Answer:
w = -8
Step-by-step explanation:
43 = -3w - 6w -29
combine w terms on right side:
43 = -9w -29
add 29 to both sides:
43 + 29 = -9w -29 + 29
72 = -9w
divide both sides by -9:
72/-9 = -9w/-9
w = -8
ABCDE is a circle centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and DE = 14 cm. The radius of the circle is r
Answer:
r = 10 cmStep-by-step explanation:
It is assumed you are looking for the missing value of r.
Use the intersecting secants theorem:
[tex]FA*FC = FE*FD[/tex]Substitute known values and solve for r:
(2r + 16)*16 = (14 + 18)*1832r + 256 = 57632r = 320r = 10Answer:
(a) FB = 24 cm
(b) r = 10
Step-by-step explanation:
Part (a)Find the length, in cm, of FB.
Intersecting Secant and Tangent Theorem
When a secant segment and a tangent segment meet at an exterior point, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.
Given:
Tangent segment = FBSecant segment = FE = 18 + 14 = 32 cmExternal secant segment = FD = 18 cm[tex]\begin{aligned}\implies FB^2 & =FE \cdot FD\\FB^2&=32 \cdot 18\\FB^2&=576\\\sqrt{FB^2}&=\sqrt{576}\\FB&=24\end{aligned}[/tex]
Therefore, the length of FB is 24 cm.
Part (b)Find the value of r.
Triangle FBO is a right triangle with side lengths:
BO = r cmFB = 24 cmOF = (r + 16) cmPythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.Therefore, substitute the side lengths of triangle FBO into Pythagoras Theorem and solve for r:
[tex]\begin{aligned}\implies BO^2+FB^2&=OF^2\\r^2+24^2&=(r+16)^2\\r^2+576&=r^2+32r+256\\576&=32r+256\\32r&=320\\r&=10\end{aligned}[/tex]
Therefore, the value of r is 10.
Please help me with parts C and D, I’m struggling with them
ANSWER
[tex]\begin{gathered} c)s\imaginaryI n\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7})} \\ decimal=0.49 \\ d)cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\frac{\sqrt{13}}{7}+1)} \\ decimal=0.87 \end{gathered}[/tex]EXPLANATION
Given;
[tex]\begin{gathered} sin\theta=\frac{6}{7} \\ 0<\theta<\frac{\pi}{2} \end{gathered}[/tex]c) Hence;
[tex]\begin{gathered} sin\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7}}) \\ \end{gathered}[/tex]In decimal form;
[tex]sin\frac{\theta}{2}=0.49[/tex]d)
[tex]\begin{gathered} cos\theta=\frac{\sqrt{13}}{7} \\ cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\sqrt{\frac{13}{7}+1})} \\ decimal=0.87 \end{gathered}[/tex]Which answer choice correctly shows 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 in
exponential notation?
OA) 811
OB) 118
OC) 11⁹
OD) 1111
Answer:
it would be 11^8
Step-by-step explanation:
i dont see this as an option but i believe that there was a mistake i dont believe that any of theese are correct
4
Choose the conjecture that describes how to find the 7th term in the sequence 4, 20, 36, 52,
OA) Multiply 52 by 9.
O B) Multiply 16 to 32..
OC) Add 32 to 52
OD) Add 48 to 52.
...
The correct option D) Add 48 to 52 is the conjecture that describes for the 7th term in the sequence.
What is termed as the arithmetic progression?An arithmetic progression (AP) is just a sequence in which the differences between each successive term are the same.An arithmetic progression (AP) can be defined in two ways:An arithmetic progression is still a sequence in which the differences between each successive term are the same.An arithmetic progression is a sequence in which each term (except the first) is obtained by having to add a fixed number to the term before it.For the given question, the sequence is given as;
4, 20, 36, 52,
Where, the first term a₁ is 4.
Second term a₂ is 20 and,
Third term a₃ is 36
Common difference d for each case is;
d = a₂ - a₁
d = 20 - 4 = 16
d = a₃ - a₂
d = 36 - 20 = 16
as, common difference is same, the sequence is said to be in AP.
