Answer:
b) 30°
Additional information:-
One angle (x) = 30° Both angles (2x) = 60°Step-by-step explanation:
We know that,
→ The other two angles of the isosceles triangles are equal.
Formula we use,
→ <A + <B + <C = 180°
Forming the equation,
→ 120° + x + x = 180°
Now the value of x will be,
→ 120° + x + x = 180°
→ 120° + 2x = 180°
→ 2x = 180° - 120°
→ 2x = 60°
→ x = 60°/2
→ [ x = 30° ]
Hence, option (b) is correct.
The_____area includes all surfaces.The______area does not include bases
1st blank (lateral surface or total surface)
2nd blank (lateral surface or total surface)
Triangle ABC has vertices A(-1, 10), B(2, 1),
and C(-4, 1). What are the coordinates of
the centroid of the triangle?
The coordinates of the centroid of triangle ABC are given as follows:
(-1, 4).
How to obtain the coordinates of the centroid of the triangle?The coordinates of the centroid of a triangle are obtained finding the mean of the coordinates of the three vertices of the triangle.
This means that the x-coordinate of the centroid of triangle ABC is given as follows:
(-1 + 2 - 4)/3 = -1.
(mean of the x-coordinates of each of the three vertices).
The y-coordinate of the centroid of triangle ABC is given as follows:
(10 + 1 + 1)/2 = 4.
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I. Jill is training for a marathon
and runs 2 ⅓ miles three times
a week. How far will she run in
six weeks?
Answer:42 miles
Step-by-step explanation: She runs 3 times a week so 2 1/3 times 3 is equal to 7.
7x6=42
the back of dante's property is a creek. dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. if there is 200 feet of fencing available, what is the maximum possible area of the corral?
If there is 200 feet of fencing available, the maximum possible area of the corral is 5000 Feet.
In the question, if there is 200 feet of fencing available, then we have to find the maximum possible area of the corral.
The formula of area of rectangle is:
A = L × B, where L is the length of the rectangle and B is the breadth of the rectangle.
The A = 200 feet and rectangular area is enclosed using the creek as one side and fencing for the other three sides, to create a corral.
So, L + 2B = 200
Subtract L on both side, we get
2B = 200 - L
Divide by 2 on both side, we get
B = 100 - L/2
A = f(L)
A = L·(100 - L/2)
A = 100L - [tex]L^2[/tex]/2
Now finding the derivative.
A' = [tex]\frac{df(L)}{dL}[/tex]
A' = -L + 100
Let A' = 0
-L + 100 = 0
Subtract 100 on both side, we get
-L = -100
L = 100 feet
Now putting the value of L in B = 100 - L/2.
B = 100 - 100/2
B = 100 - 50
B = 50 feet
The maximum possible area of the corral = 100 × 50
The maximum possible area of the corral = 5000 Feet
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Half of this two digit number is 3 times half of 28 this number is ?
Answer:
84
Step-by-step explanation:
x/2=3*28/2=3*14 = 42
x=84
Amadou i going to invet $11,000 and leave it in an account for 9 year. Auming the interet i compounded continuouly, what interet rate, to the nearet tenth of a percent, would be required in order for Amadou to end up with $14,000?
The required interest rate would be 6.9% to the nearest tenth of a percent.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the percent formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
We can use the formula A = P(1+r/n)^nt, where A is the amount of money at the end of the investment, P is the principal, r is the interest rate, n is the number of times the interest is compounded, and t is the time period.
In this case: A = $14,000, P = $11,000, n = 1 (continuous compounding), and t = 9.
Plugging these values into the formula, we get: 14,000 = 11,000(1+r)^9. Solving for r, we get: r = 0.069 or 6.9%.
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Simplify fully.
[tex]3\cdot \log_{\frac{4}{9}}(\sqrt[4]{\dfrac{27}{8}})[/tex]
I know how to get the fourth root fraction inside the log to [tex](\dfrac{3}{2})^{3/4}[/tex] but don't understand how to advance from there
Answer:
-9/8
Step-by-step explanation:
You want a full simplification of ...
[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}[/tex]
Rules of logarithmsThe relevant rules of logarithms are ...
log(ab) = log(a) +log(b)
log(a/b) = log(a) -log(b)
log(a^b) = b·log(a)
logₐ(b) = log(b)/log(a)
Application[tex]3\cdot\log_{\frac{4}{9}}{\sqrt[4]{\dfrac{27}{8}}}=\dfrac{3}{4}\log_{\frac{4}{9}}\left(\dfrac{27}{8}\right)=\dfrac{3}{4}\cdot\dfrac{\log\dfrac{27}{8}}{\log\dfrac{4}{9}}\\\\\\=\dfrac{3(\log(3^3)-\log(2^3))}{4(\log(2^2)-\log(3^2))}=\dfrac{3(3\cdot\log(3)-3\cdot\log(2))}{4(2\cdot\log(2)-2\cdot\log(3))}\\\\\\=\dfrac{9(\log(3)-\log(2))}{8(\log(2)-\log(3))}=\boxed{-\dfrac{9}{8}}[/tex]
__
Additional comment
We have reduced everything to the difference of the logs of 2 and 3. You could stop the reduction to smallest parts at any point where you recognize things that will cancel. You could write numerator and denominator in terms of powers of (3/2), for example.
