Answers
Answer:
Step-by-step explanation:
Answer:
x=12
Step-by-step explanation:
To solve for the variable, we must isolate the variable, which is x.
[tex]\sqrt{x+4} -3=1[/tex]
3 is being subtracted from the square root of x+4. The inverse of subtraction is addition. Add 3 to both sides of the equation.
[tex]\sqrt{x+4} -3+3=1+3[/tex]
[tex]\sqrt{x+4} =1+3[/tex]
[tex]\sqrt{x+4} =4[/tex]
The square root of x+4 is being taken. The inverse of a square root is a square. Square both sides of the equation.
[tex](\sqrt{x+4})^2 =4^2[/tex]
[tex]x+4=4^2[/tex]
Evaluate the exponent.
4^2= 4*4=16
[tex]x+4=16[/tex]
4 is being added to x. The inverse of addition is subtraction. Subtract 4 from both sides of the equation.
[tex]x+4-4=16-4[/tex]
[tex]x=16-4[/tex]
[tex]x=12[/tex]
The solution to this equation is x=12.
Related Questions
The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.
Answers
Answer:
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
Step-by-step explanation:
[tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex]
Factorizing the expressions we have
[tex]\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}[/tex]
[tex]\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}[/tex]
[tex]\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}[/tex]
Cancelling out the like factors, (x -1) and (x - 2), we have
[tex]\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}[/tex]
= [tex]\frac{(x + 3)^{2} }{(x + 5)^{2} }[/tex]
So the quotient of [tex]\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}[/tex] has (x + 3)² in the numerator and (x + 5)² in the denominator.
PLEASE help me with this question!!! REALLY URGENT!
Answers
Answer:
The third table is the correct answer
Step-by-step explanation:
Here in this question, we are concerned with determine which of the tables correctly represents what an exponential function is.
An exponential function is a function of the form;
y = x^n
where the independent variable x in this case is raised to a certain exponent so as to give the results on the dependent variable axis (y-axis)
In the table, we can see that we have 2 segments, one that contains digits 1,2 and so on while the other contains purely the powers of 10.
Now, let’s set up an exponential outlook;
y = 10^x
So we have;
1 = 10^0
10 = 10^1
1/10 = 10^-1
1000 = 10^3
1/100 = 10^-2
We can clearly see here that we have an increase in the value of y, depending on the value of the exponent.
However it is only this table that responds to this successive correctness as the other tables in the answer do have a point where they fail.
For example;
10^-2 is not 10 which makes the fourth table wrong
10^4 is not 100 which makes the first table wrong
we have same error on second table too
What is the value of w? inscribed angles (Image down below)
Answers
Answer:
w = 100°
Step-by-step explanation:
Opposite angles in an inscribed quadrilateral in a circle are supplementary.
Therefore, [tex] w + 80 = 180 [/tex]
Subtract 80 from both sides
[tex] w + 80 - 80 = 180 - 80 [/tex]
[tex] w = 100 [/tex]
The value of w = 100°
Susan Johnson earns a yearly salary of $83,280. a. How much would Susan be paid if she were
paid monthly? b. How much would she be paid if she were paid bi-weekly?
Answers
So, Susan Johnson would earn 6940$ per month if she would be paid per month and if she was paid per week she would earn 1735$ per week.
Please answer this question now
Answers
Answer:
65.94 square inches
Step-by-step explanation:
Surface area of a cone=πr(r+√h^2+r^2)
π=3.14
r=diameter/2
=14/2
=7 in
h=?
h=a
To find h using Pythagoras theorem
c^2 = a^2 + b^2
14^2 = a^2 + 7^2
14^2 - 7^2= a^2
196-49=a^2
147=a^2
Square root both sides
√147=√a^2
12.12=a
a=12.12 in
Surface area of a cone=πr(r+√h^2+r^2)
=3.14(7+√12.12^2+7^2)
=3.14(7+√147+49)
=3.14(7+√196)
=3.14(7+14)
=3.14(21)
=65.94 square inches
6 sqrt (x-2) +4 < 28
How do you solve? Btw.. x-2 is under sqrt sign.
