Evaluate the following without using the calculator
[tex] \cos(30) \sin( \frac{\pi}{4} ) + \frac{ \sec(60) }{3} [/tex]
Answers
[tex]\sec x=\dfrac{1}{\cos x}\to \sec60^o=\dfrac{1}{\cos60^o}\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=\dfrac{\sqrt3}{2}\\\\\sin\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\\cos60^o=\dfrac{1}{2}\to\sec60^o=\dfrac{1}{\frac{1}{2}}=2\\\\\text{Substitute:}\\\\\cos30^o\sin\dfrac{\pi}{4}+\dfrac{\sec60^o}{3}=\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}+\dfrac{2}{3}=\dfrac{\sqrt6}{4}+\dfrac{2}{3}\\\\=\dfrac{3\sqrt6}{3\cdot4}+\dfrac{4\cdot2}{4\cdot3}=\dfrac{3\sqrt6}{12}+\dfrac{8}{12}\\\\=\boxed{\dfrac{8+3\sqrt6}{12}}[/tex]
![Evaluate The Following Without Using The Calculator[tex] \cos(30) \sin( \frac{\pi}{4} ) + \frac{ \sec(60)](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/5Umt9TNkw0E9enog300m6pikoODJegOy.png)
Related Questions
State weather ADB~CDB, and if so , explain how you know
Answers
Answer:
SAS
Step-by-step explanation:
AD = DC Given
<ADB = <CDB Givien
BD = BD Reflexive property.
The angle is between the 2 sides. The triangles are congruent by SAS.
Eli's office recycled a total of 12 kilograms of paper over 6 weeks. After 9 weeks, how many kilograms of paper will Eli's office have recycled
Answers
Answer:
18 kg
Step-by-step explanation:
Recycling rate = 12 kg/6wk
Recycled = 9 × 12/6
Recycled = 9 × 2
Recycled = 18 kg
Bill has a swiming pool that holds 7,500,00 milliliters of water he needs to have his pool treated and the company he hired wants to know how many liters his pool has how can bill solve this
Answers
Answer:
If it was 750,000 liters it would be 750 liters
Step-by-step explanation:
Bill can solve this by first thinking that 1 liter is 1,000 milliliters. Then 1,000 times 750 equals 750,000. Then he would do 750 times 1 and get 750. Bill would then realize that 750,000 milliliters is equal to 750 liters
a number m plus 4 is greater than or equal to 7
Answers
[tex]m + 4 \geqslant 7 \\ m \geqslant 3[/tex]
the point on the graph where the line crosses the y-axis is what part of a line??
Answers
The point where the line crosses the x-axis is called the [x-intercept]. The [y-intercept] is the point where the line crosses the y-axis.
Y-intercept.
What is the cartesian plane?By calculating the separations between two perpendicular lines that pass through a fixed point in Cartesian coordinates, we may find the location of a point P. Assume that O is the fixed point known as the origin and that XOX' and YOY' are the two perpendicular lines that pass through O and are referred to as the Cartesian or Rectangular co-ordinate axes.
given, the graph crosses the y-axis A point having an x-value and a y-value, is a coordinate: (x, y). The origin is the place where the two number lines converge, and it has the following coordinates: (0, 0). The x-value is zero when the graph of a function crosses the y-axis at a value b. As a result, the point is the y-intercept (0, b).
Therefore, A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
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Write the fact family for 1 , 5 , and 5 ?
Answers
5÷5=1
this is the fact family hope it helps
An item is regularly priced at 75 $ . It is on sale for 60% off the regular price. How much (in dollars) is discounted from the regular price?
Answers
Answer: $45.00
Step-by-step explanation:
75 x 0.60 = 45
Answer:
$30
Step-by-step explanation:
First, change the percentage into decimal:
60% = 60/100 = 0.6
Multiply 75 with 0.6:
75 * 0.6 = 45
Note that this number 45 (0.6 of 75) is the amount off from the original price (75). Subtract 45 from 75
75 - 45 = 30
$30 is your answer
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Please help me out with this problem
Answers
Answer:
First picture:
1)Given
2)Substitution
3) Subtraction Property of Equality
4)if altenate interior angles are equal, then the lines are parallel
Second picture:
1) Given
2)if lines are parallel, then the corresponding angles are equal
3)Substitution
4)if altenate interior angles are equal, then the lines are parallel
Please do this 24th prblm......
Answers
Answer:
6x^2 - 4y^2 + 2x^2 + 6xy
Step-by-step explanation:
Each of the adjacent sides of the rectangle has a congruent, opposite sides. The perimeter is the sum of the lengths of the 4 sides.
P = 2(3x^2 - 2y^2) + 2(x^2 + 3xy)
P = 6x^2 - 4y^2 + 2x^2 + 6xy
24.
