[tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.
What is exponentiation?Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as [tex]b^n[/tex]. Its pronunciation is "b (raised) to the (power of) n."Now,
[tex]2^{(x + 3)} = 512[/tex]
=> [tex]2^{(x + 3)} = 8^3 = (2^3)^3[/tex]
As [tex](a^b)^c = a^{bc}[/tex],
=> [tex]2^{(x + 3)} = 2 ^9[/tex]
=> x + 3 = 9
=> x = 6
Hence, [tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.
To learn more about exponentiation, refer to the link: https://brainly.com/question/11975096
#SPJ4
Which expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power?
WHOEVER GETS IT RIGHT GETS A CROWN!!
The expression is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power is [tex]z^{-18}.y^{18}[/tex] .
The given expression is [tex](\frac{y^{-3}.z^5}{z^{-4.y^6}} )^{-2}[/tex]
Let us take the numerator terms to denominator.
When shifting numerator terms to denominator the sign of the power will be changed.
[tex](\frac{1}{z^{-4.y^6.y^{3}.z^{-5}}} )^{-2}[/tex]
Combine like terms in denominator:
[tex](\frac{1}{z^{-9}.y^9} )^{-2}[/tex]
[tex](z^9.y^{-9})^{-2}[/tex]
[tex]z^{-18}.y^{18}[/tex]
Hence, [tex]z^{-18}.y^{18}[/tex] is equivalent to quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ3
0.05 multiply blank = 0.5
The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.
Given that, 0.05 × ----- = 0.5.
How to multiply the decimals?To multiply decimals, first, multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Let the number should fill in the blank be x.
So, 0.05 × x = 0.5
⇒ x = 0.5/0.05
⇒ x = 10
The number that should fill in the blank is 10. Therefore, the complete equation is 0.05 × x = 0.5.
To learn more about the multiplication of decimals visit:
https://brainly.com/question/19655879.
#SPJ1
The table below shows the recorded temperature on a certain day starting at 6:00 am
PLS HELPPPPP
Answer:
A) y = 2.91x + 64.61 with x hours after 6:00 am
B) at 2:00pm, temperature is 87.89°
Step-by-step explanation:
(>>Regression Equation y = bx + a )With b- Sum of products/Sum of Square = sq/SSx. a = My- bMx,)
set 6.00 am is an original time, when x = 0
use the unit: hour to get a new table
X time 0, 0.75, 1.5, 2.5, 3, 3.75, 4.5, 5
Y temp 65°, 67", 68° ,72° ,74", 75° ,77° ,78°
a). with temperature y and x hour after 6:00 am,
can get Sum of x = 21 Mx = 2.63
Sum of - 578 My = 72.25
SSx = Sum of (X-Mx)² = 22.25
= sum of (X-Mx)(}-My)= 64.75
So b= sq/SSx =64.75/22.25 = 2.91
a= My- bMx = 72.25 - 291 x 2.63 = 64.61
So regressing equation Y= 2.91x + 64.61
b). at 02:00 pm , means 8 hours after 6:00 am
meaning X-8, )= 2.91×8 + 64.61 = 87.8)
The required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°
Given that,
The table shows the recorded temperature on a certain day starting at 6:00 am.
The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.
Here,
The standard form of the regression equation,
y = bx + a,
where b = sum of product/sum of squares a = My - bMx
Since
b = 2.91 , My = 72.25, Mx = 2.63
a = 72.25 - 2.91 * 2.63
a = 64.6
The required regression equation is,
y = 2.91x + 64.6
B)
For 2.00 PM, x = 8
Now,
y = 2.91 * 8 + 64.6
y = 87.8°
Thus, the required equation of regression is y = 2.91x + 64.6 and at 2.00 pm temperature is 87.8°
Learn more about the equation here:
brainly.com/question/10413253
#SPJ1
What is the equation of the line that passes through the point (3,-7) and has a slope of -2?
Answer:
y=-2x-1
Step-by-step explanation:
y=mx+b
-7=-2(3)+b
-7=-6+b
-1=b
y=-2x-1
One half + four fifths vertical
Answer:
1 1/2+4/5 and the vertical would be graphed?