Answers
Answer:
Step-by-step explanation:
[tex]6\sqrt{x-2}+4<28\\6\sqrt{x-2}<28-4\\\sqrt{x-2}<\frac{24}{6}\\\sqrt{x-2}<4\\\\x-2 <16\\x<16-2\\x<14x-2 \geq 0\\x\geq 2\\so~2 \leq x < 14[/tex]
suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order does not matter? B) how many ways can this be done if order of choices matters
Answers
Answer: A) 1716 B) 1235520
Step-by-step explanation:
If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-[tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given, Total distinct letters = 13
To choose = 6 letters
A) Number of ways to choose (if order does not matter)=[tex]^{13}C_6[/tex]
[tex]=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716[/tex]
B) Number of ways to choose (if order matters)=[tex]^{13}P_6[/tex]
[tex]=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520[/tex]
Hence, A) 1716 B) 1235520
10) Find the least number that must be subtracted from the following numbers to make them perfect squares. a) 1098 b) 4498
Answers
Answer:
a. 9
b. 9.
Step-by-step explanation:
a) √1098 = 33.136
33^3 = 1089
So the answer is 1098 - 1089
= 9.
b) √4498 = 67.067
67^2 = 4489
Answer = 9.
Answer:
a). 9
b). 9
Step-by-step explanation:
a) If you try to subtract 1 to 8 from 1098, it won't make a perfect square. But if you subtract 9 from 1098 (that will make it 1089), it will make a perfect square.
√1089 = 33
33² = 33 × 33 = 1089
So the answer is 9.
b). If you try to subtract 1 to 8 from 4498, it won't make a perfect square. But if you subtract 9 from 4498 (that will make it 4489), it will make a perfect square.
√4489 = 67
67² = 67 × 67 = 4489
So the answer is 9.
Hope you understand ◉‿◉ (◠‿◕)
Solve: 5x2 + 25x = 0
Answers
Answer:
x = -0.4
x = -(2/5)
Answer:
x = ± √5
Step-by-step explanation:
Please indicate exponentiation by using the symbol " ^ ":
5x^2 + 25x = 0
Divide all three terms by 5. We get:
x^2 + 5 = 0, or x^2 = -5
Then x = ± √5
What are the solutions to the equation (2x – 5)(3x – 1) = 0? x = or x = 3 x = x = 5 or x = 1
Answers
Answer:
x = 5/2 x=1/3
Step-by-step explanation:
(2x – 5)(3x – 1) = 0
Using the zero product property
2x-5 =0 3x-1 =0
2x=5 3x =1
x = 5/2 x=1/3
Answer:
C on edg 2021
Step-by-step explanation:
Sophie is making a copy of an angle. The original angle will be labeled G and the new angle will be labeled B. She has just finished using a compass, with the point on G, to draw an arc that intersects both rays of angle G. Which of the following should she do next
Answers
Answer:
The next step is;
Label the two intersection points
Step-by-step explanation:
To make a copy of an angle, the steps are;
1) Draw the rays of the original angle passing through the point B
2) Open the compass slightly and place the compass point on the vertices G where the two rays meet to draw an arc that intersect both rays
3) Label the point of intersection of both rays points C and D
4) With the compass still opened to the same width, move the compass to the point B on the line the angle is to be copied and draw a similar arc intersecting the ray at J
5) Open the compass to the width of C and D on the original angle and place the compass at point J to mark the arc on the copied angle location at M
6) Draw a line from B passing through M to complete the second ay of the copied angle.
Determine what type(s) of angles are described by the following angle measures. Angle of 35 degrees.
Answers
Answer:
Acute.
Step-by-step explanation:
An angle of measure between 0 and 90 degrees is an acute angle.
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answers
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
A baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of$458. How many apples pies did they sell and how many blueberry pies did they sell
Answers
The total number of apple pies is 22 and the total number of blueberry pies is 17.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that baker sold apples pies for $10 and blueberry pies for$14. One Saturday they sold a total of 39 pies and collected a total of $458.
