The value of d in the given angles using the concept of complementary angles is; d = 13
How to find complementary angles?Complementary angles are defined as angles that add up to 90 degrees.
Now, we are told that one angle measures 18°, and another angle measures (6d − 6)°. This tells us that;
(6d - 6) + 18 = 90
Expanding the bracket gives us;
6d - 6 + 18 = 90
6d + 12 = 90
6d = 90 - 12
6d = 78
Use division property of equality to divide both sides by 6 to get;
6d/6 = 78/6
d = 13
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What is the slope of this line? and can you provide me with the formula for the slope of the line too please?
Answer:
slope = 1/2
Step-by-step explanation:
The slope formula:
The slope of a line that passes through points [tex] (x_1, y_1) [/tex] and [tex] (x_2, y_2) [/tex] is
[tex] slope = m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
To find the slope, we find two easy-to-read points. Easy-to-read points are usually on grid line intersections.
Points (0, 0) and (2, 1) are on grid line intersections and are easy to read.
We will now input the information from our two points into the slope formula to calculate the slope.
[tex] slope = m = \dfrac{1 - 0}{2 - 0} = \dfrac{1}{2} [/tex]
Find the zeros of the function.
Enter the solutions from least to greatest.
f(x) = 8x² - 800
lesser x =
greater x =
The zeros of the function are -10 and +10
lesser x = -10
greater x = +10
What are zeros of a quadratic equation?The zeros of a quadratic equation are the points where the graph of the quadratic equation crosses the x-axis. . The zeros of quadratic equation will always have two values.
f(x) = 8x²- 800
f(x) = y
y = 8x²-800
when the graph crosses x axis the value of y = 0
therefore 0 = 8x²-800
divide both sides by 8
0 = x² - 00
x² = 100
x= √100
x= ±10
therefore lesser x = -10
greater 10 = +10
therefore the zeros of the quadratic equation f(x) = 8x²- 800 = +10 and -10
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Evaluate each of the following expressions given that: f ( x ) = √ x + 5 f(x)=x+5 g ( x ) = 3 x − 7 g(x)=3x-7 h ( x ) = 5x(x)=5x f ( g ( 5 ) ) = f(g(5))= Preview g ( f ( 78 ) ) = g(f(78))= Preview h ( g ( f ( 2 ) ) ) = h(g(f(2)))=
Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8. This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.
The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.
Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.
In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.
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A shipping container will be used to transport several 150-kilogram crates across the country by rail. The greatest weight that can bee loaded into the container is 26000 kilograms. Other shipments weighing 11300 kilograms have already been loaded into the container. Write an inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container
An inequality representing c, the total number of 150-kilogram crates that can be loaded into the shipping container: c ≤ 98
We know that an inequality is a mathematical statement that represents the inequalities between two algebraic expressions with two variables .
It is an unequal relation between two algebraic expressions.
Here, the greatest weight that can be loaded into the container = 26,000 kilograms
the weight of each crate = 150 kilogram
and the weight of other shipment = 11300 kilograms
Let c be the total number of 150-kilogram crates that can be loaded.
So, we get an inequality:
150 c + 11300 ≤ 26,000
150 c ≤ 26,000 - 11300
150 c ≤ 14700
c ≤ 98
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The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
Answer:
Step-by-step explanation:
a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525
b) Overestimate
Find the logarithmic function f(x) = log a (x-h) that describes the graph *image included*
The logarithmic function that describes the graph is given as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
How to define the logarithmic function?The parent logarithmic function is defined as follows:
f(x) = log(x).
Which, no matter the base, has the vertical asymptote given as follows:
x = 0.
The vertical asymptote of the graphed function is given as follows:
x = -1.
Hence:
[tex]f(x) = \log_a{(x + 1)}[/tex]
When x = 3, f(x) = 2, hence the base a is obtained as follows:
[tex]2 = \log_a{(4)}[/tex]
Meaning that:
a² = 4.
a = 2.
And the function is then defined as follows:
[tex]f(x) = \log_2{(x + 1)}[/tex]
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Need asap will give brainlist!
Answer:
10,37
Step-by-step explanation:
for EF= [tex]\sqrt{17^{2} -14^{2} } =10[/tex]
for D= we have 2 knowns which are 53 and 90, so we need to minus them from each other to get D. 90-53=37
Select the correct answer.
What is the y-intercept of function f?
