Answer:
7 ft ×6 ft
Step-by-step explanation:
Area of rectangle= length ×width
Let the length and width of the rectangle be L and W ft respectively.
Form 2 equations using the given information:
LW= 42 -----(1)
L= 3W -11 -----(2)
Substitute (2) into (1):
(3W -11)(W)= 42
Expand:
3W² -11W= 42
3W² -11W -42= 0
[tex]\boxed{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }[/tex]
Applying quadratic formula:
[tex]W= \frac{ - ( - 11)± \sqrt{( - 11) {}^{2} - 4(3)( - 42) } }{2(3)} [/tex]
[tex]W= \frac{ 11± \sqrt{625 } }{6} [/tex]
[tex]W= \frac{ 11± 25}{6} [/tex]
W= 6 or W= [tex] - \frac{7}{3} [/tex] (reject)
Substitute W= 6 into (1):
L(6)= 42
L= 42 ÷6
L= 7
Thus the dimensions of the rectangle is 7 ft ×6 ft.
The pirate captain ordered his men to dig
For treasure. Six men dug, one at a time, im
qual shifts for a total of three and a half
hours. How long was each man's shift?
Asap help
+) First, simplify the fraction.
180
?
t
4
m
Answer:
hope this will help you
[tex] \frac{180}{t} = \frac{?}{4} \\ t = 180 \times 4 \\ t = 720[/tex]
find the perimeter and the area of the figure
Answer:
area=112
perimeter=56
A cylinder has a base area of 50π cm². Express the volume V of the cylinder as a function of its height h. (V = πr²h)
Step-by-step explanation:
the last option is your answer
What is the volume of a
triangular pyramid that is
12 ft tall and has a base
area of 5 squar & ft?
Answer:
60 ft³
Step-by-step explanation:
Concepts
The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.
Application
In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.
Solution
12 × 560 feet³Write an equation of the circle with center (7, 6) and radius 5.
Answer:
( x-7)^2+(y-6)^2 = 25
Step-by-step explanation:
The equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
( x-7)^2+(y-6)^2 = 5^2
( x-7)^2+(y-6)^2 = 25
Answer:
(x-7)^2+(y-6)^2=25
Explanation:
If I were you, I would mark 7 as x and 6 as y. Whatever is in your parenthesis for center of the circle, do the opposite in your equation. Since you have positive 7 & positive 6, turn those into negative numbers for your equation. And for the radius, just times it two times. So 5•5=25
item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week? item 3 lamar gives his dog a pill once each day. each pill contains 3.6 milligrams of medicine. how many grams of medicine does lamar's dog get after one week?
Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,
The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams
Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
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Technology required. A function f gives the number of stray cats in a town t years since the town started an animal control program. The program includes both sterilizing stray cats and finding homes to adopt them. An equation representing fis f(t) = 243()': a. What is the value of f (t) when t is 0?
The number of stray cats in the town in t=0 years will be 243.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The given function is:-
[tex]f(t) = 243(\dfrac{1}{3})^t[/tex]
f(t) is representing the number of the stray cats in t years so in t=0 years the number of the cats will be:-
[tex]f(t) = 243(\dfrac{1}{3})^0= 243[/tex]
f(t) = 243 cats
It states that initially at t=0 years there were 243 cats in the town.
Therefore the number of stray cats in the town in t=0 years will be 243.
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Y = -2x x + y = 7 what does x equal what does y equal
Answer:
[tex]x = 0[/tex]
[tex]y = 7[/tex]
Help me with this question please /:
Answer:
B) D) E)
Step-by-step explanation:
Basically, the more days missed, the lower their grades are, so it is a negative linear relationship that has no clusters or outliers.
Solve the following equations for x.
A. 7(x)^3=243
B. 5(x)^4+7=42
The values of x given the following expression are ∛243/7 and 7^1/4
Indices expressionGiven the following expression
7x³ =243
x³ = 243/7
x = ∛243/7
For the expression
5x⁴ + 7 = 42
5x⁴ = 42 - 7
5x⁴ = 35
x⁴ = 7
x = 7^1/4
Hence the values of x given the following expression are ∛243/7 and 7^1/4
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Which could be the missing data item for the given set of data if the median of the complete data set is 50?
21 23 60 60 50 54 54 59 26 15 43 15
A. 18
B. 24
C. 45
D. 57
Answer:
D. 57
PLEASE GIVE BRAINLIEST THANK YOU!!!
