Answer: [tex]750\ ft^2[/tex]
Step-by-step explanation:
Given
Rate of painting 50¢ per square foot
Cost of paint is $100
If the total bill is $475
We can write,
[tex]\Rightarrow 475=100+0.5\times x\quad [x=\text{area in square foot}]\\\Rightarrow 375=0.5x\\\Rightarrow x=750\ ft^2[/tex]
Thus, [tex]750\ ft^2[/tex] must be painted.
What is the solution set to this equation? Log2(x - 2) + log2x = 3
The required, solution set to the given equation is {4}. Option A is correct.
What are logarithmic functions?A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).
Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:
log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)
So the given equation becomes:
log2(x² - 2x) = 3
2³ = x² - 2x
8 = x² - 2x
x² - 2x - 8 = 0
Factor this quadratic equation as:
(x - 4)(x + 2) = 0
x - 4 = 0, which gives x = 4
x + 2 = 0, which gives x = -2
However, the logarithm function is only defined for positive values of x, so the only possible solution is:
x = 4
Therefore, the solution set to the given equation is {4}.
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Write the coordinates as an ordered pair for any point that is a solution to the of inequality graphed below.
Answer:
The inequality that represents the graph must have the following form:
[tex]y > -4\cdot x + 6[/tex]
Step-by-step explanation:
First, we need to determine the equation of the line which represents the "lower" bound of the inequality:
[tex]y = m\cdot x + b[/tex] (1)
Where:
[tex]x[/tex] - Independent variable, horizontal axis.
[tex]y[/tex] - Dependent variable, vertical axis.
[tex]m[/tex] - Slope.
[tex]b[/tex] - Intercept.
Given two distinct points of the line, we can solve for both slope and intercept: [tex](x_{1}, y_{1}) = (1, 2)[/tex], [tex](x_{2}, y_{2}) = (0, 6)[/tex]
[tex]m + b = 2[/tex] (2)
[tex]b = 6[/tex] (3)
The solution of the system is: [tex]m = -4[/tex], [tex]b = 6[/tex]
Then, the inequation must have the following form:
[tex]y > -4\cdot x + 6[/tex]
i already have A but I do not have B
Answer:
-4 , -1 , -2 , 0 , +1 , +3
Step-by-step explanation:
Answer:
the integers -4,-2,-1,0, +1, +3
Step-by-step explanation:
because when you put them in order you find which pairs are located between -5 and +5
-8,-4,-2,-1,0,+3,+8,+9
which tells you that
-4,-2,-1,0, +1, +3 are between -5 and +5
For f(x) = 4x + 2 and g(x) = x^2 - 6, find (f+g)(x)
Answer:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x + 2[/tex]
[tex]g(x) = x^2 - 6[/tex]
(f+g)(x)
We add the common terms. Thus:
[tex](f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4[/tex]
Thus:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
A university classifies its classes as either "small" (fewer than 40 students) or "large." A dean sees that 62% of Department A’s classes are small, while Department B has only 40% small classes. She wonders if she should cut Department A’s budget and insist on larger classes. Department A responds to the dean by pointing out that classes for third- and fourth-year students tend to be smaller than classes for first- and second-year students. The following three-way table gives the counts of classes by department, size, and student audience. Write a short report for the dean that summarizes these data. Start by computing the percents of small classes in the two departments and include other numerical and graphical comparisons as needed. Here are the numbers of classes to be analyzed: CSIZE
Department Year Size Count
A First Large 2
A First Small 0
A Second Large 9
A Second Small 1
A Third Large 5
A Third Small 15
A Fourth Large 4
A Fourth Small 16
B First Large 18
B First Small 2
B Second Large 40
B Second Small 10
B Third Large 4
B Third Small 16
B Fourth Large 2
B Fourth Small 14
Total 158
Answer:
trffhuuuygreertttf 5
Step-by-step explanation:
fffffffftfdeerrr10
Which graph shows the solution to this system of inequalities?
y>-1/3x+1
y>2x-3
Given:
The system of inequalities is:
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
To find:
The graph of the given system of inequalities.
