"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5
For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say
x/y = 4/5
also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.
Let's cross multiply on the first equation to get...
x/y = 4/5
5*x = 4*y
Now replace y with 90-x. Solve for x
5x = 4(90-x)
5x = 360 - 4x
5x+4x = 360
9x = 360
x = 360/9
x = 40
Use this to find y
y = 90 - x = 90 - 40 = 50
So the two angles are 40 degrees and 50 degrees.
To find two complementary angles with a ratio of 4 to 5, set up the equation 4x + 5x = 90, where x is the common multiplier. Solve for x to find each angle's measure. Check that the sum equals 90 degrees to confirm the solution.
Explanation:To determine the measures of two complementary angles with a ratio of 4 to 5, you first need to understand that complementary angles add up to 90 degrees. Let's call the angles A and B, with A being the smaller angle. Since they are in a ratio of 4 to 5, we can represent them as 4x and 5x, respectively, where x is a common multiplier. The equation to solve for x is set up based on the definition of complementary angles:
4x + 5x = 90
Combine like terms to simplify:
9x = 90
Now, divide both sides by 9 to solve for x:
x = 90 ÷ 9
x = 10
Once you have the value of x, you can find the measures of the angles:
A = 4x = 4(10) = 40 degrees
B = 5x = 5(10) = 50 degrees
Always check your answer to confirm it makes sense. In this case, A + B should equal 90 degrees, which it does (40 + 50 = 90).
Please answer this question! 30 points and brainliest!
Answer:
c x >=3
Step-by-step explanation:
9-2x <= 3
Subtract 9 from each side
9-9-2x <=3-9
-2x <-6
Divide by -2. Remember to flip the inequality when multiplying or dividing by a negative number.
-2x/-2 >= -6/-2
x >=3
Answer: i think it would be letter c plz mark brainliest and add as friend
A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the oceanis 12.5°. If a point on the ocean floor is 60 meters directly below the ship, how many meters is it from that point on the ocean floor to the wreck?
Answer:
The 13.2 meters from that point on the ocean floor to the wreck.
Step-by-step explanation:
As given
A ship's sonar finds that the angle of depression to a ship wrack on the bottom of the ocean is 12.5°.
If a point on the ocean floor is 60 meters.
Now by using the trigonometric identity.
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
As shown in the figure given below.
Perpendicular = CB
Base = AC = 60 meters
[tex]\theta = 12.5^{\circ}[/tex]
Put in the identity
[tex]tan\ 12.5^{\circ} = \frac{CB}{AC}[/tex]
[tex]tan\ 12.5^{\circ} = \frac{CB}{60}[/tex]
[tex]tan\ 12.5^{\circ} = 0.22[/tex]
[tex]tan\ 12.5^{\circ} = 0.22[/tex]
[tex]0.22= \frac{CB}{60}[/tex]
CB = 60 × 0.22
CB = 13.2 meters
Therefore the 13.2 meters from that point on the ocean floor to the wreck.
The distance from the point on the ocean floor directly below the ship to the shipwreck is approximately 13.3 meters.
We will use the tangent function, which relates the angle of depression to the opposite side (the distance from the point directly below the ship to the shipwreck) and the adjacent side (the depth of the ocean at the point directly below the ship).
Given:
The angle of depression [tex]\theta[/tex] is [tex]12.5^o.[/tex]
The depth of the ocean at the point directly below the ship, h, is 60 meters.
We want to find the distance from the point directly below the ship to the shipwreck, which we will call [tex]d.[/tex]
Using the tangent function :
[tex]\[ \tan(\theta)[/tex] = [tex][\frac{\text{opposite}}{\text{adjacent}}][/tex]
[tex]\[ \tan(12.5^o) = \frac{d}{60} \][/tex]
To find d, we rearrange the equation: [tex]\[ d = 60 \times \tan(12.5^o) \][/tex]
Now we calculate the tangent of 12.5 and multiply it by 60:[tex]\[ d = 60 \times \tan(12.5^o) \][/tex]
[tex]\[ d \approx 60 \times 0.22169\][/tex]
[tex]\[ d \approx 13.3014 \][/tex]
Therefore, the distance from the point on the ocean floor directly below the ship to the shipwreck is approximately 13.3 meters.
