Triangle that is congruent to triangle CBE could be any of the following, for instance:BED, ABC, or FCE.
What are two sets of angles that are similar?The triangles are congruent when the respective sides between two pairs of corresponding angles are also congruent. Two triangles having a congruent side in the middle and two congruent angles on either side.
What is the congruent pair?In geometry, two shapes or objects are said to be congruent if they have the same dimensions, or if one is the mirror image of the other.
1. The angles formed by the same line FA and two parallel lines running between it, FCE and CAB, are congruent angles. For the same reason, FEC and EDB are congruent angles.
2. Based on the assertion, we will write the measure of each angle.
The line AD contains the triangles ABC, CBE, and EBD. If we add all of the triangles together to form the line, which has a measure of 180 degrees, the angle CBE is 72°.
3. Congruent triangles are those with all of their angles equal. Since all of the triangles are replicas of triangle ABC, they are all congruent because they all measure the same but are positioned differently. Therefore, a triangle that is congruent to triangle CBE could be any of the following, for instance:
BED, ABC, or FCE
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the price of a new pair of headphones is 128.50 of the 15% off what is the sale price of the headphones
Answer:
$109.23
Step-by-step explanation:
Discount = 128.5 × 15/100
Discount = 128.5 x 0.15
You save = $19.28
Final Price = Original Price - Discount
Final Price = 128.5 - 19.275
Final Price = $109.23
The nth term of a sequence is -5 + n
Work out the 40th term of the sequence.
The 40th term of the sequence is 35 if the nth term is given as -5 + n.
Given,
nth term, aₙ = - 5 + n or n - 5
For 40th term n = 40
or 40th term = a₄₀ = 40 - 5
a₄₀ = 35
Therefore, the 40th term of the sequence is 35, if the nth term is given as -5 + n.
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20. Choose the correct solution graph for the inequality. (1 point)
-6x > 42
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
1 2
The solution is Option D.
The inequality equation is x < -7
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
-6x > 42 be equation (1)
On simplifying the equation , we get
Divide by -1 on both sides of the equation , we get
6x < -42
Divide by 6 on both sides of the equation , we get
x < -42/6
On further simplification , we get
x < -7
So , the values of x are all integers which are less than -7 but not including -7
So , the values of x are = { -8 , -9 , -10 , ..... }
Therefore , the values of x are integers less than -7
Hence , the inequality equations is x < -7
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3. A music store sells a guitar for $45. If the local sales tax is 6%, what is the total cost of the guitar, including tax? Do NOT use a dollar sign in your
Answer:
47.70
Step-by-step explanation:
6%= 2.7
2.7 +45
=47.7
The equation of line p is y=ax+b. Which of these could be the equation of line q?.
The equation of line p is y = ax + b then y = -2ax + b + 3 could be only the equation of line q out of the given options.
Therefore, the answer is C) y = -2ax + b + 3.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. So in case of line p, a is the slope and b is the y-intercept. Let equation of q by y = m'x + b'.
From the figure it is evident that line p has a positive slope while line q has a negative slope. So slope of q is negative of slope of line q multiplied by a positive constant, say c, then
m' = -2ac
From figure we can observe that y-intercept of p is 0 and q has a positive y-intercept, so
b' = b + k, k is a positive constant
So equation of q is y = -2acx + b + k, where c and k are positive constants. So only option C is of this format.
--The question is incomplete, answering to the question below--
"The equation of line p is y = ax + b. Which of these could be the equation of line q?
A. y = -2a(x + 3) + b
B. y = -2ax + b
C. y = -2ax + b + 3
D. y = -2ax + b - 3"
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345 x 564 divided by 3x - 2y
Answer:
-97290
Step-by-step explanation:
Snacks and more sells a 3-pound bag of mixed nuts for $15.75. Healthy snacking sells a 2.5-pound bag of mixed nuts for $13.50
The unit price at Snacks and Healthy are $5.25 and $5.4 respectively.
