Answer:
[tex]\boxed{b = -3}[/tex]
Step-by-step explanation:
[tex]\sf -11b+7 = 40\\Subtracting\ 7\ to\ both\ sides\\-11b = 40-7\\-11b = 33\\Dividing\ both\ sides \ by \ -11\\ b = 33/-11\\b = -3[/tex]
If ABC~DEF and the scale factor from ABC to DEF is 3/4, what is the length of DF?
Answer:
the length of DF = 3/4 AC
see below for explanation
Step-by-step explanation:
ABC is said to be approximately equal to DEF
The scale factor from ABC to DEF = 3/4
From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.
We can deduce from the question, ΔABC was dilated to form ΔDEF
In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.
In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :
AB, BC and AC
ΔDEF has 3 sides : DE, EF and DF
If AB corresponds to DE
BC corresponds to EF
AC corresponds to DF
Then:
length DE = scale factor × AB = 3/4 AB
length EF = scale factor × BC = 3/4 BC
length DF = scale factor × AC = 3/4 AC
Therefore, the length of DF = 3/4 AC
What are the next three terms in the sequence -27, -19, -11, -3, 5, ...?
Answer:
13, 21
Step-by-step explanation:
Add 8 to the next number from the left to the right.
Answer:
The next three numbers in the sequence are: 13, 21, 29.
Step-by-step explanation:
Common Pattern: +8
-27 +8 = -19
-19 + 8 = -11
-3 + 8 = 5
5 + 8 = 13
13 + 8 = 21
21 + 8 = 29
In a regional high school swim meet, women’s times (in seconds) in the 200-yard freestyle ranged from 108.5 to 140.6. Estimate the standard deviation, using the Empirical Rule. (Round your answer to 2 decimal places.)
Answer: Estimated the standard deviation α = 5.35
Step-by-step explanation:
According to Empirical rule, the largest value is approximately:
ц + 3α
And the smallest value is approximately:
ц + 3α
Based on the given figures in the question, we can say
ц + 3α = 140.6
ц - 3α = 108.5
Now subtracting these two; we have
ц + 3α - ( ц - 3α ) = 140.6 - 108.5
ц + 3α - ц + 3α = 32.1
6α = 32.1
α = 32.1 / 6
α = 5.35
Estimated the standard deviation α = 5.35
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. VIEW FILE ATTACHED
Answer: see below
Step-by-step explanation:
[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]
P(x) ÷ Q(x)
[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]
P(x) + Q(x)
[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]
P(x) - Q(x)
[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]
P(x) · Q(x)
[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]
Ava is buying paint from Amazon. Ava needs 3⁄4 cup of blue paint for every 1 cup of white paint. Ava has 28 ounces of white paint. How much blue paint does he need?
Answer:
Blue paint=21 ounces
Step-by-step explanation:
3/4 cup=6 ounces
1 cup=8 ounces
3/4 cup of blue paint=6 ounces of blue paint
1 cup of white paint= 8 ounces of white paint
Ava has 28 ounces of white paint
Find the required blue paint
Let the required blue paint=x
Blue paint ratio white paint
6:8=x:28
6/8=x/28
Cross product
6(28)=x(8)
168=8x
x=168/8
x=21 ounces
mark wants to invest $10,000 for his daughter’s wedding. Some will go into a short term CD that pays 12% and the rest in a money market savings account that pays 5% interest. How much should he invest at Each rate if he wants to earn $1095.00 in interest in one year.
A rectangle is to be inscribed in a right triangle having sides of length 6 in, 8 in, and 10 in. Find the dimensions of the rectangle with greatest area assuming the rectangle is positioned as in Figure 1. Figure1
Answer: width = 2.4 in, length = 5
Step-by-step explanation:
The max area of a right triangle is half the area of the original triangle.
Area of the triangle = (6 x 8)/2 = 24
--> area of rectangle = 24 ÷ 2 = 12
Next, let's find the dimensions.
The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.
length = 10 ÷ 2 = 5
Use the area formula to find the width:
A = length x width
12 = 5 w
12/5 = w
2.4 = w
The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.
Let the length and width of the rectangle be x and y.
Then Area of the rectangle = xy
Now, from the triangle we can conclude that
[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]
Put the value of y in Area we get
[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]
Differentiating it w.r.t x we get
[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]
Put A'(x)=0 for maximum /minimum value
[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]
Now, [tex]A''(3)=-\frac{8}{3} <0[/tex]
Therefore the area of the rectangle is maximum for x=3 inch
Now,
[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]
Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.
Learn more:httpshttps://brainly.com/question/10678642
volume= (can someone explain please, im not really understanding this)
Not the greatest picture; I think it's trying to be a house, an A frame with a rectangular base.
This is a prism with a side 3 equilateral triangle at the end and a length of 6.
The area of the triangle is
[tex]\Delta = \dfrac{\sqrt{3}}{4} s^2[/tex]
The volume is area times length,
[tex]V = L \Delta = \dfrac{\sqrt{3}}{4} s^2 L[/tex]
[tex]V = \dfrac{\sqrt{3}}{4} (3^2) 6 = \dfrac{27}{2} \sqrt{3}[/tex]
Answer: (27/2) √3
A rectangle has length 4 inches and width 2 inches. If the length and width of the rectangle are
reduced by 50 percent, by what percent will the area of the rectangle be reduced?
