The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
a² + b² – 2ab cos C = c²
Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.
Then we have
7² + c² – (2 · 7 · c) cos 105° = 10²
c² + 3.62c – 51 = 0
On solving, we have
c = 5.56
Then the angle C will be
10² + 7² – 2 · 7 · 10 · cos C = 5.56²
149 – 140 cos C = 30.91
cos C = 0.8435
C = 32.49°
We know that
∠A + ∠B + ∠C = 180°
105° + ∠B + 32.49° = 180°
∠B = 42.51°
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What is the standard form of 0.00849
Answer:
8.49 × 10⁻³
Explanation:
Standard form of a number: A. × 10ᵇ
(where 'A' is the number, b is the exponent over 10)
For the number "0.00849", move the decimal point 3 places right so the exponent of 10 is -3.
Standard form: 8.49 × 10⁻³
Other examples of standard/scientific forms are: standard forms
i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²
ii) 4030, move the decimal point 3 places left = 4.03 × 10³
Answer:
when a number is given in that manner you have to take that decimal between two whole numbers.
and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.
at what height will the air pressure equal 50%
Answer:
Im pretty sure its C which is 5776.2m
Step-by-step explanation:
Tristan has a points card for a movie theater.
He receives 25 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 110 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Tristan can make to earn his first free movie ticket.
Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
Let v be the number of visits Tristan makes to the movie theater.
He receives 25 rewards points just for signing up, and he earns 8.5 points for each visit. So, the total rewards points he will have is
25+8.5v.
He needs at least 110 points for a free movie ticket. Therefore, we can write the inequality:
25+8.5v≥110
To solve for v, we can subtract 25 from both sides of the inequality and then divide by 8.5:
8.5v≥85
v≥85/8.5
v≥10
So, Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
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Last week, you went to the water park with friends on Monday, Wednesday, and Friday. If you stayed at the water park 3.5 hours each of those days, how many hours did you spend at the water park last week?
A. 15 hours
B. 9 hours
C. 5.5 hours
D. 10.5 hours
Answer: D. 10.5 hours
Step-by-step explanation:
3 days, 3.5 hours each
3.5 * 3 = 10.5 hours
Answer:
D. 10.5
Step-by-step explanation:
3.5 x 3 = 10.5
If a(x) = 3x + 1 and b (x) = square root of x-4, what is the domain of (b o a)(x)
( 1, ∞) is the domain of (b o a)(x)
What is Function?
A function is defined as a relation between a set of inputs having one output each.
According to the question,
[tex]a(x) = 3x + 1 \\\\b (x) =\sqrt{x+4}[/tex]
To find the domain of the composite function,
[tex](b o x) (x) = b(a(x))\\\\(b o x) (x) = b(a(3x-1))\\\\(b o x) (x) = \sqrt{3x+ 1 -4} \\\\(b o x) (x) = \sqrt{3x -3}\\\\[/tex]
Therefore,
[tex]3x - 3 \geq 0\\3x \geq 3\\x \geq 1\\\\[/tex]
Hence , [ 1, ∞ ] is is the domain of (b o a)(x).
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What is the value of f(1)?
0
1
2
4
Answer:
Solution*-1
Step-by-step explanation:
because 1 is the value of (1)
Please help due in soon
1) Rotate triangle A 90° clockwise around O
C (5, 6) ⇒ D (1, 2)
2) Move triangle A' 6 spaces to the right
O (1, 6) ⇒ O' (7, 6)
D (1, 2) ⇒ D' (7, 2)
So Shape A ⇒ Shape B
Jacob traveled 171 miles in 3.8 hours. He wants to know how many miles he traveled in one hour, so he set up this problem:
Answer:
so first we have to divide each side by 38
4.5miles=0.1
45miles=1 hour
Hope This Helps!!!
If n= 1999 ! then [tex]\large \sf\sum\limits_{x = 1}^{1999} log_{n}(x) [/tex] is equal to
a) -1
b) 0
c) 1
d) [tex] \sf \sqrt[1999]{1999} [/tex]
Answer:
a) 1
Step-by-step explanation:
added in the picture
Suppose the mean height for men is 70 inches with a standard deviation of 2 inches. What percentage of men are more than 72 inches tall?
The percentage of men is more than 72 inches tall will be 0.15866.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x – μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
Suppose the mean height for men is 70 inches, with a standard deviation of 2 inches.
Then the percentage of men are more than 72 inches tall will be
z = (72 – 70) / 2
z = 1
The percentage of men is more than 72 inches tall will be
P(x > 72) = P(z > 1)
P(x > 72) = 1 – P(x < 72)
P(x > 72) = 1 – 0.84134
P(x > 72) = 0.15866
Thun, the percentage of men are more than 72 inches tall will be 0.15866.
