Use the figure below to complete the following problem.Given:ZH= 2x + 60Z T= x+ 30HALT is aT=
Answers
Answer: 60 degrees
The figure there is a parallelogram
< H = 2x + 60
< T = x + 30
Therefore, supplementary angles is 180 degrees
< H + < T = 180
2x + 60 + x + 30 = 180
Collect the like terms
2x + x + 60 + 30 = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
Divide both sides by 3
3x/3 = 90/3
x = 30
Since < T = x + 30
Hence,
< T = 30 + 30
< T = 60 degrees
Related Questions
USMZABC = 40'and BỎ is the anglebisector of ZABC3y+6B.3x-134-2xD5y-18MZABD =[ ? 1°Enter
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We want to calculate the value of
[tex]3x-1[/tex]However, x is unknown. For BD is "angle bisector"
[tex]3x-1=34-2x[/tex]Let us solve that equation for x:
[tex]3x+2x=34+1[/tex](-2x was sent to the left-hand side, and -1 was sent to the right-hand side)
[tex]5x=35[/tex][tex]x=7[/tex]Then,
[tex]3x-1=3(7)-1=21-1=20[/tex]Thus,
[tex]m\measuredangle ABD=20[/tex]Can you help me find the angles of x°, R, Q, and P?
Answers
SOLUTION
Using the theorem
The sum of angles in a triangle is 180°
Then we have
[tex]P^0+Q^0+R^0=180^0[/tex]from the diagram in the questions
[tex]\begin{gathered} P=x-11 \\ Q=3x+6 \\ R=x \end{gathered}[/tex]Substituting the parameters we have
[tex]\begin{gathered} (x-11)^0+(3x+6)^0+x^0=180^0 \\ \text{ Remove the parenthesis} \\ x-11+3x+6+x=180^0 \\ \text{ Rearrange the expression} \\ x+3x+x+6-11=180^0 \end{gathered}[/tex]Simplify the equation above
[tex]\begin{gathered} 5x-5=180^0 \\ 5x=180+5 \\ 5x=185 \\ \text{Divide both sides by 5} \\ x=\frac{185}{5} \end{gathered}[/tex]Therefore
[tex]x=39^0^{}[/tex]Hence
The value of x is 39°
If 8 more than twice a number is 14, what is 8 times the number?
Answers
Let the unkonwn number be
[tex]=x[/tex]Twice the number means
[tex]\begin{gathered} =2\times x \\ =2x \end{gathered}[/tex]8 more than twice the number means the sum of twice the number and 8
[tex]=2x+8[/tex]8 more than twice a number is 14, will be represented below as
[tex]2x+8=14[/tex]collect similar terms from the equation above to get
[tex]\begin{gathered} 2x+8=14 \\ 2x=14-8 \\ 2x=6 \\ \text{divide both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]8 times the number will then be,
[tex]\begin{gathered} =8\times x \\ =8\times3 \\ =24 \end{gathered}[/tex]Hence,
The correct answer is OPTION C
A multivitamin tablet contains 12.5mg of calcium how much calcium does a bottle of 40 tablets contain write your answer in grams
Answers
One multivitamin tablet contains 12.5mg.
Therefore, 40 tablets will contain
[tex]40\times12.5=500[/tex]40 tablets will contain 500mg.