Asumme the total number of apple pies be 'x' and the total number of blueberry pies be 'y'.
The linear equation that represents the total number of pies is:
x + y = 39
x = 39- y --- (1)
The linear equation that represents the total amount collected is:
10x + 14y = 458--- (2)
Substitute the value of 'x' in equation (2).
10(39- y) + 14y = 458
y = 17
Then Substitute the value of 'y' in the equation (1).
x = 39 - 17
x = 22
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ5
Write the equation of a circle with a center at (12, 6) and a radius of 6.
Answers
Answer:
(x-12)² + (y-6)² = 36 (Option C)
Step-by-step explanation:
use circle formula
(x-h)² + (y-k)²= r²
h= 12 and k= 6 and r= 6
(x-12)² + (y-6)² = 6²
6 squared = 36 (6·6)
(x-12)² + (y-6)² = 36
What is the square root of 48? what is the square root of 1/49 ? what is the square root of 4/100 ?
Answers
Answer:
Step-by-step explanation:
√48 = √(3*16) = 4√3
√1
√(1/49) = ------- = 1/7
√49
√4
√(4/100) = --------------- = ±2/10 =
√100
Helppppp!!!! Thank you
Answers
Greetings from Brasil...
In a triangle the sum of the internal angles is 180 °.... Thus,
Ô = 180 - 30
Ô = 60
The desired area is the area of the rectangle triangle, minus the area of the circular sector whose angle 60
A1 = area of the rectangle triangle
TG B = OA/AB
AB = OA / TG B
AB = 6 / TG 30
AB = 6√3
A1 = (AB . OA)/2
A1 = (6√3 . 6)/2
A1 = 18√3A2 = area of the circular sector
(rule of 3)
º area
360 ------------ πR²
60 ------------ X
X = 60πR²/360
X = 6π
So,
A2 = 6πThen the area shaded is:
A = A1 - A2
A = 18√3 - 6πWhich one of these relations are functions ?
Please helpppp fast
Answers
Answer:
the 4th and 6th one
Step-by-step explanation:
A function is when there are x- and y-values but each x value has only 1 y-value
Simple: If the x-value is repeated its not a function
Answer:
Step-by-step explanation:
1,2,3
Which of the following shows the correct solution steps and solution to 7x-4= -18?
Answers
7x = -14
x = -2
Answer:
x = -2
Step-by-step explanation:
To solve for x always get x on one side
First add 4 on each side, 4 + 7x - 4 = -18 + 4
Next subtract 18 from 4, making it -14 7x = -14
Now divide 7 on each side, x = -2
Which of the following best represents the average rate at which the human hair grows (1 point)
a
0.25 inches per second
b
0.25 meters per hour
с
0.25 meter per month
d
0.25 inches per month
Answers
Answer:
D.0.25 inches per months
Step-by-step explanation:
The average rate or speed of human hair growth is about 0.25inches per month.
In circle O, AC and BD are diameters. Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x. What is mArc A B?
Answers
Answer:
120
Step-by-step explanation:
Got it right on the assigment
Answer:
c. 120
Step-by-step explanation:
Look at the figure below: Triangles ABC and BDC have a common base BC. E is the point of intersection of BD and AC. AE = EC and ED = BE Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? HELPPPPP MEEEEEE WILL GIVE BRAIN POINTS
Answers
Answer:
AEB and CED
Step-by-step explanation:
Given the two pairs of congruent sides, you now use the vertical angles as the pair of congruent included angles, <AEB and <DEC.
The congruent triangles are:
AEB and CED
Answer:
B- Triangle AEB and triangle CED
Step-by-step explanation:
I took the test and it was correct
Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Answers
Answer: 0.008
Step-by-step explanation:
We have 3 experiments.
Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".
in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:
p = 1/5.