The perimeter of a rectangle l × w is P = 2l + 2w.
We have l = 3x² - 2y² and w = x² + 3xy. Substitute:
P = 2(3x² - 2y²) + 2(x² + 3xy) use distributive property
P = (2)(3x²) + (2)(-2y²) + (2)(x²) + (2)(3xy)
P = 6x² - 4y² + 2x² + 6xy combine like terms
P = 8x² + 6xy - 4y²round .1287 to the nearest thousandth
Answers
To round 0.1287 to the nearest thousandth, we look at the next place value which here is 7. Since 7 is more than 5, we round up the thousandth place. Hence, 0.1287 becomes 0.129.
Explanation:To round the number 0.1287 to the nearest thousandth, you need to look at the ten-thousandth place (which is the fourth numeral after the decimal point). In this number, the ten-thousandth place is 7. If this digit is 5 or above, we need to round up. If it is less than 5, we stay with the number as is. Since 7 is bigger than 5, we round up. Therefore, 0.1287 rounded to the nearest thousandth is 0.129.
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How do you write y=4x^2 -64x -265 in vertex form
Answers
Answer:
4(x-8)^2 -521
Suppose you deposit $1500 in a savings account that pays interest at an annual rate of
6%. No money is added or withdrawn from the account How many years will it take for the account to contain 2500?
Answers
Explanation
2,500×6%=150
1500÷150=10
Can sum one help me this is my last question
Answers
Answer:
Option B is correct.
the value of discriminant is, -7
Step-by-step explanation:
Given the equation: [tex]x^2 + x +2 = 0[/tex]
To find the value of discriminant [tex]b^2-4ac[/tex]
A quadratic equation is of the form [tex]ax^2+bx+c = 0[/tex] where a, b and c are coefficient of the equation.
On comparing with given equation we have;
a = 1 , b = 1 and c = 2
then;
Discriminant = [tex]b^2-4ac =(1)^2 -4(1)(2) =1 -8 = -7[/tex]
Therefore, the value of discriminant is, -7
PLEASE HELP! I also need an in depth explanation, not just the answer. I want to understand how to do these types of problems. How do you know which side to shade? How do you know how to graph inequalities? Thank you! Will reward the most helpful to be the brainliest!
Answers
Answer:
The correct answer option is C. y<= -4x + 25.
Step-by-step explanation:
Firstly, we will find out the equation of the line with the help of using two points (0, 25) and (-6, 49).
The slope (m) = [tex]\frac{49-25}{-6-0} =-4[/tex].
We know the standard form of the equation is [tex]y=mx+c[/tex] so the y-intercept (c) can be found by putting in the values of the slope and the coordinates of a point.
[tex]25=-4(0)+c\\\\c=25[/tex]
Therefore, the equation of the line is y = -4x + 25.
Now since the inequality is dealing with the value of y and we know that the values of y go vertically (up and down). So if we look at the graph, the shaded area includes the smaller values of y and the line is a solid one.
Therefore, the inequality will be y<= -4x + 25.
If you don't understand it this way, you can pick up a point and test the inequality.
Taking the easiest point (0, 0) to check.
0 <= -4 (0) + 25
0 <= 25 --- True
Drag and drop numbers into the boxes so that the paired values are in a proportional relationship.
x 2 4 [A] 7 9
y 1 2 3 3.5 [B]
Options: 3 / 3.5 / 4.5 / 5 / 6
Answer Examlpe:
A= 6 and B= 3.5
Answers
Answer:
A=6 and B=4.5
Step-by-step explanation:
You are given table
[tex]\begin{array}{cccccc}x&2&4&[A]&7&9\\y&1&2&3&3.5&[B]\end{array}[/tex]
If the paired values are in a proportional relationship, then
[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{[A]}{3}=\dfrac{7}{3.5}=\dfrac{9}{[B]}.[/tex]
Note that
[tex]\dfrac{2}{1}=\dfrac{4}{2}=\dfrac{7}{3.5}=2,[/tex]
then
[tex]\dfrac{[A]}{3}=2\Rightarrow [A]=6,\\ \\\dfrac{9}{[B]}=2\Rightarrow [B]=\dfrac{9}{2}=4.5.[/tex]
Answer:
the answer is 6
Step-by-step explanation: im 100% right this guy is wrong i repeat this guy is wrong!
state the gradient of the line y= 5-5x
Answers
The gradient of the line y= 5-5x is -5 which is the coefficient of 'x'. This connotes a negative slope, meaning the line descends as we move along the positive x-axis.