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Which number has a repeating decimal form?
O A.
[tex] \sqrt{15} [/tex]
OB.
[tex] \frac{11}{25} [/tex]
O C.
[tex] \frac{3}{20} [/tex]
O D.
[tex] \frac{2}{6} [/tex]
Answer:
D. [tex] \frac{2}{6} [/tex]
Step-by-step explanation:
2÷ 6 = 0.33333
As you can see 3 is repeating.
Therefore [tex] \frac{2}{6} [/tex] as repeating decimal form.
Can somebody help me, i would really appreciate it!!
It will take 5 seconds for the waste to hit the ground.
How many seconds will it take for the waste to hit the ground?We know that the bird releases the waste from a height of 400ft, so the height equation is:
[tex]h(t) = -16t^2 + 400[/tex]
The waste will hit the ground when its height is equal to zero, so we just need to solve the quadratic equation:
[tex]h(t) = 0 = -16t^2 + 400\\\\16t^2 = 400\\\\t^2 = 400/16 = 25\\\\[/tex]
Now we can apply the square root in both sides:
[tex]t = \sqrt{25} = 5[/tex]
It will take 5 seconds for the waste to hit the ground.
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Drag each tile to the correct box.
A certain kind of bacteria multiplies at a rate of 150 percent per hour. When a person’s blood has 45,000,000 of these bacteria, the person will fall sick. Let’s suppose 100 such bacteria entered a person’s blood. How many hours will it take for the person to become sick? Arrange the steps in the right order to show how to find the number of hours it will take for the person to fall sick.
The steps arranged in the right order are:
45,000,000 = [tex]100(1 + 1.5)^{t}[/tex]
45,000,000 = [tex]100(2.5)^{t}[/tex]
450,000 = [tex](2.5)^{t}[/tex]
log 450,000 = log [tex](2.5)^{t}[/tex]
log 450,000 = log t (2.5)
[tex]\frac{log 450,000}{log 2.5} = t[/tex]
5.632 / 0.3979 = t
t = 14.21 hours
What are the correct steps?The equation that can be used to represent the growth rate of the bacteria is an exponential equation. The form of exponential equations is:
FV = P(1 + r)^t
Where:
FV = future value of the bacteria PV = present population r = rate of increase t = number of hours45,000,000 = 100( 2.5)^t
t = log 450,000 / log 2.5
t = 14.21 hours
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Chords AC and BD intersect in circle O as shown in the diagram. Two of the angle measurements are marked. What is mL CED?
Answer:
By using the formulas of circle and geometry, we find that ∠CED = 65°.
Step-by-step explanation:
We know that the measure of the interior angle is the half sum of the arcs comprising it and its opposite, so
∠CED = 0.5 × (arc AB + arc CD)
See the attached figure with letters to better understand the problem
arc AB = 82° (by central angle)
arc CD = 48° (by central angle)
Substitute the values in the formula above
∠CED = 0.5 × (82° + 48°)
∠CED = 0.5 × 130°
∠CED = 65°
Therefore the answer is ∠CED = 65°
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. If we start with one bacterium and it doubles in
number every 15 minutes, HOW LONG WILL IT
TAKE for one bacterium to become one million??
Answer:
298.97 minutes
Step-by-step explanation:
2^x = 1 000 000 where 'x' is the number of 15 minute periods
x = 19.931 15 minute periods = 298.97 minutes
The price of a pack of kitchen rolls is reduced by 1/6
The new price is £1.20
Work out the original price.
Answer: 1.44
Step-by-step explanation:
(original price) - (1/6 of the original price) = 1.20
If you let x = original price, then the equation is:
x - 1/6 x = 1.20
5/6 x = 1.20
x = 1.44
the original price is £1.44.
Credits to the person who also answered :)
I hope this helps!
Answer:
£1.44
Step-by-step explanation:
Since the original price was reduced by 1/6, that means the new price is 5/6 of the original price.
Let x = original price.
Write an equation and solve it.
5/6 x = £1.20
x = £1.20 × 6/5
x = £1.44
Now evaluate f(x)=2x^4-4x^3-11x^2+3x-6 for x=-2.