The diagram of question is:
Y is inversy proportional to x. When y=7 , x=9 A) work out an equation connecting y and x? B) work out the value of y when x=21
Answer:
see explanation
Step-by-step explanation:
since y is inversely proportional to x the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportionality
to find k use the given condition when y = 7, x = 9
k = yx = 7 × 9 = 63
y = [tex]\frac{63}{x}[/tex] ← is the equation connecting them
when x = 21, then
y = [tex]\frac{63}{21}[/tex] = 3
The equation connecting y and x is y = 9 + 3x. When x = 21, y = 72.
Explanation:The equation connecting y and x is given by y = 9 + 3x. In this equation, the constant term, also known as the y-intercept, is 9. The coefficient of x, also known as the slope, is 3. This means that for every increase of 1 in x, y increases by 3.
To calculate the value of y when x = 21, substitute x = 21 into the equation: y = 9 + 3(21) = 9 + 63 = 72. Therefore, when x = 21, y = 72.
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To find the quotient of 8 :- 1/3, multiply 8 by
Answer:
3
Step-by-step explanation:
A bar of gold has a volume of 722 cubic centimeters and weighs 13.949 kilograms. What's its density in grams per cubic centimeter?
Answer:
The density of the bar of gold is 19.32 grams per cubic centimeter .
Step-by-step explanation:
Formula
[tex]Density = \frac{Mass}{Volume}[/tex]
As given
A bar of gold has a volume of 722 cubic centimeters and weighs 13.949 kilograms.
As 1 kilogram = 1000 gram
Than convert 13.949 kilograms into grams.
13.949 kilograms = 13.949 × 1000 grams
= 13949 grams
Mass = 13949 grams
Volume = 722 cubic centimeter
As put in the formula
[tex]Density = \frac{13949}{722}[/tex]
Density = 19.32 grams per cubic centimeter (Approx)
Therefore the density of the bar of gold is 19.32 grams per cubic centimeter .
If JK and LM are congruent and parallel, then JKL and MLK are congruent.
Answer:
Given statement is TRUE.
Step-by-step explanation:
Given that line segment JK and LM are parallel. From picture we see that LK is transversal line.
We know that corresponding angles formed by transversal line are congruent.
Hence ∠JKL = ∠ MLK ...(i)
Now consider triangles JKL and MLK
JK = LM {Given}
∠JKL = ∠ MLK { Using (i) }
KL = KL {common sides}
Hence by SAS property of congruency of triangles, ΔJKL and ΔMLK are congruent.
Hence given statement is TRUE.
Write the sentence as an inequality. 14 is no less than 8 times a number x plus 6.
Answer:
[tex]x \leq 1[/tex]
Step-by-step explanation:
Multiplying 8 by x can be written as 8x, and +6 on end:
8x + 6
Because it says 14 is no less than, the equal to or more than sign needs to be used:
[tex]8x + 6 \leq 14[/tex]
The -6 can be moved over to the other side making it a -6:
[tex]8x \leq 14 - 6[/tex]
[tex]8x \leq 8[/tex]
Simplify by dividing both sides by 8:
[tex]x \leq 1[/tex]
Which is the inequality!
Answer:
The given statement can be written as [tex]14\geq 8x+6[/tex] or [tex]x\leq 1[/tex].
Step-by-step explanation:
It is required to write the sentence as an inequality.
The given sentence is "14 is no less than 8 times a number x plus 6".
