Answer:
Step-by-step explanation:
cd(x) would equal c(x) multiplied by d(x) so we get [tex]\frac{5(x+3)}{x-2}\\[/tex] = [tex]\frac{5x+15}{x-2}\\[/tex].
The domain of [tex]\frac{5x+15}{x-2}[/tex] is anything except 2, so the domain of (cd)(x) is (-inf, 2) U (2, inf).
3(-n + 4) + 5n = 2n A) n = 3 B) no solution C) infinitely many solutions
Answer:
the answer should be no solution
Answer:
B
Step-by-step explanation:
Given
3(- n + 4) + 5n = 2n ← distribute and simplify left side
- 3n + 12 + 5n = 2n
2n + 12 = 2n ( subtract 12 from both sides )
2n = 2n - 12 ( subtract 2n from both sides )
0 = - 12 ← not possible
This indicates the equation has no solution
Comparing the types of solutions
A n = 3
Indicates that there is only one unique solution to the equation.
B no solutions
This is indicated when you solve and obtain a ridiculous statement, similar to the one obtained in part A, that is
0 = 12
C infinite solutions
This is indicated when you solve the equation and obtain
4 = 4 or - 3 = - 3
Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140
apples, went to market and sold all their apples at the same price, and each
received the same sum of money. What was the price?
Answer:
The amount each took home was 20 unit currency.
Step-by-step explanation:
We are given that Seven apple women, possessing respectively 20, 40, 60, 80, 100, 120, and 140 apples, went to market and sold all their apples at the same price, and each received the same sum of money.
Formula : [tex]a \times n + (n - 1)[/tex], [tex](a + b)\cdot n + (n - 2)[/tex], [tex](a + 2 \cdot b) \cdot n + (n - 3)[/tex], [tex](a + 3 \cdot b) \cdot n + (n - 4)[/tex], [tex](a + 4 \cdot b) \cdot n + (n - 5)[/tex], [tex](a + 5 \cdot b) \cdot n + (n - 6)[/tex], [tex](a + 6 \cdot b) \cdot n + (n - 7)[/tex]
[tex]a \cdot n + (n - 1) = 20[/tex]
[tex](a + b) \cdot n + (n - 2)=40[/tex]
[tex](a + 2 \cdot b) \cdot n + (n - 3) = 60[/tex]
[tex](a + 3 \cdot b) \cdot n + (n - 4) = 80[/tex]
[tex](a + 4 \cdot b) \cdot n + (n - 5) = 100[/tex]
[tex](a + 5 \cdot b) \cdot n + (n - 6) = 120[/tex]
[tex](a + 6 \cdot b) \cdot n + (n - 7) = 140[/tex]
On solving :
n = 7, a = 2, b = 3
So,
[tex]2 \times 7 + 6 = 20[/tex]
[tex]5 \times 7 + 5=40[/tex]
[tex]8 \times 7 + 4 = 60[/tex]
[tex]11 \times 7 + 3 = 80[/tex]
[tex]14 \times 7 + 2 = 100[/tex]
[tex]17 \times 7 + 1 = 120[/tex]
Based on market pricing if groups of apples are sold at 1 unit currency for 7, and extras are sold for 3 unit currency per extra 1, we have the amount :
2×1 + 6×3 = 20
5×1 + 5×3=20
8×1 + 4×3 = 20
11×1 + 3×3 = 20
14×1 + 2×3 = 20
17×1 + 1×3 = 20
20×1 = 20
Therefore, the amount each took home was 20 unit currency.
Please help I do not get
Answer:
(a) 51%
(b) 41%
Step-by-step explanation:
We can simplify this problem down by realizing that the amount of girls over 200 will get us our percentage as a decimal.
Looking at this table, we can see that [tex]30+72=102[/tex] girls were asked. So, [tex]102\div200=0.51[/tex], and [tex]0.51\cdot100=51[/tex].
We can also see that [tex]30+52=82[/tex] people preferred video games, so [tex]82\div200=0.41[/tex], and [tex]0.41\cdot100=41[/tex].
Hope this helped!
