Answers
Answer:
(a) 8x-16 [tex]cm^2[/tex]
Step-by-step explanation:
From the given figure of trapezoid:
Height, h=8 cm
Bases, [tex]b_1=(x-6)cm \; and \; b_2=(x+2)cm[/tex].
Area of the trapezoid,
[tex]A=\frac 1 2 h (b_1 + b_2) \\\\=\frac 1` 2 \times 8 ( x-6+x+2) \\\\=4(2x-4) \\\\[/tex]
[tex]=8x-16 cm^2[/tex]
Hence, option (a) is correct.
Related Questions
Which graph represents the solutions to the inequality |2x - 6 < 4? (5 points)
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
9
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
-9-8-7 -6 -5 -4 -3 -2 -1
0 1 2 3 4 5 6 7 8 9
Answers
Answer:
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Step-by-step explanation:
Given the expression
[tex]|2x\:-\:6|\:<\:4[/tex]
[tex]\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex]
[tex]-4<2x-6<4[/tex]
[tex]2x-6>-4\quad \mathrm{and}\quad \:2x-6<4[/tex]
condition 1
[tex]2x-6>-4[/tex]
Add 6 to both sides
[tex]2x-6+6>-4+6[/tex]
[tex]2x>2[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}>\frac{2}{2}[/tex]
[tex]x>1[/tex]
condition 2
[tex]2x-6<4[/tex]
Add 6 to both sides
[tex]2x-6+6<4+6[/tex]
[tex]2x<10[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}<\frac{10}{2}[/tex]
[tex]x<5[/tex]
combine the intervals
[tex]x>1\quad \mathrm{and}\quad \:x<5[/tex]
Merging overlapping intervals
[tex]1<x<5[/tex]
Thus,
[tex]\left|2x-6\right|<4\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:1<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(1,\:5\right)\end{bmatrix}[/tex]
Therefore, the 3rd graph represents the solutions to inequality.
Please also check the graph below.
Tyler has a ramp for his skateboard that measures 17 feet long. The vertical height is 8
feet from the ground to the top of the ramp. What is the horizontal distance from the base
of the ramp to the support? (Hint: draw a picture)
Answers
Answer:
15
Step-by-step explanation:
Hypotenuse: 17ft long
Height: 8ft long
17^2 = 8^2 + b^2
b^2 = 17^2 - 8^2
b = √225
b = 15
julian needs to spend at least seven hours each week practicing the drums. he has already practiced five and one third hours this week. he wants to sp
Answers
The minimum number of hours is 5/6 and the inequality is x ≥ 5/6 hours.
What exactly is an inequality?An inequality is a relationship that compares two numbers and perhaps other mathematical expressions that are not equal. It is most commonly used to compare the sizes of two numbers on a number line.
According to the given data:Let x = the number of hours practicing the drums
we know that Julian needs to spend at least seven hours each week practicing
the drums x ≥ 7 hours
He has already practiced 5*(1/3) hours this week.
Convert mixed number to an improper fraction 5*(1/3) = 16/3hours.
Subtract 16/3 from 7,
7 - (16/3)
= 5/3
Divide 5/3 by 2,
(5/3)/2
=5/6
Hence,
The inequality that represent the minimum number of hours he needs to practice on each of the two days is x ≥ 5/6 hours.
To learn more about inequality visit:
https://brainly.com/question/20383699
#SPJ4
The given question is not complete.
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced 5 1/3 hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
6 cm
5 cm
Determine the value of x.
A. 11 cm
O B. 461 cm
OC V11 cm
D. 3 cm
OE. 1 cm
Answers
Answer:
A.
Step-by-step explanation:
A car traveled 180 miles at a constant rate.
Part 1. Complete the table to show the rate at which the car was traveling if it completed the same distance in each number of hours.
travel time (hours) rate of travel (miles per hour)
(5:
1040)
(4.5:
520)
(3:
360)
(2.25:
180)
Answer 1:
1040
Answer 2:
520
Answer 3:
360
Answer 4:
180
Answers
help what does 2 1⁄3 ÷ 1 1⁄2 =
Answers
Answer:
[tex]1\frac{5}{9}[/tex]
Step-by-step explanation:
This is the answer because:
1) Reduce the expression, if possible, by cancelling the common factors.
