Answer:
12, 5, -7, 14/7, 9
Step-by-step explanation:
Integers are numbers that are either positive or negative and are whole numbers (no decimals).
What is the solution to the system of equations? {6x−2y=−144x−3y=−31 (−6, 11) (2, 1) (−2, 1) (2, 13)
Answer:
Answer:
(x , y)=(-31/306 , 775/51)
Step-by-step explanation:
6x-2y=-144x-3y=-31
Write as a system of equations.
6x-2y=-31
-144x-3y=-31
Multiply both sides of the equation by 24.
144x-48y=-744
-144x-3y=-31
Sum the equations vertically to eliminate at least one variable.
-51y=-775
Divide both sides of the equation by -51.
y=775/51
Substitute the given value of y into the equation 6x-2y=-31.
6x-2x775/51=-31
Solve the equation for x.
x=-31/306
The possible solution of the system is the ordered pair (x , y).
(x , y)=(-31/306 , 775/51)
Step-by-step explanation:
Choose the improper fraction that is equivalent to the mixed number 2 17/24
Answer:
31/24
Step-by-step explanation:
multiple 2 by 24, then add 17, which you get 31, and put it over 24
31/24
Which set of numbers is arranged in increasing order?
Answer:
B
Step-by-step explanation:
To solve this, we can make all of the numbers decimals.
π=3.14159265 and so on
Root 10 is about 3.16227766
22/7 is about 3.14285714
3.14 is already a decimal.
Now, our numbers are far easier to compare.
Let's put the numbers in increasing order.
3.14, 3.14159265, 3.14285714, 3.16227766
Substitute the original numbers in.
3.14, π, 22/7, Root 10
Therefore, option B is correct.
7. The function ƒ(x) = sqrt x is reflected across the x-axis and vertically stretched by a factor of 2. Select the correct graph for the resulting function.
Answer:
the answer is NOT b, i got that wrong on the quiz
Step-by-step explanation:
Answer:
The correct answer is C.
Step-by-step explanation:
(1,-2) (4,-4) (9,-6)
Evaluate j(5+k) + 15, when j=3 and k=4
Answer:
42
Step-by-step explanation:
j(5+k) + 15
Let j = 3 and k = 4
3(5+4) + 15
Parentheses first
3 (9) +15
Multiply
27 + 15
Add
42
Answer:
42
Step-by-step explanation:
j(5+k)+15
=3(5+4)+15
=3(9)+15
=27+15
=42
A= 47 sq. in.
Find the value of x. If necessary, round to the nearest tenth.
Answer:
x = 9.7
Step-by-step explanation:
The area of a triangle is A = b * h / 2 where A, b, and h are the area, base and height respectively. We know that A, b, and h equal 47, x, and x respectively so we can write:
47 = x * x / 2
47 = x² / 2
94 = x²
x = ±√94
In context, x can't be negative so the answer is x = √94 = 9.7.
Answer:
9.70 inches
Step-by-step explanation:
Area of a triangle is equal to base times height divided by 2.
[tex]bh/2[/tex]
Base and height is x.
[tex]xx/2=47[/tex]
Solve for x.
[tex]x^2=47 \times 2[/tex]
[tex]x^2=94[/tex]
[tex]x=\sqrt{94}[/tex]
[tex]x=9.69536[/tex]
please need help I will be MARKING as BRIANILIST. thank you so much.
Answer:
C. Multiply 3 by 18
Step-by-step explanation:
Susan reads:
1 page in 3 mins
So,
1 page = 3 mins
If we want the time for 18 pages, we would multiply both sides by 18
So,
18 pages = 3×18 mins
18 pages = 54 mins
Answer:
C
Step-by-step explanation:
1 page every 3 minutes
18 pages will take 3 × 18 = 54 minutes to read.
4.
Here is the proof of (sin x - cos x)2 = sec2 x - tan2 x - 2sin x cos x.
What is the missing line
Answer:
See Explanation Below
Step-by-step explanation:
Given
[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.[/tex]
Required
Prove
To start with; we open the bracket on the left hand side
[tex](sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)[/tex]
[tex](sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)[/tex]
[tex](sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x[/tex]
[tex](sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x[/tex]
Reorder
[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]
From trigonometry;
[tex]sin^2x + cos^2x = 1[/tex]
So;
[tex](sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x[/tex]
becomes
[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]
Also from trigonometry;
[tex]sec^2x - tan^2x = 1[/tex]
So,
[tex](sin x - cos x)^2 = 1 - 2sinx cos x[/tex]
becomes
[tex](sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x[/tex]
Proved
i need help pleaseeee ASAP!!!!!!
