Answer:
b = (a - 6)^2
Step-by-step explanation:
Solve for b:
a = sqrt(b) + 6
a = sqrt(b) + 6 is equivalent to sqrt(b) + 6 = a:
sqrt(b) + 6 = a
Subtract 6 from both sides:
sqrt(b) = a - 6
Raise both sides to the power of two:
Answer: b = (a - 6)^2
The formula is simplified as the equation b = a² - 6
Given data:
To make "b" the subject of the formula "a = √(b + 6)", we need to isolate "b" on one side of the equation.
Here are the steps to rearrange the equation and solve for "b":
Start with the equation: a = √(b + 6).
Square both sides of the equation to eliminate the square root:
(a)² = (√(b + 6))².
Simplify the right side of the equation:
a² = b + 6.
Subtract 6 from both sides of the equation to isolate "b":
a² - 6 = b.
So, the equation "a = √(b + 6)" can be rearranged as "b = a² - 6". This new equation allows us to calculate the value of "b" based on a given value of "a".
Hence, the equation is b = a^2 - 6.
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Answer the following 3 question(s) using the information from the scenario below.
Katrina is looking at banquet halls for her parents’ anniversary party. Moonlight Hall charges a fixed cost of $1000 plus $75 per guest. Riverside Hall charges $1500 plus $50 per guest. Let C represent the total cost, in dollars, and let n represent the number of guests.
Identify the system of linear equations that represents this situation.
Select one
a. Moonlight: C=75n+1000
Riverside: C=50n+1500
b. Moonlight: C=1500−75n
Riverside: C=1000−50n
c. Moonlight: C=1000−75n
Riverside: C=1500−50n
d. Moonlight: C=50n+1000
Riverside: C=75n+1500
What are the coordinates of the solution?
Select one
a. (-20, 0)
b. (20, 0)
c. (20, 2500)
d. (-20, 2500)
Identify the statement that best describes the solution to this linear system.
Select one
a. When there are 20 guests attending, the price is less at the Moonlight Hall.
b. It always costs more to use the Riverside Hall.
c. When there are 20 guests attending the price is $2500.
d. It always costs more to use the Moonlight Hall.
Answer:
Answer 1: a. Moonlight: C=75n+1000
Riverside: C=50n+1500
Answer 2: c. The solution coordinates are c. (20, 2500)
Answer 3: c. When there are 20 guests attending the price is $2500.
Step-by-step explanation:
Moonlight Hall:
Fixed cost = $1000
Cost per guest = $75
Cost of 'n' guests = 75 [tex]\times n[/tex]
Total cost of moonlight hall = Fixed cost + Cost of 'n' guests
[tex]\Rightarrow 1000 + 75 \times n[/tex]
Riverside Hall:
Fixed cost = $1500
Cost per guest = $50
Cost of 'n' guests = 50 [tex]\times n[/tex]
Total cost of moonlight hall = Fixed cost + Cost of 'n' guests
[tex]\Rightarrow 1500 + 50 \times n[/tex]
Hence, Answer 1:
a. Moonlight: C=75n+1000
Riverside: C=50n+1500
Answer 2: Coordinates of solution:
Option c. (20,2500) satisfies both the equation.
When there are 20 number of guests, the cost of both moonlight and riverside hall comes out to be 2500.
Moonlight Hall cost
[tex]75 \times 20 + 1000\\\Rightarrow \$2500[/tex]
Riverside Hall cost
[tex]50 \times 20 + 1500\\\Rightarrow \$2500[/tex]
Answer 3: c. When there are 20 guests attending the price is $2500.
The solution is done in Answer 2.
So,
Answer 1: a. Moonlight: C=75n+1000
Riverside: C=50n+1500
Answer 2: c. The solution coordinates are c. (20, 2500)
Answer 3: c. When there are 20 guests attending the price is $2500.
Please please please I need help
Answer:
The alternative interior angles theorem.
Step-by-step explanation:
The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
What is the value of x?
