The required formula with b subject is [tex]b = a^{2} - 6[/tex].
Given that ,
a is the subject of the formula,
[tex]a = \sqrt{ b + 6}[/tex]
We have to make b is the subject for the formula,
[tex]a = \sqrt{ b + 6}[/tex]
Squaring both the sides,
[tex]a^{2} = b + 6[/tex]
[tex]b = a^{2} - 6[/tex]
Hence , The required formula with b subject is [tex]b = a^{2} - 6[/tex]
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To make b the subject of the formula a = √(b+6), you need to isolate b on one side of the equation. The solution is b = a² - 6.
Explanation: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:
Square both sides of the equation to remove the square root: a² = b + 6Subtract 6 from both sides: a² - 6 = bTherefore, b = a² - 6.
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What is the ratio of blue shapes to all shapes in the set below?
2 blue triangles, 1 blue circle, and 2 blue squares. 1 orange square, 2 orange circles, and 1 orange triangle.
4:9
5:9
4:5
5:4
Answer:
[tex]ratio=\frac{5}{9}[/tex]
Step-by-step explanation:
Let
x ----> the number of blue shapes in the set
y ----> all shapes in the set
we know that
To find out the ratio of blue shapes to all shapes in the set , divide the number of blue shapes in the set by the number of all shapes in the set
we have
[tex]x=5\\y=9[/tex]
therefore
The ratio is equal to
[tex]ratio=\frac{x}{y}[/tex]
substitute
[tex]ratio=\frac{5}{9}[/tex]
Answer: It would be letter B (5:9)
Step-by-step explanation:
write an equation that is parallel to the line Y equals 1/2 x -4 and passes through the point 6 / -2
Answer:
Y equals 1/2 x -4 and passes through the point 6 / -2
Step-by-step explanation:
The table of values shows the output values of three different equations for the same
input values, 3.
Drag the correct expression to each row to complete each equation.
Answer:
x+33x^23^xStep-by-step explanation:
Relationship 1
The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.
__
Relationship 2
The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is (3x^2), which matches the values of y2.
__
Relationship 3
The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3^x), which matches the values of y3.
The relations are:
x+3
3x^2
3^x
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the
Finding the relations:Relationship 1:
The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.
Relationship 2:
The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is (3x^2), which matches the values of y2.
Relationship 3:
The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3^x), which matches the values of y3.
The relations are:
x+3
3x^2
3^x
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what is the total cost with sales tax? $370.00 tax 5%
Answer: $388.5
Step-by-step explanation:
Total cost = cost + sales tax
Given that cost = $370
Sales tax = 5% of $370
5/100 × 370 = $18.5
Total cost = $370 + $18.5
= $388.5
I hope this is clear.
CAN SOMEONE PLEASE HELP WITH THIS???
Answer:
B) 384
Step-by-step explanation:
Hello! This is the answer.
Volume of a square pyramid:
V = (1/3)a2h
Slant Height of a square pyramid:
By the pythagorean theorem we know that
s2 = r2 + h2
since r = a/2
s2 = (1/4)a2 + h2, and
s = √(h2 + (1/4)a2)
This is also the height of a triangle side
Lateral Surface Area of a square pyramid (4 isosceles triangles):
For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a and for this calculation our height for the triangle is slant height s. With 4 sides we need to multiply by 4.
L = 4 x (1/2)as = 2as = 2a√(h2 + (1/4)a2)
Squaring the 2 to get it back inside the radical,
L = a√(a2 + 4h2)
Base Surface Area of a square pyramid (square):
B = a2
Total Surface Area of a square pyramid:
A = L + B = a2 + a√(a2 + 4h2))
A = a(a + √(a2 + 4h2))
Therefore your answer is B 384.
What value of x makes the equation true? 4x - 3= -9 + 7x
2
-2
−12
12
Answer:
x = 2
Step-by-step explanation:
Given
4x - 3 = - 9 + 7x ( subtract 7x from both sides )
- 3x - 3 = - 9 ( add 3 to both sides )
- 3x = - 6 ( divide both sides by - 3 )
x = 2
Simplify -2 ^3. -------------------------------------------
Answer:
-8
Step-by-step explanation:
-2^3
-8
Answer: -8
Answer: -8
Step-by-step explanation:
-2x-2x-2=-8
Which expressions are equivalent to
-6 +49 + (-69) ?