Find the equation of the line that passes through the point (-8,15) and is perpendicular to the equation below.
y = -4/5x + 5
A. y = -5/4x + 5
B. y = -4/5x - 7
C. y = -4/5x + 23
D. y = 5/4x + 25
Please help asap!
Answer:
[tex]y = \frac{5}{4} x + 25[/tex]
Step-by-step explanation:
We were told that the equation of the line we are looking for is perpendicular to
[tex]y = - \frac{4}{5} x + 5[/tex]
We know that the gradient of perpendicular lines when multiplied is equal to -1, therefore
[tex] line \: .1 \times \: line \: .2 = - 1 \\ \\ \frac{4}{5} \times line \: .2 = - 1 \\ \\ line \: .2 = \frac{ - 1}{ \frac{4}{5} } [/tex]
[tex]line\: .2 = \frac{5}{4} \: \: \: \: y = 15 \: \: \: \: x = - 8 \\ \\ y = mx + c \\ \\15 = ( \frac{5}{4} ) - 8 + c \\ \\ 15 = - 10 + c \\ 15 + 10 = c[/tex]
[tex]25 = c \\ \\ therefore \: the \: equation \: of \: the \: line \: is \: \\ \\ y = \frac{5}{4} x + 25[/tex]
Please help asap please
Answer:
3rd one
Step-by-step explanation:
Spencer took $21 with him to the mall. At the music store he spent 2/3 of his money on a DVD. He spent ¼ of what he had left on a drink. How much money did Spencer have left after he bought the drink?
Answer:
$10.50
Step-by-step explanation:
2/3 of $21 = $14
1/4 of $14 = $3.50
$14 - $3.5 = $10.50
A hyperbola has its foci at (1, 7) and (1, –13). a directrix of the hyperbola is y = . what is the equation of the hyperbola?
The equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
How to determine the hyperbola equation?The foci are given as:
(1, 7) and (1, -13)
The foci of a hyperbola are represented using: (m, n+p) and (m, n-p)
Where the center of the hyperbola is (n,p)
By comparison, we have:
m = 1
n + p = 7
n - p =13
Where n = ae
The solution to the above system of equations is
m = 1, n = 10 and p = -3
The directrix is given as:
y = 64/10
The directrix is represented as:
y = a/e
So, we have:
a/e = 64/10
Substitute n = ae in n = 10
ae = 10
Solving ae = 10 and a/e = 64/10, we have:
a = 8 and e = 10/8
To calculate b, we make use of:
[tex]b = a\sqrt{(e^2 - 1)[/tex]
So, we have:
[tex]b = 8\sqrt{(\frac{10}{8}^2 - 1)[/tex]
Evaluate
b = 8 * 0.75
b = 6
The equation of the hyperbola is then calculated using:
[tex]\frac{(y - p)^2}{a^2} -\frac{(x - m)^2}{b^2} = 1[/tex]
This gives
[tex]\frac{(y + 3)^2}{8^2} -\frac{(x - 1)^2}{6^2} = 1[/tex]
Evaluate
[tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{(y + 3)^2}{64} -\frac{(x - 1)^2}{36} = 1[/tex]
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Pete is 14 and his grandfather is 54. How many years
ago was his grandfather 6 times as old as Pete?
Answer:
6 years ago
Step-by-step explanation:
[tex]6(14-x)=54-x\\84-6x=54-x\\30-6x=-x\\30=5x\\6=x[/tex]
So, Pete's grandfather was 6 times as old as Pete 6 years ago. This means that when Pete was 8 years old, his grandfather was 48 years old.
Which of the following is a compound event?
Getting sum 12 when rolling two dice
Getting sum 2 when rolling two dice
Getting sum 6 when rolling two dice
None of the choices
Answer:
Getting sum 6 when rolling two dice
GIVING BRAINLIEST!!!!!
Cooper asked his classmates, "How many days do you floss your teeth in a
typical week?" The table shows Cooper's data.
Days of Flossing per Week
4
5
4 2
3
3
1
0
3
3
6
7
2
6
0
5
3
2
7
0
4
4
4
3 3
0
1
2
2
3
5 3
7
1
3
How many observations did he record?
OA. 40
OB. 35
OC. 30
D. 7
сл
Considering the given table, it is found that he recorded 35 observations, hence option B is correct.
How do we find the number of observations on the table?We have to look at the number of rows and columns the table. The table has 7 rows, each with 5 columns, hence the number of observations is given by:
N = 7 x 5 = 35.
Hence option B is correct.
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Three times a number decreased by 2 equals forty
Answer:
14
Step-by-step explanation:
40 plus 2 is 42
42 divided by 3 is 14
what is the solution to this inequality?
