The correct option is C.
In an isosceles triangle ABC with base angles A and the sides b and c equal, you can use the Law of Cosines to find the length of the other side (a) in terms of b and c. The Law of Cosines is given by:
[tex]\[a^2 = b^2 + c^2 - 2bc \cos(A)\][/tex]
Given that A = π/4, b = c = 4, you can substitute these values into the equation:
[tex]\[a^2 = 4^2 + 4^2 - 2 \cdot 4 \cdot 4 \cos\left(\frac{\pi}{4}\right)\][/tex]
Simplify the expression:
[tex]\[a^2 = 16 + 16 - 32 \cos\left(\frac{\pi}{4}\right)\][/tex]
Now, you know that [tex]\(\cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}\)[/tex], so substitute that in:
[tex]\[a^2 = 16 + 16 - 32 \cdot \frac{\sqrt{2}}{2}\][/tex]
[tex]\[a^2 = 32 - 16\sqrt{2}\][/tex]
Now, factor out 16 from the expression:
[tex]\[a^2 = 16(2 - \sqrt{2})\][/tex]
So, the correct answer is:
[tex]\[a^2 = 4^2(2 - \sqrt{2})\][/tex]
Complete the question:
Suppose an isosceles triangle ABC has A= π /4 and b=c=4. What is the length of a^2 ？ A. 4^2sqrt(2) B. 4^2(sqrt(2)-2) C. 4^2(2-sqrt(2)) D. 4^2(2+sqrt(2))
Final answer:
By applying the Pythagorean theorem to the 45-45-90 isosceles triangle, we find that since both the sides a and b are 4, the square of side a is a² = 16.
Explanation:
In the context of an isosceles triangle with sides labeled a, b, and c, where side a is opposite angle A and side b equals side c, we can utilize the Pythagorean theorem to find the length of side a given that it's a right triangle. The Pythagorean theorem states:
a² + b² = c².
Given that angle A = π/4 radians (45 degrees), it implies that triangle ABC is a 45-45-90 right triangle, which tells us that sides a and b are equivalent in length. Under these conditions, the Pythagorean theorem simplifies to:
2a² = c².
We're given that b = 4, accordingly a would also be 4 (since a=b in an isosceles right triangle), and we're asked to find the length of a². Squaring side a, we get:
a² = 4² = 16.
Therefore, the length of a² is 16.
Solve 2x2 + 12x - 14 = 0 by completing the square
Answer:
x = -7 or x = 1Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\2x^2+12x-14=0\qquad\text{divide both sides by 2}\\\\x^2+6x-7=0\qquad\text{add 7 to both sides}\\\\x^2+2(x)(3)=7\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=7+9\\\\(x+3)^2=16\Rightarrow x+3=\pm\sqrt{16}\\\\x+3=-4\ or\ x+3=4\qquad\text{subtract 3 from both sides}\\\\x=-7\ or\ x=1[/tex]
Shyanne drops a rock from a hill at initial height of 975 feet above ground level. How many seconds after the rock is released will it hit the ground below
61 seconds
7.8secdons
5.2 seconds
11.6seconds
Answer:
61 second I would say but what is the weight of the rock?
Answer:
Option B. 7.8 seconds
Step-by-step explanation:
Shyanne drops a rock from a hill at initial height of 975 feet above the ground level.
We have to calculate the time taken by rock to hit the ground.
As we know the formula of motion under gravity is
h = ut + [tex]\frac{1}{2}gt^{2}[/tex]
Here h = initial height = 975 feet
u = initial velocity = 0
t = time taken by the rock to hit the ground
g = 32.174 [tex]\frac{\text{Feet}}{\text{Second}^{2}}[/tex]
Now we plug in these values in the formula
975 = 0 + [tex]\frac{1}{2}(32.174)(t)^{2}[/tex]
975 = 16.087t²
t² = [tex]\frac{975}{16.087}[/tex]
t = [tex]\sqrt{60.60}[/tex]
t = 7.78 ≈ 7.8 seconds
Option B. 7.8 seconds is the answer.
To make a fruit punch orange juice and apple juice are mixed together in the ratio 3:1
Beth wanted to make 16 litres of punch and calculates that she would need 12 litres of orange
juice.
Is this correct?
