The value of angle A and B are 60° and 120° respectively.
How to calculate the angles?It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.
Therefore A = D
B = C
When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:
ABK = 30°
Also, KBC = 90°
Therefore, B = 30° + 90° = 120°
A = D = 180° - 120° = 60°
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Complete question:
Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4
Find: mA and mB.
PLEASE HELP GIVING 75 POINTS!!
184) If 15
Toby the Turkey needs you to buy place cards so that everyone will know where to sit during his Thanksgiving dinner. He would like to buy them in bulk. The card shop offers 3 different packs. Use the chart below to determine which pack offers Toby the best deal, then find the price per card.
Pack #1
Quantity 12 place cards
Cost $29 per pack
Pack #2
Quantity 24 place cards
Cost $89 per pack
Pack #3
Quantity 24 place cards
Cost $213 per pack
( This is confusing to me I don't even understand why my math teacher decided to give us it when she didn't explain it. currently gonna cry on this I need to show work what.)
The solution is Pack #1
The pack which offers Toby the best deal is Pack #1
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 price per card of each pack be = A
Now , the equation is
a)
Pack #1
The number of cards = 12 cards
The cost per pack = $ 29
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 2.416
Therefore , the cost of one card in pack 1 is $ 2.416
b)
Pack #2
The number of cards = 24 cards
The cost per pack = $ 89
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 3.708
Therefore , the cost of one card in pack 2 is $ 3.708
c)
Pack #3
The number of cards = 24 cards
The cost per pack = $ 213
The equation is
So , the cost of 1 card = cost per pack / number of cards
= $ 8.875
Therefore , the cost of one card in pack 3 is $ 8.875
And ,
cost of one card in pack 3 is $ 8.875 > cost of one card in pack 2 is $ 3.708 > cost of one card in pack 1 is $ 2.416
Therefore , the cost of one card in pack 1 is $ 2.416 and this is the best deal
Hence , The pack which offers Toby the best deal is Pack #1
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Solve the following:
a) a/5+3=8
b) 3b/7-1=5
a) a/5 + 3 = 8
Step 1 : Minus both sides by 3
a/5 + 3 - 3 = 8 - 3 -> a/5 = 5
Step 2 : Multiply both sides by 5
a/5 x 5 = 5 x 5 -> a = 25.
b) (3b)/7 - 1 = 5
Step 1 : Add both sides by 1
(3b)/y - 1 +1 = 5 + 1 -> (3b)/7 = 6
Step 2 : Multiply both sides by 7
(3b)/7 x 7 = 6 x 7 -> 3b = 42
Step 3 : Divide both sides by 3
3b : 3 = 42 : 3 -> b = 14.
find the missing length
21 is missing length of parallel lines.
What is an example of parallel lines?
In terms of geometry, parallel lines are two separate lines that never cross each other and are located in the same plane. They may be vertical or horizontal. In our daily lives, parallel lines can be seen in the form of zebra crossings, rows of notebooks, and the nearby railroad tracks.Because lines are parallel
so they cut into equal proportion
then , 4/10 = x/15
4 * 15/10 = x
x = 6
length of line = 15 + 6 = 21
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What’s the inequality for the sum of a number w is more than -12? Please help it’s already missing
The sum of a number w is more than -12 becomes w > -12
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.
We have been given that the sum of a number w is more than -12.
Now the sum of a number = w
It is more than -12 means the inequality form as;
w > -12
Therefore, the overall expression becomes w > -12
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represent the following expressions as a power of the number a (a≠0) (a^-1xa^-2)^-3
The solution of the exponential expression will be a⁹.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied.
Given exponential expression is (a⁻¹ x a⁻²)⁻³. The expression will be solved as below,
E = (a⁻¹ x a⁻²)⁻³
The base is the same and the variables are in multiplication with powers then the powers will be added,
E = (a⁻³)⁻³
E = a⁹
Therefore, the solution of the exponential expression will be a⁹.
