Answers
1. 4x + 7 + 2x - 1 = 180
They equal 180 because they add up to a linear pair (equals 180) and they’re a straight line (equals 180).
2. 6x + 6 = 180
Combine like terms
3. 6x = 174
Subtract 6 from both sides so x is on one side and the numbers on the other.
4. x = 29
Divide both sides by 6
ANSWER: x = 29
Second question
1. 6x + 13 = 10x - 7
They equal each other because they’re vertical angles, and vertical angles are congruent.
2. 20 = 4x
Move the x and numbers to opposite sides
3. 5 = x
Divide both sides by 4 to get x
ANSWER: x = 5
Answer:
Step-by-step explanation:
Hi Debbie, the tricky part about these types of problem is recognizing that you know the total angle. 180° for the ABCD question and the angles are equal to each other for the TUWXY question , this tip lets you find X for each.
just add the two angle and set equal to 180 in each problem. I'll do the problems below, but , now that you know how, maybe you could try them and check your answer against mine.
The ABCD question
4x+7 + 2x -1 = 180
6x +6 = 180
6x = 174
x = 29
4(29)+7 = 123°
2(29)-1 = 57°
The TUWXY question
6x+13 = 10x-7
20 = 4x
5=x
then
6(5)+13 = 43°
and the next one should be the same
10(5) -7 =43°
check. so there are your answers. :) get it?
Related Questions
Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, after h hours
Answers
The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the number of hours be given as h.
Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:
c = 3 + (5 × h)
c = 3 + 5h
where c = total cost
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For the following, based on the information given which would you use to find the missing variable?
Answers
The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively
How to find the missing variables?We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
1st triangle
tan 25° = b/8 (tan = opp/adj)
b = 8 tan 25° = 3.73m
2nd triangle
sin 21° = x/22 (sin = opp/hyp)
x = 22 sin 21° = 7.88 units
3rd triangle
cos 47° = 28/x (cos = adj/hyp)
x = 28/cos 47° = 41.06 units
4th triangle
Use Pythagoras' theorem:
12² = 8² + y²
y² = 12² - 8²
y² = 144 - 64
y² = 80
y = √80 = 8.94 units
Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units
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Triangle EFG is similar to triangle HIJ. Find JH. Round your answer to
the nearest tenth if necessary. Figures are not drawn to scale.
Answers
The length of the side JH in the triangle ΔHIJ is 97.9.
We are given two triangles. The vertices of the first triangle are E, F, and G. The vertices of the second triangle are H, I, and J. The triangles ΔEFG and ΔHIJ are similar to each other. The lengths of the sides FG, GE, and IJ are 12, 25, and 47, respectively. We need to find the length of the side, JH. The figure of the triangles is attached below.
Let the length of the side JH in the triangle ΔHIJ be represented by the variable "x". The side IJ is proportional to the side FG. Let the constant of proportionality be "k".
IJ ∝ FG
IJ = k*FG
k = IJ/FG
k = 47/12
The side JH is proportional to the side GE.
JH = k*GE
x = (47/12)*25
x = 97.9
Hence, the length of the side JH is 97.9 units.
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What is the end behavior of the graph of f(x) = x5 - 8x4 + 16x³?
O
O f(x)→→∞ as x→∞; f(x) →→∞ as x→ +∞
f(x)→∞ as x→-∞0; f(x) → +∞o as x→ +∞
O f(x) +∞o as x→-∞; f(x) →→→∞as x→ +∞
+∞o as x→∞0; f(x)→ +∞ as x→→ +00
O
f(x)
DONE
Answers
The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
In the question ,
it is given that ,
the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,
In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .
In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .
that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
let us find the roots of the function ,
f(x) [tex]=[/tex] 0
x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0
taking x³ common ,
x³(x² - 8x [tex]+[/tex] 16) = 0
x³(x² - 4x - 4x + 16) = 0 .... by using splitting the middle term method
x³(x(x - 4) - 4(x - 4)) = 0
x³(x - 4)(x - 4) = 0
which means x³ [tex]=[/tex] 0 and x-4 = 0
that is x=0 and x = 4 .
So , the roots of the function f(x) are x=0 and x=4 .
This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.
Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
The given question is incomplete , the complete question is
What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?
