Answer:
5.5 hours
Step-by-step explanation:
time = distance/speed
t = 330/60
t = 5.5 hours
Solve for q.
7q+17q–14q–8q=14
q=
[tex](7 + 17 - 14 - 8)q = 14[/tex]
[tex](24 - 22)q = 14[/tex]
[tex]2q = 14[/tex]
Divide both sides by 2
[tex] \frac{2q}{2} = \frac{14}{2} \\ [/tex]
[tex]q = 7[/tex]
There u go...
Have a great day ❤
1) Trent made a scale drawing of the elementary school. The schoolyard, which is 85
meters wide in real life, is 102 millimeters wide in the drawing. What scale did Trent use?
6 millimeters:
The scale Trent used for his elementary school which has a school yard of 85
meters wide in real life and 102 millimetre wide in drawing is 51 : 42500
Firstly, let's do the conversion of the units
1 meters = 1000 millimetres
85 meters = ?
cross multiply
length in millimetres = 85 × 1000 = 85000 millimetres
Since the schoolyard width is 85000 millimetres in real life but it's 102 millimetres wide in drawing , the scale will be as follows:
= 102 / 85000
= 51 / 42500
Therefore, the scale is as follows:
51 : 42500
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A scale is chosen to plot the large graphs on smaller paper representing each unit by a supposed unit.
1.2 mm is used to represent 1 meter.
In the scale given the 102 mm is drawn to represent 85 meters.
So dividing the graph line with the original length the scale Trent has used can be found.
102/85= 1.2
This shows that 1.2 mm is used to represent 1 meter.
Multiplying 85 with 1.2 gives 102 .
https://brainly.com/question/25798457
if line 1 has a slope of -4 and line 2 has a slope of 1/4, they are parallel
True
O False
need some help with these!!
Answer:
RS = XY
Step-by-step explanation:
Corresponding sides will be equal. So
RS = XY
The price of an item has risen to $343 today. Yesterday it was $140. Find the percentage increase.
Answer:
145% increase
Step-by-step explanation:
343 - 140 = 203
203/140 = 1.45
1.45 x 100 = 145
what is the area of the rectangle below?
Answer:
B. 120sq. unitsStep-by-step explanation:
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
so
8 * 15 = 120sq. units
Lol pls hurry!!
I need this asap
Answer: 2, D
Step-by-step explanation: f=-2, so 4x-2 would give -8 add 10 would give 2 as it is for the negative
A 15-g sample of radioactive iodine decays in such a way that the mass remaining after t days is given by
m(t) = 15e−0.073t,
where
m(t)
is measured in grams. After how many days is there only 5 g remaining?
15 days
Step-by-step explanation:
The half-life equation is given as
[tex]m(t) = m(0)e^{-0.073t}[/tex] (1)
where m(0) is the initial mass of radioactive iodine at t = 0. To solve for the time t, let's put the exponential part on the left-hand side:
[tex]e^{-0.073t} = \dfrac{m(t)}{m(0)}[/tex]
Taking the natural logarithm of both sides to get
[tex]\ln{e^{-0.073t}} = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex] (2)
Recall the following properties of logarithms:
[tex]\ln{A}^b = b\ln{A}[/tex]
[tex]\ln{e} = 1[/tex]
We can rewrite Eqn(2) as
[tex]-0.073t = \ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Solving for t, we get
[tex]t = -\dfrac{1}{0.073}\ln\left[\dfrac{m(t)}{m(0)}\right][/tex]
Since m(0) = 15 gm and m(t) = 5 gm, then the amount of time that elapses to reduce the mass down to 5 gm is
[tex]t = -\dfrac{1}{0.073}\ln\left(\dfrac{5\:\text{g}}{15\:\text{g}}\right)[/tex]
[tex]\:\:\:\:\:= 15\:\text{days}[/tex]
© Write
[tex] \sqrt{8} [/tex]
power of 2
Answer:
2³
Step-by-step explanation:
2×2×2=8
so √8 = 2³
Hope this helps you
I need to know how to subtract fractions 4 2/3 - 3/4
Answer: The answer would be 3.91666666667
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{4 \dfrac{2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{4\times3+2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{12 + 2}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{14}{3} - \dfrac{3}{4}}[/tex]
[tex]\mathsf{= \dfrac{56}{11} - \dfrac{9}{12}}[/tex]
[tex]\mathsf{= \dfrac{14\times4}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{56 - 9}{12}}[/tex]
[tex]\mathsf{= \dfrac{47}{12}}[/tex]
[tex]\mathsf{= 3 \dfrac{11}{12}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: }\huge\boxed{\\\mathsf{\dfrac{47}{12} \ or\ 3 \dfrac{11}{12}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
The formula for the area of a trapezoid is A= 1/2h(b1+b2), Where h is the height and b1 and b2 are the two bases. Rewrite the formula to solve for b1 in terms of A, h, and b2.
