The length of side c would be 8.
Step-by-step explanation:
Given that,
a = 4
b = 6
cosC = -1/4
If we are given two sides and angle, the law of Cosines can be used to find the third side:
[tex]c^{2} = a^{2} + b^{2} - 2ab (cos(c))[/tex]
By inserting the values in the formula, we get
[tex]c^{2} = 4^{2} + 6^{2} - 2.4.6 (-\frac{1}{4} )[/tex]
[tex]c^{2} = 16 + 36 + 12[/tex]
[tex]c^{2} = 64[/tex]
[tex]\sqrt{c^{2} } = \sqrt{64}[/tex]
c = 8.
Therefore, the length of side c would be 8.
The length of side [tex]\( c \)[/tex] is 8. The option (1) is correct.
To find the length of side [tex]\( c \)[/tex] in triangle ABC given [tex]\( a = 4 \), \( b = 6 \)[/tex], and [tex]\( \cos C = -\frac{1}{4} \),[/tex] we use the cosine rule:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos C \][/tex]
Substitute the given values:
[tex]\[ c^2 = 4^2 + 6^2 - 2 \cdot 4 \cdot 6 \cdot \left(-\frac{1}{4}\right) \][/tex]
[tex]\[ c^2 = 16 + 36 + 12 \][/tex]
[tex]\[ c^2 = 64 \][/tex]
Now, take the square root of both sides to find [tex]\( c \):[/tex]
[tex]\[ c = \sqrt{64} \][/tex]
[tex]\[ c = 8 \][/tex]
Therefore, the length of side [tex]\( c \)[/tex] is 8.
Simplify this power raised to a power: (54)4 1. Expand using four factors of 54: 54 ∙ 54 ∙ 54 ∙ 54 2. Apply the product of powers rule: 54+ 4+ 4+ 4 3. Simplify: 5x What is the value of x in the simplified power?
Answer:
X = 16
Step-by-step explanation:
I put 16 and it was correct.
Hope this works for you
Answer:
x=16
Step-by-step explanation:
You add all the 4s from the second step and get a product of 16.
Which statements about the circle graph are correct? Check all that apply.
25% of the students said blue was their favorite color.
33% of the students said green was their favorite color.
25% of the students said orange was their favorite color.
50% of the students said either green or orange was their favorite color.
66% of the students said either orange or blue was their favorite color.
Answer: C and D
Step-by-step explanation:
25% of the students said orange was their favorite color.
50% of the students said either green or orange was their favorite color.
Answer:
the answer my friend would likley be c and:D
Step-by-step explanation:
Hope this helps
What is the solution to the following graph? Write it as an ordered pair to get credit.
Answer:
(2,6)
Step-by-step explanation:
Samatha needs 6 lengths of ribbon cut into 1.2 foot segments. How many feet of ribbon should she buy
Answer:
7.2 feet
Step-by-step explanation:
1.2 x 6 = 7.2
hope this helps <3
The total length of the ribbon Samantha would need is given by the equation A = 7.2 feet
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 ,
Let the total length of the ribbon be represented as A
Now , the equation will be
The number of pieces of ribbon required = 6 pieces
The length of each piece of ribbon = 1.2 feet
So , the total length of the ribbon A = number of pieces of ribbon required x length of each piece of ribbon
Substituting the values in the equation , we get
The total length of the ribbon A = 6 x 1.2
On simplifying the equation , we get
The total length of the ribbon A = 7.2 feet
Therefore , the value of A is 7.2 feet
Hence , the total length of the ribbon is 7.2 feet
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Can someone help me with this homework problem?
Answer:
I've already answered this question in another post:
full
[tex]\frac{\theta}{2\pi }[/tex]
[tex]A=\frac{\theta}{2}r^2[/tex]
Find f(2) it f(x)=(x+1)^2
Steps to solve:
f(x) = (x + 1)^2; x = 2
~Substitute
f(2) = (2 + 1)^2
~Add.
f(2) = (3)^2
~Multiply the exponent
f(2) = 9
Best of Luck!
In circle C, SQ = 10 cm.
Circle C is shown. Chords S Q and R P intersect at point C. Angle P C Q is 30 degrees.
Which statements about the circle are correct? Check all that apply.
Arc PQ is congruent to arc SR.
The measure of arc QR is 150°.
The circumference of circle C is 20π cm.
Arc PS measures about 13.1 cm.
Arc QS measures about 15.7 cm.
Answer:
1-Arc PQ is congruent to arc SR.
2-The measure of arc QR is 150°.
4-Arc PS measures about 13.1 cm.
5-Arc QS measures about 15.7 cm
Step-by-step explanation:
1,2,4,5
Answer:
A
B
D
E
Step-by-step explanation:
C is dum and wrong
What is the positive solution of 3x2 -10x =0
The answer should be:
x=0, 10/3
thes Tano mare paranet.
