The length of AC in triangle BAC is equal 10.7 units
Cosine RuleIn trigonometry, the cosine rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.
The formula is given as
AC² = AB² + BC² - 2(AB)(BC) cos AC
AC² = 6² + 7² - 2(6)(7)cos110
AC = 10.7
Using cosine rule, the length of AC is 10.7 unit.
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Help please. It's means with expression and it's due by the end of this class and I legit forgot how to do it because I havent done this since 4th grade.
Answer:
the two middle students are 63
Pls, HELP ASAP!!!!!!!!!!!!!!!!!
The locations of student desks are mapped using a coordinate plane where the origin represents the center of the classroom. Maria's desk is located at (5, −1), and Monique's desk is located at (−2, 4). If each unit represents 1 foot, what is the distance from Maria's desk to Monique's desk?
square root of 10 feet
square root of 72 feet
square root of 74 feet
square root of 100 feet
Answer: it’s the square root of 10
Step-by-step explanation: I took this test
Answer:[tex]\sqrt{74}[/tex]
Step-by-step explanation:
Carmen tutors history. For each hour that she tutors , she earns 30 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H. Then use the equation to find Carmen’s earnings after tutoring for 13 hours.
Equation: ______
Carmen’s earnings for 13 hour’s: ____ dollars
An equation is formed from two equal expressions. Carmen earns $390 for her 13 hours of tutoring.
Equation: An equation is created by equating two equations with an equal sign '='.
Let's say Carmen is earning $30 per hour of her tutoring her.
Therefore, the formula for Carmen's income after H hours of tutoring can be written as:
Income = hourly wage for individual instruction x number of hours
I = 30 × H
I = 30H
After 13 hours of tutoring, Carmen's income will be:
I = 30 (13)
I = 390
So, after 13 hours of tutoring, Carmen's income will be $390.
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Monica has $20. She needs to buy a gallon of milk that costs $2.50. She also wants to buy yogurt, which costs $1.20 a cup. What is the greatest number of cups of yogurt Monica can buy? Use the inequality 1.20x + 2.5 ≤ 20 to solve the problem. Monica can buy | cups of yogurt.
The greatest number of cups of yogurt that Monica can buy is 14 cups
The amount that she has = $20
The cost of one gallon of milk = $2.50
The cost of one cup of yogurt = $1.20
Consider the number of cups of yogurt = x
Then the inequality will be
1.20x + 2 .50 ≤ 20
Solve the inequality and find the value of x
Subtract 2.50 from both side of the inequality
1.20 + 2.50 - 2.50 ≤ 20 - 2.50
1.20x ≤ 17.5
Divide both side of the equation by 1.20
1.20x / 1.20 ≤ 17.5 / 1.20
x ≤ 17.5 / 1.20
x ≤ 14.58
Hence, the greatest number of cups of yogurt that Monica can buy is 14 cups
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Given g(x)=-2x+5, find g(-4)
Answer:
13
Step-by-step explanation:
Given g(x)=-2x+5, find g(-4)
so you are substituting in -4 for x:
g(-4) = -2(-4) + 5
g(-4) = 8 + 5
g(-4) = 13
In 2015, ed spent $800 buying lunches. In 2017, he spent $300 buying lunches. What was the rate of change from 2015 to 2017?.
The rate of change from 2015 to 2017 is -$250
The amount he spend for lunch in 2015 = $800
The amount he spend for lunch in 2017 = $300
Therefore the total change = The amount he spend for lunch in 2017 - The amount he spend for lunch in 2015
Substitute the values in the equation
= 300 - 800
= -500
The total years from 2015 to 2017 = 2 years
The rate of change from 2015 to 2017 = The total change / The total years from 2015 to 2017
= -500 / 2
= -$250
Hence, the rate of change from 2015 to 2017 is -$250
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what is (h - 3)² for h = 5
Answer:32
Step-by-step explanation:
You plug in 5 for H and then you solve
Answer:
the answer to yo question is 4
Step-by-step explanation:
The boys and girls soccer clubs are trying to raise money for new uniforms.