Answer:
Correct choice: B
Step-by-step explanation:
Equation Solving
The area of a trapezoid with height h and bases b1 and b2 is given by:
We must solve this formula for h.
First, multiply by 2 to eliminate denominators:
Now, divide by b1+b2:
Swapping sides:
Correct choice: B
Fast help on this!!
Answer:
5 seconds
Step-by-step explanation:
hope it helps
correct me if i'm wrong
Write the expression 4^4(4^-7)(4) using a single exponent
[tex]4^4(4^7)4\implies 4^4\cdot 4^7\cdot 4^1\implies 4^{4+7+1}\implies 4^{12}[/tex]
Answer:
real answer 4^-2
Step-by-step explanation:
just did on edge
Why do you have a premium? That's :(
Answer:
i dont have a premium
Step-by-step explanation:
Answer:
Step-by-step explanation:
can anyone solve this step by step for me
Answer:
0.5 ㏑ | 1-2x | +c
Step-by-step explanation:
Formula: ∫ 1/ax+b dx = 1/a ln Iax+bI +c
GIVING BRAINLIST TO FIRST RIGHT ANSWER NO BOTS
In Diagram 6, JCK is a tangent to the circle ABC
Find the value of x.
A 1149 B 76° C 52° D 26°
Answer:
C
Step-by-step explanation:
if you don't know it choose C
A car was valued at 380,000 in the year 2014. By 2019, the value had depreciated to 110,000. If the cars value continues to drop by the same percentage,what will it be worth by 2017?
Please help thanks and Godbless
Answer:
160000
Step-by-step explanation:
1/2+y=5 1/4 complete the following addition equations
Answer:
So first you can find a common denominator to make this equation solvable
in this case 4 is the common denominator
2/4+y=5 1/4
Now subtract to isolate the variable (y)
4 3/4 =y
Help quick 20points please please
Answer:
AB = 23.6
BC = 18.5
CD = 23.6
DA = 18.5
Step-by-step explanation:
4.
Both sets of opposite sides are parallel, so this is a parallelogram.
In parallelogram ABCD:
AB≅CD
AD≅BC
Knowing that, you can write 2 equations with the given information:
[tex]2a-20.4=a+1.6\\a-3.5=18.5[/tex]
You can solve whichever one you want, but I'll do both to be sure.
[tex]2a-20.4=a+1.6\\2a=a+1.6+20.4\\2a-a=1.6+20.4\\a=22[/tex]
Now for the second one:
[tex]a-3.5=18.5\\a=18.5+3.5\\a=22[/tex]
a = 22, so now you can solve for the side lengths.
[tex]2(22)-20.4=23.6\\22-3.5=18.5\\22+1.6=23.6\\18.5=18.5[/tex]
Use a system of equations to find the partial fraction decomposition of the rational expression. Solve the system using matrices.