In grams:
By conversion,
[tex]1g=1000mg[/tex]Hence, 500mg can be converted as
[tex]\frac{500}{1000}=0.5[/tex]Hence, there are 0.5g of calcium in
which is a better buy? 20 items for $5.99 or 30 items for $7.99
Answers
Answer:
Step-by-step explanation:
Obisouly 20 items for $5.99
How to write a rule for the nth term of the geometric seq
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The nth term of a geometric sequence is expressed as:
[tex]a_n=ar^{n-1}[/tex]were:
• a is the first term
,• r is the common ratio
,• n is the number of terms
If the 2nd term a₂ = 28, then;
[tex]\begin{gathered} 28=ar^{2-1} \\ ar=28 \end{gathered}[/tex]If the 5th term a₅ = 1792, then;
[tex]\begin{gathered} 1792=ar^{5-1} \\ ar^4=1792 \end{gathered}[/tex]Take the ratio of both equations to have:
[tex]\begin{gathered} \frac{ar^4}{ar}=\frac{1792}{28} \\ r^3=64 \\ r=\sqrt[3]{64} \\ r=4 \end{gathered}[/tex]Substitute r = 4 into any of the equations to have:
[tex]\begin{gathered} ar=28 \\ 4a=28 \\ a=\frac{28}{4} \\ a=7 \end{gathered}[/tex]Determine the rule for the nth term of the geometric sequence. Recall that;
[tex]\begin{gathered} a_n=ar^{n-1} \\ a_n=7(4)^{n-1} \end{gathered}[/tex]This gives the nth term of the geometric sequence
What is the lateral surface area of the square pyramidrepresented by this net?11 ft8 ftEnter your answer in the box.11 ft11 ftA8 ft다ft?111 ft
Answers
Surface area of a square pyramid is given as:
[tex]\begin{gathered} \text{Surface area = }Area\text{ of base + }\frac{1}{2}PS \\ \text{where P = perimeter of base} \\ S\text{ = slant height} \end{gathered}[/tex][tex]\begin{gathered} \text{Area of base = area of square} \\ \text{Area of base = }(length)^2 \\ \text{length = 8 }ft \\ \text{Area of base = 8}^{\text{ 2}}=64ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Perimeter of base = 4(length)} \\ \text{Perimeter of base = 4(8) = 32 ft} \end{gathered}[/tex][tex]\begin{gathered} \text{slant height = }11\text{ ft} \\ \\ \text{The surface area = 64 + }\frac{1}{2}(32\times11) \\ \\ \text{The surface area = 64 + }\frac{1}{2}(352) \end{gathered}[/tex][tex]\begin{gathered} \text{The surface area = 64 + 176} \\ \text{The surface area = }240ft^2 \end{gathered}[/tex]what value of y will make the equation true? √34 × √y = 34
Answers
Clear y from the equation to find its value
[tex]\begin{gathered} \sqrt[]{34}\cdot\sqrt[]{y}=34 \\ \sqrt[]{y}=\frac{34}{\sqrt[]{34}} \\ \sqrt[]{y}=\sqrt[]{34} \\ y=(\sqrt[]{34})^2 \\ y=34 \end{gathered}[/tex]The value of y that will make the equation true is 34.
Answer:
The value of y=√34 will make the equation true.
Step-by-step explanation:
What is an equation?
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given expression is:-
√34 x √y =34
Putting the value of y=√34 will satisfy the equation.
√34 x √34 =34
34 = 34
Therefore the value of y=√34 will make the equation true.
To know more about equations follow
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solve for x 3/5x-1/3x =4
Answers
Answer:
3/5x times 3 = 9/15. 1/3x times 5 =5/15. 9/15x-5/15x=(4/15x)
Step-by-step explanation:
Give ordered pairs that are solutions and graph the equation.2y = 5x – 10Complete the ordered pairs so they are solutions to the given equation.
Answers
Answer:
The equation is given below as
[tex]2y=5x-10[/tex]Concept:
To calculate the value of y when x=0, we will substitute the x=0 in the equation above and solve for y
By substituting the values, we will have
When x=0
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(0)-10 \\ 2y=-10 \\ \frac{2y}{2}=-\frac{10}{2} \\ y=-5 \\ (0,-5) \end{gathered}[/tex]When x=1
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(1)-10 \\ 2y=5-10 \\ 2y=-5 \\ \frac{2y}{2}=-\frac{5}{2} \\ y=-2.5 \\ (0,-2.5) \end{gathered}[/tex]When x=2
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(2)-10 \\ 2y=10-10 \\ 2y=0 \\ \frac{2y}{2}=\frac{0}{2} \\ y=0 \\ (2,0) \end{gathered}[/tex]When x=3
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(3)-10 \\ 2y=15-10 \\ 2y=5 \\ \frac{2y}{2}=\frac{5}{2} \\ y=2.5 \\ (3,2.5) \end{gathered}[/tex]When x=4
[tex]\begin{gathered} 2y=5x-10 \\ 2y=5(4)-10 \\ 2y=20-10 \\ 2y=10 \\ \frac{2y}{2}=\frac{10}{2} \\ y=5 \\ (4,5) \end{gathered}[/tex]Hence,
By graphing using the ordered pairs below, we will have
[tex]\begin{gathered} (2,0) \\ (0,-5) \end{gathered}[/tex]Chris earns $298.65 each week. The federal government withholds 17% ofthat for federal income tax. How much is withheld from her pay annuallyfor federal income tax?a. $15,529.80b. $50.77c. $2,640.07d. $2,963.77
Answers
Remember that
1 year=52 week
so
17%=17/100=0.17
Multiply $298.65 by 0.17
$298.65*0.17=$50.7705
Multiply by 52
$50.7705*52=$2,640.07
the answer is option CIn the news you hear “ tuition is expected to increase from the current cost of $1,050 to $2,050 over the next ten years.” This represents a __% increase from the current tuition.