Answer:
[tex]\Large \boxed{\mathrm{(a) \ 51\% }} \\ \\ \Large \boxed{\mathrm{(b) \ 41\%}}[/tex]
Step-by-step explanation:
(a) To find the percentage of the students that are girls:
[tex]\displaystyle \sf \frac{total \ number \ of \ girls}{number \ of \ students }[/tex]
[tex]\displaystyle \sf \frac{30+72}{200 }= \frac{102}{200 } =51\%[/tex]
(b) To find the percentage of students that prefer playing video games:
[tex]\displaystyle \sf \frac{total \ number \ of \ students \ that \ prefer \ playing \ video \ games}{number \ of \ students }[/tex]
[tex]\displaystyle \sf \frac{30+52}{200 }=\frac{82}{200} = 41\%[/tex]
The density of Venus, compared to Earth having a density of 1,
is 0.943. The density of Mercury is 0.983, compared to the
density of Earth. Which planet has a greater density, Venus or
Mercury?
Answer:
Mercury
Step-by-step explanation:
We'll translate this into ratios.
First, V:E = 0.943:1
Then, M:E = 0.983:1
We already have their density in terms earth's density. They are in the same unit. So, we can compare them directly, with greater ratio means greater density. It's clear that Mercury has the greater density.
Given that El bisects ZCEA, which statements must be
true? Select three options,
mZCEA = 90°
mZCEF = m ZCEA + m ZBEF
mZCEB = 2(m ZCEA)
ZCEF is a straight angle.
ZAEF is a right angle.
Question: Given that BE bisects ∠CEA, which statements must be true? Select THREE options.
(See attachment below for the figure)
m∠CEA = 90°
m∠CEF = m∠CEA + m∠BEF
m∠CEB = 2(m∠CEA)
∠CEF is a straight angle.
∠AEF is a right angle.
Answer:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
Step-by-step explanation:
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Angle on a straight line = 180°. Therefore, m<CEA + m<AEF = m<CEF. Each right angle measures 90°.
Thus, the three statements that must be TRUE are:
m∠CEA = 90°
∠CEF is a straight angle.
∠AEF is a right angle
The correct statements from the given diagram is m∠CEA = 90°, m∠CEF = m∠CEA + m∠BEF and m∠CEB = 2(m∠CEA)
Lines and anglesFrom the given diagram, we have the following information
∠CEF is a straight angle.
∠AEF is a right angle.
Line AE is perpendicular to line CF, which is a straight line. This creates two right angles, <CEA and <AEF.
Since the angle on a straight line is 180 degrees, hence;
<CEA + m<AEF = m<CEF
Hence, the three statements that must be TRUE are m∠CEA = 90°, ∠CEF is a straight angle and ∠AEF is a right angle
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While solving an equation, if the variable term becomes zero, and the equation make a false statement, then the solution is
Answer:
no solution
Step-by-step explanation:
Then there is no solution.
Answer:
No solution.
Step-by-step explanation:
Then the equation has no solution.
For example
2x - 2 = 2x + 1
-2x - 2x
-2 = 1.
Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $7.50 fee and $14 She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60. Each pizza is cut into 8. She wonders how many total slices she can afford.
Answer:
The answer is 24
Step-by-step explanation:
If the restaurant fee is $7.5 and the price is $14 per pizza, she has $52.5 to spend on the pizzas after we deduct the restaurant fee.
That means she can get 52.5 / 14 = 3.75 pizzas.
Since she can't get .75 pizza, we can assume that she will order 3, which in total makes 8 x 3 = 24 slices.If she can however order 3.75 pizzas, .75 x 8 makes 6 slices so it is a total of 30 slices for 3.75 pizzas.I hope this answer helps.
The total slices she can afford is 30 and this can be determined by using the unitary method and forming the linear equation.
Given :
Jacque needs to buy some pizzas for a party at her office.She's ordering from a restaurant that charges a $7.50 fee and $14 for delivery.She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $60.The following steps can be used to determine the total slices she can afford:
Step 1 - Total cost to order one pizza is given by:
= 7.5 + 14
= $21.5
Step 2 - Let the total number of pizzas she can order be 'x'. So, the delivery fee plus the cost of the pizzas under $60 is represented by the equation:
14x + 7.5 = 60
14x = 52.5
x = 3.75
Step 3 - Now, according to the given data if one pizza contains 8 slices then 3.75 pizza contains:
[tex]= 3.75\times 8[/tex]
= 30 slices
The total slices she can afford is 30.
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Andre's school has 20 clubs, which is five times as many as his cousin's school.
His cousin's school has x clubs.
Answer:
4
Step-by-step explanation:
you would do 20÷5=x
to check it it would be 5x=20
5×4=20
Answer: X=4
Step-by-step explanation:
If your school has 20 clubs, 20 divided by 5 is 4
A new youth center is being built in erie. The perimeter of the rectangular playing field is 274 yards. The length of the field is 4 yards less than double the width. What are the dimensions of the playing field? need width and length in yards
Answer:
width is 47 and the length is 90
Step-by-step explanation:
Hello!
