The area of the shape with parallel sides is 35 unit² of trapezoid .
Describe the trapezoid shape?
An open, flat object with four straight sides and one pair of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases. The legs of a trapezium can also be parallel.A = (1/2) * (a + b)h
Where a, b is the length of the parallel sides and h is the height of the trapezoid.
Given that a = 8, b = 6 and h = 5, hence:
A = (1/2) * (8 + 6) * 5 = 35 unit²
The area of the shape with parallel sides is 35 unit².
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John's test grade is 5 points less than twice Ariana's test grade. If x represents Ariana's test grade, write an expression for John's test grade.
In linear equation, 2x - 5 is an expression for John's test grade.
What is linear equation in one variable?
The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable.A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."Let Ariana's test grade = x
twice Ariana's test grade = 2x
then, John's test grade = 2x - 5
an expression for John's test grade = 2x - 5
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if f (x) =x2-4x-6 find f(o) F(3) f(-2) show that f (1/2) f(7/2) and f(2-h) f (2+h)
If f(x) = x² ₋ 4x ₋ 6 then we get the following answers for f(0),f(3) and f(-2) respectively. And the expression f(1/2) = f(7/2) and f(2₋h) = f(2₊h) is therefore proved.
f(0) = -6
f(3) = -9
f(-2) = 6
Given the function is f(x) = x² ₋ 4x ₋ 6
we need to find for f(0):
f(0) = 0² ₋ 4(0) ₋ 6
f(0) = ₋6
f(3) = 3² ₋ 4(3) ₋ 6
f(3) = 9 ₋ 12 ₋ 6
f(3) = ₋9
f(₋2) = (₋2)² ₋ 4(₋2) ₋ 6
f(₋2) = 4 ₊ 8 ₋ 6
f(₋2) = 6
we need to prove f(1/2)f(7/2)
now, f(1/2) = (1/2)² ₋ 4(1/2) ₋ 6
f(1/2) = 1/4 ₋ 2 ₋ 6
f(1/2) = 1 ₋ 8 ₋ 24 / 4
f(1/2) = ₋31/4
f(7/2) = (7/2)² ₋ 4(7/2) ₋ 6
f(7/2) = 49/4 ₋ 14 ₋ 6
f(7/2) = 49 ₋ 56 ₋ 24 / 4
f(7/2) = ₋31/4
therefore, f(1/2) = f(7/2)
f(2₋h) = (2₋h)² ₋ 4(2₋h) ₋ 6
f(2₋h) = (4 ₊ h² ₋ 4h) ₋ 8 ₊ 4h ₋ 6
f(2₋h) = h² ₊ 4 ₋ 4h ₋ 8 ₊ 4h ₋ 6
f(2₋h) = h² ₋ 10
f(2₊h) = (2₊h)² ₋ 4(2₊h) ₋ 6
f(2₊h) = 4 ₊ h² ₊ 4h ₋ 8 ₋ 4h ₋ 6
f(2₊h) = h² ₋ 10
therefore, f(2₋h) = f(2₊h)
Hence proved.
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A quality control inspector has drawn a sample of 19 light bulbs from a recent production lot. If the number of defective bulbs is 1 or more, the lot fails inspection. Suppose 20% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection? Round your answer to four decimal places.
The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856
How find the probability of the lot that will fail inspectionGiven data
p = 20%
sample drawn = 19 bulbs
20% of the bulbs in the lot are defective
n = 19
p = 20% = 0.20
if 20% of the bulbs are defective to find the non defective bulbs we solve as follows
q = 1 - p
= 1 - 0.20
= 0.80
Using binomial theorem,
[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]
[tex]= 1 - P ( x < 1 )[/tex]
[tex]= 1 - P ( X = 0)[/tex]
[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]
[tex]= 1 - 1 * 1 * 0.01441[/tex]
[tex]= 1 - 0.01441[/tex]
= 0.98559
= 0.9856 (to four decimal place)
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In simplest terms, Adam can see a√b feet farther than Pam. a = , b =
It is recommended that the expressions
d = 400 - 256 and
d = 256 - 400 be considered when attempting to determine how much farther Adam can see to the horizon.
The calculation for the expression is as follows:Since, the eye-level height of Pam is 256 feet above sea level, whereas the eye-level height of Adam is 400 feet above sea level.
Therefore, the formula that indicates how much farther Adam can see to the horizon should be taken to be
d = 400 - 256 and
d = 256 - 400.
This expression may be found by subtracting 400 from 256.
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CQ
Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.