F(-2)=
Answer:
8
Step-by-step explanation:
f(x)=2x^4-4x^3-11x^2+3x-6
f(-2)=2(-2)^4-4(-2)^3-11(-2)^2+3(-2)-6
f(-2)=2(16)-4(-8)-11(4)-6-6
f(-2)=32+32-44-12
f(-2)=64-44-12
f(-2)=20-12
f(-2)=8
A 12 foot ladder leans against a wall so that the base of the ladder is 7 feet from the wall. How high up on the wall will the ladder reach? Round to the nearest hundredth of a foot.
g Lovely Lawns, Inc., intends to use sales of lawn fertilizer to predict lawn mower sales. The store manager estimates a probable six-week lag between fertilizer sales and mower sales. The pertinent data are: PeriodFertilizer SalesNumber of Mowers Sold 11.915 21.612 31.713 41.915 52.116 61.813 71.914 81.713 91.815 101.412 111.814 121.714 131.714 141.612 a. Determine the correlation between the two variables.
The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
What is correlation?The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when other data value is increased or decreased respectively.
The pertinent data are:
Period Fertilizer Sales Number of Mowers Sold
1 1.6 12.0
2 1.3 10.0
3 1.8 13.0
4 2.0 15.0
5 2.2 15.0
6 1.5 11.0
7 1.6 12.0
8 1.4 10.0
9 1.8 13.0
10 1.4 10.0
11 1.9 15.0
12 1.4 11.0
13 1.7 14.0
14 1.4 13.0
To determine the correlation between the two variables
Regression equation ( y ) = a + bx
y = dependent variable ( mower )
x = independent variable ( fertilizer)
a = intercept point ( y-axis and regression line )
b = slope ( regression line )
From the given data;
N = 14 , Σ x = 22.8,
Σy = 131, Σy^2 = 1269,
Σx^2 = 38.18, (Σx)^2 = 519.84
Σxy = 219.8, (Σy)^2 = 17161
Hence, The correlation between variables (r) = 0.959, and signifies a positive relationship between the variables.
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Richard has a debt of $45. Express it in the form of absolute value.
The absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
What is debt?It is defined as the amount one party needs to pay to another party as the first party borrowed an amount that will be credited by the second party. Debt occurs when one party cannot be able to purchase something under normal circumstances.
As we know,
The absolute value of a negative account balance is equal to the amount of debt. A balance of $0 on an account means there is no debt. Credit is shown by a positive account balance.
Richard has a debt of $45.
The negative of 45 value represents the debt.
-$45 = debt
Absolute value = |-45| = 45
Thus, the absolute value of debt of $45 is 45 because a balance of $0 on an account means there is no debt, and a negative of 45 value represents the debt.
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Type the correct answer in each box. Use numerals instead of words. Function g is a transformation of function f. Graph shows 2 exponential functions. First curve f enters quadrant 3 at (minus 6, minus 2) rises through (0, minus 1) and (1, 0) and (2, 2) in quadrant 1. Second curve g enters quadrant 2 at (minus 6, 6) falls through (0, 3) and (1, 0) in quadrant 1. What is the equation of function g? g(x) = f(x)
An equation is formed of two equal expressions. The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given graph is the graph of an exponential function, the general equation of an exponential function is given by the y=aeᵇˣ. To get the function f(x) and g(x), you need to substitute the points in the given function and produce the equation of each function.
The equation for f(x) from the given graph can be written as,
[tex]f(x)=e^{(\ln2)x}-2[/tex]
Now, similarly from the graph the function of g(x) can be written as,
[tex]g(x)=-3e^{(\ln2)x}+6[/tex]
Further, the equation of function g(x) in terms of f(x) can be written as,
g(x) = -3[f(x)]
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Step-by-step explanation: I got it right!
EMERGENCY!! 25 POINTS!! Find 40th term of 5n - 3
Answer:
197
Step-by-step explanation:
the answers 197 because if an=5n-3 then a40= 197
If y varies inversely as x, and y = 58 when x = 9, find y when x = 261.
Answer:
2
Step-by-step explanation:
y=k/x
58=k/9
k=58×9
k=522
y=522/x
when x=261
y=522/261
y=2
Which is the graph of f(x) = (2)* ?
a graph
I assume you meant to type f(x)=2^x.
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
3 , 6
Step-by-step explanation:
Answer: (2,-3), (2, -3)
Step-by-step explanation: Substitute 2 into each equation. See Attachment and don’t forget to check the work just in case ;)
Solve for x :
[tex] \sf \: \: \: \: \: \: \: \: \: \: \: 29x + x = 30[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \sf bluh... \: \: so \: \: boring[/tex]
Answer:
x = 1
Step-by-step explanation:
Step 1: Combine like terms.
[tex](29x + x) = (30)[/tex] [tex]30x=30[/tex]Step 2: Divide both sides by 30.
