Answer:
84°
Step-by-step explanation:
smallest angle=x
3x=2nd angle
x+40=3rd angle
angles in a triangle add up to 180 degrees so
5x+40=180
5x=140
x=28
largest angle = 3x
so 3 x 28 = 84 degrees
The largest angle is 84 degrees
Answer:
Largest angle = 84°
Step-by-step explanation:
According to the given information, we are assuming the smallest angle of the triangle to be [tex]x[/tex] degrees, next angle to be [tex]3x[/tex] degrees and the last angle to be [tex]x+40[/tex] degrees.
We know that all three angles of a triangle add up to 180 degrees so:
[tex]x+3x+x+40=180[/tex]
[tex]5x=140[/tex]
[tex]x=28[/tex]
Smallest angle = 28°
Next angle = [tex]3(28)[/tex] = 84°
Last angle = [tex]28+40[/tex] = 68°
Therefore, the largest angle = 84°
The sum of two numbers is 58. The first number is 8 less than half the second number. Let c represent the first number. Let d represent the second number. Which statements about solving for the two numbers are true? Check all that apply.
Answer : The true statements are:
The equation [tex]c+d=58[/tex] represents the sum of two numbers.
The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.
The number c is, 14
The number d is, 44
Step-by-step explanation :
Given:
Let 'c' represent the first number. Let 'd' represent the second number.
The sum of two numbers is 58. The equation will be:
[tex]c+d=58[/tex] .........(1)
The first number is 8 less than half the second number. The equation will be:
[tex]c=\frac{d}{2}-8[/tex] .........(2)
Now by solving the two equations, we get the value of c and d.
As, [tex]c+d=58[/tex]
or, [tex]c=58-d[/tex] ..........(3)
Now put equation 3 in 2, we get the value of d.
[tex]58-d=\frac{d}{2}-8[/tex]
[tex]58-d=\frac{d-16}{2}[/tex]
[tex]2(58-d)=d-16[/tex]
[tex]116-2d=d-16[/tex]
[tex]3d=132[/tex]
[tex]d=44[/tex]
Now put the value of 'd' in equation 3, we get the value of 'c'.
[tex]c=58-d[/tex]
[tex]c=58-44[/tex]
[tex]c=14[/tex]
Thus, the value of c and d is, 14 and 44 respectively.
Answer:
ABGH
Step-by-step explanation:
Which pairs of triangles appear to be congruent? Check all that apply.
Answer:
Step-by-step explanation: just did it on apex
The pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E. This can be obtained by understanding the concept of congruence.
Which are the required pairs?Congruent triangles have same size and shape.Corresponding sides and angles are equal. Two congruent triangles can overlap perfectly.In the question, Triangle 2 is larger than the other triangles.
Triangle 1, Triangle 3 and Triangle 4 appears to have the same size and shape.
Thus Triangle 1, Triangle 3 and Triangle 4 appears to be congruent to each other.
Hence the pairs of triangles appear to be congruent are Triangles 1 and 4, Triangles 1 and 3 and Triangles 3 and 4, that is option B, option C and option E.
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Write as percents
1) 3/5
2)7/8
3)4/25
4)27/50
Write as fractions
1)50%
2)34%
3)56%
4)33 1/3%
Answer:
1)3/5=60%
2)7/8=87.5%
3)4/25=16%
4)27/50=54%
fractions
1)50%=0.5
2)34%=0.34
3)56%=0.56
4)331/3%=1.1033
pls mark as brainliest..
In 2015,in buffalo,new York there were 8.625 arrest,2.678 robberies,865 assaults and 20 murders.The population of Buffalo is 258.959.What is the ratio of number of assaults to the number of robberies in simplest form
Answer:
[tex] \frac { 8 6 5 } { 2 6 7 8 } [/tex]
Step-by-step explanation:
We are given the following information for year 2015:
Number of arrests = 8625
Number of robberies = 2678
Number of assaults = 865
Number of murders = 20
Population of Buffalo = 258959
We are to find the ratio of number of assaults to the number of robberies in simplest form.
Ratio of number of assaults to number of robberies = [tex]\frac{865}{2678}[/tex]
Hello,..... I will mark you as a brainliest
A frog is there in a 12m deep well. The frog wants to jump out of the well . Every time it jumps 3m & falls back by 1m. In how many jumps will he come out of the well ???
Remember, I will mark you as a brainliest...
Answer:
5 jumps
Step-by-step explanation:
Personally I would write it out, although there surely is a formula for it.
