Answer:
• Gayle: 14
• Crystal: 3
Step-by-step explanation:
Let g represent the number of paperclips Gayle has. Then 42/g is the number Crystal has. The relationship between the two numbers is said to be ...
g - (42/g) = 11
Multiplying by g gives ...
g^2 -42 = 11g
g^2 -11g -42 = 0 . . . . subtract 11 g to put into standard form
To factor this, you are looking for two factors of -42 that sum to -11.
-42 = -42·1 = -21·2 = -14·3 = -7·6
You can see that -14 and 3 sum to -11, so the factoring is ...
(g -14)(g +3) = 0
g = 14 . . . . . . . . . . makes the product zero. (The g=-3 solution is extraneous.)
Gayle has 14 paperclips and Crystal has 3.
A rock is dropped from a bridge 320 feet above the river. The pathway that the rock takes can be modeled by the equation h= -16t2+320. How long will it take the rock to reach the river?
Answer:
288
Step-by-step explanation:
Answer: 4.47 seconds.
Step-by-step explanation:
Hi, the rock will reach the river when the height (h) is 0.
So, replacing in the equation given:
h= -16t2+320
Where t is the time
0= -16t2+320
Solving for t
-320 = -16t2
-320/-16 =t2
20 = t2
√20 =t
4.47 = t
Assuming that t is the time in seconds, the rock will reach the river after 4.47 seconds.
Feel free to ask for more if needed or if you did not understand something.
Write the standard form of the equation of the circle with the center (0,2) that passes through (7,3)
Answer:
x²+y²-4y-46=0
Step-by-step explanation:
the equation of a circle is in the form (x - a)² + (y - b)² = r², where (a,b) is the center of the circle
the equation is (x - 0)² + (y - 2)² = r², where r is the radius. But r is the distance from (0,2) to (7,3)
the distance from two points is given by r² = (x₁ -x₂)² + (y₁ - y₂)²
r²= (0 - 7)² + (2 - 3)²
r² = 49 + 1 = 50
hence the equation is
(x)² + (y - 2)² = 50
x²+y²-4y+4 = 50
x²+y²-4y-46= 0
What is the value of x?
Enter your answer in the box.
x =
Answer:
25
Step-by-step explanation:
use pythagoras theorem:
sqrt of: a^2+b^2 = c
where
a=24
b=7
c=x
so substitute these values in the theorem:
sqrt: 24^2+7^2=25
hope this helps!
Answer:
25
Step-by-step explanation:
a²+b²+c²
24²+7²=c²
576+49=625
√625=25
Factor x^3+2x^2-9x-18 , given that -2 is a zero.
Answer:
x
3
+
2
x
2
+
9
x
+
18
x3+2x2+9x+18
Factor out the greatest common factor from each group.
Tap for more steps...
x
2
(
x
+
2
)
+
9
(
x
+
2
)
x2(x+2)+9(x+2)
Factor the polynomial by factoring out the greatest common factor,
x
+
2
x+2
.
(
x
+
2
)
(
x
2
+
9
)
(x+2)(x2+9)
Step-by-step explanation:
Answer:
(x + 2)(x + 3)(x - 3)
Step-by-step explanation:
Given that x = - 2 is a zero then (x + 2) is a factor
Dividing x³ + 2x² - 9x - 18 by (x + 2) gives
x³ + 2x² - 9x - 18 = (x + 2)(x² - 9) = (x + 2)(x + 3)(x - 3)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch apothem
A = sq. in.
Answer:
[tex]\boxed{108\sqrt{3}\text{ in}^{2}}[/tex]
Step-by-step explanation:
An apothem is a perpendicular drawn from the centre of the triangle to one of its sides.
The three apothems OD, OE, and OF divide ∆ABC into six smaller congruent triangles.
1. Area of ∆OCD
CotOCD = OD/OC
cot30 = CD/6
√3 = CD/6
CD = 6√3
A= ½bh
A = ½ × 6√3 × 6 = 18√3 in²
2. Area of ∆ABC
A = 6 × area of ∆OCD = 6 × 18√3 = 108√3 in²
[tex]\text{The area of the triangle is }\boxed{108 \sqrt{3} \text{ in}^{2}}[/tex]
Answer:
just had this question :/ 108√3
Step-by-step explanation:
Find the area of the composite figure.
