Answer:
t = 5, 6
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{11t-t^2=30}[/tex]
First, arrange the expression in the standard quadratic form ax² + bx + c = 0
[tex]\displaystyle{t^2-11t+30=0}[/tex]
Then factor the expression, find two numbers that add up which result in -11 and multiply which result in 30 - that two numbers are -6 and -5
[tex]\displaystyle{(t-6)(t-5)=0}[/tex]
Solve like a linear equation
[tex]\displaystyle{t=5,6}[/tex]
Therefore, the solutions to the equation are t = 5, 6
Answer:
The solution set is {5, 6}.
Step-by-step explanation:
11t-t^2=30
t^2 - 11t + 30 = 0
(t - 5)(t - 6) = 0
t = 5, 6.
Mona's math certificate is 10 inches tall and 14 inches wide. Mona wants to put the certificate in a fancy frame that costs $1.02 per inch. How much will it cost to frame Mona's math certificate?
Answer:
$48.96
Step-by-step explanation:
Given data
Length= 10inches
Width=14 inches
Let us find the perimeter of the certificate
P=2L+2W
P= 2*10+2*14
P=20+28
P= 48 inches
Hence if 1 inche cost $1.02
Then 48 inches will cost x
cross multiply we
x= 48*1.02
x= $48.96
Hence it will cost $48.96 to frame the certificate
A prism with length of 3 units, height of 3 and one-fourth units, and width of 1 unit.
What is the volume of the prism?
whole-unit cubes fit inside the prism.
quarter-cubic units fit inside the prism.
The total volume of the prism is
units3
Answer:
9 3/4 cubic units
Step-by-step explanation:
The formula for the volume of a rectangular prism =
Length × Width × Height
From the question:
Length = 3 units
Height = 3 1/4 units
Width = 1 unit.
Volume of the prism =
3 units × 3 1/4 units × 1 unit
= (3 × 13/4 × 1 )cubic units
= 39/4 cubic units
= 9 3/4 cubic units
The total volume of the rectangular prism = 9 3/4 cubic units
Answer:
✔ 9
whole-unit cubes fit inside the prism.
✔ 3
quarter-cubic units fit inside the prism.
The total volume of the prism is
✔ 9 3/4 units3.
Directions:Identify the area of the shaded region of the following composite figures.
URGENT
simplify (sinx+cosx)^2-(sinx-cosx)^2
Answer:
Solution given:
(sinx+cosx)^2-(sinx-cosx)^2sin²x+2sinxcosx+cos²x-(sin²x-2sinxcosx+cos²)1+2sinxcosx-1+2sinxcosx2(2sinxcosx)2sin2xStep-by-step explanation:
[note: sin²x+cos²x=1]
Answer:
(sinx+coax+sinx-cosx) ( sinx+cosx-sinx+cosx)
4sinxcosx
2sin2x
Joan flipped a coin 100 times during a mathematics experiment. The coin landed on tails 36 times. Based on Joan's results, which of these statements is true?
(A)The coin landed on tails more than expected.
(B)The coin landed on heads less than expected.
(C)The coin landed on heads more than tails.
(D)The coin landed on heads less than tails.
Simplify the expression please!
Using the provided expression and the law of indices, The power get subtracted in division, The answer is [tex]6^{22}[/tex] .
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.
What do you mean by law of indices?The laws of indices, also known as the laws of exponents, are a set of rules that govern how exponents (or indices) are used in mathematical operations. These laws include:
a^m * a^n = a^(m+n) (product of powers)(a^m)^n = a^(m*n) (power of a power)a^m / a^n = a^(m-n) (quotient of powers)(a^m)^(-n) = a^(-m*n) (power of a reciprocal)These laws allow us to simplify expressions with exponents and make it easier to perform calculations involving them.
[tex]= \frac {6^{15}}{6^{-7}}\\= 6^{15-(-7)}\\= 6^{15+7}\\=6^{22}[/tex]
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Pls sm1 help I been asking for help for hours and no answer plss help
Answer:
6 kilometers
Step-by-step explanation:
2x3=6
please brainiest
Answer:
It explicitly states that 1cm represents a distance of 3km.
