Answer:
the interest for 100 in 5 years us 12.5
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. the length TP in cm is:
Here, ΔTPQ is isosceles and TO is the angle bisector of ∠PTO.
[∵ TP=TQ = Tangents from T upon the circle]
⠀⠀⠀⠀⠀⠀⠀⠀∴ OT⊥PQ
So, PR = RQ = 4cm.⠀⠀⠀
___________________________________________
[tex]\longmapsto{}[/tex]By Applying Pythagoras Theorem in ∆OPR :
OR = √OP² - PR²
OR = √5² - 4²
OR = 3cm
__________________________________________
Now,
[tex]\leadsto[/tex]∠TPR + ∠RPO = 90° (∵TPO=90°)
[tex]\leadsto[/tex]∠TPR + ∠PTR (∵TRP=90°)
[tex]\leadsto[/tex]∴ ∠RPO = ∠PTR
⠀⠀
∴ Right triangle TRP is similar to the right triangle PRO. [By A-A Rule of similar triangles]
⟼[tex]\frac{TP}{PO} = \frac{RP}{RO} [/tex]
⟼[tex]\frac{TP}{5} = \frac{4}{3} [/tex]
⟼[tex]TP= \frac{20}{3} [/tex]
Hence you got your answer here.⠀⠀⠀⠀⠀
-MissAbhiChris opened up a new credit card and credit line with U.S bank. He is paying a 15% APR on all new purchases
A. if he has a balance of 2,800 on his credit card, how much does he owe in interest to the bank next month?
B. if he sends in a payment to U.S bank for $140, how much of that will go towards paying off his principle balance
Answer:
Which one does not belong to the group
URGENT: Which equation correctly uses the value of b to solve for a?
Triangle ABC is a right triangle and cos(22.6°) = [tex]\frac{b}{13}[/tex]. Solve for b and round to the nearest whole number.
OPTIONS:
1 ) tan(22.6°) = [tex]\frac{a}{13}[/tex]
2 ) tan(22.6°) = [tex]\frac{13}{a}[/tex]
3 ) tan(22.6°) = [tex]\frac{a}{12}[/tex]
4 ) tan(22.6°) = [tex]\frac{12}{a}[/tex]
Answer:
Option 1
Step-by-step explanation:
See attached image
2^x - 3^x = √(6^x - 9^x)
[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]
[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]
For [tex]x=0[/tex], our initial equation is obviously true.
Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].
Answer to the miscellaneous equation, is x=0 and x=-1.71
Miscellaneous equation are the equations which are not polynomial
The question can be solved by:
Factorising Splitting the terms to find the required solution
Completing the squares, etc
2ˣ - 3ˣ = √(6ˣ - 9ˣ)
Squaring both sides,
2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ
2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0
Factorising the terms,
2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0
(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0
Equating the braces to zero,
Either,
2ˣ=3ˣ
x=0
or
2ˣ=2.3ˣ
Taking log on both sides
xln2=ln2+xln3
x=ln2/(ln2-ln3)
=-1.71
Therefore, x=0 and x=-1.71 is the only solution
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what are the zero of f(x)=x(x-8)
The zeroes of the function f(x) = x (x – 8) will be 0 and 8.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The function is given below.
f(x) = x (x – 8)
The zeroes of the function f(x) is given by the factor equals to zero.
Then we have
f(x) = 0
x(x – 8) = 0
x = 0, 8
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What is the solution to the equation below? (Round your answer to two
decimal places.)
7•Inx=2.4
A. x=99.48
B. x = 18.48
C. x=1.41
D. x= 1.9
Answer:
C
Step-by-step explanation:
7 × ln(x) = 2.4
ln(x) = 2.4/7 = 0.342857143...
x = e^0.342857143... = 1.408967466... ≈ 1.41
Embáulate the given function for f(8) f(x)=(x-5)2 f(8=
Answer:
f(8) = 9
Step-by-step explanation:
f(x)=(x-5)^2
Let x = 8
f(8)=(8-5)^2
= 3^2
= 9
what is the mean of 4,7
Answer:5.5
Step-by-step explanation:first we have to plus 4 and 7 and then we to divide the answer we get by 2 because there are only 2 digits and then the mean is 5.5
hope it helps
Please help me with my math
The value of z is 119° and the value of y is 28°.
