Answer:
A. 3
Step-by-step explanation:
Let the integers be
x
(x+1)
(x+2)
(x+3)
Sum the integers
We have,
x+(x+1)+(x+2)+(x+3)=18
x+x+1+x+2+x+3=18
4x+6=18
Subtract 6 from both sides
4x-6=18-6
4x=12
Divide both sides by 4
4x/4=12/4
x=3
The smallest integer which is x is equal to 3
Check:
3+4+5+6=18
A rectangular carton has twice the height, one-
third the length, and four times the width of a
second carton. The ratio of the volume of the
first carton to that of the second is
A)16:3
B)3:1
C)8:3
D)3:8
Laura’s overall monthly living expenses are $1,600. How much money does she have at the end of the month to put into savings?
Step-by-step explanation:
The question has missing details nevertheless we can make head way with the information on ground.
Given that Laura's overall monthly living expenses are $1,600
in order to calculate her savings for the month we need to know her income for the month, that is the overall sum she has at hand before incurring any expenses(this is the missing detail).
Say this overall amount is "x"
her saving for the month = [tex](x- 1600)[/tex]
PLEASE!!! HELP!!! Question: If you have points on a graph that plot (1,7), (2,8), (3,5) and (4,6) what would be the slope?
Answer:
1
Step-by-step explanation:
You only need two points to find the slope.
Let's use (1,7) and (2,8).
The formula for slope is (y2-y1)/(x2-x1)
Let's plug the values in:
(8-7)/(2-1) = 1.
So, the slope is 1.
PLSSS HELP State the maximum number of turns the graph of each function could make 1. f(x)=x^5-3x+1 2.f(x)=-x^7-7x^5-4x^3
Answer:
max for 5th-degree: 4 turns. This function: 2 turns.max for 7th-degree: 6 turns. This function: 0 turns.Step-by-step explanation:
In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.
__
1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.
__
2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.
NEED HELP ASAPPP!!! Drag each scenario to show whether the final result will be greater than the original
value, less than the original value, or the same as the original value.
1. A $30 increase followed by a $30 decrease
2. A 20% decrease followed by a 40% increase
3. A 100% increase followed by a 50% decrease
4. A 75% increase followed by a 33% decrease
5. 55% decrease followed by a 25% increase
Answer:
Greater than the original = 2, 4
Less than the original = 5
Same as the original = 1, 3
Step-by-step explanation:
Let the original value be x.
1. A $30 increase followed by a $30 decrease.
New value [tex]=x+30-30=x[/tex], it is same as original value.
2. A 20% decrease followed by a 40% increase.
Afer 20% decrease.
New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]
Afer 40% increase.
New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.
Similarly check the other values.
3. A 100% increase followed by a 50% decrease.
New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.
4. A 75% increase followed by a 33% decrease
New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.
5. 55% decrease followed by a 25% increase
New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.
Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .
A 100% increase followed by a 50% decrease
A $30 increase followed by a $30 decrease
Less Than The Original:55% decrease followed by a 25% increase
Greater Than The Original:A 20% decrease followed by a 40% increase
A 75% increase followed by a 33 1/3% decrease
Elijah created the scatterplot to show the relationship between the temperature in degrees Fahrenheit and the number of visitors to a zoo. A graph titled Temperature versus Zoo Visitors has Degrees Fahrenheit on the x-axis, and Visitors on the y-axis. Points are at (70, 100), (77, 96), (90, 75), (93, 73), (98, 60). Which is true regarding the data in his scatterplot? As the temperature increases, the number of visitors decreases. As the temperature increases, the number of visitors increases. As the temperature increases, the number of visitors remains the same. As the temperature increases, the number of visitors increases then decreases.
Answer:
A
Step-by-step explanation:
it right on edge
Answer:
A.
Step-by-step explanation:
Did the unit test in edge and got 100
how would a bank represent a withdrawal of 19.43 dollars?
Answer:
-19.43
Step-by-step explanation:
Withdrawals are negative
Find the missing side to the triangle in the attached image. Thanks.
Answer:
Let's use Pythagorean Theorem which states:
6² + 10² = x²
36 + 100 = x²
136 = x²
x = ± 2√34
Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.
Answer:Answer:
Let's use Pythagorean Theorem which states:
6² + 10² = x²
36 + 100 = x²
136 = x²
x = ± 2√34
Since the side lengths of a triangle cannot be negative, x = -2√34 is an extraneous solution which means that x = 2√34.
