Answer:
[tex]mean = \frac{sum}{number} \\ 102 = \frac{(100 + 122 + 103 + 113 + 109 + x)}{6} \\ 612 = 547 + x \\ x = 65[/tex]
In ΔSTU, the measure of ∠U=90°, TU = 28 feet, and ST = 39 feet. Find the measure of ∠T to the nearest tenth of a degree?
Answer:
∠T≈44.1
Step-by-step explanation:
Please see the attached image.
Relative to ∠T, we know the adjacent side and the hypotenuse, 28 and 39 respectively.
We can use a trig function to solve for ∠T. When given the adjacent side and hypotenuse, we can use cosine.
The cosine of an angle is the adjacent side to that angle over the hypotenuse.
cos(T)=28/39
T=[tex]cos^-1[/tex](28/39)
T≈44.1
The quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
Drag each function to show whether it has roots at x=−1 and x=5, roots at x=1 and x=−5, or neither.
Answer:
Roots x = -1 and x =5
k(x) = (x + 1)(x - 5)
m(x) = 1/2(x + 1 )(2x - 10)
Roots x = 1 and x = -5
n(x) = (3x + 15)(x - 1)
f(x) = (x - 1)(x + 5)
q(x) = (2x - 2)(3x + 15)
Neither
h(x) = 1/2(x + 1)(2x - 20)
Step-by-step explanation:
We have given that ,the quadratic functions shown are written in factored form. The roots of a quadratic function will make the factors equal to 0.
What are the step for finding the polynomial from its root?1. Write root as factor changing the sign and put each factor in paranthesis
2.Multiply paire of roots together using box to find the multiplication
3.Make sure that each factor multiplied by every other factor.
The function has roots x = -1 and x =5
[tex]k(x) = (x + 1)(x - 5)\\\\k(x)=x^2-5x+x-5\\k(x)=x^2-4x-5\\[/tex]
[tex]m(x) = 1/2(x + 1 )(2x - 10)\\m(x)=1/2(2x^2-10x+2x-10)\\m(x)=1/2(2x^2-8x-10)\\m(x)=x^2-4x-5[/tex]
The function k(x) and m(x) has root x=-5 and x=5
The function has roots x = 1 and x = -5
[tex]n(x) = (3x + 15)(x - 1)\\n(x)=3x^2-3x+15x-15\\n(x)=3x^2+12x-15\\n(x)=1/3(x^2+4x-5)[/tex]
[tex]f(x) = (x - 1)(x + 5)\\f(x)=x^2+5x-x-5\\f(x)=x^2+4x-5[/tex]
[tex]q(x) = (2x - 2)(3x + 15)\\q(x)=6x^2+30x-6x-30\\q(x)=6x^2+24x-30\\q(x)=1/6(x^2+4x-5)[/tex]
The function n(x),q(x) and f(x) has roots x=1 and x=-5
h(x) = 1/2(x + 1)(2x - 20)
h(x) has no roots from roots at x=−1 and x=5, and x=1 and x=−5.
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x - (-3) + 8 - 2x - 6 =
Answer:
-x + 5
Step-by-step explanation:
x - (-3) + 8 - 2x - 6 = x - 2x + 3 + 8 - 6 = -x + 5
Answer:
[tex] \sf \: -x + 5 [/tex]
Step-by-step explanation:
Given expression,
→ x - (-3) + 8 - 2x - 6
Let's simplify the expression,
→ x - (-3) + 8 - 2x - 6
→ x + 3 + 8 - 2x - 6
→ (x - 2x) + (3 + 8 - 6)
→ (-x) + (5)
→ -x + 5
Hence, the answer is -x + 5.
how to solve the Quadratic formul
Answer:
The answer is x=-6, x=8
Step-by-step explanation:
I recommend using the quadratic formula to solve this problem.
x^2=a
-2x=b
-48=c
Plug it into the quadratic formula.
New equation:[tex]\frac{2+-\sqrt{(-2)^2-4(1)(-48)}}{2(1)}[/tex]
Simplify
Equation: [tex]\frac{2+-\sqrt{4+192}}{2}[/tex]
Add 4 and 192.
Equation: [tex]\frac{2+-\sqrt{196}}{2}[/tex]
Do the square root of 196.
Equation: [tex]\frac{2+-14}{2}[/tex]
Make into two different equations.
Equation 1: [tex]\frac{2+14}{2}[/tex]
Equation 2: [tex]\frac{2-14}{2}[/tex]
Solve the two equations and you will get -6 and 8. Hope this helps!
