Answer:
a = .5
h= -2
k = -4
Step-by-step explanation:
h(x) = 0.5(x+2)²-4
The vertex form of a parabola is written as
y = a(x-h)²+k
Where (h,k) is the vertex
h(x) = 0.5(x- -2)²-4
a = .5
h= -2
k = -4
The measure of central angle RST is pi radians. What is the area of the shaded sector? 4pi units^2 8pi units^2 16pi units^2 20pi units^2
Answer:
8π units²
Step-by-step explanation:
Area of the circle can be defined as pi 'π' times the radius squared 'r²'
A= πr²
radius given is 4 (see attachment for the figure)
r=4
A = π4²
A= 16π
Now, if you look at the figure, you can see that the shaded area of the circle is 'half' of the whole circle.
We will half the Area which we have found it above in order to determine the area of shaded sector
Therefore,
area of the shaded sector = 16π/2 => 8π units²
Answer:
8[tex]\pi[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
did it on edge
The ratio of dogs to cats at the local pet store is 5:3
If there is 12 cats at the pet store, how many dogs
are at the pet store?
Answer:
20 dogs
Step-by-step explanation:
Answer:
20 Dogs.
Step-by-step explanation:
5:3=x:12
12/3=4
5x4=20
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
21
Step-by-step explanation:
2³ = 8
8/2
= 4
3.4(5)
= 17
4 + 17
= 21
Answer:
Your answer is going to be: 21.
Step-by-step explanation:
In this problem, we're going to be using PEMDAS.
[tex]\frac{1}{2} x^{3} +3.4y[/tex]
Now, we have to fill the blanks:
[tex]\frac{1}{2} 2^{3} +3.45[/tex] [tex](5)\\[/tex]
There's no parenthesis (3.45(5) is just another way of multiplying so that doesn't count). So, we move to the exponent part.
[tex]\frac{1}{2} 8+3.4(5)[/tex]
Everything else is just multiplication.
[tex]\frac{8}{2} + 17[/tex] = 4+ 17
Add it all together and your answer is going to be:
21.
P.S. Good luck with the rest of your assignment!!
Evaluate the piecewise function for ƒ(4).
A) −7
B) 9
C) 16
D) 24
f(4)= 16.
The answer is **C) 16**.
Here's how to evaluate the piecewise function f(4):
1. **Identify the appropriate rule:**
- Since 4 is greater than 2 (4 > 2), we'll use the second rule of the function: f(x) = 5x - 4.
2. **Substitute x = 4:**
- f(4) = 5(4) - 4
3. **Simplify:**
- f(4) = 20 - 4 = 16
Therefore, f(4) = 16.
The other options are incorrect because they either use the wrong rule (A and D) or miscalculate the result (B).
use the pythagorean theorem to prove whether or not each set of numbers represent the side length of a right triangle in your final answer, include your proof A. 6,12,15 B. 5,,12, and 13
Answer:
a. no, it is not a right triangle
b. yes, it is a right triangle
Step-by-step explanation:
The volume of a cylinder is 180 cubic meters. The height of the cylinder is 11.25 meters. What is the radius of the cylinder?
Answer:
2.26 meters
Step-by-step explanation:
so the volume for a cylinder is
v= π r² x h
now just substitute in the numbers you know:
180= π r² x 11.25
now rearrange the formula:
180= r² x 11.25π
(rearranging allows you to do this next bit with ease)
now divide by 11.25π on both sides to get
[tex]\frac{180}{11.25\pi }[/tex]= r²
to maintain accuracy, don't divide yet
now you know what r² is but you want r, so square root it:
[tex]\sqrt{\frac{180}{11.25\pi } }[/tex]=r
type that into a calculator and i think the answer is ...
2.25675833419
write the long answer in case you make a mistake when rounding
round appropriately : 2.26 meters ( I've done it to 2 decimal places)
and hopefully that's the correct answer.
Solve for p
p/8=7/9
P=?
Answer:
56/9
Step-by-step explanation:
Ariana just started a running plan where she runs 8 miles the first week and then
increases the number of miles she runs by 5% each week. If she keeps up this plan for
9 weeks, how many total miles would Ariana have run, to the nearest whole number?