Answer:
A= 2 B= 6
Step-by-step explanation:
the dude above me is wrong
Michael is playing a game of chance in which he tosses a dart into a rotating dartboard with 8 equal-sized slices numbered 1 through 8. The dart lands on a numbered slice at random.
Answer:
6 I belive it should land on 6
D(7,3) is the midpoint, (MP), of AB.
E(10, 4) is the MP of BC.
F(5,5) is the MP of AC
Find the coordinates of A, B, and C
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
Midpoint :
The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
x= x1+x2/2
y=y1+y2/2
Now ,
D(7,3) is the midpoint of AB.
D (x',y') = (7,3)
vertex of A = (x1,y1)
vertex of B = (x2,y2)
x' = x1+x2/2
7 = x1+x2/2
14 = x1+x2 ...1
y' = y1+y2/2
3= y1+y2/2
6= y1+y2 .....2
E (x'',y'') = (10,4)
vertex of c = (x3,y3)
vertex of B = (x2,y2)
x''= x3+x2/2
y''=y3+y2/2
20= x3+x2 ....3
8 =y3+y2.......4
F (x''',y''') = (5,5)
vertex of c = (x3,y3)
vertex of A = (x1,y1)
10= x1 +x3 ...5
10 =y1+y3 .....6
For 1 & 3 & 5
14 = x1+x2 ...1
20= x3+x2 ....3
10= x1 +x3 ...5
Add all 1 & 3 & 5
44 = 2(x1+x2+x3)
22 = (x1+x2+x3) .....7
For 1 & 7
x3 = 8
For 3 & 7
x1 = 2
For 5&7
x2 = 12
For 2 , 4 & 6
6= y1+y2 .....2
8 =y3+y2.......4
10 =y1+y3 .....6
Add all 2 & 4 & 6
24 = 2 (y1+y2+y3)
For 2 & 8
y3 = 6
For 4 & 8
y1 = 4
For 6 & 8
y2 = 2
vertex of A = (x1,y1) =(2,4)
vertex of B = (x2,y2)= (12,2)
vertex of c = (x3,y3) = (8,6)
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which are the partial products of 3,706×4?
The partial products of 3706 × 4 is ( 3000 × 4 ) + ( 706 × 4 ).
Calculating the product of two or more numbers is the procedure known as multiplication in mathematics. When two integers are multiplied together in mathematics, the result is a product or an expression that describes the factors to be multiplied.
The decimal numeral system is widely used to express both integer and non-integer numbers. The way of representing numbers in the decimal system is known as decimal notation.
The given product is 3706 × 4 and can be written as:-
3706 × 4 = [ 3000 + 706 ] × 4
3706 × 4 = ( 3000 × 4 ) + ( 706 × 4 )
Therefore, the partial products of the given expression is ( 3000 x 4 ) + ( 706 x 4 ).
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work this out please
Answer:
1/16
Step-by-step explanation:
32= 2^5
Thus:
(2^5) ^-4/5
= (2)^ - 4
= (16) ^ - 1
= 1/16
Question 20 of 20
The functions f(x) and g(x) are shown on the graph.
f(x) = x²
What is g(x)?
10
10
f(x)
Answer:
g(x) = - x² - 4
Step-by-step explanation:
g(x) is a reflection in the x- axis of f(x) followed by a vertical translation of 4 units down.
f(x) = x² , then
g(x) = - x² ( reflection in the x- axis )
g(x) = - x² - 4 ( a translation of 4 units down )
2.12 rounded to the nearest hundedth.
Answer: 2.12
Step-by-step explanation:
it's in the hundredths place
2 . 1 2
ones tenths hundredths
whats 26/7 as a mixed number
Answer:3 and 5/7
Step-by-step explanation:
17x12 help what do it equal
Answer:
Step-by-step explanation:
17
12
-----
do 7 x 2
14
then carry the 1
2x1 is 2 plus the 1 from before. it becomes 3
then do 1 x 7 then 1 x 1 but with an extra zero
so it becomes
17
12
---------
34
170
---------
then add it all together
34+170=204
Answer: 17*12=204
Step-by-step explanation: because of G O O G L E
How to do domain and range
Answer:
bjuk
Step-by-step explanation:
ftftrtt987652123456789
esse rode his bike for 2 hours at a constant rate. During the first 1.5 hours, he rode 12 miles. How many miles did Jesse ride his bike during the last half hour? (Enter an exact number.)
mi
In the last half hour 4 miles did Jesse ride his bike.