2a - 3=15 What is the answer
Answer:
a = 9
Step-by-step explanation:
Step 1: Add 3 to both sides
2a – 3 = 15
2a – 3 + 3 = 15 + 3
Step 2: Simplify
add the numbers ( 2a = 18 )
Step 3: Divide both sides by the same factor
2a = 18
2a 18
––– = –––
2 2
Step 4: Simplify
l
Cancel the terms that are in both the numerator and the denominator
l
l
Divide the numbers
l
a = 9
Answer: a = 9
find angle measure GRS if QRS=179 and QRG= 105
Answer:
∠ GRS = 74°
Step-by-step explanation:
∠ GRS + ∠ QRG = ∠ QRS , that is
∠ GRS + 105° = 179° ( subtract 105° from both sides )
∠ GRS = 74°
Answer:
75°
Step-by-step explanation:
While it may appear that QRS is a straight line, it is not so since m∠QRS = 179° and if it was a straight line, it would be 180°
The figure actually represents three rays with endpoint at R
The three rays are RQ, RS and RG
Draw another ray RT with endpoint at R and opposite to ray RG. Opposite rays have angles that add up to 180°
Therefore m∠GRT = 180°
m∠SRT = m∠QRG since they are opposite angles
Since m∠QRG = 105°, therefore m∠SRT = 105°
m∠GRS + m∠SRT=180° since these angles are formed by two opposite rays
Substituting we get
m∠GRS + 105 = 180
m∠GRS = 180-105 = 75°
Josh is looking for the best deal on a refrigerator that has a wholesale price of $549. Help him compare the price of the refrigerator at two different stores by completing the following.
a) Josh goes to the super store that marks up the refrigerator’s wholesale price 50%. Ignoring tax, how much would he pay for the refrigerator at this store?
b) Josh then looks at the refrigerator in a department store that marks up the refrigerator’s wholesale price 60%. But because of customer loyalty program, he would receive a 10% discount off the in-store price. Ignoring the tax, how much would he pay for the refrigerator at this store?
pls help i hope this makes sense!!
Answer:
B store is cheaper since 790.56<823
B price<A price
Step-by-step explanation:
A:
549(0.5)=274
264+549=823
Josh need to pay the refrigerator for $823 in this store without tax.
B:
549(0.6)= 329.4
329.4+549=878.4
878.4(09)=790.56
Josh need to pay $790.56 in this store without the tax.
C:
B, department store is cheaper so he could pay less
Could someone help me find how to extract the root from this equation?2y ^ 2 - 8 = 6 - 2y ^ 2
Answer:
y = ± √ 7/2
Step-by-step explanation:
2*y^2-8-(6-2*y^2)=0
(2 • (y2)) - 8) - (6 - 2y2) = 0
(2y2 - 8) - (6 - 2y2) = 0
Pull out like factors :
4y2 - 14 = 2 • (2y2 - 7)
4.2 Factoring: 2y2 - 7
difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
2 • (2y2 - 7) = 0
5.1 Solve : 2 = 0
5.2 Solve : 2y2-7 = 0
Add 7 to both sides of the equation :
2y2 = 7
Divide both sides of the equation by 2:
y2 = 7/2 = 3.500
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
y = ± √ 7/2
Triangle ABC with coordinates A (2, 4),
B (3, 6), and C (5, 1) is translated
4 units horizontally.
Triangle ABC with coordinates A (2, 4),
B (3, 6), and C (5, 1) is translated
4 units horizontally is (6,4), (7,6) ,( 1,9)
A triangle is a basic polygon with three sides and three internal angles. It is one of the fundamental shapes in geometry in which the three vertices are connected together, and it is represented by the symbol. Triangles are categorized into many sorts based on their sides and angles. All geometrical shapes have unique qualities relating to sides and angles that aid in their identification. The following are some of the most important qualities of a triangle.
There are three sides, three vertices, and three internal angles in a triangle.
The angle sum property of a triangle asserts that the sum of a triangle's three internal angles is always 180°. Consider the triangle PQR shown above .
To learn more about Triangle from the given link:\
https://brainly.com/question/2773823
#SPJ9
Zoe says that 2³.42 can be rewritten as 86. Juana says that it can be rewritten as 85. Danladi says that it cannot be rewritten as either of these expressions. Who is correct? Explain.
Danladi says that it cannot be rewritten as either of these expressions. He is correct.
How to calculate the value?It should be noted that 2³ × 42 will be:
= 2³ × 42
= 8 × 42
= 336
Therefore, Zoe says that 2³.42 can be rewritten as 86 and Juana says that it can be rewritten as.85. They're both wrong.