If the two places are 2cm apart...
it simply means that they're 6km apart!.
The amount of money in a savings account is given by � = 580(1.03)" where t is the
time in years. After how many years will the account have reached $1000? Clearly
demonstrate your strategy for figuring it out.
An initial investment of $580, earning 3% annually-compounded interest, will take 18.429 years (investment period) to reach $1,000.
How the period is determined?The period for the investment to accumulate to $1,000 at 3% compounded interest is computed using an online finance calculator.
The parameters required include identifying the interest rate, compounding period, present investment, and future value., from the given formula:
A = 580(1.03)^t
$1,000 = 580(1.03)^18.429
Investment Period:I/Y (Interest per year) = 3%
PV (Present Value) = $580
PMT (Periodic Payment) = $0
FV (Future Value) = $-1000
Results:
N = 18.429
= 18 years and 5 months
Total Interest = $420
Thus, for the account to reach $1,000, it will take 18 years and 5 months.
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Question Completion:A = 580(1.03)^t
Jeff bought a 5-gallon bucket of paint. He used 1.25 gallons to paint his bedroom, then he used two-thirds of the remaining paint for his living room. How many gallons of paint did he use to paint his living room?
Answer:
2.5 gallons
Step-by-step explanation:
5-1.25=3.75
3.75/3=1.25
1.25*2=2.50
Answer:
2.5, or 2 1/2 gallons
Step-by-step explanation:
The measure of an inscribed angle is 110°. What is the measure of the intercepted arc?
559
110°
220°
Answer: 220
Step-by-step explanation: See photo. The measure of an inscribed angle is equal to half the measure of the included arc.
110 = 1/2 x
220 = x
6 the standard deviation of human body temperatures is equal to 0. 62 F. Identify the null hypothesis and alternative hypothesis in symbolic form
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62. The alternative hypothesis exists that it does not equivalent 0.62.
What are null and alternative hypotheses?Statistical hypothesis testing employs null and alternate hypotheses. While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no association between variables.
A proposed claim or defense in the hypothesis test is referred to as an alternative hypothesis in statistics. In most cases, it supports the research premise and shows that there is a statistical relationship between the variables. It is one of the two statements in statistical hypothesis testing that are mutually exclusive.
H₀: σ = 0.62
H₁: σ ≠ 0.62
The null hypothesis exists that the standard deviation σ exists equivalent to 0.62.
The alternative hypothesis exists that it does not equivalent 0.62.
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In parallelogram IJKL, what is the measure of angle K?
Answer:
<K = 67degrees
Step-by-step explanation:
From the parallelogram given, the opposite angles are equal i.e <L = <J
Given
<L = 5x + 18
<J = 7x - 20
Equating both sides
5x + 18 = 7x - 20
Collect the like terms
5x - 7x = -20 -18
-2x = -38
x = 38/2
x = 19
Also <J + <K = 180
7x - 20 + <K = 180
7(19) - 20 + <K = 180
133 - 20 + <K = 180
113 + <K = 180
<K = 180 - 113
<K = 67degrees
Find the mean and standard deviation for the set of data.
{31,12,21,6,28,5,26,23,19}
A. mean: 19; standard deviation: 8.87
B. mean: 19; standard deviation: 9.24
C. mean: 20; standard deviation: 8.87
D. mean: 20; standard deviation: 9.24
Answer:
if it says bit .ly etc don't click it
The volume of a cylinder is 1,0291 cubic centimeters. The height of the cylinder is 21 centimeters. What is the radius, to the nearest centimeter, of the cylinder?
Answer:
12.49 = r
13 = r to the nearest cm.
Step-by-step explanation:
The formula to calculate the volume is:
V = π*r^2*h
We know that V = 10291 cm^3 and Height (h) = 21cm
V = π*r^2*h
10291 = π*r^2*21
Divide both side by 21
10291/21 = (π*r^2*21)/21
490.05 = π*r^2
Now divide both side by π
490.05/π = (π*r^2)/π
155.99 = r^2
Now square root both side
√155.99 = √(r^2) Note: square and square root cancel eachother out.