Justify your answer by calculation.
© Pegasys 2013
Answer:
It is correct.
Step-by-step explanation:
Orange to Apple juice = 3:1.
Work out the 'multiplier':
3 + 1 = 4.
3 parts are orange so we need 3 * the multiplier = 3*4 = 12 litres.
The function shown in the graph is vertically stretched by a factor of 2 to produce a new graph.
Which function represents the new graph?
Answer: Third option.
Step-by-step explanation:
We know that the sine function is:
[tex]f(x)=Asin(bx)[/tex]
Where "A" is the amplitude of the function( This is half the vertical distance between minimum value and maximum value of the function) and [tex]\frac{2\pi }{b}[/tex] is the period.
Observe in the graph that the amplitude is:
[tex]A=1[/tex]
And the period is 1, then "b" is:
[tex]1=\frac{2\pi }{b}\\\\b=\frac{2\pi }{1}\\\\b=2\pi[/tex]
Then the function shown in the graph is:
[tex]f(x)=sin(2\pi x)[/tex]
By definition in the transformation of the function:
When [tex]kf(x)[/tex] and [tex]k>1[/tex] then the function is stretched vertically by a factor of "k".
In this case we know that the function shown in the graph is vertically stretched by a factor of 2 to produce a new graph. Then:
[tex]k=2[/tex]
Therefore,the function that represents the new graph is:
[tex]f(x)=2sin(2\pi x)[/tex]
please help asap 50 points
Answer:
9⁹ ÷ 9⁶.
The expression 9³ is equivalent to 9⁹ ÷ 9⁶.
Step-by-step explanation
hope it
If Logx (1 / 8) = - 3 / 2, then x is equal to
A. - 4
B. 4
C. 1 / 4
D. 10
Answer:
B
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{x}[/tex] ([tex]\frac{1}{8}[/tex] ) = - [tex]\frac{3}{2}[/tex], then
[tex]\frac{1}{8}[/tex] = [tex]x^{-\frac{3}{2} }[/tex]
Square both sides
[tex]\frac{1}{64}[/tex] = [tex]x^{-3}[/tex]
[tex]4^{-3}[/tex] = [tex]x^{-3}[/tex] ⇒ x = 4 → B
how do you simplify this rational expression? please show your work.
Answer:
3(x-2)÷(x-2)=3.....
Answer:
3Step-by-step explanation:
[tex]3x-6\qquad\text{distributive}\\\\=(3)(x)-(3)(2)=(3)(x-2)=3(x-2)\\\\\dfrac{3x-6}{x-2}=\dfrac{3(x-2)}{x-2}\qquad\text{cancel}\ (x-2)\\\\=\dfrac{3(1)}{1}=3[/tex]
Who was responsible for inventing the first working four-stroke engine?
Answer:
Nikolaus Otto was responsible for inventing the first working four-stroke engine.
Step-by-step explanation:
which equation in point-slope form contains the point (-3, 5) and has slope -1 ANSWERS y + 3 = -1(x-5) y-3= -1(x+5) y+5=-1(-3) y-5=-1(x+3)
Answer:
y - 5 = -1(x + 3)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have m = -1 and the point (-3, 5). Substitute:
[tex]y-5=-1(x-(-3))\\\\y-5=-(x+3)[/tex]
Can you help me with the top one please thnx
Answer:
1:4
Step-by-step explanation:
24 divided by 6 is 4. and 6 divided by 6 is 1
Answer:
1:4
Step-by-step explanation:
24÷6=4 and 6÷6=1 this is all you need
a cityhas a population density of approximately 46 people per square mile.if the city is 6,521.74 mi2, then approximately how many people live in that city
Answer:
[tex]300,000.04\ people[/tex]
Step-by-step explanation:
we know that
To find how many people live in that city multiply the population density by the area of the city
so
[tex](46\ \frac{people}{mi^{2}})(6,521.74\ mi^{2})=300,000.04\ people[/tex]
I need to simplify this problem as much as I can. But I’m confused I just need step for step then the answer
[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta )=1-sin^2(\theta ) \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin^2(\theta )}{1-sin^2(\theta )}\implies \cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \left[ \cfrac{sin(\theta )}{cos(\theta )} \right]^2\implies tan^2(\theta )[/tex]
I need help with number 4 I can’t get an answer
Answer:
14.93
Step-by-step explanation:
For this problem you need to know distance formula, which is
d=√(x2-x1)²+(y2-y1)². You'll want to plug in (0,3) and (-2, 9) and go on to plug in all of them at some point. You'll get 6.32 as the distance between (0,3) and (-2, 9), 3.61 as the distance between (-2, 9) and (-4, 6), and 5 as the distance between (-4, 6) and (0, 3). You add them up and get your answer.