Answer:
180 degrees
Step-by-step explanation:
Can someone help me please!!!
Answer:
65°
Step-by-step explanation:
180°-50°:130°
130°÷2:65°
130° divide by 2 because the shape was isosceles triangle
Alex drives at an average speed that is 1/4 of the average speed that Roy's train travels. Alex takes 20 minutes to travel 12 km in her car. Roy travels for 2 hours and 20 minutes on his train. How far does Roy travel to 2 dp?
Answer:
336.00 km distance of train
Step-by-step explanation:
Alex = 20mins =12km We distribute to 1hr to find 60mins = 36km p/h.
Roy = 2hrs 20 mins and is 4x the speed of the car.
So 36km x 4 p/h = 144km p/h
2hrs and 20 = 144 x 2.3333 = 335.9952 = 336km
Answer:
336 km
Step-by-step explanation:
"Alex takes 20 minutes to travel 12 km in her car."
Alex's speed = (12 km)/(20 min) = 0.6 km/min
"Alex drives at an average speed that is 1/4 of the average speed that Roy's train travels."
Therefore, Roy's speed is 4 times Alex's speed.
Roy's speed = 4 * 0.6 km/min = 2.4 km/min
Roy travels for 2 hours and 20 minutes = 2 * 60 min + 20 min = 140 min
speed = distance/time
distance = speed * time = 2.4 km/min * 140 min = 336 km
Shruthi has a total of ₹590 as currency notes in the denominations of ₹50, ₹20 and ₹10. The ratio of the number of ₹50 notes and ₹20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination she has?
Answer:
50 = 6 notes
20 = 10 notes
10 = 9 notes
Step-by-step explanation:
to check whether it is correct :
50×6 + 20×10 + 10×9 = 590 (total money of Shruti)
Answer:
What does this mean
Step-by-step explanation:
A restaurant gets an average of 5.3 complaints per
day from its patrons. Use the Poisson distribution
formula to find the probability that on a given day
the restaurant will receive
a. exactly 4 complaints.
b. between 2 and 6 complaints.
Answer:
a. 16.41%
b. 68.57%
Step-by-step explanation:
We have that the poisson formula is as follows:
P (x = x) = (e ^ l) * (l ^ x) / x!
In this case l = 5.3
a. 4 exactly therefore x = 4, replacing:
P (x = 4) = (e ^ 5.3) * (5.3 ^ 4) / 4!
P (x = 4) = 0.1641
That is, the probability is 16.41%
b. between 2 and 6 complaints.
P (2 <= x <= 6) = P (x = 2) + P (x = 3) + P (x = 4) + P (x = 5) + P (x = 6)
replacing:
P (2 <= x <= 6) = (e ^ 5.3) * (5.3 ^ 2) / 2! + (e ^ 5.3) * (5.3 ^ 3) / 3! + (e ^ 5.3) * (5.3 ^ 4) / 4! + (e ^ 5.3) * (5.3 ^ 5) / 5! + (e ^ 5.3) * (5.3 ^ 6) / 6!
P (2 <= x <= 6) = 0.6857
In other words, the probability is 68.57%
The radius of a circle is 9.7 m. Find the circumference to the nearest tenth?(help its urgent)
Answer:
Step-by-step explanation:
Circumference C=2πr r=radius [tex]\pi =3.14[/tex]
C=2(3.14)9.7
C=60.9
The amount of money, in dollars, Sarah has in her savings account is modeled as a function of time in months. This function is represented by the graph below. What is the average rate of change for the amount of money, in dollars per month, from month 0 to month 12? A $25 per month B $50 per month C $300 per month D $500 per month
Answer:
The average rate of change for the amount of money is A) $25 per month
Step-by-step explanation:
From the graph we can see Sarah earn $50 every two months, 50/2 = 25/1 so we can determine Sarah's average rate of change from month 0 to month 12 is $25 dollars per month. Hope this helped, let me know if you have any questions! :)
The weight of a body above sea level varies inversely with the square of the distance from the center of Earth. If a woman weighs 123 pounds when she is at sea level, 3960 miles from the center of Earth, how much will she weigh when she is at the top of a mountain, 3.2 miles above sea level?
Answer:
Her weight is approximately 122.8lb
Step-by-step explanation:
Given
Inverse proportion;
Weight = 123lb when distance = 3960 miles from center of earth
Required
Calculate the weight when distance is 3.2 miles above sea level
Let weight be represented by W and distance by D
From the question, we understand that;
Weight is inversely proportional to square of distance;
Mathematically; this is
[tex]W \alpha \ \frac{1}{D^2}[/tex]
Convert proportion to equation
[tex]W = \frac{k}{D^2}[/tex]
Where k is the constant of proportionality
When W = 123; D = 3960.