How to determine the unit price?Generally speaking, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In order to determine the unit price, we would determine the unit rate for the cost per pound bag of mixed nut by using the following mathematical expression;
Unit price = Cost of a pound bag of mixed nuts/number of nuts
Substituting the given parameters into the unit price formula, we have the following;
Unit price for Snacks = 15.75/3
Unit price for Snacks = $5.25.
Unit price for Healthy = 13.50/2.5
Unit price for Healthy = $5.4.
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Complete Question:
Snacks and more sells a 3-pound bag of mixed nuts for $15.75. Healthy snacking sells a 2.5-pound bag of mixed nuts for $13.50. What is the unit price at Snacks and Healthy?
Point N is located at -12−12. Points O and P are each 1010 units away from Point N. Where are O and P located? help
Answer:
Step-by-step explanation:
something
6x-5+x+8+2x-3=180 help I have a test tomorrow
Answer:
x=20
Step-by-step explanation:
6x-5+x+8+2x-3=180
6x+x+2x-5+8-3=180
9x=180
x=20
Answer:
x=20
Step-by-step explanation:
1. Add all like terms together.
(9x=180)
2. Then divide 9 to isolate the variable.
(x=20)
What is an equation of the line that passes through the points (5,-4) and
(-5,4)
The equation of the line will be 8x+10y=0
The equation of a line when two points are given is
y-y₁=m(x-x₁)
where,m=(y₂-y₁)/(x₂-x₁)
Here, m=(4--4)/(-5-5)
=8/-10
Now,
y-(-4) = (8/-10)(x-5)
-10y-40=8x-40
8x+10y=0
The equation is 8x+10y=0
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Question Progress Homework Progress 26/ 5 + √2 4+√8 can be written in the form where r and s are both integers. What are the values of r and s? r - s√2 4 66%
A rhombus has an angle measure of 120 and it’s longer diagonal has a length of 10 inches. Find the area of the rhombus.
If a rhombus has an angle measure of 120 and it’s longer diagonal has a length of 10 inches. The area of the rhombus is 28.85.
How to find the area?Obtuse angle = 120 so, the other two angles must add up to 60 and each would be half of 60 or 30.
Hence,
Sin 30° = 0.5
Sin 60° = 0.86602540378
Now let find the length of breadth
Length of breadth = 0.5 / 0.86602540378
Length of breadth = 0.577
Now let find the area using this formula
A =b × h
Where:
b=0.577
h=0.5
A = 0.577 x 0.5
A = 0.2885
A = 28.85
Therefore the area is 28.85.
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pls solve this question (i will mark the brainliest who answer rightly)
Answer:
the first answer is 18, the second is -16, the third answer is 26, and the last is 24
Step-by-step explanation:
What is the product of the complex numbers (- 3i 4 and 3i 4?
The product of these two complex numbers is calculated by multiplying the real numbers and imaginary parts separately and then combining them, resulting in -25.
Step 1: Multiply the real parts: (-3i * 3i = -9i^2
Step 2: Multiply the imaginary parts: 4 * 4 = 16
Step 3: Combine the results: -9i^2 + 16 = -25
(-3i * 3i) + (4 * 4) = -9i^2 + 16 = -25
Complex numbers consist of two parts - a real part and an imaginary part. To find the product of two complex numbers, both the real and imaginary parts must be multiplied separately, and then the results combined. In this example, (-3i 4 and 3i 4), the real parts are multiplied together to get -9i2. The imaginary parts are multiplied together to get 16. These results are then combined to get the product of the complex numbers, which is -25. To complete the calculation, we must also take into account that the imaginary part is always multiplied by the coefficient i. This means that the result of the real part multiplication is -9i2, not just -9.
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The given lengths 80 and 82 are two sides of a right triangle. All three side lengths of the triangle are integers and together
form a Pythagorean triple. Find the length of the third side and tell whether it is a leg or the hypotenuse.