which of the following choices describes the bases of a cylinder a disks be congruent C similar D parallel
Answer: Disc, Congruent, parallel
Step-by-step explanation:
The disks, congruent, and parallel choices describes the bases of a cylinder option (A), (B), and (D) are correct.
What is a cylinder?In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.
We know the volume of the cylinder is given by:
[tex]\rm V = \pi r^2 h[/tex]
We have given a statement:
Which of the following choices describes the bases of a cylinder:
The options given:
A) disks
B) congruent
C) similar
D) parallel
As we know, the cylinder has two circular bases at height h between them.
The bases of a cylinder can be described as disks, congruent, and parallel.
Thus, the disks, congruent, and parallel choices describes the bases of a cylinder option (A), (B), and (D) are correct.
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how many terms does the polynomial have?
3 terms. Just count the terms (which are separated by the +/- signs)
The answer is:
The polynomial have 3 terms. (it's a trinomial).
Why?A polynomial is an expression which consists of one or more terms (numbers or variables) being added or subtracted.
So, we are given the polynomial:
[tex]x^{2} +xy-y^{2}[/tex]
We have that there are three terms separated by differents being added and subtracted, so, the polynomial has 3 terms, and it's a trinomial.
Have a nice day!
Linda, Dale, and Jim sent a total of 83 text messages over their cell phones during the weekend. Jim sent 7 more messages than Linda. Dale sent 4 times as many messages as Jim. How many did they each send?
Answer: The answer is 94
Step-by-step explanation: First you should pay attention to the main numbers and since more and many are addition word than you should add 7 + 4 which equals 11 then add 83 + 11 which would equal 94. Tell me if the answer is wrong and I would find another way to answer it.
Final answer:
Linda sent 8 text messages, Jim sent 15 messages, and Dale sent 60 messages during the weekend.
Explanation:
The question asks to solve a word problem to find out how many text messages Linda, Dale, and Jim sent over the weekend.
Let's denote the number of messages Linda sent as L, Jim as J, and Dale as D.
The problem states that Jim sent 7 more messages than Linda, so J = L + 7.
Dale sent 4 times as many messages as Jim, so D = 4J.
Together they sent 83 messages, which gives us the equation L + J + D = 83.
Substituting the expressions for J and D in terms of L into the equation, we get L + (L + 7) + 4(L + 7) = 83.
This simplifies to 6L + 35 = 83. Solving for L gives us L = 8.
This means Linda sent 8 messages, Jim sent 15 messages (8 + 7), and Dale sent 60 messages (4 times 15).
The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units. What is the width, in units, of the rectangle.
Answer:
4
Step-by-step explanation:
Let's call the width W and the length L.
We know the width is 3 less than the length, so:
W = L - 3
And we know the area is 28, so:
28 = WL
If we solve for L in the first equation:
L = W + 3
And substitute into the second equation:
28 = W (W + 3)
28 = W² + 3W
0 = W² + 3W - 28
0 = (W + 7) (W - 4)
W = -7, 4
Since W can't be negative, W = 4 units.
The width, in units, of the rectangle, if the area of the rectangle is 28 units, is 4 units.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given:
The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units,
Write the equation as shown below,
b = l - 3 (Here, l is the length and b is the width)
l × b = 28
Solve the above equations,
l = 7 units and b = 7 - 3 = 4 units
Therefore, the width, in units, of the rectangle, if the area of the rectangle is 28 units, is 4 units.