The given statement can be written as " 14 can be equal or more than 8 times a number x plus 6"
Now, in the inequality form, the statement will be,
[tex]14\geq 8x+6[/tex]
Solve the above inequality as,
[tex]14\geq 8x+6\\8\geq 8x\\1\geq x\\x\leq 1[/tex]
Therefore, the given statement can be written as [tex]14\geq 8x+6[/tex] or [tex]x\leq 1[/tex].
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The ___________ is the center of gravity in a triangle.
A) centroid
B) circumcenter
C) incenter
D) orthocenter
Answer:
A) centroid
Step-by-step explanation:
I just looked it up.
Answer:
A. Centroid
Step-by-step explanation:
A centroid of a triangle is the point where the three medians of the triangle meet. A median of a triangle is a line segment from one vertex to the mid point on the opposite side of the triangle. The centroid is also called the center of gravity of the triangle.
The male elephant weighs 8,000 pounds wich is the is th same as 4 tons the female weighs 7,000 pounds how many tons does the female weighs
Answer:
3.5 tons
Step-by-step explanation:
In the figure shown, what is the measure of angle x?
150 degrees
110 degrees
105 degrees
100 degrees
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
In ΔABC,
∠A= 30°
∠B=75°
We need to find the value of ∠ACD=x
As we know that "Sum of interior angles is equal to exterior angle":
So, we will have,
[tex]\angle A+\angle B=\angle ACD\\\\30\textdegree+75\textdegree=\angle ACD\\\\105\textdegree=\angle ACD[/tex]
Hence, Third option is correct.
Answer:
The answer is 105 degrees
180-75=105
Is the following true or false? the derivative with respect to x of the product of x squared and e raised to the x power equals the product of x times e to the x power and the quantity x plus 2 True False
Answer:
It is true
Step-by-step explanation:
How to solve this problem?
Answer:
Can not be determined.
Step-by-step explanation:
We can easily notice that the limit is x tends to infinity, whereas x is not present in the given function, we are given (1 + 1/n). So we can not evaluate the given limit for x as parameter, we must have some function of x to solve this problem.
Hence, option C is correct i.e. the limit can not be determined.
Answer:
cannot be determined
Step-by-step explanation:
If we have, [tex]\lim_{n \to \infty} {1+\frac{1}{n}}[/tex]
We plug in infinity for n directly
1/∞ =0
So when we plug in infinity for n then 1/n becomes 0
[tex]\lim_{n \to \infty} {1+\frac{1}{n}}[/tex]
[tex] {1+\frac{1}{infinity}}[/tex]
1+ 0 = 1
In our problem , limit says x-> ∞
there is no x term inside
[tex]\lim_{x \to \infty} {1+\frac{1}{n}}[/tex]
so we can clearly say limit cannot be determined
A summer camp has 32 campers. A total of 22 of them swim, 20 play softball, and 5 do not swim or play softball. Which values complete the table?
a = 15, b = 10, c = 7, d = 5, e = 12
a = 15, b = 7, c = 5, d = 10, e = 12
a = 14, b = 7, c = 5, d = 12, e = 10
a = 14, b = 12, c = 7, d = 5, e = 10
Answer:
a = 15, b = 7, c = 5, d = 10, e = 12
Step-by-step explanation:
You only need to find d.
22+d=32, d=10
Only one choice has d=10
Don't waste time checking the others.
Answer:
It’s B
Step-by-step explanation:
One ounce of solution x contains only ingredients a and b in the ratio of 2:3 one ounce of solution y count aims only ingredients a and b in the ratio of 1:2 if solution z is created by mixing solutions x and y in the ration of 3:11 then 2520 ounces of solution z contains how many ounces of a
Answer:
Volume of a in z = 876 ounces
Step-by-step explanation:
For z, the ratio of x and y is 3 : 11
x : y = 3 : 11 , which means in 14 parts of solution z : x will be 3 parts and y will be 11 parts
So, in 2520 ounces solution of z ,
[tex]x=\frac{2520*3}{14}=540\\y=\frac{2520*11}{14}=1980[/tex]
Volume of a in z = { Volume of a in x + Volume of b in x }
Therefore,
[tex]Volume \thinspace of \thinspace a\thinspace in\thinspace x = 540\cdot \frac{2}{5} = 216\\Volume \thinspace of \thinspace b \thinspace in \thinspace x = 1980\cdot \frac{1}{3}=660[/tex]
So, Volume of a in z = 876 ounces
The matrix shows the number of different basketball shots three players made in two minutes. These players want to double these results. Which matrix shows what the players want to do?