What is distance?The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given:
Jesse rode his bike for 2 hours at a constant rate.
First 1.5 hours, he rode 12 miles.
According to given question we have
1.5 hours=12 miles
1 hours=12/1.5
0.5 hours=12*0.5/1.5
0.5 hours=4 miles
Therefore, in the last half hour 4 miles did Jesse ride his bike.
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HELP PLESSE i need to hrr it turned in 4 horus
Answer: 5358
Step-by-step explanation:
282
x 18
----------
2538
+282
-----------
5358
Hello can someone please help
The correct statements for this problem are given as follows:
20. Plane N contains line l.
21. Point P lies in line l.
22. PQ lies on plane N.
23. Line l and line m are coplanar.
24. Line l passes through P and Q.
25. Line m and line l intersect at P.
26. Points P and Q are colinear.
What is each thing in this problem?From the graph, we have these following items:
Plane N.Lines m and l.Segment PQ.Points P and Q.For item 20, we have that:
Line l is on plane N, hence:
Plane N contains line l.
For item 21, we have that point P is on both lines, m and l, hence:
Point P lies in line l.
For item 22, we have that points P and Q are on the plane N, hence:
PQ lies on plane N.
For item 23, we have that the lines are on the same plane, hence:
Line l and line m are coplanar.
For item 24, we have that points P and Q are both on line l, hence:
Line l passes through P and Q.
From it, we can also solve item 26, as follows:
Points P and Q are colinear.
And for item 25, the two lines intersect at point P, hence:
Line m and line l intersect at P.
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(a) Write an equation in terms of x that represents the problem.
(b) Solve the problem.
The difference of a number and 16 is the same as the product of the number and 3. Find the number.
Answer:
-8
Step-by-step explanation:
x - 16 = 3x
Solve for x
-2x = 16
x = -8
Marty placed $4000 into an account earning 4% simple interest. At the end of the year he moved the total amount to a new account earning 5% interest. Determine the amount of money Marty would have at the end of the second year.
Simple interest , 4368 is the amount of money Marty would have at the end of the second year.
What does the term "simple interest" mean?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.P = $4000 R = 4% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4000 * 4 * 1}{100}[/tex] = 160
So, the total amount is ( 4000 + 160) = 4160
Second year
P = 4160 , R = 5% T = 1
then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]
= [tex]\frac{4160 * 5 * 1}{100}[/tex] = 208
So, the total amount is ( 4160 + 208 ) = 4368
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Ken is playing with building blocks. He wants to put all 64 blocks into the same number of stacks. How many blocks could he put in each stack
Answer: He could put 8 blocks in 8 stacks
Step-by-step explanation:
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.
So we have:
Number of blocks = 64
Number of stacks = x
To find out how many blocks can be put in each stack, we can set up the following equation:
64 / x = y
where y is the number of blocks in each stack.
Solving for y, we get:
y = 64 / x
So if Ken wants to put all 64 blocks into the same number of stacks, he can put:
64 blocks in 1 stack
32 blocks in 2 stacks
16 blocks in 4 stacks
8 blocks in 8 stacks
4 blocks in 16 stacks
2 blocks in 32 stacks
1 block in 64 stacks
Therefore,
Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.
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A second degree polynomial with zeros at 4 and at 7 passes
through the point (1,9). Its equation has the form p(x) = ax² +
bx + c.
Find the value of a.
The value of a in Quadratic function ax^2 + bx + c is 1.
In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.
the polynomial function f(x)=Ax^2+Bx+C, where A 0 and A, B, and C R. A quadratic function is a second-degree polynomial function in which all the coefficients of the terms with a degree less than 2 are zeros.
Roots of the given equation are 4 and 7.
then the quadratic function whose roots are 4 and 7 is
x^2 - (4+11)x + (4*7)
x^2-11x+28
on comparing this to the Quadratic function ax^2+bx+c
the value of a is 1.
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What is the size of the sample space for
the outcomes of rolling two 20 sided
dice?
Step-by-step explanation:
So, the total number of joint outcomes (a,b) is 6 times 6 which is 36. The set of all possible outcomes for (a,b) is called the sample space of this probability experimentWhat lowest terms fraction equal to 15%
Answer:
3 / 20
Step-by-step explanation:
Take only after the decimal point part for calculation.
.15
Then, divide that value by 1.
.15
1
Multiply both numerator and denominator by 100 (because there are 2 digits after the decimal point so that is 102 = 100).
.15 × 100
1 × 100
=
15
100
;
To simplify
15
100
its lowest terms, find GCD (Greatest Common Divisor) for 15 & 100, which is 5. Here's How to Find GCD of 15 and 100?