In the other hand, Danladi says that it cannot be rewritten as either of these expressions. Therefore, he is correct.
Learn more about numbers on:
brainly.com/question/25734188
#SPJ1
Solve each equation. Check for extraneous solutions. 2(x-1)³/₄=16
Answer:
[tex]x = 17[/tex].
Step-by-step explanation:
Simplify the given equation:
[tex]2\, (x - 1)^{3/4} = 16[/tex].
[tex](x - 1)^{3/4} = 8[/tex].
[tex]((x - 1)^{1/4})^{3} = 8[/tex].
Take the cubic root of both sides to eliminate the numerator of the exponent. Only roots of even degree could introduce alternative solutions. Since the degree of this root is an odd number, this step would not create extraneous solutions.
[tex]\sqrt[3]{((x - 1)^{1/4})^{3}} = \sqrt[3]{8}[/tex].
[tex](x - 1)^{1/4} = 2[/tex].
Raise both sides to the fourth power to eliminate the denominator of the exponent:
[tex](x - 1) = 2^{4}[/tex].
[tex]x - 1 = 16[/tex].
[tex]x = 17[/tex].
Substitute the solution [tex]x = 17[/tex] into the equation:
[tex]\begin{aligned}& 2\, (17 - 1)^{3/4} \\ =\; & 2\times (16^{1/4})^{3} \\ =\; & 2 \times 2^{3} \\ =\; & 16\end{aligned}[/tex].
Thus, [tex]x = 17[/tex] isn't an extraneous solution since setting [tex]x[/tex] to [tex]17[/tex] satisfies the original equation.
(-9 6) and (0 1) in slope intercept form
In Δ ABC, a=8m, b=5 m , and c=10 m . Find m∠ A .
Answer:
arccos(51/100)
Step-by-step explanation:
By the Law of Cosines,
[tex]a^2 = b^2 + c^2 - 2bc \cos A \\ \\ a^2 - b^2 - c^2=-2bc \cos A \\ \\ \cos A=\frac{b^2 + c^2 - a^2}{2bc} \\ \\ m\angle A=\arccos \left(\frac{b^2 + c^2 - a^2}{2bc} \right) \\ \\ =\arccos \left(\frac{10^2 + 5^2 - 8^2}{2(5)(10)} \right) \\ \\ =\arccos(51/100)[/tex]
Describe the difference between direct variation and inverse variation.
When two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y, direct variation occurs, whereas indirect or inverse variation occurs when an increase in the value of X results in a decrease in the value of Y and vice versa.
Difference between direct variation and inverse variation:To give the reader a hint, direct variation equations use the same phrase. The phrase is either "directly proportional" or "directly varies." The area of a square, for example, varies directly from the square of its side. Direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y.Inverse variation is a relationship between two variables in which the value of one increases while the value of the other decreases. Indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.
Therefore, direct variation occurs when two quantities, say X and Y, are related in such a way that an increase or decrease in the value of X results in an increase in the value of Y whereas indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that an increase in the value of X results in a decrease in the value of Y and vice versa.
Know more about inverse variation here:
https://brainly.com/question/13998680
#SPJ4
The projectile motion of an object can be modeled using s(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.
An object is launched at an initial velocity of 19.6 meters per second from an initial height of 24.5 meters. Which equation can be used to find the number of seconds it takes the object to hit the ground?
0 = –4.9t2 + 19.6t + 24.5
0 = –4.9t2 + 24.5t + 19.6
19.6 = –4.9t2 + 24.5t
24.5 = –4.9t2 + 19.6t
Question 6 (5 points)
(01.04)
Solve the following for y: 2x + 2y = 8 (5 points)
O a
Ob
Oc
Od
y = -x + 4
y = x + 4
y = 3x
y = -3x
We get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.
We are given an equation:
2 x + 2 y = 8
Divide both the sides by 2, we get that:
2 x / 2 + 2 y / 2 = 8 / 2
x + y = 4
Now, we will subtract x from both the sides, so, we get that:
x + y - x = 4 - x
y = 4 - x
Therefore, we get that, for the equation 2 x + 2 y = 8, when we solve for y, we get the result as y = 4 - x.
Learn more about equation here:
https://brainly.com/question/1214333
#SPJ9
3m^2+2p^2-15 what the answer kinda got stuck
Answer:
212.
