In a rhombus, the diagonals are perpendicular bisectors of each other, meaning they divide each other into two equal parts at a right angle. Let's denote the measure of ∠BAD as x degrees. The measure of ∠BAD is [tex]\( 26^\circ \)[/tex].
Since the angle bisector of ∠ACD makes a 64° angle with the diagonal BD, and BD bisects ∠ACD, then ∠ACB = 64° as well. Additionally, since ABCD is a rhombus, opposite angles are equal. Therefore, ∠ABD = ∠ACB = 64°.
Now, considering triangle ABD, we know that the sum of angles in a triangle is 180°. Thus:
[tex]\[ \angle BAD + \angle ABD + \angle ADB = 180^\circ \][/tex]
Substituting the known values:
[tex]\[ x + 64^\circ + 90^\circ = 180^\circ \][/tex]
[tex]\[ x + 154^\circ = 180^\circ \][/tex]
[tex]\[ x = 180^\circ - 154^\circ \][/tex]
[tex]\[ x = 26^\circ \][/tex]
So, the measure of ∠BAD is [tex]\( 26^\circ \)[/tex].
To summarize:
1. The angle bisector of ∠ACD in the rhombus makes a 64° angle with diagonal BD.
2. By the properties of a rhombus, ∠ACB = 64° as well.
3. Since opposite angles in a rhombus are equal, ∠ABD = ∠ACB = 64°.
4. In triangle ABD, the sum of angles is 180°.
5. Solving for ∠BAD, we find [tex]\( 26^\circ \).[/tex]
Volume is always measured in square units. True False
what id is 29/4 improper
What is the slope of the line that goes through (2, 5) and (-6, -2) ?
If a family has three pets, what is the theoretical probability that they have three dogs or three cats?
Write equations for the horizontal and vertical lines passing through the point (5, -6)
Horizontal line:
Vertical line:
which collection of three side lengths will not form a triangle
6, 10 18
10, 12 ,15
10, 15, 6
10, 18 ,12 please tell me how you figured it out.
To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem to each collection of side lengths given, we can determine which ones will form a triangle.
Explanation:A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For the collection 6, 10, 18, the sum of the two smaller sides (6 + 10) is less than the largest side (18), so this collection will not form a triangle.For the collection 10, 12, 15, the sum of the two smaller sides (10 + 12) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 15, 6, the sum of the two smaller sides (6 + 10) is greater than the largest side (15), so this collection will form a triangle.For the collection 10, 18, 12, the sum of the two smaller sides (10 + 12) is greater than the largest side (18), so this collection will form a triangle.How much money does the average professional football fan spend on food at a single football game? that question was posed to 10 randomly selected football fans. the sample results provided a sample mean and standard deviation of $14.00 and $2.50, respectively. use this information to construct a 90% confidence interval for the mean?
Solve this derivative using the quotient rule
PLEASE HURRY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Exponential Growth/Decay Function
The value of a car is $21,500. It loses 12% of its value every year.
(a) Write a function that represents the value y (in dollars) of the car after x years. (b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
Mr. Valenzuela’s new bottle of shampoo contains 60 ounces of shampoo. He uses ounce of shampoo each time he washes his hair. Which equation can be used to find x, the number of washes after which 24 ounces will remain in the bottle?
Answer:the number of washes after which 24 ounces will remain in the bottle is:
36 washes.
Step-by-step explanation:
The correct answer is 18.
To find the equation that can be used to determine the number of washes (x) after which 24 ounces of shampoo will remain in the bottle, we need to set up an equation based on the given information.
Given information:
- Initial amount of shampoo in the bottle (I) = 60 ounces
- Amount used per wash (U) = 2 ounces
- Remaining amount after x washes (R) = 24 ounces
[tex]I - (U \times x) = R[/tex]
[tex]60 - (2 \times x) = 24[/tex]
[tex]60 - 24 = 2x[/tex]
[tex]36 = 2x[/tex]
[tex]x = \frac{36}{2}[/tex]
[tex]x = 18[/tex]
Therefore, the equation that can be used to find x is:
[tex]60 - (2 \times x) = 24[/tex]
And the number of washes after which 24 ounces of shampoo will remain in the bottle is 18.
How to find turning point of (c-2)^3+8
Hannah keeps her marbles in bags with for marbles in each bag she writes 3/4 to show the number of red marbles in each bag find another fraction to name the number of red marbles in 2 bags
She keeps 4 marbles in every bag and mark it with 3/4 to represent red marbles in the bag. It means there are 3 Red marbles out of total 4 marbles in the bag.
It says to write another fraction to represent number of red marbles in two bags.
Since one-bag contains 3 Red marbles out of total 4 marbles in the bag.
Then two-bags would contain 2x3 Red marbles out of total 2x4 marbles in the bag i.e. 6 Red marbles out of total 8 marbles in the bag.
So, [tex] \frac{6}{8} [/tex] is the another fraction to show number of red marbles.
F = {(-1, 2), (3, 2), (4, 2), (0, 2)} Is F a function and why/why not?
How do you do question number 5? If you do it can you please explain how to do it? Thank you!!
Answer:
F(-3) = 4(-3) - 3 = -12 - 3 = -15.