12.49 = r or,
13 = r
Find the value of xx in the equation below.
11=
11=
\,\,x -6
x−6
The required value of x is 17 for the given equation 11 = x - 6.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The equation is given in the question, as follows:
11 = x - 6
We can determine the value of x by adding 6 to both sides of the equation.
As per the question, we have
⇒ 11 = x - 6
⇒ 11 + 6 = x - 6 + 6
⇒ x = 11 + 6
Apply the addition operation, and we get
⇒ x = 17
Therefore, the required value of x is 17.
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Graph the system.
What is the estimated solution of the system?
Enter your answer in the blanks. Round each coordinate to the nearest integer.
The lines intersect closest to the integer coordinates
The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.
What is Graph of System of Linear EquationsA graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.
In the given problem, we have two linear equations which are
y = 3x - 6 ...eq(i)
y = 2/5x + 5 ...eq(ii)
Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.
The coordinates to the nearest integer are (x, y) 4 and 7
The value of x is 4 and y is 7
Kindly find attached graph below.
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WHat is the largest multiple of 5 that is less than 24
Answer:
20
Step-by-step explanation:
5*4=20
5*5=25, but it is bigger than 24.
So the ans is 20
How do I solve/graph 2x + 3y <12
The graph has plotted and attached below
What is inequality?
Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.
2x + 3y <12.
Here The graph have plotted and attached below.
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A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use. In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use. For what amounts of monthly phone use will Plan A cost no more than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.
34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
In Plan A, the customer pays a monthly fee of $20 and then an additional 7 cents per minute of use
20+7m
In Plan B, the customer pays a monthly fee of $26.30 and then an additional 4 cents per minute of use
26.3+4m
We need to find the amounts of monthly phone use will Plan A cost no more than Plan B
20+7m<26.3+4m
7m-4m<26.3-20
3m<6.3
m<2.1
Hence, 34.7 is the monthly phone use will Plan A cost no more than Plan B and 2.1 is the value of m in the inequality.
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who can help me with this question Determine if each figure is a polygon or non-polygon. *
Answer:
A polygon is a two-dimensional closed figure that has three or more straight sides. Any figure with straight edges, such as a triangle or rectangle, is a polygon. Figures that have any curved sides or open sides are not classed as polygons
Step-by-step explanation:
A regular polygon is a polygon where all of the side lengths are equal and all of the angle measures are equal. ... However, the sides are not congruent. Therefore, it is an irregular pentagon. Irregular polygons have side lengths that are not congruent.
there's no pic that helps determine which is which but I hope this explanations helps you.
yes i need help anyone please give me the answer
Answer:
x = 25
y = 65
Step-by-step explanation:
I'm not sure if I'm right but..
To solve x:
Since there is a 90 degree angle with 65 degrees and x, the total should sum up to 90. (ofc)
90 - 65 = 25 <--- the missing angle (x)
To solve y:
I'm pretty sure that it is also a 90 degree angle because there is a 90 degree across from you, so they should have the same angles. Since you know x=25, You would do this:
90 - 25 = 65 <--- y
Your welcome!!
The figure below is a scale drawing of a playhouse. In the drawing, the side of each house represents two and a half feet. Find the actual length of each segment.
5. The width of the house. = 30 feet
6. The height of the house. = 22.5 feet
7. The height of the first floor. = 12.5 feet
8. The height of the roof. = 10 feet
9. The width of the door. = 5 feet
10. The height of the door. = 7.5 feet
How to find the actual length of each segmentThe actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor
In the problem, the scale factor is two and a half feet = 2.5 feet
5. The width of the house
number of units from the drawing = 12 units
actual length = number of units from the drawing * scale factor
actual length = 12 * 2.5 = 30 feet
6. The height of the house
number of units from the drawing = 9 units
actual length = 9 * 2.5 = 22.5 feet
7. The height of the first floor
number of units from the drawing = 5 units
actual length = 5 * 2.5 = 12.5 feet
8. The height of the roof
number of units from the drawing = 4 units
actual length = 4 * 2.5 = 10 feet
9. The width of the door.
number of units from the drawing = 2 units
actual length = 2 * 2.5 = 5 feet
10. The height of the door.
number of units from the drawing = 3 units
actual length = 3 * 2.5 = 7.5 feet
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What is the difference 19√5 - 3√5 A.16 B.22 C.16√5 D.25
Answer:
C - 16√5
Step-by-step explanation:
Simply subtract 19 and 3 while keeping √5 the same.
