Answer: The area, in square feet, of the piece of wood is [tex]32 ft^{2}[/tex].
Step-by-step explanation:
Give: Length = 8 feet
Width = [tex]\frac{1}{2} \times 8[/tex] = 4 feet
As piece of wood is similar to that of a rectangle. Hence, formula to calculate area is as follows.
[tex]Area = length \times width[/tex]
Substitute the values into above formula as follows.
[tex]Area = length \times width\\= 8 feet \times 4 feet\\= 32 ft^{2}[/tex]
Thus, we can conclude that the area, in square feet, of the piece of wood is [tex]32 ft^{2}[/tex].
What is the length of the hypotenuse of the triangle below?
Answer:
Correct option is A
Step-by-step explanation:
According to given question,
[tex]sin 45^{0} =\frac{5\sqrt 2}{h} \\0.707=\frac{5\sqrt 2}{h} \\h=\frac{5\sqrt 2}{0.707} \\h=1[/tex]
Therefore, correct option is A.
ABC was dilated to create A' B' C'. What is the center of dilation? And what is the scale factor of the dilation?
Given:
In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).
The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).
To find:
The center of dilation and the scale factor.
Solution:
In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.
From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).
Therefore, the center of dilation is (0,0).
If a figure is dilated by factor k and the center of dilation is origin, then
[tex](x,y)\to (kx,ky)[/tex]
[tex]A(-2,2)\to A'(k(-2),k(2))[/tex]
[tex]A(-2,2)\to A'(-2k,2k)[/tex]
It is given that A'(-4,4). So,
[tex](-2k,2k)=(-4,4)[/tex]
On comparing both sides, we get
[tex]-2k=-4[/tex]
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2.
A flower bed is in the shape of a triangle, with a base of 11 feet and a height of 7 feet. What is the area of the flower bed?
a. 38.5 square feet
b. 42.5 square feet
c. 72 square feet
d. 77 square feet
Answer:
a. 38.5 square feet.
Step-by-step explanation:
11*7 = 77
77/2 = 38.5
Hope this helps! Good luck with your work.
Mark as brainliest if you'd like :D
Answer plzzzzzzzzzzzzzzzz
Answer:
120 m squared
Step-by-step explanation:
Volume problems are very simple:
Just multiply the base x height x length
So 10 x 2 x 6, which is 120.
Therefore, the volume of this shape is 120 m squared.
Answer:
120 m
Step-by-step explanation:
Simply Multiply all the given measurements so
10m x 2m x 6m = 120m
So as simple as that.
Thank you! ^^
2x+1>
[tex]2x + 1 \geqslant 5 - x[/tex]
5-x
Solve the rational equation: x/x+1 = 2/x+1
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{x}{x+1} =\frac{2}{x+1}[/tex]
x ≠ 0
x ≠ - 2
x ≠ - 1
[tex]\frac{x}{x+1}(x+1) =\frac{2}{x+1}(x+1)[/tex]
x = 2
Find the missing angle measurements
Answer:
look at picture.
Step-by-step explanation:
every angle in a triangle equals 180° and every straight line equals 180°. So you just take the angles given in each triangle and subtract from 180° to get the total of the 3rd angle.
A. The scale along the vertical axis is not appropriate for the data.
B. The intervals along the vertical axis are not equal.
C. The average temperatures of some of the days are not correctly plotted.
D. On January 4 the temperature was higher than any other day.
Answer:
A
Step-by-step explanation:
beacuse it is more reasonable hope this helps
What is the measure of the angles? (Help pls)
Answer:
13 degrees
Step-by-step explanation:
working out is attached
hope it helps:)
Find the surface area of the "unrolled" cylinder where a = 4 cm and b= 10 cm.
