Answer:
The measure of ∠A = 107.5°
Step-by-step explanation:
Given that
ABCD is a kite such that
AB = BC and AD = DC
Join A and C
Since AB = BC
→ ∠BAC = ∠BCA
Since , the angles opposite to equal sides are equal.
Let ∠BAC = ∠BCA = x°
and
Since AD = DC
→ ∠CAD = ∠ACD
Since , the angles opposite to equal sides are equal.
Let ∠CAD = ∠ACD = y°
Now
In ∆ ADC ,
∠ADC + ∠CAD + ∠ACD = 180°
Since , the sum of the all angles in a triangle is 180°
⇛ 30° + y°+ y° = 180°
⇛ 30°+2y° = 180°
⇛ 2y° = 180°-30°
⇛ 2y° = 150°
⇛ y° = 150°/2
⇛ y° = 75°
Therefore, ∠CAD = ∠ACD = 75°
and
In ∆ ABC,
∠ ABC + ∠BAC + ∠BCA = 180°
Since , the sum of the all angles in a triangle is 180°
⇛ 115° + x° + x° = 180°
⇛ 115°+2x° = 180°
⇛ 2x° = 180°-115°
⇛ 2x° = 65°
⇛ x° = 65°/2
⇛ x° = 32.5°
Therefore, ∠BAC = ∠BCA = 32.5°
Now, ∠ A = ∠BAC + ∠CAD
⇛ ∠A = 32.5° + 75°
⇛ ∠A = 107.5°
Therefore, ∠A = 107.5°
Answer:-
) The measure of ∠ADC = 145°) The measure of ∠A = 107.5°Read more:
Similar Questions
ABCD is a kite with AD=AB A= 116° B=2x° D=(5x-147)° Find the size of the smallest angle of the kite.
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The product of 6 and the sum of a number and 3 is 60
Answer:
8(x+3) is the answer
Step-by-step explanation:
The equation is 6(x + 3) = 60. Then the solution of the equation is 3.
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.
The product of 6 and the sum of a number and 3 is 60.
Let the number be 'x'. Then the equation is written as,
6(x + 3) = 60
Simplify the equation, then the value of the variable 'x' will be calculated as,
6(x + 3) = 60
x + 3 = 60 / 6
x + 3 = 10
x = 10 - 3
x = 3
The equation is 6(x + 3) = 60. Then the solution of the equation is 3.
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The value of the digit 8 in 1,857 is how many times the value of the digit 8 in 3,083?
Answer:
10 times
Step-by-step explanation:
The 8 in 1,857 is in the hundreds place and the 8 in 3,083 is in the tens place.
Are repeating decimals like 34.79 rational numbers?
Answer:
Yes. 34.79 is a rational number because it can be written as a fraction.
Step-by-step explanation:
Hoped this helped.
find the total tax to the nearest cent $58 bill; 20% tip
Answer:
$ 68 $ 58
Step-by-step explanation:
I'm not sure answer is $ 68 $ 58
A researcher wants to study the effect of weather on college students' study habits. On a sunny day, the researcher sits in the quad and records the number of minutes of study per student. Identify the crucial element missing in this design.
In this experiment design, the missing element is the control group.
In most experiments, the researcher will need to have a control group and an experimental group.
The control group is the one that is not given a treatment, for example, if you are testing an antibiotic, then the control group is the individuals that do not receive the medicine.
This group is important because it acts as a reference to measure the real effect in the experimental group or those receiving the treatment.
The control group is missing in this experiment because the research will need to measure the hours students spend studying on a regular cloudy day, in this way, he can later determine if there is a real difference between the number of hours on a sunny day vs the number of hours on a day that is not sunny.
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If 2/15 is 40 then 1/15 is?