Answer: the answer you chose was correct x+y <1000
x=<75
Step-by-step explanation:
first they are selling 3 dollar and 4 doallar items to get above 1000 dollars
then they sayed at least 75 bags of hot chips so it has to be 75 or higher
The expression a^5/2 is equivalent to which
Answer:
[tex] a^\frac{5}{2} = \sqrt{a^5} = (\sqrt {a})^5 [/tex]
Step-by-step explanation:
A number raised to a fraction as an exponent means the number is raised to the numerator of the exponent, and then take the root shown by the denominator of the exponent.
For example, if the exponent is 2/3, raise the number to the 2nd power and take the third root.
Here is the definition:
[tex]a^{\frac{m}{n}} = \sqrt[n]{a^m} = (\sqrt[n]{a})^m[/tex]
[tex] a^\frac{5}{2} = \sqrt{a^5} = (\sqrt {a})^5 [/tex]
−9−(−12) as an addition expression
The value of 9−(−12) as an addition expression is 3.
What is a expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
In this case, the expression given is illustrated as:
-9 - (-12)
It's important to note that (-) × (-) = +
Therefore, -9 - (-12)
= - 9 + 12
= 3
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How many steel rods are in a staircase frame with 12 steps?
Casey has no less than 52 model toy cars in his collection.
Which graph represents the number of cars in the collection?
number line with open circle on point 52, shaded left
number line with closed circle on point 52, shaded left
number line with closed circle on point 52, shaded right
number line with open circle on point 52, shaded right please give right answer
Answer: The answer is b
Step-by-step explanation: Please give me thanks and 5 star
Have Great Day :)
Times for the three parts of a journey are 20 minutes 40 minutes 1 hour and 30 minutes work out the total time for the journey give your answer in hours
Total time for whole journey can be calculated by adding the three parts of the journey which would give answer as 2.5 hours.
What is a fraction?
The components of an entire or group of items are represented by fractions. A fraction consists of two components. The numerator is that the figure at the top of the line. It details the amount of equal portions that were taken from the total or collection. The denominator is that the figure that appears below the line.
Main Body:
total time = 20 minutes + 40 minutes + 1 hour 30 minutes
= 2.5 hours or 5/2 hours.
Hence total time for journey is 2.5 hours.
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10 Can this be simplified? If "yes", then
simplify it. If "no", then explain why.
a²/b^8
Answer:
No
Step-by-step explanation:
You can't simplify this equation any further because the bases (a, b) aren't the same.
For example:
You can simplify a^2/a^8 to be 1/a^6
Steps:
a^8=(a^2*a^6)
a^2/a^2*a^6
a^2 ÷ a^2=1
1/a^6
(You can only break the exponent up and divide the quotient if the base is the same!)
14 Which equation describes the nth term of the arithmetic sequence
7, 10, 13, 16, ...?
A a=3n + 4
B a₁ = 7+3n
C a = - 4n+ 3
D a₁ = 3n - 4
Answer:
I think it's B
Step-by-step explanation:
Because the pattern starts at 7 then plus 3 etc...
Use the diagram to find lengths. BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.
Suppose AC = 48 cm and QD = 51 cm. What is the length of QC?
pq
QC is
cm in length.
The length of segment QC, using the Pythagorean Theorem, is of:
QC = 45 cm.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the length of the hypotenuse is obtained according to the equation presented as follows
[tex]h^2 = l_1^2 + l_2^2[/tex]
The length of QC is obtained considering that QC is a leg of a right triangle in which:
BC is the other leg.QB is the hypotenuse.The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the segment's endpoints, thus the length of segment QB is given as follows:
QB = QD = 51 cm.
B is the midpoint of AC, hence the length of segment BC is given as follows:
BC = 0.5 x AC = 0.5 x 48 = 24 cm.
Hence the length of QC is obtained as follows:
QC² + 24² = 51²
QC = sqrt(51² - 24²)
QC = 45 cm.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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In triangle efg and triangle yxz, angle x and angle e are congruent to angle y. If angle e = 62 degrees and x = 80 degree, what is the measure of angle Z
The measure of the angle ∠Z is 38°.
We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are Y, X, and Z. The angle ∠F is congruent to the angle ∠X. The angle ∠E is congruent to the angle ∠Y. The measures of the angles ∠E and ∠X are 62° and 80°, respectively. We need to find the measure of the angle ∠Z. The measure of the angle ∠Y must be equal to the measure of the angle ∠E.