You find the perimeter by adding all the sides
l + l + w + w = p
The perimeter is 274
l + l + w + w = 274
It says the length is 4 less than double the width
l = 2w - 4
We can put this into the original equation
2w - 4 + 2w - 4 + w + w = 274
Now we solve
Combine like terms
6w - 8 = 274
Add 8 to both sides
6w = 282
Divide both sides by 6
w = 47
We can put w into the orginal equation to find l
l + l + 47 + 47 = 274
Combine like terms
2l + 94 = 274
Subtract 94 from both sides
2l = 180
Divide both sides by 2
l = 90
The answer is the width is 47 and the length is 90
Hope this helps!
Answer:
lenght: 90 yards
width: 47 yards
Step-by-step explanation:
perimeter = 2(length + width)
274 = 2(h + w)
h = 2w - 4
h = length
w = width
then:
274 = 2((2w-4) + w)
274/2 = 2w - 4 + w
137 = 3w - 4
137 + 4 = 3w
141 = 3w
w= 141/3
w = 47 yd
h = 2w - 4
h = 2*47 - 4
h = 94 - 4
h = 90 yd
probe:
274 = 2(47 + 90)
274 = 2(137)
find the square root of 2304 by division method
Answer:
Hope it helps you ♥️
Step-by-step explanation:
Find mNMKˆ. A. 222 B. 183 C. 213 D. 246
Answer:
B. 183 degrees.
Step-by-step explanation:
m arc MN = 360 - 107 - 177
= 360 - 284
= 76
m NMK = 76 + 107
= 183
The measure of the arc NMK will be 183°. Then the correct option is B.
What is a circle?The circle is at equidistant of points drawn from the center. The radius of a circle is the distance between the center and the circumference.
The measure of the angle ∠MLK is 35°.
The major and minor arc is 117x and 107x.
We know that the angle ∠MLK is the half of the difference of the major arc to minor arc.
∠MLK = (arc KN – arc KM) / 2
35° = (177x - 107x) / 2
70° = 70x
x = 1°
Then the measure of the arc KN will be
Arc NK = 177 x 1
Arc NK = 177°
We know that the sum of the arc KN and KMN will be 360°.
mNK + mNMK = 360°
177° + mNMK = 360°
mNMK = 360° – 177°
mNMK = 183°
The measure of the arc NMK will be 183°.
Then the correct option is B.
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58:49 A pound of raisins costs $2.00, and a pound of almonds costs $5.00. Six pounds of a trail mix contains 2 more pounds of raisins than almonds. What is the cost of the 6 pounds of trail mix
Answer:
$18
Step-by-step explanation:
1 pound of raisins = $2
1 pound of almonds = $5
Let the number of raisins be represented by a
Let the number of almonds be represented by b
We are told in the question that:
Six pounds of a trail mix contains 2 more pounds of raisins than almonds.
a + b = 6 pounds
Hence, Almonds = 2 pounds
Raisins = 4 pounds
The cost of the 6 pounds of trail mix
= 4 × $2 + 2 × $5
=$8 + $10
= $18
help.....ASAP!!!.....
Answer:
B
Step-by-step explanation:
[tex] \sqrt{19} + \frac{7}{2} \: is \: irrational \: \\ \because \: \sqrt{19} \: is \: irrational \: and \: \frac{7}{2} is \: rational \\ adding \: any \: rational \: number \: in \: irrational \: number \\ results \: in \: irrational \: number.[/tex]
PLEASE help me. I am stuck on this question for a long time.
Answer:
b.28% of the patients tested received the medication and experienced a decrease in blood pressure
Answer:
The second one
Step-by-step explanation:
The total of patients is 100% wich is equivalent to 1.
● 0.5 of them received medication and ● 0.54 of them experienced a decrease in blood pressure.
The intersection of both is worth 0.28
So out of 1, 0.28 took medication and experienced a blood pressure decrease
A function f(x) has range {yer 1-50}. Explain why reflecting the function vertically would not affect the range
Answer:
For the reflection property, we have;
For reflection vertically, which is equivalent to reflection across the y-axis, we have;
Let the location or point of the pre-image before, reflection be (x, y), then, the location or point of the image after reflection will be (-x, y)
Therefore, the y-coordinates remains the same
Given that the range of the function is the value of f(x) or y from 1 - 50, which are the y-coordinate values of the function, it will not be affected by the vertical reflection of the function.