(-3x - 2,
-∞ <
-x + 1,
-2 ≤ x ≤ 3
2x + 5,
3 ≤ x < 00
f(x)
=
OA. -1
OB. 5
O C. 1
OD. -2
< -2
Answer:
The correct answer is C. 1
(1/5 x 5)^5 this is the problem
The problem involving exponents (1/5 x 5)⁵ is calculated to get 1
How to solve the problem involving exponentsInformation made available in the question is an equation of the form
= (1/5 x 5)⁵
The math question is solved using the idea of PEMDAS which is an acronym for order of arrangement of mathematical operations as
the full meaning include
P - parenthesis
E - exponents
M - multiplication
D - division
A - addition
S - subtraction
applying the sequence the problem is solved using parenthesis first
= (1/5 x 5)⁵
= (1)⁵
Then exponents
= (1)⁵
= 1 * 1 * 1 * 1 * 1
= 1
The solution is 1
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PLSSS HELP TURLY KNOW THISSS
Answer:
[tex] \sf \: x = 5[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 15 - x = 10
Then the value of x will be,
→ 15 - x = 10
→ -x = 10 - 15
→ -x = -5
→ [ x = 5 ]
Hence, the value of x is 5.
the maked pieceof a t shirt is 220. a discount of 20% is announced on sales. then the selling price is
In this case, the marked price of 220 is the cost price and discount of 20% is announced on sales, so the selling price is 176.
How is this determined?The t-shirt costs $166.5 to purchase. To do this, multiply the listed price (220) by the discount rate (20%) stated as a decimal. This will give you the amount of the discount (0.20).
220*0.20 =44
The selling price is then determined by deducting the discount (44) from the marked price (220):
220-44 =176
Before applying any markups or reductions, the retailer paid the item's cost price, commonly referred to as the wholesale price. The price a consumer pays to purchase an item is known as the selling price. The selling price will be less than the advertised price if a discount is being offered, and the difference between the two represents the discount.
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Three years ago,a father was three times as old as his so.in five years time,the father will be twice as old as his son,what will be the sum of their ages in four years
let f = father's present age, let s = son's
:
write an equation for each statement, simplify
:
Three years ago a father was thrice as old as his son
f - 3 = 3(s-3)
f - 3 = 3s - 9
f = 3s - 9 + 3
f = 3s - 6
in 5 years time the father will be twice as his son
f + 5 = 2(s+5)
f + 5 = 2s + 10
f = 2s + 10 - 5
f = 2s + 5
replace f with 3s - 6, from the 1st statement
3s - 6 = 2s + 5
3s - 2s = 5 + 6
s = 11 yrs is the son's age
find the fathers age
f = 3(11) - 6
f = 33 - 6
f = 27 yrs is the father's age
:
what will be the sum of their age in four years
27+4 + 11+4 = 46
7. Calculate the selling price of a sound system costing R499 if it is sold at a loss of 45%. 8. The price of milk increased by 8%. If the original price is R10,84, what is the new price? 9. A cell phone costing R747 was advertised at a reduced price of R599. Calculate the percentage discount being offered.
10. Mandisa planned to spend RI 000 for shoes this week. On Monday she spent R228,95 and on Thursdays she spent R573,38 on shoes. How much money does she have left for the week?
II. Kate's food budget for the month is R700. The first week she spent R189,75, the second week she spent R203,20 and the third week she spent R146,95. How much does she have left for the last week?
The answers to all parts are shown below.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
7. CP of sound system = 499
loss= 45%
So, the selling price = 499 - 45% of 499
= R 274.45
8. original price is =1084
The new price = 1084 + 8% of 1084
= R 1,170.72
9. Percentage decreased
= ( 747 - 599) / 747 x 100
= 19.81%
10. Mandisa left with
= 1000 - (228.95 + 573.38)
= R 197.67
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Mia and her children went into a bakery that sells cupcakes for $2.50 each and donuts for $1.25 each. Mia has $30 to spend and must buy no less than 14 cupcakes and donuts altogether. If � x represents the number of cupcakes purchased and � y represents the number of donuts purchased, write and solve a system of inequalities graphically
Answer:
2.50x + 1.25y ≤ 30
x + y ≥ 14
x ≤ 10 and y ≤ 24
Step-by-step explanation:
we can by elimination if we multiply the second inequality by -2.5, we get:
-2.50x - 2.5y ≥ -35
if we add the first inequality to the above we get:
2.50x + 1.25y ≤ 30
+ -2.50x - 2.5y ≥ -35
-1.25y = -5
divide each side by -1.25 to get:
y = 4
therefore, x = 10
if you graph each system you must look for the area where the shading of each inequality overlaps
upon graphing, the solution is x ≥ 10 and y ≤ 24
Rewrite the ff. Quadratic Formula from General Form to Vertex Form or vice versa.