Jacob is a construction worker who earns a yearly Income given by the expression 2000x + 3000, where X is the number of
hours he works each week. Carlos works with Jacob and earns a yearly Income given by the expression 3800x - 39000.A
manager predicts that if Carlos and Jacob each work 42 hours, they will earn the same amount of money.
Answer:20
Step-by-step explanation:
you do it
1+1=??????
Help me I am stuck
Which of the following represents "36 is 18 times as many as 2"?
Answer:
36 = 2 x 18
Step-by-step explanation:
Mark charged a battery . Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent after 17 minutes of charging the battery was 61.5 percent full
how full was the battery when the charging began ??
percent
how long from the time that mark started charging did it take the battery to be fully charged ?
minutes
The initial battery charge was of:
19%.
The time it takes for the battery to be full is of:
32.4 minutes.
What is a linear function?The linear function in slope-intercept format is given as follows:
y = mx + b
In which:
m is the slope, representing the rate of change of the battery change.b is the intercept, representing the initial battery charge.Each minute , the percentage of battery’s capacity that was charged increased by 2.5 percent, hence the slope m is given as follows:
m = 2.5.
Hence:
y = 2.5x + b.
After 17 minutes of charging the battery was 61.5 percent full, hence when x = 17, y = 61.5, and the intercept b is obtained as follows:
61.5 = 2.5(17) + b
b = 61.5 - 2.5 x 17
b = 19.
The battery is fully charged when y = 100, hence the time is obtained as follows:
2.5x + 19 = 100
2.5x = 81
x = 81/2.5
x = 32.4 minutes.
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Please answer these questions step-by-step
the area of trapezoid $abcd$ is $80$. one base is $12$ units longer than the other, and the height of the trapezoid is $5$. find the length of the median of the trapezoid.
The trapezoid abcd median is 16 lengths long.
Regarding the query,
Considering that,
The trapezoid's area is equal to 80,
The trapezoid abcd is 5 inches tall.
Let a be the base of the trapezoid abcd.
So, b = a + 12 ,
In the formula Area of the trapezoid = A =(a+b)h/2, the value is substituted.
(a + a + 12)5/2 = 80
(2a + 12)5 = 160
2a + 12 = 160/5
2a + 12 = 32
2a =32 - 12
2a = 20
a = 20/2
a = 10 units
additional base is 10 + 12 = 22 units.
Therefore, the median's length will be equal to (10 + 22)/2.
= 32/2 = 16 units
As a result, the median's length is 16.
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A triangle has an area of 100 square feet and a height of 5 feet. What is the length of the base of the triangle? Responses 10 ft 10 ft 20 ft 20 ft 40 ft 40 ft 160 ft
The length of the base of the triangle is 40ft
How to find the length of the base?A triangle is a polygon with three sides, three angles, three vertices, and sum of angles is s 180 degrees
The given parameters that will help us to solve the problem are
the triangle has area of 100height of the triangle is 5ftthe length of the base is = xThe area of the triangle is given as
Area = 1/2 *b*h
Area = 1/2*b*5 = 100
Area = 5b/2 = 100
Area = 5b = 200
Making b the subject of the relation
b= 200/5 =40 ft
Therefore the response for 40 ft is correct
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HELPPPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!
YALL AMAZING :)
Answer:
11 and 12
Step-by-step explanation:
Solving this would be the case of finding that square root of 131, then rounding both up and down.
First, to solve
The square root of 131 is 11.45
Now we take that 11.45 and round both up and down
Rounding down is 11 and rounding up is 12.
11 and 12 are next to each other, making them consecutive.
Answer:
I think its 11 and 12
Step-by-step explanation:
the population of algae in an experiment increases by %5 each day. if there were 50 algae at the beginning, predict the number of algae after 7 days.
The number of algae after 7 days is approximately 70.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
Given that,
Initial population of algae = 50
Percentage increase = 5%
To calculate the number of algae at any day, we need to find a formula.
Initial population = 50
After 1 day, population = 50 + (5% × 50) = 50 + (0.05 × 50) = 50 (1 + 0.05)
After 2 days, population = 50 (1 + 0.05)²
So, population after n days = 50 (1 + 0.05)ⁿ
Population of algae after 7 days = 50 (1 + 0.05)⁷
= 50 (1.05)⁷
= 70.355 ≈ 70
Hence there will be approximately 70 algae after 7 days.
