Answer:
[tex] x = \dfrac{5}{2} \pm {\dfrac{\sqrt{57}}{2} [/tex]
Step-by-step explanation:
[tex] x^2 - 5x = 8 [/tex]
[tex] x^2 - 5x + \dfrac{25}{4} = 8 + \dfrac{25}{4} [/tex]
[tex] (x - \dfrac{5}{2})^2 = \dfrac{57}{4} [/tex]
[tex] x - \dfrac{5}{2} = \pm \sqrt{\frac{57}{4}} [/tex]
[tex] x = \dfrac{5}{2} \pm {\dfrac{\sqrt{57}}{2} [/tex]
There is a rectangular path for running in Kaylee's town. She runs around the path everyday. one side of the path is 5 1/2 kilometers long. Another sode is 3 1/2 kilometers long.
Answer:
3.45
Step-by-step explanation:
calculator
Answer:
16.8 km
Step-by-step explanation:
Perimeter is the sum of all sides.
For a rectangle , perimeter = lenght + lenght + base + base
Perimeter = 5.2 + 5.2 + 3.2 + 3.2
Perimeter = 16.8 km
Find the area of a sector, whose perimeter is 40 cm, and the radius is 8 cm.
Answer:
96 cm²
Step-by-step explanation:
From the question,
s = (2πr∅/360)+2r................. Equation 1
Where s = Perimeter of a sector, r = radius, ∅ = angle subtend by the sector at the center of the circle.
Given: s = 40 cm, r = 8 cm
Constant : π = 3.14.
Substitute into equation 1 and solve for ∅
40 = (2×8×3.14×∅/360)+(2×8)
40 = (50.24∅/360)+16
40-16 = 50.24∅/360
50.24∅/360 = 24
50.24∅ = 24×360
50.24∅ = 8640
∅ = 8640/50.24
∅ = 171.97°
Area of a sector (A') = ∅πr²/360
A' = 171.97×3.14×8²/360
A' = 95.997
A' ≈ 96 cm²
The order is for 500 mL D5 1/2 NaCl to run in 6 hours. Set calibration is 15 gtt/mL calculate the flow rate in mL/hrs
Answer:
16 is correct
Step-by-step explanation:
Turtles and tortoises have long life spans. A tortoise can live as long as 150 years. There are 365 days in one year. About how many days could a tortoise live?
Answer:
54,750 days
you just multiply 150 by 365
At the beginning of the year, Evelyn had $30 in savings and saved an additional $12 each week thereafter. Cooper started the year with $75 and saved $7 every week. Let E E represent the amount of money Evelyn has saved t t weeks after the beginning of the year and let C C represent the amount of money Cooper has saved t t weeks after the beginning of the year. Write an equation for each situation, in terms of t , t, and determine the interval of time when Evelyn has more in savings than Cooper.
Answer:
E=12t+30 C=7t+75
Evelyn has more in savings than Cooper when t > 9 weeks.Step-by-step explanation:
find the area of the figure 4m 7m
Answer:
Step-by-step explanation:
where is the picture?!
Answer:
28m squared
Step-by-step explanation:
7*4 is 28
HELP PLS HURRY! The graph shows the proportional
relationship between the total cost and the
number of pounds of cashews purchased.
What would the total price in dollars be for
11.5 pounds of cashews?
Answer:
57.5$
Step-by-step explanation:
5$ a pound, 11.5 pounds, multiply them and you get 57.5$
Answer:
45
Step-by-step explanation:
a line has a slope of 9/5 if one of the points on the line is (-10, -16), which of the following could be another point on the line?
Answer:
(0,2) is the answer - Option C.
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, is given by:
[tex]y - y_0 = m(x - x_0)[/tex]
In which m is the slope and the point is [tex](x_0,y_0)[/tex]
Slope of 9/5 if one of the points on the line is (-10, -16)
This means that [tex]m = \frac{9}{5}, (x_0,y_0) = (-10,-16)[/tex]. So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - (-16) = \frac{9}{5}(x - (-10))[/tex]
[tex]y + 16 = \frac{9}{5}(x + 10)[/tex]
Which of the following could be another point on the line?
We have to find a point for values of x and y which gives us an identity. So
Option A:
x = -5, y = -6
Lets see
[tex]-6 + 16 = \frac{9}{5}(-5+10)[/tex]
[tex]10 = \frac{9*5}{5}[/tex]
[tex]10 = 9[/tex] -> False
So this is not the answer.
Option B:
x = 4, y = 11
[tex]11 + 16 = \frac{9}{5}(4 + 10)[/tex]
[tex]27 = 9*14/5[/tex]
False
Option C:
x = 0, y = 2
[tex]2 + 16 = \frac{9}{5}(x+10)[/tex]
[tex]\frac{90}{5} = 18[/tex]
[tex]18 = 18[/tex]
True, so (0,2) is the answer - Option C.