Answer:
Look at your answer choices and see which one has multiplied each of the shots by 2
Step-by-step explanation:
Step-by-step explanation:
To find the right matrix, you have to look which matrix among the options has doubled each item.For example, if you have:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Then, your answer would be:
[tex]\left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right][/tex]
Because each term is the double of the original matrix.
Remember that, this operation is between a scalar and a matrix. That operation is done according to this property:[tex]aM=a\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] = \left[\begin{array}{ccc}1a&2a&3a\\4a&5a&6a\\7a&8a&9a\end{array}\right][/tex]
In fewer words, the scalar will multiply each element of the matrix.
Sam is building a model of an antique car the scale of his model to the actual car is 1:10 his model is 16 1/2 inches long. How long is the actual car
16.5(10)=165
The length of the actual car is 165in.
It takes layla 2/5 hour to swim 1/2 mile what is the unit rate of miles that layla can swim per hour
Good Morning!
Distance = rate x time
1/2 mile = R x 2/5 hour
1/2=2/5R
/2/5 /2/5
R=1/2 x 5/2
R=1 1/4
She can swim 1 1/4 per hour.
I hope this helps! :)
Answer:
1 1/4
Step-by-step explanation:
Please help me!!!!!!
Answer: 243, 729
Step-by-step explanation:
1, 3, 9, 27, 81 is a geometric sequence where r = 3
a₁ = 1
a₂ = 1 x 3 = 3
a₃ = 3 x 3 = 9
a₄ = 9 x 3 = 27
a₅ = 27 x 3 = 81
To find the next two terms, multiply the previous term by 3:
a₆ = 81 x 3 = 243
a₇ = 243 x 3 = 729
Sammy bought a new car. The depreciation equation is given by f(x) = 30,000(.85)x, where x represents the number of years since the purchase of the car, and f(x) represents the value of the car. By what percent does Sammy's car depreciate each year?
In a depreciation equation, you multiply the value of the car by the percent of depreciation minus 1.
In the given equation you are multiplying the value of the car by (.85)
This means the percent of depreciation would be 1 - 0.85 =0.15 which is 15%
The car depreciates by 15% every year.
Answer:
The car depreciates by 15% every year.
Step-by-step explanation:
A pair of shoes usually sells for $62. If the shoes are 40% off, and sales tax is 8%, what is the total price of the shoes, including tax?
Answer:
45.57
Step-by-step explanation:
Final answer:
After applying a 40% discount to the original $62 price of the shoes and adding an 8% sales tax, the total cost of the pair of shoes is $40.18.
Explanation:
The question involves calculating the total price of a pair of shoes after a discount and adding sales tax. To find the discounted price, we take 40% off the original price of $62. To calculate 40% of $62, we multiply 62 by 0.40 (which is 40% as a decimal), giving us $24.80. We subtract this discount from the original price: $62 - $24.80 = $37.20, which is the discounted price of the shoes.
Next, calculate the sales tax on the discounted price by converting the sales tax rate from a percent to a decimal. The sales tax rate is 8%, which as a decimal is 0.08. Multiply the discounted price by the sales tax rate: $37.20 x 0.08 = $2.976, which we round to $2.98.
Finally, add the sales tax to the discounted price to find the total cost: $37.20 + $2.98 = $40.18. Therefore, the total price of the shoes, including tax, is $40.18.
