Answers
The measure of the angle ∠ABD is calculated as 138° from the given data and figure.
What is triangle's angle sum property?The total of a triangle's three internal angles is 180 degrees, according to the angle sum property. When the values of the other two angles are known, the angle sum property is utilized to compute the measure of an unknown interior angle.
What exactly is the SAS rule of similarity?SAS stands for Side-Angle-Side Similarity. If the proportion of the two sides of one triangle is the same as the proportion of the two sides of another triangle, and the angle inscribed by the two sides of both triangles is equal, two triangles are said to be similar.
Given: ΔACD and ΔBCD are isosceles.
AD ≅ AC
BD ≅ BC
∠BAC = 18°
∠BDC = 48°
We need to determine the measure of ∠ABD.
Since, AD ≅ AC
∠DAB = ∠BAC = 18°
Since, BD ≅ BC
∠BDC = ∠BCD = 48°
By triangle's angle sum property,
∠BDC + ∠BCD + ∠DBC = 180°
48° + 48° + ∠DBC = 180°
∠DBC = 84°
Also, ∠ABD = ∠ABC [By SAS rule of ΔABD + ΔABC]
From the figure we can see that,
∠DBC + ∠ABD + ∠ABC = 360°
84° + 2∠ABD = 360° [∵ ∠ABD = ∠ABC]
2∠ABD = 276
∠ABD = 138°
Therefore, the measure of the angle ∠ABD is calculated as 138° from the given data and figure.
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Related Questions
there are 55 stickers in each box how many stickers are in 7 boxes
Answers
explanation: 7x55=385
6(3n+10) whats the answer
Answers
Problem: 6(3n+10)
Solution:
Applying the distributive law of natural or real numbers, we obtain:
[tex]6(3n+10)\text{ = 6.3n+ 10.6 = }18n+60[/tex]then, the correct answer is:
[tex]6(3n+10)\text{ =}18n+60[/tex]I don’t under stand help
Answers
E is the same shape and around the same size as A. A tales up a total of around 6 squares as well as E. E would be a rotation of 90°
what is the value of the expression y - x?
Answers
Answer:
[tex]y-x=-10[/tex]
Step-by-step explanation:
In any trapezoid, the sum of all angles is 360°. Additionally, the sum of both angles on the same side of the trapezoid is 180°. Therefore, we know that:
[tex](7x+40)+(68-6y)=180[/tex]
[tex](17y+73)+(121-4x)=180[/tex]
To solve for [tex]x[/tex] and [tex]y[/tex], we must set up a system of equations and solve by substitution, elimination, or graphing.
To start, simplify the first formula, then isolate the [tex]x[/tex] variable:
[tex](7x+40)+(68-6y)=180[/tex]
[tex]7x-6y+68+40=180[/tex]
[tex]7x-6y+108=180[/tex]
[tex]7x-6y=72[/tex]
[tex]7x=72+6y[/tex]
[tex]x=\frac{72+6y}{7}=\frac{72}{7}+\frac{6}{7}y[/tex]
Next, simplify the second formula, then substitute the value above for [tex]x[/tex]:
[tex](17y+73)+(121-4x)=180[/tex]
[tex]-4x+17y+121+73=180[/tex]
[tex]-4x+17y+194=180[/tex]
[tex]-4(\frac{72}{7}+\frac{6}{7}y)+17y+194=180[/tex] (substituted for [tex]x[/tex] here)
[tex]-\frac{288}{7}-\frac{24}{7}y+17y+194=180[/tex]
[tex]-\frac{288}{7}-\frac{24}{7}y+\frac{119}{7}y+\frac{1358}{7}=\frac{1260}{7}[/tex]
[tex]-288-24y+119y+1358=1260[/tex]
[tex]95y+1070=1260[/tex]
[tex]95y=190[/tex]
[tex]y=2[/tex]
Finally, substitute 2 for [tex]y[/tex] in the first formula as simplified:
[tex]7x=72+6y[/tex]
[tex]7x=72+6(2)[/tex]
[tex]7x=72+12[/tex]
[tex]7x=84[/tex]
[tex]x=12[/tex]
Therefore:
[tex]x=12[/tex] and [tex]y=2[/tex]
And the expression [tex]y-x[/tex] equals:
[tex]y-x=2-12=-10[/tex]
16 oz harbor peanut butter for 2.49 or a 64 oz jar of peanut butter for 6.99 round everything up to the nearest cent or hundreth. yes mam
Answers
We have to find the "better buy" between two options:
1) 16 oz jar for $2.49
2) 64 oz jar for $6.99
We can compare this two options with the unit price of each one. The unit price will be expressed in "$ per oz" or "$/oz". The option with the smaller unit price is the "better buy".