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Can I get help on this question ?
The solution of the expression is 3m-5.
How to simplify the equation?Basic Guidelines and Procedures for Condensing Any Algebraic Expression
By multiplying factors, remove the parentheses and brackets.If the terms have exponents, you should eliminate grouping using the exponent rule.Add or subtract coefficients to combine similar terms.Incorporate the constants.step1:
(6m² -13m+5)/(2m-1): 3m-5
6m² -13m+5/2m-1
factor 6m² -13m+5 : (2m-1) (3m-5)
=(2m-1) (3m-5)/2m-1
step2:
cancel the common factor 2m-1
=3m-5
The solution of the expression is 3m-5
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I need help understanding how to do this
Answer:
113.04
Step-by-step explanation:
see attached
For the translation below, give the vertices of ABC
Answer:
see explanation
Step-by-step explanation:
a translation [tex]T_{(-5,-4)}[/tex]
means subtract 5 from the original x- coordinate and subtract 4 from the original y- coordinate.
A (2, - 1 ) → A' (2 - 5, - 1 - 4 ) → A' (- 3, - 5 )
B (- 4, - 2 ) → B' (- 4 - 5, - 2 - 4 ) → B' (- 9, - 6 )
C (3, 2 ) → C' (3 - 5, 2 - 4 ) → C' (- 2, - 2 )
A triangle was dilated by a scale factor of 6. if sin a° = four fifths and segment de measures 30 units, how long is segment ef? triangle def in which angle f is a right angle, angle d measures a degrees, and angle e measures b degrees segment ef = 15.5 units segment ef = 24 units segment ef = 30 units segment ef = 37.5 units
The triangle DEF's section EF measures 24 units in length.
As per the data given in the above question are as bellow,
The provided details are as follow,
Procedure: Calculating the length that results from distorting a triangle by a scale factor
The triangle mentioned in the previous sentence is summarised in the diagram below. Using a trigonometric relationship, we discover that the following formula best describes the length of the section EF:
[tex]$\sin a^{\circ}=\frac{E F}{D E}$[/tex]
If we know that DE=30 and [tex]$\sin a^{\circ}=\frac{4}{5}$[/tex], then the length of the segment EF is:
[tex]E F=D E \cdot \sin a^{\circ} \\& E F=30 \cdot\left(\frac{4}{5}\right) \\[/tex]
EF=24
Sine (sin), cosine (cos), and tangent (tan), which are defined in terms of the ratios of the sides of a right triangle, are the fundamental trigonometric functions.
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Note: The correct question would be as bellow,
A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF?triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees
15.5 units
24 units
30 units
37.5 units
How many solutions does the equation 6x + 12 = 2(3x + 6) have? Explain.
Answer: No solution
Step-by-step explanation:
6x + 12 = 2(3x + 6)
Expand the right side:
6x + 12 = 6x + 6
Subtract 6x from both sides:
12 = 6
This is obviously not true, so there are no solutions to this equation :>
I just need the answer to UV
Answer:
In a rhombus, all sides are equal. Therefore, you can set WV (s+12) and UV (3s) equal to each other.
s+12 = 3s
Subtract s from both sides, so the variables are all on one side.
12 = 2s
Divide both sides by 2 to isolate the variable.
6 = s
UV = 3s
UV = 3(6)
UV = 18
Your savings account increased by 3% in the last year. Write an expression as a product to represent the amount of money in your savings account(s) now.
help thank you :)
You are beautiful. Don't let anyone tell you different<3
Answer:
11/20
Step-by-step explanation:
Add 1/5 and 1/4. You get 9/20.
Subtract that from 1 and you get 11/20 :)
Answer:
11/20
Step-by-step explanation:
1/5+1/4
4/20+5/20= 9/20
20/20-9/20=11/20
1 A line passes through (8, -2) and has a slope of ¼.
a. Write an equation for the line in point-slope form.
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \implies {\large \begin{array}{llll} y +2= \cfrac{1}{4} (x -8) \end{array}}[/tex]
Gilowing 50 Hz. A, B, C and D are points on the wave A Direction of wave motion 10 m B 3 m Calculate the time that the wave takes to travel the distance AB. Calcuplate the wavelength of this wave. Calculate the amplitude of this wave. Are points A and B on the wave in phase? Explain your answer
The time it takes for the wave to travel from point A to point B is 0.0086 seconds.
How to find the time of wave to travel from point A to point B?Assuming the question is referring to a sinusoidal wave with a frequency of 50 Hz, we can use the wave speed formula to calculate the time it takes for the wave to travel from point A to point B.
Wave speed (v) = frequency (f) x wavelength (λ)
Since the frequency is given as 50 Hz, we need to determine the wavelength to find the wave speed.
