Answer:
8^18
Step-by-step explanation:
We know that a^b ÷ a^c = a^(b-c)
8^15÷8^−3
8^(15 - -3)
8^(15+3)
8^18
1)Sheyna drive to the lake and back. It took two hours less time to get there than it did to get back. The average speed on the trip there was 60 mph. The average speed on the way back was 36 mph. How many hours did the trip there take?
Answer:
8 hours
Step-by-step explanation:
Given:
Sheyna drives to the lake with average speed of 60 mph and
[tex]v_1 = 60\ mph[/tex]
Sheyna drives back from the lake with average speed of 36 mph
[tex]v_2 = 36\ mph[/tex]
It took 2 hours less time to get there than it did to get back.
Let [tex]t_1[/tex] be the time taken to drive to lake.
Let [tex]t_2[/tex] be the time taken to drive back from lake.
[tex]t_2-t_1 = 2[/tex] hrs ..... (1)
To find:
Total time taken = ?
[tex]t_1+t_2 = ?[/tex]
Solution:
Let D be the distance to lake.
Formula for time is given as:
[tex]Time =\dfrac{Distance}{Speed }[/tex]
[tex]t_1 = \dfrac{D}{60}\ hrs[/tex]
[tex]t_2 = \dfrac{D}{36}\ hrs[/tex]
Putting in equation (1):
[tex]\dfrac{D}{36}-\dfrac{D}{60} = 2\\\Rightarrow \dfrac{5D-3D}{180} = 2\\\Rightarrow \dfrac{2D}{180} = 2\\\Rightarrow D = 180\ miles[/tex]
So,
[tex]t_1 = \dfrac{180}{60}\ hrs = 3 \ hrs[/tex]
[tex]t_2 = \dfrac{180}{36}\ hrs = 5\ hrs[/tex]
So, the answer is:
[tex]t_1+t_2 = \bold{8\ hrs}[/tex]
(a) How could you calculate 23 x 4 on your calculator if the 4 button is broken? (b) How could you calculate 23 x 21 if the 2 button on your calculator is broken?
Answer:
23 x 4
=> 23 x (2 + 2)
=> 23 x 2 + 23 x 2
23 x 21
=> 23 x (3 x 7)
=> (23 x 3) x (23 x 7)
23 + 23 + 23 + 23 = to get the answer of 92
23 x 2 + 23 x 2 =.92
Two thirds of the students in a class have pets. There are
36 students in the class. How many of the students have pets?
Find the wrong number in the series. 1, 4, 9, 15, 25, 36, 49
Answer:
15
Step-by-step explanation:
I THINK THIS IS CORRECT
Answer:
15
Step-by-step explanation:
1x1=1
2x2=4
3x3=9
No 2 same numbers can be multiplied to give a result of 15.
5x5=25
6x6=36
7x7=49
if x = 3+root8 find the value of :- 1/x
Answer:
Value is 3 - √8
Step-by-step explanation:
[tex]x = 3 + \sqrt{8} \\ \\ \frac{1}{x} = \frac{1}{3 + \sqrt{8} } \\ [/tex]
rationalise the denominator:
[tex] = \frac{1}{3 + \sqrt{8} } . \frac{3 - \sqrt{8} }{3 - \sqrt{8} } \\ \\ = \frac{3 - \sqrt{8} }{ {3}^{2} - {( \sqrt{8}) }^{2} } \\ \\ = \frac{3 - \sqrt{8} }{9 - 8} \\ \\ = 3 - \sqrt{8} [/tex]
not sure how to solve this
Answer:
x=11
Step-by-step explanation:
(x+7)×7=6×(6+15)
or, 7x+49=6×21
or, 7x=126-49
or, 7x=77
or, x=11
Determine which one of the following statements is true. A. Exponential growth will always exceed linear growth. B. Linear growth will always exceed quadratic growth. C. Linear growth will always exceed exponential growth. D. Quadratic growth will always exceed exponential growth.
Answer:
A. Exponential growth will always exceed linear growth.
Step-by-step explanation:
The rate of growth of a linear function is always constant, that means it remains the same for any value of x or y. For an exponential growth, the rate of change is not constant, it continues to increase as the value of x increases. Therefore since the rate of growth of an exponential growth increases as the x value increases, while that of the linear growth remain constant there would be a point in which the exponential growth will exceed linear growth.