We can calculate the unit price as teh quotient between the price and the weight of each option.
Unit price for Option 1:
[tex]u_1=\frac{2.49\text{ \$}}{16\text{ oz}}\approx0.16\frac{\$}{oz}_{}[/tex]Unit price for Option 2:
[tex]u_2=\frac{6.99\text{ \$}}{64\text{ oz}}\approx0.11\frac{\$}{oz}[/tex]As the Option 2 (64 oz jar) has a smaller unit price, the better buy is the 64 oz jar for $6.99.
Answer: the better buy is the 64 oz jar for $6.99.
three times the measure of an angle is equal to twice the measure of the angle's supplement. what is the measure of the angle
Answers
Answer:
The angle has measure 72°.
Step-by-step explanation:
Definition:
Two angles are supplementary angles if the sum of their measures equals 180°.
Let x and y be the supplementary angles.
According to the definition above, then,
x + y = 180
We can the above equation for y:
x + y = 180
y = 180 - x
The two angles have measures:
x
180 - x
Now we look carefully at this statement:
"three times the measure of an angle is equal to twice the measure of the angle's supplement"
We translate the above statement into an equation, using x for one angle, and 180 - x for the supplement.
3x = 2(180 - x)
Solve the equation for x.
Distribute 2 on the right side.
3x = 360 - 2x
Add 2x to both sides.
5x = 360
Divide both sides by 5.
x = 360/5
x = 72
The angle has measure 72°.
Write the equation of the linear relationship in slope-intercept form, using decimals as needed.
x 25 35 45 55
y 85 77 69 61
The equation that represents this relationship is y =
Answers
The equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
Given:
x 25 35 45 55
y 85 77 69 61
slope between (25,85) and (35,77) is m = 77-85/35-25
= -8/10
m= -4/5
y=mx+c passes though (25,85)
85 = -4/5*25 + c
85 = -4*5+c
85 + 20 = c
c = 105.
y = mx + c
y = (-4/5)x + 105
Therefore the equation of the linear relationship in slope-intercept form is y = (-4/5)x + 105.
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Zeke wants to build a fence around his backyard with the 200 feet (ft) of fencing he bought at Lowe's. Zeke wants to use all of the fencing he bought. he also wants the length of the fencing to be 10 times the width. the equation A=200w-10w^2 can be used to find the area of the garden, where w is the width of the garden, in ft
Answers
Considering the vertex of the quadratic equation, the width that will maximize the area of the garden, and the maximum area, are as follows:
Width: 10 ft.Maximum area: 1000 ft².What is the vertex of a quadratic equation?A quadratic equation is defined as follows:
y = ax² + bx + c.
The vertex can be either a maximum point or a minimum point, depending on the coefficient a, as follows:
Maximum: a < 0.Minimum: a > 0.The coordinates of the vertex are given as follows:
x = -b/2a.y = -(b² - 4ac)/4a.For this problem, the equation is:
A(w) = -10w² + 200w.
Hence the coefficients are:
a = -10, b = 200, c = 0.
The width that will maximize the area is:
w = -200/(2(-10)) = 200/20 = 10 ft.
The maximum area is of:
A = -(200)²/(4(-10)) = 1000 ft².
Missing InformationThe problem is incomplete and could not be found on any search engine, hence we suppose that it asks for the width that will maximize the area of the garden, and the maximum area.
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Three functions are shown.
Linear
Quadratic
Exponential
Which of the following statements is true?
Answers
The correct statement C. Exponential growth will always exceed linear growth.
What is termed as the Exponential growth?Exponential growth is a data pattern that exhibit good increases over time, resulting in the curve of such an exponential function.Whereas exponential growth is frequently used in corporate finance, the actuality is frequently more complex. In the case of a savings account, the implementation of exponential growth did work well because the rate of interest is assured and does not change over time. This isn't the case with the majority of investments.For the given question;
In the end, a "exponential growth function" would always outperform a "linear growth function" because "x-values" tend to increase in continuation, and as such the change rate affiliated with the "exponential function" as well increases in continuation, whereas the "linear function's" change rate is considered constant.