Solution:
We have,
[tex]y>-\dfrac{1}{3}x+1[/tex]
[tex]y>2x-3[/tex]
The related equations are:
[tex]y=-\dfrac{1}{3}x+1[/tex]
[tex]y=2x-3[/tex]
Table of values for the given equations is:
[tex]x[/tex] [tex]y=-\dfrac{1}{3}x+1[/tex] [tex]y=2x-3[/tex]
0 1 -3
3 0 3
Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].
Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].
The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.
Therefore, the graph of the given system of inequalities is shown below.
Calculate the measure of segment KL
HELP PLS
I need help I’ll give u brainlest
Answer:
[tex]252[/tex] cubic yards
Step-by-step explanation:
[tex]V=lwh[/tex]
Volume = length * width * height
[tex]V=7*4*9[/tex]
[tex]V=252[/tex]
Answer:
252 yd³
Step-by-step explanation:
Volume of rectangular prism = length * width * height
= 9 * 7 * 4 yd³
= 252 yd³
A candy distributor needs to mix a 40% fat-content chocolate with a 60% fat-content chocolate to create 150 kilograms of a 52% fat-content chocolate. How many kilograms of each kind of chocolate must they use?
Answer:
60 kg of 40% and 90 kg of 60%
Step-by-step explanation:
Let the amount of 40% chocolate be x.
Let the amount of 60% chocolate be y.
x + y = 150
0.4x + 0.6y = 0.52 * 150
x + y = 150
4x + 6y = 780
-4x - 4y = -600
(+) 4x + 6y = 780
--------------------------
2y = 180
y = 90
x + y = 150
x + 90 = 150
x = 60
Answer: 60 kg of 40% and 90 kg of 60%
What is the value for y?
Enter your answer in the box.
y=
Answer:
[tex]y =112[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find y
The attached triangle is isosceles; so:
[tex]x - 5=34[/tex]
Also, we have:
[tex]y + x - 5 + 34=180[/tex] --- angles in a triangle
Substitute: [tex]x - 5=34[/tex]
[tex]y + 34 + 34=180[/tex]
Collect like terms
[tex]y =- 34 - 34+180[/tex]
[tex]y =112[/tex]
What is the solution to this inequality?
15 + x 24
O A. x 39
O B. X29
O C. XS 39
O D. XS9
The solution of the inequality will be;
⇒ x ≤ 9
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ 15 + x ≤ 24
Now,
Since, The inequality is,
⇒ 15 + x ≤ 24
Solve the inequality as;
⇒ 15 + x ≤ 24
Subtract 15, we get;
⇒ 15 + x - 15 ≤ 24 - 15
⇒ x ≤ 9
Thus, The solution of the inequality will be;
⇒ x ≤ 9
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1. EF is (a secant of, tangent to) OX.
2. DF is a (chord, locus) of OX.
3. AABC is made of (chords in, tangents to) OX.
4. ZDEF is an (intercepted arc, inscribed angle) of OX.
Answer:
1 . EF is a secant of OX
2. DF is a chord of OX.
3. AABC is made of tangents to OX
4. ∠DEF is an inscribed angle of OX.
Step-by-step explanation:
Secant is line which intersects a circle from two distant points. Locus is a set of points which is same distance from the center of a circle. Chord is a straight line whose end points lie on circular arc of a circle. Tangent is a line which touches the circle at one point only.
A man takes a 375-mile trip to Miami. His large car gets 18 miles per gallon, and his small car gets 32 miles
per gallon. How many gallons of gas will he save if he takes the smaller car?