(2x)
Vr-10)
What is the measure of angle 3?
Mark this and return
Answer:
∠ 3 = 25°
Step-by-step explanation:
The sum of the 3 angles 85, 2x and x - 10 are a straight angle = 180°
85 + 2x + x - 10 = 180, that is
3x + 75 = 180 ( subtract 75 from both sides )
3x = 105 ( divide both sides by 3 )
x = 35
Thus x - 10 = 35 - 10 = 25
∠ 3 and x - 10 are Alternate angles and congruent, thus
∠ 3 = 25°
What is the name of the figure?
triangular prism
triangular pyramid
rectangular prism
rectangular pyramid
Answer:
Triangular Prism.
The name of the figuare is triangular prism, the correct option is A.
What is the trianular prism?In geometry, a triangular prism is a type of prism with three sides and two bases.
The sides are of rectangle shape and bases are of triangle shape.
A triangular prism is a popular polyhedron. It is having two triangular bases and three rectangular sides.
According to the nature of prism, the two triangular bases are parallel and congruent to each other. It is a pentahedron with nine distinct nets.
The edges and vertices of the bases are connected with each other.
The rectangular sides of this prism are rectangular in shape and are joint with each other side by side.
All the cross-sections parallel to the base faces are triangle.
The given image has the shape of trigular prism.
Hence, the name of the figuare is triangular prism, the correct option is A.
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Solve for x and then find the measure of A
Answer:
x=18
m∠A=110°
Step-by-step explanation:
∠A and ∠B are supplementary
[tex]5x+20+9x-92=180\\14x-72=180\\14x-72+72=180+72\\14x=252\\x=18[/tex]
plug in 18 for x
[tex]5x+20\\5(18)+20\\90+20\\110[/tex]
distributive property of 7(5j + 8 +3j)
Answer:
35j+56+21j
Step-by-step explanation:
Hope it helps!!
The ratio of guppies to angelfish in a shop is 2 : 3. The number of angelfish was 23the number of goldfish. The shopkeeper decided to replace 14of the guppies with some angelfish. The number of angelfish she added was equal to the number of guppies she replaced. There were 30 more goldfish than angelfish in the end. How many guppies were in the shop in the beginning?
Answer:
The number of guppies were in the shop in the beginning = 60
Step-by-step explanation:
guppies ⇒ x , angelfish ⇒ y , goldfish ⇒ z
guppies to angelfish = 2 : 3 ⇒ x : y = 2 : 3 ⇒ x = 2/3 y
The number of angelfish was 2/3 the number of goldfish ⇒ y = 2/3 z
Or z = 3/2 y
The shopkeeper decided to replace 1/4 of the guppies with some angelfish. The number of angelfish she added was equal to the number of guppies she replaced
so, the number of guppies = 0.75x
and the number of angelfish = y + 0.25 x = y + 0.25 * 2/3 y
There were 30 more goldfish than angelfish in the end
z - (y + 0.25 * 2/3 y) = 30
so, 3/2 y - (y + 0.25 * 2/3 y) = 30
3/2 y - y - 1/6 y = 30
1/3 y = 30
y = 90
x = 2/3 y =2/3 * 90 = 60
z = 3/2 * 90 = 135
so, the number of guppies were in the shop in the beginning = 60
Final answer:
By setting up variables for the number of guppies (G) and angelfish (A) and establishing equations based on the given ratios, we can determine that the shop initially had 40 guppies.
Explanation:
To determine how many guppies were in the shop originally, let's set up variables for the number of guppies (G) and angelfish (A). According to the information provided, the ratio of guppies to angelfish is 2:3, which can be represented by the equation G/A = 2/3. The number of angelfish was also 2/3 the number of goldfish (F), meaning A = (2/3)F. When 1/4 of the guppies are replaced with angelfish, the number of guppies becomes 3/4G, and the number of angelfish becomes A + 1/4G. In the end, we are told there are 30 more goldfish than angelfish. Therefore, we have F = A + 30.
From A = (2/3)F and F = A + 30, we can substitute (2/3)F for A in the second equation, yielding F = (2/3)F + 30. Solving this equation for F gives us F = 90. Using the earlier equation A = (2/3)F, we find A = 60. Now, since A was 2/3 the number of goldfish originally, and using G/A = 2/3, we solve for G by setting up the equation G/60 = 2/3, leading to G = 40. Hence, there were 40 guppies in the shop initially.
Maxine and Sammie have to also mow their parking strips that are the
same size. Maxine can mow her parking strip in 6 minutes and Sammie
can mow his parking strip in 9 minutes. After how many minutes will
Sammie have twice as much grass to mow as Maxine?