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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph. f(x) = (x – 2)(x – 3)(x – 5) Simplify the right side. What is the equation? f(x) = x3 + 31x – 30 f(x) = x3 – 10x2 + 31x – 30 f(x) = x3 – 10x2 + 19x – 30 f(x) = x3 + 19x – 30 graph
The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.
What is the equation of the polynomial with zeroes 2, 3 and 5?It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).
Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;
f(x) = (x - 2) (x - 3) (x - 5)
Therefore, by simplification; we have;
f(x) = (x² - 5x + 6) (x - 5)
f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.
f(x) = x³ - 10x² + 31x - 30.
Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.
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help ASAP 20 points and will mark you brainleast
Solve the system of equations by the addition method.
look at the image ---->
Answer:
x=3 y=4
Step-by-step explanation:
-4x= -6y+12 -1
8x-4y = 8 -2
-4x+6y=12 -1
8x-4y = 8 -2
multiply first equation by 2:
2(-4x+6y=12)
= -8x+12y=24
add with 2nd equation;
-8x+12y=24
+
8x-4y=8
-8x+8x=0
+12-4y=8y
24+8=32
0+8y=32
y=32/8
y=4
input y into any equation to get x:
-4x= -6(4)+12
-4x = -24+12
-4x= -12
-x= -12/4
x=3
a four-digit number uses each of the digits 1, 2, 3, and 4 exactly once. what is the probability that the number is a multiple of 4? express your answer as a common fraction.
The probability that the number is a multiple of four is 0.25.
we know that if a number is multiple of four then its last 2 digits must be divisible by four.( i.e. ten's and one's places)
We are given only four numbers 1,2,3,4 , which can't be repeated.
So here , in this case , such numbers with last two digits divisible by four are 12,24 and 32 only
Having last two digits ‘12’ ;
the first two digits can be formed using 3 and 4 only . This can be done in (2!) = 2 ways.
Similar case will be happening with 24 and 32 as well.
So the total ways of getting a multiple of four will be = 2 + 2 + 2
= 6 ways
Now total numbers that can be made from given four digits = [tex]P_{4} ^{4}[/tex]
= 24
So the probability of getting a multiple of four is = 6/ 24
= 0.25
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- 4≤2w + 2 and 3w+1 <4
Answer:
[tex] - 3 \leqslant w < 1[/tex]
Step-by-step explanation:
as shown in picture attached
Solve these using the balance method show steps of working out pls I’ll brainlist/5star it’s urgent!!!!!!
1) 5x - 4 = 31
2) 7(x+5) = 49
3) 3x + 7 = -2x + 22
4) x+8 = 6
3
What is the angle amount of m
The angle amount of m is 128⁰
What is meant by an angle?Angle can also refer to the length of a rotation or an angle. The Greek word , which means "crooked, curled," and the English word "ankle," are related words. Both stem from the Proto-Indo-European root which means "to bend" or "bow," in some way.
A plane angle, according to Euclid, is the inclination to each other of two intersecting lines in a plane that are not perpendicular to one another. Proclus asserts that an angle must be either a quality, a number, or a connection. Eudemus used the first idea, viewing an angle as a departure from a straight line; Carpus of Antioch used the second idea, viewing an angle as the distance or space between intersecting lines; and Euclid used the third idea. Vertical angles, opposing angles, or vertically opposite angles refer to a pair of angles that are directly across from one another and are created by two straight lines meeting to form a "X". Vert is the shorthand for them. opp.
The vertical angle theorem states that angles that are vertically opposing are equal. The assertion shown that since both of a pair of vertical angles are supplementary to both of the neighboring angles, the vertical angles are equal in measure, according to Eudemus of Rhodes' attribution of the proof to Thales of Miletus. When Thales visited Egypt, it is recorded in history[9] that he noticed the Egyptians measuring the vertical angles whenever two intersecting lines were drawn to ensure that they were equal. Thales came to the conclusion that one might establish
4x+6=7x-21
3x=27
x=9
x+x+42+42=360
2x+84=360
x=128⁰
Therefore, the angle amount of m is 128⁰
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Can you please help me in this question.