1. y=x²+6x+14
2. y=2x²+8x+12
3. y=3(x+3)²-7
4. y=(x+2)²+4
Answer:
1. y= (x-3)^2+5 vertex form
2. y= 2(x+2)^2+4 vertex form
3. y= 3x^2+18x+20 general form
4. y= x^2+4x+8 general form
A helicopter is descending from an altitude of 1,500 feet. The helicopter descends at a constant rate of 280 feet per minute. Which function can be used to determine H, the height of the helicopter above the ground after m, minutes? A H=280m+1,500H=280m+1,500H=280m+1,500 B H=1,500−280mH=1,500-280mH=1,500−280m C H=1,500m+280H=1,500m+280H=1,500m+280 D H=280m−1,500H=280m-1,500H=280m−1,500
The function that can be used to get the height of the helicopter above the ground is: H=280m−1,500
What is a function in mathematics?A function is a statement, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable).
How to solve for the function
The value 280 is the constant rate that the helicopter is said to be descending.
The altitude from which it is coming down is given as 1500 feet
The function would be written as H=280m−1,500
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What is the relationship between 30 hours and 15 hours complete this statement.
the number of hours spent using electronic devices is ? times the number of hours spent playing sports.
The relation between the number of hours spent using electronic devices is 2 times the number of hours spent playing sports.
The term called relation is defined as the relationship between sets of values of ordered pairs and the set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
Here we have know that the number of hours spent using electronic devices is 30 and the number of hours spent playing sports 15.
As per the definition of relation, in order to find the relation we need to do the division operation on then we get,
=> 30/15
=> 2
Which means that the first one is 2 times of the second one.
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A class plants a tree. sketch the graph of the height of the tree overtime.
a. Identify the two variables.
b. How can you describe the relationship between the two variables?
c. Sketch the graph.
I will give brainiest for full answer!
Answer:
a) The two variables are the number of years and the height of the tree in feet
b) It is a positive linear relationship.
c) Put a point at (0,3) and one at (3,7), and connect the dots.
HURRY PLEASE!!! What are the marginal
column totals?
The marginal column total for the given data is option D: 39; 16.
What is marginal total?
A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.
The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.
The number of men who prefer to eat fish = 11
The number of women who prefer to eat fish = 6
The number of men who prefer to eat red meat = 28
The number of women who prefer to eat red meat = 10
So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -
11 + 28 = 39
The marginal column total for the number of women who prefer to eat fish and red meat collectively is -
6 + 10 = 16
Therefore, the marginal total is 39, 16.
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Find the 14th term of the arithmetic sequence whose common difference is d = 8 and whoose first term is a1=5
The 14th term of the arithmetic sequence is 109 whose common difference is d = 8 and whose first term is a(1)=5.
The value of 14th term of an AP is 109.
In the given question
The common difference = 8
The value of first term=5
And we have to find the value of 14th term of Arithmetic progression
We utilize the method for locating the nth term to locate a specific term in an arithmetic series. An arithmetic sequence's nth term is determined by an = a + (n - 1)d in step 1.
Putting the given value in formula:
an = a + (n - 1)d
a 14th=5+(14-1)8
a 14th=5+13*8
a 14th=5+104
a 14th=109
So the value of 14th term of an AP is 109.
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Calculate the theoretical mass of precipitate produced if calcium chloride solution was reacted with excess sodium bicarbonate
If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.
The theoretical mass of precipitate produced in a reaction between calcium chloride and sodium bicarbonate can be calculated by using the balanced chemical equation for the reaction. The balanced equation for this reaction is given as follows:
CaCl₂ + NaHCO₃ → CaCO₃ + NaCl + H₂O
In this reaction, one mole of calcium chloride reacts with one mole of sodium bicarbonate to produce one mole of calcium carbonate precipitate, one mole of sodium chloride solution, and one mole of water.
The mass of the precipitate can be calculated by multiplying the molar mass of calcium carbonate by the number of moles of calcium carbonate produced.
So, to calculate the theoretical mass of precipitate produced, you need to know the amount (in moles) of calcium chloride and sodium bicarbonate used in the reaction. If the reaction was done with excess sodium bicarbonate, the amount of calcium chloride would determine the amount of precipitate produced.
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find the number in which when subtracted from both 17 and 12 , the product will be 1.04 (qudratic equation)
The required number in which when subtracted from both 17 and 12 , the product will be 1.04 is x = 11.8 or 17.2.
What is quadratic equation?ax^2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.
According to question:
Let the number is x, then
(17 - x)(12 - x) = 1.04
204 - 17x - 12x + x² = 1.04
x² - 29x + 204 = 1.04
x² - 29x + 202.96 = 0
On solving for x, we get
x = 11.8 or 17.2
Thus, the number can be x = 11.8 or 17.2.
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The needed value is either x = 11.8 or 17.2, which when deducted from both 17 and 12 will result in a product of 1.04.