A) 17 yd2
B) 21 yd2
C) 23 yd2
D) 24 yd2
Answer:
C) 23 yd^2
Step-by-step explanation:
We can break this figure into two rectangles.
One rectangle is a vertical triangle that is 3 yd across by 7 yds down
The area of this figure is
A = lw
= 3 * 7 = 21
The other rectangle is 1 yd across and by 2 yds down
The area of this figure is
A = lw
= 1 * 2 = 2
The total area is the sum of the two figures
A = 21 +2 = 23
Its c hope this helped
Michael is 25 years younger than his father. The sum of their ages is 53. What is Michael’s age
Answer: 14
Step-by-step explanation:
⇒ Michael's age = x −25
⇒ x − 25 + x = 53
⇒ 2x = 53 + 25
⇒ 2x =78
⇒ x =39
Hence, Michael's age
= x − 25 = 39 − 25 = 14* Hopefully this helps:) Mark me the brainliest:)!!!
~234483279c20~
Help me
it an emergency
Answer:
40
Step-by-step explanation:
165% * ? = 66
66 / 165%
66 / (165 / 100)
(100 * 66) / 165
6600 / 165 = 40
HELP ME , I CANNOT POST PICTURE & I HAVE 2 THINGS THAT REQIRE A PICTURE WHAT DO I DO ??!
Answer:
Step-by-step explanation:
so when you post your picture you wanna click the thing that looks like a paper clip and attach a file or picture. or your can copy your photo and paste it in your question if you dont know how to take a picture just screenshot it *depends what kind of computer your using*
Hello there! I answered a few questions like this before so here is my answer from that question:
- Click "Ask your question."
- Type out the question in the field.
- Click the paperclip icon below the answering field.
- Click "add attachments"
- Select the photo you want to use
- Click "Open" and wait for the photo to load.
There you go! I hope this helped. An easier way to do this is to drag your photo straight into the answer field and you can skip the last 4 steps, I am sure this works on mac but not sure if it works on windows. Have a great day! :)
How u do this bro?!,?,!,!
Answer:
c=3
Step-by-step explanation:
We have 2 points, we can find the slope using
m = (y2-y1)/(x2-x1)
Substituting into this equation
-1/4 = (4-5)/(7-c)
-1/4 = -1/(7-c)
Multiply both sides by -1
1/4 = 1/(7-c)
The denominators have to be the same
4 = 7-c
Subtract 7 from each side
4-7 = 7-7-c
-3 = -c
Multiply by -1
3 =c
Which of the following describes how geometric figures move without changing shape?
A. Transformation
B. Image
C. Map
D. Isometric
Answer:
A. Transformation
Step-by-step explanation:
Transformation is the responsible for the changing the size of the object without changing the shape. Then the correct option is A.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The transformation is the process of making the shape of an object to be increased or decreased without changing the shape of the object that depends on the scale factor.
If the size of the object is increased then the scale factor is greater than one.
If the size of the object is decreased then the scale factor is less than one.
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6. Solve for x.
10x - 4 = +(8x + 14)
Simplify brackets
10x - 4 = 8x + 14
Add 4 to both sides
10x = 8x + 14 + 4
Simplify 8x + 14 + 4 to 8x + 18
10x = 8x + 18
Subtract 8x from both sides
10x - 8x = 18
Simplify 10x - 8x to 2x
2x = 18
Divide both sides by 2
x = 18/2
Simplify 18/2 to 9
x = 9
10x - 4 = 8x + 14
Step 1: Combine like terms
x's go with x's (10x and 8x). To do this subtract 8x to both sides
(10x - 8x) - 4 = (8x-8x) + 14
2x - 4 = 14
Normal numbers go with normal numbers (-4 and 14). To do this add 4 to both sides
2x + (-4 + 4) = 14 + 4
2x = 18
Step 2: Isolate x by dividing 2 to both sides
2x/2 = 18/2
x = 9
Hope this helped!