40 percent
50 percent
60 percent
75 percent
Answer:
75%
Step-by-step explanation:
First we can solve the area of the rectangle originally the answer is:
4 × 2 = 8
Then we decrease both measurements by 50% to get the dimensions 1 and 2. The new area will be 1 × 2 which is 2.
2 is 25% of 8 which means that the area of the rectangle has been reduced by 75%.
Graph the linear equation. Find three points that solve the equation. - 3x +2y=2
Answer:
y=3/2x+1 0,1 2,4 4,7
Step-by-step explanation:
-3x+2y=2
+3x
2y=3x+2
/2 /2 /2
y=3/2x+1
Cynthia invested $12,000 in a savings account. If the interest rate is 6%, how much will be in the account in 10 years by compounding continuously? Round to the nearest cent.
Answer:
In 10 years she'll have approximately $21865.4 in her account.
Step-by-step explanation:
When an amount is compounded continuously its value over time is given by the following expression:
[tex]v(t) = v(0)*e^{rt}[/tex]
Applying data from the problem gives us:
[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]
In 10 years she'll have approximately $21865.4 in her account.
Answer:
21,865.43
previous answer left out the last digit
Step-by-step explanation:
Which of the following points is a solution of the inequality y <-Ixl
You did not give any options but i will try to answer.
y < -lxl basically means that the value of y is less than the absolute value of x time - 1.
So if x = 2, then y is any number less than -2.
And if x is -3. then y is any number less than -3.
Happy to help!
Simplify the expression.(4+2i)-(1-i)
ANSWER :
6i - (1-i)
Step - by - step explanation:
( 4 + 2i ) - ( 1 - i )
( 4 + 2 × i) - ( 1 - i )
( 6× i ) - ( 1 - i )
= 6i- (1-i)
Hope this helps and pls mark as brainliest :)
Determine the relationship between the measure of angle ADE and the measure of arc AE by circling one of the statements below.
Answer:
The answer c is correct.
Step-by-step explanation:
When two chords share an endpoint, the inscribed angle has half of the measure of the intercepted arc. In this example, ADE is the inscribed angle, so its measure is one half of the arc AE's measure. m<ADE= 1/2(mAE)
i hope this helped :)
The relationship between the measure of angle ADE and the measure of arc AE is m∠ADE = [tex]\frac{1}{2}[/tex] m (arc AE) .
What seems to be the relationship between an inscribed angle and its intercepted arc?The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent. This is called the Congruent Inscribed Angles Theorem
According to the question
The relationship between the measure of angle ADE and the measure of arc AE .
∠ADE is a inscribed angle
arc AE is a intercepted arc
According to Inscribed Angle Theorem
∠ADE = [tex]\frac{1}{2}[/tex] arc AE
Hence, the relationship between the measure of angle ADE and the measure of arc AE is m∠ADE = [tex]\frac{1}{2}[/tex] m (arc AE) .
To know more about Inscribed Angle Theorem here :
https://brainly.com/question/23902018
# SPJ2
A city's population is currently 50,000. If the population doubles every 70 years, what will the population be 280 years from now?
Answer:
200,000
Step-by-step explanation:
The current population: 50,000
Doubling time:70
Population after 280 years=?
280/70=4
50,000*4=200,000
Hope this helps ;) ❤❤❤
Answer: 800,000
Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.
A theater is presenting a program on drinking and driving for students and their parents or other responsible adults. The proceeds will be donated to a local alcohol information center. Admission is $6.00 for adults and $3.00 for students. However, this situation has two constraints: The theater can hold no more than 240 people and for every two adults, there must be at least one student. How many adults and students should attend to raise the maximum amount of money?
Answer:
160 adults and 80 students
Step-by-step explanation:
With the information from the exercise we have the following system of equations:
Let x = number of students; y = number of adults
I want to maximize the following:
z = 3 * x + 6 * y
But with the following constraints
x + y = 240
y / 2 <= x
As the value is higher for adults, it is best to sell as much as possible for adults.
So let's solve the system of equations like this:
y / 2 + y = 240
3/2 * y = 240
y = 240 * 2/3
y = 160
Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.
Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years
Answer:
The value of annuity is [tex]P_v = \$ 7929.9[/tex]
Step-by-step explanation:
From the question we are told that
The periodic payment is [tex]P = \$ 250[/tex]
The interest rate is [tex]r = 5\% = 0.05[/tex]
Frequency at which it occurs in a year is n = 4 (quarterly )
The number of years is [tex]t = 10 \ years[/tex]
The value of the annuity is mathematically represented as
[tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)
substituting values
[tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]
[tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]
[tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]
[tex]P_v = \$ 7929.9[/tex]
ANSWER ASAP. Which number line correctly shows –3 – 1.5? A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from 0 to 3 and from 3 to 4.5. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 3 to negative 1.5 and from 0 to negative 3. A number line going from negative 4.5 to positive 4.5. An arrow goes from negative 1.5 to 1.5 and from 0 to negative 1.5.