Then, the formula for finding the 7th term is -
a₇ = a₁ + 6d
a₇ = 4 + 6×16
a₇ = 100
Now, this 7th term from the options can be found as;
Add 48 to 52 = 100.
Thus, the conjecture that describes for the 7th term in the sequence is add 48 to 52.
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Find the measure of angle b
Simplify the expression √9x^3/25y^2 and be sure to explain your steps!
The value of the expression given as√9x^3/25y^2 is 3x^3/25y^2
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to simplify the value of the expression?The expression is given as
√9x^3/25y^2
Evaluate the square root of 9 in the expression
So, we have the following equation
√9x^3/25y^2 = 3x^3/25y^2
The above expression cannot be further simplified
Hence, the solution to the expression is 3x^3/25y^2
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Please help me with this asappppp
The perimeter of the rectangle is 32 feet.
Perimeter of the rectangle:
The perimeter of a rectangle is stated that the sum of all the sides of a rectangle.
Through the definition, the perimeter of a rectangle,
P = 2 (a + b) units
where
“a” is the length of the rectangle
“b” is the width of the rectangle
Given,
Here we have the diagram of the rectangle and the measurements are given in it.
And we need to find the perimeter of the rectangle.
Through the given diagram, we know that, the values of
length = 12 feet
width = 4 feet
Now, we have to apply the values on the formula in order to solve it,
So, the perimeter is,
P = 2 ( 12 + 4)
When we simplify it then we get,
P = 2 (16)
After the multiplication we get the result as
P = 32 feet.
Therefore, the perimeter of the rectangle is 32 feet.
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50 POINTS!!!
Decide whether inductive reasoning or deductive reasoning is used to reach the conclusion. Explain
1. even numbers are divisible by 2. odd numbers are not divisible by 2 so 4 is an even number
2. all photosynthetic organisms produce oxygen. phytoplankton and photosynhetic organisms. So phytoplankton produces oxygen.
3. Each time you clean your room, you are allowed to go out with your friends. So, the next time you clean your room, you are allowed to go out with your friends
Answer:
1. Deductive reasoning, because it is testing the ecisting theory that odd numbers are not divisible by 2 and gives an example that 4 is an even number and is divisible by 2.
2. This statement would be deductive reasoning because the person stating this is establishing the truth that all photosynthetic organisms produce oxygen, they are not creating a theory, just stating facts.
3. This would be inductive reasoning because they have given good reasons to base their theory however it is not simple fact.
Step-by-step explanation:
Hope i helped explain
After 4 months of a new nutrition program, Rashid has lost 16% of his original weight. he lost 36 lb. What was Rashid's original weight?
Answer:
225 lb
Step-by-step explanation:
Let x be Rashid's original weight.
If 16% of Rashid's original weight is 36 lb then:
[tex]\implies 0.16x=36[/tex]
To find Rashid's original weight solve for x:
[tex]\implies \dfrac{0.16x}{0.16}=\dfrac{36}{0.16}[/tex]
[tex]\implies x=225[/tex]
Therefore, Rashid's original weight is 225 lb.
Aiyana wrote the ratio 3:5 to compare a number of Paris of shorts that she owns to the number of pairs of jeans that she owns which ratio is equivalent to Aiyana’s ratio
3:5 is equivalent to Aiyana’s ratio
Since 3 and 5 are both prime numbers, you must multiply them by the same number (or any other integer) in order to have a ratio that is the same as Aiyana's. Ex 3:5=6:10=9:15 etc. The three ratios are identical.
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
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On a map, Elmwood Drive passes through R(4,-11) and S(0,-9) and Taylor Road passes through
J(6,-2) and K(4,-5). If the streets are straight lines, determine if the streets are parallel or
perpendicular.
The streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
Elmwood Drive passes through R(4,-11) and S(0,-9)
Slope of this line is (y₁-y₂)/(x₁-x₂)
Here (x₁,y₁) is (4,-11) and (x₂,y₂) is (0,-9)
slope of this line is (-11 - (-9))/(4-0)
= (-11 + 9)/4
= -2/4 = -1/2
Taylor Road passes through J(6,-2) and K(4,-5)
Slope of this line is (y₁-y₂)/(x₁-x₂
Here (x₁,y₁) is (6,-2) and (x₂,y₂) is (4, -5)
slope of this line is (-2 - (-5))/(6 - 4)
= (5 - 2)/2
= 3/2
The slopes of both the line is not same, so they are not parallel.