Solve the system of equations 8x+13y=2 y=x-2
Answer:
x = 1.33333333
y = -0.66666667
Step-by-step explanation:
The answers have to be those numbers EXACTLY.
8x + 13y = 2
8(1.33333333) + 13(-0.66666667) = 2
10.66666667 - 8.66666667 = 2
2 = 2
y = x - 2
-0.66666667 = 1.33333333 - 2
-0.66666667 = -0.66666667
Answer:
x = 1.34
y = -0.67
Step-by-step explanation:
Use the following information to find the test statistic of the sample used to test the claim that FICO credit scores are greater than 675. n = 50, = 719, s = 92
t = 32.437
t = –32.437
t = –3.382
t = 3.382
Answer:
t = –3.382
Step-by-step explanation:
Claim: FICO credit scores are greater than 675
Thus, x = 675
We are given:
Sample size = n = 50
Sample Mean = u = 719
Sample Standard deviation = s = 92
The formula to find the t-statistic is:
[tex]t=\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
Using the above values, we get:
[tex]t=\frac{675-719}{\frac{92}{\sqrt{50} } }\\\\ t=-3.382[/tex]
Thus, the value of test statistic is -3.382. So 3rd option gives the correct answer.
Answer:
t = 3.382
Step-by-step explanation:
gradpoint
4×10 + 3×1 + 5×(
1
10
) + 3×(
1
100
) + 2×(
1
1,000
) =
Answer:
this answer is 25893
Step-by-step explanation:
Which angle is congruent to angle 1?
The angle that is congruent to angle 1 is angle 4 (m∠ 4).
What is congruent angle?
Congruent angles are angles that have the same measure in degrees or radians. So, if two angles are congruent, it means that they are equal in size.
From the diagram of the parallel lines, the angle that is all congruent to angle 1 include;
m∠ 1 = m∠ 4 (vertically opposite angles are equal)
m∠ 2 = m∠ 5 (vertically opposite angles)
m∠ 3 = m∠ 6 (vertically opposite angles)
So m∠ 1 = m∠ 4
Thus, the angle that is congruent to angle 1 is angle 4.
What is the solution of the inequality c-8>-1
Answer:
The solution of inequality is c>7
Step-by-step explanation:
We need to solve the inequality c-8>-1.
c-8 > -1
Adding +8 on both sides
c-8+8 > -1+8
c>7
So, the solution of inequality is c>7
Which situation will have the greatest number of permutations?
A.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits cannot be repeated.
B.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits cannot be repeated.
C.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits can be repeated.
D.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits can be repeated.
Please select the best answer from the choices provided
A
B
C
D
Answer:
Option C will have greatest number of permutations.
Step-by-step explanation:
A.
The number of license plates with 4 letters followed by 3 numbers, where letters and digits cannot be repeated.
We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter
25 letters options for 2nd letter
24 letter options for 3rd letter
23 letter options for 4th letter.
So total options for 4 letters 26*25*24*23 = 358800
Now, 3 numbers are required. We have total 10 numbers (0-9)
10 number options for 1st number
9 number options for 2nd number
8 number options for 3rd number
Total options for 3 numbers= 10*9*8 = 720
total options for 4 letters and 3 numbers will be: 358800 * 720 = 258,336,000
B.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits cannot be repeated.
We have total 26 letters (A_Z) and the letters can't be repeated. So we have 26 letter options for 1st letter
25 letters options for 2nd letter
24 letter options for 3rd letter
So total options for 3 letters= 26*25*24 = 15600
Now, 4 numbers are required. We have total 10 numbers (0-9)
10 number options for 1st number
9 number options for 2nd number
8 number options for 3rd number
7 number options for 4th number
Total options for 4 numbers = 10*9*8*7 = 5040
total options for 4 letters and 3 numbers will be: 15600 * 5040 = 78,624,000
C. The number of license plates with 4 letters followed by 3 numbers, where letters and digits can be repeated.
Now, the letters and digits can be repeated. So we have 26 options for each 4 letters and 10 options for each 3 numbers
26*26*26*26 *10*10*10 = 456,976 * 10,00 = 456,976,000
total options for 4 letters and 3 numbers will be: 456,976,000
D.