Leave your answer in terms of Pi
Answer:
= 140.544cm^2
Step-by-step explanation:
Given data
a is the radius=4cm
b is the lenght= 10cm
We two circles, hence the area of the circles is given as
Area= 2(πr^2)
Area= 2(3.142*4^2)
Area= 2(50.272)
Area= 100.544cm^2
Area of the rectangular shape= 4*10= 40cm^2
Hence the total area = 100.544+40
= 140.544cm^2
Describe the relationship between ∠2 and ∠8
Answer:
Alternate Interior Angles
Step-by-step explanation:
Angles can be corresponding; alternate or same side; or interior or exterior. The angles 2 and 8 are on opposite sides of the transversal; this means that they must be alternate angles. Additionally, they are both within the parallel lines, so they are interior. Alternate interior angles are always congruent. Therefore, their measurements must be equal.
Answer:
They are alternate interior angles
Step-by-step explanation:
<2 and <8 are inside the parallel lines and on opposite sides of the transversal
They are alternate interior angles
How to solve a+52/3=9
Answer:
-25/3
Step-by-step explanation:
Answer:
a+52/3=9
a + 52/3 - 52/3 = 9 - 53/3
a=[tex]\frac{27- 53}{3}[/tex]
a= [tex]\frac{26}{3}[/tex]
Step-by-step explanation:
what are the step for distributive property to find the product for (a+8) (a-3)?
Answer:
---
Step-by-step explanation:
(a+8)(a-3)
You multiply a*a and a*-3 first.
a²-3a
Then you multiply 8*a and 8*-3.
8a-24
Then combine.
a²-3a+8a-24
Combine like terms.
a²+5a-24
So dat the answer.
---
hope it helps
Answer:
See below
Step-by-step explanation:
(a+8)(a-3)
See image for extra explanation.
a * a = a^2
a * -3 = -3a
8 * a = 8a
8 * -3 = -24
a^2 - 3a + 8a - 24
a^2 + 5a - 24
What is the area of a figure with the measurements of 3,6, and 5?
Answer:
I think it is 181m.
Step-by-step explanation:
[tex]by \: imagination \: you \: separate \: all \: the \: shapes[/tex]
you also name it .
I name the triangle area A
I name the rectangle area B
it is a triangle because it has different measurements on its sides.
I name the semi- circle area C.
[tex]area \: of \: a \: triangle \: = \\ \frac{1}{2} \times b \times h \\ \frac{1}{2} \times 5 \times 3 \\ \frac{1}{ 2} \times 15 \\ 7.5[/tex]
[tex]aea \: of \: a \: rectangle \: = l \times b \\ 5 \times 6 = \\ 30[/tex]
[tex]area \: of \: a \: semi \: circle \: = \frac{1}{2 } \times \pi \times {r}^{2} \\ \frac{1}{2} \times 3.14 \times 3 \times 3 \\ \frac{1}{2} \times 3.14 \times 9 \\ \frac{1}{2} \times \frac{314}{10} \times 9 \\ [/tex]
[tex]you \: then \: cancle \: 134 \: by \: 2[/tex]
[tex] = \frac{154}{10} \times 9[/tex]
[tex] = \frac{1431}{10} \\ 143.1[/tex]
[tex]you \: now \: add \: all \: the \: ares \: to \: get \: your \: full \: area \\ 7.5 + 30 + 143.1 \\ = 180.6 \\ to \: the \: nearest \: hundred \: will \: be \: 181m[/tex]
Find the circumference of a circle whose area is /. A. B. C. D. Please select the best answer from the choices provided A B C D
Answer:
Circumference of circle = (15.5)π cm
Step-by-step explanation:
Missing information:
Area of circle = 60π cm²
Find:
Circumference of circle
Computation:
Area of circle = πr²
Area of given circle = π(Radius of circle)²
60π = πr²
60 = r²
Radius of circle = 7.75 cm (Approx)
Circumference of circle = 2πr
Circumference of circle = 2(π)(7.75)
Circumference of circle = (15.5)π cm
pls help me ill give brainliest and no links pls ty!:)
Given : GH bisects ∠FGI
It means : ∠FGH and ∠HGI are equal
Given :
∠FGH = (5x - 8)°
∠HGI = (6x - 15)°
⇒ 5x - 8 = 6x - 15
⇒ 6x - 5x = 15 - 8
⇒ x = 7°
Substituting the value of x, We get :
∠FGH = 5(7) - 8 = (35 - 8) = 27°
∠HGI = 6(7) - 15 = (42 - 15) = 27°
∠FGI = ∠FGH + ∠HGI = (27 + 27) = 54°
If y = 100 when x = 15, which equation could you use to find the value
of k?