Using the linear combination method, what is the solution to the system of linear equations 7x-2y=-20 and 9x+4y=-6 ?
Answer:
The answer would be well, B.(-2,3)
The given system of equations are solved to obtain x = -2 and y = 3.
What are the types of a system of equations?The given system of equation can either have a unique solution, more than one solutions or no solution.
On this basis they are divided into two parts consistent and inconsistent.
A consistent system has one or more solutions while for an inconsistent system there are no solutions.
The equations are given as,
7x - 2y = -20 (1)
9x + 4y = -6 (2)
Multiply equation (1) by 2 and then add to (2) to get,
2(7x - 2y) + 9x + 4y = -20 × 2 + (-6)
⇒ 23x = -46
⇒ x = -2
Then, substitute x = -2 in equation (1) to get,
7 × -2 - 2y = -20
⇒ y = 3
Hence, the solution of the given system of equations is given as x = -2 and y = 3.
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Please please help me!!!!!!!!
Answer: 20%
Step-by-step explanation:
200\1000
HELP CHECK THIS
The work of a student to solve a set of equations is shown:
Equation A: y = 15 − 2z
Equation B: 2y = 3 − 4z
Step 1: −2(y) = −2(15 − 2z) [Equation A is multiplied by −2.]
2y = 3 − 4z [Equation B]
Step 2: −2y = 15 − 2z [Equation A in Step 1 is simplified.]
2y = 3 − 4z [Equation B]
Step 3: 0 = 18 − 6z [Equations in Step 2 are added.]
Step 4: 6z = 18
Step 5: z = 3
In which step did the student first make an error?
Step1
Step 2
Step 3 <<<<<
Step 4
Which statement is true ? Help plzzzz
Answer:
Correct choice is B
Step-by-step explanation:
The quadratic function g(x) has equation [tex]g(x)=ax^2+bx+c.[/tex] Find values of a, b and c:
[tex]g(0)=2=a\cdot 0^2+b\cdot 0+c\Rightarrow c=2.[/tex]
[tex]g(2)=3=a\cdot 2^2+b\cdot 2++2\Rightarrow 4a+2b=1.[/tex]
[tex]g(4)=2=a\cdot 4^2+b\cdot 4+2\Rightarrow 16a+4b=0.[/tex]
From the last equation [tex]b=-4a[/tex] and [tex]4a-8a=1,\\ \\a=-\dfrac{1}{4},\\ \\b=1.[/tex]
The equation of the quadratic function g(x) is
[tex]g(x)=-\dfrac{1}{4}x^2+x+2.[/tex] This quadratic function determines the parabola with vertex at point (3,2). Thus,
1. The maximal value of f(x) is 4 at x=2.
2. The maximal value of g(x) is 3 at x=2.
Thus, the maximal value of f(x) is greater than the maximal value of g(x). So option B is correct.
NeeD HELP ASAP ! Please. the function f(x)=x^2. The graph of g(x) is f(x) translated to the right 3units and down 3 units what is the function rule for g(x) ? Please show me step by step
Answer:
g(x) = (x-3) ^2 -3
Step-by-step explanation:
f(x) = x^2
To shift down 3 units, subtract 3 ( When we move up, we add)
h(x) = x^2 -3
To shift to the right 3 units, replace x with (x-3). I know it seems backwards, but right is minus and left is plus.
g(x) = (x-3) ^2 -3
i think it is a check my answer?
What function equation is represented by the graph?
f(x)= 4 x +4
f(x)= 4 x +5
f(x)= 3 x +5
f(x)= 3 x +4
Answer:
I am 99% sure the answer is f(x)= 4x + 5
Step-by-step explanation:
That is because the line intercepts y at 5 and every 4 cubes the line hits a corner...