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Solve this sumutaneous equation
2x-5 y=9
3x+4y=2
Answer:
x = 2 and y = -1 → (2, -1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x-5y=9&\text{multipy both sides by 4}\\3x+4y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}8x-20y=36\\15x+20y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=46\qquad\text{divide both sides by 23}\\.\qquad x=2\\\\\text{put it to the second equation}\\\\3(2)+4y=2\\6+4y=2\qquad\text{subtract 6 from both sides}\\4y=-4\qquad\text{divide both sides by 4}\\y=-1[/tex]
true or false one milliliter of water has a mass of 2.00 grams
Answer:
false
Step-by-step explanation:
One milliliter of water has one gram of mass, and weighs one gram in typical situations
One milliliter of water does not have a mass of 2.00 grams.
Water has a density of 1g/mL, so one milliliter of water has a mass of 1 gram.
What is the completely factored form of 12xy-9x-8y+6
Answer: (4y - 3)(3x - 2)
Step-by-step explanation: Factor the polynomial.
Hope this helps! :) ~Zane
For this case we must factor the following expression:
[tex]12xy-9x-8y + 6[/tex]
So:
We group the first two and two last terms:
[tex](12xy-9x) + (- 8y + 6) =[/tex]
we factor the maximum common denominator of each group:
[tex]3x (4y-3) -2 (4y-3) =[/tex]
We factor the polynomial by factoring the highest common denominator:
[tex](3x-2) (4y-3)[/tex]
ANswer:
[tex](3x-2) (4y-3)[/tex]
HELP PWEASEE Brainliestt
Meg has a can that contains 80% orange juice and the rest water. The can has 1 liter of water.
Part A: Write an equation using one variable that can be used to find the total number of liters of orange juice and water in the can. Define the variable used in the equation and solve the equation. Hint: 0.8x represents the number of liters of orange juice in the can. (5 points)
Part B: How many liters of orange juice are present in the can? Show your work. (5 points)
A)x+4x = Juice and water
x = Water
4.00 is total juice relative to water
+
1.00 is total water
B) 4 liters
(1 liter)+4(1 liter) = Total
1 + 4 = 5
What is the midpoint of OA
Answer:
Step-by-step explanation:
if i had to guess i would say a
ANSWER
The midpoint is a) (m,n)
EXPLANATION
The point O has coordinate (0,0) and the point A has coordinate (2m,2n)
The x-coordinate of the midpoint is
[tex]x = \frac{0 + 2m}{2} [/tex]
[tex]x = \frac{2m}{2} [/tex]
[tex]x = m[/tex]
Also,
[tex]y = \frac{0 + 2n}{2} [/tex]
[tex]y = \frac{ 2n}{2} [/tex]
[tex]y = n[/tex]
The answer is A
Leo needs 10 red roses and 15 pink daisies for every 5 bouquets he makes for a flower shop. Drag red roses and pink daisies into the box to show how many Leo needs for 3 bouquets.
Leo needs 6 red roses and 9 pink daisies for 3 bouquets, calculated by dividing the number of flowers needed for 5 bouquets by 5 and then multiplying by 3.
Explanation:To calculate the amount of red roses and pink daisies Leo needs for 3 bouquets, we first determine the number needed for one bouquet. Since Leo needs 10 red roses and 15 pink daisies for every 5 bouquets, we divide each amount by 5 to find the number per single bouquet:
Red roses per bouquet: 10 red roses / 5 bouquets = 2 red roses per bouquetPink daisies per bouquet: 15 pink daisies / 5 bouquets = 3 pink daisies per bouquetNow, we multiply the number of flowers needed per bouquet by 3 to find the total number for 3 bouquets:
Red roses for 3 bouquets: 2 roses per bouquet × 3 bouquets = 6 red rosesPink daisies for 3 bouquets: 3 daisies per bouquet × 3 bouquets = 9 pink daisiesTherefore, for 3 bouquets, Leo needs 6 red roses and 9 pink daisies.
Find the length of a square with an area of 169 in2.
A. 338 in
B. 106 in
C. 26 in
D. 13 in
Find the length of a side of a square with an area of 169 in^2.
Answer:
D. 13 in
Step-by-step explanation:
A square has sides of equal length.
A = L^2 where: A = area and L = side
L^2 = 169
L=√169
L=13 in^2.
The length of a side of a square with an area of 169 in2 is calculated by taking the square root of the area, which is 13 inches. The correct answer is D. 13 in.