Answers
According to the information given in the exercise, the tuition is expected to increase from $1,050 to $2,050 over the next ten years.
Then, you need to use the following formula in order to solve this exercise:
[tex]Percentage\text{ }Increase=\frac{Final\text{ }value-Initial\text{ }value}{|Initial\text{ }value|}\cdot100[/tex]In this case:
[tex]\begin{gathered} Initial\text{ }value=1,050 \\ Final\text{ }value=2,050 \end{gathered}[/tex]Therefore, substituting these values into the formula and evaluating, you get:
[tex]\begin{gathered} PercentageIncrease=\frac{2,050-1,050}{|1,050|}\cdot100 \\ \\ PercentageIncrease=95.24 \end{gathered}[/tex]Hence, the answer is: 95.24% increase.
(5x 10-6)(3x 10-4)(5x 10-6) (3 x 10 - 4) =PLS HELP IT’S DUE TNNNN !
Answers
we can multiply the normal numbers on the one hand and the scientific notation on the other hand
so
[tex]\begin{gathered} (5\times3)(10^{-6}\times10^{-4}) \\ (15)(10^{-6+(-4)}) \\ =15\times10^{-10}=1.5\times10^{-9} \end{gathered}[/tex]Share it: Due:Friday, Aug 28, 2020, 12:00 AM How is comparing and ordering rational numbers different from comparing and ordering integers? Be specific.
Answers
hello
to compare or know the difference between rational numbers and integers
rational numbers are numbers in which are expressed as fractions of two integers eg a/b where b is a non zero number
integers are whole numbers in mathemathics without the expression in fraction or rather they're expressed in fractions but the denominator must be equal to 1
now when we want to compare and order integers, they're prefereably done using the number line system.
for an integer
[tex]\begin{gathered} in\text{ the number line system} \\ -3>\text{ }-4 \\ 2\text{ }<\text{ 3} \end{gathered}[/tex]while in rational numbers,
[tex]\begin{gathered} \frac{1}{2}\text{ }>\text{ }\frac{1}{4} \\ -\frac{2}{3}\text{ <}\frac{1}{2} \end{gathered}[/tex]Find the sales tax and total cost of a wireless mouse that costs $20.99. The tax rate is 4%. Round your answer to the nearest cent.
Answers
Sales tax = $0.84
Total cost = $21.07
Explanations:Cost Price = $20.99
Tax rate = 4% = 4/100 = 0.04
Sales tax = (Tax rate) x (cost Price)
Sales tax = 0.04 x 20.99
Sales tax = $0.8396
Sales tax = $0.84 (to the nearest cent)
Total cost = Cost price + sales tax
Total cost = $20.99 + $0.84
Total cost = $21.074
Total cost = $21.07 (to the nearest cent)
Which of the following proportions can be used to solve the problem below?Suppose you are using a photocopier to reduce the size of a picture that is 10 inches wide by 12 inches long. If you reduce the picture so that it is 9 inches wide, how long will it be?
Answers
We are asked to determine the length of a picture that is originally 10 inches wide and 12 inches long.