∠Y = ∠E = 62°
Now, in the triangle ΔYXZ, we will use the angle sum property. The sum of all the angles in a triangle is equal to 180°.
∠Y + ∠X + ∠Z = 180°
62° + 80° + ∠Z = 180°
∠Z = 180° - (62° + 80°) = 180° - 142° = 38°
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Piecewise function of the graph
A piecewise function of the graph is a function y=f(x) which has different definitions in different intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions.
What is a piecewise function?
A function with many parts of curves in its graph is said to be piecewise. It implies that based on the value of the input, it has many definitions. In other words, a piecewise function responds differently to various inputs.
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can anybody tell me how to solve the value of 6a+9a?
Answer:
15a
Step-by-step explanation:
6a+9a
We just add the coefficients together since they share the same variable
6+9=15
15a
Hopes this helps please mark brainliest
What is the graph for -1/2x+y=10
What is the measure of angle B in this triangle?
Enter your answer in the box.
Answer:
22 degrees
Step-by-step explanation:
Sum of all three angles of a triangle equal 180 degrees so we can add these angles and set it equal to 18” degrees to find x
x+16+120+x=180
2x+136=180
-136. -136
2x=44
/2. /2
x=22
So angle b is 22 degrees
Hopes this helps please mark brainliest
Why area of square is a2?.
By using diagonal properties of square, we can prove the area of triangle as a².
What is square?A square is a flat object in geometry that has four equal sides and four right angles (90°). An equilateral rectangle is a specific sort of square, while a parallelogram is a special kind of square (an equilateral and equiangular one).
Prove: Area of square = a²
Suppose, there is a square of side length a.
Let, d be the length of each diagonal. We know, both diagonals of square have equal length.
So, d^2 = a^2 + a^2 = 2 * (a^2)
Or, d = a * (√2).
Also, we know that diagonals of a square are perpendicular bisectors.
So, we can consider that the square as four isosceles right angled triangles.
Length of each perpendicular side of every isosceles right angled triangle = (1 / 2) * d = (d / 2).
So, area of each isosceles right angled triangle = (1 / 2) * (d / 2) * (d / 2) = {(d^2) / 8}
Area of the square = 4 * {(d^2) / 8} = {(d^2) / 2}.
Since, d = a * √2; so we put in the above formula, the area becomes equal to that of (a^2).
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b. Jada squared a number and got-4. Elena squared a different number and got-4. What were the numbers that Jada and
Elena squared?
Type the answers in the boxes below.
Answer: The answer is -2
Lora's phone records data for screen time each week. last week, she used 920 minutes. this week, lora used 690 screen time minutes on the phone. calculate the percent decrease in screen time this week. 25% 33% 40% 75%
The percentage decrease in Lora's screen time on phone is 25% this week.
Percentage related problems work around a certain reference value. This reference value is what the output percentage refers to when showing any growth or decay in the other value.
For this problem, last week's screen time is that reference value i.e. 920 minutes per week.
Now, current week's usage is 690 minutes per week. For calculating percentage decrease, we first find our the difference (in minutes).
[tex]Decrease=S_{1}- S_{2}=920-690=230[/tex]
Now, for its percentage we compare this value to our reference value i.e. last week's screen time. This will tell us about the decrease in screen time with reference to last week. This is what percentage does i.e. compares two sets of data.
[tex]Decrease=\frac{difference}{S_{1}}*100= \frac{230}{920}*100[/tex]
[tex]Decrease=25[/tex]%
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Answer:25
Step-by-step explanation:
One piece of statistical evidence used against ms. Gilbert was a low p-value for the pattern of death observed on her shifts. What does this p-value mean and what is the relevance of the p-value to the trial?.
The level of marginal significance inside a statistical hypothesis test, or P-value, represents the likelihood that a particular event will occur.
P-value;
The likelihood of getting a result that is equivalent to or more extreme than what was actually seen, under the null hypothesis, is what is meant by the term "P value." The probability (P) indicator indicates the likelihood that any observed variation between groups is the result of chance.
