Answer:
x = 2
Step-by-step explanation:
expand the brackets firstly,
so 12x-4 = 20
then add the -4 onto the other side
so 12x = 24
then divide 24 by 12 to get x
so x = 2
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. A circle has a diameter of 28 centimeters. Estimate the area of the circle. Use 22 7 for π .
Answer:
The area of the circle is [tex]616\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
In this problem we have
[tex]r=D/2=28/2=14\ cm[/tex] ----> the radius is half the diameter
substitute
[tex]A=(22/7)(14)^{2}=616\ cm^{2}[/tex]
ARE E,F & H collinear?
Yes;they lie on EH
NO;the three points are not collinear
Yes;they lie on FH
Yes;they lie on EG
Answer:
Step-by-step explanation:
Yes; the 3 points all lie on EG.
Answer: Yes;they lie on EG
Step-by-step explanation:
The line plot shows the number of points scored by Josh in his basketball games. How many games did Josh score more than six points?
Without the line plot data for Josh's basketball game points, we cannot determine how many games he scored more than six points. However, to create a side-by-side stem-and-leaf plot, you separate the tens and ones to form stems and leaves and compare wins and losses.
Explanation:To answer the question of how many games Josh scored more than six points, you would need to refer to the specific line plot data, which is not provided here. Since we don't have the actual line plot, we cannot accurately determine the number of games in which Josh scored more than six points.
In general, if you have a line plot illustrating the points scored by Josh in his basketball games, you would count the number of times the data points exceed the number six on the plot. That count would represent the number of games he scored more than six points.
For the task of creating a side-by-side stem-and-leaf plot for the wins and losses of a sports team over 42 seasons, you would first separate the tens and the ones to make the stems and leaves. For example, if a team won 10 games in a season and lost 9 games, the stem would be '1' for both, and the leaves would be '0' for wins and '9' for losses. This process would repeat for all 42 seasons, organizing the data side-by-side to easily compare wins and losses.
The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours. The salary the she is paid is given by the function S(T) = 15T, where S is measured in dollars.
A. If the worker produces 18 units, what will she be paid?
B. How many units would the worker need to produce to be paid $3,030?
Answer:
A. $1,110
B. 50 units.
Step-by-step explanation:
A. Substitute [tex]x=18[/tex] into the function [tex]T(x)=4x+2[/tex] for calculate the time in hours required for the worker to produce 18 units:
[tex]T(18)=4(18)+2=74[/tex]
Now you need to substitute [tex]T=74[/tex] into the function [tex]S(T)=15T[/tex] to calculate the amount in dollars she will be paid for 74 hours:
[tex]S(74)=15(74)=1,110[/tex]
She will be paid $1,110.
B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute [tex]S(T)=3,030[/tex] into the function [tex]S(T)=15T[/tex] and solve for T (to find the number of hours she requires to work to be paid $3,030)
[tex]3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202[/tex]
Now, substitute [tex]T(x)=202[/tex] into [tex]T(x)=4x+2[/tex] and solve for x, to calculate the number of units she produces in 202 hours:
[tex]202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50[/tex]
She would need to produce 50 units to be paid $3,030
Tan 64 degrees = height / 75 ft
Answer:
176.08952318965774 or 176.1
Step-by-step explanation:
Tan(64) = h/75
Tan(64) * 75
= 176.08952318965774
Show that the points (6,1), (5,6), (-4,3), (-3,2) are the vertices of a parallelogram
The points (6,1), (5,6), (-4,3), (-3,2) are the vertices of a parallelogram.
As we know mid point of diagonal are same.
Mid point of (6,1) and (-4,3) = (1,2)
Mid point of(5,6) and (-3,-2) = (1,2)
This is parallelogram.
The points (6,1), (5,6), (-4,3), (-3,2) are not the vertices of a parallelogram
What is Parallelogram?Parallelogram is a simple quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
let the vertices of a parallelogram be A(6,1), B(5,6), C(-4,3) and D(-3, 2)
by distance formula we have,
Distance between two points
Distance=√(x₂-x₁)²+(y₂-y₁)²
AB=√(5-6)²+(6-1)²=√1+25=√26
BC=√(-4-5)²+(3-6)²=√81+9=√90
CD=√(-3-4)²+(2-3)²=√49+1=√50
DA=√(-3-6)²+(2-1)²=√81+1=√82
AB is not equal to CD and BC not equal to AD
Opposite sides are not equal.
Hence, the points (6,1), (5,6), (-4,3), (-3,2) are not the vertices of a parallelogram
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Julia swam 3/4 of a mile in the pool.if each lap is 1/16 of a mile,how many laps did she swim.
The answer is twelve.