By reducing it we must keep the same proportion between length and width. Therefore, the ratio between length and width must remain the same. The ratio between width and length is:
[tex]\frac{10}{12}[/tex]Now, we set this equal to the ratio of the reduced picture:
[tex]\frac{10}{12}=\frac{9}{x}[/tex]Therefore, the right proportion is B
The equation ^2 − 4 − 4^2 + 13 = 0 will produce a hyperbola. How can we tell by simply observing the equation?In what directions do the branches of this hyperbola open? How do you know? Explain. Sketch a graph of this hyperbola, clearly indicating how you have determined thekey characteristics (center, vertices, eccentricity, foci). Give the domain and range of this hyperbola.
Answers
we have the equation
[tex]^2−4−4^2+13=0[/tex]Group similar terms and move the constant to the right side
[tex](^2−4)−4^2=-13[/tex]Complete the square
[tex]\begin{gathered} (y^2-4y+2^2-2^2)-4x^2=-13 \\ (y^2-4y+2^2)-4x^2=-13+2^2 \\ (y^2-4y+2^2)-4x^2=-9 \end{gathered}[/tex]Rewrite as a perfect square
[tex](y-2)^2-4x^2=-9[/tex]Divide both sides by -9
[tex]\begin{gathered} \frac{(y-2)^2}{-9}-\frac{4x^2}{-9}=\frac{-9}{-9} \\ \\ -\frac{(y-2)^2}{9}+\frac{x^2}{\frac{9}{4}}=1 \\ \\ \frac{x^{2}}{\frac{9}{4}}-\frac{(y-2)^{2}}{9}=1 \\ \end{gathered}[/tex]The coordinates of the center are (0,2)
The transverse axis is on the x-axis
a^2=9/4 -----------> a=3/2
b^2=9 -----------> b=3
The vertices are --------> (0+1.5,2) and (0-1.5,2)
so
Vertices at (1.5,2) and (-1.5,2)
Find out the value of c
c^2=a^2+b^2
c^2=(9/4)+9
c^2=45/9
c=√5
Find out the coordinates of the foci
(0+√5,2) and (0-√5,2)
using a graphing tool
The domain is the interval (-infinite, -1.5) U (1.5, infinite)
The range is the interval (-infinite, infinite)
What are the dimensions of a parallelogram in terms of the demensioms of the circle?
Answers
If we divide a circle into a number of equal segments then stack them in a row head-to-tail, the new shape is a parallelogram with bumpy sides, with the same area as the circle.
We can conclude the following:
1. The base of a parallelogram is approximately equal to half the circumference of the circle
2. The height of the parallelogram is approximately equal to the radius of the circle
3. The area of the parallelogram is equal to the area of the circle.
Hi, can you help me to solve this problem, please!!!
Answers
The given parabola is:
[tex]y=-3x^2+3x-6[/tex]It is written in the form:
[tex]y=ax^2+bx+c[/tex]The axis of symmetry is given by the following formula:
[tex]x=-\frac{b}{2a}[/tex]Where a=-3 and b=3. Replace these values and solve for x:
[tex]\begin{gathered} x=-\frac{3}{2(-3)}=-\frac{3}{-6}=\frac{3}{6} \\ \text{Divide numerator and denominator by 3 to simplify} \\ x=\frac{3/3}{6/3}=\frac{1}{2} \end{gathered}[/tex]Therefore, the axis of symmetry is x=1/2
The diagonales of this rhombus are 3 meterse and 8 meters
Answers
Area of a rhombus = 1/2 x d1 x d2
d1= diagonal 1 = 8m
d2 = diagonal 2 = 3m
Replacing:
A = 1/2 x 8 x 3 = 12 m2
16 The water level of a river was measured each day during a two-week period. The graph models the linear relationship between the water level of the river in feet and the number of days the water level was measured. Water Level of River 28 20 16 Water Level (0) 3 4 6 8 10 12 14 Number of Days Which statement best describes the y-intercept of the graph?
Answers
From the graph, it can be observed that line intersect the y-axis at (0,16) and after that level of water increases with increase in number of days.