Here,
The statistical test's extremely low p-value indicates that the null hypothesis must be accepted, and the conclusion that Gilbert is guilty is based on the fact that Gilbert's existence is dependent on the shift deaths.
Relevance of p-value to the trial;
The p-value evaluates the agreement between the trial's actual outcomes and the "pure chance" explanation for them. When the only differences between groups A and C are the result of chance, a p-value of 0.002 favoring group A very extremely seldom occurs.
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what is 3/4 plus 6/10?
Answer:
Step-by-step explanation:
3/4 + 6/10
= 15/20 + 12/20
= 27/20
You have d dollars to buy fence to enclose a rectangular plot of land. the fence for the top and bottom costs $a per foot and for the sides it costs $b per foot. find the dimensions of the plot with the largest area. for this largest plot, how much money was used for the top and bottom , x, and for the sides, y?
You have d dollars to buy fence to enclose a rectangular plot of land. the fence for the top and bottom costs $a per foot and for the sides it costs $b per foot.
To find the dimensions of the plot with the largest area.
Total Money = D dollars
Total cost for top and bottom fence = $4(2x)
Total cost for sides fence = $8(2y)
Hence total cost of fencing = 4(2x)+8(2y) = 8x+16y
C = 8x+16y
Given cost (c) = D dollars
D = 8x+16y
Now Area of the plot A = xy
A = xy is optimizing function and D = 8x+16y
= [tex](\frac{D-16y}{8})=x[/tex]
A = [tex]\frac{D-16y}{8}y[/tex]
For A to be maximum [tex]\frac{dA}{dy}=0[/tex]
A = [tex]\frac{D}{8}y-\frac{16}{8}y^{2}[/tex]
[tex]\frac{dA}{dy} = \frac{D}{8}-\frac{16}{8}(2y)[/tex]
[tex]\frac{dA}{dy} = \frac{D}{8}-4y[/tex]
[tex]\frac{dA}{dy} = 0 = \frac{D}{8}-4y=0[/tex]
[tex]\frac{D}{8} = 4y = y = \frac{D}{32}[/tex]
Now [tex]\frac{d^{2}A }{dy^{2}} = -4 = -ve number[/tex]
for y = [tex]\frac{D}{32}[/tex] area is maximum
[tex]x = \frac{D-16y}{8} = \frac{D-16 (\frac{D}{32} )}{8} = \frac{D}{16}[/tex]
Say the top and bottom dimensions are = [tex]\frac{D}{16}[/tex]
Sides dimensions are = [tex]\frac{D}{32}[/tex]
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In a 30 60 90 triangle where the long side is equal to 4, what are the values of the hypotenuse and short side ?
For given 30 60 90 triangle, the values of the hypotenuse = 4 units and short side = 2 units
We know that, a 30 60 90 triangle is right triangle.
In right triangle the longest side is hypotenuse.
Here, hypotenuse = 4 units
The short side of triangle is the opposite to the side of smallest angle.
So, we need to find the length of the side opposite to angle 30.
Consider sin(30) = short side/hypotenuse
1/2 = short side/4
short side = 4/2
short side = 2 units
Therefore, for given 30 60 90 triangle, the values of the hypotenuse = 4 units and short side = 2 units
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Brad graphs the function y = |x-2|Cindy graphs the function y=-|x-2| How does Cindy's graph compare to Brad's graph?
O Cindy's graph is a reflection of Brad's graph across the x-axis.
O Cindy's graph is a reflection of Brad's graph across the y-axis.
O Cindy's graph is one unit to the right of Brad's graph.
O Cindy's graph is one unit to the left of Brad's graph.
Cindy's graph is a reflection of Brad's graph across the x - axis.
What is transformations of graph?
The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. In particular, the change of algebraic equations, it is a typical kind of algebraic problem.
Given:
Brad graphs the function y = |x-2|
Cindy graphs the function y=-|x-2|
If f(x) = |x - 2| and f(x) = - |x - 2|
Since, if the transformation of the graph is f(x) changes to -f(x) then there is reflection over x - axis.
Here y changes to -y.
Therefore, Cindy's graph is a reflection of Brad's graph across the x-axis.
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2x² + 3x - 14
Please helppp!