Answer:
88
Step-by-step explanation:
What is the average rate of change for f(x) = -3* + 1 over the interval -2 < x <-1?
A. -1/9. B. -2/9. c. 1/9. d. 2/9
Answer:
B
Step-by-step explanation:
You can check it before choosing the answer.
I think 85% correct.
Please help, I’m not too smart
Answer:
x = - 4
Step-by-step explanation:
Given
r(x) = - 5x - 1 and r(x) = 19, then equating the right sides gives
- 5x - 1 = 19 ( add 1 to both sides )
- 5x = 20 ( divide both sides by - 5 )
x = - 4
Find the common difference Ce:-34,-29,-24,-19,...
Answer:
d = 5
Step-by-step explanation:
The common difference d is the difference between consecutive terms in the sequence
- 29 - (- 34) = - 29 + 34 = 5
- 24 - (- 29) = - 24 + 29 = 5
- 19 - (- 24) = - 19 + 24 = 4
Thus the common difference is d = 5
The common difference between consecutive terms in the given sequence is 5.
Explanation:The given sequence is {-34, -29, -24, -19, ...}
To find the common difference, we need to look for a pattern between consecutive terms. So, let's observe the differences between consecutive terms:
-29 - (-34) = 5
-24 - (-29) = 5
-19 - (-24) = 5
As we can see, the common difference between consecutive terms is 5.
The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway. The dimensions of the outside border of the walkway are
Answer:
(x+11) by (x+10)
Step-by-step explanation:
We know that Area = Length x width
Given: Area = x²+9x+20
Lets sort this out first
Area = x²+5x + 4x + 20
Area = x(x+5) + 4(x+5)
Area = (x+5) (x+4)
Therefore, it is concluded that:
Length 'l' = (x+5) feet
Width 'w' = (x+4) feet
if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides
Therefore,
Outer Length = (x+5+3+3) = (x+11) feet
Outer Width = (x+4+3+3) = (x+10) feet
Answer:
The fountain is (x+5) by (x+4).
dimensions of the outside border of the walkway are (x+11) by (x+10)
In rhombus ABCD, m∠XCB = 6a − 2 and m∠XBC = 4a + 12. What is the measure of ∠XCB?
Answer: Angle XCB = 46 degrees ( ∠XCB = 46°)
Step-by-step explanation: Please refer to the picture attached for details.
A rhombus basically is a parallelogram with a diamond shape. All four sides have equal length, opposite sides are parallel and opposite angles are equal.
The sides have been labelled ABCD as stated in the question, and the point X is extended to point B to form angle XBC and also extended to point C to form angle XCB. Upon careful observation we shall notice that a triangle has been formed with sides BXC and angle X is a right angle, which measures 90 degrees.
The sum of angles in a triangle equals 180, therefore,
Angle XBC + Angle XCB + Angle X = 180
Substituting for the given values we now have the following;
4a + 12 + 6a - 2 + 90 = 180
10a + 10 + 90 = 180
10a + 100 = 180
Subtract 100 from both sides of the equation
10a = 80
Divide both sides of the equation 10
a = 8
If XCB = 6a - 2,
Substitute for the value of a
XCB = 6(8) - 2
XCB = 48 - 2
XCB = 46
Therefore angle XCB measures 46 degrees.
A cruise ship can cover 21 nautical miles in 483 minutes. How many nautical miles will it travel in 161 minutes?
A. 7
B. 5
C. 9
D. 11
Answer:
A. 7
Step-by-step explanation:
483 ÷ 21 = 23. that means 1 nautical miles happens every 23 minutes. 7 × 23 = 161.
Answer:7
Step-by-step explanation:483 divided by 3 is 161 and 21 divided by 3 is 7
Find the value of x in the triangle
Answer:
x = 28
Step-by-step explanation:
The sum of the angles of a triangle add to 180
85+67+x = 180
Combine like terms
152 +x =180
Subtract 152 from each side
152-152+x = 180-152
x = 28
Answer:
x=28 degrees
Step-by-step explanation:
180-85=95
95-67=28
The ages of the members of four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
(a) Based on the information above, which team has the youngest members on average?