(Sorry I know this is a easy question but my brain isn't processing the question right now so I need help)
Answer:
20
Step-by-step explanation:
[tex]\frac{2}{15}[/tex] = 40
[tex]\frac{2}{15}[/tex] ÷ [tex]\frac{2}{1}[/tex] = [tex]\frac{1}{15}[/tex]
40 ÷ [tex]\frac{2}{1}[/tex] = 20
Find the monomial if the expression is a cube of that monomial (find the cube root)
-27/64a^9b^6
-0.0001a^3n+3
I can't figure this out and need helppppppppp
Answer:
first one is -3/4a^3b^2
Step-by-step explanation:
i dont know the second one and i need help on that one too im sorry
The monomial of the functions are;
1. - 3/4 a³b²
2. - 0.1 aⁿ⁺¹
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
the expression are;
1. - 27/64 a⁹b⁶
2. - 0.001 a³n³ⁿ⁺³
Now,
Solve the expression as;
1. - 27/64 a⁹b⁶
Take cube root, we get;
∛- 27/64 a⁹b⁶ = ∛ - 3 × - 3 × - 3/4×4×4 a³a³a³ b²b²b²
= - 3/4 a³b²
And, - 0.001 a³n³ⁿ⁺³
∛ - 0.001 a³n³ⁿ⁺³ = ∛-0.1×0.1×0.1 aⁿ⁺¹ aⁿ⁺¹ aⁿ⁺¹
= - 0.1 aⁿ⁺¹
Thus, The monomial of the functions are;
1. - 3/4 a³b²
2. - 0.1 aⁿ⁺¹
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Nicole was given a box of assorted chocolates for her birthday. Each night, Nicole
treated herself to some chocolates. There were originally 24 chocolates in the box and
Nicole ate 3 chocolates each night. Make a table of values and then write an equation
for C, in terms of t, representing the number of chocolates remaining in the box t
days after Nicole's birthday.
Number of Days After Nicole's
Birthday
Number of Chocolates Remaining in the
Box
0
1
2
3
Step-by-step explanation:
T | 0 | 1 | 2 | 3 |
C | 24 | 21 | 18 | 15 |
Rule:
To find a rule, we need to find 2 things- what T is multiplied by and what is added.
To find what it is multiplied, we need to see the increase or decrease in C for every T. In this equation, there is a decrease of 3, so we multiply T by -3.
To find what is added, we go to 0 T and find the corresponding number. When T is 0, C is 24 so we add 24.
We write a rule as: y = mx + c, or in this case, c = mt + a
So the rule is c = -3x + 24
sale 90%Luca buys a swing set during the sale. If the original price was $270, how much does Luca pay?
Answer:
$243
Step-by-step explanation:
Would appreciate your help a lot!
Answer:
None of those answers are right. It should be
[tex] - \frac{23}{24} [/tex]
Step-by-step explanation:
You have to find common denominators first. Multiply -5/6 by 4/4 to get -20/24. Multiply 1/8 by 3/3 to get 3/24.
[tex] - \frac{20}{24} = z + \frac{3}{24} [/tex]
Subtract 3/24 from both sides since it is being added.
[tex] - \frac{20}{24} = z + \frac{3}{24} \\ - \frac{3}{24} \: \: \: \: \: \: \: \: \: \: - \frac{3}{24} [/tex]
Since there are two negatives on the left, add the fractions together and keep the negative sign.
[tex] - \frac{23}{24} = z[/tex]
You cannot reduce this fraction.
Guided Practice
Type your answer and then click or tap Done.
What is the vertex of the parabola with the equation y=15x^2+2x−8?
Answer:
(Fill in the blank text field 1
-5
, Fill in the blank text field 2
-13
)
Step-by-step explanation:
(Fill in the blank text field 1
-5
, Fill in the blank text field 2
-13
)
Done
The vertex of the parabola is (−5, −13).
Rewrite in vertex form and use this form to find the vertex
(
h
,
k
)
.
(
−
1
/15
,
−
121
/15
)
Find the vertex form.
y
=
15
(
x
+
1
/15
)
2
−
121
/15
At the produce store you can buy 5 bags of bananas for $23.15 . How much would it cost if you were to buy 6 bags?
Answer: $26.16
Step-by-step explanation:
23.15 / 5 = 4.63
4.63 x 6 = $26.16
order -9, -16, -13, 0 from least to greatest
Answer:
_16,-13,-9,0
Step-by-step explanation:
hope this helps u out!!