Answer:
k = - 6 , c = 8
Step-by-step explanation:
f(x) = x² + kx + c
given f(2) = 0 , substitute (2, 0 ) into f(x)
0 = 2² + 2k + c
0 = 4 + 2k + c ( subtract 4 from both sides )
- 4 = 2k + c → (1)
given f(- 3) = 35 , substitute (- 3, 35 ) into f(x)
35 = (- 3)² - 3k + c
35 = 9 - 3k + c ( subtract 9 from both sides )
26 = - 3k + c → (2)
subtract (2) from (1) term by term to eliminate c
- 4 - 26 = 2k - (- 3k) + (c - c)
- 30 = 2k + 3k
- 30 = 5k ( divide both sides by 5 )
- 6 = k
substitute k = - 6 into (1) and solve for c
- 4 = 2(- 6) + c
- 4 = - 12 + c ( add 12 to both sides )
8 = c
then
k = - 6 and c = 8
What is the value of x, given that the two pyramids are similar?
OA. 8
OB. 18
O C. 6
D. 24
8
8
6
24
24
The value of x is 18 which is option B.
Given:
Two pyramids are similar.
if two figures are similar then the ratio of their sides are equal.
So, 24/8 = x/6
24*6 = 8*x
144 = 8x
divide by 8 on both sides
8x/8 = 144/8
x = 144/8
x = 18.
Therefore the value of x is 18 which is option B.
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A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.
Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.
Enter your inequality without a thousands separator.
The inequality expression of the volume of the balloon is V < 4,400
How to determine the inequality expression?From the question, we have the following statement:
The initial volume of the balloon is 4,400 cubic centimeters
Also, we understand that:
The balloon leaks out over time
This means that the volume of air in the balloon decreases over time.
So, we have the following representation
V = Less than the initial volume
Rewrite as
V < 4400
Hence, the volume of the balloon at any time after it starts leaking is V < 4,400
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the sum of a particular two digit number is 11. if this number's digits are reversed, the number is decreased by 63. what is this number?
The required number is 94.
Let the digit on unit's place be 'x'
Digit on ten's place be 'y'
Therefore,
Original number = 10y + x
Given, the sum of the digits = 11
=> x + y = 11 →(I)
When the digits are reversed, new number = 10x + y
Therefore,
(10y + x) - (10x + y) = 63
10y + x - 10x - y = 63
9y - 9x = 63
=> y - x = 7 →(II)
Adding (I) and (II) we get
2y = 18
y = 9
Substituting the value of y in (I) we get
x + 9 = 11
x = 2
Therefore,
Original number = 10y + x = 10(9) + 4 = 94
The required number is 94.
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adam and ben each have a fair coin. adam throws it 101 times, and ben throws it 100 times. what is the probability that adam gets strictly more heads than ben?
There is a change of 1/2 for Adam to get strictly more heads than Ben.
What is meant by the term probability?Probability originally referred to potential. A random event's occurrence is the subject of this field of mathematics. The range of the value is 0 to 1. Mathematics has employed probability to foresee the frequency of various events.The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)
If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.
Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.
Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.
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36 and 30 percentage of 10
Answer: 120
explanation: We already have our first value 36 and the second value 30. Let's assume the unknown value is Y which answer we will find out.
As we have all the required values we need, Now we can put them in a simple mathematical formula as below:
STEP 136 = 30% × Y
STEP 236 =
30
100
× Y
Multiplying both sides by 100 and dividing both sides of the equation by 30 we will arrive at:
STEP 3Y = 36 ×
100
30
STEP 4Y = 36 × 100 ÷ 30
STEP 5Y = 120
Finally, we have found the value of Y which is 120 and that is our answer.
You can easily calculate 36 is 30 percent of what number by using any regular calculator, simply enter 36 × 100 ÷ 30 and you will get your answer which is 120
a circle is always sometimes or never similar to the other circle because we can always sometimes or never map one onto the other using dilations and rigid transformations
Answer: always, always
Step-by-step explanation:
Every circle is similar to every other circle.
