The area A of a triangle with base b and height h is given by A = = bh. Find the area when b = 18 m (meters) and h = 30 m.
The area is m?
Answers
Answer:
\(Area = 270m^2\)
Step-by-step explanation:
Given
\(A = \frac{1}{2}bh\)
\(b = 18m\)
\(h = 30m\)
Required
Solve for A
Simply substitute 18 for b and 30 for h
\(A = \frac{1}{2}bh\)
\(A = \frac{1}{2} * 18 * 30\)
\(A = 270\)
Hence:
The area is
\(Area = 270m^2\)
Related Questions
Use SSS to explain why the triangles in each pair are congruent.
Answers
The order in which the sides are listed does not matter for the SSS criterion. As long as the three sides of one triangle have the same lengths as the three sides of another triangle, the triangles are congruent.
SSS stands for Side-Side-Side, which is a congruence criterion in geometry. It states that if the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
To explain why the triangles in each pair are congruent using SSS:
Pair 1:
Triangle ABC and Triangle DEF are congruent because they have the same lengths for all three sides.
AB = DE
BC = EF
AC = DF
Pair 2:
Triangle PQR and Triangle STU are congruent because they have the same lengths for all three sides.
PQ = ST
QR = TU
PR = SU
The order in which the sides are listed does not matter for the SSS criterion. As long as the three sides of one triangle have the same lengths as the three sides of another triangle, the triangles are congruent.
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HELP NEEDED! Thanks if you do!!
Answers
Answer:
We conclude that:
csc (U) = 26 / 24
Step-by-step explanation:
Given
The angle ∠U The opposite of the angle ∠U = 24The hypotenuse = 26To determine
csc (U) = ?
Using the trigonometric ration
sin Ф = opposite / hypotenuse
substituting Ф = U, opposite = 24, hypotenuse = 26
sin (U) = 24/26
We know that: csc (U) = [1 ] / [sin(U)]
Therefore,
csc (U) = [1 ] / [sin(U)]
= 26 / 24
Therefore, we conclude that:
csc (U) = 26 / 24
Solve the given initial-value problem.
y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) =
1
2
, y'(0) =
5
2
, y''(0) = −
11
2
the values for the first 3 derivatives derivatives of y are 1/2, 5/2, -11/2 respectively
Answers
The given differential equation:
y''' − 2y'' + y' = 2 − 24ex + 40e5x,
y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2
Therefore, the next solution is 13/2
Differential Equation:
In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.
Now,
Given differential equation is
y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ ------------ (1)
Auxiliary equation is m³ - 2m² +2m = 0
Now,
m(m² - 2m +2) = 0
⇒ m(m-1)² = 0
Therefore, m = 0,1,1
Therefore,
\(y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}\)
Now, we have to find the particular solution by method of undetermined coefficient.
\(y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}\)
⇒ \(y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}\)
⇒ \(y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}\)
⇒ \(y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}\)
Putting these values in differential equation (1), we get:
y'''(0) = 13/2
Complete Question:
Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2
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if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
a coffee shop sells coffee beans by the pound. A container hold 16 kilograms of coffee beans. For every 1 kilogram, there are approximately 2.2 pounds
Answers
Answer:
23.6
Step-by-step explanation:
Answer: 23.6
Step-by-step explanation:
What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3? Please show step by step solution,
Answers
Answer:
The equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We have the point (-6,8) and a slope of -5/3.
Step 1: Use the point-slope formula to find the equation of the line in point-slope form.
y - y1 = m(x - x1)
where x1 and y1 are the coordinates of the given point.
y - 8 = (-5/3)(x - (-6))
Simplify this equation:
y - 8 = (-5/3)(x + 6)
Step 2: Convert the equation to slope-intercept form.
Distribute (-5/3) to get:
y - 8 = (-5/3)x - 10
Add 8 to both sides:
y = (-5/3)x - 2
This is the equation of the line in slope-intercept form. Therefore, the equation of the line that passes through the point (-6,8) and has a slope of -5/3 is y = (-5/3)x - 2.
can someone please help me
Answers
Answer: C
Step-by-step explanation:
The slope is positive, so m>0.
The y-intercept is negative, so b<0.
I AM GIVING + 20 POINTS !!!!! PLEASE ANSWER SOON!!!!! Which is NOT a good reason to perform step 1 in the solution shown? equation: 4x = 88 step 1: 4x/4 = 88/4 step 2: x = 22 a. divide by 4, because 4 is a factor of 88. b. dividing 4x by 4 isolates x on one side of the equation. c. dividing is the inverse of multiplying d. dividing both sides by 4 keeps the equation balanced
Answers
Answer:
c. dividing is the inverse of multiplying because it doesn't really relate the equation like the others do.