Solve (x-1)(x+5)=0 using zero product property
How would you write 12 as a Roman numeral?
Answer:
ⅠⅠⅩ
Step-by-step explanation:
ok
Answer:
Step-by-step explanation:
Therefore, 12 in roman numerals is written as XII = X + II = 10 + 2 = XII.
Which table is not a proportional relationship
Answer:
B and D
Step-by-step explanation
Answer:
D
Step-by-step explanation:
sequence in the earnings is unproportional difference between 27 and 54 is not 9Which would be the most appropriate way to estimate -6.1(0.22)? Check all that apply.
Use rounding to get -6(0.2), and then multiply.
Use compatible numbers, such as -6(0.5), and then multiply.
Use the benchmark numbers -6 and 1, and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Round the factors to the nearest whole number, and then multiply.
Answers to choose Please help me.
Use rounding to get -6(0.2), and then multiply.
Use compatible numbers, such as -6(0.5), and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Estimate -6.1(0.22)
Answer:
Use rounding to get -6(0.2), and then multiply.
Use front-end estimation to get -6(0.2), and then multiply.
Round the factors to the nearest whole number, and then multiply.
Step-by-step explanation:
Actual answer:
-6.1(0.22) = -1.342
Estimate answer:
-6 (.2) = 1.2
Answer:
A B D
Step-by-step explanation:
need help with pre-cal please
Answer:
x = n² ± n√(n² + 8)Step-by-step explanation:
x ≠ 0, n ≠ 04/x² + 1/x = 1/(2n²)(x + 4)/x² = 1/(2n²)2n²(x + 4) = x²x² - 2n²x - 8n² = 0D = (-2n²)² - 4(-8n²) = 4n⁴ + 32n² = 4n²(n² + 8)x = (2n² ± 2n√(n² + 8))/2x = n² ± n√(n² + 8)What is the meaning of the statement ((30) =76?
Answer:
A) 30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F
B) [tex]f(x)=-0.4x+88[/tex]
Step-by-step explanation:
A)
In this problem, f(x) represents temperature, in degrees Fahrenheit, of Sam’s house x minutes after the air conditioner started to cool the house.
So we have:
x = minutes after the air conditioner started to cool the house
f(x) = temperature
Here we want to find what is the meaning of
[tex]f(30)=76[/tex]
Which implies that:
[tex]x=30[/tex], which means that 30 minutes have passed after the conditioner has started to cool the house
[tex]f(x)=76[/tex], which means that the temperature of the room at that time is 76°F
So, the interpretation of f(30) =76 is that:
"30 minutes after the air conditioner started to cool the house, the temperature inside the house has dropped to 76°F"
B)
Here we want to write explicitly a function that tells us how the temperature inside the house varies as a function of x, the number of minutes passed after the air conditioner has turned on.
We know the following information:
- At time x = 0, the temperature inside the house is 88°F
- At time x = 30 min, the temperature inside the house is 76°F
We can assume that the temperature inside the house changes linearly with time; so, we can describe the temperature function with the equation of a line:
[tex]f(x)=mx+q[/tex]
where
[tex]q[/tex] is the value of the temperature at x = 0, so q = 88
m is the rate of change of the temperature
The rate of change can be found by calculating the rate of change of the temperature with respect to the change in time; so we find:
[tex]m=\frac{76-88}{30-0} =-0.4[/tex]
which means that the temperature decreases by 0.4°F every minute. So, the function can be written as
[tex]f(x)=-0.4x+88[/tex]
Please help! WILL MARK BRAINLIEST
Answer:
2nd option is correct
.........................
Answer:
1 1/9 ft^3
Step-by-step explanation:
5/3*1*2/3=10/9*1=10/9
10/9=1 1/9
Cindy made a scale drawing of a game room. The pool table, which is 8 feet long in real life,
is 4 inches long in the drawing. What is the scale of the drawing?