Answer:
F(x)=4x +5
Step-by-step explanation:
Find the ordered pair (s, t) that satisfies the system
s/2 - 3t = -1
3t - 2s = 3
[tex]\left\{\begin{array}{ccc}\dfrac{s}{2}-3t=-1&\text{multiply both sides by 4}\\3t-2s=3\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2s-12t=-4\\3t-2s=3\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad -9t=-1\qquad\text{divide both sides by (-9)}\\.\qqud\qquad\boxed{t=\dfrac{1}{9}}\\\\\text{Put the value of t to the second equation}\\\\3\left(\dfrac{1}{9}\right)-2s=3\\\\\dfrac{1}{3}-2s=3\qquad\text{subtract}\ \dfrac{1}{3}\ \text{from both sides}[/tex]
[tex]-2s=2\dfrac{2}{3}\qquad\text{divide both sides by (-2)}\\\\s=\dfrac{8}{3}\cdot\left(-\dfrac{1}{2}\right)\\\\\boxed{s=-\dfrac{4}{3}}\\\\Answer:\ \boxed{\left(-\dfrac{4}{3},\ \dfrac{1}{9}\right)}[/tex]
By simplifying and rearranging the given system of equations, we find that the ordered pair (s, t) that satisfies the system is (2, 1 + 2/3).
Explanation:The system of equations given in the question is:
s/2 - 3t = -1
3t - 2s = 3.
We can begin solving this system by first multiplying the first equation by 2 to eliminate the fraction, giving us:
s - 6t = -2.
Next, we rearrange the second equation to be in terms of 's':
2s = 3t + 3.
We then substitute this into the first equation and solve for 't':
(3t + 3) - 6t = -2,
simplifying to:
-3t + 3 = -2,
leading us to t = 1 + 2/3.
Substituting 't' into the second equation to find 's', we get:
2s = 3(1 + 2/3) + 3, which simplifies to s = 2. Therefore the ordered pair (s,t) that satisfies the system of equations is (2, 1 + 2/3).
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Choose which of the following functions has a domain of all real numbers. Select all that apply. y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, y = 3 - x^2.
Answer:
all of the above
Step-by-step explanation:
Every one of these functions is defined for all values of x.
All the provided functions: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, have a domain of all real numbers. This means any real value can be input into these functions to get a real output.
Explanation:The domain of a function is the set of all possible input values (usually represented by x) that will give an output value. In this case, we are asked to identify which of the provided functions have a domain of all real numbers. For the functions given: y = x, y = 2x^2 + x - 3, y = 3x - 4, y = 2, and y = 3 - x^2, all of them have a domain of all real numbers. This is because no matter what value of x you choose, these functions will always provide a valid output of y. In other words, you can input any real number into these functions and get a real number out.
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Please answer this question! 25 points and brainliest!
Answer:
a -5/2 <=x
Step-by-step explanation:
5(x-2) <= 9x
Distribute the 5
5x -5*2 <= 9x
5x-10 <= 9x
Subtract 5x from each side
5x-5x-10 <= 9x-5x
-10 <= 4x
Divide by 4 on each side
-10/4 <=4x/4
-5/2 <=x
The winter clothing drive has received donations of 5 coats, 23 pairs of gloves, 19 scarves, and 3 hats so far. Based on this data, what is a reasonable estimate of the probability that the next donation is not a pair of gloves?
Answer: Probability that the next donation is not a pair of gloves is 0.54.
Step-by-step explanation:
Since we have given that
Number of coats = 5
Number of pairs of gloves = 23
Number of scarves = 19
Number of hats = 3
Total number of winter clothing is given by
[tex]5+23+19+3=50[/tex]
Probability that the next donation is not a pair of gloves is given by
Not gloves = 50-23=27
P(not gloves ) is given by
[tex]=\frac{Not\ gloves}{total}\\\\=\frac{27}{50}\\\\=0.54[/tex]
Hence, Probability that the next donation is not a pair of gloves is 0.54.
Answer:
.54
Step-by-step explanation:
I know khan, ok?