Answer:
71/84
Step-by-step explanation:
Answer:
1229/1764, 1231/1764, 179/252, 1255/1754 and 185/252.
Step-by-step explanation:
(5/6)^2 = 25/36
(6/7)^2 = 36/49
LCM of 36 and 49 is 1764
So 25/36 = 25 * 49 / 1764 = 1225/1764
and 36/49 = 36 * 36 / 1764 = 1296/1764
So the 5 rational numbers could be:
1229/1764, 1231/1764, 1253/1764 ( = 179/252), 1255/1764 and 1295/1764 (= 185/ 252).
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
i need help on figuring this out and the answer plz!!
Answer:
$76
Step-by-step explanation:
The amount changed is the total amount of the whole entire thing.
Therefore, we use absolute value or simply find the difference.
21 - (-55) = 76
So the bank account changed $76 over the 2 days.
What two numbers multiply to negative 12 and add up to negative 13
Answer:
−13.8654599313 and 0.8654599313
Step-by-step explanation:
The two numbers of interest will be the solutions to ...
xy = -12
x +y = -13
Substituting for y, this becomes the quadratic ...
x(-13 -x) = -12
x^2 +13x = 12 . . . . . multiply by -1
x^2 +13x +6.5^2 = 12 +6.5^2 . . . . . complete the square
(x +6.5)^2 = 54.25
x = -6.5 ± √54.25 . . . . . . take the square root, subtract 6.5
x ≈ -13.865499313 or 0.8654599313
The value of y is the other of these two numbers. So, the two numbers of interest are {-13.865499313, 0.8654599313}.
pls help with sum geometry
YES! quite easily.
I hope you can see the two pairs of corresponding angles between the parallel lines. they'll be equal
and then there's a pair of vertically opposite angle at centre.
that means all pairs of corresponding angles are equal, thus, triangles are similar by AAA
Answer:
[tex]\Large \boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
The triangles can be proven by AA or Angle-Angle similarity.
[tex]\angle QUR \cong \angle TUS[/tex]
The vertical angles are congruent.
[tex]\angle R \cong \angle S[/tex]
The alternate interior angles are congruent.
Solve for X answer asap thanks
Answer:
Step-by-step explanation:
The formula we need for this is
4(4 + x) = 5(5 + 3) and
16 + 4x = 5(8) and
16 + 4x = 40 and
4x = 24 so
x = 6, choice C.
If the initial amount of iodine-131 is 537 grams , how much is left after 10 days?
Answer:
225.78 grams
Step-by-step explanation:
To solve this question, we would be using the formula
P(t) = Po × 2^t/n
Where P(t) = Remaining amount after r hours
Po = Initial amount
t = Time
In the question,
Where P(t) = Remaining amount after r hours = unknown
Po = Initial amount = 537
t = Time = 10 days
P(t) = 537 × 2^(10/)
P(t) = 225.78 grams
Therefore, the amount of iodine-131 left after 10 days = 225.78 grams
On the first day in each month, Enid deposited $4 into her bank account and Jim deposited $3 into his. They opened these accounts on May 15, 1990. On December 31, 1990, they each had $72 dollars in their account. How much did each person deposit on May 15?
Answer:
The amount of money in Enid bank account can be written as a linear equation.
Ye = Xe + $4*m
where Ye is the money that Enid has in her account, m is the number of months that have passed since she opened it, and Xe is the initial deposit.
For Jim, the equation is similar:
Yj = Xj + $3*m
where Yj and Xj are similar as above.
Between May 15 and December 31 of the same year, we have 7 months (where i am counting December because the deposit is made in the first day of the month).
Then we have that:
Ye = $72 = Xe + $4*7 = Xe + $28
Xe = $72 - $28 = $44
So in May 15, Enid deposited $44.
For Jim we have:
Yj = $72 = Xj + $3*7 = Xj + $21
Xj = $72 - $21 = $51
So in May 15, Jim deposited $51.
The loudness, L , of a sound (measured in decibels, dB) is inversely proportional to the square of the distance, d , from the source of the sound. When a person 14 feet from a jetski, it is 70 decibels loud. How loud is the jetski when the person is 46 feet away?
Answer:
Loudness (L) = 6.48 dB
Step-by-step explanation:
Given:
Loudness (L) = k / d² , where k = constant
So,
70 = k / 14²
k = 13,720
New distance = 46 feet
Find:
Loudness (L) = ?
Computation:
Loudness (L) = 13,720 / 46²
Loudness (L) = 13,720 / 2,116
Loudness (L) = 6.48 dB
A square has a perimeter of 24cm. Work out its area.
Answer:
A = 36 cm^2
Step-by-step explanation:
The perimeter of a square is given by
P =4s
24 = 4s
Divide by 4
24/4 = 4s/4
6 =s
The area of a square is
A =s^2
A = 6^2
A = 36 cm^2
All the edges of a cube have the same length. Tony claims that the formula SA = 6s, where s is the length of
each side of the cube, can be used to calculate the surface area of a cube.
a. Draw the net of a cube to determine if Tony's formula is correct.
b. Why does this formula work for cubes?