Answer:
-26
Step-by-step explanation:
-6+49+(-69)
43+(-69)
43-69
-26
Write a linear equation in Slope-Intercept Form for a line that goes through the
points (-4, -1) and (-2,-5). *
Answer:
-2x-9=y
Step-by-step explanation:
If the difference between the 7th and 9th terms
of an arithmetic sequence is 25. Find the
Common difference.
The common difference is [tex]d=-\frac{25}{2}[/tex]
Explanation:
The difference between the 7th and 9th terms of an arithmetic sequence is 25
Since, we know the general form of an AP is [tex]a_{n}=a_{1}+(n-1) d[/tex]
For [tex]n=7[/tex], we have,
[tex]a_{7}=a_{1}+(7-1) d[/tex]
[tex]a_{7}=a_{1}+6 d[/tex] ---------(1)
For [tex]n=9[/tex], we have,
[tex]a_{9}=a_{1}+(9-1) d[/tex]
[tex]a_{9}=a_{1}+8 d[/tex] ----------(2)
Subtracting (1) and (2), we get,
[tex]a_7-a_9=6d-8d[/tex]
Since, it is given that the difference between 7th and 9th term is 25.
Hence, we have,
[tex]25=-2d[/tex]
Dividing both sides by -2, we have,
[tex]d=-\frac{25}{2}[/tex]
Hence, the common difference is [tex]d=-\frac{25}{2}[/tex]
What is one half after 4:00 in the morning
Answer:
Step-by-step explanation:
4:30am
What is the the equation??
You have $512.50. You earn additional money by shoveling snow. Then you purchase a new cell phone for $249.95 and have $482.55 left. How much money do you earn shoveling snow?
The person earned $220.
What is subtraction?The process of subtracting one number from another is known as subtraction.
The person initially has $512.50.
The total money person spends is:
$249.95 + $482.55
=$732.5
Now, subtract 512.50 from 732.5 to get the money earned by the person:
$732.5 - $512.50
= $220
Hence, the person earned $220.
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Find the maximum value of
C = 4x + 2y
Subject to the following constraints:
x > 0
y>0
2x + 2y < 10
3x + y < 9
Answer:
The maximum value of C is 14
Step-by-step explanation:
we have the following constraints:
[tex]x\geq 0[/tex] ----> constraint A
[tex]y\geq 0[/tex] ----> constraint B
[tex]2x+2y\leq 10[/tex] ----> constraint C
[tex]3x+y\leq 9[/tex] ----> constraint D
Solve the system of inequalities by graphing
using a graphing tool
The solution is the quadrilateral shaded area
see the attached figure
The vertex of the figure are
(0,0),(0,5),(2,3) and (3,0)
To find out the maximum value of the objective function C, substitute the value of x and the value of y of each vertex in the objective function C and then compare the results
we have
[tex]C=4x+2y[/tex]
[tex]For (0,0) -----> C=4(0)+2(0)=0\\For (0,5) -----> C=4(0)+2(5)=10\\For (2,3) -----> C=4(2)+2(3)=14\\For (3,0) -----> C=4(3)+2(0)=12[/tex]
therefore
The maximum value of C is 14
Answer:
The maximum value is c=14
Step-by-step explanation:
I hope this helps
I also did the question on acellus
why is it that |-9| = |9|
PLEASE HELP ASAP
A: The absolute value of a number gives its distance from zero on the number line.
B: when you multiply either number by -1, you get the other.
C: The absolute value of a number always gives the opposite of a negative number in the square of a positive number.
D: when the numbers are squared, they give the same answer.
Answer:
The answer A. "The absolute value of a number gives its distance from zero on the number line."
Step-by-step explanation:
An absolute number has these in it '| |'. An absolute number always is positive, because it represents a difference.
For example, the difference of 0 and -30 is |30|.
Though 0 - 30 is -30, the DIFFERENCE is |30|.
As the answer says, "its distance from zero on the number line".
Final answer:
The absolute value of -9 equals the absolute value of 9, which is 9, because absolute value represents the distance from zero on the number line, and both -9 and 9 are 9 units away from zero, regardless of their direction.
Explanation:
The reason why |-9| = |9| is because the absolute value of a number refers to its distance from zero on the number line. This distance is always a non-negative number since it does not refer to direction, just the magnitude of separation from zero. Therefore, both -9 and 9 are 9 units away from zero, and their absolute values are equal.