Read more on Brainly.com - https://brainly.com/question/17033938#readmore
Step-by-step explanation:
What is the slope of the line?
Answer:
5/3
Step-by-step explanation:
it should be y/x
you can count 5 up and 3 over
Answer:
8/5
Step-by-step explanation:
You can use the formula [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex] with a pair of points [tex](x_{1},y_{1})[/tex][tex](x_{2},y_{2})[/tex]. We can use points (1,4) and (-4,-4). Plugging in the equation we get (4-(-4))/(1-(-4)), which simplifies to 8/5, which is the slope.
Choose the single logarithmic expression that is equivalent to the one shown.
log2 6 + log2 2 − log2 8
Answer:
C. log2 3/2.
Step-by-step explanation:
When you are adding two logs with the same base, you multiply.
So, log2 6 + log2 2 = log2 6 * 2 = log2 12
When you subtract two logs with the same base, you divide.
So, log2 12 - log2 8 = log2 12 / 8 = log2 3/2
The answer is C. log2 3/2.
Hope this helps!!
Find the volume of a right circular cone that has a height of 18.8 in and a base with a
diameter of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the cone is 1006.9in³
Step-by-step explanation:
Given
[tex]Height = 18.8\ in[/tex]
[tex]Diameter = 14.3\ in[/tex]
Required
Calculate the volume;
The volume of a cone is calculated as thus;
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where V represents volume; r represents radius; and h represents height
The radius is calculated as thus;
[tex]r = \frac{1}{2}Diameter[/tex]
[tex]r = \frac{1}{2} * 14.3[/tex]
[tex]r = 7.15[/tex]
Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]
[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes
[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]
[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]
[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]
[tex]V = \frac{21144.266}{21}[/tex]
[tex]V = 1006.86980952[/tex]
[tex]V = 1006.9\ in^3[/tex] (Approximated)
Hence, the approximated volume of the cone is 1006.9in³
Answer:1006.5
Step-by-step explanation:
URGENT HELP NEEDED! YOU WILL GET BRAINLIEST! Convert to a product: cot(α) - 1
Answer:
WHAT
Step-by-step explanation:
Karl set out to Alaska on his truck.
The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is
graphed.
How much fuel did the truck consume every 100 kilometers
Answer:
the amount of fuel consumed every 100 kilometers is 62.5 litres.
Step-by-step explanation:
To determine the amount of fuel consumed every 100 kilometers.
Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.
From the graph, the amount of fuel consumed for the first 100 kilometers is;
[tex]F = F_0 - F_{100} .........................1[/tex]
[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]
substituting into equation 1.
[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]
Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.
Answer:500
Step-by-step explanation:got it on Kahn
What is a number of subsets for the set which contains the 10 elements.
Answer:
The number of subsets of a set containing 10 elements is 2^10=1024.
Step-by-step explanation:
MATH— Please help me answer this question. Hopefully you can see the picture
Find the missing side lengths. Leave your answers as radicals in simplest form.
ANSWER QUICK
Answer:
C
Step-by-step explanation:
It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.
Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.
3^2 is 9 so you get 18
the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18
Hope this helps!
A restaurant offers 6 choices of appetizer, 8 choices of main meal and 5 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?
Answer:
377 choices
Step-by-step explanation:
The following values were given in the question:
The restaurant offered
6 choices of appetizer
8 choices of main meal
5 choices of dessert.
We are also told in the question that the customer can choose to eat just one course, or two different courses, or all three courses.
Let us represent each choice by :
A = Appetizer = 6
B = Main meal = 8
C = Dessert = 5
a) The 3 choices together
ABC=6 × 8 × 5=240 choices
b) AB= Appetizer and Main meal
= 6 × 8 = 48 choices
c) AC= Appetizer and Dessert
= 6 × 5 = 30 choices
d) BC = Main meal × Dessert
= 8 × 5 = 40 choices
e) A,B,C = the customer having each of the choices only
Appetizer + Main meal + Dessert
= 6 + 8 + 5
= 19 choices
The number of possible meals is calculated as:
240 choices + 48 choices + 30 choices + 40 choices + 19 choices
= 377 choices
Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓64*36=✓8^2*6^2
x=8*6
x=48
Determine the approximate area of a sector with a central angle of 75° and a radius of 14 yards. Question 16 options: A) 9.2 yards2 B) 128.3 yards2 C) 40.8 yards2 D) 0.21 yards2
Answer:
B) 128.3 square yards
Step-by-step explanation:
A = (n/360 deg)(pi)r^2
where n = central angle of sector.