(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞
(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞
(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞
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At his most recent medical checkup, a boy was 40 inches tall. Currently, he is 46 inches tall. What percent taller is the boy now?
im not smart at this lol
Answers
Answer:
15%
Step-by-step explanation:
15%*40=46
Answer:
15%
Step-by-step explanation:
[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]
The boy was 40 inches tall so that means 40 inches is the old value
The boy is currently 46 inches tall now, so 46 is the new value
Plug these values into the equation:
[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]
Simplify:
[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]
[tex]Percent of change =\frac{600}{ 40} \\[/tex]
[tex]Percent of change =15[/tex]
I hope this answers your question :)
2*8/3 give me answer
Answers
Answer:
Exact Form: 16/3
Decimal Form: 5.3
Mixed Number Form: 5 1/3
Step-by-step explanation:
A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .
can you help me use compatible numbers to find two estimates of 478/12 i will give you 100000 points
Answers
Answer:
48
Step-by-step explanation:
4. Using the Place Value Method, order the following from least to greatest.
.134
.2
.051
.46
Answers
Answer: 0.051, 0.134, 0.2, 0.46
Step-by-step explanation:
write 28 plus 24 as a product of two factors
Answers
Answer:
4(13)
Step-by-step explanation:
[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]
(18x³ - x² + 9x - 3) and (5x³ + 6x² - 14x +11) Add the polynomials (Provide only the coefficients. If a coefficient is negative, include the negative sign on the left side of the number. Do not type 'plus' sign)
Answers
Answer: put it in a caculator
Step-by-step explanation:
Combine 18x^3 and 5x^3.
23x³ - x² + 9x-3 + 6x² - 14x+11Combine x^2 and 6x^2.
23x³ + 5x² + 9x -3 - 14x + 11Combine 9x and −14x.
23x³ + 5x² + -5x -3 + 11Add −3 and 11.
23x³ + 5x² -5x + 8what is 2 1/2 + 1 1/8 + 1 1/4 - 1 1/2
Answers
Answer:
27/8 or 3.375 or 3 3/8
Step-by-step explanation:
Why does completing the square always result in a perfect square trinomial?
Answers
Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.
When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.
Hope this helps.
Step-by-step explanation:
For questions 9-11, find the values of x and y if l || m.
Answers
The values of x and y using angle relationships are as follows:
x = 9, y = 13x = 22, y = 15x = 7, y = 24How to find angles in parallel line cut by a transversal?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles.
Therefore, the angle relationship can be used to find the value of x and y in the diagram.
In the diagram, l and m are parallel lines and are cut by a transversal line.
Therefore,
10.
10x - 17 = 8x + 1(alternate exterior angles are congruent)
10x - 8x = 1 + 17
2x = 18
x = 18 / 2
x = 9
8x + 1 + 6y + 29 = 180(sum of angles on a straight line is 180 degrees)
72 + 1 + 29 + 6y = 180
102 + 6y = 180
6y = 180 - 102
6y = 78
y = 78 / 6
y = 13
11.
7x - 30 = 5x + 14(Corresponding angles)
Corresponding angles are congruent.
7x - 5x = 14 + 30
2x = 44
x = 44 / 2
x = 22
3y + 11 + 7x - 30 = 180(sum of angles on a straight line)
3y + 11 + 7(22) - 30 = 180
3y + 11 + 154 - 30 = 180
3y = 180 - 11 - 154 + 30
3y = 45
y = 45 / 3
y = 15
12.
7y - 23 = 23x - 16 (vertically opposite angles)
7y - 23x = 7
8x - 21 + 23x - 16 = 180 (same interior angles are supplementary)
31x - 37 = 180
31x = 180 + 37
31x = 217
x = 217 / 31
x = 7
7y - 23(7) = 7
7y = 7 + 161
7y = 168
y = 168 / 7
y = 24
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (−4,1)
Answers
Answer:
[tex]y=-43x-173[/tex]
Step-by-step explanation:
[tex]y+1=-43(x+4) \\ \\ y+1=-43x-172 \\ \\ y=-43x-173[/tex]
if I make 11 dollars an hour and i worked 20 hours for 4 days, how much would I earn?
Answers
Answer: I think you would earn $8.35 per hour
Step-by-step explanation:
Answer: $880
Step-by-step explanation:
As I understand you are working 20 hours a day for 4 days.
[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880
Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 4, 8, 11
O 6, 8, 13
O√3, √5,8
O√3, √13, 4
K
Answers
The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d) .
In the question ,
four set of sides is given ,
we need to find the set of side that forms a right triangle ,
we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .
Option(a)
the sides are 4 , 8 , 11.