Explanation:The equation y = 5 - 5x represents a straight line in the xy-plane. The coefficient of 'x' in the equation represents the slope of the line. Therefore, the gradient of the line is -5. This means for every unit increase in x, y will decrease by 5 units. This negative slope suggests that the line moves downwards as the x-value increases, similar to our reference figure A1 where the slope caused a rise or fall on the vertical axis for every increase of 1 on the horizontal axis.
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Use the drop-down menus to complete each equation so the statement about its solution is true?
Answers
5 - 4 + 7x + 1 = 7x + (5 - 4 + 1) = 7x + 2
NO SOLUTIONS:
5 - 4 + 7x + 1 = 7x + a (a - any real number, except 2)
ONE SOLUTION:
5 - 4 + 7x + 1 = bx + c (b - any real number, except 7, c - any real number)
INFINITELY MANY SOLUTIONS:
5 - 4 + 7x + 1 = 7x + 2
Examples:
2x + 3 = 2x + 5 subtract 2x from both sides
3 = 5 FALSE (NO SOLUTIONS)
2x + 3 = x - 4 subtract x from both sides
x + 3 = -4 subtract 3 from both sides
x = -7 (ONE SOLUTION)
2x + 3 = 2x + 3 subtract 2x from both sides
3 = 3 TRUE (INFINITELY MANY SOLUTIONS)
1) For No Solution
5 - 4 + 7x +1 = 7x
2) For One Solution
5- 4 +7x + 1 = 3
3) For No Solution
5 - 4 + 7x + 1 = 7x + 2
What is 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. LHS = RHS is a common mathematical formula.
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:
1) For No Solution
5 - 4 + 7x +1 = 7x
2) For One Solution
5- 4 +7x + 1 = 3
3) For No Solution
5 - 4 + 7x + 1 = 7x + 2
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At the depth of x metres the temperature of the water in an ocean is T degrees celsius at depths below 900 metres T is inversely proportional to x. T is given by T= 4500/x work out the difference in temperature of the water at a depth of 1200 metres and the temperature of the water at a depth of 3750 metres
Answers
Answer:
The difference in temperature between a depth of 1200 meters and 3750 meters is 2.55
Step-by-step explanation:
The temperature T of the water in an ocean at depth X below 900 meters is given by:
T= 4500/X
To calculate the difference between a depth of 1200 meters and 3750 meters, it is necessary to calculate the temperature individually.
first, 1200 meters and 3750 meters are below 900 meters, so the equation describe before is applicable.
As a result, for 1200 meters, the temperature (symbolized as T1) is given by:
T1=4500/X
T1=4500/1200
T1=3.75
For 900 meters, the temperature (simbolized as T2) is given by:
T2=4500/X
T2=4500/3750
T2=1.2
The difference between the temperature T1 and T2 is:
Difference in temperature = T1 - T2
Difference in temperature = 3.75 - 1.2
Difference in temperature = 2.55
So, the difference in temperature between a depth of 1200 meters and 3750 meters is 2.55
Abigail Eddy purchased 200 shares of stock at $11.58 per share. Her online stock-broker charged her $12.50 commission. What is the total amount that she paid for the stock? Show work.
A) 1,547.20
B) 2,328.50
C) 2,154.54
D) 2,316.00
Answers
Answer:
B) 2328.50
Step-by-step explanation:
We are given 200 shares at $11.58 per share. By multiplying the number 200 with each share value will get the cost of all shares.
Total shares = 200
Cost per share = $11.58
Cost of 200 shares: Total shares * cost per share
= 200 * 11.58 = 2316
Commission charged = $12.50
Total amount: Cost of 200 shares + Commission charged
= 2316 + 12.50
Total amount = 2328.50
find the nonpermissible for a in this expression a^2/2a+6
Answers
Answer:
The value not permissible for a is -3.
Step-by-step explanation:
Considering real numbers, the expression is undefined for any value a for which the denominator expression is zero.
[tex]\frac{a^2}{2a+6}, \,\,\,2a+6\neq 0\implies a\neq -3[/tex]
The expression is valid for all real numbers, except -3.
Answer:
a≠-3
Step-by-step explanation:
We cannot divide by zero, so the denominator cannot be zero
2a+6≠ 0
Subtract 6 from each side
2a+6-6≠ 0-6
2a ≠-6
Divide each side by 2
2a/2 ≠-6/2
a≠-3
Which number is NOT in the solution set of the inequality x > −15?
A) 10
B) −5
C) −10
D) −20
Answers
Answer: D).-20
Step-by-step explanation:
Answer:
-20
Step-by-step explanation:
Mr. Moore needs to share 4 ounces of red among 5 art student's. How much red paint will each student receive?
Answers
Answer:
0.8 ounces each student
Step-by-step explanation:
You divide 4 by 5 and get your response.
