Answers
In any pair of similar triangles, (side side side )
Each correspondent side has the same ratio so let's examine
ΔCDE and ΔFGH
Related Questions
Factor the quadratic expression2x²+x-62x+ +x-6= (Factor completely.)
Answers
2x² + x - 6
The coefficient of x² is 2 and the constant term is -6. The product of 2 and -6 is -12. The factors of -12 which sum 1 are -3 and 4 so:
2(2x - 3) + x(2x - 3)
Factor 2x - 3 from 2(2x - 3) + x(2x - 3):
(2x - 3)(x + 2)
I’m confused on this question. I just have to choose which one
Answers
SOLUTION:
Case: Circle theorems
Method:
From the given circle
Theorem: The angle at the center of the circle is twice the angle at the circumference formed by the same segment.
The implication to the circle in the question is:
[tex]\begin{gathered} \hat{mST}=2m\angle2 \\ OR \\ m\angle2=\frac{1}{2}(\hat{mST}) \end{gathered}[/tex]Final answer
[tex]m\operatorname{\angle}2=\frac{1}{2}(\hat{mST})[/tex]I need help on doing this finding the slope of a line
Answers
Given:
[tex](x_1,y_1)=(1,6)and(x_2,y_2)=(6,1)[/tex][tex]\text{Slope(m)=}\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\text{Slope(m)=}\frac{1-6}{6-1}[/tex][tex]\text{Slope(m)}=-\frac{5}{5}[/tex][tex]\text{Slope (m)=-1}[/tex]Find the expression for the possible width of the rectangle.
Answers
Given the area of the rectangle is given by the following expression:
[tex]A=x^2+5x+6[/tex]The area of the rectangle is the product of the length by the width
So, we will factor the given expression
To factor the expression, we need two numbers the product of them = 6
and the sum of them = 5
So, we will factor the number 6 to find the suitable numbers
6 = 1 x 6 ⇒ 1 + 6 = 7
6 = 2 x 3 ⇒ 2 + 3 = 5
So, the numbers are 2 and 3
The factorization will be as follows:
[tex]A=(x+3)(x+2)[/tex]So, the answer will be the possible dimensions are:
[tex]\begin{gathered} \text{Length}=x+3 \\ \text{Width}=x+2 \end{gathered}[/tex]A stock is worth $28,775 and drops 33% in one day. What percent does the stock have to grow the next day to get back to $28,775
Answers
ANSWER:
49.254%
STEP-BY-STEP EXPLANATION:
The first thing is to calculate the value after it has drops by 33%, like this:
[tex]\begin{gathered} 28775-28775\cdot33\% \\ \\ 28775-28775\cdot0.33 \\ \\ 28775-9495.75=19279.25 \end{gathered}[/tex]Now, we calculate what should grow by the following equation:
[tex]\begin{gathered} 19279.25+19279.25\cdot \:x=28775\: \\ \\ x=\frac{28775\:-19279.25}{19279.25} \\ \\ x=\frac{9495.75}{19279.25} \\ \\ x=0.49254\cong49.254\% \end{gathered}[/tex]The percent that should grow is 49.254%
Find all solutions in[0, 2pi): 2sin(x) – sin (2x) = 0
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Based on the answer choices, replace the pair of given values and verify the equation, as follow:
For x = π/4, π/6
[tex]2\sin (\frac{\pi}{4})-\sin (\frac{2\pi}{4})=2\frac{\sqrt[]{2}}{2}-1\ne0[/tex]the previous result means that the given values of x are not solution. The answer must be equal to zero.
Next, for x = 0, π
[tex]\begin{gathered} 2\sin (\pi)-\sin (2\pi)=0-0=0 \\ 2\sin (0)-\sin (0)=0-0=0 \end{gathered}[/tex]For both values of x the question is verified.
The rest of the options include π/4 and π/3 as argument, you have already shown that these values of x are not solution.
Hence, the solutions for the given equation are x = 0 and π
[tex] f(x) = 3x^{2} - 2x + 3[/tex]if (-3,n) is an element of the function what is the value of n?
Answers
SOLUTION
[tex]\begin{gathered} f(x)=3x^2\text{ - 2x + 3 } \\ \text{Here, (-3, n) can be written as (x, y), where x = -3 and y = n} \\ \text{Also y is also = f(x). } \\ \text{That is y = }3x^2\text{ - 2x + 3 } \end{gathered}[/tex]Now putting x = -3 into f(x) or y, we have that
[tex]\begin{gathered} y=3(-3)^2\text{ -2(-3) + 3} \\ y\text{ = 3(9) + 6 + 3} \\ y\text{ = 27 + 6 + 3} \\ y\text{ = 36. } \\ \text{Since y = n, therefore, n = 36. } \end{gathered}[/tex]The value of n is 36
Finding an output of a function from its graphThe graph of a function fis shown below.Find f (0).543-2f(0) =I need help with this math problem.
Answers
Given:
Given a graph of the function.
Required:
To find the value of f(0), by using graph.
Explanation:
From the given graph
[tex]f(0)=-4[/tex]Final Answer:
[tex]f(0)=-4[/tex]Jackson purchased a pack of game cards that was on sale for 22% off. The sales tax in his county is 6%. Let y represent the oeiginal price of the card.. Wrote an expression that can be used to determine the final cost of the cards.