The product of slopes of both the lines is equal to 1, then it can be said as perpendicular lines.
The product of slope of streets passed by Elmwood and Taylor is
- 1/2 x 3/2 = -3/4
The result is not equal to 1, so they are not perpendicular lines.
Therefore, the streets where Elmwood and Taylor drive are neither perpendicular nor parallel.
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A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.(b) If the water is rising at a rate of 3/8 inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough. ft3/min
Given:
A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
The volume of the trough will be as follows:
[tex]undefined[/tex]What is 10+409 bc I really need help
If f(x) = |x|, what is the equation of the graphed function?
A. y = f(-x+3)
B. y=f(-x) +3
C. y= -f(x+3)
D. y = -f(x) +3
The equation of the graphed function is y = -f(x) +3.
What is translation?Translation is the act of moving a form or a figure from one location to another. A figure can move in translation up, down, right, left, or anyplace else in the coordinate system. Only the object's location changes during translation; its size stays the same.
In mathematics, a translation is the up, down, left, or right movement of a form. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more routes have been altered.
Given:
f(x) = |x|
The graph given here is reflected over x- axis.
Now, to make it up- side down the parent function should be negative.
So, g(x)= -f(x)
then, the graph is also shifted 3 units up.
Thus, g(x)= -f(x) + 3
y = -f(x) +3
Hence, the equation of the graphed function is y = -f(x) +3.
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What is the slope of a parallel line whose equation is x-2y=-18. Fully simplified answer.
Answer:
slope of 1/2
Step-by-step explanation:
x-2y=-18
First, get the equation in slope intercept form
y = mx+b where m is the slope and b is the y-intercept
-2y = -x -18
Divide each side by -2
y = 1/2 x + 9
The slope is 1/2
Parallel lines have the same slope, so lines that are parallel will have a slope of 1/2
5. What is an equation of the line in slope-intercept form?
m=2/7 and the y-intercept is (0, -12)
Oy=2/7x+12
Oy=2/7x-12
Oy=12x-2/7
Oy=12x+2/7
Answer:
[tex]y=\dfrac{2}{7}x-12[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given:
slope = ²/₇y-intercept = (0, -12)The y-intercept is the y-value when x = 0.
Substitute the slope and y-intercept into the formula to create the equation of the line in slope-intercept form:
[tex]\implies y=\dfrac{2}{7}x-12[/tex]
PLS HURRYYYYY
Think about what you know about ratios and comparisons. Fill in each box. Use
words, numbers, and pictures. Show as many ideas as you can.
14.14 / 14 Is what ? Please show work ┐( ∵ )┌
Answer:
1.01
Step-by-step explanation:
14.14/14
14/14=1
0.14/14=0.01
1+0.01=1.01
I need some help with my math please
From a 128-foot tree, an object is thrown straight up into the air then follows a trajectory. The height S(t) of the ball above the building after t seconds is given by the function S(t) = 96t - 16t^(2). How long will it take the object to reach maximum height?
Answer:
3 seconds
Step-by-step explanation:
We can solve this in either of two ways: Graphing or taking the first derivative, I'll use both,
Graphing
Plot the equation. My DESMOS graph is attached. One can find the vertex of this curve at 3 seconds. Bonus: It reaches a height of 144 units at this point.
Derivative
The first derivative of this function will produce an equation that returns the slope of the line at any point x.
S(t) = 96t - 16t^(2)
S'(t) = 96 - 2*16t
S'(t) = 96 - 32t
The slope of the curve will be 0 when the ball reaches it's maximum height and begins to fall. Since we want the time it takes to reach a slope of zero, we can set S'(t) to 0 and solve:
S'(t) = 96 - 32t
0 = 96 - 32t
32t = 96
t = 3 seconds
Juan paid 13.46 for a 3.47-pound bag of shrimp at one store. the following week, he paid 18.75 for a 5.15-pound bag at another store. find the unit price for each bag is the better buy based on the unit price. round the answers to the nearest cent.