The student is asking to find the length of a side of a square given that the area of the square is 169 square inches. The formula to calculate the area of a square is side length squared, which can be written as:
Area = side × side
To find the side length, we need to take the square root of the area:
Side = √169
Upon calculation, the side length is:
Side = 13 {in}
Therefore, the correct answer is D. 13 in.
Explain why the solution of 5x – 3 > 14.5 or 2x+5
4 has a solution of all real numbers, with one exception
ANSWER: THE SOLUTION OF GIVEN INEQUALITIES IS ALL REAL NUMBER EXCEPT [1.167,3.5].
Answer:
Sample Response: When solving the first inequality, you get x > 3.5. When solving the second inequality, you get x < 3.5. The solution of an "or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.
Step-by-step explanation:
State if each angle is an inscribed angle. If it is name the angle and the intercepted arc.
Answer:
Part 1) The inscribed angle is the angle ∠TRS and the intercept arc is the arc LST
Part 2) The inscribed angle is the angle ∠YWX and the intercept arc is the minor arc XY
Part 3) The inscribed angle is the angle ∠YXZ and the intercept arc is the arc YBZ
Part 4) The figure does not show an inscribed angle
Step-by-step explanation:
Part 1) The figure shown a inscribed angle
The inscribed angle is the angle ∠TRS
The intercept arc is the arc LST
Remember that
The inscribed angle measures half that of the arc comprising
so
∠TRS=(1/2)[arc LST]
Part 2) The figure shown a inscribed angle
The inscribed angle is the angle ∠YWX
The intercept arc is the minor arc XY
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YWX=(1/2)[minor arc XY]
Part 3) The figure shown a inscribed angle
The inscribed angle is the angle ∠YXZ
The intercept arc is the arc YBZ
Remember that
The inscribed angle measures half that of the arc comprising
so
∠YXZ=(1/2)[arc YBZ]
Part 4) The figure does not show an inscribed angle
The figure shown a interior angle ∠BAC
What is the difference between the rational expressions below? 3x+1/x^2-5/x
Answer:
(3x^2-5x-5)/(x^2+x) <--- answer
Step-by-step explanation:
3x/(x+1) - 5/x = (3x^2 - 5(x+1) )/[ x(x+1) ]
= (3x^2 - 5x - 5)/(x^2 + x)
The difference between the rational expressions 3x+1/x and 5/x is 3x - 4/x.
Explanation:The difference between these two rational expressions will be obtained by subtracting the second expression from the first. To do this, we first need to simplify the expressions wherever possible. The first expression, 3x + 1/x, remains as it is. The second expression, 5/x, is a simple fraction and can't be simplified any further either.
Subtracting the second from the first, you get (3x + 1/x) - (5/x) which simplifies to 3x - 4/x. The difference between these two rational expressions is hence 3x - 4/x.
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Two fair dice are rolled
What is the SAMPLE SPACE of the possible outcomes?
SHOW YOUR WORK!
ANSWER
See sample space below
EXPLANATION
The sample space refers to the set of all the possible outcomes.
When two fair dice are rolled, the possible by outcomes are:
{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
The total number of outcomes is 36.
The value in dollars, v(x), of certain truck after x year’s is represented by the equation v(x)= 32500(0.92)^x. To the nearest dollar, how much is the truck worth after 2 years?
[tex]\bf v(x)=32500(0.92)^x\qquad \qquad \stackrel{\textit{2 years later, x = 2}}{v(2)=32500(0.92)^2} \\\\\\ v(2)=32500(0.8464)\implies v(2)=27508[/tex]
Answer:
$27508.
Step-by-step explanation:
We have been given that the value of certain truck after x years is represented by equation [tex]v(x)=32500(0.92)^x[/tex]. We are asked to find the value of truck after 2 years.
To find truck's value after 2 years, we need to substitute [tex]x=2[/tex] in our given equation.
[tex]v(2)=32500(0.92)^2[/tex]
[tex]v(2)=32500*0.8464[/tex]
[tex]v(2)=27508[/tex]
Therefore, the truck is worth $27508 after 2 years.
is the number 1 Prime
Answer:
No.
Step-by-step explanation:
To be prime, it has to be a number more than 1.
Answer:
No
Step-by-step explanation:
The number 1 is only divisible by itself, so it is neither prime nor composite.