[tex] \frac{3x ^{2} + 3x - 2 }{(x + 1)^{2} (x - 1)} = \frac{a}{x + 1} + \frac{b}{x - 1} + \frac{c}{(x + 1)^{2} } [/tex]
A=
B=
C=
Combine the fractions on the left with a common denominator:
[tex]\dfrac a{x+1} + \dfrac b{x-1} + \dfrac c{(x+1)^2} = \dfrac{a(x+1)(x-1) + b(x+1)^2 + c(x-1)}{(x-1)(x+1)^2}[/tex]
It follows that
[tex]3x^2+3x-2 = a(x+1)(x-1) + b(x+1)^2 + c(x-1)[/tex]
Expand the right side and collect like powers of x :
[tex]3x^2+3x-2 = a(x^2-1) + b(x^2+2x+1) + c(x-1)[/tex]
[tex]3x^2+3x-2 = (a+b)x^2 + (2b + c)x -a +b - c[/tex]
Then we have the system of equations
[tex]\begin{cases}a+b=3\\2b+c=3\\-a+b-c=-2\end{cases}[/tex]
or in matrix form,
[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} \begin{bmatrix}a\\b\\c\end{bmatrix} = \begin{bmatrix}3\\3\\-2\end{bmatrix}[/tex]
Compute the determinant of the coefficient matrix:
[tex]\det\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix} = -4[/tex]
Then the inverse of the coefficient matrix is equal 1/det times the adjugate of the coefficient matrix (a.k.a the transpose of the cofactor matrix):
[tex]\begin{bmatrix}1&1&0\\0&2&1\\-1&1&-1\end{bmatrix}^{-1} = \dfrac1{-4} \begin{bmatrix}-3 & -1 & 2 \\ 1 & -1 & -2 \\ 1 & -1 & 2\end{bmatrix}^\top = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix}[/tex]
Multiply both sides of the equation by the inverse :
[tex]\begin{bmatrix}a\\b\\c\end{bmatrix} = -\dfrac14 \begin{bmatrix}3&-1&-1\\1&1&1\\-2&2&-2\end{bmatrix} \begin{bmatrix}3\\3\\-2\end{bmatrix} = \begin{bmatrix}2\\1\\1\end{bmatrix}[/tex]
So, we have a = 2 and b = c = 1, and the partial fraction decomposition is
[tex]\dfrac{3x^2+3x-2}{(x+1)^2(x-1)} = \dfrac 2{x+1} + \dfrac 1{x-1} + \dfrac 1{(x+1)^2}[/tex]
Answer:
A = 2B = 1C = 1Step-by-step explanation:
One can solve for a, b, c a little more directly than using a system of 3 equations.
If we multiply the rational expression by (x+1)², we get ...
(3x² +3x -2)/(x -1) = (x+1)²(a/(x+1) +b/(x-1)) +c
Evaluating this for x = -1 gives ...
(3(-1)² +3(-1) -2)/(-1 -1) = c
-2/-2 = 1 = c
Similarly, multiplying by (x -1) gives ...
(3x² +3x -2)/(x +1)² = (x -1)(a/(x +1) +c/(x +1)²) + b
Evaluating this for x = 1 gives ...
(3·1² +3·1 -2)/(1 +1)² = b
4/4 = 1 = b
Now, we need to find the value of 'a'. The identity will hold true for any value of x, so we can see what happens when we substitute x=0. We can use the values of 'b' and 'c' that we found above.
(3·0² +3·0 -2)/((0 +1)²(0 -1)) = a/(0 +1) +1/(0 -1) +1/(0 +1)²
-2/-1 = a -1 +1 ⇒ a = 2
_____
System of equations solution
When the terms of the right-side expansion are combined, the numerator of the result is ...
a(x +1)(x -1) +b(x +1)^2 +c(x -1) = (a+b)x² +(2b+c)x +(-a+b-c) ≡ 3x² +3x -2
Equating the coefficients gives the system of equations whose augmented matrix is:
[tex]\left[\begin{array}{ccc|c}1&1&0&3\\0&2&1&3\\-1&1&-1&-2\end{array}\right][/tex]
Transforming this to reduced row-echelon form using any of a variety of available tools gives ...
[tex]\left[\begin{array}{ccc|c}1&0&0&2\\0&1&0&1\\0&0&1&1\end{array}\right][/tex]
which tells you the solution is (A, B, C) = (2, 1, 1).
round to the nearest hundred 104,549 help 6th
grade
epic gamer question, i'll mark brainlist
Answer:
It has to be an isosceles because it has 2 congruent sides (and angles) in the same relative position. The two congruent angles both measure 30 degrees each; the total of degrees in any triangle is always 180. So, the other side has an angle measure of 120 degrees, which is more than 90. Therefore, it is
an obtuse isosceles
How do I do this problem?
Answer:
hey you can use scan and search
Answer:
I got : 0.42264973
Step-by-step explanation:
1/ -√3 + 1
-√3 = -1.73 ( 2 decimal place )
1/ -1.73 + 1
and found the answer
Find the equation of the line through (−8,1) which is perpendicular to the line y=−x/2−6.