[tex]30x/30=30/30[/tex] [tex]x=1[/tex]Step 3: Check if solution is correct.
[tex]29(1)+(1)=30[/tex] [tex]29+1=30[/tex] [tex]30=30[/tex]Therefore, x = 1.
Solution: X=1
[tex]\searrow[/tex]
Detailed explanation:
Here we need to solve for x. x is our unknown. It's what we should find.
[tex]\searrow[/tex]
Note right up front that we can add the x's. This is a process that is known as "Combining Like Terms". We can combine them by adding, like here.
[tex]\twoheadrightarrow\sf 29x+x=30[/tex]
"x" is the same as 1x.
[tex]\twoheadrightarrow\sf 30x=30[/tex]
We're getting closer to finding the value of the unknown!
Now we know that if we multiply 30 times the unknown, we will get 30.
What will we get if we multiply 1 times the unknown? 1 is what we will obtain upon dividing by 30.
So our unknown, or x, is 1.
Voila! There's our answer!
Cheers! ^-^_____________________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_____________________________
Which ordered pair makes both inequalities true?
y < –x + 1
y > x
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 1) and (1, 0). Everything below and to the left of the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 1) and (1, 1). Everything above and to the left of the line is shaded.
(–3, 5)
(–2, 2)
(–1, –3)
(0, –1)
Answer:
-9
Step-by-step explanation:
-9
Find the area and perimeter.
The figure shows a triangle. One side is given by 4 x minus 3 units. The second side is given by x plus 9 units. The third side is equal to 8 units. The height from the third side is given by 3 x units.
Hint: The height of a non-right triangle is the length of the segment of a line that is perpendicular to the base and that contains the opposite vertex
Answer:
Area=12x square units; Perimeter=5x+14 units
Step-by-step explanation:
Recall the formulas for area and perimeter of a triangle:
Area of a triangle is half of the product of a base its corresponding height:
[tex]A=\frac{1}{2}bh[/tex]
Perimeter is the sum of all of the side lengths:
[tex]P=a+b+c[/tex]
In arbitrary triangles ABC, the sides are labeled across from a vertex with a matching lowercase letter. So, in my diagram, side "b" is the bottom with length "8". Side "b" is also the base, so the corresponding height is the perpendicular line segment that connects side "b" with vertex "B", which measures "3x"... 3 times some unknown value.
Side "a" is length "4x-3", and side "c" is length "x+9".
In this situation, where the sides have their specific relationship with "x" and the height is exactly triple "x", solving for x (and thus exact numerical values for the Perimeter and Area) involves trying to relate the two equations, possibly done with Heron's formula for area, or with trigonometry. Ultimately, it involves solving a 4th degree polynomial to get an exact answer, which is not what the question intends, so we'll leave the Area and Perimeter in terms of x (meaning there will still be "x" in our expressions to represent the Area and Perimeter).
Area
[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(8)(3x)\\A=12x[/tex]
So the Area of the triangle equals 12x square units.
Perimeter
[tex]P=a+b+c\\P=(4x-3)+(8)+(x+9)\\P=5x+14[/tex]
So the Perimeter of the triangle equals 5x+14 units
can someone please help meee
Answer:
with a line accross the points
Which expression is equivalent to (startfraction 4 m n over m superscript negative 2 baseline n superscript 6 baseline endfraction) superscript negative 2? assume m not-equals 0, n not-equals 0.
The equivalent expression to [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex] is given by [tex]=\mathbf{\frac{n^{10}}{16m^6}}[/tex].
From the principle of indices we get,
Addition of exponent, [tex]a^{m+n}=a^m.a^n[/tex]
Subtraction, [tex]a^{m-n}=\frac{a^m}{a^n}[/tex]
Multiplication, [tex]a^{mn}=(a^m)^n[/tex]
negative exponent, [tex]a^{-m}=\frac{1}{a^m}[/tex]
Here in the problem given expression is [tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
Calculating we get,
[tex]\left(\frac{4mn}{m^{-2}n^6}\right)^{-2}[/tex]
[tex]=\left(4m^{1-(-2)}n^{1-6}\right)^{-2}[/tex], using addition and subtraction of indices formulae
[tex]=\left(4m^3n^{-5}\right)^{-2}[/tex]
[tex]=16^{-1}m^{-6}n^{10}[/tex], using multiplication of indices
[tex]=\frac{n^{10}}{16m^6}[/tex], using negative exponent formula
Hence the equivalent required expression is [tex]=\frac{n^{10}}{16m^6}[/tex].
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Answer:
b
Step-by-step explanation:
edge 23