Answer:
An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5
Step-by-step explanation:
Start at 0 and move 3 units to the left since it is negative
Move 1.5 units to the left since we are subtracting
We end up at - 4.5
Answer:
An arrow goes from 0 to negative 3 and from negative 3 to negative 4.5
Step-by-step explanation:
-3 is also 0-3
arrow goes from 0 to -3 backwards.
arrow goes from -3 to -4.5 because -3-1.5=-4.5
Convert to a mixed number 8/5
Answer:
The improper fraction 8/5 can be changed to the mixed number 1 3/5 by dividing the numerator (8) by the denominator (5). This gives a quotient of 1 and a remainder of 3.
Step-by-step explanation:
People start waiting in line for the release of the newest cell phone at 5\text{ a.m.}5 a.m.5, start text, space, a, point, m, point, end text The equation above gives the number of people, PPP, in line between the hours, hhh, of 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text and 11\text{ a.m.}11 a.m.11, start text, space, a, point, m, point, end text, when the doors open. Assume that 6\text{ a.m.}6 a.m.6, start text, space, a, point, m, point, end text is when time h = 1h=1h, equals, 1. What does the 232323 mean in the equation above?
Answer:
There are 23 people in line at 6:00 A.M
Step-by-step explanation:
When you plug in h=1, we get 23 people
h corresponds with the time 6:00 am, as a result there are 23 people in line
The equation represents how many people will come as the hour increases.
23 represents the initial amount of people in line.
(got this from Khan academy too:))
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Betty has $33 to buy plants for her greenhouse. Each plant costs $8. How
many plants can she buy? Do not include units in your answer.
Answer:
4 plants
Step-by-step explanation:
If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4
(8 * 4 is 32)
She will have one dollar left but she can't buy another plant since that's not enough.
Answer:
4 plants
Step-by-step explanation:
Take the amount of money she has and divide by the cost per plant
33/8
The amount is 4 with 1 dollar left over
4 plants
Con proceso por favor
Answer:se
Step-by-step explanation:
Which expression is equivalent to x^-5/3?
Answer:
[tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
Step-by-step explanation:
[tex]x^{-\frac{5}{3} }[/tex] = [tex](\sqrt[3]{x} )^{-5}[/tex] = [tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]
Question 15
1 pts
The cost of three avatars and three bats is $29.85. The cost of
three avatars and two bats is $23.90. How much will you pay
altogether if you purchase one of each.
O $5.95
O $8.92
$9.95
O $10.99
O $11.00
1 pts
Question 16
9
Answer:
$9.95.
Step-by-step explanation:
Let's say that you are buying a avatars and b bats.
3a + 3b = 29.85
Divide all terms by 3.
a + b = 9.95
You will pay $9.95 if you buy one of each.
Hope this helps!
Please answer this correctly without making mistakes
Answer:
Step-by-step explanation:
2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.
Graph the equation y = 1/2x + 5 on the coordinate plans provided below.
Answer:
Well, of course, i can not graph it in the coordinate plane in the image, but i can try to teach you how to do it.
We have the function y = (1/2)*x + 5
The first step is to generate pairs (x, y)
You can do it by evaluating the function in different values of x.
For example;
if x = 0
y = (1/2)*0 + 5 = 5
then we have the point (0,5)
if x = 2
y = (1/2)*2 + 5 = 6
Then we have the point (1, 6)
Now, with only two points you can graph the line.
First find the points in the coordinate plane, and mark them.
Now, with a ruler, draw a line that connects the two points.
That line is the graph of the function.
An example of the graph is:
What type of model best fits the height of a tree increases by 2.5 feet each growing season
Answer:
Step-by-step explanation:
A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)
This is the model that best fits the graph describing a growth of a plant
The answer choices below represent different hypothesis tests. Which of the choices are one-tailed tests? Select all correct answers. Select all that apply: H0:p=0.46, Ha:p<0.46 H0:p=0.34, Ha:p≠0.34 H0:p=0.63, Ha:p≠0.63 H0:p=0.35, Ha:p≠0.35 H0:p=0.39, Ha:p<0.39
Answer:
H0:p=0.46, Ha:p<0.46
H0:p=0.39, Ha:p<0.39
Step-by-step explanation:
A one tailed test occurs in such a way that the value/results gotten is one sided and can either be lesser or greater than the particular given value but cannot be both.
Thus, in this case a one sided test includes
H0:p=0.46, Ha:p<0.46
H0:p=0.39, Ha:p<0.39
The number of users on a website has grown exponentially since its launch. After 1 month, there were 120 users. After 4 months, there were 960 users. Find the exponential function that models the number of users x months after the website was launched. Write your answer in the form f(x)=a(b)x.
Answer:
f(x) = 60(2)ˣ
Step-by-step explanation:
f(x) = a(b)ˣ
After one month:
120 = a(b)¹
After four months:
960 = a(b)⁴
Divide the second equation by the first:
8 = b³
b = 2
Plug into either equation and find a.
120 = a(2)¹
a = 60
Therefore, f(x) = 60(2)ˣ.