Answers
The measure of ∠C in the given triangle is 58°.
According to the question,
We have the following information:
ACD is a triangle where we have BD as an altitude on the side AC.
Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.
Now, we have two right-angled triangle: ABD and CBD.
We have ∠ADB = 32°.
Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).
We know that the sum of the three angles in a triangle is 180°.
In ΔCBD, we have:
∠B + ∠C + ∠CDB = 180°
90° + ∠C + 32° = 180°
∠C + 122° = 180°
∠C = (180-122)°
(Moving 122 from the left hand side to right hand side will result in the change of sign.)
∠C = 58°
Hence, the measurement of ∠C in the given triangle is 58°.
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Related Questions
NEED HELP ASAP 25 pointsWhich equation best describes the data in the table?x y-2 -41 -73 1 6 28options:a. y=x-2b. y=3x-4c. y=x^2-8d. y=2x^2-3
Answers
To determine the equation that best describe the data in the table, let us substitute the value of x given on the table into each equation and check for the equation that gives us the corresponding values of y;
for x = -2, y=-4; substituting x= -2 into each equation, we have;
[tex]\begin{gathered} a)y=x-2=-2-2=-4 \\ b)y=3x-4=3(-2)-4=-16 \\ c)y=x^2-8=-2^2-8=4-8=-4 \\ d)y=2x^2-3=2(-2)^2-3=5 \end{gathered}[/tex]From the first substitution, only equation a and c gave us the corresponding value of y.
Secondly, let's substitute another value of x into the two right right equaabove to confirm the best;
At x=1, y= -7; substituting x=1 into equation a and c we have;
[tex]\begin{gathered} a)y=x-2=1-2=-1 \\ c)y=x^2-8=1^2-8=-7 \end{gathered}[/tex]From the above only equation c gave us the corresponding value of y at x=1.
Since only equation c gave us the corresponding values of y for both substituttions. The equation that best describe the data on the table is equation cequatio
[tex]c\text{. }y=x^2-8[/tex]Can someone solve this I don’t understand the graph
Answers
The graph given in the problem is the function of cosine that is;
y = -cos x
How to find the function which was used to make a graph?A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it. If the function crosses x-axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
Suppose that we've got:
f(x) = a cos (bx - c) + d
Then, this function has the Amplitude (the maximum distance of the graph from the middle line) = a
Period = [tex]\dfrac{2\pi}{b}[/tex]
Phase shift = [tex]\dfrac{c}{b}[/tex]
Maximum value: a + d
Minimum value: -a + d
Here we can see that the graph is the function of cosine that is;
y = -cos x
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What is an equation of the line that passes through the points (4, -3) and
(5, -5)?
Answers
Hope this helps :)
Britany is bringing birthday cake and cookies to her office. She has already spent $10.00 on the cake. Cookies cost $0.70 each, and she does not wish to spend more than $34.50 for all desserts. If x represents the number of cookies she can buy, which of the following inequalities symbolizes this situation?
A.
$10.00x + $0.70 < $34.50
B.
$0.70x + $10.00 < $34.50
C.
$0.70x + $10.00 < $34.50
D.
$10.00x + $0.70 < $34.50
Answers
Considering the definition of an inequality, the correct answer is option C. the inequiality $0.70x + $10.00 < $34.50 symbolize this situation
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.The solution of an inequality is the set of numbers that make the inequality true.
Inequality in this caseIn this case, you know that:
Britany has already spent $10.00 on the cake. Cookies cost $0.70 each. She does not wish to spend more than $34.50 for all desserts.Being "x" the number of cookies Britany can buy, the inequality that expresses the previous relationship is
10 + 0.70x <34.50
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The Winchester Opera House sold 4,600 tickets this year, but it has been experiencing a 10%drop in sales from one year to the next. If this trend continues, then how many tickets willthe opera house sell 8 years from now?
Answers
Exponential decay formula:
[tex]y=a(1-r)^t[/tex]y is the number of tickets sold at t years
a is the initial number of tickets sold
r is the rate of drop (in decimal form)
t is the time in years
[tex]y=4600(1-0.1)^t[/tex]8 years from now:
[tex]\begin{gathered} y=4600(1-0.1)^8 \\ \\ y=4600(0.9)^8 \\ \\ y=1980.149 \end{gathered}[/tex]Then, if the trend continues, 8 years from now the number of tickets sell will be approximately 1980if the work required to stretch a spring 3 ft beyond its natural length is 15 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length? give your answer in decimal form.