Answer: 9 gallons
Step-by-step explanation:
How many gallons needed for small car: 375/32 = 11.7 or 12
How many gallons for large car: 375/18 = 20.8 or 21
21-12 = 9
Solve Only estimation
Answer:
3a)1680
b)2620
4a)2130
b)13300
c)460
d)7540
Step-by-step explanation:
3a)1500+180
b)2800-170
4a)1800+330
b)7300+6000
c)670-210
d)8000-460
Answer:
a) 1600
b) 2600
c) 2200
d) 13200
e) 500
Step-by-step explanation:
a) 1463 + 179
1400 + 200
1600
b) 2806 - 176
2800 - 200
2600
c) 1831 + 329
1900 + 300
2200
d) 7345 + 5893
7300 + 5900
13200
e) 665 - 213
700 - 200
500
6. (15 points) Lucy can mow her yard in 3 hours and 15 minutes. Her brother Will
can mow the same yard in 4 hours and 45 minutes. How long will it take them to
mow the lawn together?
How to solve?
Answer:
1 hour 56 minutes
Step-by-step explanation:
Given :
Time taken by Lucy = 3 hours 15 minutes = 3.25 hours
Time taken by brother = 4 hours 45 minutes = 4.75 hours
Rate = 1 / time taken
Lucy's rate = 1 / 3.25
Brother's rate = 1 / 4.75
Combined rate = Lucy's rate + brother's rate
Combined rate = 1/3.25 + 1/4.75
Combined rate = 0.5182186
Time taken if they work together = 1/ combined rate
= 1 / 0.5182186
= 1.9296 hours
= 1 hour (0.9296 * 60) minutes
= 1 hour 56 minutes (approximately)
What is the surface area of a square pyramid if the base has an area of 16 cm2 and the lateral faces have a slant
height of 12 cm?
O 112 cm
O 208 cm2
O 400 cm?
O 640 cm
Answer:
640
Step-by-step explanation:
pleas check my answer
Answer:
112
Step-by-step explanation:
If you add all the triangle faces and the square.
What is the sum of additive inverse and multiplicative inverse of 2?
answer fast
Answer:
-3/2
Step-by-step explanation:
Additive inverse of 2 = -2
Multiplicative inverse of 2 = ½
→ Sum = -2 + ½
→ Sum = (-4 + 1)/2
→ Sum = -3/2
4 out of every 5 students made it to class on Monday. If there are 7500 students enrolled how many made it to class?
Answer:
6000
Step-by-step explanation:
7500x4/5=6000
or
7500/5=1500
1500x4=6000
Solve this proportion mentally by scaling up or scaling down.
Answer: 63 miles
Step-by-step explanation: 21 miles x 3 = 63 miles
you times it by 3 because to get 3 gallons to 9 gallons, you have to multiply it by 3
A museum has a model of an Egyptian pyramid. It has a rectangular base that is 10 feet by 8 feet, with a height of 12 feet.
What is the volume of the pyramid?
Answer: 320ft^3
Step-by-step explanation:
Assuming the pyramid is just a normal rectangular pyramid and isn't made of stairs...
10x8x12/3 = 320 ft^3
PLS HELP! WILL GIVE BRAINLIEST IF CORRECT!
What is the value of P for the following triangular prism?
36 cm
48.5 cm
48 cm
36.5 cm
Answer:
36 cm
Step-by-step explanation:
if p is perimeter then 10+13+13=36 is the correct answer
a and b are complementary angles and a and c are supplementary angles. If a=xº, (a) express b and c in terms of x
(b) find c - b.
Step-by-step explanation:
a + b = 90
a + c = 180
a) If a = x, the. we can write
x + b = 90 and x + c = 180
or
b = 90 - x
c = 180 - x
b) c - b = (180 - x) - (90 - x)
= 180 - x - 90 + x
= 90
Evaluate the given equation for the indicated function values. pls help
Answer:
The answer in each numeral is:
f(4) = 28f(10) = -19f(-5) = -33f(9) = -9Step-by-step explanation:
To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:
1. f(n) = 5n + 8 f(4) = ?As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:
1. f(4) = 5*(4) + 8f(4) = 20 + 8f(4) = 28The first answer is 28, now we'll continue with the next exercises:
2. f(n) = -2n + 1f(10) = -2*(10) + 1f(10) = -20 + 1f(10) = -193. f(n) = 6n - 3f(-5) = 6*(-5) - 3f(-5) = -30 - 3f(-5) = -334. f(n) = -nf(9) = -9In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.