So 16 feet represents the initial water level of the river. The correct answer is,
The initial water level was 16 ft.
Simplify each expression by distributing8(x + 5)
Answers
ok
8(x + 5) Just multiphy 8 by each term
8x + 40 This is the result
what digit is in the
Answers
So, let's turn the notation from mixed number to fraction:
[tex]1\frac{11}{100}\text{ = }\frac{100}{100}+\frac{11}{100}=\text{ }\frac{111}{100}[/tex]As you can see, the whole becomes 100/100 and then you just add the numerators.
Answer: 111/100
Is TAG BAG? IF so, identif th similarity postulate or theorem that applies
Answers
Step 1
Given;
[tex]Triangle\text{ TAG \textasciitilde Triangle BAG}[/tex]Required; To find the similarity postulate or theorem that applies.
Step 2
Both triangles share one side AG
They also have a common angle;
[tex]90^o[/tex]Side AG = 10 units and ∠AGT ≅ ∠AGB.
Thus, options A and B are discarded.
Step 3
Now, as for the SAS criteria, we need two sides to be congruent and their included angles to be congruent.
But, as no other information is given, we cannot determine whether the given triangles are congruent or not.
Therefore, the answer is; Option D
[tex]cannot\text{ be determined}[/tex]HELP ASAP!
Put (-3y + 6 < x) in slope-intercept form.
Answers
Step-by-step explanation:
so slope intercept form is y=mx+b or in this case y<mx+b
so you just need to solve for y
start by subtracting 6 from both sides getting -3y< x + 6 than you just divided by a -3 when you divide by a negative number you have to change the inequality so you would get y> -(x+6)/3 that would be your answer hopefully that helps. have a great day
Given a right triangle, what is the measure of 2B if ZA = 35º and b = 7?(Round your answer to the nearest degree.)
Answers
Let us make a drawing of the triangle:
Let's remember that the three angles of a triangle add up to 180 degrees. Then,
[tex]\measuredangle A+\measuredangle B+\measuredangle C=180\degree[/tex]Since our triangle is right, we have
[tex]\measuredangle C=90\degree[/tex]Thus
[tex]35\degree+\measuredangle B+90\degree=180\degree[/tex][tex]\measuredangle B=180\degree-90\degree-35\degree=55\degree[/tex]This means that the answer is 55°.
Let f(x) = 3x – 3 and g(x) = x + 5. Find f(g(x)) and g(f(x)).
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given data:
[tex]\begin{gathered} f\mleft(x\mright)=3x-3 \\ g\mleft(x\mright)=x+5 \end{gathered}[/tex]to find:
[tex]f\mleft(g\mleft(x\mright)\mright)\text{ and }g\mleft(f\mleft(x\mright)\mright)[/tex][tex]\begin{gathered} g(x)=x+5 \\ =f(x+5) \\ =3(x+5)-3 \\ =3x+12 \end{gathered}[/tex][tex]\begin{gathered} f(x)=3x-3 \\ =g(3x-3) \\ =(3x-3)+5 \\ =3x+2 \end{gathered}[/tex]Please help me with the last part of the question thanks
Answers
There is a direct proportion between two values when one is a multiple of the other.
In this case, we have:
[tex]1\text{ hour = 60 minutes}[/tex]This means that to convert hours to minutes, the multiplier is always 60.
The equation of a direct proportion is:
[tex]undefined[/tex]Judy is buying 6 pint of ice cream for her party at $3.45 each if she has a $20 bill does she have enough to buy the ice cream
Answers
the cost of the ice cream is,
3.45 $
also, she has only 20 $
SO, the number of icecreams bought by
Find the area of the triangle. Round to the nearest tenth. a=28.5 b=33.4 c=22.3
Answers
solution
for this case we can use the Herons formula given by:
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]Where s is the semiperimeter given by:
[tex]s=\frac{a+b+c}{2}=\frac{33.4+28.5+22.3}{2}=42.1[/tex]And we can find the area on this way:
[tex]A=\sqrt[]{42.1(42.1-33.4)(42.1-28.5)(42.1-22.3)}=314.05[/tex]And rounded to the nearest tenth would be:
314.1