14Y - 7y = 35. solve for y
Answer:
y = 5
Step-by-step explanation:
\(14y-7y=35\\7y=35\\y=5\)
14 minus 7 is 7
7Y is equal to 35
divide both sides by 7 is equal to 5
Study the diagram of circle A, where BC is tangent to circle A at point C.Also, BC = 3, BA = 5, and AC is a radius.
A tangent to a circle is a straight line that touches the circle at only one point. This point is called the point of tangency.
One of the Circle Theorems states that the radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. This means that in the circle in the question, lines AC and BC are perpendicular.
Therefore, the triangle ABC is a right-angled triangle where AB is the hypotenuse.
The Pythagorean Theorem can be used to evaluate the measure of the radius. This theorem is stated to be
\(hyp^2=opp^2+adj^2\)From the image, we have:
\(\begin{gathered} hyp=AB=5 \\ opp=AC=r \\ adj=BC=3 \end{gathered}\)Substituting, we have:
\(\begin{gathered} 5^2=r^2+3^2 \\ 25=r^2+9 \\ r^2=25-9 \\ r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}\)The FIRST OPTION is the correct option.
use newton's method to find all real roots of the equation correct to six decimal places. (enter your answers as a comma-separated list.) 4 x = 1 + x3
Using newton's method to find all real roots of the equation, 4x = 1+ x³ is
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
We have the equation,
4x = 1+ x³
To find the real roots of equation we have,
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
The cubic equation formula in mathematics is how the cubic equation is represented. An equation with degree three is said to be cubic. In nature, the roots of all cubic equations are either one real root and two real roots or three real roots. Cubic polynomials are the name given to three-degree polynomials.
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How many significant figures are in the number
43.6? 43.6 has [?] significant figures.
Answer:
43.6 has 3 significant figures.
can anyone help me with this?
Answer:
120 degrees is x
Step-by-step explanation:
because both are equal angles
btw nice Pikachu meme
If XY=16, XZ=14, JQ=6, and the radius of the circumscribed circle of triangle XYZ is 10, find QK
Check the picture below.
Please answer the question with details and answer each part and box it.
The sequence \(b_n = \frac{{2^n \cdot 3^n}}{{n!}}\) is strictly increasing for all values of n. It is bounded above by 6 and bounded below by 0. Thus, it is both a bounded and monotonic sequence.
To determine where the sequence is increasing or decreasing, we need to analyze the behavior of consecutive terms.
Let's analyze the sequence:
\(b_n = \frac{{2^n \cdot 3^n}}{{n!}}\)
To check if the sequence is increasing or decreasing, we can compare the ratio of consecutive terms:
\(\frac{{b_{n+1}}}{{b_n}} = \frac{{2^{n+1} \cdot 3^{n+1}}}{{(n+1)!}} \cdot \frac{{n!}}{{2^n \cdot 3^n}}\)
Simplifying this expression, we have:
\(\frac{{b_{n+1}}}{{b_n}} = \frac{{2 \cdot 3}}{{n+1}}\)
Since the numerator is a constant value (6), the ratio bₙ₊₁ / bₙ will always be greater than 1. Therefore, the sequence is strictly increasing for all values of n.
Next, let's determine if the sequence is bounded. To do this, we need to find both an upper bound and a lower bound.
Let's consider the value of bₙ when n approaches infinity:
\(\lim_{{n \to \infty}} b_n = \lim_{{n \to \infty}} \left[ \frac{{2^n \cdot 3^n}}{{n!}} \right]\)
By applying the ratio test, we can simplify this limit:
\(\lim_{{n \to \infty}} b_n = \lim_{{n \to \infty}} \left[\frac{{2 \cdot 3 \cdot 2 \cdot 3 \cdot \ldots \cdot 2 \cdot 3}}{{n \cdot (n-1) \cdot \ldots \cdot 2 \cdot 1}}\right]\)
Since the numerator remains constant while the denominator grows factorially, the limit of bₙ as n approaches infinity is 0.
Therefore, the sequence is bounded above by a constant value (6) and bounded below by 0.
To summarize:
- The sequence is strictly increasing for all values of n.
- The sequence is bounded above by 6 and bounded below by 0.
- The sequence is both monotonic and bounded.
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It costs $120 for 20 students to visit an aquarium. How much does it cost for 152 students? Set up a proportion to solve.
Answer:
152 times 6=912
Step-by-step explanation:
$120 for every 20 students
it cost $6 for every 1 student
$6 times 152=912
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2/1/2+2/3/4+3=8/1/4 pounds
The correct total weight of the bags of granola is 8 1/4 pounds.