This implies that
[tex]123 = \frac{k}{3960^2}[/tex]
Make k the subject of formula
[tex]k = 123 * 3960^2[/tex]
[tex]k = 1928836800[/tex]
Calculating her weight when she's at the top of mountain, 3.2 miles above sea level
First, her distance from center of earth has to be calculated
Distance = Previous distance + 3.2
Distance = 3960 + 3.2
Distance = 3963.2
Now, her weight can be calculated using [tex]W = \frac{k}{D^2}[/tex]
Substitute for k and D
[tex]W = \frac{1928836800}{3963.2^2}[/tex]
[tex]W = \frac{1928836800}{15706954.24}[/tex]
[tex]W = 122.801452817[/tex]
[tex]W = 122.8\ (Approximated)[/tex]
Bud's cheeseburger and fries contained 1310 milligrams and 350 milligrams of sodium, respectively. Together they contained 66.4% of the recommended daily intake of sodium for
diet. What is the daily recommended intake of sodium for a 2,000 calorie diet?
Answer:
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Step-by-step explanation:
In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.
[tex]\text{total sodium} = 1310 + 350 = 1660 \text{ mg}[/tex]
We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:
[tex]\frac{1660}{x} \frac{mg}{mg} = \frac{66.4\%}{100\%}[/tex]
[tex]66.4*x = 1660*100\\x = \frac{166000}{66.4} = 2500 \text{ mg}[/tex]
The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.
Answer:
2,500 mg
1,310 + 350 = 1,660
1,660 is 66.4% of 2,500
8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How
much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?
The amount of pure gold that should be added is
grams.
(Type an integer or a decimal.)
Answer: 65 grams
Step-by-step explanation:
If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, you should first calculate the amount of gold that makes up this percentage.
That is, 85% of 130 grams.
85/100 × 130 = 110.5
Then, let X be what will be added to the above value to make 90%. So,
(110.5 + X) / ( 130 + X ) × 100 = 90
Divide both sides by 100
(110.5 + X) / ( 130 + X ) = 90/100
(110.5 + X) / ( 130 + X ) = 0.9
Cross multiply and open the bracket
110.5 + X = 117 + 0.9X
Collect the like terms
X - 0.9X = 117 - 110.5
0.1X = 6.5
Divide both sides by 0.1
X = 6.5/0.1
X = 65 grams
Therefore, the amount of pure gold that should be added is 65 grams
Find x in the given figure. answers: A) 120° B) 60° C) 72° D) 168°
Answer:
x =72
Step-by-step explanation:
120 = x+48 alternate interior angles are equal
Subtract 48 from each side
120-48 = x
72 =x
IMAGE 1: Find the value of the indicated trigonometric ratio cos α
IMAGE 2: Find the value of the indicated trigonometric ratio sin β
IMAGE 3: Find the value of the indicated trigonometric ratio cot γ
IMAGE 4: Find the value of the indicated trigonometric ratio tan α (WORTH 30 POINTS!) Thanks!
Answer:
28.07° ; 70.53° ; 53.13° ; 36.87°
Step-by-step explanation:
Using PYTHAGORAS RULE :
IMAGE 1:
value of cos α equals :
cos α = Adjacent / Hypotenus
cos α = 15 / 17
cos α = 0.88235
α = cos^-1 (0.88235)
α = 28.07°
IMAGE 2:
sin β = Opposite / Hypotenus
sin β = 14√2 / 21
sin β = 0.9428
β = sin^-1(0.9428)
β = 70.53°
IMAGE 3:
From trigonometry :
cot = 1 / tan
Tan = Opposite / Adjacent
Therefore, Cot = Adjacent / Opposite
cot γ = 3/4
cot γ = 0.75
γ = cot^-1 (0.75)
γ = 53.13°
IMAGE 4:
tan α = Opposite / Adjacent
tan α = 15 / 20
tan α = 0.75
α = tan^-1 (0.75)
α = 36.87°
Answer:
15
Step-by-step explanation:
Can u please help me , I’m stuck on this .
Answer:
Use this website it gives you the answer and show the work
math
way
dot
com
Step-by-step explanation:
Answer:
24a: n = 5/14
24b: p = 18
25a: (x + 11) (x - 12)
25b: x (x + 2) (x - 2)
Step-by-step explanation:
I hope this helps
Help please I don’t understand the concept
Answer:
B
Step-by-step explanation:
The question is asking for what y would be when x is 2.
So, look on the graph where x = 2.
When x = 2, y = 6.