2) You can also find the reciprocal of 1 1/2 = 3/2 while dividing the expression:
1. Convert both fractions into improper fractions:
[tex]2\frac{1}{3} = \frac{7}{3}[/tex]
[tex]1\frac{1}{2} = \frac{3}{2}[/tex]
2. Divide both fractions:
[tex]\frac{7}{3}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{7}{3}[/tex] x [tex]\frac{2}{3}[/tex] = [tex]\frac{14}{9}[/tex] = [tex]1\frac{5}{9}[/tex]
Therefore, the answer is [tex]1\frac{5}{9}[/tex]
Hope this helps! :D
A parabola can be drawn given a focus of (0, 2) and a directrix of y = 0. Write the
equation of the parabola in any form.
Answers
Given:
Focus of a parabola = (0,2)
Directrix: y=0.
To find:
The equation of parabola.
Solution:
The equation of parabola is
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex] ...(i)
where, (h,k) is vertex, (h,k+p) is focus, y=k-p is directrix.
Focus : [tex](h,k+p)=(0,2)[/tex]
On comparing both sides, we get
[tex]h=0[/tex]
[tex]k+p=2[/tex] ...(ii)
On comparing y=k-p and y=0, we get
[tex]k-p=0[/tex] ...(iii)
Adding (ii) and (iii), we get
[tex]2k=2[/tex]
[tex]k=1[/tex]
Putting k=1 in (ii).
[tex]1+p=2[/tex]
[tex]p=2-1[/tex]
[tex]p=1[/tex]
Putting h=0, k=1 and p=1 in (i).
[tex]y=\dfrac{1}{4(1)}(x-(0))^2+(1)[/tex]
[tex]y=\dfrac{1}{4}x^2+1[/tex]
Therefore, the equation of required parabola is [tex]y=\dfrac{1}{4}x^2+(1)[/tex].
3x + 4 = -11 what is the value of x in this equation?
Answers
Answer:
Step-by-step explanation:
3x + 4 = - 11
3x = - 11 - 4
3x = - 15
x = - 15/3
x = - 5
Answer:
x = -5
Step-by-step explanation:
3x + 4 = -11
Isolate 3x.
3x = -11 - 4
Evaluate.
3x = -15
Find x.
x = -15 ÷ 3
x = -5
Darien could swim 30 laps an
hour last year. This year he can
swim 36 laps an hour. Determine the
percent change
Answers
Answer:
D
Step-by-step explanation:
If the percent change is 30 to 36 you can already see that it is an increase
here is the work
36 - 30
30
x 100% = 20%
Answer:
20% increase, which corresponds to the light
Step-by-step explanation:
(y - x)/x * 100
(36 - 30)/30 * 100
(6 * 100)/30
600/30
20% increase
Yesterday 3. Hali was making a bouquet of flowers. 60% of her bouquet was made up of roses. Show much of her bouquet was made up of roses on the model below. Write the fraction and decimal equivalent to 60%. h 441
Answers
Answer:
0.6, 3/5
Step-by-step explanation:
60%=
100% * 60/100=
1*60/100=
60/100=6/10=0.6
6/10=3/5
use the substituation method to solve 6=-4x+y -5x-y=21
Answers
Answer:
x=-3 y=-6
Step-by-step explanation:
solve for y on the first equation then plug the answer into the second
In an equation, y varies directly as x varies. If y = 72 when x = 12 what is the value of x when y = 48?
Answers
Answer:
8
Step-by-step explanation:
y=kx where k is a constant.
72=12k
k=72/12=6
y=6x
48=6x
x=48/6=8
Step 2 of the Coefficient Method involves blank x-term and y-term coefficients.
Answers
Answer:
Dividing
Step-by-step explanation:
A school has 109 students signed up for a science workshop. The school will buy every student attending the workshop a pencil, a folder, and an eraser. A package of 12 erasers is $0.75. Only whole packages of erasers can be bought. Folders are $0.10 each. A package of 8 pencils is $0.50. Only whole packages of pencils can be bought. How much will the school spend?
Answers
Answer:
The amount is $25.4
Step-by-step explanation:
There are 109 students to attend the science workshop.
Number of erasers needed is 109, but whole packages of erases can be bought which consist 12 erasers. The total packages of erasers needed would be 10.
The cost of 10 packages of erasers = $0.75 x 10
= $7.5
The cost of 109 folders = 109 x $0.10
= $10.9
Number of pencils needed is 109, but whole packages of pencils can be bought which consist 8 pencils. The total packages of pencils needed would be 14.