Help! find the area of the parallelogram
28.2
Step-by-step explanation
A=bh=6·4.7≈28.2
6) Identify the slope (6,2) and (6,-5) *
The graph shows the distance traveled by an Olympic-level sprinter over time during a race.
Find the slope of the line, and complete the sentences below.
100 meter race graph of a diagonal line on a coordinate plane going up and to the right with Time in seconds on the x axis and Distance in meters on the y axis. The line begins at the origin and passes through the point 2 comma 20.
9514 1404 393
Answer:
slope: 10 m/srepresents speed in meters per secondStep-by-step explanation:
The slope is the change in the quantity on the vertical scale, divided by the corresponding change in the quantity on the horizontal scale.
Here, the line goes from 0 to 100 meters on the vertical scale, corresponding to a change from 0 to 10 seconds on the horizontal scale. So, the slope is ...
m = (100 m)/(10 s) = 10 m/s . . . . slope of the line
The ratio of distance to time is given the name "speed", so ...
the slope represents the sprinter's speed in meters per second.
PLEASE ANSWER QUICK!
Simplify the expression 7(2g+7)-4
Helps me is urgent Match each type of insurance with an example of what it would pay for.
Renter's
insurance
?
Repair on a car involved in
an accident
Auto insurance
2
Replacement of a
computer stolen from an
apartment
Life insurance
2
Funeral expenses
Health insurance
?
A trip to the emergency
room
PREVIOUS
a line is parallel to y=4x+1 and intersects the point (-2,4) what is the equation of this parallel line
Answer: y=4x+12
Step-by-step explanation:
a parallel line has the same slope, so the slope remains 4
use point slope formula to write the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-4=4(x--2)\\y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]
Answer:
y=4x+12
Step-by-step explanation:
When two lines are parallel, their slopes are the same. In y=mx+c form, m is the slope. So the slope of our parallel line is 4:
y=4x+c
To find c, plug in (-2,4) into the equation because we know it's a point on the line:
4=4(-2)+c
4=-8+c
c=12
So our equation is y=4x+12
PLEASE HELP ASAPPPP!!
question: write in standard form.
2x^2+x^3-3+4x^5
Answer:
+4X^5+X^3+2X^2-3
Step-by-step explanation:
Hope this helps :*
BRAINLEST TO WHOEVER GETS THIS CORRECT
Consider matrix V.
Step-by-step explanation:
The inverse of matrix V the one in answer B
What are the growth/decay factors and rates for the following functions?
a. y=1000(1.03)x
b. f(x)=200(0.8)x
Answer:
gududu0hxosjvacsivhxhvsaiojvxsaxisahvhvhxsaixjs
A dress that is size x in France is equaivalent to size d(x) in the United States, where d(x)x32.
(a). Find a function that will convert U.S. dress size to French dress size.
(b) Use the inverse function to find the French size of a dress if it is U.S. size .
Answer:
[tex](a)\ d'(x) = x + 32[/tex] i.e. The inverse function
[tex](b)\ d'(10) = 42[/tex] i.e. The French size of a dress if it is U.S. size 10 is 42.
Step-by-step explanation:
Given
[tex]d(x) = x - 32[/tex]
Solving (a): The inverse function
[tex]d(x) = x - 32[/tex]
Replace d(x) with y
[tex]y = x - 32[/tex]
Swap y and x
[tex]x = y - 32[/tex]
Make y the subject
[tex]y = x + 32[/tex]
Replace y with d'(x)
[tex]d'(x) = x + 32[/tex]
Hence, the inverse function is: [tex]d'(x) = x + 32[/tex]
Solving (b): US size of 10
[tex]d'(x) = x + 32[/tex]
Substitute [tex]x =10[/tex]
[tex]d'(10) = 10 + 32[/tex]
[tex]d'(10) = 42[/tex]
A triangle has angles measuring 58 and 93 degrees. What is the measure of the third angle?
find the volume of the rectangular prism. geometry hw plz help
Answer:
189 cm^3
Step-by-step explanation:
7 times 9 times 3=189
Find the perimeter of the figure.
A standard bathtub holds 60 gallons of water. A full tub drains 12 gallons per minute. Which of the following tables best represents the situation?
J.
x represents the minutes and y shows how many gallons over that time.
The correct table for best represents the situation is shown in Table J.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
A standard bathtub holds 60 gallons of water.
And, A full tub drains 12 gallons per minute.
Now, From table J;
Rate of change is,
⇒ (24 - 12) / (2 - 1)
⇒ 12 / 1
⇒ 12 gallons per minutes
Which is given in situation.
Thus, The correct table for best represents the situation is shown in Table J.
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find the geometric mean of 9 and 14
Answer:
foće de moçhò de casà là ocoreatane
An animal shelter houses rabbits, cats, and dogs. There are 160 animals at the shelter. Of the animals,
1
5 are rabbits.