The number of license plates with 3 letters followed by 4 numbers, where letters and digits can be repeated.
Now, the letters and digits can be repeated. So we have 26 options for each 3 letters and 10 options for each 4 numbers
26*26*26 *10*10*10*10 = 17,576 * 10,000 = 175,760,000
total options for 3 letters and 4 numbers will be: 175,760,000
So, Option C will have greatest number of permutations.
Which phrase is represented by the expression 5x ( 36+ 9)?
Answer: 225x
Step-by-step explanation:
Use distribution to get rid of the parenthesis.
5x * 36 + 5x*9
180x + 45x
Now combine like terms
225x
Solve for u. 4u=10.24. Please answer thanks :)
Answer:
Simplifying
4u = 10.24
Solving
4u = 10.24
Solving for variable 'u'.
Move all terms containing u to the left, all other terms to the right.
Divide each side by '4'.
u = 2.56
Simplifying
u = 2.56
Step-by-step explanation:
Answer:
[tex]u=2.56[/tex]
Step-by-step explanation:
The given equation is
[tex]4u=10.24[/tex]
We want to solve for the variable u, in the linear equation above.
We divide both sides by 4 to obtain;
[tex]\frac{4u}{4} =\frac{10.24}{4}[/tex]
We simplify to get;
[tex]u=2.56[/tex]
What is the first step in evaluating the expression shown below?
12÷(7.4−3.6)+8−2
A. Subtract 7.4−3.6.
B. Divide 12÷7.4.
C. Add 3.6+8.
D. Subtract 8−2.
The first step would be to A. Subtract 7.4 - 3.6.
You use the PEMDAS rule
Steps:
1. Parenthesis
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
Subtract 7.4−3.6 is the first step in evaluating the expression
What is expression ?In mathematics, an expression or mathematical expression exists as a finite combination of signs that stands well-formed according to laws that depend on the context.
The Bodmas rule is arranged according to the letters in the acronym BODMAS, which stand for brackets, order of powers or roots, division, and multiplication. A stands for addition and S for subtraction. According to the BODMAS rule, multi-operator mathematical equations must be resolved in the BODMAS order from left to right.
Given
According to BODMAS rule
Subtract 7.4 - 3.6 will be performed since it is within brackets.
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m ∠CAD = _____. Please help!
Check the picture below.
Answer:
B. [tex]m\angle CAD=\frac{m\widehat {CD}-m\widehat {GE}}{2}[/tex].
Step-by-step explanation:
We have been given an image of a circle. We are asked to find the measure of angle CAD.
We can see that angle CAD is formed by two intersecting secants outside the circle.
Intersecting secants theorem states that when two secants intersects outside a circle, then the measure of angle formed by secants is half the difference of intercepted arcs.
[tex]m\angle CAD=\frac{\text{Larger arc-Smaller arc}}{2}[/tex]
[tex]m\angle CAD=\frac{m\widehat {CD}-m\widehat {GE}}{2}[/tex]
Therefore, option B is the correct choice.
given: f(x) = x + 2 and g(x) = 3x + 5
f (x)/g (x) =
For this case we have two functions of the form y = f (x). We must find the quotient of the following functions:
[tex]f (x) = x + 2\\g (x) = 3x + 5[/tex]
So, we have by definition:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
Answer:
[tex]\frac {f (x)} {g (x)} = \frac {x + 2} {3x + 5}[/tex]
with 3x + 5 different from zero, so that the function is defined
Answer:
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
where [tex]x\ne -\frac{5}{3}[/tex]
Step-by-step explanation:
The given functions are:
f(x) = x + 2 and g(x) = 3x + 5
[tex]\frac{f(x)}{g(x)}=\frac{x+2}{3x+5}[/tex]
Since this is a rational function, the function will not be defined where denominator equals zero.
We need to restrict the function or define the domain.
This is a rational function defined for [tex]x\ne -\frac{5}{3}[/tex]
A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. Which type of functions best models this situation?