The cost of 14 packages of pencils = $0.50 x 14
= $7.0
Total cost = $7.5 + $10.9 + $7.0
= $25.4
The amount that would be spent by the school is $25.4
Answer:
25.4
Step-by-step explanation:
Which expression is equivalent to (3x-2)(x+3) ?
A. 4x^2 + 4x + 1
B. 3x^2 + 11x + 6
C. 3x^2 + 7x - 6
D. 4x + 1
Answers
Answer: C. 3x^2 + 7x - 6
Step-by-step explanation:
3x^2 + 9x -2x -6
3x^2 + 7 - 6
Hope you got it.
Mark me as Brainliest Please.
Which equation represents the linear function that is shown on the graph below ?
A. Y=1/2 x+4
B. Y=1/2 x-2
C. Y=4 x-2
D. Y= -2 x +4
Answers
Answer:
First one
Step-by-step explanation:
Y=1/2x+4
i will give brainliest to best answer
Answers
That's a Congruent Triangle question.
The first thing that we should to analize is it: What figure is EFGH? The question say for us that [tex]\overline{EF} \cong \overline{GH}[/tex] and [tex]\overline{EH} \cong \overline{GF}[/tex], therefore, EFGH is a parallelogram because its parallel sides are congruents (equals).
Now, we should to proof that [tex]\triangle EFH \cong \triangle GHF[/tex]. The simbol "≅" means congruence, that is, [tex]\triangle EFH \cong \triangle GHF[/tex] means that the triangles EFH and GHF are equals.
Let's proof:
[tex]\overline{HF}[/tex] is a diagonal of the parallelogram EFGH. When we have a diagonal in a parallelogram, the opposite angles are congruents (look at the picture: the blue angles are congruent and the red angles are congruents too). Therefore, [tex]E\hat{F}H \cong F\hat{H}G[/tex] and [tex]E\hat{H}F \cong H\hat{F}G[/tex].
Both triangle has a comum side: the diagonal [tex]\overline{HF}[/tex]. The diagonal [tex]\overline{HF}[/tex] is between two angles that we know that are congruents, Therefore, by the case ASA (Angle, Side, Angle), we proof that [tex]\triangle EFH \cong \triangle GHF[/tex].
What expressions are equal to -5
Answers
-5+0
-3-2
-2-3
-4-1
-1-4
PLEASE HELP MEEEEE!!!!!
Answers
Answer:
The mass of 10mL of this liquid would be 25g.
Step-by-step explanation:
The formula for mass in relation to density and volume is:
mass=Density*volume
Knowing this, we could plug in the given volumes and solve:
m=Dv
m=(2.5g/mL)*(10mL)
m=25g
I hope this helps!
Which function is linear?
A)
f(x) = 8x² + 2
B)
8
f(x) -
X
+ 2
f(x) - 8x? - 2
D)
f(x) = -2
Answers
Answer:
4
Step-by-step explanation:
5-1=4
Answer:
B)
Step-by-step explanation:
Assuming the numbers following the variables are exponents, (ex: 8x2, x8), the only function that is linear would be option B. This is because linear functions do not have exponents following their variables. If graphed, t are a straight line.
6.
Write an equation of the line that passes through (3,8) and is perpendicular to the line y=5x−4.
Answers
Answer:
use desmos graphing and put (3,8) and y=5x-4 it help me
if a bag has 22 orange 18 red and 8 blue marbles what is the probability, that I draw blue marble, keep it, then draw another blue marble?
Answers
Answer:
The probability is 8/48
Step-by-step explanation:
There is a total of 48 marbles and 8 of them are blue.
\left|\left|x-5\right|+2\right|\le 3
Answers
Answer:= x +27 Solve for x x = 326 = 8 32 ≈ 8.666666667
Find the area with 12 and 4
Answers
Answer:
48
Step-by-step explanation:
The area is multiplying.
12 x 4 = 48
Hope It Helps
Sorry If I'm Wrong
state if the triangle is a right triangle.
a²+b²=c²
4²+ 8\sqrt 2²=12²
16+11.3=144
27.3=144
this answer in the back says that this triangle is supposed to be a right triangle so could you help me if you see an errors that I made. I'm pretty sure I did in regards to the square root section.
Answers
Yes, it is a right-angled triangle.