To calculate the wavelength, we can use the distance between two consecutive points on the wave that is in phase, such as points A and D or B and C. From the given information, we know that the distance between A and D or B and C is one wavelength. Therefore, we can calculate the wavelength as follows:
wavelength (λ) = distance between A and D or B and C = 10 m - 3 m = 7 m
Using the wave speed formula and the calculated wavelength, we can find the wave speed:
v = f x λ = 50 Hz x 7 m = 350 m/s
Now we can use the wave speed formula to find the time it takes for the wave to travel from point A to point B:
v = d / t
where d is the distance between A and B (which is 3 m) and t is the time it takes for the wave to travel that distance.
Rearranging the formula, we get:
t = d / v = 3 m / 350 m/s = 0.0086 s
Therefore, the time it takes for the wave to travel from point A to point B is 0.0086 seconds.
To find the amplitude of the wave, we would need additional information, as the amplitude is the maximum displacement of the wave from its equilibrium position.
As for whether points A and B are in phase, we need to compare the phase difference between the two points to the wave period. The period of a wave is the time it takes for one complete oscillation, and it is given by:
period (T) = 1 / frequency (f) = 1 / 50 Hz = 0.02 s
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In a right triangle, sin (8x - 9)° = cos (x+6)°. Solve for x. Round your answer to the nearest hundredth if necessary.
To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents. The x is 8 .
Find value of x ?To solve the triangle, or identify unknown portions in terms of known portions, we can apply the Pythagorean theorem and the properties of sines, cosines, and tangents.
Pythagorean theorem: a2 + b2 = c2.
Sine: sin A=a/c, sin B=b/c.
Cosines: cos A = b/c, cos B = a/c.
Identity based on trigonometry
cos x sin (90-x)
therefore, if we have
(4x plus 10) o = Cos (6x)
(4x plus 10) o = Sin (90- 6x)
4x + 10 = 90 - 6x
4x+6x = 90 - 10
10x = 80
x = 80/10
x = 8
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Solve the equation with the quadratic
formula. Enter the smallest solution
first and round to the nearest tenth.
2x² - 4x - 48 = 0
x = [?], [?]
For the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
What is quadratic equation?
The second-degree equation is a quadratic equation. This indicates that it has at least one (1) squared phrase. Ax2 + bx + c = 0 is one of the most used formulas for solving quadratic equations. Here, a, b, and c are constants or numerical coefficients. Here, the variable "X" is unknowable.
ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
We have a quadratic equation;
2x² - 4x - 48 = 0
To find the value of x we have to follow these steps ;
(2x^2 - 4x) - 48 = 0
Pull out like factors :
2x^2 - 4x - 48 = 2 • (x^2 - 2x - 24)
x2 multiplied by 2x and 24
x^2 is the initial term, and it has a coefficient of 1.
The coefficient of the middle term, which is -2x, is 2.
"The constant," the final term, is -24.
⇒ x^2 - 6x + 4x - 24
⇒ (x+4) • (x-6)
⇒ 2 • (x + 4) • (x - 6) = 0
therefore x+4 = 0
x = -4
and x-6 = 0
Add 6 to both sides of the equation :
x = 6
Hence, for the quadratic equation 2x² - 4x - 48 = 0 value of x is 6 and -4.
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stressed out, part ii. in a study evaluating the relationship between stress and muscle cramps, half the subjects are randomly assigned to be exposed to increased stress by being placed into an elevator that falls rapidly and stops abruptly and the other half are left at no or baseline stress. can this study be used to conclude a causal relationship between increased stress and muscle cramps?
The following type of study can be concluded as an observational study.
An observational study is a type of study that is used to gather data on the characteristics and behaviors of a particular group of people or subjects without actively manipulating or interfering with the subjects.
This study can be used to suggest a causal relationship between increased stress and muscle cramps, but it cannot conclusively prove causality.
There are several reasons why this study design cannot be used to conclude a causal relationship. First, the study is a non-randomized, uncontrolled experiment, which means that there may be other factors that could be influencing the results.
For example, the subjects in the stress group may have other characteristics or preexisting conditions that are related to muscle cramps. Additionally, the study does not have a control group for comparison, so it is not possible to determine if the muscle cramps are caused by stress or by some other factor.
Second, the study design is a single-blind study, which means that only the subjects are not aware of their group assignment, but the experimenter knows which group the subjects are in. This can lead to bias in data collection, analysis, or interpretation.
Therefore, The following type of study can be concluded as an observational study.
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the numberline shows the temperatures at 2:00 AM. and 2:00 P.M. in the Gobi Desert. Find and interpret the distance between the points?
2:00am -13F 2:00pm 38F
Answer:
There is a difference of 51 degrees
Step-by-step explanation:
-13 to zero is 13 degrees
zero to 38 degrees is 38 degrees
13 + 38 is an increase of 51 degrees