A = (75/360)(3.14159)(14 yd)^2
A = 128.3 yd^2
Answer:
B. 128.3 yards
Step-by-step explanation:
Area of a Sector Formula: A = ∅/360πr²
Simply plug in our variables:
A = 75/360(π)(14)²
A = 5π/24(196
A = 128.3
Please could I have some help :)
Answer:
a) x = 128 degrees
b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
Step-by-step explanation:
Given:
attached diagram
ABC is a straight line
Solution:
a) Find x
ABC is a straight line
angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.
x is the central angle of the arc APD
so angle ABD is the inscribed angle which equals half of the arc angle =>
angle ABD = x/2 = 64 degrees
Solve for x
x/2 = 64
x = 2*64
x = 128 degrees
b.
Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
The graph of F(x) shown below resembles the graph of G(x) = x ^ 2 but it has been changed somewhat. Which of the following could be the equation of F(x)
Answer:
Option (A)
Step-by-step explanation:
Parent function of the function graphed is,
G(x) = x²
Graph shows the vertex of the given parabola is at (3, 3).
Vertex form of a parabola is,
F(x) = a(x - h)² + k
where (h, k) is the vertex.
By substituting the coordinates of the vertex in the equation,
F(x) = a(x - 3)² + 3
Since the given parabola is opening upwards, value of 'a' will be positive.
So the equation will be,
F(x) = 2(x - 3)² + 3
Therefore, from the given options, equation given in Option (A) matches the answer.
Answer:
A is the correct answer.
Step-by-step explanation:
What's the standard equation of the circle with the general equation x2 + y2 + 4x – 2y – 20 = 0? answers: 1) (x + 2)2 + (y – 1)2 = 5 2) (x – 2)2 + (y + 1)2 = 25 3) (x + 1)2 + (y – 2)2 = 5 4) (x + 2)2 + (y – 1)2 = 25
Answer:
4). (x + 2)^2 + (y - 1)^2 = 25.
Step-by-step explanation:
x^2 + y^2 + 4x - 2y - 20 = 0
x^2 + 4x + y^2 - 2y = 20
Completing the square on the x and y terms:
(x + 2)^2 - 4 + (y - 1)^2 - 1 = 20
(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1
(x + 2)^2 + (y - 1)^2 = 25.
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The given circle equation is x²+ y²+4x-2y-20=0.
Here, x²+ y²+4x-2y=20
By completing the square on the x and y terms:
Now, add 4 on both the sides of an equation, we get
x²+ y²+4x-2y+4=20+4
x²+4x+4+y²-2y=24
Add 1 on both the sides of an equation, we get
(x+2)²+y²-2y+1=24+1
(x+2)²+(y-1)²=25
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
To learn more about an equation of a circle visit:
https://brainly.com/question/23799314.
#SPJ2
Attachment Below, please help, I'm not timed
Answer:
Step-by-step explanation:
x + 2x + 4x = 49
7x = 49
x = 7
2(7)= 14 hours he worked on Wednesday
simplify this please 41 =12d-741=12d−7
Answer:
Simplifying
41 = 12d + -7
Reorder the terms:
41 = -7 + 12d
Solving
41 = -7 + 12d
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-12d' to each side of the equation.
41 + -12d = -7 + 12d + -12d
Combine like terms: 12d + -12d = 0
41 + -12d = -7 + 0
41 + -12d = -7
Add '-41' to each side of the equation.
41 + -41 + -12d = -7 + -41
Combine like terms: 41 + -41 = 0
0 + -12d = -7 + -41
-12d = -7 + -41
Combine like terms: -7 + -41 = -48
-12d = -48
Divide each side by '-12'.
d = 4
Simplifying
d = 4
Thuy is substituting t = 3 and t = 8 to determine if the two expressions are equivalent.
Answer:
The expressions are not equivalent.
Step-by-step explanation:
The answers would be 196 and 193 for t = 8
The answers would be 76 and 73 for t = 3
I need help with this question
Answer:
It's the first option.