And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:
P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008
Two stores sell the same computer for the same original price. Store A advertises that the computer is on sale for 25% off the original price. Store B advertises that it is reducing the computer’s price by $180. When Brittany compares the sale prices of the computer in both stores, she concludes that the sale prices are equal. Let p represent the computer’s original price. Which equation models this situation?
Answers
Answer:
p= 25/100 = 180/x
Step-by-step explanation:
In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.
Answer:
0.75p=p-180
Step-by-step explanation:
0.75p=p-180 is your answer
In 5 hours a small plane can travel downwind for 4000 kilometers
or upward 3000 kilometers. Find the speed of this plane with no wind and the speed of the wind current.
write as an equation
Answers
Answer:
the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h
Step-by-step explanation:
Let V be the speed of the plane and v the speed of the wind. Down current, they are in opposite directions, and the plane travels a a distance of 4000 km in 5 hours,so
5(V - v) = 4000
V - v = 800 (1)
For upwind movement, since the plane travels 3000 km in 5 hours, so
5(V + v) = 3000
V + v = 600 (2)
adding equations (1) and (2), we have
V - v = 800
+
V + v = 600
2V = 1400
V = 1400/2 = 700 km/h
subtracting equations (2) from (1), we have
V - v = 800
-
V + v = 600
-2v = 200
v = -200/2 = -100 km/h
So, the speed of the plane with no wind is 700 km/h and the speed of the wind is 100 km/h
The perpendicular bisector of the line segment connecting the points $(-3,8)$ and $(-5,4)$ has an equation of the form $y = mx + b$. Find $m+b$.
Answers
Answer:
m = -1/2 and b = 6.5
Step-by-step explanation:
To find the slope of the original line segment, we have to do the change in y/the change in x:
(4-8)/(-5--3) = -4/-2 = 2
2 is the slope of the original line segment, but since this is the perpendicular bisector, we have to take the negative reciprocal of 2 so m = -1/2
To find b we substitute the values of x, y, and m into the equation. Let's use the x value of -3 and the y value of 8:
y = mx + b
8 = -1/2(-3) + b
8 = 3/2 + b
6.5 = b
How do I find DG. A. 3 B. -7 c. 16 d. 13
Answers
Answer:
x = -7
Step-by-step explanation:
DE + EF + FG = DG
2x+17 + 8+2 = x+20
Combine like terms
2x+ 27 = x+20
Subtract x from each side
2x+27-x = x+20-x
x+27 = 20
Subtract 27 from each side
x+27-27 = 20-27
x = -7
Find the constant of proportionality (r) in the equation y = r x
Answers
Answer:
r = 11Step-by-step explanation:
y = r x
r is the constant of proportionality
To find r pick any values of x and y provided and substitute it into the above formula and solve for r.
That's
using
x = 2
y = 22
We have
22 = 2r
Divide both sides by 2
r = 11Therefore the constant of proportionality is 11
Hope this helps you
use the formula S = 40,000 (1.06)t to calculate your salary after 4 years. Round your answer to the nearest dollar.
a. $42,400
b. $44,944
c. $47,641
d. $50,499
Answers
Answer:
d. $50,499
Step-by-step explanation:
Given:
S = 40,000 (1.06)^t
Where,
t=4 years
S=40,000(1.06)^4
=40,000(1.26247696)
=50,499.0784
To the nearest dollar
S=$50,499
The answer is d. $50,499
If you're good at exact values of trig ratios pea shell me with 13a
Answers
It is an equilateral triangle so its angles are equal 60°. From the definition, we know that:
[tex]\sin60^\circ=\dfrac{h}{4}[/tex]
and
[tex]\sin60^\circ=\dfrac{\sqrt{3}}{2}[/tex]
so
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{h}{4}\quad \Big|\cdot4\\\\\\h=\dfrac{4\cdot\sqrt{3}}{2}\\\\\boxed{h=2\sqrt{3}}\\[/tex]
Answer:
h = √12
Step-by-step explanation:
use the Pythagorean
h² = 4² - 2²
h² = 16 - 4
h = √12