Answers
The amount of work needed to stretch the spring 18 in. from its natural position is 3.75 ft-lb.
According to the Hooke's Law, the work done on the spring is:
W = 1/2. k . x²
Where:
k = spring constant
x = displacement.
Notice that the work done is directly proportional to x².
Hence,
W₁ : W₂ = x₁² : x₂²
Parameters given:
W₁ = 15 ft-lb
x₁ = 3 ft
x₂ = 18 in. = 1.5 ft
Plug the above parameters into the ratio equation:
15 : W₂ = 3² : (1.5)²
W₂ = (1.5)² . 15 / 3² = 15/4 = 3.75 ft-lb
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For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar-water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
Answers
The container whose sugar water mixture is a darker shade of red is: A. the small bowl's mixture is a darker shade of red.
What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, the ratio of the sugar water mixture in the small bowl (S) to the sugar water mixture in the large bucket (L) can be represented by this mathematical expression:
S:L = 1:3
Also, when red coloring is added to both containers, we have:
S:L = 1r:3r
In this context, we can reasonably and logically deduce that the mixture in the small bowl would have a darker shade of red because it is less diluted in comparison with the sugar water mixture in the large bucket.
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Complete Question:
For her science fair project, Madelyn is growing crystals with sugar water. She wants to know if the size of the container has an effect on crystal growth. To start, Madelyn pours a sugar water mixture into a small bowl. Then she pours triple the amount of the mixture into a large bucket. She decides to add red coloring so the crystals are more visible. Madelyn adds the same amount of red coloring to both containers. Which container's sugar water mixture is a darker shade of red?
answer choices
The small bowl's mixture is a darker shade of red.
The large bucket's mixture is a darker shade of red.
Neither. The mixtures are the same shade of red.
solve B please thanks
Answers
The remaining zeroes of p are x = [tex]\sqrt{6}[/tex] or x = -[tex]\sqrt{6}[/tex].
Given,
The equation is :
p(x) = [tex]4x^3+x^2-24x-6[/tex]
c = -1/4
To find the remaining zeroes of p
Now, According to the question:
[tex]4x^3+x^2-24x-6[/tex]
Apply grouping
[tex](4x^3+x^2)+(-24x-6)=0[/tex]
Factor out common factor
[tex]x^{2} (4x+1)-6(4x+1)=0[/tex]
[tex](x^2-6)(4x+1)=0[/tex]
Apply zero Product Property
4x +1 = 0 or [tex]x^{2} -6=0[/tex]
x = -1/4 or x = [tex]\sqrt{6}[/tex] or x = -[tex]\sqrt{6}[/tex]
Hence, The remaining zeroes of p are x = [tex]\sqrt{6}[/tex] or x = -[tex]\sqrt{6}[/tex].
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Write the equation in slope intercept form: x-3y=12
Answers
Answer:
[tex]\\ y = \frac{1}{3} x - 4[/tex]
Step-by-step explanation:
Hope this helps! :))
-9 (-5 - 4c) simplify the expression and show your work. please this is due tomorrow
Answers
The simplified value of the expression given as -9 (-5 - 4c) is 45 + 36c
How to simplify the expression?From the question, the expression is given as
-9 (-5 - 4c)
To simplify the expression, we start by opening the bracket
So, we have the following equation
-9 (-5 - 4c) = -9 (-5 - 4c)
Remove the brackets
So, we have
-9 (-5 - 4c) = -9 x -5 -9 x - 4c
Evaluate the products
So, we have
-9 (-5 - 4c) = 45 + 36c
Hence, the value of the expressions is -9 (-5 - 4c) = 45 + 36c
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Two models are shown. Which expression does each model represent?
Move the correct answer to each box. Not all answers will be used.
Answers
Put this shopping list into BIMDAS format (as above) and then show the steps to reach the answer.
Answers
Based on the given shopping list, when put in BIMDAS format and then solved, the total amount would be $26.90
How to find the total?In BIMDAS format, we have to solve the problem in the brackets first and then use the order of operations to find the total shopping cost.
The BIMDAS format would be:
= (Number of orange dozens x Cost per dozen) + (Number of bacon packets x Cost per packet) + (Number of strawberry packets x Price per packet)
= (3 x 4.50) + (2 x 2.50) + (2 x 4.20)
The solve those in the brackets:
= 13.5 + 5 + 8.40
Then add the costs to find the total cost on the shopping list:
= 13.5 + 5 + 8.40
= $26.90
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Based on the shopping list given in the problem, in BIMDAS format and then solved, the total amount will be; $26.90
How to find the total?In BIMDAS format, we need to solve the problem in the brackets first and then use the order of operations to determine the total shopping cost.