Give your answer in the form y=mx+b.
Linear equations can represent parallel lines, perpendicular lines and lines with no relationship at all.
The equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]
The equation is given as:
[tex]\mathbf{y =-\frac x2 - 6}[/tex]
For a linear equation y = mx + b, the slope of the equation is m
So, by comparison:
[tex]\mathbf{m =-\frac 12}[/tex]
The relationship between the slopes of perpendicular lines is:
[tex]\mathbf{m_2 =-\frac 1{m_1}}[/tex]
So, we have:
[tex]\mathbf{m_2 =-\frac 1{-1/2}}[/tex]
[tex]\mathbf{m_2 =2 }[/tex]
This means that, the slope of the line that passes through point (-8,1) is 2
The line equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = 2(x + 8) + 1}[/tex]
Open brackets
[tex]\mathbf{y = 2x + 16 + 1}[/tex]
Simplify
[tex]\mathbf{y = 2x + 17}[/tex]
Hence, the equation of the line in form of y =mx + b is [tex]\mathbf{y = 2x + 17}[/tex]
Read more about linear equations at:
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Can you help me with this ?:)
With explanation step-step Thanks
Part A
The given angle is 4pi/3. Multiply it by the factor 180/pi to convert from radians to degree mode.
Note how the given angle has pi in the numerator, while the conversion factor has pi in the denominator. The two pi terms will cancel.
(4pi/3)*(180/pi)
(4/3)*(180/1)
(4*180)/(3*1)
720/3
240
The angle 4pi/3 radians is equivalent to 240 degrees. This 240 degree angle is in quadrant 3. Any angle in this quadrant is between 180 degrees and 270 degrees, excluding both endpoints. This is the bottom left quadrant, aka the southwest quadrant.
Answer: Quadrant 3===========================================================
Part B
To find the reference angle, we'll subtract off pi. This only works for angles in quadrant 3. This is because the first pi radians, aka 180 degrees, is taken up by the first two upper quadrants. The remaining bit in the third quadrant is all we care about to find the reference angle.
reference angle = (given angle in quadrant 3) - pi
reference angle = (4pi/3) - pi
reference angle = (4pi/3) - (3pi/3)
reference angle = (4pi - 3pi)/3
reference angle = pi/3
Answer: pi/3 radians===========================================================
Part C
Use a calculator or a reference table to find that
tan(4pi/3) = tan(pi/3) = sqrt(3)
Alternatively, you can compute the sine and cosine values first
sin(pi/3) = sqrt(3)/2cos(pi/3) = 1/2Dividing the two items in the order mentioned will get us the tangent value
tan = sin/cos
tan(pi/3) = sin(pi/3) divide cos(pi/3)
tan(pi/3) = sqrt(3)/2 divide 1/2
tan(pi/3) = sqrt(3)
In the jump from the second to last step, to the last step, the denominators '2' cancel out when dividing.
Answer: sqrt(3)through: (1, 3) and (-3,-5)
m = (Y2 - Y1)/(X2 - X1)
m = (-5 - 3)/(-3 - 1)
m = -8/-4
m = 2
Simplify the following and write your answer in simplest radical form:
√-14*√-22
Steps are in the attachment.
Note :-
=》2 is taken as negative & also taken out of the square root as it's the common factor.
______
⚜ Hope it helps :))
lets simplify
please help step by step
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 240 mg and a standard deviation of 47 mg. In a random sample of 600 adults, how many consume at least 320mg of caffeine daily?
The confidence interval is between (48.2%, 57.7%)
Using the proportion formula expressed as:
[tex]CI=p\pm z\cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
Get the proportion:
p = 320/600 = 0.53
[tex]z=\frac{x- \mu}{\sigma}[/tex]
[tex]z = \frac{320-240}{47}\\z=\frac{80}{47}\\z= 1.70[/tex]
Substitute into the formula to get the confidence interval to have:
[tex]CI=0.53\pm 1.7\cdot \sqrt{\frac{0.47}{600}}\\CI = 0.53\pm 0.04757\\CI = (0.53-0.04757, 0.53+0.04757)\\CI = (0.482, 0.577)[/tex]
Hence the confidence interval is between (48.2%, 57.7%)
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