What is corresponding angles?When two parallel lines meet any other line, comparable angles are generated in matching corners or corresponding corners with the transversal, these angles are called corresponding angles.
If the given diagram is modified a bit it will look as shown below, the two angles will be 61° because the two angles are corresponding angles.
Now, since 61° and x lie on the same side of the line, therefore, the sum of the two angles will be,
61° + x = 180°
x = 119°
Also, the angles measured at 61° and (3y-23)° lie on the same side of the transversal, therefore, these two angles are corresponding angles. Thus,
61° = (3y-23)°
61 = 3y - 23
y = 28
Hence, the value of z is 119° and the value of y is 28°.
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Howard drew a square in Quadrant IV and correctly reflected it across the y-axis.Which statement explains one method Howard could have used to determine the coordinates of the vertices of the image?
Using translation concepts, the method that Howard could have used to determine the coordinates of the vertices of the image is:
(x,y) -> (-x,y).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A reflection over the y-axis can be described according to the following rule:
(x,y) -> (-x,y).
Hence this rule can be applied to find the vertices.
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Which ordered pair is the solution to the system of linear equations y =5x +8 and y= -4 x-1
Answer:
(-1,3)
y=5x+8 , y=-4x-1y=5x+8,y=−4x−1
Both sides have y on the left hand side so make the right hand side equal and solve for x
5x+8= -4x-15x+8=−4x−1
To solve for x , add 4x on both sides
9x+8=-19x+8=−1
Subtract 8 on both sides
9x=-99x=−9
Divide by 9 on both sides
x=-1x=−1
Now plug in -1 for x in the first equation and find out y
y=5x+8y=5x+8
y=5(-1)+8y=5(−1)+8
y=-5+8y=−5+8
y=3y=3
Ordered pair is (x,y) that is (-1,3)
Step-by-step explanation:
Mark me as brainliest plsss
Use the algebra tiles to model the equation 2x + 4 = 3x + (−1). Then complete the sentences. To model 2x + 4, you need:
The value of x would be 5 for the model 2x+4.
Rearrange unknown terms to the left side of the equation,
[tex]= > 2x-3x = -1 - 4[/tex]
Combine like terms[tex]= -x = -1-4[/tex]
By calculating the sum or difference : -x = -5
Lets divide both sides of the equation by the resulting coefficient 5
So x = 5
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Anyone knows how to do this please tell me how?
Step-by-step explanation:
0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴
Scientific notation is a way of writing numbers that looks like the following:
[tex]a\times10^n[/tex]
a is any number between 1 and 10n is any integerFor instance, we can write 2930 in scientific notation.
First, move the decimal so that the number is between 1 and 10:First, write all the given values in scientific notation:
[tex]6.72\times10^5[/tex] ⇒ [tex]6.72\times10^5[/tex][tex]67.2\times 10^{-4}[/tex] ⇒ [tex]6.72\times 10^{-3}[/tex][tex]672\times 10^4[/tex] ⇒ [tex]6.72\times 10^6[/tex][tex]0.000672[/tex] ⇒ [tex]6.72\times10^{-4}[/tex]Now, let's compare the values of n, and organize the numbers from least to greatest:
[tex]6.72\times10^{-4}[/tex]
[tex]6.72\times 10^{-3}[/tex]
[tex]6.72\times10^5[/tex]
[tex]6.72\times 10^6[/tex]
Finally, rewrite all the numbers as their given format:
[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
Answer[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
Ragan makes beaded jewelry. The graph below shows the number of beads on varying cord lengths.
Jewelry
A graph has cord length (inches) on the x-axis and number of beads on the y-axis. A line goes through points (16, 48) and (24, 72).
Which is the best estimate of the number of beads on a cord that is 16 inches long?
5
8
44
48
Answer:
48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
edge 2023
Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answers so I can do the rest myself. please
All of these questions require one thing: trigonometric functions.
There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.
Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse
Tangent = opposite / adjacent
When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.
---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.
Let's set up our function with the given information from problem a.
tan(x) = 9.7 / 5.2
---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.
Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.
---Ensure that your calculator is in degrees, not radians!
x = tan^-1(9.7 / 5.2)
x = 61.805 = 62 degrees
Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.
Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.
cosine(38) = 53.1 / r
---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.
Use your algebra skills to isolate the variable r.
r * cosine(38) = 53.1
r = 53.1 / cosine(38)
---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.
r = 67.385 = 67.4 units
Hope this helps!