A hypotenuse of 162
A leg of 162
A hypotenuse of 115
A hypotenuse of 18
A leg of 13
A hypotenuse of 13
A leg of 18
A leg of 115
A hypotenuse of 4
A leg of 4
By using Pythagorean theorem to find the length of the hypotenuse, we get the answer as hypotenuse of 115
What is Pythagorean triple?A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the legs of the right triangle.
What is hypotenuse?In a right triangle, the hypotenuse is the side that is opposite the right angle. It is the longest side of the triangle and it is always opposite the 90-degree angle. The other two sides of the right triangle are called the legs, and they form the right angle.
we can use the Pythagorean theorem to find the length of the hypotenuse:
a^2 + b^2 = c^2
82^2 + 80^2 = c^2
6724 + 6400 = c^2
c = √(6724 + 6400) = √13124
c = 114.74
Since all three sides of the triangle have to be integers and the hypotenuse is the one that should have the largest value, we can round the value of c up to 115
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SOMEONE PLEASE HELP ME ANSWER ….If 3 is added to a number and the sum is triple the results is 17 more than the number find the number
The number that represents the system in this problem is given as follows:
x = 4.
How to obtain the number?The number is unknown, hence the variable that represents the number is given as follows:
x.
Then an equality is built from the sentence in the problem, which is then solved to obtain the number.
The addition of 3 to a number is given as follows:
x + 3.
The triple the sum is given as follows:
3(x + 3).
The result is 17 more than the number, hence the equality is given as follows:
3(x + 3) = 17 + x.
Then the solution for the equality, which gives the number, is obtained as follows:
3x + 9 = 17 + x
3x - x = 17 - 9
2x = 8
x = 8/2
x = 4.
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leo reads 12 pages in 1/4 hour. what is the unit rate for pages per hour? For hours per page?
Answer:
3
Step-by-step explanation:
to find the rate you have to multiply the fraction so...
12 (the pages) times 1/4 (the hour) you get 3
Answer:
48 pages per hour; 3 hours per page
Step-by-step explanation:
A). You can find the unit rate for pages per hour by first multiplying the hours by its reciprocal, 4, which essentially becomes 1 hour and what you do to one side must be done to the other side, so multiplying 12 by 4 gets you 48 pages. Therefore, Leo reads 48 pages per hour.
B). To find hours per page, you do the same thing, except that this time, you divide 12 on each side because you are trying to find the hours per page. 12 pages divided by 12 gets you 1 page and dividing 1/4 by 12 is the same thing as multiplying 1/4 by 12 since when dividing fractions with another fraction, the method is to use the reciprocal of the second fraction (in this case, 1/12 becomes 12) and you change the sign to its inverse and you simplify. A helpful acronym you can use is this. KEEP IT, CHANGE IT, FLIP IT . You keep the first fraction as it is, change the sign to its inverse, and flip the second fraction (virtually, the reciprocal). Therefore, in this case, it becomes 1/4 times 12 and 12 divided by 4 is nothing but 3.
Thus, Leo takes 3 hours to read each page.
Hope this helped! :D
A survey was conducted to investigate whether alcohol consumption and smoking are related. In a random
sample of 300 smokers, 196 said they had consumed alcohol at least once in the past week. In an
independent random sample of 300 non-smokers, 159 said they had consumed alcohol in the past week. If
P, is the proportion of smokers in the population who have had a drink in the past week and P is the
corresponding proportion of non-smokers, then a test of the hypotheses H, P, -P-0 against the two-sided alternative produces a test statistic of z=3.07 and a P-value of 0.002. If we had instead analyzed these results with a chi-square test of homogeneity, which of the following would be the test statistic and P-value?
a-942, P-value = 0.002
b. -942, P-value-0.004
-3.07, P-value - 0.004
d. -1.75, P-value = 0.002
e-1.75, P-value=0.004
e) The test statistic and P-value for the chi-square test of homogeneity would be -1.75 and 0.004, respectively.