4 + 8 = 11
16 + 64 = 121
80 = 121
we know that 80 121 ,
So , the sides do not form a right triangle
Option(b)
the sides are 6 , 8 , 13
6 + 8 = 13
36 + 64 = 169
100 169
we know that 100 169 ,
So , the sides do not form a right triangle .
Option(c)
the sides are √3, √5 , 8
√3 + √5 = 8
3 + 5 = 64
8 = 64
we know that 8 64 ,
So , the sides do not form a right triangle .
Option(d)
the sides are √3, √13 , 4
√3 + √13 = 4
3 + 13 = 16
16 = 16
Yes , the sides form a right triangle .
Therefore , The sides {√3 , √13 , 4} forms a right triangle .
The given question is incomplete , the complete question is
Determine which set of side measurements could be used to form a right triangle ?
(a) 4, 8, 11
(b) 6, 8, 13
(c)√3, √5,8
(d)√3, √13, 4
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Kathleen’s grandfather has a very old pet tortoise. He told Kathleen that the tortoise was 61 years old when she was born 10 years ago. Kathleen is amazed and wants to know how old the tortoise is now. Write an equation Kathleen can use to find the tortoise’s age t and solve.
Answers
Answer:
t - 10 = 61
Step-by-step explanation:
We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61
so t = 71.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each set of prices with the correct percent of increase or decrease.
11% decrease
11% increase
8.7% decrease
7.4% increase
8% decrease
12.4% decrease
9.9% increase
8% increase
original price: $63.00
new price: $56.07
arrowRight
original price: $98.00
new price: $108.78
arrowRight
original price: $37.50
new price: $34.50
arrowRight
original price: $12.25
new price: $13.23
arrowRight
Answers
Each set of prices should be matched with the correct percentage of increase or decrease as follows:
12.4% decrease = original price: $63.00 and new price: $56.07.11% increase = original price: $98.00 and new price: $108.78.8.7% decrease = original price: $37.50 and new price: $34.50.8% increase = original price: $12.25 and new price: $13.23.How to calculate percentage change?Mathematically, percentage increase can be calculated by using this formula:
Percentage increase = [original price - new price]/new price × 100
At original price: $63.00 and new price: $56.07, we have:
Percentage decrease = [63.00 - 56.07]/56.07 × 100
Percentage decrease = 6.93/56.07 × 100
Percentage decrease = 0.124 × 100
Percentage decrease = 12.4%.
At original price: $98.00 and new price: $108.78, we have:
Percentage increase = [108.78 - 98.00]/98.00 × 100
Percentage increase = 10.78/98.00 × 100
Percentage increase = 0.11 × 100
Percentage increase = 11%.
At original price: $37.50 and new price: $34.50, we have:
Percentage decrease = [37.50 - 34.50]/34.50 × 100
Percentage decrease = 3/34.50 × 100
Percentage decrease = 0.087 × 100
Percentage decrease = 8.7%.
At original price: $12.25 and new price: $13.23, we have:
Percentage increase = [13.23 - 12.25]/12.25 × 100
Percentage increase = 0.98/12.25 × 100
Percentage increase = 0.08 × 100
Percentage increase = 8%.
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Solve the system of equations by graphing. List the coordinates.
u=v
4u=2v-12
Answers
By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).
What is a graph?A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
In order to plot the system of equations on a graph, we would simplify the second equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have the following:
4u/4 = 2v/4 - 12/4
u = v/2 - 3
Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.
By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).
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I need help with this please help me
Answers
The measurement of angles ∠1 is 126° and ∠2 is 154°.
According to the question,
We have the following information:
We have a figure of two triangles and some of the measurements of the angles are given.
We know that the sum of three angles of a triangle is 180°.
So, for the larger triangle, we have the following expression:
96+30+third angle = 180
Third angle = 180-126
Third angle = 54°
We know that sum of angles on a straight line is 180°.
So, we have:
∠1+54 = 180
∠1 = 180-54
∠1 = 126°
Now, finding the sum of angles in smaller triangle:
126+28+third angle = 180
Third angle = 180-154
Third angle = 26°
Now, angle 2 and this angle will make a straight line.
∠2+26 = 180
∠2 = 180-26
∠2 = 154°
Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.
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NO LINKS! Please help me with this problem #3
Answers
Answer:
b) f(x) = -16x² + 8x + 30
Step-by-step explanation:
When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.
The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.