Match the circle equations in general form with their corresponding equations in standard form. x2 y2 − 4x 12y − 20 = 0 (x − 6)2 (y − 4)2 = 56 x2 y2 6x − 8y − 10 = 0 (x − 2)2 (y 6)2 = 60 3x2 3y2 12x 18y − 15 = 0 (x 2)2 (y 3)2 = 18 5x2 5y2 − 10x 20y − 30 = 0 (x 1)2 (y − 6)2 = 46 2x2 2y2 − 24x − 16y − 8 = 0 x2 y2 2x − 12y − 9 = 0
The equation given is matched with the respective vertex forms.
What is the standard Equation for a circle ?The standard equation for a circle is given by
(x-h)² + (y-k)² = r²
The equation given in the question are
x² + y² − 4x + 12y − 20 = 0
(x − 6)² + (y − 4)² = 56
x² + y² + 6x − 8y − 10 = 0
(x − 2)² + (y + 6)² = 60
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
5x² + 5y² − 10x + 20y − 30 = 0
(x+3)² + (y-4)² = 35
2x² + 2y² − 24x − 16y − 8 = 0
(x-1)² + (y+2)² = 11
The first equation is
x² + y² − 4x + 12y − 20 = 0
It can be written ad
x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0
(x-2)² +(y+6)²= 60
The second equation is
x² + y² + 6x − 8y − 10 = 0
x² +6x +9-9 +y² -8y +16-16 -10 = 0
(x+3)² + (y-4)² = 35
The third equation is
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
The fourth equation is
5x² + 5y² − 10x + 20y − 30 = 0
(x-1)² + (y+2)² = 11
The fifth equation is
2x² + 2y² − 24x − 16y − 8 = 0
(x − 6)² + (y − 4)² = 56
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The circuit is working, and all three bulbs are lit. If a switch at A is opened,
what will happen to the circuit?
•
A. All three bulbs will stay lit
B. All three bulbs will go out.
C. Bulbs 1 and 2 will go out, but bulb will remain lit.
D. Bulb 1 will go out, but bulbs 2 and 3 2 will remain lit.
Answer:
B.
Step-by-step explanation:
Since all bulbs are connected in series, by opening switch A, you break the series connection, and all bulbs go out.
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime. During store inventory she worked 48.5h. Her gross earnings were $1,471.88. What is Gracie’s overtime rate of pay? show work please
Gracie’s overtime rate of pay would be $635.06.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.
For one hour she earns $17.25
For 37.5h she earns = 37.5h x 17.25
= $646.87
The total money she earns = $646.87 + overtime pay
During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.
= 48.5h x 17.25
= $836.625
So, $836.625 + overtime pay = $1,471.88
overtime pay = $1,471.88 - $836.625 = $635.06
Hence, Gracie’s overtime rate of pay would be $635.06.
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The cost of the fruit is given by the function y = 3x + 1, where x is the number of fruits and y is the total cost. Find the range of the function.
The range of the given function will lie from ( -0.333,0) to ( 0,1).
What is the range?A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that:-
The cost of the fruit is given by the function y = 3x + 1, where x is the number of fruits and y is the total cost.When we plot the graph of the function we will see that the straight line will cut the x-axis at point (-0.333 ) and the y-axis cut at ( 0,1 ) the points between the two points will be the solutions of the equation.
Therefore range of the given function will lie from ( -0.333,0) to ( 0,1).
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Answer:i think the answer is B
Step-by-step explanation:
Find the value of z
[tex]\textsf {Finding y :}[/tex]
[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]
[tex]\implies \mathsf {y^{2} = 8}[/tex]
[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]
[tex]\textsf {Finding z :}[/tex]
[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]
[tex]\implies \mathsf {z^{2} = 72}[/tex]
[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]
Answer:
z =8.49 or 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]
Length of hypotenuse = 8+1=9
length of one side = 3
so, a²+3²=9²
a²+3²=9²
a²=81-9
a²=72
a=√72=8.49 or 6[tex]\sqrt{2}[/tex]
3 erasers cost $4.41. Write a proportion that would solve for the cost of 4 erasers.