What is the image of (-8,-4) after a dilation by a scale factor of 4 centered at the origin
Answers
Answer:
(-32, -16)
Step-by-step explanation:
(-8-0, -4-0)*4=
(-8*4, -4*4)=(-32, -16)
Air is being pumped into a spherical balloon at the rate of 7 cm3/sec. What
is the rate of change of the radius at the in stant the volume equals 36π cm3
? The volume of
the sphere of radius r is (4 over PI )r power of 3
Answers
Answer:
Step-by-step explanation:
\(V=\frac{4}{3} \pi r^3\\\frac{dV}{dt} =\frac{4}{3} ~\pi \times ~3r^2\frac{dr}{dt} \\\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} \\7=4\pi r^2\frac{dr}{dt} \\\frac{dr}{dt} =\frac{7}{4\pi r^2} \\when~V=36 \pi cm^3\\36\pi =\frac{4}{3} \pi r^3\\r^3=\frac{36\pi \times 3}{4\pi } =27=3^3\\r=3~cm\\\frac{dr}{dt} =\frac{7}{4\pi \tmes 3^2} \\\frac{dr}{dt} =\frac{7}{36 \pi } cm/sec\)
John's salary is $1600. Peter 's salary is $400 less than John's salary. Find the ratio Peter's salary to John's salary in the simplest form.
Answers
$300 to $400
Step-by-step explanation:
Find 62,208 divide 36
Answers
Answer:
1728
Step-by-step explanation:
Which equation represents this statement?
The product of 1/5 and a number is equal to 1 1/2.
Responses
15÷n=1 1/2
fraction 1 over 5 end fraction divided by n equals 1 and 1 half
15−n=1 1/2
fraction 1 over 5 end fraction minus n equals 1 and 1 half
15+n=1 1/2
fraction 1 over 5 end fraction plus n equals 1 and 1 half
15n=1 1/2
Answers
The statement as an equation is 1/5x = 1 1/2.
How to determine the statement as an equation?From the question, we have the following statement that can be used in our computation:
The product of 1/5 and a number is equal to 1 1/2.
Represent the numbers as x
So, we have the following representation
The product of 1/5 and x is equal to 1 1/2.
Introduce the equality symbols
So, we have
The product of 1/5 and x = o 1 1/2.
Next, we have
1/5 * x = 1 1/2.
Express as products
1/5x = 1 1/2.
hence, the expression is 1/5x = 1 1/2.
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A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Answers
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 16 salespeople using Jefferson's method given the information below.
Shift Morning Midday Afternoon Evening
Average number of customers 125 280 460 560
Salespeople to assign
What modified divisor did you use?
Answers
a) Using the standard divisors according to Jefferson's apportionment method, the number of salespeople assigned to work each shift is as follows:
Shift Morning Midday Afternoon Evening Total
Number of
salespeople assigned 1 3 5 7 16
b) The modified or adjusted divisor used represents the average number of customers for each shift divided by the standard divisor.
What is the standard divisor?The standard divisor shows the ratio of the total population to the number of seats.
The standard divisor gives an insight about the number of people each seat represents.
Standard divisor = Total number of customers / Total number of salespeople
The total number of customers = 1,425
The number of salespeople = 16
a) Standard divisor = 1,425 ÷ 16
= 89.0625
Shift Morning Midday Afternoon Evening Total
Average number of
customers 125 280 460 560 1,425
Standard divisor 89.0625 89.0625 89.0625 89.0625
b) Modified divisor 1.4035 3.1438 5.165 6.288
Number of
salespeople assigned 1 3 5 7 16
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What expression as a sum of 11/12 
Answers
Answer:
D the last expression
unit 4: congruency triangles
Answers
Answer:
What about congruency triangles i think you need a picture so we can see
Step-by-step explanation:
Calculate the value for the for the following scores 20, 60, 30, 50 given:
begin inline style begin display style sum for blank of end style end style x squared =
Answers
The sum of the scores is equal to 160.
What is a mean?In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the mean for a data set?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of scores (data set), we have;
∑x = 20 + 60 + 30 + 50
∑x = 160.
Mean = [F(x)]/n = 160/4 = 40.