Frances believes this formula can be applied to calculate the surface area of any rectangular prism. Is
she correct? Why or why not?
d. Using the dimensions of Length, Width and Height, create a formula that could be used to calculate the
surface area of any rectangular prism, and prove your formula by calculating the surface area of a
rectangular prism with dimensions L = 5m, W = 6m and H=8m.
Answer:
Here's what I get
Step-by-step explanation:
a. Net of a cube
Fig. 1 is the net of a cube
b. Does the formula work?
Tony's formula works if you ignore dimensions.
There are six squares in the net of a cube.
If each side has a unit length s, the total area of the cube is 6s.
c. Will the formula work for any rectangular prism?
No, because a rectangular prism has sides of three different lengths — l, w, and h — as in Fig. 2.
d. Area of a rectangular prism
A rectangular prism has six faces.
A top (T) and a bottom (b) — A = 2×l×w
A left (L) and a right (R) — A = 2×l×h
A front (F) and a back (B) — A = 2×w×h
Total area = 2lw + 2lh + 2wh
If l = 5 m, w = 6 m and h = 8 m,
[tex]\begin{array}{rl}A &=& \text{2$\times$ 5 m $\times$ 6 m + 2$\times$ 5 m $\times$ 8 m + 2 $\times$ 6 m $\times$ 8 m}\\&=& \text{60 m}^{2} + \text{80 m}^{2} + \text{96 m}^{2}\\&=& \textbf{236 m}^{2}\\\end{array}[/tex]
Solve the equation for x. the square root of the quantity x plus 4 end quantity minus 7 equals 1 x = 4 x = 12 x = 60 x = 68
Answer:
x = 60
Step-by-step explanation:
Given
[tex]\sqrt{x+4}[/tex] - 7 = 1 ( add 7 to both sides )
[tex]\sqrt{x+4}[/tex] = 8 ( square both sides )
([tex]\sqrt{x+4}[/tex] )² = 8² , that is
x + 4 = 64 ( subtract 4 from both sides )
x = 60
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2
Answer:
C. x-2
Step-by-step explanation:
edge
Answer: the 3rd the answer c
x-2
Step-by-step explanation:
What are the solutions of x2 + 20 = 12x.
Answer:
x₁ = 2
x₂ = 10
Step-by-step explanation:
x² + 20 = 12x
x² - 12x + 20 = 0
(x-2)(x-10) = 0
then:
x₁ = 2
x₂ = 10
Check:
x₁
2² + 20 = 12*2
3 + 20 = 24
x₂
10² + 20 = 12*10
100 + 20 = 120
Express 3a2b-1 with positive exponents.
Answer:
a = 2b/3−1/3
Step-by-step explanation:
...........
Find the value of x. Round to the nearest tenth.Find the value of x. Round to the nearest tenth.
Answer:
x = 55.6Step-by-step explanation:
In order to find the value of x we use sine
sin ∅ = opposite / hypotenuse
From the question
x is the hypotenuse
the opposite is 19
So we have
sin 20 = 19/x
x = 19/sin 20
x = 55.55
We have the final answer as
x = 55.6 to the nearest tenthHope this helps you
Answer:
x = 55.6
Step-by-step explanation:
8 more than a number
Answer:
[tex]\boxed{ 8 + x}[/tex]
Step-by-step explanation:
Hey there!
In most cases "the number" would be x.
So if the statement says 8 "more than a number",
It is saying 8 plus x or 8 + x.
Hope this helps :)
Answer:
x + 8 is the meaning.
Step-by-step explanation:
“more” means addition. Take the number as “x”, so it will be x + 8.
That's the answer.
Reduce 5/15 to its lowest terms
Answer:
The answer is 1/3
Answer:
1/3
Step-by-step explanation:
The factors of 5 are 1,5;
* The factors of 15 are 1,3,5,15.
We can see that the GCD is 5 because it is the largest number by which 5 y 15 can be divided without leaving any residue.
To reduce this fraction, simply divide the numerator and denominator by 5 (the GCF).
So, 5 /15
= 5÷5 /15÷5
= 1 /3
Two buildings are 12m apart on the same horizontal level. From the top of the taller building, the angle of depression of the bottom of the shorter building is 48degrees and from the bottom, the angle of of elevation of the top of the shorter building is 36 degrees. Calculate the difference in the heights of the buildings
Answer:
4.61 m
Step-by-step explanation:
The angle of depression of the bottom of the shorter building from the top of the taller building = 48° equals the angle of elevation of the top of the taller building from the bottom of the shorter building
Using trig ratios
tan48° = H/d where H = height of taller building and d = their distance apart = 12 m
H = dtan48° = 12tan48° = 13.33 m
Also, the angle of elevation of the top of the shorter building from the bottom of the taller building is 36°
Using trig ratios
tan36° = h/d where h = height of shorter building
h =dtan36° = 12tan36° = 8.72 m
Now, the difference in height of the buildings is thus H - h = 13.33 m - 8.72 m = 4.61 m
I need help and fast!!!!