Answer:
y+x=k
Step-by-step explanation:
Solve for x.
Please helpppp!
Answer:
Pythagoreas Theorem
Step-by-step explanation:
a^2+b^2=c^2
4^2+b^2=15^2
16+b^2=225
b^2= 209
14.45=b
A school has two photocopiers. On any given day, machine A has an 8% chance of malfunctioning
and machine B has a 12% chance of malfunctioning. Determine the probability that on any given
day, both machines will: malfunction
according to a survey, the population of a city doubled in 12 years.
The annual rate of increase of the population of this city is approximately _____. The population will grow to three times its current size in approximately ______.
First box of answers: 2.50, 5.78, 12.0, 50.0
Second box of answers: 18, 19, 23, 24.
Answer:
5.78
19
Step-by-step explanation:
Let original population be, P = x
Growth in 12 years, A = 2x
Rate be = r
Time = 12years
Find the rate :
[tex]A = P(1 + \frac{r}{100})^t[/tex]
[tex]2x = x(1 + \frac{r}{100})^{12}\\\\\frac{2x}{x} =(1 + \frac{r}{100})^{12}\\\\2 = (1 + \frac{r}{100})^{12}\\\\ \sqrt[12]{2} = (1 + \frac{r}{100})\\\\\sqrt[12]{2} - 1 = \frac{r}{100}\\\\2^{0.08} - 1 = \frac{r}{100}\\\\1.057 - 1 = \frac{r}{100}\\\\0.057 \times 100 = r\\\\r = 5.7 \%[/tex]
The annual rate of increase of the population of this city is approximately 5.78.
Find time in which the population becomes 3 times.
That is A = 3x
P = x
R= 5.78%
[tex]A = P( 1 + \frac{r}{100})^t\\\\3x = x ( 1 + \frac{5.78}{100})^t\\\\3 = (1.0578)^t\\\\log \ 3 = t \times log \ 1.0578 \\\\t = \frac{log \ 3}{ log \ 1.0578 }\\\\t = 19.55[/tex]
The population will grow to three times its current size in approximately 19years .
5.78% ,19 years are the answers.
2=(1+r)^12
r=(2)^(1÷12)−1
R=0.0578*100=5.78%
3=(1+0.0595)^t
t=log(3)÷log(1.0595)
t=19 years
What is an exponential growth model?
Exponential growth and exponential decay are two of the most common uses of exponential functions. Systems with exponential growth follow a model of the form y = y0ekt. In exponential growth, the growth rate is proportional to the amount present. In other words, for y'= ky
exponential function, multiply a by x to produce y. The exponential graph looks like a curve that starts with a very flat slope and becomes steep over time.
The exponential model, like the sphere model, starts at the origin and operates linearly near it. However, the increasing slope of the curve is less than the slope of the spherical model.
Learn more about exponential function here:https://brainly.com/question/2456547
#SPJ2
A study of a population of 102
parrakeets revealed that 4 out
of every 12 parakeets in the
population are blue.
Based on the results of this
study, how many parakeets in
the population are NOT blue?
Answer:
68
Step-by-step explanation:
4 out of 12 are blue.
Then 8 out 12 are not blue.
8 out of 12 is the same as the fraction 8/12 which can be reduced to 2/3.
2/3 of the birds are not blue.
2/3 of 102 = 2/3 * 102 = 68
Answer: 68
12. You are driving on a major highway. If you drive in the left lane traffic is moving at 60mph, if you drive in the right lane, traffic is moving at 40mph. You can drive a maximum of 10 hours and need to go a minimum of 500 miles. Use the above information to answer part a and b below: 12a. Create a system of inequalities to model the potential travel time in 3 points each lane.