If a > 0, the parabola opens upwards.If a < 0, the parabola opens downwards.Therefore, f(x) = -16x² + 8x + 30 could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.
If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).
Monica’s dose from the fluoroscopy tower, at a distance of 9 feet, is 100 mR/hr. What is the radiation intensity, in Roentgens, at 1 foot from the fluoroscopy tower?
Answers
The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr
How to the radiation intensity, in Roentgens?
Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray
The equation below relates the radiation intensity and distance:
I₁/I₂ = D₂²/D₁²
where: I₁ = intensity at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source
Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot
Using the formula:
100/I₂ = 1²/9²
100/I₂ = 1/81
I₂ = 100 × 81
I₂ = 8100 mR/hr
I₂ = 8100×10⁻³ R/hr (1 mR/hr = 1×10⁻³ R/hr)
I₂ = 8.1 R/hr
Therefore, the radiation intensity in Roentgens is 8.1 R/hr
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The temperature in the United States last night was -9℃. It is now -3℃. What was the change in temperature?
Answers
The change in temperature in United States since last night is -6 degree centigrade.
Given the temperature in United States last night is = -9 degree C
Now the temperature is = -3 degree C
So the change in temperature is given by,
= Final Temperature - Initial Temperature
= -9 - (-3)
= -9 + 3
= -6 degree C
Hence the change in temperature in United States since last night is -6 degree centigrade.
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In the figure, A.ABC is congruent to AADC t the square ABCD is dilated by a factor of 2 to form ABCD, what
ASCO to the area of ABCD?
A 2:1
B 3:1
c. 4:1
d 5:1
Answers
Answer:
C. Trust me on this one, it is an easy one.
Help please! 15 points!!!!! give me an answer!!!!!
Billy has 15 apples he eats 3 ands sells 4 for $4 dollars each, How many apples are left. And what's Billy's total profit at the end of the day?
Answers
Answer:
Step-by-step explanation:
7*5
Answer:
he got 8 apples left and made a profit of 16
Step-by-step explanation:
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
Answers
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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Find the perimeter and area of the polygon shown below 15 8 17 16
Answers
The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.
How to calculate the perimeter?It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:
= 16 + 15 + 16 + 8 + 17
= 72 feet
The area will be:
= Area of triangle + Area of rectangle
= (1/2 × base × height) + (length × width)
= (1/2 × 8 × 17) + (15 × 16)
= 68 + 240
= 308ft²
Therefore, the correct option is B.
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José is climbing a mountain. Using a rope, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. How far from the top of the cliff is he after 14 minutes?
Enter the correct answer in the box.
Please help this is due tomorrow
Answers
The distance from the top of the cliff that Jose is after 14 minutes is 12.8 feet downward.
What is an elevation?An elevation simply means the height above sea level.
In this case, José climbs down from the top of a steep cliff for 4 minutes at a rate of 12.2 feet per minute. The total feet will be:
= 12.2 × 4
= 48.8 feet
He then climbs back up for 10 minutes at a rate of 3.6 feet per minute. This will be:
= 3.6 × 10
= 36 feet.
Therefore, the change in elevation will be:
= Elevation up - Elevation down
= 36 - 48.8
= 12.8 feet.
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QUATIONS
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make true equations of
the following. Use each digit once
Answers
The true equations are :
2 + 7 = 9
8 × 5 = 4 0
6 ÷ 3 = 2
2 - 1 = 1
We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.
The first true equation is 2 + 7 = 9.
The second true equation is 8 × 5 = 4 0.
The third true equation is 6 ÷ 3 = 2.
The fourth true equation is 2 - 1 = 1.
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Write an equation and solve:
Sandy has $60 and saves $10 a month. Randy has
$45 and saves $20 per month. After how many
months will they have the same amount of
money?
Answers
Answer:
3/2 month
Step-by-step explanation:
Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?
When x = months:
Sandy: 10x + 60
Randy: 20x + 45
You are looking for x when:
Sandy = Randy
10x + 60 = 20x + 45
subtract 45 from both sides:
10x + 60 - 45 = 20x + 45 - 45
10x + 15 = 20x
subtract 10x from both sides:
10x + 15 - 10x = 20x - 10x
15 = 10x
divide both sides by 10:
15/10 = 10x/10
x = 15/10
reduce:
x = 3/2
It will take 3/2 months of Sandy and Randy to have the same amount of money.
[3/2 month also equals 1.5 months, depending on the format of the answer you need]