I believe the answer is 3 minutes
At the 3 minute mark, Maxine will be half way done and Sammie will still have 6 minutes left to mow the grass
EASY QUESTION NEED HELP
Answer:
620
Step-by-step explanation:
20% = 124
20%*5 = 124*5
100% = 620
Which decimal is equivalent to 7.5%?
Answer:
0.075
Step-by-step explanation:
To convert 7.5% to a decimal you would simply divide 7.5 by 100.
1) Divide 7.5 by 100.
[tex]7.5/100=0.075[/tex]
Answer:
0.075
Step-by-step explanation:
This one is correct.
consider the formula F=NM/P, where F represents the fertility of the soil. N represents the amount of nutrients in the soil. M represents the amount of moisture in the soil. And P represents the amout of pollutants in the soil. select an apropriate measurment unit for fertility of soil
The options are missing, so i have attached it.
Answer:
Measurement unit for F = (Nutrients • Moisture)/Pollutants.
Option C is correct
Step-by-step explanation:
From the question, we are given the formula; F = NM/P
where;
N is the amount of nutrients in the soil
M is the amount of moisture in the soil.
P is the amount of pollutants in the soil
From the definition of the terms above, the units of the can be expressed as;
N = nutrients
M = moisture
P = pollutants
Thus, the measurement unit for fertility is;
F = NM/P = (Nutrients • Moisture)/Pollutants
Jordana was shown this diagram of an isosceles trapezoid and its reduction. She was asked to find the perimeter of the reduced trapezoid. Her work is shown below.
A trapezoid with side lengths 30 centimeters, 12 centimeters, and 36 centimeters. A trapezoid with side lengths A, 4 centimeters, B.
Figures not drawn to scale.
Jordana’s Work
Scale factor
StartFraction 4 over 12 EndFraction = one-third
Side A
30 times one-third = 10
Side B
30 times one-third = 10
Perimeter
10 + 10 + 4 + 4 = 28
Where, if any, did Jordana first make a mistake in her work?
Jordana made a mistake when finding the scale factor.
Jordana made a mistake when she calculated the length of side A.
Jordana made a mistake when she calculated the length of side B.
Jordana did not make any mistakes in her work.
Answer:
C: Jordana made a mistake when she calculated the length of side B.
Step-by-step explanation:
Jordana made a mistake while calculating the length of side B.
What is a scale factor?A scale factor is a factor by which dimensions of an object are enlarged or diminished.
One parallel length i.e. side A of original isosceles trapezoid = 12cm
One parallel length i.e. side A of reduced isosceles trapezoid =4cm
So, scale factor = 4/12 =1/3
Other parallel length i.e. side B of original isosceles trapezoid =
So, the other parallel length i.e. side B of reduced isosceles trapezoid = 36*1/3 = 12cm
The side lengths of the reduced isosceles trapezoid = 30*1/3 = 10cm
So, the perimeter of the reduced isosceles trapezoid =4+12+10+10 =36cm
While Jordana calculated the length of side B as 4.
Thus, Jordana made a mistake while calculating the length of side B.
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Find the distance between point E and point C.
A) 5
B) 9
C) 10
D) 11
there is $412 and 3 purses how much is in each purse????
Answer:
$412/3 purses = $137.33/purse
Please Help! Will mark brainliest if correct! THANK QQQQQQQQQQQQQQQQQQ!
Answer:
About 28.26 inches.
Step-by-step explanation:
The formula for circumfrence is c = 2(pi) * r.
We know that r = 4.5 (because the diameter is 9 inches).
So, the equation is c = 2(pi) * 4.5
Let's solve:
c = (2*3.14) * 4.5
c = 6.28 * 4.5
c = 28.26
Therefore, the final answer is 28.26 inches.
Of course, this is not exact because pi is irrational and goes on forever, but the question is asking for an estimate anyways.
Answer:
28.26
Step-by-step explanation:
Just multiply 9x3.14 It would be different if it was the diameter and the diameter is 4.5
Is one half percent equal to 50%?
Answer:
i know the answer
Step-by-step explanation:
The first data set represents a linear function with ___ slope.
Answer:
the first Data set represent alinear function with linear slope
Answer:
a
Step-by-step explanation:
Which graph shows a negative rate of change for the interval 0 to 2 on the x-axis?
On a coordinate plane, a parabola opens up. It goes through (negative 6, 3), has a vertex of (negative 1.5 negative 3.75), and goes through (3.2, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 5.5, 4), has a vertex of (negative 1, negative 3.2), and goes through (3.5, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex of (2.5, 0.25), and goes through (5.8, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 3.4, 4), has a vertex of (1.5, negative 3.75), and goes through (6, 3).