12b. If you want to spend an amount of time in each lane, would this allow you to reach your goal of driving 50 miles? just to fight your conclusion
you are driving onajor highway 94 mp
Jackson's cupcake recipe calls for 1 3/4 cups of sugar. He plans to make 3 1/2 times the recipe. How much sugar, in
cups, will Jackson need?
Answer:
6 1/8 cups
Step-by-step explanation:
multiply both numbers together
Twice the complement of an angle is 25 less than 3 times the angle. Find the measure of both angles.
Answer:
Step-by-step explanation:
Let the angles size = x
The complement of the angle is 90 - x
Two times the compliment is 2*(90 - x)
Three times the angle is 3x
25 less than 3 times the angle = 3x - 25
Now you have to equate the two bolded pieces of information.
3x - 25 = 2(90 - x) Remove the brackets
3x - 25 = 180 - 2x Add 25 to both sides
25 25
3x = 205 - 2x Add 2x to both sides.
2x 2x
5x = 205 Divide by 5
5x/5 = 205/5
x = 41
The compliment of x = 90 - 41 = 49
The angle itself = 41
Which Statement About The Data Is True? 52 56 60 64 68 72 76 80 A. The difference between the medians is about 4 times the range. B. The difference between the medians is about 4 times the IQR. C. The difference between the medians is about 2 times the range. D. The difference between the medians is about 2 times the IQR.
Answer:
The answer is "Option B".
Step-by-step explanation:
IQR for the first boxplot [tex]= Q_3 - Q_1 = 77-73 = 4[/tex]
IQR for the first boxplot [tex]= Q_3 - Q_1 = 63-59 = 4[/tex]
Calculating the median for the first boxplot [tex]= 76[/tex]
Calculating the median for the second boxplot [tex]= 60[/tex]
Calculating the difference:
[tex]\to 76-60 = 16[/tex]
therefore, the difference between medians is about 4 times the IQR.
Answer:
B
Step-by-step explanation:
did the test
Please help me! Thank you so much.
Answer:
57
Step-by-step explanation:
3^r = 19
Multiply each side by 3
3 * 3^r = 19 *3
We know that a^b * a^ c = a^ ( b+c)
3^1 * 3^r = 19 *3
3^(r+1) = 19*3
3^(r+1) = 57
a circle shown below, m AC = 89° and m BC = 153°. Determine m∠ACB.
Answer:
m<ACB = 59degrees
Step-by-step explanation:
To get <ACB, first we need arcAB
arcAB + arcAC + arcBC = 360
arcAB + 89 + 153 = 360
arcAB+242 = 360
arcAB = 360 - 242
arcAB = 118
Also, m<ACB = 1/2arcAB
m<ACB = 1/2*118
m<ACB = 59degrees
Solve the equation y - 2.7 = -2.0 + 2y
Answer:
y = -0.7
Step-by-step explanation:
Reorder the terms:
-2.7 + y = -2.0 + 2y
Solving
-2.7 + y = -2.0 + 2y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-2y' to each side of the equation.
-2.7 + y + -2y = -2.0 + 2y + -2y
Combine like terms: y + -2y = -1y
-2.7 + -1y = -2.0 + 2y + -2y
Combine like terms: 2y + -2y = 0
-2.7 + -1y = -2.0 + 0
-2.7 + -1y = -2.0
Add '2.7' to each side of the equation.
-2.7 + 2.7 + -1y = -2.0 + 2.7
Combine like terms: -2.7 + 2.7 = 0.0
0.0 + -1y = -2.0 + 2.7
-1y = -2.0 + 2.7
Combine like terms: -2.0 + 2.7 = 0.7
-1y = 0.7
Divide each side by '-1'.
y = -0.7
Simplifying
y = -0.7
2) find the volume of the trapezoid prism 7in 6in 4in 12in
Answer: 228 in3 (sorry I don’t know how to do the mini number at the top)
A prism with a volume of 148 cubic cm is dilated by a factor of 5.5.
The volume of the dilated prism is ___ cubic cm.
volume = 148 × 5.5 cube
= 24623.5 cubic cm