Answer:
$5.88
Step-by-step explanation:
3 erasers ⇒ $4,41
4 erasers ⇒ $A
A = 4 erasers * $4.41 / 3 erasers
A = $ 5.88
Answer:
see below
Step-by-step explanation:
Proportion:
4.41 is to 3 erasers as 'x' is to 4 erasers:
4.41 /3 = x / 4 <======this is your proportion
or rearrange
4 * 4.41/3 = x
(this results in x = $ 5.88 for 4 erasers )
A bottle holds
5
55 milliliters of perfume.
How many bottles can we fill with
2
22 milliliters of perfume?
Answer:
0.4 bottles can be filled
Step-by-step explanation:
divide the amount that is present by the max amount
the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.
the amount that is present is 2.22 millimeters.
[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]
0.4 bottles
if the given values are 555 and 222 then the answer is still .4
Answer:
0.4 bottles can be filled
The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 15 minutes.
What is the probability that washing dishes tonight will take me between 13 and 14 minutes?
Give your answer accurate to two decimal places.
What is the range of f(x) = 3x + 9?
Answer:
The range is all real numbers.
Step-by-step explanation:
The function shown is a line (and not a horizontal line).
The range is all the y's on the graph or all the y's that can be generated by the equation of the function.
f(x) = 3x + 9
You could put ANY, literally any, number in place of the f(x) and be able to calculate an x for it. Looking at the graph of this line, you could go up and down the y-axis to infinity in either direction, and the graph of the line would be there.
The range is All Real Numbers.
A particular beach is eroding at a rate of 4 centimeters per year. A realtor converts this rate to millimeters per day. Which expression, when evaluated, results in the correct units and numerical value?
The correct expression is : [tex]\frac{4 cm }{1 year}[/tex] x [tex]\frac{10 mm}{1 cm}[/tex] x [tex]\frac{ 1 year }{365 days}[/tex]
What is the correct expression?
The first step is to convert year to days.
1 year = 365 days
The next step is to convert cm to mm.
1cm = 10 mm
4 x 10 = 40mm
Now, divide 40 mm by 365 days
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An Amazon delivery driver receives a bonus if he delivers a package to a customer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus
[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.
What us the absolute value of inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs.
According to the question:
Mathematically absolute value inequality is represented as :
|X -20|≤ 5
Solving the equation using
|z| ≤ a→ -a ≤ z ≤ a :
here, z = X- 20 and a = 5:
[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]
By Solving X adding 20 on the three sides of the inequality
[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]
By simplifying it:
[tex]15 \leq X \leq 25[/tex]
Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]
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Which of the following is equal to 5 1/3?
OA. 1/5
OB. 5 3
O C. √5.3
OD. √5
The correct answer is option B which is ( 5 / 3)
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
The value will be calculated as:-
[tex]5\times \dfrac{1}{3}[/tex] = [tex]\dfrac{5}{3}[/tex]
1.67 = 1.67
Therefore the correct answer is option B which is ( 5 / 3)
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Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total $46.21 on gas.
In the first week, Micah bought
x gallons of gas.
In the second week, Micah bought
x gallons of gas.
Answer: In the first week, Micah bought 11 gallons of gas,
and in the second week, he bought 8 gallons of gas
Step-by-step explanation:
In the first week, Micah bought x gallons of fuel at $2.39/gallon
In the second week, he bought (x - 3) gallons at $2.49/gallon
Formulating an equation and solving for x gallons of fuel:
x × 2.39 + (x - 3) × 2.49 = 46.21
2.39x + x × 2.49 − 3 × 2.49 = 46.21
2.39x + 2.49x − 7.47 = 46.21
4.88x − 7.47 = 46.21
4.88x = 53.68
[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]
x = 11
Therefore,
In the first week, Micah bought 11 gallons of gas
In the second week, he bought (11 - 3) = 8 gallons of gas
Use separation of variables to solve the differential equation with initial condition y(1)=-2
Answer: A
Step-by-step explanation:
[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]
Substituting in the initial condition,
[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]
So,
[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]
Answer:
[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Step-by-step explanation:
To solve the differential equation:
Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]
[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]
[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]
[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]
[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]
Integrate both sides:
[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]
Find the value of C using the given values of x and y:
when x = 1, y = -2
[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]
[tex]\implies 2=0+1+C[/tex]
[tex]\implies C=1[/tex]
Substitute the found value of C:
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
In question 1, you found the cubes of both positive and negative numbers. Does x3 = 8 have two solutions as x2 = 4 does? Why or why not?