Answer:
x = 9
Step-by-step explanation:
→Looking at the angles, you can see that a right angle is formed. This means that there must be another right angle (90 degrees) formed with the numbers. You can set up the equation, like so:
3x + 6 + 57 = 90
→Add like terms (6 and 57):
3x + 63 = 90
→Subtract 63 from both sides:
3x = 27
→Divide both sides by 3:
x = 9
Answer:
x=9
Step-by-step explanation:
a right angle is 90 degrees
90-57= 33
33-6=27
27/3 = 9
Its my request to you to mark this as the brainiest
which graph function of x?
the horizontal is the graph function of x
find the fifth term of this sequence? 3n^2-1
Answer:
Step-by-step explanation:
50^2 is 2500, 3 times that is 7500, minus 1 and the answer would be 7499
What is the scale factor of Xyz to UVW?
Answer & Step-by-step explanation:
In order to solve this problem, we are going to have to divide. Since the triangles are similar, then that means that we are going to have to find the ratio between the sides which will also be our scale factor.
We can divide 75 by 15 since they are corresponding sides. Once we find the ratio between the sides, then we can conclude that the scale factor would be that number.
75 / 15 = 5
So, the scale factor of XYZ to UVW is 5.
The scale factor of [tex]Xyz[/tex] to [tex]UVW[/tex] is 5.
What is scale factor?The ratio that we get when you divide corresponding side lengths of similar figures is called the scale factor.
According to the given question.
We have a two triangles Xyz and UVW. And both the triangles are similar to each other.
In triangle Xyz we have
[tex]Xy = 60[/tex]
[tex]yz = 75[/tex]
and
[tex]zX = 90[/tex]
Also, in triangle UVW we have
[tex]UV = 12[/tex]
[tex]VW = 15[/tex]
and, [tex]WU = 18[/tex]
Therefore, the scale factor of Xyz to UVW is given by
[tex]\frac{Xy}{UV} =\frac{yz}{VW} =\frac{zX}{WU}[/tex]
⇒ [tex]\frac{60}{12} =\frac{75}{15} =\frac{90}{18} =5[/tex]
Hence, the scale factor of [tex]Xyz[/tex] to [tex]UVW[/tex] is 5.
Thus option B is correct.
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Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Answer:
2x^2-x+4
Step-by-step explanation:
2x^2-x+4 because they are not like terms so u cant simplify it
How do you solve the three forms: Slope Y-intercept form Standard Form Point slope form
Answer:An equation in the slope-intercept form is written as
y=mx+b
Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.
Example
Find the equation of the line
Choose two points that are on the line
Calculate the slope between the two points
m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23
We can find the b-value, the y-intercept, by looking at the graph
picture28
b = 1
We've got a value for m and a value for b. This gives us the linear function
y=−23x+1
In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.
We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope
m=−23
This gives us the equation
y=−23x+b
From this we can solve the equation for b
b=y+23x
And if we put in the values from our first point (-3, 3) we get
b=3+23⋅(−3)=3+(−2)=1
If we put in this value for b in the equation we get
y=−23x+1
which is the same equation as we got when we read the y-intercept from the graph.
To summarize how to write a linear equation using the slope-interception form you
Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.
Once you've got both m and b you can just put them in the equation at their respective position.
Write the fraction as a percent. Round to the nearest tenth of a percent if necessary.
17/40
Answer:
the answer is-
Step-by-step explanation:
42.5% and the estimation is 43%
Answer:
42.5%
Step-by-step explanation:
17/40 = 0.425
Move decimal to the tenths place.
0.425 --> 42.5
use a power reduction identity to simplify 8cos^4x
The simplified value is 8*cos^4(x) = 3+ 4 cos2x + cos 4x.
What is power reduction identity?The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers. This becomes important in several applications such as integrating powers of trigonometric expressions in calculus.