3/4 x 4 = 12/16
12/16 divided by 1/16 is 12z
The number of laps that she swam will be 12 laps.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Julia swam 3/4 of a mile in the pool. If each lap is 1/16 of a mile.
Then the number of laps that she swam will be given as,
⇒ (3/4) ÷ (1/16)
⇒ 3 x 16 / 4
⇒ 3 x 4
⇒ 12 laps
The number of laps that she swam will be 12 laps.
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1)
Find function domain
f(x) = sqrt( 2sin x - 1 )
Answer:
{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}
Step-by-step explanation:
sinx can run from -1 to +1
2sinx can run from -2 to +2
2sinx -1 can run from -3 to +1
However, the square root is imaginary when x < 0. So, the condition is
2sinx -1 ≥ 0
2sinx ≥ 1
sinx ≥ ½
x ≥ π/6 (30°)
So, in the interval [0, 2π], π/6 ≤ x ≤ 5π/6
However, the sine is a cyclic function and repeats itself every 2π.
Over all real numbers, the condition is (π/6 +2πn) ≤ x ≤ (5π/6 + 2πn).
The domain is then
{x ∈ ℝ : x ≥ π/6 +2πn and x ≤ π/6 + 2πn and n ∈ ℤ}
Given: PKHE - inscribed, m∠E=120°
m∠EPK=51°, PF ∥EH
Find: m∠KPF, m∠H.
Answer:
KPF = 9 and H = 129
Step-by-step explanation:
An inscribed quadrilateral in a circle has all diagonal angles add up to 180, so we can use this to find the angles of the quadrilateral.
H= 180-EPK and K = 180-E so H = 129 and K = 60
Now PF and EH are parallel, so PE is a transversal. That means FPE = 180 - E = 60. Now it's pretty easy to solve for KPF = FPE - EPK = 60 - 51 = 9.
Let me know if you don't see how I did any of this and I'll be happy to explain it..
y is directly proportional to X
When y = 30, x = 6
a) work out an equation connecting y and x.
b) Work out the value of y when x = 12
y = kx
30 = 6k
k = 5
a) y = 5x
y = 5 × 12
b) y = 60
The equation that connects y and x here is y = 5x, found by realizing y is directly proportional to x. Substituting the given values into this equation reveals that when x = 12, y = 60.
Explanation:In the given question, y is directly proportional to x. This can be written as y=kx, where 'k' is the constant of proportionality. When y=30 and x=6, substituting these values into the equation gives us 30=k*6. Solving for 'k', we get k=30/6 = 5, meaning our equation becomes y = 5x.
For part b), we can find the value of y when x=12 by substituting the value of x in our equation, y = 5x. This gives us y = 5*12, which results in y = 60.
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7 to the -4 power x 7 to the 4 power
the answer is supposed to be one, i just dont know how to get to it
Answer:
The answer is 1
So first you will multiply the terms with the same base by adding their exponents. Then solve the exponents. Then the only thing you will have left is 7 to the power of 0. Which equals 1
Sheila eats 3/4 of a bag of baby carrots each week.How many bags of carrots does she eat in 6 weeks? Write in Simplest Form
Answer:
9/2
Step-by-step explanation:
Apply the distributive property to simplify the expression. -7(4x-3)
Answer:
Step-by-step explanation:
(-7*4x)(-7*-3)
-28x+21
Thats the answer
To simplify the expression -7(4x-3), distribute -7 to each term inside the parentheses and multiply. The simplified expression is -28x + 21.
Explanation:To simplify the expression -7(4x-3) using the distributive property, you need to distribute the -7 to each term inside the parentheses. This means multiplying -7 by both 4x and -3.
The product of -7 and 4x is -28x, and the product of -7 and -3 is 21.
Therefore, the simplified expression is -28x + 21.
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A standard deck of 52 cards has four 13-card suits: diamonds, hearts, clubs, and spades. The diamonds and hearts are red, and the clubs and spades are black. Each 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king, and an ace. The jack, queen, and king are called face cards.
Roger drew one card from a standard deck of 52 cards. What is the probability that the card Roger drew is not red?
Answer:129
Step-by-step explanation:you just have to add them together
Final answer:
The probability that the card drawn by Roger from a standard deck is not red is 50%, as exactly half of the cards in a standard deck are black (non-red).
Explanation:
The student has asked what the probability is that a card drawn from a standard deck of 52 cards is not red. Given that half the cards are red (diamonds and hearts) and the other half are black (clubs and spades), we can easily calculate this probability.
Since there are 26 black cards (13 clubs and 13 spades) out of a total of 52 cards, the probability of drawing a black card is 26 out of 52, which can be simplified to 1/2 or 0.5. Therefore, the probability that Roger draws a card that is not red is 50%.
Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation? {–12, 2} {–2, 12}
Answer: I could be wrong so don't get your hopes up but I believe the solution set would be {-2,12}
Step-by-step explanation:
Answer:
The solution set is {-12,2}.
Step-by-step explanation:
We have given a quadratic equation.
x² + 10x = 24
We have to find the solution of above equation by completing square.
Adding (5)² to both sides of above equation, we have
x²+10+(5)² = 24+ (5)²
(x+5)² = 24+25
(x+5)² = 49
Taking square root to both sides of above equation, we have
x+5 = ±7
x+5 = 7 or x+5 = -7
x = 7-5 or x = -7-5
x = 2 or x = -12
Hence, the solution set is {-12,2}.
The answer options are
A. X/7 ≥ y/3 + 2
B. Y/2 ≤ x/3 +2
C. Y/7 ≤ x/3 + 3
D. X/7 ≤ y/3 +2
Ansgilcx dhsvguydfsjhujvcouwaihgraeuvyjsghdnvufyiekghabsuivkjkesd
Step-by-step explanation:
Which is greater? The square root of 121 or the cube root of 125. Explain your answer.
Answer:
The square root of 121.
Step-by-step explanation:
The square root of 121 is 11. 11x11=121 which makes the square root of 121, 11. The cube root of 125 is 5. Cube roots are numbers that are multiplied by each other to make a number, 125 is 5x5x5 so the cube root is 5. 11 is a greater number than 5 which makes the square root of 121 greater.
[tex]\bold{Hey\ there!}\\ \\ \bold{\sqrt{121}=11^2=11\times11=121} \\ \bullet{\sqrt{121}=11} \\ \\ \bold{\sqrt{125}=\sqrt[5]{5}=5} \\ \bold{\bullet{The\ cubed\ root\ of\ 125\ is\ 5}} \\ \\ \boxed{\boxed{\bold{Answer:\sqrt{121}\ is\ bigger\ than\ \sqrt[125]}}}[/tex][tex]\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your\ day!} \\ \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Find the probability of not rolling factors of 5 on both die
Answer:
Step-by-step explanation:
2 factors of 5 on each die (2x2=4-12=8) so the answer would be 8
A cylinder has a radius of 10 feet and a height of 11.4 feet. What is the approximate volume of the cylinder? Use 3.14 for pi
Answer:
3,579.6
Step-by-step explanation:
Volume of a cylinder: V = πr^2h
Answer:
3580 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is
V = πr²h
Data:
r = 10 ft
h = 11.4 ft
Calculations:
V = πr²h = 3.14 × 10² × 11.4 = 3580 ft³
The approximate volume of the cylinder is 3580 ft³.
find the surface area of this triangular prism
To find the surface area, find the area of each side and then add them together.
The bottom is 8 x 2 = 16
The left side is 6 x 2 = 12
The slanted side is 10 x 2 = 20
The front triangle is 1/2 x 8 x 6 = 24
The back triangle is the same as the front = 24
Total surface area = 16 + 12 + 20 + 24+24 = 96 square inches.
algebraic expression for x subtracted from 15
Answer:
15-x
Step-by-step explanation:
x subtracted from 15 - key word is subtracted from
that means flip it when it is written so it is 15-x
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ The algebraic expression for x subtracted from 15 is:
15-x
This is because it says x subtracted from 15, meaning x is taken out of 15.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
A parallelogram has an area of 216.24 cm2
and a height of 15.9 cm.
How long is the base of the parallelogram?
Enter your answer as a decimal in the box.
Answer:
200.34 cm²
Step-by-step explanation:
Answer:
13.6 cm
Step-by-step explanation:
The area (A) of a parallelogram is calculated using the formula
A = bh ← b is the base and h the height
here A = 216.24 and h = 15.9, hence
15.9b = 216.24 ( divide both sides by 15.9 )
b = [tex]\frac{216.24}{15.9}[/tex] = 13.6 cm
In a 45-45-90 triangle, what is the length of the hypotenuse when the length of one of the legs is 11 in.?
Answer:
= 15.556 in
Step-by-step explanation:
Since this is a 45-45-90 triangle, we can tell that;
This is a right triangle This is an isosceles triangleOne of the theorems of geometry, the Isosceles Right Triangle Theorem, says that the hypotenuse is √2 times the length of a leg.
Therefore;
hypotenuse = leg × √2
If we take hypotenuse as x
Since the leg is 11;
Then; x = 11√2
x = 11/√2
x = 15.556 in
An angle, θ, is in standard position. The terminal side of the angle passes through the point (6, -5).
Find sinθ.