Step-by-step explanation:
What’s the square root of 10 to the nearest thousandth
Answer:
3.162
Step-by-step explanation:
on a calculator type in sqrt of 10 and round it to three decimal places
What is the distance between (6, 2) and (-3, -2)?
Answer:
√97 ≈ 9.85 units
Step-by-step explanation:
The distance formula can answer this question.
d = √((x2 -x1)^2 +(y2 -y1)^2) = √((-3-6)^2 +(-2-2)^2) = √(81 +16) = √97
The distance between the points is √97 ≈ 9.85 units.
a way to make a approximation to a given number by using fewer digits is called.
Answer:
Rounding
Step-by-step explanation:
Rounding is a way to make an approximation to a given number by using fewer digits.
Answer:
Rounding
Step-by-step explanation:
A way to make a approximation to a given number by using fewer digits is called rounding
How you round:If the next smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding to by one (+1). Any remaining digits before the decimal point become zeros, and any that are after the decimal point are dropped.6. Christopher can make enough iced coffee for one
person by mixing two teaspoons of espresso
with 4 ounces of water. How many tablespoons
of espresso would he need to make enough iced
coffee for 24 people? (3 teaspoons =
1 tablespoon
A) 12
B) 16
C) 48
D) 144
R
Answer:
B) 16
Step-by-step explanation:
Espresso required for one person:
2 teaspoonsEspresso required for 24 people:
2*24 = 48 teaspoons3 teaspoons = 1 tablespoon
48 teaspoons = 48/3 = 16 tablespoons
Christopher needs 16 tablespoons of espresso.
Correct answer choice: B) 16
Translate the statement 9n+3>5n
Three more than nine times a number is at least five times the number.
What is the value of the expression below?
Negative 8 + 19 + 8
A. 0
B. 11
C. 19
E. 35
I believe it's 19 but next thing you know it's a complete different equation :
Answer:
c .19
Step-by-step explanation:
Ally sliced 32 \text{ kg}32 kg32, start text, space, k, g, end text of watermelon for a party. She divided the watermelon slices equally between 888 large bowls
Complete question :
Ally sliced 32 kg of watermelon for a party. She divided the watermelon slices equally between 8 large bowls.
How many grams of watermelon did Ally put in each bowl?
Answer:
4000g
Step-by-step explanation:
Given the following :
Mass of water melon sliced = 32kg
Number of bowls water melon was shared equally in = 8
Therefore, mass of water melon on each bowl :
Mass of water melon / number of bowls
= 32kg / 8
= 4kg
Note:
1000g = 1kg
Therefore,
4kg = (4 * 1000)
= 4000 grams
Therefore, amount in gram of watermelon put in each bowl is 4000g
Marissa has a Master's degree and earns an annual salary of $80,400. She works 40 hours per week for 48 weeks per year. Her sister has a Bachelor's degree and earns an average salary of $58,000. She works 40 hours a week for 52 weeks. How much greater is Marissa's hourly wage than her sister's hourly wage? Round your answer to the nearest whole dollar.
Answer:
$14
Step-by-step explanation:
Marissa has a Master's degree and earns annual salary of $80,400.
She works 40 hours per week for 48 weeks per year.
Her sister has a Bachelor's degree and earns an average of $58,000 per year.
She works 40 hours per week for 52 weeks per years.
Marissa works for a total of 40 × 48 = 1920 hours a year.
Her hourly wage = [tex]\frac{80,400}{1920}[/tex] = $42 (rounded up to nearest dollar).
Her sister works for a total of 40 × 52 = 2080 hours
Her hourly wage = [tex]\frac{58,000}{2080}[/tex] = $28 (rounded up to nearest dollar)
So Marissa's hourly wage is $42 - $28 = $14 more than her sister's hourly wage.
What is 18/100 written as a decimal?
Answer:
18/100 as a decimal is:
0.18
Hope this helps! （づ￣3￣）づ╭❤～
Step-by-step explanation:
Answer:
0.18
Step-by-step explanation:
18 divided by 100 is 0.18 18 divided by 1000 is 0.018
you move the decimal to the left when you divided a number by ten how many zeros is how many times you move the decimal. every number is a decimal like if you have a number 20 it actually looks like 20. so when you divide it by a 10 or 100 to move the decimal to the left the same number of zeros in 100 so that would be 0.20 hope you understand
Solve the formula 4x + 7y = 5 for y.