Answer:
H. b/a
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Label our variables
y₂ = 2b
y₁ = b
x₂ = 2a
x₁ = a
Step 2: Plug into formula
m = (2b - b)/(2a - a)
Step 3: Evaluate
m = b/a
Answer:
b/a
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 2b - b)/ ( 2a -a)
= b/a
What’s is the greatest common factor of 100x^2 - 250xy + 75x
Answer:
The greatest common factor of the expression is 25x
Step-by-step explanation:
Here, we are interested in giving the greatest common factor of the expression.
We can do this by factorization till we have no common factors left.
the expression is;
100x^2 -250xy + 75x
we start with the common factor x;
x(100x -250y + 75)
The next thing to do here is to find the greatest common factor of 100,250 and 75.
The greatest common factor here is 25.
Thus, we have;
25x(4x -10y + 3)
There is no more factor to get from the terms in the bracket. This simply means that the terms in the bracket are no longer factorizable
So the greatest common factor we have is 25x
Suppose that $9500 is placed in an account that pays 9% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
so
(b) Find the amount in the account at the end of 2 years.
$
?
Answer:
$11286.95 second year
$10335 first year
Step-by-step explanation:
9% of 9500 is 855, 9500 plus 855 = 10335. (first year)
9% of 10335 is 931.95, and 10335+931.95 is 11286.95. (second year)
The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
here, we have,
$9500 is placed in an account that pays 9% interest compounded each year.
so, we get,
9% of 9500 is 855,
9500 plus 855 = 10335. (first year)
again,
9% of 10335 is 931.95,
and 10335+931.95 is 11286.95. (second year)
Hence, The amount in the account at the end of 1 year $10335 (first year)
The amount in the account at the end of 2 years $11286.95.
To learn more on Compound interest click:
brainly.com/question/29335425
#SPJ2
[tex] \frac{w}{ -6} = 6[/tex]
I cant figure out the answer
3(q−7)=27 need help plzz 1st peep gets brainlest
━━━━━━━☆☆━━━━━━━
▹ Answer
q = 16
▹ Step-by-Step Explanation
3(q - 7) = 27
3q - 21 = 27
Add 21 to both sides:
21 + 21 = na
27 + 21 = 48
3q = 48
Divide both sides by 3:
3/3 = q
48/3 = 16
q = 16
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
q=16
Step-by-step explanation:
3q-21=27
27+21=48
48/3=16
(x^2-4x)^2+7x^2-28x+12=0
Answer:
[tex]x^4-9x^2-28x=-12[/tex]
Step-by-step explanation:
[tex](x^2-4x)^2+7x^2-28x+12=0[/tex]
[tex](x^4-16x^2)+7x^2-28x=-12[/tex]
[tex]x^4-9x^2-28x=-12[/tex]
2( -4n+ 2)
6n = 4(-2 - 2n)
Answer:
(n^(2)+6n-4)(2n-4)
8 kids bought a 3 cakes. How many equal parts will need to divide it so that everyone can have it. Easy one!
Answer:
3/8 is your answer.
Step-by-step explanation:
Given:
8 kids bought a 3 cakes.
Required:
How many equal parts will need to divide it so that everyone can have it.
Solution:
3/8
Hope this helps ;) ❤❤❤
URGENT PLZ HELP THANK YOU!
Answer:
[tex](-5)^{11}[/tex]
Step-by-step explanation:
We can use the exponent rules. If we have [tex]\frac{a^b}{a^c}[/tex], then it will simplify to [tex]a^{b-c}[/tex].
b is 5, c is -6, and a is -5 so:
[tex]-5^{5-(-6)}\\-5^{11}[/tex]
Hope this helped!
help!! im stuck on this and i can't remeber how to sove this.... 6/3c = 2/3
Hello!
Answer:
[tex]\huge\boxed{c = 3}[/tex]
Given:
[tex]\frac{6}{3c} = \frac{2}{3}[/tex]
Cross multiply:
[tex]6 * 3 = 3c * 2[/tex]
Simplify:
[tex]18 = 6c[/tex]
Divide both sides by 6:
[tex]c = 18/6 = 3[/tex]
Answer:
c=3
Step-by-step explanation:
6 2
----- = -----
3c 3
Using cross products
6*3 = 2*3c
18 = 6c
Divide each side by 6
18/6 = 6c/6
3 =c
In a previous poll, % of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the significance level.
Answer:
We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.
Step-by-step explanation:
The complete question is: In a previous poll, 46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.
Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.
So, Null Hypothesis, : p 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}
Alternate Hypothesis, : p < 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44
n = sample of adults with children under the age of 18 = 1081
So, the test statistics =
= -1.32
The value of z-statistics is -1.32.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)
= 1 - 0.9066 = 0.0934
Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.