A chi-square test of homogeneity is a useful tool for comparing two or more categorical variables. In this case, the two variables are smoking (smokers and non-smokers) and alcohol consumption (those who had consumed alcohol in the past week and those who hadn't).
The chi-square statistic is calculated by finding the difference between the observed and expected frequencies of the two groups and squaring it. The expected frequencies are found by multiplying the sample size by the overall probability of success (in this case, drinking alcohol).
The P-value is then calculated based on the chi-square statistic and the degrees of freedom (in this case, one). In this case, the chi-square statistic is -1.75 and the P-value is 0.004.
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Find the Least Common Multiple of 9 and 20.
A.180
B. 90
C. 120
D. 20
E. 60
The coordinate 3 has a weight of 2, and the coordinate 9 has a weight of 1. Find the weighted average
For the coordinates and their weights, the weight average is 5
How to determine the weight average of the points?From the question, we have the following parameters that can be used in our computation:
Coordinates and weights
The coordinates and weights are then given as:
Coordinate 3 has a weight of 2Coordinate 9 has a weight of 1The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
Substitute the known values in the above equation
So, we have the following equation
Weight average = (3 * 2 + 9 * 1)/(2 + 1)
Evaluate the product in the above equation
So, we have the following equation
Weight average = (6 + 9)/(2 + 1)
Evaluate the sum in the above equation
So, we have the following representation
Weight average = (15)/(3)
Evaluate the quotient in the above equation
So, we have the following equation
Weight average = 5
Hence, the weight average of the coordinates is 5
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graph the sentence to this inequality on the number line.
-16 > —4p
p<4 is the solution of the given inequality.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is -16>-4p
Minus sixteen greater than minus four p
Divide both siders by -4
4>p
p<4
Now we have to draw this on number line.
a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
The attached figure has the graph of p<4.
Hence, p<4 is the solution of the given inequality.
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Simplify the expression.
v686a4y?
• A.
• B. 7,27 1/223°
O c. 7223 1229
O D.
Answer:
A
Step-by-step explanation:
[tex]\sqrt[3]{686x^{4}y^{7}} = \sqrt[3]{343*2x^{3+1}*y^{6+1}}=\sqrt[3]{343*2x^{3}*y^{6}*xy}=\sqrt[3]{7^{3}}\sqrt[3]{x^{3}}\sqrt[3]{y^{6}}\sqrt[3]{2xy}=7xy^{2}\sqrt[3]{2xy}[/tex]
Please I really need help with this question
The equation of the line is y = 0.5x + 1 having a slope of 0.5 and y intercept of 1
How to solve an equationThe equation of a line is:
y = mx + b
Where m is the slope and b is the y intercept
From the table shown, the points are:
(-6, -2), (-4, -1), (-2, 0), (0, 1) and (2, 2)
Using any two points to get the equation. Let us use (-2, 0) and (0, 1):
y - 0 = [(1 - 0)/(0-(-2))](x - (-2))
y = 0.5x + 1
The equation of the line is y = 0.5x + 1
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At a certain university, students who live in the dormitories eat at a common dining hall. Recently, some students have been complaining about the quality of the food served there. The dining hall manager decided to do a survey to estimate the proportion of students living in the dormitories who think that the quality of the food should be improved. One evening, the manager asked the first 100 students entering the dining hall to answer the following question. Many students believe that the food served in the diniog tall necds improvement. Do you think that the quality of food served here needs improvement, even though that would increase the cost of the meal plant? a. In this setting, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. b. In this setting, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.
Based on the provided information, a) bias is introduced through convenience sampling there could be specific variable associated with the first hundred students. It can be avoided by simple random sampling. b) bias is introduced through wording as it includes a negative consequence. It can be avoided by just asking for an opinion without any associated reasoning or consequences.