Thus, Exponential growth will always exceed linear growth.
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The complete question is-
Three functions are shown.
A. Linear growth will always exceed exponential growth.
B. Quadratic growth will always exceed exponential growth.
C. Exponential growth will always exceed linear growth.
Clarissa and Koko solve 3x + 5 = 2x + 4 by graphing the related function. Is either of them correct? Explain your reasoning.
Answers
Answer:
clarissa
Step-by-step explanation:
please help me dhdjjdjejejejdjejejejejejkenensndd
Answers
Answer: area=8cm
Step-by-step explanation:
Answer:
a) Area of shape = 8 square cm.
Step-by-step explanation:
Area of composite shape:
Area of shape = area of rectangle + 2* area of triangle
Rectangle:l = 3 cm ; w = 2 cm
[tex]\sf \boxed{\text{Area of rectangle = l *w}}[/tex]
= 3 * 2
= 6 cm²
Triangle:
b = 2 cm
h = 1 cm
[tex]\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}[/tex]
[tex]\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2[/tex]
Area of two triangles = 2 *1
= 2 cm²
Area of shape = 6 + 2
= 8 cm²
b) Area of rectangle ABCD = 4 * 2
= 8 cm²
Solve the following inequality, 6 < 3r-45 < 36 Which graph shows the correct solution?
Answers
We know that:
6 < 3r-45 < 36
We want to re arrange the inequations:
Step 1: all terms with an unkown value on one side.
We want to let 3r "be alone" in the middle side:
6 < 3r-45 < 36
6 + 45 < 3r < 36 + 45 [adding 45 in each part]
51 < 3r < 81 [6 + 45 = 51 and 36 + 45 = 81]
Step 2: we want to clear r
51 < 3r < 81
51/3 < r < 81/3 [dividing by 3 all sides]
17 < r < 27 [51/3 = 17 and 81 /3 = 27]
Answer: 17 < r < 27GRAPHIf point A(-5, -7) lies on the terminal arm of an angle, determine the exact value for the
primary trigonometric ratios of the angle.
Answers
Answer:
[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]
[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]
[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]
Step-by-step explanation:
Given the terminal side of an angle we can calculate the distance between the point given and the origin:
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]r=\sqrt{|(-5^2)+(-7^2)|}[/tex]
[tex]r=\sqrt{74}[/tex]
y = opposite side
x = adjacent side
r = hypotenuse
Now we have
[tex]r=\sqrt{74}[/tex]
[tex]x=-5[/tex]
[tex]y=-7[/tex]
[tex]sin(a)=\frac{y}{r}=-\frac{7\sqrt{74} }{74}[/tex]
[tex]cos(a)=\frac{x}{r} =-\frac{5\sqrt{74} }{74}[/tex]
[tex]tan(a)=\frac{y}{x} =\frac{7}{5}[/tex]
3 (3+4k)=45 can you help me with this one
Answers
Given 3 ( 3 + 4k ) = 45
So, divide both sides by 3
3 + 4k = 45/3
3 + 4k = 15
subtract 3 from both sides
3 + 4k - 3 = 15 - 3
4k = 12
divide both sides by 4
k = 12/4 = 3
So, the value of k = 3
Yvette maps out several locations in her town, with distances and angles between them. Two triangles are formed within the map.
To conclude that these triangles are congruent by SAS Congruence Postulate, what must the distance between the school and the park be
Answers
To be both triangles to be congruent the distance between the school and the park be 1.1 miles.
What is congruence?If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
As per the given two triangles,
The side 2.7 miles is the common side.
The angle is 52 degrees in both triangles same.
To be congruent any one side must be the same by the SAS rule.
Thus, the school-to-park corresponding side is school-to-store.
school to park = 1.1 miles
Hence "To be both triangles to be congruent the distance between the school and the park be 1.1 miles".
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95% of ____ is 427.5
Answers
Answer: Hi! The answer is 406,125.
Step-by-step explanation: You can either go by 1%, meaning you divide 427,5 by 100 and then do x95, which gives you 95%, or you can do 427,5x0,95. Either way you get 406,125!
Answer:
406.125
Step-by-step explanation:
Find the distance between the points J(-8, 0) and K(1, 4).
Answers
The distance between two points of coordinates (x₁, y₁ ) and (x₂, y₂) is calculated using the formula:
[tex]undefined[/tex]Which of the following determines the range of spectral lines produced during electron transition?