19√5 - 3√5 = 16√5
How many solutions does the equation 4y + 7 = 5 + 2 + 4y have?
A. One
B. Two
C. None
D. Infinitely many
Answer:
D. infinitely many
Step-by-step explanation:
5+2 = 7 so 4y + 7 = 5 + 2 + 4y just equals 4y + 7=4y + 7 and any value of y is true in that equation.
Answer:
D :)
Step-by-step explanation:
Add 55 and 22.
4y+7=7+4y4y+7=7+4y
Move all terms containing yy to the left side of the equation.
Subtract 4y4y from both sides of the equation.
4y+7−4y=74y+7-4y=7
Combine the opposite terms in
Subtract 4y4y from 4y4y.
0+7=70+7=7
Add 00 and 77.
7=77=7
Since 7=77=7, the equation will always be true for any value of yy.
All real numbers
The result can be shown in multiple forms.
All real numbers
Interval Notation:
(−∞,∞)
7.9 , 8.37 , 7.293 , 7.785 , 7.476 greatest to least..pls help!!
Answer: 7.785,7.476,7.293,8.37.7.9
Step-by-step explanation:
What's the volume in 16m 16m 12.4m
Answer: 3174.4
Step-by-step explanation:
Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height.
Sarah's teacher wrote this expression on the whiteboard. Where could she place brackets in the expression for it to be equal to 36?
Answer:
A. 24 ÷ [6 − 2] × 5 + 6
Step-by-step explanation:
Sarah's teacher wrote this expression on the whiteboard. 24 ÷ 6 − 2 × 5 + 6 Where could she place brackets in the expression for it to be equal to 36? A. 24 ÷ [6 − 2] × 5 + 6 B. 24 ÷ 6 − [2 × 5 + 6] C. [24 ÷ 6] − 2 × 5 + 6 D. 24 ÷ 6 − 2 × [5 + 6]
Rule of operations
BODMAS
B = Bracket
O = 0f
D = Division
M = Multiplication
A = Addition
S = Subtraction.
Check all options
A. 24 ÷ [6 − 2] × 5 + 6
= 24 ÷ (4) × 5 + 6
= 6 × 5 + 6
= 30 + 6
= 36
B. 24 ÷ 6 − [2 × 5 + 6]
= 4 - (10 + 6)
= 4 - 10 + 6
= 0
C. [24 ÷ 6] − 2 × 5 + 6
= 4 - 10 + 6
= 0
D. 24 ÷ 6 − 2 × [5 + 6]
= 4 - 2(11)
= 4 - 22
= -18
Option A is the correct answer
Can you help I’ll mark brainliest
Answer:
[tex]7\sqrt{3}[/tex]
Step-by-step explanation:
Since this is a 30-60-90 triangle, we know that the sides have the following characteristic:
The side opposite to 30 degree angle: n
The side opposite to 60 degree angle: [tex]n\sqrt{3}[/tex]
The side opposite to 90 degree angle: 2n
Since we know that 7 is opposite to 30-degree, and x is opposite to 60 degree, than we know that x = [tex]7\sqrt{3}[/tex]
Factor: 0.25x^2 - 0.16y^4
0.25x^2 - 0.16y^4
Both terms are perfect squares so use the difference of squares formula
A^2 - b^2 = (a+b)(a-b) where a = 5x and b = 4y^2
Answer is 0.01(5x + 4y^2)(5x-4y^2)
Answer:
Solution given:
0.25x^2 - 0.16y^4
[0.5x]²-[0.4y²]²
[Note: Using formula: x²-y²=(x+y)(x-y)]
(0.5x+0.4y²)(0.5x-0.4y²) is a required answer.
Find the measure of angle F