3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.
This makes 5 jumps, since once he is out he won't fall back in.
What is the vertex if angle XYZ
A Vertex is the point that 2 or more lines connect.
When an angle is written given the letters of the lines/ points, the point where the lines connect are always the middle letter.
For ∠XYZ, the vertex would be point Y, because it is the middle letter.
An angle is formed by two rays that have a common endpoint which is known as the vertex of the angle
The vertex of the angle ∠XYZ is point Y
The reason the above selection is correct is as follows;
There are three methods used in naming an angle, including;
Using three capital letters with the middle letter representing the vertexUsing only one capital letter, if the angle will not be confused with other anglesUsing a small letter or number in the middle of the angle. The given angle is ∠XYZ, therefore, the middle letter, Y, is the vertex
The vertex point is Y
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Of the 425 tickets sold, 275 were adult tickets. What percent of the tickets were adult tickets? Round to the nearest tenth of a percent.
Answer:
64.7%
Step-by-step explanation:
Write a proportion:
275 / 425 = x / 100
x = 64.7
64.7% of the tickets were adult tickets.
ABCD is a rectangle. What is the value of x?
Explanation
We can use pythagorean theorem to solve for the value of x:
45^2 + x^2 = 53^2
2025 + x^2 = 2809
We now subtract 2025 from both sides:
2809 - 2025 = 784
x^2 = 784
Square both sides
[tex]\sqrt{784}[/tex] = 28
x = 28
Answer
The value of x is 28
One angle of a right triangle measures 19∘. What is the measure of the other angle?
Answer:
71°
Step-by-step explanation:
The equation should be 19+90+x=180
Step 1: Add 19+90=109
Step 2: Subtract 180-109=71
So, you're answer is 71°
Final answer:
To find the measure of the other angle in a right triangle when one angle is given, subtract the given angle and the right angle from 180 degrees to get the third angle, which is the measure of the other angle.
Explanation:
One angle of a right triangle measures 19∘. In a right triangle, one angle is always 90 degrees. Therefore, to find the measure of the third angle, you need to subtract the sum of the given angle and the right angle from 180 degrees.
Third angle = 180° - 90° - 19° = 71°. So, the measure of the other angle in the right triangle is 71 degrees.
what is the rise of ramp if slope is 2% and run is 4 feet
Answer:
.08 feet
Step-by-step explanation:
So slope=rise/run.
You are given slope is 2% or .02.
You are also given run is 4 ft.
Plug these into the formula
.02=rise/4
To solve this for rise multiply both sides by 4:
4(.02)=rise
.08=rise
The rise is .08 feet.
Please help me do question 21, 22 and 23. I am in 6th grade.
Question 21: 24 minutes
[tex]\frac{3}{\frac{3}{2} } = \frac{x}{12}[/tex]
x = [tex](\frac{3}{\frac{3}{2} })(12)[/tex]
x = 24
Question 22: 20 centimeters
x = one side of the square
x² = 25
x = 5
4x = perimeter
4(5) = perimeter
20 = perimeter
Question 23: 17 sides
Hexagon = 6 sides
Octagon = 8 sides
Triangle = 3 sides
Total amount of sides = 6 + 8 + 3
Total amount of sides = 17
What is the solution to the system of equations below? y = -3X+5 and y=4x-2 (1, 2) (1, –18) (–1, 8) (–1, –6)
Answer:
(1, 2 )
Step-by-step explanation:
Given the 2 equations
y = - 3x + 5 → (1)
y = 4x - 2 → (2)
Substitute y = 4x - 2 into (1)
4x - 2 = - 3x + 5 ( add 3x to both sides )
7x - 2 = 5 ( add 2 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Substitute x = 1 into (2) for corresponding value of y
y = (4 × 1) - 2 = 4 - 2 = 2
Solution is (1, 2 )
The following box plot shows the class scores on a particular math test:
box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum
Which of the following data sets is represented in the box plot?
{40, 50, 50, 77, 77, 100}
{0, 50, 60, 75, 85, 100}
{50, 60, 60, 75, 75, 85, 85, 100}
{60, 65, 70, 75, 85, 85, 85}
Answer:
Choice C
Step-by-step explanation:
Because,
50 is min
75 is middle
100 is max
The correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
Given,
The box plot with number line titled percent with 50 as the minimum, 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
We need to determine the following data sets are represented in the box plot.
Let us segregate the following data set by taking the help of a minimum value.
