option B: [tex]x=\frac{8}{3}[/tex] is the solution
Explanation:
The given expression is [tex]\log _{2} 9 x-\log _{2} 3=3[/tex]
We need to determine the solution for the given expression.
The solution can be determined by solving the expression for x.
Adding [tex]\log _{2} 3[/tex] to both sides of the expression, we have,
[tex]\log _{2}9 x=3+\log _{2}3[/tex]
Using the logarithmic definition that if [tex]\log _{a}(b)=c[/tex] then [tex]b=a^{c}[/tex]
Thus, we have,
[tex]9 x=2^{3+\log _{2}3}[/tex]
[tex]9 x=2^{3}\cdot 2^{\log _{2}3}[/tex]
Simplifying, using the identity [tex]a^{\log _{a}(b)}=b[/tex], we have,
[tex]9 x=8\cdot 3[/tex]
Multiplying, we get,
[tex]9x=24[/tex]
Dividing both sides by 9, we have,
[tex]x=\frac{24}{9}[/tex]
Simplifying, we have,
[tex]x=\frac{8}{3}[/tex]
Thus, the solution of the expression is [tex]x=\frac{8}{3}[/tex]
Answer:
B. x = eight-thirds
Step-by-step explanation:
edge 2021 ;)
what is the value of the constant in the equation that relates the height and width of the rectangle
Answer:
2
Step-by-step explanation:
as H=20 and W=10
So H=constant.(W)
H=2(10)
H=20
So constant is 2
The value of the constant in the equation that relates the height and width of the rectangle is 2
The given expression is:
H(w) = constant x w
where w represents the width
H represents the height
The point (w, H) is given as (10, 20)
That is:
w = 10, H = 20
Substitute w = 10 and H = 20 into the equation H(w) = constant x w
20 = constant x 10
constant = 20/10
constant = 2
Therefore, the value of the constant in the equation that relates the height and width of the rectangle is 2
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Is 36/6 a rational number
Answer:
yes
Step-by-step explanation:
Any ratio of two integers is a rational number, as long as the denominator is not zero.
Is 14.2 an integer and why
Answer:
No
Step-by-step explanation:
This is not an integer because integers can be positive or negative but never decimals or fractions.
Answer:No
Integers are whole numbers.
In the diagram, HK is tangent to Circle O. If HK is 24mm and the length from H to the
edge of the circle along OH is 18mm, what is the length of the radius of the circle?
Answer:
The length of the radius of the circle is 7 mm
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
If HK is tangent to circle O at point K
then
The radius OK is perpendicular to segment HK and triangle OKH is a right triangle
Applying the Pythagorean Theorem
[tex]OH^2=OK^2+HK^2[/tex]
we have
[tex]OH=(r+18)\ mm\\OK=r\ mm\\HK=24\ mm[/tex]
substitute
[tex](r+18)^2=r^2+24^2[/tex]
solve for r
[tex]r^2+36r+324=r^2+576[/tex]
[tex]36r=576-324\\36r=252\\r=7\ mm[/tex]
therefore
The length of the radius of the circle is 7 mm
Think about your plans to go to college, even if you have never considered it before. What plan would you develop to help pay for college? Explain your plan using vocabulary terms from this lesson.
Answer: I would develop a savings plan with my parents. Then I would research what scholarships and grants were available. I would wait until I was ready to attend college before filling out the FAFSA. Finally, I would review the results from the FAFSA and determine the best financial aid options.
Step-by-step explanation:
Answer:
i dont want to go and noone can make me
Step-by-step explanation:
how long is the arc subtended by an angle of 32 on a circle of radius 27 cm
[tex]\bf \textit{arc's length}\\\\ s = \cfrac{\pi r\theta }{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=27\\ \theta =32 \end{cases}\implies s = \cfrac{\pi (27)(32)}{180} \\\\\\ s = \cfrac{24\pi }{5}\implies s\approx 15.08[/tex]
3) 8а - 5а answer please
Answer:
8a-5a=3a
Step-by-step explanation:
8-5=3, basically simple subtraction, just bring the variable to the other side.