A right triangle, sometimes known as a right-angled triangle, or more technically an orthogonal triangle, formerly known as a rectangled triangle, is a triangle with one right angle or two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.Use the Pythagorean theorem.The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.a² + b² = c²(4)² + (8√2)² = (12)²16 + (64*2) = 14416 + 128 = 144144 = 144The left hand side is equal to the right hand side.Hence, it is a right angled triangle.To learn more about the Pythagorean theorem, visit :
https://brainly.com/question/14930619
#SPJ9
Today the temperature in New York City is -3 degrees and is expected to rise one half of a degree each day. It's 6 degrees in Juneau, Alaska and expected to fall 1 degree every 4 days. How long will it take for the temperature to be the same in the two cities? What will the temperature be?
Answers
Answer:
12 days
3 degrees
Step-by-step explanation:
Let y be the temperature of the cities after x days have passed.
Temperature of New York City
[tex]y=-3+\dfrac{1}{2}x[/tex]
In Juneau the temperature falls by 1 degree per 4 days. So, in 1 day the temperature falls be [tex]\dfrac{1}{4}[/tex] degree.
The minus sign is due to the fact that the temperature is falling
Temperature in Juneau Alaska
[tex]y=6-\dfrac{1}{4}x[/tex]
We need to find the value of x for which y will be equal
[tex]-3+\dfrac{1}{2}x=6-\dfrac{1}{4}x\\\Rightarrow \dfrac{1}{2}x+\dfrac{1}{4}x=6+3\\\Rightarrow \dfrac{3}{4}x=9\\\Rightarrow x=\\\Rightarrow x=9\times \dfrac{4}{3}\\\Rightarrow x=12\ \text{days}[/tex]
[tex]y=-3+\dfrac{1}{2}x=-3+\dfrac{1}{2}\times 12\\\Rightarrow y=3\ \text{degrees}[/tex]
Hence, in 12 days the temperature will be same in both the cities will be 3 degrees.
There are 270 calories in 5 ounces of a certain ice cream how many calories are there in 2 pounds
Answers
1 pound = 16 ounces (general knowledge)
270 calories divided 5 ounces
1 ounce= 54 calories
2 pounds = 32 ounces
32 ounces × 54 calories = 1728
2 pounds = 1728 calories
The original cost of Sam’s investment is $10,000. After liquidating the investment, Sam calculated his real return to be $10,700. What is the return on investment (ROI)?
Answers
Answer:
7%
Step-by-step explanation:
Step one:
given data
The original cost of Sam’s investment is $10,000
Sam calculated his real return to be $10,700
Required:
the interest made from the investment is
10700-10000= $700
Step two:
The ROI is a percentage that tells us the interest made
interest/investment*100
=700/10000*100
=0.07*100
= 7%
The ROI is 7%
Which point lies on the circle x^2+y^2=100
A (0,-100)
B (10,-10)
C (25,75)
Answers
Answer:
NOT a single ordered pair satisfies the equation.
Step-by-step explanation:
Given the equation
[tex]x^2+y^2=100[/tex]
Let us substitute all the given ordered pairs to find which ordered pair satisfies the equation.
For (0, -100)
[tex]x^2+y^2=100[/tex]
substitute x=0 and y=-100
[tex]0^2+\left(-100\right)^2=100[/tex]
[tex]10000=100[/tex]
FALSE
Thus, the ordered pair (0, -100) does NOT satisfy the equation.
For (10, -10)
[tex]x^2+y^2=100[/tex]
substitute x=10 and y=-10
[tex]10^2+\left(-10\right)^2=100[/tex]
[tex]200=100[/tex]
FALSE
Thus, the ordered pair (10, -10) does NOT satisfy the equation.
For (25, 75)
[tex]x^2+y^2=100[/tex]
substitute x=25 and y=75
[tex]25^2+\left(75\right)^2=100[/tex]
[tex]6250=100[/tex]
FALSE
Thus, the ordered pair (25, 75) does NOT satisfy the equation.
Therefore, NOT a single ordered pair satisfies the equation.
Find the compound interest on ₹ 31,250 at 12% pa for 2 1/2 years
pls give step by step explanation
Answers
Answer:
42,183
Step-by-step explanation:
We will use the Continuous Compounding Interest since a regular interval was not stated.
P(t) = Pe^(rt)
We will plug in the variables to the formula
P(t) = 31250 * e^(.12 * 2.5)
We can simplify and evaluate the compound interest.
P(t) = 42183.08