This means after 2 hours, the cost is $6
DF is the angle bisector of ADE. Determine the value of x. ANSWERS: A) – 8 B) 8 C) – 4 D) 4
Answer:
D) [tex]x=4 \textdegree[/tex]
Step-by-step explanation:
Before answering this question, we must first understand what an angle bisector is. An angle bisector is any ray, line, or line segment that splits an angle into two congruent, smaller angles.
That being said, since [tex]DF[/tex] bisects [tex]\angle ADE[/tex], we can say that [tex]\angle ADF \cong \angle FDE[/tex]. If you'll remember, congruent angles have equal measures, so [tex]m\angle ADF = m\angle FDE[/tex].
Substituting the given values of the angle measures into the equation and solving, we get:
[tex]9x-1=8x+3[/tex]
[tex]9x=8x+4[/tex] (Add 1 to both sides)
[tex]\bf x = 4 \textdegree[/tex] (Subtract 8x from both sides)
Hope this helps!
Answer:
[tex]x = 4[/tex]
Answer D is correct.
Step-by-step explanation:
( ADF angle = FDE angle)
[Because DF is the angle bisector]
[tex]9x - 1 = 8x + 3[/tex]
[tex]9x - 8x = 1 + 3 \\ x = 4[/tex]
hope this helps you.
Two surveys are chosen at random from the group of surveys. After the first survey is chosen, it is returned to the stack and can be chosen a second time. What is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family? StartFraction 1 Over 50 EndFraction StartFraction 2 Over 15 EndFraction StartFraction 3 Over 20 EndFraction StartFraction 17 Over 60 EndFraction
Answer:
StartFraction 1 Over 50 EndFraction
Step-by-step explanation:
Hope this helps
Correct me if this is wrong
Answer: 1/50
Step-by-step explanation:
edge
4x-(6x-1)<8x+2(x-3)
Answer:
7/12 <x
Step-by-step explanation:
4x-(6x-1)<8x+2(x-3)
Distribute
4x - 6x +1 < 8x +2x -6
Combine like terms
-2x +1 < 10x -6
Add 2x to each side
-2x+1+2x < 10x-6+2x
1 < 12x-6
Add 6 to each side
1+6 < 12x-6+6
7 < 12x
Divide by 12
7/12 <x
Answer:
x > 7/12
Step-by-step explanation:
4x-(6x-1)<8x+2(x-3)4x- 6x+1 < 8x +2x - 6-2x +1 < 10x -612x > 7x > 7/12Which represents the solution set of 5(x+5) < 85?
X<12
x>12
x<16
x>16
Answer:
x<12
Step-by-step explanation:
Divide both sides by 5
5(x+5) < 85
5 5
then simply
Answer:
x < 12
Step-by-step explanation:
[tex]5(x+5)<85\\\\5 * x = 5x\\\\5 * 5 = 25\\\\5x+25<85\\\\5x+25-25<85-25\\\\5x<60\\\\\frac{5x}{5}<\frac{60}{5}\\ \boxed{x<12}[/tex]
The system of equations y = one-fourth x minus 5 and y = negative one-half x minus 3 is shown on the graph below. On a coordinate plane, 2 lines intersect around (2.8, negative 4.2). Which statement is true about the solution to the system of equations? The x-value is between 2 and 3, and the y-value is between –4 and –5. The x-value is between –4 and –5, and the y-value is between 2 and 3. The x-value is between –2 and –3, and the y-value is between 4 and 5. The x-value is between 4 and 5, and the y-value is between –2 and –3.
Answer:
The x-value is between 2 and 3, and the y-value is between –4 and –5
Step-by-step explanation:
The system of equations:
y = 1/4x - 5
y = -1/2x - 3
is shown in the figure attached. There it can be seen that the solution is (2.667, -4.333). This can be corroborated as follows:
y = 1/4(2.667) - 5 = -4.333
y = -1/2(2.667) - 3 = -4.333
Answer:
A its a
Step-by-step explanation:
can someone help me with this pleaseee
Answer:
The real part is -1
Step-by-step explanation:
The real axis is the horizontal axis
The value on the horizontal axis is -1
?????????????? Anyone?
The answer is E) 22
This is the answer because the triangles are similar, so a proportion can be made. So it would be 28/42=x/33. Then you solve for x, which equals 22.
What is the measure of ∠E? Enter the correct value. Do not enter the degree symbol.
Answer:
To find < E we use tan
tan E = opposite / adjacent
DF is the opposite
EF is the adjacent
DF = 11
EF = 11
tan E = 11/11
tan E = 1
E = 45
Hope this helps
Answer:
45 degrees
Step-by-step explanation:
Since this triangle is isosceles, we know that the other angles, D and E, are both 45 degrees because of the sum of interior angles of a triangle always equaling 180 degrees.