Answer:
.8 ounces (could be written 4/5)
Step-by-step explanation:
5 students, 4 ounces. divide ounces by students, so 4/5
Collins middle school has 280 sixth grader students. if the sixth grade is 40% if the total school, how many students are in the middle school?
Answers
Answer:
700
Step-by-step explanation:
280 / 0.40 = 700
Answer:
280 *0.40 +96 STUDENTS
or
280/100 = x/40 cross multiply
9600=100x divide by 100
x=96
Step-by-step explanation:
which of the following options best describes the function graphed below
Answers
Answer:
Option B.
Step-by-step explanation:
The given graph is of a line which is parallel to the x axis.
Let the equation of the line is y = mx + c
where m is the slope and c is a constant representing y - intercept.
Since the graphed line is parallel to x = 0
So for the values of x = 0 equation of the line will be
y = c (constant)
Therefore, Option B. Linear constant is the answer.
Jake is riding an escalator. After riding for 3 seconds, he was 25 inches above the ground. A. How many inches is Jake rising per second? B. At the rate Jake is rising, how many inches above the ground will he be after riding the escalator for 15 seconds? Justify your answer. C. The top of the escalator is 30 feet, or 360 inches, above the ground. Will Jake have reached the top 45 seconds after first getting on the escalator? Why or why not?
Answers
then to find out how far he is moving for 15 seconds multiply 8.333 x 15= 125
8.333x= 360
divide 360 by 8.33 which equals 43.2
and the answer to "C" is yes because it took 43.2 sevonds
Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.
What is the unit rate?Unit rate is the ratio of two different units, with denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc. Arithmetic is probably the most basic and ancient branch of mathematics and is quite commonly used in our day-to-day life.
Given here: Jake reaches 25 inches above the ground in 3 seconds.
The unit rate of Jake's ascend is = 25/3
=8.33 inches/second
If Jake rides the escalator for 15 seconds then we would climb
=8.33×15
=124.95 inches
After 45 seconds Jake would have climbed =45×8.33
=374.85 inches
Thus after 45 seconds Jake reaches the top of the escalator.
Hence, Jake reaches the top of the escalator because he exceeds the height of the escalator if he travels at the rate of 8.33 inches/second.
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A road construction crew paves 1/5 mile every day. How much would they pave in 2 days?
Answers
Answer: 0.4 miles
Step-by-step explanation:
You can use the equation y=1/5x to help you figure it out where x is the days and y is the length. y=1/5(2). y=2/5 or 0.4 miles. Please vote my answer as brainliest
The road construction crew would pave 2/5 of a mile in 2 days, as they pave 1/5 mile every day.
Explanation:The road construction crew paves 1/5 mile each day. If they were to work for 2 days, to find out how much they would pave, you would simply multiply the pace per day by the number of days. So, 1/5 mile * 2 days = 2/5 miles. Therefore, the crew would pave 2/5 of a mile in 2 days.
To find out how much the road construction crew would pave in 2 days, we need to multiply the amount they pave in 1 day by 2. So, if they pave 1/5 mile every day, they would pave 1/5 * 2 = 2/5 mile in 2 days.
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Please help!! What is the value of -(-2)^3
Answers
-(-2)^3=-(-8)=8. So the answer is 8. or the fourth answer choice.
I need help, I don't understand this question.
what is f(-3) if f(x)=|2x+1|+5
Answers
Answer:
f(-3) =10
Step-by-step explanation:
When given a function f(-3), they want you to substitute x=-3 into the function f(x) and solve
f(x) =|2x+1|+5
Let x=-3
f(-3) =|2 *-3+1|+5
f(-3)=|-6+1|+5
f(-3)=|-5|+5
The absolute value of -5 is positive 5 (absolute values means always positive).
f(-3)=5+5
f(-3) =10
write the pair of fractions as a part of fractions with a common denominator 1/4 and 2/3
Answers
Answer:
[tex]\frac{3}{12} and \frac{8}{12}[/tex] are the fractions with common denominator
Step-by-step explanation:
fractions are 1/4 and 2/3
[tex]\frac{1}{4} and \frac{2}{3}[/tex]
To get common denominator we take LCD
LCD of 4 and 3 is 12
To get 12 in the denominator we multiply first fraction by 3 and second fraction by 4
[tex]\frac{1*3}{4*3} and \frac{2*4}{3*4}[/tex]
[tex]\frac{3}{12} and \frac{8}{12}[/tex]
You can buy 3 apples at the Quick Market for $1.29.You can buy 5 of the same apples from the Stop and Save for $2.50.Which place is the better buy?
Answers
Answer: Quick market
Step-by-step explanation:
At quick market each apple is .43 each
At Stop and Save they are .50 each