Answer:
The answer is C :)
Step-by-step explanation:
Just took the quiz and got it right
The statement that shows a negative rate of change for the interval 0 to 2 on the x-axis is option C; On a coordinate plane, a parabola opens up. It goes through (negative 1, 4), has a vertex of (2.5, 0.25), and goes through (5.8, 4).
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
The statement that shows a negative rate of change for the interval 0 to 2 on the x-axis is option C.
On a coordinate plane, a parabola opens up. It goes through (-1, 4), has a vertex of (2.5, 0.25), and goes through (5.8, 4).
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An airplane flies from point A to point B. Point A is 40 kilometers from a ground signal at point C. Point
B is 56 kilometers from the same ground signal. If AB = 80 kilometers, find the measure of ACB to
the nearest degree.
Answer:
112°
Step-by-step explanation:
The law of cosines can be used to find angle C from the three side lengths. The usual formulation of that law is ...
c^2 = a^2 + b^2 -2ab·cos(C)
Then the angle C can be found to be ...
C = arccos((a^2 +b^2 -c^2)/(2ab))
For the given side lengths,
C = arccos((40^2 +56^2 -80^2)/(2·40·56)) = arccos(-1664/4480)
C ≈ 112°
What is the decimal multiplayer to increase by 4.1%
Answer:
1.041
Step-by-step explanation:
In order to increase by 4.1%, you must multiply whatever number you have by the decimal: 1.041.
Say the number we want to increase by 4.1% is x. Then:
x + (4.1%) * x = x(1 + 4.1%) = x(1 + 0.041) = 1.041x
So, you would multiply by 1.041.
Hope this helps!
Answer:
1.041
Step-by-step explanation:
Increase of 4.1% is basically
100 + 4.1 = 104.1% of the previous value
In decimals,
1.041
Jefferson middle school is selling tickets to a choral performance. On the first day of ticket sells they sold 4 adult tickets and 1 child ticket for a total of 55 dollars on the next day of sales they sold 3 adult ticks and 2 child tickets for a total of 50 dollars find the price of an adult and child ticket
Answer:
Adult is $12 and child is $7
Step-by-step explanation:
Adult=x and Children=y
first day: 4x+1y=55
second: 3x+2y=50
Get one letter the same but opposite
(4x+1y=55) times that by -2
-8x+-2y=110
3x+2y=50
minus all of that u get
-5x=60
divide 60 by 5
x=12
fill in X
3(12)+2y=50
36+2y=50
-36 -36
2y=14
/2 /2
y=7
The question is about solving a system of equations representing the sales of adult and child tickets. You would use either substitution or elimination methods to find the individual prices of the adult (A) and child (C) tickets.
Explanation:The subject of your query pertains to system of equations. In this problem, we can establish two equations based on the information provided: 4A + C = 55 and 3A + 2C = 50, where A represents the cost of an adult ticket and C is the cost of a child ticket. We can solve this using the substitution or elimination method. If we solve the first equation for A, we will obtain A = (55-C)/4. Substituting this into the second equation gives us 3((55-C)/4) + 2C = 50. Simplifying and solving this equation will provide us with the cost of the child ticket (C), which we can then substitute back into one of our original equations to find the price of an adult ticket (A).
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Don collects trading cards. His favorites are baseball and football
cards. For every 8 baseball cards he owns, Don has 15 football cards.
What is the ratio of baseball cards to football cards in his collection?
1 of 5 QUESTIONS
8 and 15
8 to 15
15:8
SUBMIT
The ratio of baseball cards to football cards in Don's collection is 8 to 15.
Explanation:Given that for every 8 baseball cards, Don has 15 football cards, the ratio between baseball and football cards can be expressed as 8 to 15. This ratio signifies the comparative quantity of baseball cards to football cards in Don's collection.
Understanding ratios is essential to represent the relationship between different quantities or values. In this scenario, the ratio 8 to 15 indicates that for every 8 baseball cards, Don owns 15 football cards.
The ratio 8 to 15 is simplified, representing the proportional relationship between the number of baseball cards and football cards in a manner that showcases the relative quantity of each type of card Don possesses.
Ratios help in understanding and comparing quantities, providing a concise way to express relationships between different values or items, as demonstrated in the comparison between the number of baseball and football cards in Don's collection.
A city has 4 new houses for every 9 old houses. If there are 20 new houses in the city, how many old houses are there?
A. 43
B. 49
C. 45
D. 47
Answer:
b
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
4 times 5 =20 and 9 times 5=45
Write an expression, using an exponent, that is equivalent to 8 X 8 X 8 X 8.
Answer:
8 to the 4th power
Step-by-step explanation:
Answer:
8 to the 4th power (but with the 4 to the top right of the 8)
Step-by-step explanation:
each 8 is one power
8x8x8x8
1 2 3 4