A.
the total number of energy levels the electron can jump to
B.
the lower energy level to which the electron returns
C.
the higher energy level to which the electron jumps
D.
the number of electrons under electron transition at the same time
Answers
The range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.
Spectral lines are bright or dark lines over continuous spectrum which occur due to emission or absorption of energy.
When an electron jumps to or from one energy level to another energy level, spectral lines are produced. The range of spectral lines depends on the number of energy levels available to which the electron can jump. This depends the amount of energy gained/lost by the electron.
Thus, the range of spectral lines produced during electron transition is determined by the total number of energy levels the electron can jump to.
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There are f flavors of ice cream at the shop. Dominic has sampled 7 of them. Choose the expression that shows the number of flavors Dominic has not sampled.
Answers
In linear equation, Jen planned to spent 3.75 hours paddleboarding.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Dominic has sampled = 7
flavors of ice cream at shop = f
the expression that shows the number of flavors Dominic has not sampled
= 7 * f = 7f
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Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
Answers
SOLUTION
The coordinate of the vector P and Q are
[tex]\begin{gathered} P(-13,\text{ 11)} \\ \text{And } \\ Q(-18,2) \end{gathered}[/tex]To find the vector PQ. we have
[tex]\begin{gathered} t=\bar{PQ} \\ PQ\text{ is having the coordinate } \\ PQ=(-18-(-13),2-11)=(-5,-9) \end{gathered}[/tex]To find the vector, we use
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \text{Where } \\ x=-5,y=-9 \\ r=\sqrt[]{(-5)^2+(-9)^2}=\sqrt[]{25+81}=\sqrt[]{106}=10.296 \end{gathered}[/tex]Then we obtain the angle using
[tex]\begin{gathered} \text{tan}\theta=(\frac{y}{x})_{} \\ \text{Substituting the value of x and y, we have } \\ \tan \theta=(\frac{9}{5})=\tan \theta=(1.8) \end{gathered}[/tex]Hence
[tex]\begin{gathered} \tan \theta=1.8 \\ \theta=\tan ^{-1}(1.8) \\ \theta=60.945 \end{gathered}[/tex]Hence
The vector in trigonometry form will be
[tex]\begin{gathered} t=r(i\cos \theta+j\sin \theta) \\ \text{Then} \\ t=10.296\cos 60.945i+10.296\sin 60.945j \end{gathered}[/tex]Therefore
t= 10.296 cos 60.945 i + 10.296 sin 60.945j
Answer: Option C(third option ).
Xavier Knox's annual salary is $61,100. He is paid semimonthly. His personal exemptions total $4,000. How
much does his employer deduct from each of Knox's paychecks for state income tax of 3.5 percent?
a. $166.54
c.
b. $83.27
$83.13
d. $166.26
Answers
The amount that Xavier Knox's employer deducts from his paychecks for state income tax is b. $83.27
How to find the state income tax?First find his taxable income:
= Annual salary - Personal exemptions
= 61, 100 - 4, 000
= $57, 100
The state income tax per year is:
= 57, 100 x 3.5% state income tax rate
= $1, 998.50
The semimonthly state income tax deducted is:
= 1, 998.50 / (12 months x twice a month)
= $83.27
In conclusion, on a semimonthly basis, $83.27 is deducted for state income tax.
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I need help please with [tex]6409 \div 61[/tex]. I know the answer is 105.06the problem is it has to be written as a a whole number with a fraction. we put 105 and 3/50 but its saying it's wrong.
Answers
Given the expression
[tex]\frac{6409}{61}[/tex]Next is to know how many 61 can go in 6409. Using the calculator, you can see that it is 105 with a remainder of 4
We will then have to express the fraction in the form:
[tex]Q\text{ +}\frac{R}{D}[/tex]Q is the quotient = 105
R is the remainder = 4
D is the divisor = 61
Substituting these values into the expression we will have:
[tex]\begin{gathered} \frac{6409}{61}=105+\frac{4}{61} \\ \frac{6409}{61}=105\frac{4}{61} \end{gathered}[/tex]Hence the solution written as a whole number and fraction is 105 4/61
many wholes are in 21 / 5
Answers
Divide the numbers:
21/5 = 4.2
The radius of the front wheel of Terry's bike is 61cm.
Terry goes for a cycle and travels 60.32km.