Now, we require a data set that has a minimum value of 50.
There is only one data set given in the option that is a minimum value of 50.
Thus, data set is {50, 60, 60, 75, 75, 85, 85, 100}.
Cross-checked the above data set with more information that is already given in the question.
We required 60 as quartile 1, 75 as the median, 85 as quartile 3, and 100 as the maximum.
Thus, all the above requirements are fulfilled by the data set {50, 60, 60, 75, 75, 85, 85, 100}.
Hence, the correct data set is {50, 60, 60, 75, 75, 85, 85, 100}
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Ralph is 3 times as old as Sara in 4 years Ralph will be twice as old as Sara will be then. Find Ralph’s age now.
If x represents Sarah’s age now, which of the following expressions represents Ralph’s age in four years.
3x
6x
2x+4
3x+4
Answer:
3x+4 Ralph is currently 12 years old.
Step-by-step explanation:
You can find the equation by reading the scenario given. When you read it, it says that Ralph is 3 times as old as Sara and since her current age is going to be used to represent x you will first get 3x. That automatically eliminates the second and third choice given. It then says the equation is for Ralph's age in four years which means to add four to the equation. This gives you 3x+4 as your equation.
When something is tripled and then in a few years it is doubled, it is easiest to first try the number that is being added. So in this case the number is four. When you multiply 4 by 3 you get 12. If Sara is 4 she'll turn eight in four years and if Ralph is 12 he'll turn 16 in four years. 16 divided by 2 is 8 which shows you that Ralph is currently 12
choose the graph that represents the equation y=-|x+4|+1
The graph that represents y = -|x + 4| + 1 is graph (a)
The equation is given as:
y = -|x + 4| + 1
The above equation is a transformation from the parent function, which is represented as:
y = |x|
First the function is reflected across the x-axis, then translated 4 units left, and lastly 1 unit up.
The graph that represents this transformation is graph (a)
Hence, the graph that represents y = -|x + 4| + 1 is graph (a)
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The pH of a solution is a measure of how acidic it is. The greater the acidity, the lower the pH. The function f(x) = −log x gives the pH of a solution, where x is the concentration of hydrogen ions, in moles per liter.
The graph of f(x) = −log x is________________of the graph of g(x)=log x
answer options:
a: vertical translation (not correct answer)
b: horizontal translation
c: reflection in the x-axis
d: reflection in the y-axis
Answer:
c. a reflection in the x-axis.
Step-by-step explanation:
All values of log x are made negative by the transformation so it is a reflection in the x axis.
The graph of [tex]f(x) =-log x[/tex] is the reflection in the x-axis of the graph of [tex]g(x)=log x[/tex].
What is a graph?" Graph is defined as a pictorial representation of the relation between the variables in the coordinate plane along x-axis and y-axis."
According to the question,
Given function on the graph,
[tex]f(x) =-log x[/tex]
[tex]g(x)=log x[/tex]
[tex]'x'[/tex] represents the concentration of hydrogen ions, in moles per liter.
value of [tex]'x'[/tex] remain the same in both cases.
[tex]f(x)[/tex] value is negative.
[tex]g(x)[/tex] value is positive.
The graph of [tex]f(x)[/tex] lying in the first quadrant and the graph of [tex]g(x)[/tex] lying in the fourth quadrant.
Therefore, the graph of [tex]f(x)[/tex] is the reflection in the x-axis of the graph of [tex]g(x)[/tex].
Hence, Option(C) is the correct answer.
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pleaseeeee helppppppp
Answer:
[tex]\large\boxed{A.\ \sqrt{-4}}[/tex]
Step-by-step explanation:
[tex]A.\ \sqrt{-4}=\sqrt{(4)(-1)}=\sqrt4\cdot\sqrt{-1}=2i\ -\ \text{complex number}\\\\i-\text{imaginary unit}[/tex]
[tex]B.\ \sqrt{13}\approx3.61\ -\ \text{real number}\\\\C.\ \sqrt{16}=4\ -\ \text{real number}\\\\D.\ \sqrt1=1\ -\ \text{real number}[/tex]
What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?
Answer:
y=-2x+4
Step-by-step explanation:
2x+y-1=0
2x+y=0+1
2x+y=1
y=1-2x
y=-2x+1
y=mx+b where m=slope and b=y-intercept
parallel means same slope,
so the slope would still be -2.