One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.
In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.
To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:
2 + 2 + 3 = 7 (sum of whole numbers)
1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)
Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.
By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.
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The probable question may be:
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.
what is one thing that you could do to Roberto's Reasoning
Explain what probability is. Identify
the two types of probability and
how we find them.
Answer:
a. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are
b. Theoretical Probability. Experimental Probability.
Use theoretical probability by counting the favorable outcomes and put that in a fraction above all possible outcomes.
Use experimental probability by comparing the number of times the event occurs to the total number of trials.
Step-by-step explanation:
I don't really know what to explain. :v
Alyanna spent 1/6 of her savings to buy a gift for her father. If her saving was Php900.00,how much did she spend for the gift
Answer:
Php150.00
Step-by-step explanation:
1/6 X 900
= Php150.00
URGENT PLEASE HELP
Which question is not a good survey question?
A.
How many hours do you study each night?
B.
Which student in your class has the best study habits?
C.
What is your preferred time to study?
D.
Where do you prefer to study?
Answer:
b
Step-by-step explanation:
Answer:
B.
Which student in your class has the best study habits?
Step-by-step explanation:
plato 2022
A sience teacher uses an overhead projector to display a diagram of a pulley sytem. the actual diagram is 6'' by 7.2''. The image projected onto the wall is 4' 2'' by 5'' what is the scale factor of the projection
Answer:
25/36, or .694444
Step-by-step explanation:
First, let's convert 6" to inches.
That gives us 72. After we convert 4'2" into inches, we get 50.
This means that the diagram goes from 72 inches wide to 50. Put this into a proportion to find the scale factor:
50/72 = 25/36 = .6944444
Need help with this equation 8x²+10x-3
Answer:
Step-by-step explanation:
You have to use the quadratic formula
x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)
and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2
you usually have to reject an answer but since there is no equal sign in the question, you should be fine
Mario makes 30 calls in 15 hours. How many calls can he make in 3 hours?
Answer:
6
Step-by-step explanation:
15/5=3
30/5=6
Answer:
6
Step-by-step explanation:
Which function represents a reflection of f(x) = 3/8 (4)^x across the y-axis?
A function that represents a reflection of \(f(x) = \frac{3}{8} (4)^x\) across the y-axis include the following: D. \(g(x) = \frac{3}{8} (4)^{-x}\).
What is a reflection over the y-axis?In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).
This ultimately implies that, a reflection over or across the y-axis or line x = 0 would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the parent exponential function, we would have the following transformed exponential function:
(x, y) → (-x, y).
\(f(x) = \frac{3}{8} (4)^x\) → \(g(x) = \frac{3}{8} (4)^{-x}\)
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elena bought 24 sandwich buns. there were 8 buns in each pack. complete the equation below to show how many packs elena bought
The number of packs Elena bought is 3 packs
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
The number of sandwich buns Elena bought = 24 sandwich buns
The number of buns in each pack = 8 sandwich buns
So ,
The equation is given by
The number of buns in 1 pack = 8
So , the number of buns in x pack = 8x
And , the number of packs =
number of sandwich buns Elena bought / number of buns in each pack
The number of packs = 24 / 8
= 3 packs
Hence , the number of packs Elena bought is 3 packs
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4 There are between 20 and 50 flags.
They can be shared equally among
2 tents or 4 tents or 5 tents.
How many flags are there?
When there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents. The number of flags will be 40.
How to illustrate the information?From the information, there are between 20 and 50 flags and they can be shared equally among 2 tents or 4 tents or 5 tents.
It should be noted that this simply means that we should find the highest multiple for 2, 4, and 5 between 20 and 50. This is 40.
Therefore, the number of flags is 40.
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Christine got a prepaid debit card with $30 on it . For her purchase with the card , she bought some bulk ribbon at a craft store . The price of the ribbon was 12 cents per yard. If after that purchase there was $27.48 left on the card, how many yards of ribbon did christine buy?
Answer:
2.52 dollars
Step-by-step explanation:
subtract
6/12 is less than 2/12?
Answer:
no
Step-by-step explanation:
Answer:
no its not
Step-by-step explanation:
cause they have the same denominator and 6 is more than 2 so there for 6/12 is not less than 2/12
show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1
Answer:
y³ + x³ = 1
First, differentiate the first time, term by term:
\({3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}\)
↑ we'll substitute this later (4th step onwards)
Differentiate the second time:
\(3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\\)
\(3y^{2}.\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} = - \frac{-2x}{y^{5}}\)
A drilling machine can drill 12 holes in 6 minutes. If the machine drills holes at a constant speed, it can drill
holes in 25 minutes. HELPPP
Answer:
The machine can drill 50 holes in 25 minutes!