Step-by-step explanation:
Given: 3m^2 + 2p^2 - 15
When m = 3 and p = 10
Substituting the values
= 3(3)^2 + 2(10)^2 - 15
By further calculation
= 3(9) + 2(100) - 15
So we get
= 27 + 200 - 15
= 212
Therefore, the value of the expression is 212.
1. A machine on a production line
packages calculators at a steady
rate. After 10 minutes, it has
packaged 25 calculators, and after
30 minutes it has packaged
75 calculators.
Complete the equation to model
the number of calculators, y, the
machine has packaged after
x minutes.
Please help !!!
The equation which models the number of calculators packed by the machine in certain minutes is x = 2.5y
No. of calculators packed after 10 minutes = 25 calculators
No. of calculators packed after 30 minutes = 75 calculators
Using the unitary method for finding calculators packed in a minute,
10 minutes = 25 calculators
1 min = 25/10 = 2.5 calculators
Let x be the number of minutes the machine is running
Let y be the number of calculators packed
Formulation of the equation we get:
x = 2.5y
Hence, the equation which gives the number of calculators packed after certain minutes is given by: x = 2.5y
Learn more about algebra:
https://brainly.com/question/24875240
#SPJ9
question in image thank you!
Using proportions, it is found that:
1. a) 1/5 of the marbles are red.
b) 40% of the marbles are yellow.
c) 60% of the marbles are not yellow.
d) 11/20 of the marbles are green or yellow.
2) Event A, B and C are the most likely, each with equal probabilities.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For the first problem, we have that there are 3 + 4 + 5 + 8 = 20 marbles, hence:
a) 4/20 = 1/5 of the marbles are red.
b) 8/20 x 100% = 0.4 x 100% = 40% of the marbles are yellow.
c) 12/20 x 100% = 0.6 x 100% = 60% of the marbles are not yellow.
d) 3 are green and 8 are yellow, hence 11/20 of the marbles are green or yellow.
A die has 6 possible outcomes, numbered 1 to 6, hence the probabilities(number of desired outcomes divided by number of total outcomes) are given as follows:
Event A: 3/6 = 1/2.Event B: 3/6 = 1/2.Event C: 3/6 = 1/2.Event D: 2/6 = 1/3.Event A, B and C are the most likely, each with equal probabilities.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
how do you simplify this expression? can you explain it step step by step
Answer:
-4
Step-by-step explanation:
-12+3(-8+(-4)^2-6)+2
first the -4^2
-12+3(-8+16-6)+22
now everything in the parenthesis
-12+3x2+2
now the multiplying.
-12+6+2
now calculate this all together.
-4
If you invest $1,500 today in a bank that gives you 5% annual interest rate, which of theses items can you buy in two years
Answer: electronics worth $1,650
1500 (1+5%)^2 = $1653.75
3.75 dollars will be left over.
Step-by-step explanation:
Victor walked 6.4 kilometers on Sunday, and he will also walk to school a few times this
week. Each round trip is 1.9 kilometers long. If Victor walks to school 3 days this week, what
will be his total walking distance for the week?
Write and solve an equation to find the answer.
kilometers
The total walking distance of the week is 12.1 km.
What are equations?An equation, in its most basic form, is a mathematical statement that shows that two mathematical expressions are equivalent. For example, 3x + 5 = 14 is an equation wherein the expressions 3x + 5 and 14 are separated by a 'equal' sign.So, let the total walking distance be 'x'.
Then,
6.4 + 1.9 + 1.9 + 1.9 = x6.4 + 5.7 = x12.1 = xSo, x = 12.1 km.Therefore, the total distance of walking in the week is 12.1 km.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ9
Find the inverse of each function. Is the inverse a function?
y=2 x³+10
The inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].
What is an inverse variation exactly?Inverse variation describes a relationship between two variables in which one increases while the other decreases.Indirect or inverse variation occurs when two quantities, say X and Y, are related in such a way that increasing X causes a decrease in Y and vice versa.So,
All we have to do to find the inverse of an equation is switch the variables x and y.
x = 2y³ + 10Now, solve for y as follows:
2y³ = x - 10y³ = (x-10)/2y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex]Therefore, the inverse of the fuction y=2x³+10 is y = [tex]\sqrt[3]{\frac{x-10}{2} }[/tex].