Are you local grocery store? You can buy 3 pounds of rice for 9 dollars use this information to fill in the missing parts
The proportional relationship that gives the cost of x pounds of rice is given as follows:
y = 3x.
What is a proportional relationship?A proportional relationship is a special case of a linear function, with slope represented by k and intercept of 0, hence the output variable y is obtained with the multiplication of the input variable x and the slope k, as follows:
y = kx.
In this problem, the input and the output are given as follows:
Input: pounds of rice.Output: cost.You can buy 3 pounds of rice for 9 dollars use, hence the constant representing the cost per pound is given as follows:
k = 9/3 = 3.
Hence the equation is:
y = 3x.
Missing InformationThis problem is incomplete but we suppose that it asks for a proportional relationship giving the cost of x pounds of rice.
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someone please help me im begging u for points
The solution of the algebraic equation is x = -2. The proof is elaborated below.
The algebraic equation given to us is 14(x + 1) = -7(4 + x). An equation is a mathematical statement that proves the equality of two mathematical expressions. The first step is to simplify the brackets. The equation becomes 14x + 14 = -28 - 7x. Now, we will add 7x to both sides of the equation. The equation is modified as 21x + 14 = -28. Now, we will subtract 14 from both sides of the equation. The equation is modified as 21x = -42. Now, we will divide both sides of the equation by 21. The equation is modified as x = -2.
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please help me out. i’ll give brainliest
Answer:
y = -2x + 1
Step-by-step explanation:
y = mx + b you must find the m (slope) and the b (y intercept) to write the equation for the graph.
The slope is negative. If you start on the very left side of the graph and follow it, you will see that it goes in a down hill direction. That means that the slope is negative. If I start on the very left and the line goes up from there, the slope is positive. If the line is a straight horizontal line, then the slope is zero, it does not go up or down.
The slope is -2. Select one of the dots and travel to the next dot, but you can only move horizonaly and vertically. You cannot move diagonally. You will notice that the two closes dots are two units up (or down) and only 1 unit left (or right) depending on which dot you start at. Since you move 2 units up and 1 unit left that is a slope of 2. 2/1 = 2.
The b (y-intercept) is just where you see the line cross the y axis. It crosses it at 1.
Answer:
y = -2x + 1
Step-by-step explanation:
Slope intercept form: y= mx + bHere m is the slope and b is y-intercept.
Pick any two points on the line.
(-1,3) & (2,-3).
Find the Slope.
[tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{-3-3}{2-[-1]}\\\\=\dfrac{-6}{2+1}\\\\=\dfrac{-6}{3}\\\\=-2[/tex]
m = -2.
Equation of the line:
y = -2x + b
Substitute any one point in the above equation and find the y-intercept. (-1,3)
3 = -2*(-1) + b
3 = 2 + b
3 - 2 = b
b = 1
Equation of the line:
y = -2x + 1
What is the slope of the line passing through the points A(−2,5) and B(1,10)
Answer:
Slope is equal to the change in y y over the change in x x, or rise over run. m = change in y change in x m = change in y change in x. The change in x x is equal to the difference in x-coordinates (also called run ), and the change in y y is equal to the difference in y-coordinates (also called rise ). m = y2 −y1 x2 −x1 m = y 2 - y 1 x 2 - x 1.
The graph of y=f(x) is drawn on the grid.
a) Write down the coordinates of the turning point of the graph. (1)
b) Write down the roots of f(x) = 0
c) Use the graph to find an estimate for f(2.5)
The solution to the points are:
Turning point: (1, -3.2)Root: (-1, 0) and (3, 0)Estimate of f(2.5) is -1.4The coordinates of the turning pointThis is the point where the curve or curves of the graph changes direction.
In this case, the turning point in the vertex
The graph has its vertex at (1, -3.2)
This means that
Turning point = (1, -3.2)
The roots of the functionThis is the point where the curve or curves of the graph touches the x-axis i.e. f(x) = 0
In this case, the points are: (-1, 0) and (3, 0)
This means that
The roots are (-1, 0) and (3, 0)
The estimate of f(2.5)This is the point where the curve or curves of the graph passes through x = 2.5
In this case, the points are: (2.5, -1.4)
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Find the asymptotes and intercept of the following rational function
Show your work for the intercepts!