Bias refers to a deviation of feedback which is based on certain influences by the surveyor and respondent. Sampling bias or selection bias refers to a type of bias in which a researcher gathers a sample of respondents for a questionnaire that does not accurately represent the population. Survey bias refers to the way the question is phrased or formatted, leading people to choose a certain answer instead of another. In the given case,
a) A bias may have been introduced based on the way the convenience sample was selected as there could be specific variable associated with each of the first hundred students that walk into the dining room. The first hundred students could possibly like the food and that is the reason why they come early to the dining room. Selecting students at the dining room may also exclude the students who dislike the food and choose to eat elsewhere. A simple random sample can help avoid this bias. By randomly selecting students at the university campus would provide a more inclusive and true representation of the population.
b) A bias may have been introduced based on the way the question is worded is to maintain the current meal plan as it presents a negative consequence to introducing a new meal plan. It states that a new meal plan would result in more cost. In order to avoid bias, the survey should ask students opinion about the food without introducing any external reasoning.
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Kimberley is taking part in a race. For the first 160 m she runs at 4 m/s. The remaining 420 m of the race takes her 120 seconds. What is Kimberley's average speed, in m/s, over the whole race? If your answer is a decimal, give it to 2 d.p.
if BCF ~ BDE, solve for x
Answer:
x = 10
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{BE}{BF}[/tex] = [tex]\frac{BD}{BC}[/tex] ( substitute values )
[tex]\frac{56+5x-8}{56}[/tex] = [tex]\frac{52+39}{52}[/tex] , that is
[tex]\frac{48+5x}{56}[/tex] = [tex]\frac{91}{52}[/tex] ( cross- multiply )
52(48 + 5x) = 56 × 91 = 5096 ( divide both sides by 52 )
48 + 5x = 98 ( subtract 48 from both sides )
5x = 50 ( divide both sides by 5 )
x = 10
60 POINTS ANSWER THE QUESTION FOR BRAINLIST AND HEARTS, USE MY GRAPTH PLS!
Answer:
Step-by-step explanation:
What is the factored form of -15w+9wz-6z+10
The factored form of the equation -15w + 9wz - 6z + 10 is,
⇒ (3w - 2) (3z - 5)
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 equation is,
⇒ -15w + 9wz - 6z + 10
Now, Factor the equation as;
⇒ -15w + 9wz - 6z + 10
⇒ 3w (- 5 + 3z) - 2(3z - 5)
⇒ 3w (3z - 5) - 2 (3z - 5)
⇒ (3w - 2) (3z - 5)
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Which of the following quadratic equations has roots 3, 5 ?
(A) x²-15x+8=0
(B) x²-8x+15=0
(C) x²+3x+5=0
(D) x²+8x-15=0
Answer:
[tex]x^2-8x+15=0[/tex]
Step-by-step explanation:
If the roots are [tex]3[/tex] and [tex]5[/tex], the factors are [tex](x-3)[/tex] and [tex](x-5)[/tex].
Taking the leading coefficient as 1, the equation is [tex](x-3)(x-5)=0 \implies x^2-8x+15=0[/tex].
Quadrilateral DEFG is a rhombus and angle CED=s-25. What is the value of s?
The value of s, considering that quadrilateral DEFG is a rhombus, is given as follows:
s = 55.
How to obtain the value of s?To obtain the value of S, we must consider triangle CED, and the fact the sum of the measures of the internal angles of a triangle is of 180º.
The measures of the internal angles of triangle CED are given as follows:
<C = 90º. (the diagonals of the rhombus are perpendicular).<D = 60º. (the center of the rhombus is a bisection).<E = s - 25.As the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle E is given as follows:
90 + 60 + <E = 180
150 + <E = 180
<E = 30º.
As <E = s - 25, the value of s is obtained as follows:
s - 25 = 30
s = 30 + 25
s = 55.
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