In mathematical terms, the absolute value function, denoted by | |, strips away the sign of a number, turning any negative number into its positive counterpart. So, |9| is already positive, and |-9| transforms -9 into 9 because you remove the negative sign, rendering both absolute values equivalent.
Find the circumference of each circle with the given radius or diameter. Round to the nearest tenth. Use 3.14 for T.
d = 14.2 mm
Answer:
C=44.6mm
Step-by-step explanation:
C=pi times d
C=3.14 times 14.2
Final answer:
The circumference of a circle with a diameter of 14.2 mm is 44.6 mm when rounded to the nearest tenth.
Explanation:
To find the circumference of a circle with a given diameter, you can use the formula C =
(D), where
is approximately equal to 3.14, and D is the diameter. For a circle with a diameter of 14.2 mm, the circumference would be calculated as follows:
C = 3.14 x 14.2 mm
After performing the multiplication:
C = 44.588 mm
When rounded to the nearest tenth, the circumference is:
C = 44.6 mm
Therefore, the circumference of the circle is 44.6 mm.
Evaluate each expression if x = 5
8x
—-
2
Answer:
I think you should divide 40 by 2 and get 20
Step-by-step explanation:
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x-4
h(x) = x
h(x) = 2x
ANSWER IS D HOPE IT HELPS
I need help understanding this homework. I am totally lost. It says Solve the problem, show your work and PQPA your answer. My daughter has to turn this paper in tomorrow morning.
Step-by-step explanation:
I'm guessing that "PQPA" means like Problem Question, Problem Answer (so what you are trying to find, and what it is (I think)).
That means the first problem is (3/4)+(7/8) = 13/8 and "How much water is collected in two hours?"
This means the second problem is (2 1/3) - (1 3/4) = (7/3)-(7/4) = 7/12 and "How many pounds of beef are left"
This means the third problem is (1 -(1/6))(2/5) = (5/6)(2/5) = 1/3 and "What fraction of her paycheck is saved"
This means that the fourth problem is (3/4)(2/3) = 1/2 and "How long did it take Megan to do her HW?"
Which expression is equivalent to y times y times y times z times z times z times z? y cubed z Superscript 4 12xy (y z) Superscript 7 7xy
Answer:
Option 1 - y cubed z superscript 4
Step-by-step explanation:
Given : Expression y times y times y times z times z times z times z.
To find : Which expression is equivalent to given expression ?
Solution :
Re-write the expression as,
[tex]y \times y \times y \times z \times z \times z \times z[/tex]
Write the number of time value repeat itself as the power,
[tex]y \times y \times y \times z \times z \times z \times z=y^3\times z^4[/tex]
[tex]y \times y \times y \times z \times z \times z \times z=y^3z^4[/tex]
or we can say that the expression is y cubed z superscript 4.
Therefore, option 1 is correct.
Answer:
it is A).
Step-by-step explanation:
The water level in a swimming pool increased from 4.5 feet to 6 feet.What is the percent increased in the water level rounded to the nearest tenth of a percent?Show your work
Step-by-step explanation:
Because 6 = 100 percent 4.5 = 80.5In the figure below, triangle RPQ is similar to triangle RTS.
What is the distance between P and Q?
0 24
0 42
50
0 54
Unmark this question
Save and Exit
Next
HELP ASAP PLZ
Answer:
PQ = 54
Step-by-step explanation:
The rest of the question is the attached figure.
As shown:
triangle RPQ is similar to triangle RTS.
So, the corresponding sides are in proportion.
[tex]\frac{PQ}{TS}= \frac{RP}{RT}[/tex]
From the figure:
TS = 36 , RP = 42 AND RT = 28
∴ [tex]\frac{PQ}{36} = \frac{42}{28} \\[/tex]
∴ PQ = 36 * 42/28 = 54
So, the distance between P and Q = 54
If Joe makes 16 out of 40 free throws in a
basketball game, what is his free throw shooting
percentage?
Answer:
the answer is 6.4%
Step-by-step explanation:
Because you have to do 16% of 40 and it will give you 6.4 and as a percent it is 640% hope it helps!!!!!!!!!
The original price of the shorts is $35. They are on sale for 25% off. What is the sale price?
Answer:
$26.25
Step-by-step explanation:
So what you do is divide 25 by 100 so its a decimal .25 then multiply that by 35 and you get 35/4 or 8.75 you take that number and subtract it from 35 and you get 26.25.