A) exponential
B) linear
C) quadratic
D) radical
Answer:
Option B. Linear
[tex]y=4x+18[/tex]
Step-by-step explanation:
Let
x----> the time in hours
y----> the total inches of snow on the ground
we know that
The function that best model this situation is the linear function
so
[tex]y=mx+b[/tex]
In this problem
[tex]m=4\frac{in}{h}[/tex]
[tex]b=18\ in[/tex] ----> the y-intercept
substitute
[tex]y=4x+18[/tex]
Question:
A ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour. Which type of functions best models this situation?
A) exponential
B) linear
C) quadratic
D) radical
Answer & Step-by-step explanation:
It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.
If a function has constant rate of change, then the it is a linear function.
It the given case the rate of change is constant so linear function best model this situation.
The slope intercept form of linear function is
f(x)=mx+b ... (1)
where, m is slope and b is y-intercept or initial value.
Ski resort has 18 inches of snow on the ground it means initial value is 18.
The snow is falling at a rate of 4 inches per hour. So, m=4.
Substitute m=4 and b=18 in equation (1).
f(x)=4x+18
Therefore Linear decreasing function best model this situation and the required function is f(x)=4x+18.
Hope this helps.
What is the value of x in the figure?
Enter your answer in the box.
Answer:
x=29
Step-by-step explanation:
x+61=90
61-61
90-61
x=29
Answer: 29
Step-by-step explanation:
Add the right angle which would equal 90 degrees with the 61 degrees. Now you get 151. Subtract 151 from 180, which is half of the circle. Now you have 29 degrees.
16) If 2x + 7 = -9, what is
the value of 15 - 4x?
2x + 7 = -9
2x = -9 - 7
2x = -16
x = -16/2
x = -8
15 - 4x
15 - 4.(-8)
15 + 32
47
mean for 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13
13+6+24+18+33+5+13+48+9+11+36+28+15+6+13(all divided by 15)
278÷15
=18.5333
The mean, or average, of the numbers 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13 is calculated by adding up all the values and dividing the total by the number of values. The mean of these numbers is approximately 18.13.
Explanation:The subject of your question is Mathematics and it appears that you are asking about how to calculate the mean, or average, of a set of values which are 13, 6, 24, 18, 33, 5, 13, 48, 9, 11, 36, 28, 15, 6, 13. To do this, you should add up all the values and divide the total by the number of values.
Add up all the numbers: 13 + 6 + 24 + 18 + 33 + 5 + 13 + 48 + 9 + 11 + 36 + 28 + 15 + 6 + 13 = 272Count how many numbers there are in total, which is 15 in this case.Divide the total by the count: 272 ÷ 15 = approximately 18.13So the mean of these numbers is approximately 18.13.
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If two sides of the triangle are 12 inches and 18 inches, what is the range of the possible lengths of the third side
A) 6
B) 12
C)7
D)15
Answer:
d is the closest to the real answer assuming the question is asking for an estimate
Which term refers to a pictorial representation of given set of data involving two variables?
A- graph
B- decimal
C- formula
D- axis
The term which refers to a pictorial representation of given set of data involving two variables is:
A- graph
Step-by-step explanation:We know that
In mathematics, a graph is a diagram that is used to represent a relationship between the two variables one is a independent variable and the other is a dependent variable.
It is just the set of all the ordered pairs of the type: (x,y) where x is the domain of the function and y is the range of the function.
Hence, the answer is:
Option: A
( A-- Graph)
find the value of x (3x+20) (5x-16)
15x+320
X=21.3
Mulitply 3 and 5 to get 15x
Multiply 20 and 16 to get 320
Divide each side by 15
The value of x (3x+20) (5x-16) is x=0 or x= 16/5 or x= -20/3
What is factorization?Writing a number or other mathematical object as the sum of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x² - 4 and the integer 15 can both be factored by the number 3 × 5.
Given
Let's solve your equation step-by-step.
x(3x+20)(5x−16)=0
15x³+52x²−320x=0
Step 1: Factor left side of equation.
x(5x−16)(3x+20)=0
Step 2: Set factors equal to 0.
x=0 or 5x−16=0 or 3x+20=0
x=0 or x= 16/5 or x= -20/3
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