Explanation:
6 by 4 is 24, which in this context will be 24 minutes. Therefore, multiply 12 by 4 to get the sum of 48. Then, to find the remaining 1 minute, divide 12 by 6 to get 2 which is the amount of holes per minute. Add 2 to 48 and that is your answer!
A. (1,1,) , (2,2) , (3,3)
B. (1,6),(2, 12) , (3, 18)
C. (1,6), (2,7), (3,8)
D. (6 ,6), (12, 12) (18,18)
A
Step-by-step explanation:
HahhagavBBgBNHafVabBgababaggvab
Solve for x when -5x - 10=25
Answer: 3
Step-by-step explanation:
80 ounces/2.5 servings
Answer:
No 80 ounces isnt 2.5 servings
Step-by-step explanation:
Unit rate means: how many of one thing you have got for 1 of something else. So you end up with something like.
count of some thing
1 of something else
→
unit rate
So for
80
o
z
2.5
servings
The unit rate is weight of 1 serving
Using the principle of ratios:
Change the 2.5 servings into 1 serving by dividing by 2.5.
For multiply and divide; what you do to the bottom you do to the top.
80
o
z
2.5
servings
≡
80
÷
2.5
2.5
÷
2.5
=
32
1
↑
Note that the sign
≡
means 'equivalent to'
So unit rate is 32 oz
C = x² + 5x + 30, find the number of units manufactured at a cost of $10,530
Answer:
100 units.
Step-by-step explanation:
I am assuming that C is the cost.
You Can form the quadratic equation: 10530=x^2+5x+30. You put the left side to zero by subtracting 10530: x^2+5x+30-10530=0. You will get that x^2+5x-10500. You can use the quadratic formula or factoring. The factors that multiply to 10530 and add up to 5 is 105 and -100. You group: (x+105)(x-100)=0, you then use the zero-product property: x+105=0, x-100=0.
you get that x=100, -105. The number of units cant be negative, so x must be 100.
Pls help
Cole is building a model rocket in science class. He selects the rocket parts from a set of solid cylinders and cones made from metal. Cole wants to build a rocket with the dimensions shown. For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. Will Cole's rocket meet the requirement for launch?
Part A
What will be the total length of the assembled rocket? Explain how you found your answer.
Part B
What is the approximate volume of the rocket.
Use 3.14 for r. Explain.
Part C
If Cole's rocket parts are made of aluminum weighing 0.006 pound per cubic centimeter, will Cole be able to launch his rocket? Explain.
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
How to solveThe volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = \(\pi* r^2 *h\)
Part A
The total length of the assembled rocket will be the length of the cone and the cylinder.
The total length of the assembled rocket = 25 + 3 = 28cm
Part B
The volume of the rocket is the combined volume of the cone and cylinder.
= 4/3 × 3.14 × 16 × 28
= 1875.62 cubic cm
To convert cm into pounds
1875.62 cubic cm = 4.135 pound
Part C
If Cole’s rocket parts are made of aluminum weighing 0.006 pounds per cubic centimeter.
Then 1875.62 cubic cm × 0.006
= 11.253
For safety purposes, the maximum lift-off weight of each rocket is 10 pounds. but Cole’s rocket doesn't meet the requirement for launch.
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PLEASE HELP, ITS URGENT!!
Joaquin has agreed to lend his younger brother $45 so that he can buy a new tank for his pet lizard.
a) Joaquin is charging his brother 2% simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back?
b) If Joaquin’s brother instead borrowed the money from a bank at 2% compound interest per month, how much would he have to pay the bank at the end of 6 months?
Answer:
Step-by-step explanation:
A) $50.40
B) $50.68
please answer the question
Answer:
science thing is ......
40 points! Please help me
Answer:
x = 8
y = 14
Step-by-step explanation:
2x + 6 = 4x - 10 (Corresponding angles so they're equal)
2x - 4x = -10 - 6
-2x = -16
x = 8
2x + 6 + 13y - 24 = 180 (Supplementary angles so they add up to 180)
2(8) + 6 + 13y - 24 = 180
16 + 6 + 13y - 24 = 180
13y - 2 = 180
13y = 182
y = 14
Answer:
2x+6=4x-10[corresponding angle]
16=2x
x=8
again
2×8+6+13y-24=180°[linear pair]
13y=180+2
y=182/13
y=14