The unit price for a 5.15 pound bag is the better buy for Juan
Juan paid $13.36 for a 3.47 pound bag of shrimp:
So, cost of one pound bag of shrimp= [tex]\frac{1*13.46}{3.47}[/tex]
=$3.88
Hence, unit price for the 3.47 pound bag=$3.88
Following week, Juan paid $18.75 for a 5.15 pound bag at another store:
So, cost of one pound bag of another store= [tex]\frac{1*18.75}{5.15}[/tex]
=$3.64
Hence, unit price for the 5.15 pound bag at another store=$3.64
It is clear from the above result that second buy (5.15-pound bag at another store) is the better buy for Juan because it cost less per pound.
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6. Given the area of the rectangle is 52 ft², find
the value of x.
(4x - 2) ft
2 ft
Answer:x=7
Step-by-step explanation: 2(4x-2)=52
8x-4=52
8x=56
x=7
A bicycle has cash price $16 319.50. It can be bought on hire purchase with a deposit of $6
900 and ten monthly installments of $1 224.50 each.
a. What is the total hire purchase price for the bicycle? [3 marks]
b. Find the difference between the hire purchase price and the cost price for the bicycle.
[1 mark]
c. Express your answer in (b) above as a percentage of the cash price.
The total cost of the hire purchase for the bicycle is $19,145.
The difference between the hire purchase price and the cost price for the bicycle is $2,825.50
The difference as a percentage of cash price 17.31%.
What is total cost?The total cost of the hire purchase is the sum of the deposit and the total monthly instalment.
Total cost of the hire purchase = amount deposited + total instalment paid
Total instalment paid = number of month x payment per month
$1224.50 x 10 = $12,245
Total cost of the hire purchase = $6,900 + $12,245 = $19,145
The difference = cost of hire purchase + cash price
$19,145 - $16 319.50 = $2,825.50
The difference as a percentage of cash price = (2,825.50 / $16,319.50) x 100 = 17.31%
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what is the 2nd ponit of x = -3
5(4x - 1.5)+12=4x - 2
NEED HELP ASAP - 100 POINTS
When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.
The advantages may be of using the method of completing the square to solve quadratic equations to estimate the values of x and y roots without calculating them.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using Completing the square.
1. First of all we can find the minimum or maximum of the equation immediately.
2. Second is to cuts out the need to use the given ones (a, b, c) in the quadratic formula.
3. It allows estimating the values of x and y roots without calculating them.
Then Estimating on a test is a very valuable asset.
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Casho went shopping for a new pair of sneakers because of a sale. The price on the tag was $25, but Casho paid $22.50 before tax. Find the percent discount
The percentage discount for the pair of sneakers is 10%.
What is percentage?A percentage is a value per hundredth. Percentages can also be fractions and decimals by decimals by dividing by 100 and vice versa. To obtain a percentage of a given value we divide the given percentage by a hundred and multiply the value with it.
The percentage discount can be determined by putting the discounted value upon the price multiplied by a hundred and subtracting the obtained percentage from the hundred percentage.
∴ The percentage discount on the pair of sneakers is,
= (22.50/25)×100.
= 0.9×100.
= 90%.
So, the percentage discount is (100 - 90)% = 10%.
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What is the value of this expression.
Answer:46
Step-by-step explanation:
Determine if the following representations or functions or not? Explain your reasoning.
The three relations given all represent functions because each has exactly one y-value that corresponds to each x-value.
What Relation can be Defined as a Function?A relation can be defined as a function if the x-values (input/domain element) each has exactly one y-value (output value/range element) that is related to or it corresponds to.
A function can have two x-values that have the same y-value but cannot have two y-values that corresponds to one x-value.
In the first relation showing a graph, each x-value on the graph has exactly one y-value it corresponds to. Therefore, it is a function.
In the second relation that is represented by the set of ordered pairs, every x-value also have only one y-value it is related to. Therefore, it represents a function.
The third function given shows a table of values of a relation that has exactly only one y-value that is assigned or related to each x-value. This also is a relation that represents a function.
Therefore, all three relations represent functions.
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The graph of a linear function IS shown.
Which word describes the slope of the line?
positive
negative
zero
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