7
8 of the remaining animals are cats. How many of the animals are dogs? Show your work.
Answer:
67
Step-by-step explanation:
help please, i need it asap. tyty
Answer:
Step-by-step explanation:
[tex]\frac{3}{x}[/tex] = [tex]\frac{2}{5}[/tex]
2x = 15
x = 7.5
Parallelogram ABCD is a rhombus. Side BC = 5cm and segment AO = 3.8cm
What is the area of ABCD?
What is the length of diagonal BD?
The area of the rhombus ABCD is 24.7 cm².
The length of diagonal BD is 6.5 cm.
What is the area of a rhombus?A rhombus have equal four sides and the diagonals of the rhombus divides it into four equal right triangles. The area of the rhombus is the sum of individual areas of the four right triangles.
The hypotenuse side of the right triangle = side of the rhombus = BC = 5 cm
One of the legs of the right triangle = AO = OC = 3.8 cmLet the second leg of the right triangle = OB = OD = xThe second leg of the right triangle is calculated as follows;
[tex]x^2 + 3.8^2 = 5^2\\\\ x^2 = 5^2 - 3.8^2 \\\\ x^2 = 10.56\\\\ x = \sqrt{10.56} \\\\ x = 3.25 \ cm[/tex]
The area of one right triangle of the rhombus is calculated as follows;
[tex]A = \frac{1}{2} (3.8)(3.25)[/tex]
The area of the rhombus ABCD is calculated as follows;
[tex]A = 4 \times \frac{1}{2} (3.8)(3.25)\\\\ A = 24.7 \ cm^2[/tex]
The length of diagonal BD is calculated as follows;
[tex]BD = OB \ + \ OD\\\\ BD = x \ + \ x\\\\ BD = 3.25 \ cm \ + \ 3.25 \ cm\\\\ BD = 6.5 \ cm[/tex]
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Will give brainliest for correct answer
Answer:
A function is a rule that assigns to each input exactly one output.
Step-by-step explanation:
If you have more than one of the same inputs for multiple outputs, it would create a vertical line at somepoint on your line.
Answer:
The correct answer is "a rule that assigns to each input exactly one output".
Step-by-step explanation:
In mathematics, a function is a binary relation between two sets that associates to each element of the first set exactly one element of the second set. Typical examples are functions from integers to integers, or from real numbers to real numbers.
Find the circumference and the area of a circle
with the dimensions listed. Use the value 3.14 for π
,and do not round your answers. Be sure to
include the correct units in your answers.
a) diameter of 3 cm
b) radius of 5 ft
In response to the question, we may say that As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
a) 3 cm diameter: The radius (r) of a circle is half its diameter, hence r = 3 cm/2 = 1.5 cm
The formula C = 2r gives the circumference of a circle, where is approximately equivalent to 3.14.
As a result, C = 2 3.14 1.5 cm = 9.42 cm.
The formula A = r2 calculates the area of a circle.
As a result, A = 3.14 (1.5 cm)2 = 7.065 cm sq.
As a result, the radius of the circle is 9.42 cm and its area is 7.065 cm sq
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Dennis Hampton earns a straight com-
mission of 7% on sales of $5,000 or less
and 9% on sales in excess of $5,000. One
week Dennis had a gross pay of $578.
What were his total sales for that week?
Answer:
Denis's total sales that week were $ 6,422.22.
Step-by-step explanation:
Since Dennis Hampton earns a straight commission of 7% on sales of $ 5,000 or less and 9% on sales in excess of $ 5,000, if one week Dennis had a gross pay of $ 578, to determine what were his total sales for that week the following calculations must be performed:
7 = 578
100 = X
100 x 578/7 = X
57,800 / 7 = X
8,257.14 = X
9 = 578
100 = X
100 x 578/9 = X
57.800 / 9 = X
6,422.22 = X
Therefore, Denis's total sales that week were $ 6,422.22.
The National Assessment of Educational Progress (NAEP) includes a "long-term trend" study that tracks reading and mathematics skills over time, and obtains demographic information. In the 2012 study, a random sample of 9000 17-year-old students was selected.24 The NAEP sample used a multistage design, but the overall effect is quite similar to an SRS of 17-year-olds who are still in school. In the sample, 51% of students had at least one parent who was a college graduate. Estimate, with 99% confidence, the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college.
Answer:
The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 9000, 51% of students had at least one parent who was a college graduate.
This means that [tex]n = 9000, \pi = 0.51[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 - 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.4964[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.51 + 2.575\sqrt{\frac{0.51*0.49}{9000}} = 0.5236[/tex]
The 99% confidence interval estimate for the proportion of all 17-year-old students in 2012 who had at least one parent graduate from college is (0.4964, 0.5236).