Step-by-step explanation:
The line which rises to the right has a slope of 1 and a y-intercept of -6.
It's equation is y = x - 6.
The one which rises to the left has slope -1 and y-intercept -2.
It's equation is y = -x - 2 or x + y = -2.
The solution is at the point where the 2 lines cross - that is (2, -4).
Find the missing segment in the attached image
Answer:
The length of the missing segment is 36
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]
[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]
Cross Multiply
[tex]20 * (24 + x) = 24 * 50[/tex]
[tex]20 * (24 + x) = 1200[/tex]
Divide both sides by 20
[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]
[tex](24 + x)= \frac{1200}{20}[/tex]
[tex]24 + x= 60[/tex]
Subtract 24 from both sides
[tex]24 - 24 + x = 60 - 24[/tex]
[tex]x = 60 - 24[/tex]
[tex]x = 36[/tex]
Hence, the length of the missing segment is 36
Find the missing segment in the attached image
Answer:
? = 78
Step-by-step explanation:
Use similar triangles.
26/12 = (26 + ?)/48
13/6 = (26 + ?)/48
6(26 + ?) = 13 * 48
156 + 6? = 624
6? = 468
? = 78
Answer:
The missing segment is equal to 78
Step-by-step explanation:
Using the similarity of triangles:
[tex]x=?[/tex]
[tex]$\frac{x+26}{48}=\frac{26}{12} $[/tex]
[tex]12(x+26)=48 \cdot 26[/tex]
[tex]12x+312=1248[/tex]
[tex]12x+312=1248[/tex]
[tex]12x=936[/tex]
[tex]x=78[/tex]
PLEASE ANSWER! FIRST CORRECT ANSWER GETS BRAINLIEST!
Answer:
The answer should be 20.
Step-by-step explanation:
First, you need to understand the abbreviated list: PEMDAS. I'm not sure if you guys learned this or not, but it helps to know when solving problems like this.
So, if you don't know: PEMDAS is a list of what order you would need to start with when solving a problem. The order is Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
With that in mind, we'll start by looking at the numbers in the numerator of this fraction. (Doesn't matter if you start with the numerator or denominator first.)
You want to start with the numbers in the parentheses as that is the first letter in the PEMDAS phrase.
[tex](7-6.35) = 0.65[/tex]
Now, we have division and an addition sign next. According to PEMDAS, you want to start with Division before you Add. So, you will end up having a 10 in the numerator. (I'm assuming you can use a calculator for this, so I'm not showing how to divide the decimals.)
[tex]\frac{(0.65)}{6.5}+9.9=0.1+9.9 =10[/tex]
Save that number somewhere for now since we will have to come back to it later. For the denominator, we have a set of parentheses that the problem wants us to focus on so, ignore the [tex]7\frac{1}{24}[/tex] for now.
Start with the first set of numbers that have the division sign in between.
[tex]\frac{1.2}{36} =0.03333[/tex]
Don't add just yet after getting this number. You want to divide the 1.2 and [tex]\frac{1}{4}[/tex] since Division needs to be done first before Adding or Subtracting.
[tex]\frac{1.2}{\frac{1}{4} }=4.8[/tex]
The resulting numbers in the parentheses should look like this now (we're still ignoring the [tex]7\frac{1}{24}[/tex] at the end after the parentheses):
[tex](0.03333+4.8-1\frac{5}{16})=3.520833333[/tex]
This expression is also the same as this if you wanted to change the fraction at the end of the parentheses:
[tex](0.03333+4.8-\frac{21}{16})=3.520833333[/tex]
Now you can finally take this number and divide it by [tex]7\frac{1}{24}[/tex] or [tex]\frac{169}{24}[/tex].
[tex]\frac{3.520833333}{\frac{169}{24} }=0.5[/tex]
These are really big numbers when you are dividing so hopefully you don't have to solve this all out in your head or by paper. Now, remember that 10 we got from the numerator earlier? We can finally use that here where we have that as our numerator and 0.5 as our denominator.
[tex]\frac{10}{0.5} =20[/tex]
This gives you the final answer of 20.
The points in a plane in a fixed distance from a given point
is called a circle. What is the fixed distance called?
a. chord
b. radius
c. diameter
d. not given
Answer:
radius
Step-by-step explanation:
That "fixed distance" is the 'radius' of the circle.