What is a quadratic equation?A quadratic equation, or a second-order polynomial equation in a single variable, is defined as ax2 + bx + c = 0. a 0. Due to the fact that it is a second-order polynomial equation, which is ensured by the algebraic basic theorem, it must have at least one solutionIf the number is x, then(17 - x)(12 - x) = 1.04204 - 17x - 12x + x² = 1.04x² - 29x + 204 = 1.04x² - 29x + 202.96 = 0We obtain x by solving for it.x = 11.8 or 17.2Thus, the value of the number can be either x = 11.8 or x = 17.2.
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Which list orders the decimal numbers 1.47, 4.01, 1.4, and 4.1 from least to greatest?
Answer:
Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.
Least to greatest is 1.4, 1.47, 4.01, and 4.1
21•15 equals
(20+1)•15
The value of 21•15 equals (20+1)•15. This is true.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of 21•15 will be:
= 21 × 15
= 315
Also (20+1)•15 will be:
= 21 × 15
= 315
Therefore, they're equal.
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Complete question
The value of 21•15 equals (20+1)•15. True or false?
Make x the subject of m=n+x/p
Answer:
x = p(m-n)
Step-by-step explanation:
we can eliminate the 'p' in the denominator by multiplying each side of the equation by 'p' to get:
mp = np + x
now we can subtract 'np' from each side to get:
mp - np = x
we can further simplify it as:
p(m-n) = x
Answer:
X=n-p×m
Step-by-step explanation:
m=n-x/p
p×m=n-x
n-p×m=n+x-n
X=n-p×m
Find an equation of the plane through the point and perpendicular to the given line. (-2, 9, 10) x = 5 + t, y = 3t, z = 4 - 3t
Let A be the point (-2, 9, 10) and n be the normal vector of the plane. The direction vector of the line is <1, 3, -3>, and since the plane is perpendicular to the line, n is orthogonal to the direction vector.
So, n is a vector that satisfies:
n . <1, 3, -3> = 0
The equation of the plane can be written in the form:
n . (x - A) = 0
Where x = (x, y, z) is any point in the plane.
We can find n by taking the cross product of two non-parallel vectors in the plane, such as <1, 0, 0> and <0, 1, 0>. Then,
n = (1, 0, 0) x (0, 1, 0) = (0, 0, 1)
Substituting the values of A and n into the equation of the plane, we get:
0 . (x - (-2, 9, 10)) = 0
0 . (x + 2, y - 9, z - 10) = 0
z - 10 = 0
z = 10
So the equation of the plane is:
z = 10
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Determine which of the lines, if any, are parallel or perpendicular.
The line a and line c are perpendicular to each other.
How to find parallel and perpendicular lines?Lines are known if they are parallel or perpendicular by there slopes.
Therefore, parallel lines have the same slopes and perpendicular have slopes that are negative reciprocals of one another.
The slope of a line is the change in the dependent variable to the change in the independent variable.
Therefore, let's find the slopes of each line.
line a:
slope = -3 - 1 / 6- 0 = - 4 / 6 = - 2 / 3
line b:
slope = -2 - 0 / 3 + 3 = - 2 / 6 = - 1 / 3
line c:
slope = 7 + 2 / 2 + 4 = 9 / 6 = 3 / 2
Therefore, line a and c are perpendicular
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Please Help Me AND HURRY!
Is \sqrt{5}+\sqrt{16} A Rational Or Irrational Number
The number √5 + √16 is an irrational number
How to determine the solution to the expressionFrom the question, we have the following parameters that can be used in our computation:
\sqrt{5}+\sqrt{16}
Express properly
So, we have the following representation
√5 + √16
Take the square root of 16
This gives
√5 + 4
Rewrite as
4 + √5
The above expression is an irrational number
This is so because of the radical symbol on 5
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Need help for math k12
Answer:
9y^8
Step-by-step explanation:
15/5 = 3
y^6 / y^2 = y^4
so you are looking at basically (3y^4)² = 3y^4 * 3y^4 = 9y^8
Carlos solved the equation below incorrectly.
13(12x−9)=12(x+18) 16x−3=12x+9 14x−3=9 14x=12 x=48
Identify Carlos' error and then solve the equation correctly. (3 points)
Enter your answer and your work or explanation in the space provided.
Answer: Please see explanation column for answer.
x= -36
Step-by-step explanation:
Step 1
from the attachment, Carlo solving is given as
1/3 (1/2x- 9) = 1/2 (x+18)
1/6x-3= 1/2x+9
1/4x-3=9
1/4x=12
x=48
Carlos error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.
Solving correctly, we have that
1/3(1/2x-9) = 1/2(x+18)
1/6x -3= 1/2x+ 9
taking like terms to like terms
1/6x-1/2x= 9+3
(1-3)/6x= 12
-2/6x= 12
-1/3x= 12
multiplying both sides by -3
-1/3x X -3 = 12 X -3
x= -36