A student who is 5 1/4 feet tall has a shadow that is 2 feet and 10 1/2 inches long. At the same time. a flag pole has a shadow that is 10 1/2 feel long. How tall, to the nearest inch, is the flag pole?
Answer:
The height of the flag pole is approximately 19 feet and 2 inches.
Step-by-step explanation:
Let suppose that length of the shadow of the object is directly proportional to its height. Hence:
[tex]l \propto h[/tex]
[tex]l = k\cdot h[/tex]
Where:
[tex]h[/tex] - Height of the object, measured in inches.
[tex]l[/tex] - Shadow length of the object, measured in inches.
[tex]k[/tex] - Proportionality constant, dimensionless.
Now, let is find the value of the proportionality constant: ([tex]h = 5\,\frac{1}{4} \,ft[/tex] and [tex]l = 2\,ft\,\,10\,\frac{1}{2}\,in[/tex])
[tex]h = \frac{21}{4}\,ft[/tex]
[tex]h = \left(\frac{21}{4}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]
[tex]h = 63\,in[/tex]
[tex]l = (2\,ft)\cdot \left(12\,\frac{in}{ft} \right) + \frac{21}{2}\,in[/tex]
[tex]l = 24\,in + \frac{21}{2}\,in[/tex]
[tex]l = \frac{48}{2}\,in+\frac{21}{2}\,in[/tex]
[tex]l = \frac{69}{2}\,in[/tex]
Then,
[tex]k = \frac{l}{h}[/tex]
[tex]k = \frac{\frac{69}{2}\,in }{63\,in}[/tex]
[tex]k = \frac{69}{126}[/tex]
[tex]k = \frac{23}{42}[/tex]
The equation is represented by [tex]l = \frac{23}{42}\cdot h[/tex]. If [tex]l = 10\,\frac{1}{2}\,ft[/tex], then:
[tex]l = \frac{21}{2}\,ft[/tex]
[tex]l = \left(\frac{21}{2}\,ft \right)\cdot \left(12\,\frac{in}{ft} \right)[/tex]
[tex]l = 126\,in[/tex]
The height of the flag pole is: ([tex]l = 126\,in[/tex], [tex]k = \frac{23}{42}[/tex])
[tex]h = \frac{l}{k}[/tex]
[tex]h = \frac{126\,in}{\frac{23}{42} }[/tex]
[tex]h = \frac{5292}{23}\,in[/tex]
[tex]h = 230\,\frac{2}{23}\,in[/tex]
[tex]h = \frac{115}{6}\,ft\,\frac{2}{23}\,in[/tex]
[tex]h = 19\,\frac{1}{6}\,ft \,\frac{2}{23}\,in[/tex]
[tex]h = 19\,ft\,\,2\,\frac{2}{23}\,in[/tex]
[tex]h = 19\,ft\,\,2\,in[/tex]
The height of the flag pole is approximately 19 feet and 2 inches.
Simplify the expression to a polynomial in standard form:
(2x - 1)(-x^2+ 4x + 6)
Answer:
[tex](2x - 1)( - {x}^{2} + 4x + 6) \\ = 2x \times - {x}^{2} + 2x \times4x + 2x \times 6 \\ - 1 \times - {x}^{2} - 1 \times 4x - 1 \times 6 \\ = - 2 {x}^{3} + 8 {x}^{2} + 12x + {x}^{2} - 4x - 6 \\ = - 2 {x}^{3} + 9 {x}^{2} - 8x - 6 \\ thank \: you[/tex]
help me im dangered plzzzzzzzzzzzzzzzzzzzz
Answer:
A
Step-by-step explanation:
Hi!
An exponent is the same thing as just multiplying the expression by itself the number of times the exponent says. So we need to multiply 1/3 by itself three times.
1/3 * 1/3 * 1/3 = 1/27
Simplify 6.920
A.-1
B.0
C.1
D.6.92
I'm pretty sure the answer is 6.92 cause when you simplify it you'll get that exact answer
Answer:
D 6.92
Step-by-step explanation:
6.920 and 6.92 are equal
the ratio of boys and girls in a 4:3.If there are 20 boys, find the number of girls.
Answer:
There are 15 girls.