[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]
Solve using the quadratic formula ⇨ x² - 2x - 48 = 0.[tex] \large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}[/tex]
[tex] \sf \: x ^ { 2 } - 2 x - 48 = 0[/tex]
All equations of the form ax² + bx + c = 0 can be solved using the quadratic formula: [tex]\sf \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.
[tex] \sf \: x^{2}-2x-48=0 [/tex]
This equation is in standard form: ax² + bx + c = 0 Substitute 1 for a, -2 for b and -48 for c in the quadratic formula.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-48\right)}}{2} \\ [/tex]
Square -2.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4-4\left(-48\right)}}{2} \\ [/tex]
Multiply -4 times -48.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{4+192}}{2} \\ [/tex]
Add 4 to 192.
[tex] \sf \: x=\frac{-\left(-2\right)±\sqrt{196}}{2} \\ [/tex]
Take the square root of 196.
[tex] \sf \: x=\frac{-\left(-2\right)±14}{2} \\ [/tex]
The opposite of -2 is 2.
[tex] \sf \: x=\frac{2±14}{2} \\ [/tex]
Now solve the equation [tex]\sf\:x=\frac{2±14}{2}[/tex] when ± is plus. Add 2 to 14.
[tex] \sf \: x=\frac{16}{2} \\ [/tex]
Divide 16 by 2.
[tex] \boxed{ \boxed{ \bf \: x=8 }}[/tex]
Now solve the equation [tex]\sf\:x=\frac{2±14}{2} [/tex] when ± is minus. Subtract 14 from 2.
[tex] \sf \: x=\frac{-12}{2} \\ [/tex]
Divide -12 by 2.
[tex] \boxed{\boxed{ \bf \: x=-6 }}[/tex]
The equation is now solved.
[tex] \underline{ \bf \: x=8 }\\ \underline{ \bf \: x=-6 }[/tex]
need this rn
solving system of linear equation in two variables. Show your COMPLETE SOLUTION
1) 4x + 8y = 24 2) 2x + y = 19 3) 3x + y = 15
4x + 2y = 12 x + y = 11 x + 2y = 10
The solution to the system of equations is x = 4 and y = 2.
CalculationsWe would use the elimination method to solve the system of equations:
4x + 8y = 242x + y = 193x + y = 154x + 2y = 12x + y = 11x + 2y = 10Let's eliminate the variable y by adding equations 1 and 2:
4x + 8y = 24
2x + y = 19
.
.
.,
6x + 9y = 43
Now we can eliminate the variable x by subtracting equation 3 from the above equation:
6x + 9y = 43
3x + y = 15
.
.
.
3x + 8y = 28
We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:
x = (28 - 8y) / 3
Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:
4x + 2y = 12
Substituting x = (28 - 8y) / 3:
4((28 - 8y) / 3) + 2y = 12
If we simplify:
28 - 8y + 2y = 128y = 16y = 2Finally, we can use this value of y to find x by plugging it into the expression we found earlier:
x = (28 - 8(2)) / 3
x = (28 - 16) / 3
x = 12 / 3
x = 4.
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Did I do the transformation correctly?
Answer:
I believe you're using a tool that I'm not gonna say because Brainly doesn't allow such sins, haha. I bet the name of the tool you're using starts with a K, correct?
Anyways, I don't think you can add values such as a, h, k. The only values you're allowed to add are x and y :(
Step-by-step explanation:
how do you say 250.611 in words please do not lie
Answer:
two hundred fifty and six hundred elensths (i dont remember the end)
Step-by-step explanation:
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph which represents the equation y = 1/2x - 1 is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ y = 1/2x - 1
Now, After draw the equation we get;
Graph of a line passing through the points (-2, - 2) and (0, - 1).
Thus, The correct statement is,
⇒ Graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1.
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Tell whether the system has one solution, infinitely many solutions, or no solution.
25y = - 30x + 35
6x + 5y = 7
Choose the correct answer below.
O A. The system has infinitely many solutions.
O B. The system has one solution.
O C. The system has no solution.
C. The system has no solution.
The length of a rectangular frame is 15 inches in the diagonal length of the frame is 17 inches what is the width of the frame in inches
The width of the frame is 8 inches.
Now, According to the question:
The length of a rectangular frame is 15 inches
The diagonal length of the frame is 17 inches.
To find the width of the frame in inches.
Let's take the width of the frame is = w
Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.
This will be:
17² = 15² + w²
289 = 225 + w²
289 - 225 = w²
64 = w²
w = [tex]\sqrt{64}[/tex]
w = 8
Hence, The width of the frame is 8 inches.