1 inch:
feet
Answer:
1 inch = 2 feet
Step-by-step explanation:
Answer:
1 inch ÷ 2 feetStep-by-step explanation:
According to given:
8 feet → 4 inDivide both by 4 to get the scale of drawing:
8/4 feet → 4/4 in2 feet → 1 inSuppose you and your friends order lunch at a mall restaurant, and the bill for your food is $28.50. If you want to leave a 12% tip, what is the total cost of the food plus the tip
Answer:
$31.92
Step-by-step explanation:
28.50 x .12 = 3.42
3.42 + 28.50 = $31.92
The total cost is thirty-one dollars and ninety-two cents, which includes a tip of three dollars and forty-two cents. Here’s one way to find these amounts.
Let’s set up a proportion. We can substitute the amounts we know into the proportion.
Now, we cross multiply. Amount of tip times one hundred equals twenty-eight dollars and fifty cents times twelve.
Then, we divide both sides of the equation by one hundred. The total cost is the food cost plus the amount of the tip. So, the total cost of the meal is thirty-one dollars and ninety-two cents.
In a raffle, 100 tickets are sold and 10 of the tickets, selected at random, win a $5 prize. A participant buys one ticket. What is the standard deviation of the amount won?
What are the solutions of y=x^2+5x-7
Answer:
You have two variables, and only one condition. It means you have infinite solutions of the form [tex](t; t^2+5t-7)[/tex]. Technically correct, probably not what you want to know.
If you wanted to know if and where the RHS crosses the x axis, the points are the solution to
[tex]x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)[/tex]
If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation [tex]x=-\frac52[/tex].
How to do the 9 multiplication trick.
Answer:
0123456789
9876543210
Step-by-step explanation:
09
18
27
36
45
54
63
72
81
90
Answer:
Step-by-step explanation:
for each 9 you add, take away 1 from the first number and add 10, like
81
72
63
52
41
32
23
18
9
(ASAP) i also need help with this plss
Answer:
The right answer is 32
Step-by-step explanation:
3/4 × 32 = 24
Answer:
18
Step-by-step explanation:
divide 24 by 4 which gives you 6. Multiply 6 by 3 which gives you 18 or (3÷4) × 24 = 18
help me please someone
Step-by-step explanation:
a scale factor means that every dimension or line in the original object is multiplied with the exact same factor to create a transformed (larger or smaller) new object.
the area of an object (including a simple form like this rectangle) is always the product of 2 dimensions.
that means the scale factor is multiplied in twice creating a squared factor for the area of the new object.
so, yes, therefore the area grows or shrinks with the square of the scale factor.
FYI - following the same reason, the volume grows or shrinks with the power of 3 of the scale factor.
1. k=2
new area = k² × old area = 4 × 12 = 48 square units.
2. k=5
new area = k² × old area = 25 × 12 = 300 square units.
3. k=1
new area = k² × old area = 1 × 12 = 12 square units.
4. k=1/4
new area = k² × old area = 1/16 × 12 = 12/16 = 3/4 square units.
5. k=1.2
new area = k² × old area = (1.2)² × 12 = (12/10)² × 12 = (6/5)² × 12 = 36/25 × 12 or 1.44 × 12 = 432/25 = 17.28 square units.
b
– 2 =
7
8
Write your answer as a fraction or as a whole or mixed number.
b =
Answer:80
Step-by-step explanation:
How to multiply decimal numbers.
Answer:
To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.
Step-by-step explanation: Hope it helps!!!!
Find the slope of each line of the graphs to the right. Which graph has the greater slope? Use pencil and paper. Explain how you know which graph has the greater slope without doing any calculations.
Answer:
Line 2
Step-by-step explanation:
line one's slope is one and line 2 is 3
Answer:
Line 2/Depending on the steepness of the line and which way it faces, we can easily determine which line has a larger slope - Any line that goes left to right is negative, and the steeper a line is, the more the farther negative/positive slope it has.
Step-by-step explanation:
Depending on the steepness of the line and which way it faces, we can easily determine which line has a larger slope - Any line that goes left to right is negative, and the steeper a line is, the more the farther negative/positive slope it has. The slope of line one is determined from rise over run. When we take the 2 points marked, we can count rise (4) and run (4), so we have 4/4, which is one. For line 2, we can do the same and get 3. Therefore, Line 2 has a greater slope