-4(d-2) <-12
d > 5
d < 5
d < 1
d > 1
Work Shown:
[tex]-4(d-2) < -12\\\\-4d+8 < -12\\\\-4d < -12-8\\\\-4d < -20\\\\d > -20/(-4)\\\\d > 5[/tex]
In the second to last step, the inequality sign flips because we divided both sides by a negative number.
Which best describes independent events?
A. The results of all events have different individual probabilities.
B. The results of any previous events affects the probability of future events.
C. The results of all events have the same individual probability.
D. The results of all previous events do not affect the probability of future events.
The option that best describes independent events is the results of all previous events do not affect the probability of future events.
What are independent events?Independents events are events whose occurrence do not depend on each other. They are random events.
For example, there is no relationship between the the colour of shoes you wear and the chances that it would rain. Thus, they are independent events.
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Answer:
D ✔️
Step-by-step explanation:
"The results of all previous events do not affect the probability of future events."
1. philosophy (intro to logic
measure your understanding of the 4 new rules of inference for predicate logic (pl): universal instantiation (ui), external instantiation (ei), existential generalization (eg), and universal generalization (ug) and one new rule of replacement: quantifier negation (qn) required for demonstrating that arguments of predicate language (pl) are valid.
question: is the following statement true or false?
the following statement is true
Football boot sizes of a football team continuous or discrete
Answer:
discrete?
according to probability of basic things we know that there are more people different than same so there is more than enough probability of those sizes being discrete.
What is the simplified value of the exponential expression 16 superscript one-fourth? 2 4
The simplified value of the exponential expression is 2.
How to get the simplified expression?
Here we need to simplify the expression:
[tex]16^{1/4}[/tex]
First, you need to remember that:
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
Then we can just write:
[tex]16^{1/4} = \sqrt[4]{16}[/tex]
And now, you can remember that:
2*2 = 4
Then:
2*2*2*2 = 4*4 = 16
From this, we can conclude that:
[tex]2^4 = 16\\\\\sqrt[4]{16} = 2[/tex]
So we conclude that the simplified value is 2.
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Answer:
The simplified value of the exponential expression is 2.
How to get the simplified expression?
Here we need to simplify the expression:
First, you need to remember that:
Then we can just write:
And now, you can remember that:
2*2 = 4
Then:
2*2*2*2 = 4*4 = 16
From this, we can conclude that:
So we conclude that the simplified value is 2.
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can you guys help me with this fast
Answer:
1/2¹⁵ or 2⁻¹⁵
Step-by-step explanation:
2³ / (2⁶)³
2³ / 2¹⁸ (The exponents multiply in such cases)
1 / 2⁽¹⁸⁻³⁾
1/2¹⁵ or 2⁻¹⁵
What is the area of a rectangle with a length of 9
centimeters and a width of 4 centimeters?
Sketch: ?
Area: ?
Answer:
We are given a length of 9 cm and a width of 4 cm and we are also told that it our shape is a rectangle. This means that we are able to use the rectangle formula which is [tex]A=l*w[/tex].
Therefore, we can just multiply 9 cm by 4 cm and we get [tex]A = 36\ cm^2[/tex]
Hope this helps! Let me know if you have any questions
On a coordinate plane, a circle has a center at (1, negative 2) and a radius of 4 units. which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)? (x – 1)2 (y 1)2 = 16 (x – 1)2 (y 1)2 = 4 (x 1)2 (y –1)2 = 4 (x 1)2 (y – 1)2 = 16
The equation of the circle of radius 4 and center at (-1, 1) is given as follows:
[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In this problem:
The circle has center at (-1,1), hence [tex]x_0 = -1, y_0 = 1[/tex].The circle has radius r = 4.Hence, the equation is given as follows:
[tex](x - (-1))^2 + (y - 1)^2 = 4^2[/tex]
[tex](x + 1)^2 + (y - 1)^2 = 16[/tex]
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Find the distance between the points (9, –6) and (–4, 7).
Question 19 options:
A) [tex]2\sqrt{85}[/tex]
B) [tex]3\sqrt{39}[/tex]
C) [tex]13\sqrt{2}[/tex]
D) [tex]3\sqrt{39}[/tex]
The distance between the points (9, –6) and (–4, 7) will be 13√2. Then the correct option is C.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
D² = (x - p)² + (y - q)²
The points are (9, –6) and (–4, 7). Then the distance will be
D² = (-4 - 9)² + (7 + 6)²
D² = 13² + 13²
D² = 169 + 169
D² = 338
D = √338
D = 13√2
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