Team A
Team B
Team C
Team D
(b) Based on the information above, which team's ages have the least variability?
Team A
Team B
Team C
Team D
The answer the statement a and statement b is
a) the answer is team C
b)we can conclude that the answer is team A.
We have given that,
The ages of the members of the four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
We have to determine the a and b
a) The information above, which team has the youngest members on average
from the above observations we can conclude that the answer is team C.
What is the least variability?
A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by 2.
b) The information above, which team's ages have the least variability
from the above observations, we can conclude that the answer is team A.
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Akikta bought 25 trees for $15.40 each. Chloe bought 35 trees for $14.30 each. What was the difference between the total amounts that the girls paid for the trees?
Answer: $115.50
Step-by-step explanation:
500.5-385 = x
Answer:
$115.50
Step-by-step explanation:
(x + 3)2 + (x + 3) - 2 = 0
Answer:
x=-7/3
Step-by-step explanation:
2(x+3)+(x+3)-2=0
2x+6+x+3-2=0
3x+7=0
3x=-7
x=-7/3
Answer:
Step-by-step explanation:
) Yoona gives guitar lessons for $70 per session. She gives a 10% discount to students who
come to her studio for the lesson.
The question is about calculating the price of guitar lessons after a 10% discount and the answer explains the steps to calculate the discounted price.
Explanation:The subject of this question is Mathematics and the grade level is High School.
To calculate the amount after the discount, subtract 10% of $70 from $70. 10% of $70 is $7, so the discounted price is $70 - $7 = $63.
Therefore, Yoona gives a 10% discount to students which means the price per session is $63.
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Which of these numbers is in the solution set of x – 12 = 4? A. 3 B. 16 C. –8 D. 8
Answer:
x=16
so B
Step-by-step explanation:
Answer:
B. 16
Step-by-step explanation:
x-12=4
+12 +12
x=16
Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
Which statements are true about the lines? Select three options.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW.
Answers: Line WZ has the same slope as line XY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line WZ.
Will mark brainlist
Given. QR I PT and
Prove: APQR – ATSR
Angles
Segments
Triangles Statements Reasons
ZQPR
ZQRP
The mathematics question involves proving two triangles congruent in geometry, likely using congruence criteria such as SSS, SAS, or ASA, with the given information that line QR is parallel to PT.
Explanation:The subject of this question is Mathematics, specifically it involves geometry and the proof of congruent triangles. The statement 'QR I PT' suggests that line QR is parallel to line PT. To prove triangles APQR and ATSR are congruent, one would need to demonstrate that they satisfy the criteria for congruence such as side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA). The angles mentioned, such as ∠QPR and ∠QRP, are likely parts of the required congruence criteria. However, additional information and a specific criteria of congruence need to be applied in a step-by-step explanation.
Oil prices are projected to increase by 100% by next june. A quart of oil currently costs $2.45. What is the projected cost of a gallon of oil next june?
Answer:
The projected cost of a gallon of oil by next june is $19.60.
Step-by-step explanation:
Given:
Oil prices are projected to increase by 100% by next june.
A quart of oil currently costs $2.45.
Now, to find the cost of a gallon of oil next june.
So, to get the projected cost of a quart of oil by next june:
Cost of one quart of oil currently = $2.45.
Rate of oil prices projected to increase by = 100%.
[tex]100\%\ of\ \$2.45+\$2.45\\\\=\frac{100}{100}\times 2.45+2.45\\\\=2.45+2.45\\\\=\$4.90.[/tex]
Now, to get the projected cost of a gallon of oil by next june we use conversion factor:
4 quart = 1 gallon.
If, 1 quart oil price = $4.90.
Then, 4 quarts oil price = [tex]\$4.90\times 4[/tex] = [tex]\$19.60.[/tex]
Thus, 1 gallon oil price = $19.60.
Therefore, the projected cost of a gallon of oil by next june is $19.60.
Answer:
19.60
Step-by-step explanation:
If e = 9 cm and f = 40 cm, what is the length of g?