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Hello! Could someone please help explain how to solve this to me please and an answer would be nice! Thanks! :)
Answers
if we notice the tickmarks on the triangle, we can see the all sides are equal, namely is an equilateral triangle, and if all sides are equal, then all interior angles are equal as well.
Let's recall that the sum of all interior angles in a triangle is 180°, now if we divide that by 3, that gives us 60, namely each angle in the equilateral triangle is 60°, that means
\(10x=60\implies x=\cfrac{60}{10}\implies \boxed{x=6} ~\hfill 12y=60\implies y=\cfrac{60}{12}\implies \boxed{y=5}\)
what is the result of adding the system of equations 2x y 43x y 6x 10x y 25x 10
Answers
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
Describe equation:Equations are statements in mathematics containing the equals (=) sign flanked on either side by two algebraic expressions. The relationship between the expressions printed on the left and right sides is shown to be equal in this way. In all mathematical equations, LHS = RHS is used. You can solve equations to find the value of an unknown variable that stands in for an unknown quantity. If a sentence lacks a "equal to" sign, it is not considered an equation. It will be considered to be a phrase.
Here,
Given:
we have to solve the system of equations given. .Each equation is added together to remove the variable Y.
2x + y = 4
+
3x - y = 6
________
=> 5x =10
Therefore the result of adding the system of equations 2x + y = 4 ,
6=3x-y is 5x =10
The value of x :
x =10 / 5 = 2
⇒ x=2
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The carts need to be as wide as possible. The widest cart that will pass
through the
doorway between the manufacturing floor and the loading dock is 30 inches
wide. The carts also should be as long as possible so they can carry the
largest quantity of finished goods per trip. Arthur tells his mother she can
solve the problem using similarity.
to manufacturing floor
30 in.
to loading dock
B
cart
48 in.
D
36 in.
c) The first similarity that Arthur's mother needs to determine is the
similarity of AABC and AGED. Write a proof to show AABC - AGED.
Answers
AABC is similar to AGED with a scale factor of 22.5/48, which means that the width of the cart is proportional to the height, with a ratio of 30:22.5.
Since AABC and Matured are comparative, their relating points are equivalent, and their comparing sides are corresponding.
By definition, point An in AABC is equivalent to point An in Matured, as they are both right points. Likewise, point E in Matured is equivalent to point C in AABC, as they are both vertical points. At long last, point B in AABC is equivalent to point D in Matured, as they are both correlative points to point An and E, separately.
To demonstrate the sides are relative, we can utilize the proportions of comparing sides:
Stomach muscle/AG = BC/ED = AC/Promotion
Subbing the given qualities, we get:
Stomach muscle/48 = BC/36 = AC/x
where x is the length of the truck.
Tackling for x, we get:
x = AC * 36/BC
x = 30 * 36/48
x = 22.5 inches
In this way, AABC is like Matured with a scale variable of 22.5/48, and that implies that the width of the truck is relative to the level, with a proportion of 30:22.5.
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Write the equation of the parabola in the standard form that passes these 3 points (-1,14),(0,7),(1,6)
Answers
We will investigate how to construct an equation of a parabola given three points.
A parabola is described as a polynomial relationship of highest order 2. The general equation of a parabola is given as follows:
\(y=ax^2\text{ + bx + c}\)Where,
\(a\text{ , b , and c are constants}\)To determine the values of these constants we will utilize a set of pair off coordinates given as follows:
\((\text{ -1 , 14 ) , ( 0 , 7 ) , ( 1 , 6 )}\)The process off evaluating the three constants ( a,b, and c ) is to plug in the respective coordinates in the general form of a parabolic function. Then develop a system of equations which can be solved simultaneously.