Half of a set of the parts are manufactured by machine A and half by machine B. Six percent of all the parts are defective. Three percent of the parts manufactured on machine Are defective. Find the probability that a part was manufactured on machine A, given that the part is defective. (Round your answer to 4 decimal places.) Probability
Answer:
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Defective
Event B: Manufactured by machine A.
Six percent of all the parts are defective.
This means that [tex]P(A) = 0.06[/tex]
Probability that a part is defective and was manufactured on machine A
3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So
[tex]P(A \cap B) = 0.03*0.5 = 0.015[/tex]
Find the probability that a part was manufactured on machine A, given that the part is defective.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25[/tex]
0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.
2. Kayli swam 0.7 kilometers at the school swimming pool. How many meters did she swim?
Kayli swam
meters in the swimming pool.
Answer:
To convert kilometres to metres, divide the value by 1000.
0.7 ÷ 1000 = 700 metres
Kayli swam 700 meters in the swimming pool
Hope this helps!
Find the equation of a line parallel to y'= -8x+6.
Answer:
The equation must include -8 as the slope
Step-by-step explanation:
Hi there!
Two key points to keep in mind:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0).Parallel lines always have equal slopesGiven the equation y=-8x+6, we can identify that -8 is in the place of m in y=mx+b, making it the slope.
For a line to be parallel to y=-8x+6, it would have to have a slope of -8 as well. This is the only quality a line needs to be parallel to this given line.
I hope this helps!
Graph the Image of square KLMN after a translation 3 units left .
Answer:
N' (-8,9) K' (-8,3) L' (-2,3) M' (-2,9)
Step-by-step explanation:
To translate the square 3 units to the left you would subtract 3 from the x-coordinates of the points shown.
The coordinates of the translated square KLMN is given by K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the square be represented as KLMN
Now , the coordinates of the square KLMN is
K ( -5 , 3 ) L ( 1 , 3 ) M' ( 1 , 9 ) N' ( -5 , 9 )
Now , let the translated square be represented as K'L'M'N'
When translating the square to three units to the left , the x coordinate of the square gets reduced by 3
So , the new coordinate of the square will be ( x - 3 , y )
Substituting the values in the equation , we get
K' = K ( -5 - 3 , 3 )
L' = L ( 1 - 3 , 3 )
M' = M ( 1 - 3 , 9 )
N' = N ( -5 - 3 , 9 )
So , on simplifying the equation , we get
The translated square is K' (-8,3) L' (-2,3) M' (-2,9) N' (-8,9)
Hence , the translated square is K' ( -8,3 ) L' ( -2,3 ) M' ( -2,9 ) N' ( -8,9 )
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32
The angles shown are supplementary. What is the value of x? 0
(2 Points)
(5x5°
95°
O 180 degree
• 17 degree
O 22 degree
45 degree
HELPP I NEED THIS ASAP ITS FOR MY FINALSS
Answer:
17degrees
Step-by-step explanation:
The sum of two supplementary angles is equation 180degrees. Hence:
5x+95 = 180
5x = 180-95
5x = 85
x = 85/5
x = 17
Hence the value of x is 17
guys plz help i’m struggling
Answer:
0.46017
Step-by-step explanation:
Given :
Mean score = 75
Standard deviation, s = 10
Areum's score = 76
Probability of scoring higher than Areum is given by :
P(x > 76)
The standardized score : (x - mean) / standard deviation
P(x > 76) = P[Z > (76 - 75) / 10]
P[(Z > 0.1)] = 0.46017 (Z probability calculator)
= 0.46017
B
(3y + 11)
116°
4y
р с
А
Find the measure of ZA.
mZA
Answer:
an exterior angle is equal to the sum of the two opposite interior angles.
3y + 11 + 4y = 116
Step-by-step explanation:
First combine like terms 7y + 11 = 116
Then undo addition or subtraction.
Then undo multiplication and division to get the value of y.