A. 43 cm
B. 39 cm
C. 31 cm
D. 41 cm
(9,40,41) is a Pythagorean Triple, farther down the list than teachers usually venture.
Answer: D. 41 cm
There's a subset of Pythagorean Triples where the long leg is one less than the hypotenuse,
a^2+b^2 = (b+1)^2
a^2 + b^2 = b^2 + 2b +1
a^2=2b+1
So we get one for every odd number, since the square of an odd number is odd and the square of an even number is even.
b = (a^2 - 1)/2
a=3, b=(3^2-1)/2=4, c=b+1=5
a=5, b=(5^2-1)/2 =12, c = 13
a=7, b=24, c=25
a=9, b=40, c=41
a=11, b=60, c=61
a=13, b=84, c=85
It's good to be able to recognize Pythagorean Triples when we see them.
Otherwise we'd have to work the calculator:
√(9² + 40²) = √1681 = 41
Which two-dimensional figure results from slicing the sphere with the blue plane?
A square
A circle
A line
A cone
A parabola
simplify 12^3 over 12^7
Answer:
12^3/12^7= 1/12^(7-3)= 1/12^4
Step-by-step explanation:
The solution to the problem '12 to the power of 3 over 12 to the power of 7' is 12 to the power of negative 4 or written as a fraction, it is 1 over 12 to the power of 4 or 1 over 20736.
Explanation:The expression 123 over 127 refers to the mathematical concept of 'division of exponentials with the same base'. The rule in this case is to subtract the exponents. Therefore, 123 over 127 simplifies to 12-4. This can be understood as 1 over 124, or further simplified, 1 over 20736 if you multiply out the exponent.
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What are the length and width of a rectangular
traffic sign if the length exceeds the width by 6
inches and the perimeter is 112inches?
Answer:
width is 25 inches
length is 31 inches
Step-by-step explanation:
We will need the formula for perimeter of a rectangle:
P = 2(l + w)
"l" is length, "w" is width
If the length exceeds the width by 6, then:
l = w + 6 <= Substitute this into the equation
P = 2(l + w)
P = 2(w + 6 + w)
Remember we also know the perimeter is 112:
112 = 2(w + 6 + w)
Collect like terms:
112 = 2(2w + 6)
Start isolating "w" to find width.
56 = 2w + 6 Divided both sides by 2
50 = 2w Subtracted 6 from both sides
25 = w Divided both sides by 2
w = 25 Variable on left for standard formatting
The width is 25 inches.
Find the length using "length exceeds width by 6".
l = w + 6
l = 25 + 6 Substitute the width
l = 31
The length is 31 inches.
∴ The length is 31 inches and the width is 25 inches.
Check your answer with the perimeter formula.
P = 2(l + w)
112 = 2(31 + 25) Substitute all the variables.
112 = 2(56)
112 = 112 Same answer
LS = RS Left side equals right side
The answer is correct.
Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5
Answer: OPTION 1
Step-by-step explanation:
For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:
[tex]arc\ length=rC[/tex]
where "C" is the central angle of the arc in radians and "r" is the radius.
Since you need to find the Central angle, you have to solve for "C" from that formula, as following:
[tex]C=\frac{arc\ length}{r}[/tex]
According to the information given in the exercise, you can identify that:
[tex]arc\ length=100\ m\\\\r=60\ m[/tex]
Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":
[tex]C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad[/tex]
Nicole sells T-shirts, t, for $8, and sells sweatshirts, s, for $18. She earns $475
in revenue. Which equation below represents this relationship?
Answer:
Step-by-step explanation:
Cost of t, T-shirts = t*8 = 8t
Cost of s, sweatshirts = s*18 = 18s
Equation:
8t + 18s = 475
Question 2
If it takes 8 meters of fabric to make 5 pairs of curtains, how many meters are required to make 22 pairs?
Answer:
35.2m
Step-by-step explanation:
8 meters of fabric make 5 pairs of curtains so divide 8 by 5 to find that it takes 1.6 meters of fabric to make 1 pairs of curtains
multiply 1.6 by 22 to get 35.2 meters of fabric