Given:
Using the power reduction identity, we have that:
cos² x= 1/2( 1+ cos 2x)
cos^4(x) = (cos² x)²= (1/2( 1+ cos 2x))²
cos^4(x) = 1/4( 1+ cos² 2x+ 2 cos (2x))
Again, cos² 2x= 1/2( 1+ cos 4x)
cos^4(x) = 1/4( 1+ 1/2( 1+ cos 4x)+ 2 cos (2x))
cos^4(x) = 1/4( 1+ 1/2 +1/2 cos 4x+ 2 cos (2x))
cos^4(x) = 1/4( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 8*1/4( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 2( 3/2 + 2 cos2x + 1/2 cos 4x)
8*cos^4(x) = 3+ 4 cos2x + cos 4x
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answer pleases I rlly need it:(
Answer: The answer is 23
Step-by-step explanation:
Good luck
Which equation represents a line that passes through (2, -1/2) and has a slope of 3?
y-2 = 3(x + 1/2)
y-3 = 2(x + 1/2)
y+1/2= 3(x - 2)
y + 1/2 = 2(x – 3)
Answer:
y+1/2= 3(x - 2)
Step-by-step explanation:
The slope can be seen to be 3 by factoring out each of the right sides. Only a and c have a slope of 3. Next if the point (2,-1/2) is plugged into the equation of c then you get an answer of 0=0. Beacuse both sides are equal when the point desired is plugged in it is the correct answer.
Answer: C
Step-by-step explanation:
I took the test
if x = 5, what is ((x+3)/4)*234
Answer:
468
Step-by-step explanation:
8/4*234=2*234=468
Answer:
468
Step-by-step explanation:
5+3/ 4 =2
2*234=468
Find the distance between the points.
(-3,2) and (0,2)
The distance is
Answer:
d=3
Step-by-step explanation:
by using distance formula
d=√(x2-x1)²+(y2-y1)²
let the points be A(-3,2) B(0,2)
d=√(0--3)²+(2-2)²
d=√(+3)²+(0)²
d=√9
d=3
express the given equation in quadratic form :
Answer: [tex]5n^2-48n-20=0[/tex]
Step-by-step explanation:
Here are the steps:
[tex]\frac{n+2}{n-2}- \frac{n-2}{n+2} =\frac{5}{6} \\\frac{(n+2)^2-(n-2)^2}{(n+2)(n-2)} =\frac{5}{6} \\\frac{n^2+4n+4-(n^2-4n+4)}{n^2-4} =\frac{5}{6}\\ \frac{n^2+4n+4-n^2+4n-4}{n^2-4} =\frac{5}{6}\\\frac{8n}{n^2-4} =\frac{5}{6}\\48n=5(n^2-4)\\5n^2-20-48n=0\\5n^2-48n-20=0[/tex]
In triangle ABC, AB = 6 cm, BC = 13 cm and angle ACB = 23°.
Calculate angle BAC, which is obtuse.
Answer:
angle BAC = 57.84°
Step-by-step explanation:
To find angle BAC given AB=6cm BC= 13 cm and ACB=23°
we will follow the steps below;
we can use the sine formula to solve the problem given
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
from the question given;
A = ?
C = 23°
c=AB = 6 cm
a=BC = 13 cm
substitute the values into the formula above
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
[tex]\frac{sin A}{13}[/tex] = [tex]\frac{sin 23}{6}[/tex]
cross -multiply
6 sinA = 13 sin23°
sin A = 13 sin23° / 6
sin A = 0.84658
take the [tex]sin^{-1}[/tex] of both-side
[tex]sin^{-1}[/tex] sin A = [tex]sin^{-1}[/tex] (0.84658)
on the left-hand side of the equation [tex]sin^{-1}[/tex] will cancel-out sin leaving us with just A
A = [tex]sin^{-1}[/tex] (0.84658)
A ≈ 57.84°
angle BAC = 57.84°
WILL MARK BRAINLIEST ASAP
Which of the following illustrates the associative property of multiplication?