Step-by-step explanation:
The ratio is 4:3, meaning there are 7 parts.
4 parts= 20 (Boys)
This means 1 part is 20 divided by 4.
1 part= 5
3 parts= Amount of girls.
3 x 5 = 15.
There are 15 girls.
Answer:
15
Step-by-step explanation:
Add:
boys : girls
4 : 3 = 7
20: ? = ?
Divide:
20 / 4 = 5
5 × 3 = 15
20: 15
So, there are 15 girls.
What is the volume of this figure?
Answer:
Volume = 480 cm³
Step-by-step explanation:
Volume = lwh
*Split the shape into 3 rectangles.
Rectangle 1: 4 x 4 x 8 = 128
Rectangle 2: 14 x 4 x 4 = 224
Rectangle 3: 4 x 4 x 8 = 128
Total: 128 + 224 + 128 = 480 cm³
Answer:
480
Step-by-step explanation:
just took the quiz
What is the reflection image of
(5,−3)across the line
y=x
Answer: The Answer is (-5,-3)
hope so my answer is correct
Step-by-step explanation:
31. Each day, Talisa exercises by first
stretching and then swimming
some laps, as shown in the table.
Make a scatter plot of the total
time she exercises as a function
of the number of laps she swims.
Draw a trend line.
Answer:
Step-by-step explanation:
Given the following :
Laps - - - - - - - - 5 - - - 6 - - - 7 - - - 8 - - - 9
Total time - - - 25 - - 28 - - 29 - - 30 - - 32
Using online graphing tool:
The y - axis named dependent variable represents the total time taken.
The x-axis, represents the number of laps.
The equation of the trend line attached to the plot is in the form :
y = mx + c
y = 1.6x + 17.6
Where y = total time taken
x = number of laps
m = 1.6 = gradient of the line (change in y / change in x)
C = 17.6 = intercept (whee the trndline intersects the y-axis).
the Marked price of a computer is rupees 30000 if it is sold after 20 percent discount and then 30% bat is levied on it find the price of the computer including vat.
if u don't know don't answer otherwise I will report u
Answer:
31200
Step-by-step explanation:
First, the starting price is 30000. We then must find the value after a 20% discount is applied. To do this, we can first convert 20% into a decimal value. That can be obtained by multiplying the percent by 1/100, so 20% * 1/100 = 0.2 . Therefore, the discount is 30000 * 0.2 = 6000 . Discounts work by subtracting the discount from the market price to get the final value, so we have
30000 - 6000 = 24000 as the value before tax.
Then, we can include the VAT, which is 30% of our new price. 30% as a decimal is 30 * 1/100 = 0.3, so we can find the tax of our product as 0.3 * 24000 = 7200. Taxes work by adding the taxed value on top of the price, so we can add 7200 to the value before tax to get 31200 as the final price including VAT
match each polynomial with its degree
degree 1
degree 2
degree 3
degree 4
a.8x^2+7+1/2x^3-3 (1/2 is a fraction)
b.3x^2-2x+4
c.(x^2)^2+(x+4)^2
d.5x+5
Answer:
d
b
a
c
Step-by-step explanation:
degree 1 - 5x+5 - d.
degree 2- 3x^2-2x+4- b.
degree 3 - 1/2x^3+8x^2-3- a.
degree 4 - x^4+(x+4)^2- c
The height of the rectangular prism is 2 m. If its volume is 72 cubic meters, what is the area of the base, in square meters?
Answer:
Base area is 36 square meters
Step-by-step explanation:
The volume of a rectangular prism is V = (height)(length)(width). We know all of these dimensions except for the area of the base, which is (length)(width).