--------------
y-y1=m(x-x1)
y-2=-2(x-1)
y=-2x+2+2
y=-2x+4
Need help in number 9. Thanks for helping
Answer:
A 6/7
Step-by-step explanation:
3/4 ÷ 7/8
Copy dot flip
3/4 * 8/7
The numerator is 3*8 = 24
The denominator is 4*7 = 28
24/28
Divide the top and botto by 4
6/7
How do you solve the following equation:
[tex]\int_2^a (3x^2+x-1) dx=52[/tex] for [tex]a[/tex]?
[tex]\displaystyle\\\int \limits_2^a(3x^2+x-1)\, dx=52\\\left|x^3+\dfrac{x^2}{2}-x\right|_2^a=52\\a^3+\dfrac{a^2}{2}-a-(2^3+\dfrac{2^2}{2}-2)=52\\a^3+\dfrac{a^2}{2}-a-(8+2-2)=52\\a^3+\dfrac{a^2}{2}-a-8=52\\a^3+\dfrac{a^2}{2}-a=60\\2a^3+a^2-2a=120\\2a^3+a^2-2a-120=0[/tex]
Now you need to solve the resulting equation, but it's not easy. The approx. solution is [tex]a\approx 3.8[/tex]
The exact solution is
[tex]a=\dfrac{1}{6}\left(-1+\sqrt[3]{6461-78\sqrt{6861}}+\sqrt[3]{6461+78\sqrt{6861}}\right)[/tex]
Answer:
a = 3.84
Step-by-step explanation:
Let's integrate the function
3x^2 becomes 3x^3/3 =x^3
x becomes x^2/2
-1 becomes -x
The intergral is x^3 +x^2/2 -x
We take the upper limit minus the lower limit
a^3 +a^2/2 -a - (2^3 + 2^2/2 -2) and that is equal to 52
Simplify
a^3 + a^2/2 -a - (8+2-2) = 52
a^3 +a^2/2 -a -(8) = 52
Subtract 52 from each side
a^3 +a^2/2 -a -8-52 = 52-52
a^3 +a^2/2 -a -60 =0
Multiply by 2
2a^3 +a^2 -2a -120 = 0
Using a graphing system, we see it only has 1 real root
This is at approximately
3.84
$6000 is invested for 15 years with an APR of 3% and monthly compounding.
Answer:
$2700.00
Step-by-step explanation:
6000 x 3% =180.00
180.00 x 15= 2700.00
Ryan is putting money into a savings account. He starts with
$450
in the savings account, and each week he adds
$30
Let S represent the total amount of money in the savings account (in dollars), and let
W represent the number of weeks Ryan has been adding money. Write an equation
relating S to W. Then use this equation to find the total amount of money in the savings account after 14 weeks.
equation=
total amount of money after 14 weeks= $?
the equation is S=30w+450
to find the answer just replace the w by 14
multiply 30 by 14 to get 420 and add 450 to it to get 870
The equation relating the total amount of money 'S' in the savings account to the number of weeks 'W' that Ryan has been saving is S = 450 + 30W. By substituting W with 14 in this equation, we find that Ryan will have $870 in his savings account after 14 weeks.
Explanation:In this case, Ryan had started with $450 in his savings account. His weekly contribution to the savings is $30. So the total amount of money 'S' in the savings account after 'W' weeks could be represented by the equation S = 450 + 30W.
Now, if you want to find out the total amount of money in the savings account after 14 weeks, just substitute W = 14 into the equation. Thus the equation becomes S = 450 + 30*14 = 450 + 420 = $870.
Therefore, Ryan will have $870 in his savings account after 14 weeks.
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4. A company found that its monthly profit, P, is
given by P = -10x2 + 120x - 150 where x is the
selling price for each unit of the product.
Which of the following is the best estimate of
the maximum price per unit that the company
can charge without losing money?
A $300
C$11
B $210
D $6
Answer:
11
Step-by-step explanation:
Ok so we aren't looking to maximize profits which is equivalent to finding the vertex of the parabola.
But we want to know what is the highest number of x so that our we aren't losing money. We aren't losing money when our profit is 0.
So we are asked to solve P(x)=0 for x and take the highest x of that equation.
[tex]P(x)=0[/tex]
[tex]-10x^2+120x-150=0[/tex]
I'm going to divide both sides by -10 to make the numbers easier to work with later.
[tex]x^2-12x+15=0[/tex]
I'm going to use the quadratic formula.