The BIMDAS format is:
= (Number of orange dozens x the Cost per dozen) + (Number of bacon packets x the Cost per packet) + (Number of strawberry packets x the Price per packet)
= (3 x 4.50) + (2 x 2.50) + (2 x 4.20)
The solutions in the brackets:
= 13.5 + 5 + 8.40
Then add the costs for the total cost on the shopping list which is;
= 13.5 + 5 + 8.40
= $26.90
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can someone help me out with this?
Answers
Answer:
area of triangle is length *breathe
4.5 * 5.5 = 24.75
23+107+x=180
It’s on triangle pls I need the answer
Answers
Answer: 50 degrees
Step-by-step explanation: 23+107+x=180
130+x=180
x=50
3.) Martin charges $10 for every 5 bags of leaves he rakes, Last weekend, he raked 25 bags of leaves. How much money did he earn?
Answers
bags of leaves : 5
Cost = $10
Divide the cost by the number of bags:
10/5 = $2 per bag
Now, multiply by 25
2 x 25 = $50
please help tell me if correct or not
Answers
What is the length of AC?
Answers
Answer:
126 units!
Step-by-step explanation:
I hope this helped!! c:
HELP! WILL GIVE BRAINLIEST
Answers
Answer:
second answer
Step-by-step explanation:
Which of the following correctly uses the distributive property to multiply 12 and 9?
(10 x 10) − (2 x 1) = 100 − 2 = 98
(10 x 10) + (2 x 1) = 100 + 2 = 102
(10 x 9) − (2 x 9) = 90 − 18 = 72
(10 x 9) + (2 x 9) = 90 + 18 = 108
Answers
Answer:
(10 x 9) + (2 x 9) = 90 + 18 = 108
Step-by-step explanation:
This is the answer because you break 12 into different parts, multiply them separately multiply them with nine. You can check the answer by doing 12*9 = 108 which matches what we need.
Which expression is equivalent to (m^−5n^−3)^−3?
Answers
Answer:
[tex]m^{15} n^{9}[/tex]
Step-by-step explanation:
When inflating a balloon, which of the following represents an equal but opposite force acting on the balloon?
A.) releasing the balloon
B) the air entering the balloon
C) tying the balloon
D) the expansion of the balloon
Answers
When inflating a balloon, the expansion of the balloon represents an equal but opposite force acting on the balloon
What is force?A force is an influence that has the power to alter an object's motion. A force can cause an object with mass to accelerate when it changes its velocity, for as when it moves away from rest. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction. It is calculated using the newton SI unit (N). Force is denoted by the letter F.Thrust, which increases an object's velocity; drag, which decreases an object's velocity; and torque, which causes changes in an object's rotational speed, are all concepts connected to force. Each part of an extended body often exerts stresses on the sections that are nearby; the distribution of these forces throughout the body is what is known as the internal mechanical stress. Due to the balance of the forces, such internal mechanical stresses do not generate acceleration of that body. Pressure is a straightforward form of stress that, if unbalanced, can cause the body to accelerate. Pressure is the distribution of several small forces applied over an area of a body. Stress typically results in the flow of fluids or the deformation of solid materials.To learn more about force, refer to
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A construction crew is lengthening a road that originally measured 10 miles. The crew is adding one mile to the road each day.Let L be the length (in miles) after D days of construction.Write an equation relating L to D. Then graph your equation using the axes below.
Answers
Let:
L = length of the road
D = Days of construction
We can write a linear equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where:
m = Slope = rate = 1 mile per day
b = y-intercept = Initial value = 10 miles
Therefore:
[tex]\begin{gathered} L=1D+10 \\ L=D+10 \end{gathered}[/tex]The graph is:
what the meaning of geometric sequence?
Answers
Answer:
What is the meaning of geometric sequence?
Step-by-step explanation:
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.
Answer:
Below.
Step-by-step explanation:
It is a sequence of numbers with a common ratio. That is, each term after the first is obtained by multiplying the previous one by the common ratio.
Examples:
2, 6, 18, 54 ... is a geometrics sequence with common ratio 3.
1, 1/2, 1/4, 1/8 ... has a common ratio of 1/2.