Solving this equation for (length)(width), we get:
volume 72 m^3
(length)(width) = (area of base) = -------------- = ------------- = 36 m^2
height 2 m
Find the length of AB
Answer:
AB = 3π
Step-by-step explanation:
The formula for the circumference of a circle is:
C = 2πr
By substituting 27 for r:
C = 2π(27)
C = 54π
The whole circumference is 54π. A circle is 360º around. We can set up a proportion to find the length of the 20º arc:
[tex]\frac{360}{54p}[/tex] = [tex]\frac{20}{x}[/tex]
Cross-multiply:
360x = 1080π
Divide both sides by 360:
x = 3π
AB = 3π
Answer:
AB = 3π
Step-by-step explanation:
The arc AB can be calculated as
AB = circumference of circle × fraction of circle
The central angle is equal to the measure of arc AB = 20° , thus
AB = 2πr × [tex]\frac{20}{360}[/tex]
= 2π × 27 × [tex]\frac{1}{18}[/tex] ( cancel 18 and 27 by 9 )
= 2π × 3 × [tex]\frac{1}{2}[/tex] = 6π × [tex]\frac{1}{2}[/tex] = 3π
The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70
[tex] d \propto v^2[/tex]
$\implies d=kv^2$
substitute the given values, $5=k(10)^2\implies k=\frac1{20}$
now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$
A big blunder from my side, now fixed!
find the surface area of each figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
Base of triangle = b = 8 cm
Height of triangle = h = 6 cm
Length of rectangle = l = 6 cm
Sides of the triangle : S1 = 6 cm ; S2 = 8 cm and S3 = 10 cm
Surface area of triangular prism= bh + l *(s1+ S2 + S3)
= 8 * 6 + 6*(6+8+10)
= 48 + 6*24
= 48 + 144
= 192 square cm
What is the difference of the rational expressions below?
Answer:
in the pic
Step-by-step explanation:
answer A
.....
Does anyone know the answer plz ?
Answer:
a = 20; b = 10sqrt(3)
Step-by-step explanation:
The ratio of the lengths of the sides of a 30-60-90 triangle is
1 : sqrt(3) : 2
b = 10 * sqrt(3)
b = 10sqrt(3)
a = 2(10)
a = 20
Answer: a = 20; b = 10sqrt(3)
Answer:
a=20,[tex]b=10\sqrt{3}[/tex]
Step-by-step explanation:
SOH-CAH-TOA
Tan = O/A
Tan(60)= b/10
[tex]b=10\sqrt{3}[/tex]
Cos = A/H
cos(60) = 10/a
a=20
Answer for Brainiest, 25 points and 5 stars with thanks
Range: 71.9
Spread out above the median
The range is the biggest number minus the smallest number. This makes sense. The range here is 81.3 - 9.4 = 71.9.
Next, see the two middle groups? You can see the median, 45.5. Does the left or right side seem more spread out? It's the right side. 34.7 is closer to 45.5 than 63.6 is to 45.5.
Hope that helped,
-sirswagger21
Given:
.
• ON is tangent to Circle L at point N
ON= 6
• OQ = 3
O
6
N
3
Q
L
P
Find the length of PQ
Answer:
9
Step-by-step explanation:
By joining N to L, you will have a right angled triangle which is right angle at N. Then r^2+36=(3+x)^2. r=9/2. PQ=2r=9
PLS HURRY!!! Charlie made a table to show how much time he spent on activities last week . Activity Time spent (hours ) Swimming Reading Cooking Soccer On which activities did Charlie spend more than hour? PLS HURRY
Answer:
None
Step-by-step explanation:
All of the fractions listed are not a whole or more than a whole. They are all parts of a whole, therefore she did not spend more than an hour on any of them
Answer:
cooking and swimming
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
9.6km
Step-by-step explanation:
Do 6x1.6 ÷1= 9.6km
Answer:9.6km
Step-by-step explanation: Recall BSM(big-small-multiply),so
1.6km×6
Line LR bisects MN at point L. Find the length of ML if MN = 152 ft.
Answer:
[tex]ML = 76\text{ feet}[/tex]
Step-by-step explanation:
Since Line LR bisects MN at point L, by the definition of bisector:
[tex]\overline{ML} \cong \overline{LN}[/tex]
We want to determine ML if MN measures 152 feet.
MN is the sum of ML and LN. Hence;
[tex]ML + LN = MN[/tex]
Since ML = LN and MN = 152:
[tex]ML + (ML) = (152)[/tex]
Simplify:
[tex]2ML = 152[/tex]
And divide. Therefore:
[tex]ML = 76\text{ feet}[/tex]
In conclusion, ML measures 76 feet.
What is the smallest odd multiple of 3 and 7 between 57 and 250?
Answer:
237 because it can come in both
Geometry, please answer question ASAP
Answer:
Option A
Step-by-step explanation:
first calculate side b
which is 35.8
Using 2 lengths, calculate Angle G
OPTION A :)