Know more about inverse variation here:
brainly.com/question/13998680
#SPJ4
Round 12,345.6789 to the nearest ten thousand
Answer:
10000
Step-by-step explanation:
Solve by factoring. Check your answers. 4 x²=-8 x+5
The factoring of the expression 4 x²=-8 x+5 is (2x-1) (2x+5)
By ordering the values, we get:
4 x² + 8 x - 5
To solve this exercise, we have to follow the rules of factoring:
1. Factor 8 from 8x:
4 x² + 8 x - 5
4 x² + (-2 + 10) x - 5
2. Apply the distributive property:
4 x² - 2x + 10x - 5
3. Groups the first two terms and the last two terms:
(4 x² - 2x) + 10x - 5
4. Factorize the greatest common denominator (GCM) of each group:
2x(2x - 1) + 5(2x-1)
5. Factor the polynomial by factoring the greatest common denominator, (2x-1):
(2x-1) (2x+5)
What is factoring?Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.
Learn more about factoring at brainly.com/question/24734894
#SPJ4
15. Bill Bob Joe is building a deck for his pool and needs to know how long to make his deck. He
knows the pool is a square prism with a height of 15 feet and a volume of 1,215ft³. Using the
volume formula V = lwh and the fact that a square has congruent length and width. Find the length
of the pool.
Answer:
9ft by 9ft
Step-by-step explanation:
Write the word sentence at an inequality. n plus 3.9 is less than or equal to 16. An inequality is What?
Answer:
n + 3.9 ≤ 16
An inequality is a mathematical expression represented by less than, greater than, or equal to symbols to compare values or to measure and solve complex equations.
Ray BD bisects angle ABC.
Find m/ABD, m/CBD, and m/ABC.
B (7x
(3x + 6)°
18) C
Answer:
The two smaller angles equal 24 and together they equal 48
Step-by-step explanation:
The bisector tells us that the smaller angles equal each other
3x + 6 = 7x - 18 Subtract 3x from both sides
6 = 4x - 18 Add 18 to both sides
24 = 4x Divide both sides by 4
6 = x
Now, plug 6 back into each equation.
3x + 6
3(6) + 6
18 + 6
24
7x - 18
7(6) - 18
42 - 18
24
Consider the diagram and proof below.
Given: WXYZ is a parallelogram, ZX ≅ WY
Prove: WXYZ is a rectangle
Parallelogram W X Y Z with diagonals is shown.
Statement
Reason
1. WXYZ is a ▱; ZX ≅ WY 1. given
2. ZY ≅ WX 2. opp. sides of ▱ are ≅
3. YX ≅ YX 3. reflexive
4. △ZYX ≅ △WXY 4. SSS ≅ thm.
5. ∠ZYX ≅ ∠WXY 5. CPCTC
6. m∠ZYX ≅ m∠WXY 6. def. of ≅
7. m∠ZYX + m∠WXY = 180° 7. ?
8. m∠ZYX + m∠ZYX = 180° 8. substitution
9. 2(m∠ZYX) = 180° 9. simplification
10. m∠ZYX = 90° 10. div. prop. of equality
11. WXYZ is a rectangle 11. rectangle ∠ thm.
What is the missing reason in Step 7?
triangle angle sum theorem
quadrilateral angle sum theorem
definition of complementary
consecutive ∠s in a ▱ are supplementary
The missing step 7 in the two column proof is; Consecutive ∠s in a ▱ are supplementary
How to carry out a two column proof?
We are told that WXYZ is a parallelogram in which we have to prove that: WXYZ is a rectangle. The two column proof is as follows;
Statement Reason
1. WXYZ is a parallelogram, 1. Given
ZX ≅WY
2. ZY ≅ WX 2. Opposite sides of parallelogram
are congruent.
3. YX≅YX 3. Reflexive property of congruence
4. ΔZYX ≅ Δ WXY 4. SSS congruence postulate
5. ∠ZYX ≅ ∠WXY 5. CPCTC
6. m∠ZYX ≅ m∠WXY 6. definition of congruence.
7.m∠ZYX + m∠WXY = 180° 7. Consecutive ∠s in a ▱ are
supplementary
8.m∠ZYX + m∠ZYX = 180° 8. By substitution
9. 2(m∠ZYX) = 180° 9. By simplification
10.m∠ZYX = 90° 10. Division property of equality
11. WXYZ is a rectangle 11. Rectangle angle theorem.
Read more about Two Column Proof at; https://brainly.com/question/7807853
#SPJ1