-1, 1, -1, 1, -1 ... has a common ratio of -1.
The nth term of a geometric sequence is given by
a r^(n-1) where a = first term and r = common ratio.
How much of a radioactive kind of nitrogen will be left after 30 minutes if you start with 1,920 grams and the half-life is 10 minutes?
Answers
1,920/10= 192
192/10= 19.2
19.2/10= 1.92
10+10+10= 30
A line has a slope of -2 and includes the points (8, 10) and (10, a). What is the value of a?
Answers
Answer: 6
Step-by-step explanation:
m = -4 / 2 = -2 / 1 = -2
5/3x+1/3x=11 1/3+8/3x
Answers
Answer:
-111/2
Step-by-step explanation:
Please look at the attachment below! :D
taylor is repairing a gate and needs to nail a brace diagnally to strengthen the posts. if the height of the post is 48 inches and there is 64 inches between posts, in inches, what should the length of the diagonal brace be in order to fit between the posts?
Answers
The hypotenuse bracing must be 80 inches long in order to fit between the posts, when the height of the post is 48 inches and there is 64 inches between posts i.e base.
We must understand that a right angle is formed by the height of a post and the horizontal space between posts. The hypotenuse of a right triangle is then the diagonal that connects one post's highest point to its lowest point. The length of this hypotenuse can then be determined using the Pythagorean theorem.
The Pythagorean theorem states that H2 = P2 + D2, where P is the height of a post (cathetus), D is the distance between posts (cathetus), and H is the hypotenuse (diagonal).
We can substitute these values since we are aware of them:
H² = (48inches)² + (64inches)² = 2,304inches² + 4,096inches² = 6,400inches²
H= [tex]\sqrt{6400}[/tex] inches
H = 80inches
Therefore, The length of the diagonal brace be in order to fit between the posts is 80 inches.
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there are 90 girls and 60 boys in the sixth grade at kimbrough middle school. Of these
students, 9 girls and 3 boys write left-handed. What percentage of the sixth graders at this middle school write left-handed?
Answers
The percentage of the sixth graders at this middle school write left-handed is 8%.
How to calculate the percentage?Since there are there are 90 girls and 60 boys in the sixth grade at kimbrough middle school. The total number will be:
= 90 + 60
= 150 students
Since 9 girls and 3 boys write left-handed, this will give a total of 9 + 3 = 12
Therefore the percentage for left handed people will be:
= Number of left handed people / Total students × 100
= 12 / 150 × 100
= 8%
The percentage is 8%.
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A cardboard box, which weighs 0.6 pound when empty, is filled with 15 bags of beans and a 4-pound bag of rice. The total weight of the box and the contents inside it is 25.6 pounds. One way to represent this situation is with the equation 0.6 + 15b + 4 = 25.6.
What does the solution represent in this situation?
Answers
The solution b = 1.4 represents the weight of one bag of bean.
In the question;
it is given that
weight of cardboard box when empty = 0.6 pounds
number of bean bags = 15 bags
weight of rice bag = 4 pounds
let the number of bean bags = b
total weight of carboard box with contents= 25.6 pounds
So , according to the question
0.6 + 15b + 4 = 25.6
solving further , we get
15b+4.6 = 25.6
15b = 25.6-4.6
15b = 21
b = 21/15
b = 1.4
Therefore , the solution b = 1.4 represents the weight of one bag of bean.
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three young brother-sister pairs from different families need to take a trip in a van. these six children will occupy the second and third rows in the van, each of which has three seats. to avoid disruptions, siblings may not sit right next to each other in the same row, and no child may sit directly in front of his or her sibling. how many seating arrangements are possible for this trip?
Answers
The number of permutations possible to seat the 3 pairs of siblings in a way that one may not sit right next to their sibling and no child may sit directly in front of his or her sibling is 96.
A permutation cannot be formed with siblings in the same row.
As a result, each row should have siblings from various families.
Any of the six youngsters can take the first seat.
After deducting the kid who currently occupies the first seat and their sibling, the second seat can be filled by any of the four children.
permutation = 6 × 4
permutation = 6 × 4 × 2
Now, for the third row, there are only 3 children left to be seated.
Only 2 out of the remaining three can be seated in the first position.
Hence, the remaining possibility is 2.
permutation = 6 × 4 × 2 × 2
Similarly, the third row can only be filled with one possibility remaining of the 6 since it is not allowed to seat siblings right up front.
permutation = 6 × 4 × 2 × 2 × 1 × 1 = 96
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