Answer:
VA: x = 1, x = -1
HA: y = 0
x-int: (4, 0)
y-int: (0, 4)
Step-by-step explanation:
x-int:
0 = (x-4)/((x-1)(x+1))
0 = (x-4) because the (x-1)(x+1) are multiplied by 0
4 = x
x = 4
(4, 0)
y-int:
y = (0 - 4)/((0 - 1)(0 + 1))
y = (-4)/((-1)(1))
y = (-4)/(-1)
y = 4/1 = 4
(0, 4)
Solve the equation A=s^2 for s. Assume s>0 answer in form s=….
For the equation A=s² for s. Assume s > 0, then s = [tex]\sqrt{A}[/tex].
What are squares and square roots?
Squares are the numbers that are produced when a value is multiplied by itself. In contrast, a number's square root is a value that, when multiplied by itself, returns the original value.
For the given equation, A = s², we have to find the value of s.
thus, taking the square root on both sides, we get
s = [tex]\sqrt{A}[/tex].
Hence, the value of s = [tex]\sqrt{A}[/tex].
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8.
y=
Which word describes the connection between the shape and its reflection?
[] congruent
[] similar
[ ] translation
[] corresponding
The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
what is congruency?Congruent in geometry refers to being the same size and shape. Congruence can be used with figures, angles, and line segments. If any two line segments are equal in length, they are said to be congruent. If two angles have the same measure, they are said to be congruent. If the matching sides and angles of two triangles are the same, they are said to be congruent. In this post, we will learn more about congruence and congruent figures.The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.Hence,The corresponding sides and angles of both the triangles [pre-image and the image] are congruent
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Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 12% for 6 months. Calculate the simple interest using I = prt.
$69
$90
$420
$1,080
Pls hurry and thank you!
The simple interest using I = prt if Oliver borrowed $1,500 to purchase a riding lawn mowerat the rate of f 12% for 6 monthsis
How can the simple interestbe calculated?The concept that will be used is the concpt of simple interest and thei can be calculates using the simple interst formular which is
I = [(prt)/100]
where p = principal = $1,500
I = intereste rate
t=time
Then this can be expressed as
I= (prt)/100
I = ($1,500* 6/12 * 12 )/100
= $90
In conclusion the simple interest is now $90 which is the second option that is given.
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18. Which of the following are solutions to the equation 19.
-11x = 2x² +15? Select all that apply.
x²
a. -5
b. -3
c. -5/2
d. 5/2
e. 3
f. 5
The solutions to the given equation are -5/2 and -3. These answer can get after using quadratic formula.
How can find solution using quadratic formula ?The quadratic formula is a formula that offers a quadratic equation's solution. In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
In the literature, there are numerous ways to derive the quadratic formula. The common one uses the completing the square method in a straightforward manner.
The given equation is :
-11x = 2x² +15
Move terms to the left side
-11x -(2x^2 +15) =0
Rearrange terms
-2x^2 - 11x -15 = 0
Common factor
-(2x^2+ 11x +15) =0
Divide both sides by the same factor
2x^2 +11x +15 =0
Use the quadratic formula
x = -11 ± √11² - 4 * 2*15/2*2
x =-11±1/4
Solve
x = -5/2
x= -3
The value of x will be -5/2 or -3.
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Tiffany has 15 teaspoons of chocolate chips she uses 1 1/2 teaspoons for each muffin the total number of teaspoons left y after making x muffins can be given by y=-3/2+15
The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15).
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.
As per the given equation,
y = (-3/2)x + 15
At y-intercept,
x = 0 so, y = 0 + 15 = 15 thus, (0,15)
At x-intercept
y = 0
0 = (-3/2)x + 15
x = 10 thus, (10,0)
Hence "The x-intercept of the given graph of the function is (10,0) while the y-intercept is (0,15)".
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For the complete question and graph image attached below,