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An equilateral triangle has sides 12cm in length. Calculate the
perpendicular height of the triangle. (to the nearest mm)
Help please
Answer:
10 mm
Step-by-step explanation:
Draw an equilateral triangle. Label each side 12 mm.
Draw one altitude from one vertex perpendicular to the opposite side. Label the length of the altitude h.
The altitude divided the opposite side into two congruent segments, each one measuring 6 mm.
Now use the Pythagorean Theorem.
a² + b² = c²
(6 mm)² + h² = (12 mm)²
36 mm² + h² = 144 mm²
h² = 144 mm² - 36 mm²
h² = 108 mm²
h = 6√3 mm
h ≈ 10 mm
Answer: 3.5 cm or 35 mm
Step-by-step explanation:
12/3 =4 for each side of triangle
cutting the triangle in half, bottom side(a) 4 becomes 2
2^2 + b^2 = 4^2
4 + b^2 = 16
subtract 4 from both sides
b^2 = 12
b = 3.464 cm or 3.5 cm
convert 3.5 cm to 35 mm
The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high. How many centimeters in the scale drawing represent one foot on the actual building?
a. 1/2
b. 30
c. 10
d. 2
Answer: 1/2
Step-by-step explanation:
The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.
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Convert the number into standard form, please!
Convert from number format to standard form as a decimal multiplied by a power of 10.
What is standard form?Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.A number is written in standard form when it is represented as a decimal number times a power of 10.As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 108.step 1
convert 1.5806*10rais to 4
Convert to decimal notation
1.5806*10^4
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)
1.5806 ->15806
step 2
final result
15806
Simplify the expression
1.581*10^4
Simplify exponents and square roots
1.581*10^4
10 ^4 = 10 × 10 × 10 × 10 = 10,000
1.581*10000
Perform any multiplication or division, from left to right:
1.581*10000
15806
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i need help with this math question HELP
How do you solve for asymptotes?
There are three types of asymptotes solved in the following way:
1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.
2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.
3. Slant asymptotes is y = mx + c.
Asymptote is the representation of the line which approaches to the given curve but never touch or meet with the curve.Three types of asymptotes : Horizontal asymptote, vertical asymptote, and the slant asymptote.1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator. 2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator. 3. Slant asymptotes is y = mx + c.Horizontal asymptote rarely cross the given curve but vertical asymptote never.Slant asymptote represents the slope of the function.Therefore, the three types of asymptotes solved in the following way:
1. Horizontal asymptotes is y = k for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.
2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.
3. Slant asymptotes is y = mx + c.
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The two smaller angles of a right triangle have equal measures. find the measure of all three angles.
Answer:
Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.
Angle 1: (right angle) 90 degrees
Angle 2: 45 degrees
Angle 3: 45 degrees
Pls help due in 5 mins
The given algebraic equation can be written in many ways as shown.
What is algebraic equation?The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
Solution:-
-5x-15+25x-30
it can be written as
-5(x+3-5x+6)
20x-45
5(4x-9)
and also
-5(9-4x)
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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].
First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]
*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up
[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]
Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].
Both have the same factor is [tex]-5[/tex].
Use the distributive property to find the equation that is equivalent.
[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]
So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]
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what is the slope intercept form of this equation: -12x + 3y = 3*
Answer:
y=4x+1
Step-by-step explanation:
i hope this helps :)
20 points, pls help, its angles
Matthew's total points scored in basketball this season were 168 points. He scored 147 of those points in the regular season and the rest were scored in his only playoff game. What percent of his total points did he score in the playoff game?
Answer:
12.5%
Step-by-step explanation:
He scored [tex]168-147=21[/tex] points in the playoff game.
This is equal to [tex]\frac{21}{168}(100)=12.5\%[/tex].
How do you find the equation of a vector given the point and direction?
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
The equation of a vector is typically written like this:
v = (x, y, z)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation. For example, let's say you are given the point (1,2,3) and the direction of the vector is (2,3,4). The components of the vector, v, would be x = 2, y = 3, and z = 4, so the equation for that vector would be:
v = (2, 3, 4)
To find the equation of a vector given a point and direction, you need to find the components of the vector and plug them into the equation: v = (x, y, z).
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3. Tell whether the set of ordered pairs {(3, 2), (4, 3), (5, 4), (6, 5)} satisfies a linear function. Explain.
a. No; there is no constant change in x that corresponds to a constant change in y.
b.
No; there is a constant change in x that corresponds to a constant change in y.
Yes; there is a constant change in x that corresponds to a constant change in y.dd T
Yes; there is no constant change in x that corresponds to a constant change in y.
d.