15/5
100/5
After simplify or reduce the fraction.
3
20
For how many positive integers n, is 3^n+81 the square of an integer?
The number of positive integers n, that satisfy 3^n+81 the square of an integer is infinite.
How to illustrate the information?Based on the information given, let 3n + 82 = p².
Therefore, 3n = p² - 81
= (p - 9)(p + 9)
Let p = 3q.
3n = (3q - 9)(3q + 9(
= 9(q - 3)(q + 4)
n = 3(q - 3)(q + 3)
n > 0 ; q >= 4 for n = 4, 5, 6....
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10. 1.4810 irrational number
Answer:
List A: 2√2, 3√2, 4√2, …
List B: 2π, 3π, 4π, …
List C: 2log35, 3log35, 4log35, …
Step-by-step explanation:
Help ASAP! 25 Points! What theorem allows you to prove line f is parallel to line g? For what value of x is line f parallel to line g?
PLEASE FIND X FOR ME TOO :) Thank you if you help!
Answer:
Theorems are stated below
x = 6
Step-by-step explanation:
The following theorems can prove that 2 lines are parallel
Two lines are parallel if they’re cut by a transversal such that
Two corresponding angles are congruent.Two alternate interior angles are congruent.Two alternate exterior angles are congruent.Two same-side interior angles are supplementary.Two same-side exterior angles are supplementary.The two angles shown are corresponding angles. They are corresponding because each is in the same position left side) in its group of four angles.
Corresponding angles are equal
Therefore,15x + 9 = 21x - 27
Subtract 9 from both sides:
15x = 21x - 27 - 9
15x = 21x - 36
Subtract 21x from both sides
15x - 21x = - 36
-6x = 36
Divide by -6 both sides
-6x/-6 = 36/-6
x = 6
The two angles are
15x + 9 = 15(6) + 9 = 90 + 9 = 99°
and
21x - 27 = 21(6) - 27 = 126 - 27 =99°
And indeed they are equal
Solve system of equations using substitution method
2x-3y=6
x + y = -12
The first steps in writing f(x) = 3x2 – 24x + 10 in vertex form are shown.
f(x) = 3(x2 – 8x) + 10
(StartFraction negative 8 Over 2 EndFraction) squared = 16
What is the function written in vertex form?
f(x) = 3(x + 4)2 – 6
f(x) = 3(x + 4)2 – 38
f(x) = 3(x – 4)2 – 6
f(x) = 3(x – 4)2 – 38
The function is written in vertex form the equation for is mathematically given as
f(x) = 3(x – 4)2 – 38
This is further explained below.
What is the function written in vertex form?Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.
y = 3(x² - 8x) + 10
We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:
y = 3(x² - 8x + 16 - 16) + 10
y = 3((x - 4)² ) - 48 + 10
y = 3(x - 4)² - 38
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Answer: option D
Step-by-step explanation:
What are the two equations to set up to solve the equation
Answer:
X is 21 (3x = 3*7) and 3x - 2 = 19.Step-by-step explanation:
Solve for X:
3x - 2 = 19= 3*7Solve for 19:
3 * 7 - 2 = 19= 21 - 2 = 19= 1919 = 19.So 3x - 2 = 19 is (3 * 7) - 2 = 19.
Mariana owns a food truck and sells tacos and burritos. Each taco costs $2.50 and each burrito costs $4.00. Th
system of equations represents the results of Mariana's sales yesterday for t tacos and b burritos.
t + b = 60
2.50t + 4.00b = 175.50
How many tacos did Mariana sell yesterday?
Let the cost of one tacos = t
Let the cost of one burritos = b
So, we have this system
t + b = 60 (eq-1)
2.50t + 4.00b = 175.50 (eq-2)
We take equation-1,
We can write,
t + b = 60
t= 60-b (eq-3)
Substitute equation-3 into equation-2,
We can write,
2.50t + 4.00b = 175.50
2.50(60-b) + 4.00b = 175.50
Multiply the values,
2.5(60)-2.5b+4b = 175.5
150-2.5b+4b = 175.50
Subtract the values,
1.5b = 175.5-150
1.5b = 25.5
b = 25.5/1.5
Divide the values,
b = 17
Replace the value 'b' in equation-3,
We can write,
t= 60-b
t= 60-17
t=43
Therefore,
Mariana sell 43 tacos yesterday.
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(2x+3) + 7 and 2x + (3+7)? Expressions equivalent