H(2) = -5(2) + 7 = -10 + 7 = -3.
F(-3) + H(2) = -15 + -3 = -18.
The solution is -18.F(-3) = 4(-3) - 3 = -12 - 3 = -15.
H(2) = -5(2) + 7 = -10 + 7 = -3.
F(-3) + H(2) = -15 + -3 = -18.
Step-by-step explanation:
A sandwich shop has 30 stores and 60% of the stores are in California. The rest of the stores are in Nevada. How many stores are in California amd bow many are in Nevada?
Answer:
18
Step-by-step explanation:
a 0.149-kilogram baseball, initially moving at 15 meters per second, is brought to rest in 0.040 seconds by a baseball glove on a catchers hand. the magnitude of the average force exerted on the ball by glove is
Using the relationship between force and acceleration, the average force exerted on the ball by the glove is :55.875 N
Given the Parameters :
Mass, m = 0.149 kg Velocity, V = 15 m/s Time, t = 0.040 secondsRecall :
Force = Mass × acceleration Acceleration = Δv / tForce = (mΔv ÷ t)
Inputting the Values into the equation :
Force = [0.149 × (15 - 0)] ÷ 0.040
Force = (0.149 × 15) ÷. 0.040
Force = 2.235 ÷ 0.040
Force = 55.875 N
Therefore, the force exerted is 55.875 N
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0.5x+78.2=287 whats the value of x
Elevator 1 moved up 10 feet from the ground level. Its position is labeled as +10. Elevator 2 moved down 5 feet from the ground level. Its position is labeled as _____. (Use the hyphen for negative such as -1)
geometric mean for 12 and 3
For the number -5/8 name the opposite, reciprocal and absolute value
opposite:
Reciprocal:
Absolute value:
You can rake a 20 square meter lawn in 10 minutes. If your mother asks you to rake your own lawn, which is 30 square meters, how long will it take you to do this?
simplify 4 (-w + 8) by distributing.
Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.) How many different card designs are possible?
Answer:
The different card designs possible are:
224
Step-by-step explanation:
It is given that:
There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
As she has to choose one from each given item this means she will use a combination to choose the item.
We know that the combination for r choices out of total n choices is given as:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Hence, the total combinations made are given as:
[tex]2_C_1\times 4_C_1\times 7_C_1\times 4_C_1\\\\\\=\dfrac{2!}{1!\times (2-1)!}\times \dfrac{4!}{1!\times (4-1)!}\times \dfrac{7!}{1!\times (7-1)!}\times \dfrac{4!}{1!\times (4-1)!}\\\\=2\times 4\times 7\times 4\\\\=224[/tex]
Hence, the different card designs that are possible are:
224
The different card designs that are possible will be 224. The formula for the combination is used to solve the problem.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order.
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
The given data in the problem is;
Paula is going to choose 2 sizes, 4 colors, 7 phrases, and 4 pictures . If the one item has to be chosen;
The total combination is;
[tex]= \rm 2C_1 \times 4C_1 \times 7C_1 \times 4 C_1 \\\\ = \frac{2!}{1!\times (2-1)!} \times \frac{4!}{1! \times (4-1)!} \times \frac{7!}{1!\times (7-1)!} \times \frac{4!}{1!\times (4-1)!} \\\\ =2 \times 4 \times 7 \times 4 \\\\ =224[/tex]
Hence different card designs are possible will be 224.
To learn more about the permutation and combination refer;
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P= s-c/s solve for c
Therefore, the solution for c in terms of P and s is c = s(1 - P).
To solve for c in the equation P = (s - c) / s, you want to isolate c on one side. Here's the step-by-step:
Multiply both sides by s to eliminate the denominator: P × s = s - c.
Distribute P within s: Ps = s - c.
Now, get all terms containing c on one side: c = s - Ps.
So, the solution for c in terms of P and s is c = s - Ps, or c = s(1 - P).
Please help asap!!!
Which expression is equivalent to -9x^-1y^-9/-15^5y^-3
A.3/5x^5y^3
B.3/5x^6y^6
C.5/3x^5y^3
D.5/3x^6y^6
during the rice of industrialization in the 1840s the majority of immigrants come from
solve the system of equations algebraically.
List 3 values that would make this inequality true 4n <_ 12
If the dimensions of a square pyramid are measured in yards, then the volume of the pyramid is measured in
Answer: The volume of the pyramid is measured in cubic yards.
Step-by-step explanation: Given that the dimensions of a square pyramid are measured in yards.
We are to find the unit in which the volume of the pyramid is measured.
We know that
the volume of a square pyramid with length of base edge 'a' units and height 'h' units is given by
[tex]V=\dfrac{1}{3}a^2h~\textup{cubic units}.[/tex]
Here, length of base edge 'a' and the height 'h' of the given square pyramid is measured in yards.
Therefore, the volume of the pyramid will be measured in
[tex]\textup{yards}\times \textup{yards}\times \textup{yards}\\\\=\textup{cubic yards}.[/tex]
Thus, the volume of the square pyramid is measured in cubic yards.
The tangent line has the form y=mx+b . use tl above to find b +juliabox