Find the x and
conto
The given set of ordered pairs does not satisfy a linear function.
What is a linear function?A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.
Given:
The given set of ordered pairs is:
{(3, 2), (4, 3), (5, 4), (6, 5)}
To find:
Whether the given set of ordered pairs satisfies a linear function or not.
Explanation:
The slope of a linear function is:
m = (y₂ - y₁)/ (x₂ -x₁)
The slope of the linear function passes through the points and is:
m₁ = (3-1)/(3-1)
m₁ = 2/2
m₁ = 1
The slope of the linear function passes through the points and is:
m₂ = (9-3)/(5-3)
m₂ = 6/2
m₂ = 3
Therefore m₁ ≠ m₂ therefore the given set of ordered pairs does not satisfy a linear function.
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There are 12 girls and 16 boys in Mr jonsons 3rd period class of these students 3 girls and 4 boys wear glasses what percentage of the Stu in Mr jonsons class wear glasses
Answer:
25%
Step-by-step explanation:
Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.
PercentageThe percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.
percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%
percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%
25% of the students in Mr. Johnson's class wear glasses.
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Does 5 12 13 make a triangle?
Yes, the sides with 5,12,13 make a triangle.
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude is called Pythagorean Triples.
Pythagorean triples describe the three integer side lengths of a right triangle.
(Hypotenuse)² = (Base)² + (Altitude)²
c²=a²+b²
which contain three positive integers a, b, and c.
the original Pythagorean triplets, two of the numbers are prime, but one is even. If all three numbers are multiplied by a factor, the triplet is called a relatively prime.
The most well-known examples are (3,4,5) and (5,12,13)
consider c=13 a=12, b=5 substitute in above formula:
13²=12²+5²
⇒169=144+25
⇒169=169
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Could someone explain to me how to do this?
solve 4x - 3 = 17
x= ?
Answer:
5
Step-by-step explanation:
4x-3=17
+3 on both sides = 4x=20
divide 20 by 4 and your answer is 5
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{4x - 3 = 17}[/tex]
[tex]\text{ADD 3 to BOTH SIDES}[/tex]
[tex]\mathsf{4x - 3 + 3 = 17 + 3}[/tex]
[tex]\text{SIMPLIFY IT}[/tex]
[tex]\mathsf{4x = 17 + 3}[/tex]
[tex]\mathsf{4x = 20}[/tex]
[tex]\text{DIVIDE 4 to BOTH SIDES}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{20}{4}}[/tex]
[tex]\text{SIMPLIFY IT}[/tex]
[tex]\mathsf{x = \dfrac{20}{4}}[/tex]
[tex]\mathsf{x = 5}[/tex]
[tex]{\huge\text{Therefore, your answer should be:}[/tex][tex]\huge\boxed{\mathsf{x = 5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Circles centered at $A$ and $B$ each have radius 2, as shown. Point $O$ is the midpoint of $\overline{AB}$, and $OA
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers. In the given diagram, the radius of the circles centered at $A$ and $B$ is 2, and the distance between their centers is the length of $\overline{AB}$, which is 5. Therefore, the distance between the two circles is 5 - (2 + 2) = 5.
The distance between the two circles is 5.
The distance between two circles is the difference between the sum of their radii and the distance between their centers.
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What is the sign of -4 divided by -8?
Choose 1 answer:
Positive
B
Negative
Zero
Answer:
Positive
Step-by-step explanation:
Positive / positive = positive
positive / negative = negative
negative / negative = positive
negative/ positive = negative
Sign of -4 divided by -8 we get positive expression.
Here we have to find the sing of expression,
When -4 divided by -8
Since we know that,
Dividing two fractions is equivalent to multiplying the first fraction by its reciprocal. The first step in splitting fractions is to get the reciprocal of the second fraction (reverse the numerator and denominator). Then, multiply the numerators.
We can write it,
-4 divided by -8 = -4/-8
= (4/8)x(-1/-1)
= 1/2 its a positive number.
Hence,
-4 divided by -8 = 1/2
Hence we get positive expression.
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Is 2x 3 a linear function?
Answer:
yes
Step-by-step explanation:
The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.
Which of the following statements is not equivalent to the others?
16-34
|34 -16|
34-16
|16 -34
Answer:
the one that is not equivalent to the others would be 116-34
Step-by-step explanation:
because its 116 and the others dont have anything to do with 116 :)
Answer: The statement that is not equivalent should be D. |16-34
Someone help me with this please
Answer:
A
Step-by-step explanation:
A triangular prism has two rectangles on each side, then two triangles on the other sides. I hope this helps! :)