-5 square root of 51/51
Answer:
[tex]Sin\theta =\frac{-5}{\sqrt{61}}[/tex]
Step-by-step explanation:
(6, -5)
According to the diagram
[tex]OA^{2}=OB^{2}+AB^{2}[/tex]
[tex]OA^{2}=6^{2}+5^{2}=36+25=61[/tex]
[tex]OA=\sqrt{61}[/tex]
[tex]Sin\theta =\frac{AB}{OA}[/tex]
[tex]Sin\theta =\frac{-5}{\sqrt{61}}[/tex]
Find the area of a triangle
Answer:
154 cm^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh
A = 1/2 (22) * 14
154 cm^2
Answer:
A = 154 cm²Step-by-step explanation:
The formula of an area of a triangle:
[tex]A_\triangle=\dfrac{bh}{2}[/tex]
b - base
h - height
From the picture we have a base b = 22cm and a height h = 14cm.
Substitute:
[tex]A_\triangle=\dfrac{(22)(14)}{2}=(11)(14)=154\ cm^2[/tex]
Find half of 6 times 8
Answer:
24
Step-by-step explanation:
6 times 8 is 48 and i divided that by 2
Answer:
The answer is 24
Step-by-step explanation:
So simple
1) just Multiply
6 x 8 = 48
then divide by 2
48/2 = 24
Hope this help you!
Convert 96 ounces to pounds.
4 lb.
5 lb.
6 lb.
10 lb.
Answer: C; 6 lbs.
Step-by-step explanation: There are 16 ounces in a pound, so 96 divided by 16 is 6.
Answer:
6 Pounds is your answer.
Step-by-step explanation:
Prove that the lines x+y=5, 2x–y=16 and x+2y=3 intersect at one point. What are the coordinates of this point?
Answer:
The coordinates of the intersection point are [tex](7,-2)[/tex]
Step-by-step explanation:
we have
[tex]x+y=5[/tex] -----> equation A
[tex]2x-y=16[/tex] -----> equation B
[tex]x+2y=3[/tex] -----> equation C
we know that
If the system of equations intersect at one point, then the system of equations has one solution
using a graphing tool
see the attached figure
The coordinates of the intersection point are [tex](7,-2)[/tex]
This point is a common solution for the three equations
Verify
Substitute the value of [tex]x=7, y=-2[/tex] in each equation
so
Equation A
[tex]x+y=5[/tex]
[tex]7-2=5[/tex]
[tex]5=5[/tex] ----> is true, therefore the point is a solution of the equation A
Equation B
[tex]2x-y=16[/tex]
[tex]2(7)+2=16[/tex]
[tex]16=16[/tex] ----> is true, therefore the point is a solution of the equation B
Equation C
[tex]x+2y=3[/tex]
[tex]7+2(-2)=3[/tex]
[tex]3=3[/tex] ----> is true, therefore the point is a solution of the equation C
A student did a survey on how people feel when they are hungry. The results were that more people felt a stabbing pain than their stomach aching. 30 people said that their stomach ached when they were hungry. 49 people said they felt a stabbing pain. How many more people felt a stabbing pain than stomach aches?
it’s 19 :)
filler
:)
hi
The number of more people who felt a stabbing pain than a stomach ache when they are hungry is obtained by subtracting the number of people who felt a stomach ache from the number of people who felt a stabbing pain. The difference, which is 19, indicates that 19 more people felt a stabbing pain.
Explanation:The subject of the question is simple subtraction in mathematics. In this scenario, find the difference between the number of people who felt a stabbing pain when they were hungry and the number who felt a stomach ache. The number of people who felt a stabbing pain is 49, and the number of people who felt a stomach ache is 30. So, to obtain the number of more people feeling stabbing pain than stomach ache: 49 (stabbing pain) - 30 (stomach ache) = 19. Thus, 19 more people felt a stabbing pain than a stomach ache when they were hungry.
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1/2- 1/4 write in simplest form
Answer:
The answer is 1/4 Also if your having a hard time with fractions use calculator soup its easy thats what i use
Step-by-step explanation:
The simplest form of the expression 1/2 - 1/4 is 1/4.
To simplify the expression 1/2 - 1/4, we first need to find a common denominator, which is the same denominator that both fractions share. In this case, the common denominator is 4.
To make 1/2 have a denominator of 4, we need to multiply both the numerator and denominator by 2. This gives us (1 * 2) / (2 * 2), which simplifies to 2/4.
So, the expression becomes 2/4 - 1/4. Now that both fractions have the same denominator, we can subtract their numerators while keeping the denominator the same:
(2 - 1) / 4 = 1/4
Therefore, the simplified form of 1/2 - 1/4 is 1/4. This means that if you have half (1/2) of something and you subtract a quarter (1/4) from it, you are left with one-quarter (1/4) of that something.
Simplifying fractions is essential in mathematics because it helps express quantities in their most reduced and straightforward forms, making them easier to work with and understand. In this case, 1/2 - 1/4 simplifies to 1/4, representing a clear and concise result.
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