Answer:
39x
Step-by-step explanation:
Just multiply 7 by 5 and that equals-35
now you just add 4x by 35 and that equals-39x
what should be multiplied to 288 to become it a perfect square
Greetings from Brasil...
Follow the reasoning.
288 ÷ 2 = 144
and 144 its a perfect square (144 = 12²)
It is visible that if we multiply 288 by 1/2, we will obtain a perfect square, but we will do this via a simple equation
288 · X = 144
X = 144 ÷ 288
X = 0,5 ⇔ X = 1/2
The formula for the volume V of a rectangular prism is V = ℓwh, where ℓ represents the length, w represents the width, and h represents the height. Rearrange the quantities in this formula to give a new formula for the width of the rectangular prism.
Answer:
w = V / lh
Step-by-step explanation:
V = ℓwh
Where,
V=volume of a rectangular prism
l= length of the rectangular prism
w= width of the rectangular prism
h= height of the rectangular prism
Rearrange the quantities in this formula to give a new formula for the width of the rectangular prism.
V = ℓwh
It can be written as
V = l * w * h
w = V ÷ l * h
= V / lh
w = V / lh
Width of a triangular prism equals Volume of the rectangular prism divided by length of the rectangular prism times height
The house Trevor's family lives in has 6 66 people (including Trevor) and 3 33 bathrooms. In the past month, each person showered for an average of 480 480480 minutes and used an average 72 7272 liters of shower water (over the entire month). Water costs 0.20 0.200, point, 20 dollars per liter. How much did Trevor's family pay per minute on shower water?
Answer:
The amount Trevor's family pay per minute on shower water is $0.005.
Step-by-step explanation:
The cost of water is,
Cost = $0.20/liter
Amount of water used over the entire month:
Amount of water used = 72 liters
Compute the total water cost as follows:
Total water cost = Amount of water used × Cost
= 72 × 0.20
= $14.4/liter
The average number of minutes each person showered is:
Average number of minutes = 480 minutes.
The number of people in Trevor's house:
N = 6
Compute the total amount of time the 6 person showered as follows:
Total amount of time = Average number of minutes × N
= 480 × 6
= 2880 minutes
Compute the pay per minute on shower water as follows:
Pay per minute on water = Total water cost ÷ Total amount of time
= $14.4 ÷ 2880
= $0.005
Thus, the amount Trevor's family pay per minute on shower water is $0.005.
Answer:
0.03
Step-by-step explanation:
E Question Help
1.3.AP-9
Two hikers are 22 miles apart and walking toward each other. They meet in 4 hours. Find the rate of each hiker if one hiker walks 1.1 mph faster than the other
The speed of the slow hiker is mph, and the speed of the fast hiker is mph.
Step-by-step explanation:
Since, the hiker are walking at different speeds they meet at a point not in the middle.
Let distance travelled by Hiker A (slower) be x at speed s.
So, distance travelled by Hiker B (faster) is (22 - x) at a speed (s + 1.1) .
[tex]speed \: = \frac{distance}{time} [/tex]
s = x / 4s + 1.1 = 22 - x / 4Solving equations 1 and 2, we get :
x = 8.8m and s = 2.2mph
Therefore,
Speed of Hiker A = 2.2 mph
Speed of Hiker A = 2.2 mphSpeed of Hiker B = 3.3 mph
Find the exact area of the shaded region. A. 16π−8 cm² B. 42.3 cm² C. 92.5 cm² D. 84.6 cm2
Answer:
A = (16π - 8) cm^2
Step-by-step explanation:
The shaded area is trhe area of the circle minus rthe area of the truiangle,.
A = πr^2 - bh/2
A = π(4 cm)^2 - (4 cm)(4 cm)/2
A = 16π cm^2 - 8 cm^2
A = (16π - 8) cm^2
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
Option (A) is correct.
To find the shaded area.
What is circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.
Given that:
Height of triangle is same as that of base because is equal to radius of circle.
The shaded area is area of the circle minus the area of the triangle.
A = π[tex]r^2 - bh/2[/tex]
A = π[tex]4^{2}[/tex] - (4 cm)*(4 cm)/2
A = (16π - 8 )[tex]cm^{2}[/tex]
A = (16π - 8) [tex]cm^{2}[/tex]
The exact area of the shaded region is (16π - 8) [tex]cm^{2}[/tex].
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