How many full revolutions did Terry's front wheel complete?
Answers
In linear equation, 157 did Terry's front wheel complete.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Terry goes for a cycle and travels 60.32km.
so, 60.32 * 1000 ÷ ( 2 * 3.14 * 61 )
= 60320 ÷ 2 * 3.14 * 61
= 60320 ÷ 6.28 * 61
= 60320 ÷ 383.08
= 6032000/ 38308
= 1508000/9577
= 157
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Write a rule to describe a transformation when a triangle hasbeen reflected over the x-axis.(x,y) →Using (-x,-y)
Answers
For a transformation that involves a reflection over the x-axis, it means the pre-image is reflected across the horizontal line.
For a reflection over the x-axis, the x coordinate remains the same while the y coordinate changes.
The rule that describes a transformation when an image has been reflected over the x-axis is:
(x, y) ==> (x, -y)
Using the pre-image (-x, -y), we have:
(-x, -y) ==> (-x, y)
For a triangle, we have:
A(-x, -y) ==> A'(-x, y)
B(-x, -y) ==> B'(-x, y)
C(-x, -y) ==> C'(-x, y)
A bag contains 15 cards numbered 1 through 15. A card is randomly chosen from the bag. What is the probability that the card has an odd number on it? Write your answer as a fraction in simplest form.
Answers
There are 15 cards numbers are from 1 to 15.
From the numbers 1 to 15:
• 8 numbers, are ,odd
,• 7 numbers, are ,even,
The probability is the possibility of an event occuring.
Probability of event to happen P(A) = Number of favourable outcomes/Total Number of outcomes
Thus, the probability of an odd card is:
total number of odd cards/total number of cards
= 8/15
the Correct Answer is:
[tex]\frac{8}{15}[/tex]use the product, quotient, and power rules of logarithms to rewrite the equation as a single logarithm.
Answers
We are given the following expression:
[tex]\log a-3\log b+4\log c[/tex]we are asked to simplify this expression. To do that we will first use the following property:
[tex]a\log b=\log ^{}b^a[/tex]we will apply this to the second and third terms, like this:
[tex]\log a-\log b^3+\log c^4[/tex]Now we will use the following property:
[tex]\log a-\log b=\log (\frac{a}{b})[/tex]we will use this property for the first and second terms:
[tex]\log (\frac{a}{b^3})+\log c^4[/tex]Now we will use the following property:
[tex]\log a+\log b=\log ab[/tex]We will use the property in the last two terms, like this:
[tex]\log (\frac{ac^4}{b^3})[/tex]And thus, we have simplified the logarithmic expression into one single logarithm
The table shows the rational approximation of several irrational numbers.
Which is the approximate value of √3?
Answers
The approximate value of √3 is 1.732 which is an irrational number.
Given that,
We have to find the value of root3.
√3 is an irrational number.
Real numbers that cannot be represented as a ratio are referred to as irrational numbers. Or to put it another way, irrational numbers are actual numbers that defy logic.
Irrational numbers are real numbers that cannot be represented by a straightforward fraction. These can't be stated as ratios, like p/q, where p and q are both integers, q≠0. In terms of statistics, it defies reason.
The approximate value of √3 is 1.732.
Therefore, The approximate value of √3 is 1.732 which is an irrational number.
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9-6 Worksheet: Dilations
Graph the polygon and its image after a dilation with the given scale factor
1. J(2, 4), K(4, 4), P(3, 2); r = 2
5.1-2.
ty
of
X
Answers
Answer:
Step-by-step explanation:
it ty
Answer:
٠٠
First write all the points on the graph
second
multiply 2 in all the numbers and write them again
Nell participated in a 3-day charity walk. Sheraised $0.50 for each 1/3 of mile that she walked. Thefirst day, Nell walked 12 miles. The second day, shewalked 8 miles. The third day, she walked 16 miles.How much money did Nell raise?
Answers
the Numbers of days = 3
The second statement(She raised $0.50 for each 1/3 of mile that she walked) means
1/3 miles = $0.50
For first day walk we have:
1/3 miles = $0.50
12 miles = 12 x 0.50 x 3 = $18
For Second day walk we have:
1/3 miles = $0.50
8miles = 8 x 0.50 x 3 = $12
For Third day walk we have:
1/3 miles = $0.50
16miles = 16 x 0.50 x 3 = $24
The amount she raised for the three days becomes
$18 + $12 + $24
=$54