Using the pair ( 0 , 7 ). We will plug in the respective coordinates in the general form and evaluate:
\(\begin{gathered} 7\text{ = a}\cdot(0)^2\text{ + b}\cdot(0)\text{ + c} \\ c\text{ = 7} \end{gathered}\)Taking the pairs ( -1 , 14 ) and ( 1 , 6 ). We get a pair of equations as follows:
\(\begin{gathered} 14\text{ = a}\cdot(-1)^2+b\cdot(-1)\text{ + 7} \\ 7\text{ = a - b }\ldots\text{ Eq1} \\ \\ 6\text{ = a}\cdot(1)^2+b\cdot(1)\text{ + 7} \\ -1\text{ = a + b }\ldots\text{ Eq2} \end{gathered}\)Now once we have developed a system of linear equations. We will solve them simultaneously by elimination:
\(\begin{gathered} Eq\text{ 1 + Eq2} \\ a\text{ - b = 7} \\ a+b\text{ = -1} \\ ======= \\ 2a\text{ = 6} \\ a\text{ = 3} \\ ======= \end{gathered}\)Now use back substitution to plug in the value of constant ( a = 3 ) into either of the equations ( Eq1 or Eq2) as follows:
\(\begin{gathered} Eq2\colon-1\text{ = 3 + b} \\ b\text{ = -4} \end{gathered}\)We have the values of the three constants:
\(a\text{ = 3 , b = -4 , c = 7}\)The equation of the parabola turns out to be:
\(y=3x^2-4x\text{ + 7}\)FInd the measure of the arc using the picture provided , please and thanks
Answers
The measure of arc angle QTP is 204 degrees.
How to find arc angle?When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
Therefore, let's find the measure of arc angle QTP as follows:
90 = 0.5(x - 68)
90 = 0.5x - 34
0.5x = 124
x = 124 / 0.5
x = 248 degrees
Where
x = arc angle TSQ
Therefore,
arc QP = 44 degrees
Therefore,
arc QTP = 248 - 44
arc QTP = 204 degrees
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Matteo is following this recipe to mak
a cake.
He wants to make three of these
cakes.
How much of each ingredient does he
need?
Recipe: Makes 1 cake
6 ounces butter
5 ounces sugar
7 ounces of flour
3 eggs
2 teaspoons (tsps) baking powder
Pls help me I'm trying too sleep and they keep sending me homework
Answers
Answer:
Below is the step by step explaination of the procedure
Step-by-step explanation:
So since he wants to make three cakes we will multiply the recipe by 3 to get the amount of ingredients this person will need.
6*3 = 18 ounces of butter
5*3 = 15 ounces of sugar
7*3 = 21 ounces of flour
3*3 = 9 eggs
2 * 3 = 6 teaspoons of baking powder.
What is the number of significant figures in 122.35 cm ?
Answers
Answer:
5
Step-by-step explanation:
Simplify the following expression. 3x(4x − 3) A. 12x2 + 13x B. 12x2 + 5x C. 12x2 − 5x D. 12x2 − 9x
Answers
Answer:
Multiply using the distributive property.
D is the best answer.
Step-by-step explanation:
The simplified form of expression 3x (4x - 3) is 12x² - 9x.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
3x (4x - 3).
Simplify the expression by solving bracket term,
3x × (4x) - 3 x (3x)
12x² - 9x
The given expression can be simplified as 12x² - 9x.
Hence, option (D) is correct.
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What are the solutions to the equation x minus StartFraction 7 Over x EndFraction = 6 x = –7 and x = 1 x = –6 and x = –1 x = –1 and x = 7 x = 1 and x = 6
Answers
Answer:
c
Step-by-step explanation:
The solution to the equation is x = -1 and x =7, the correct option is C.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
The equation is
x - (7/x) = 6
On solving the equation,
(x² -7) = 6x
x² - 7 = 6x
x² -6x -7 =
x² - 7x +x -7 = 0
x( x-7) +1(x-7)= 0
(x+1)(x-7) = 0
x = -1,7
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6/10 + 5/100
is it
65/100 or 65/110 or 56/100 or 56/110
Answers
Answer:
65/100 that is the answer to this question
5 A jewelry box has 10
items. Of those, half
are necklaces. Two-fifths of
the others are bracelets.
The rest are rings. How
many rings are there?
Answers
2/5 of 10= 2 so there’s 2 bracelets
5+2 =7
10-7= 3
There are 3 rings
Answer:
1 ring
Step-by-step explanation:
10 items total
Half are necklaces = 5 necklaces out of the total 10 items
2/5 of the other items are bracelets = 2/5*10 = 4 necklaces total 10 items
This leaves only the rings, and 5 + 4 = 9, so 10 - 9 = 1 ring out of the total 10 items.
Hope this answer helps! Don't have to mark as brainliest, I'm just happy I got to help you.
The graphs below have the same shape the equation of the bluegrass is f(x)=x^3 what is the equation of the red graph
Answers
Answer:
g(x) = x^3 - 2
Step-by-step explanation:
As you can see on the graph, the line has been translated down 2 units.
If the graph of f has the same shape as the graph of g, then the slope remains the same. The y intercept (k) changes by -2 units, so the k value is -2
g(x) = x^3 - 2
Hope this helps!!