[tex]x^2-12x+15=0[/tex] when compared to [tex]ax^2+bx+c=0[/tex] gives us [tex]a=1,b=-12,c=15[/tex].
We are going to plug this into our quadratic formula:
[tex]x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex].
[tex]x=\frac{12\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}[/tex]
[tex]x=\frac{12\pm \sqrt{144-60}}{2}[/tex]
[tex]x=\frac{12\pm \sqrt{84}}{2}[/tex]
[tex]x=\frac{12}{2} \pm \frac{\sqrt{84}}{2}[/tex]
[tex]x=6 \pm \frac{\sqrt{84}}{2}[/tex]
I'm ready to put this into my calculator.
The one with the plus gives me 10.5826 approximately.
The one with the minus gives me 1.4174 approximately.
The 10.5826 is the higher number.
So about 11 dollars.
Answer:
C $11
Step-by-step explanation:
If a company found that its monthly profit, P, is given by P = -10x2 + 120x - 150 where x is the selling price for each unit of the product, the best estimate of the maximum price per unit that the company can charge without losing money is $11.
Question 14(Multiple Choice Worth 1 points) (07.06 MC) An unknown number x is at most 30. Which graph best represents all the values of x? Number line graph with closed circle on 30 and shading to the right. Number line graph with closed circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the left. Number line graph with open circle on 30 and shading to the right
Answer:
Number line graph with closed circle on 30 and shading to the left
Step-by-step explanation:
we know that
The algebraic expression of the phrase " An unknown number x is at most 30" is equal to
[tex]x\leq 30[/tex]
The solution is the interval ------> (-∞,30]
All real numbers less than or equal to 30
Number line graph with closed circle on 30 and shading to the left
see the attached figure
In a conference room, the number of chairs,c, is equal to 6 times the number of tables,t. Which equation matches the information
Answer:
t x 6=c or c divided by 6= t
Step-by-step explanation:
Answer: [tex]c=6t[/tex]
Step-by-step explanation:
You need to analize the information provided in the exercise:
- "c" represents the number of chairs in the conference room.
- "t" represents the number of tables in the conference room.
- "6 times the number of tables" indicates a multiplication. This is:
[tex]6t[/tex]
Therefore if the number of chairs in the conference room is equal to 6 times the number of tables, you can write this equation that matches the information provided:
[tex]c=6t[/tex]
Luisa and Connor had $360 altogether . After Connor gave Luisa 2/5 of his money, she had the same amount of money has he did. How much money did Connor have in the beginning?
Answer:
$300
Step-by-step explanation:
Let's say that L is the amount of money Luisa had in the beginning, and C is the amount of money Connor had in the beginning.
C + L = 360
C - 2/5 C = L + 2/5 C
Simplifying the second equation:
3/5 C = L + 2/5 C
1/5 C = L
Substituting into the first equation:
C + 1/5 C = 360
6/5 C = 360
C = 300
Connor originally had $300, and Luisa $60. Connor gave Luisa $120, and they both had $180.
The point (0,0) is a solution to which of these inequalities?
O
O
O
O
A. y - 4<3x - 5
B. y - 5< 3x - 4
C. y +5< 3x + 4
D. y + 5 < 3x - 4
Answer:
B.
Step-by-step explanation:
Let's plug in and find out.
A. y-4<3x-5 with (x,y)=(0,0)
0-4<3(0)-5
-4<-5
This is false because -5 is not bigger than -4.
B. y-5<3x-4 with (x,y)=(0,0)
0-5<3(0)-4
-5<-4
This is true because -4 is bigger than -5.
C. y+5<3x+4 with (x,y)=(0,0)
0+5<3(0)+4
5<4
This is false because 4 is not bigger than 5.
D. y+5<3x-4 with (x,y)=(0,0)
0+5<3(0)-4
5<-4
This is false because -4 is not bigger than 5.
The only true inequality I got from plugging in (0,0) for (x,y) was B so that your answer.
the area of a circle is 113.04in^2. what is the radius of the circle
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \stackrel{using~\pi =3.14}{36}=r^2\implies \sqrt{36}=r\implies 6=r[/tex]
Calculate 1.7 x 106 times 5.3 x 10^9 by using scientific notation and the product rule.
Express your answer in scientific notation with the proper number of significant figures.
Before any dinner service, the manager confirms when the number of reservations at a restaurant is subtracted from
Nice the number of loaves of bread on hand must be greater than 5. Which graph represents this scenario?
Final answer:
To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.
Explanation:
The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.
This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.