For future reference what ever percentage you have like if says it went up 80% you divide that by a hundred also and you get .80 you multiply that by 35 you get 28 you don't subtract it from the original price but you add it so you get 35+28=63 and that's your final answer.
Remember you divide the percentage for example 25 by 100 multiply by the price it gives for example 35 if the question says off you subtract what you got from the original price if it went up you add it to the original price and that's your final answer. Hope this help :)
An ice cream store sells
28 flavors of ice cream. Determine the number of 44
dip sundaes How many 4 dip sundaes are possible if order is not considered and no flavor is repeated?
11.8#7
Total number of 4 dip sundaes , if order is not considered and no flavor is repeated is 491400 .
Step-by-step explanation:
We have , an ice cream store sells 28 flavors of ice cream, determine the number of 4 dip sundaes. how many are possible if order is not considered and no flavor is repeated? Let's find this:
There are we flavors available as the first sundae flavor. After selecting a flavor for the first sundae flavor there are 27 flavors available for the second. The same way there are 26 flavors for the third sundae flavor and 25 flavors available for the forth sundae flavor. So, Total number of 4 dip sundaes , if order is not considered and no flavor is repeated is [tex]28(27)(26)(25)=491400[/tex] available sundaes.∴ Total number of 4 dip sundaes , if order is not considered and no flavor is repeated is 491400 .
Brett has 100 feet of fence with which to
make a rectangular cage for his dog. The
area of the cage in square feet is given
by the polynomial -W + 50w, where wis
the width of the cage in feet. What is the
area of the cage if the width is 8 feet?
a) 114 ft2. b) 336 ft?
C) 384 ft? d) 464 it
Answer:
D 464
Step-by-step explanation:
lemme know if you need an explanation
Use the Distributive Property to find 1/3 x 6 1/2
.
Answer:
13/6 or 2 1/6
Step-by-step explanation:
6 1/2 = 13/2 (Improper Fraction)
1/3 = 2/6 (1/3 is just simplified)
1/3 x 1 + 1 + 4 + 6 + 1 = Answer
(13/2 x 1/3 = 13/6)
Solving the expression using the Distributive Property, we get 13.6.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following expression -
(1/3) x (6 1/2)
We have the expression -
(1/3) x (6 1/2)
(1/3) x (6 + 1/2)
(1/3 x 6) + (1/3 x 1/2)
2 + 1/6
13.6
Therefore, solving the expression using the Distributive Property, we get 13.6.
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What is 3/8 rounded to the nearest 100
Answer: 0.38
Step-by-step explanation:
Divide 3 by 8 = 0.375
To round 0.375 to the nearest hundredth means to round the numbers so there are only two digits in the fractional part. it is pertinent to know that the fractional part is 375, since the value at the end is not less than 5, the number turns 1 and we add it to the number before it.
0.375 to the nearest hundredth is 0.38.
I hope this helps.
Which of the following represents a horizontal line that passes through the point (2,-6)?
(1) y=6
(2)x=2
3) y = 2x - 6
4) y = -6x + 2
Quinn has 6 bottles of water that each weigh 3/5 pound. What is the total weight of the water bottles? Use the number line to help
Answer:
The weight of 6 bottles = [tex]3\frac{3}{5}\ pounds[/tex] or [tex]3.6\ pounds[/tex]
Step-by-step explanation:
Given:
Total number of bottles = 6
Weight of each bottle = [tex]\frac{3}{5}[/tex] pound
To find the total weight of 6 bottles.
Solution:
We can plot the number line for six bottles.
We can the plot the weights in another number line.
Each unit represents [tex]\frac{3}{5}[/tex] pound of weight.
As the number of bottles increase the number of pounds of weight increase by [tex]\frac{3}{5}[/tex] .
Thus, weight of 6 bottles = [tex]\frac{3}{5}+\frac{3}{5}+\frac{3}{5}+\frac{3}{5}+\frac{3}{5}+\frac{3}{5}[/tex] [tex]=\frac{18}{5}[/tex] pounds
Converting fraction to mixed number.
[tex]\frac{18}{5}=3\frac{3}{5}[/tex] pounds
Or in decimals [tex]\frac{18}{5}=3.6\ pounds[/tex]
Thus weight of 6 bottles = [tex]3\frac{3}{5}\ pounds[/tex] or [tex]3.6\ pounds[/tex]