4 × 8 = 8 × 4
2(12 + 3) = 2 × 12 + 2 × 3
9 × (1 × 4) = (9 × 1) × 4
8 × 1 = 8
Answer:
9 × (1 × 4) = (9 × 1) × 4
Step-by-step explanation:
Number 3 because the associative property states that it doesn't matter how you add / multiply something in sets.
9 × (1 × 4) = (9 × 1) × 4 shows 9 × 1 × 4 in 2 ways with 2 sets.
Answer:
9 × (1 × 4) = (9 × 1) × 4 is the answer because it means you can group in any combination
Step-by-step explanation:
9 × (1 × 4) = (9 × 1) × 4
A grain trader buys the following amounts from three suppliers: 3,200 pounds, 5,100 pounds and 700 pounds. What is the total weight of his purchase? Group of answer choices
Answer:
9000 lbs
Step-by-step explanation:
Since the amounts are already weighed, we just have to add all the weights together to find the total weight.
3200 + 5100 + 700 = 9000
Remember to leave it in pounds (lbs).
The Bermuda Triangle is a region in the Atlantic Ocean where many ships, planes, and people have apparently disappeared without a reasonable explanation. It lies just off the coast of the United States. And it’s angles are located at Bermuda (Angle b), San Juan (angle s), and Miami (angle m).
1. What would be the range of possible distances from Bermuda to San Juan?
2. If the actual distance from Bermuda to San Juan is 976 miles, is the Bermuda Triangle really a triangle? Justify your answer.
3. Using the distance from Bermuda to San Juan of 976 miles,list the angles of the Bermuda Triangle in order from least to greatest.
Sam uses 2/3 cup of sugar to make cookies. How many cups will Sam use to make five batches. Write your answer in two ways. Improper fraction and mixed number
Answer:
Improper fraction = 10/3 cups
Mixed fraction = 3 1/3 cups
Step-by-step explanation:
Given;
Sam uses 2/3 cup of sugar to make cookies
Rate = 2/3 cup per batch
To make 5 batches, he would need;
Amount = number of batches × rate per batch
Amount = 5 batches × 2/3 cups per batch
Amount of sugar he would need = 10/3 or 3 1/3 cups
What is the value of x in the equation StartFraction 4 Over 7 EndFraction (StartFraction 21 Over 8 EndFraction x + one-half) = negative 2 (StartFraction 1 Over 7 EndFraction minus StartFraction 5 Over 28 EndFraction x)? Write your solution in decimal form.
Answer:
x = -0.5Step-by-step explanation:
[tex]\dfrac{4}{7}\left(\dfrac{21}{8}x+\dfrac{1}{2}\right)=-2\left(\dfrac{1}{7}-\dfrac{5}{28}x\right)\\\\\text{use the distributive property}\ a(b\pm c)=ab\pm ac\\\\\left(\dfrac{4}{7}\right)\left(\dfrac{21}{8}x\right)+\left(\dfrac{4}{7}\right)\left(\dfrac{1}{2}\right)=(-2)\left(\dfrac{1}{7}\right)-(-2)\left(\dfrac{5}{28}x\right)\\\\\dfrac{4\cdot21}{7\cdot8}x+\dfrac{4\cdot1}{7\cdot2}=-\dfrac{2}{7}+\dfrac{2\cdot5}{28}x\qquad\text{simplify}[/tex]
[tex]\dfrac{3}{2}x+\dfrac{2}{7}=-\dfrac{2}{7}+\dfrac{5}{14}x\qquad\text{multiply both sides by 14}\\\\(14)\left(\dfrac{3}{2}x\right)+(14)\left(\dfrac{2}{7}\right)=(14)\left(-\dfrac{2}{7}\right)+(14)\left(\dfrac{5}{14}x\right)\qquad\text{simplify}\\\\(7)(3x)+(2)(2)=(2)(-2)+(1)(5x)\\\\21x+4=-4+5x\qquad\text{subtract 4 from both sides}\\\\21x+4-4=-4-4+5x\\\\21x=-8+5x\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\21x-5x=-8+5x-5x\\\\16x=-8\qquad\text{divide both sides by 16}[/tex]
[tex]\dfrac{16x}{16}=\dfrac{-8}{16}\qquad\text{simplify}\\\\\boxed{x=-\dfrac{1}{2}\to x=-0.5}[/tex]
Answer:
X = -0.5
Step-by-step explanation:
Edge 2020
I really need help please
Fill in this outcome (sample space) for this table showing the roll of a 6 sided dice and then the toss of a coin Coin Toss heads Tails Dice Roll What is P(4, T) What is P(odd, H)
Answer:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Step-by-step explanation:
Benidorm quiz
1. Where is Benidorm holiday resort located?
JORDAN
2. What is the average temperature of Benidorm in summer?
26 C
3. Before 1950s Benidorm was a small ___FISHING______ village.
4. Why did the town council encourage tourism in Benidorm?
TO VISIT BENIDORM
5. How many hotels were found in Benidorm in 1959?
6. Explain package holidays as they were used in Benidorm
7. Give three reasons why Benidorm is an excellent tourist resort
(a)
(b)
©
8. State four tourist attractions at Benidorm
Sunita creates a scale model of an aeroplane.
The scale of the model is 4 cm to 5 m.
Sunita's model has a wingspan of 53 cm.
What is the wingspan of the real aeroplane?
Answer:
66.25m
Step-by-step explanation:
66.25 metres is the correct answer
PLS HELP ASAP GIVING OUT BRAINLIEST.
How many positive integer solutions exist for 3(x-5)≤7?
Answer:
7 positive integer solutions
Step-by-step explanation:
3(x-5)≤7
Distribute
3x - 15 ≤7
Add 15 to each side
3x-15+15≤7+15
3x≤22
Divide by 3
3x/3 ≤22/3
x≤7 1/3
Positive integer solutions
1,2,3,4,5,6,7 = 7
0 is neither positive nor negative
solve for x, x^7-116=232
Answer:
x =348 ^ (1/7)
Step-by-step explanation:
x^7-116=232
Add 116 to each side
x^7-116+116=232+116
x^7 =348
Take the 7th root each side
x^7 ^ 1/7 = 348 ^ (1/7)
x =348 ^ (1/7)
mary thinks the triangle is equilateral. how would you support or dispute her conjecture?
Answer:
Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
Step-by-step explanation:
An equilateral triangle would have three sides that are all the same length, out of these options, only using the distance formula to calculate the length of all three sides and checking whether they are all congruent will make sure that the triangle is equilateral instead of just isosceles.
Which of the following is a geometric sequence?
0, 2, 6, 12, 72, . . .
4, 9, 14, 19, 24, . . .
1, 3, 9, 27, 81,
Answer:
1, 3, 9, 27, 81, is a geometric sequence.
Step-by-step explanation:
A geometric sequence is basically a sequence of numbers that's multiplied by or divided one specific set number each time.
0, 2, 6, 12, 72, does not have a set number it is multiplied or divided by each time.
4, 9, 14, 19, 24, adds 5 each time, it doesn't multiply
Answer:
D - 1, 3, 9, 27, 81, . . .
Step-by-step explanation:
Suppose Eric and Isaac both drive the same car, and have the same
deductible for car insurance. If Eric is five years younger, who is most likely to
pay a higher annual premium?
O
A. Isaac
O
B. Neither, they pay the same.
O
C. Can't tell from the information given
O
D. Eric
Answer:
eric
Step-by-step explanation:
just took the test
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.
Answer:
The answer is B
I WOULD LOVE IF SOMEONE CAN ANSWER THIS QUESTION FOR ME!
Answer:
32 cm^3
Step-by-step explanation:
The cube is 4 across by 4 high by 2 wide
4*4*2 = 32 cm^3
Answer:
[tex]32cm^3[/tex]
Step-by-step explanation:
[tex]V=whl=2*4*4=32cm^3[/tex]