Answers
Given:
Discount - 22% = 0.22
Sales Tax - 6% = 0.06
Required:
Expression for the final cost of the cards, x
Solution:
Let: y represent the original price of the card.
x represent the final cost of the cards
D represent the discounted cost of the cards
Assume that the the sales tax is applied to the price after the discount.
D= Original Price ( 1 - Discount) = y ( 1 - 0.22) = 0.78y
To compute for the final cost,
Final Cost = D + Tax
Tax = 0.06 D
x = D + 0.6(D)
x = 1.06D
x = 1.06 ( 0.78 y)
x = 0.827y
Answer:
The final cost of the card can be describe by the expression:
x = 0.827y
A baby cows growth. About how many pounds does the baby cow gain each week?
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Growth per week = 124 - 122 = 126 - 124 = 2
. = 2 pounds + 1 pound additional
. = 3
Then answer is
OPTION B) 3 pounds
Shaun deposits $3,000 into an account that has an rate of 2.9% compounded continuously. How much is in the account after 2 years and 9 months?
Answers
The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
find the equation of the axis of symmetry of the following parabola algebraically. y=x²-14x+45
Answers
Answer:
x = 7, y = -4
(7, -4)
Explanation:
Given the below quadratic equation;
[tex]y=x^2-14x+45[/tex]To find the equation of the axis of symmetry, we'll use the below formula;
[tex]x=\frac{-b}{2a}[/tex]If we compare the given equation with the standard form of a quadratic equation, y = ax^2 + bx + c, we can see that a = 1, b = -14, and c = 45.
So let's go ahead and substitute the above values into our equation of the axis of symmetry;
[tex]\begin{gathered} x=\frac{-(-14)}{2(1)} \\ =\frac{14}{2} \\ \therefore x=7 \end{gathered}[/tex]To find the y-coordinate, we have to substitute the value of x into our given equation;
[tex]\begin{gathered} y=7^2-14(7)+45 \\ =49-98+45 \\ \therefore y=-4 \end{gathered}[/tex]need help. first correct answer gets brainliest plus 15 pts
Answers
We are given that lines V and 0 and lines C and E are parallel.
We are asked to prove that ∠15 and ∠3 are congruent (equal)
In the given figure, angles ∠3 and ∠7 are "corresponding angles" and they are equal.
[tex]\angle3=\angle7[/tex]In the given figure, angles ∠7 and ∠6 are "Vertically opposite angles" and they are equal.
[tex]\angle7=\angle6[/tex]Angles ∠6 and ∠14 are "corresponding angles" and they are equal.
[tex]\angle6=\angle14[/tex]Angles ∠14 and ∠15 are "Vertically opposite angles" and they are equal.
[tex]\angle14=\angle15[/tex]Therefore, the angles ∠15 and ∠3 are equal.
[tex]\angle3=\angle7=\angle6=\angle14=\angle15[/tex]if [tex] \sqrt{ \times } [/tex]is equal to the coordinate of point D in the diagram above, then X is equal to:
Answers
11)
The number line is divided into 5 equal intervals. if the fourth segment is 7, then we would find the distance between each segment
The distance between the fourth segment and the first segment is 7 - - 1 = 8
Since we are considering the distance between segment 1 and segment 4, the distance between each segment would be
8/4 = 2
Thus,
point D = 7 + 2 = 9
If
[tex]\begin{gathered} \sqrt[]{x\text{ }}\text{ = D, then} \\ \sqrt[]{x}\text{ = 9} \\ \text{Squaring both sides of the equation, we have} \\ x=9^2 \\ x\text{ = 81} \end{gathered}[/tex]Option E is correct
ten B В 15 cm А 20 cm С C
Answers
Tangent segment, of a circle
Apply formulas
20^2 - 15^ 2 = AB^2
Also
15^2 = 20•( 20 - AB)
225 = 400 - 20AB
Then
20AB = 400-225= 175
AB = √ 175= 13 + 6/25 =13.24
(Algebra 1 Equivalent equations)
In a family, the middle child is 5 years older than the youngest child.
Tyler thinks the relationship between the ages of the ages of the children can be described with 2m-2y=10, where m is the age of the middle child and y is the age of the youngest.
Explain why Tyler is right.
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Let the middle child is m and youngest is y.
The middle child is 5 years older than the youngest child, it can be shown as:
m - y = 5Tyler's equation is equivalent to ours since it can be obtained by multiplying both sides of our equation by 2:
2(m - y) = 2*52m - 2y = 10 ⇔ m - y = 5So Tyler is right.
Solve the equation.k²=47ks.(Round to the nearest tenth as needed. Use a comma to separate answers as needed.
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The initial equation is:
[tex]k^2=47[/tex]Then, we can solve it calculating the square root on both sides:
[tex]\begin{gathered} \sqrt[]{k^2}=\sqrt[]{47} \\ k=6.9 \\ or \\ k=-6.9 \end{gathered}[/tex]Therefore, k is equal to 6.9 or equal to -6.9
Answer: k = 6.9 or k = -6.9
13 nickels to 43 dimes in a reduced ratio form
Answers
The reduced ratio form of 13 nickels to 43 dimes is 13/86.
What is a ratio?
a ratio let us know that how many times one number contains another number.
We are given 13 nickels and 43 dimes.
We know that 1 dime equal to 2 nickels.
Hence 43 dimes equals 86 nickels.
Now we find the ratio of the 2.
Which will be [tex]\frac{13}{86}[/tex]
Hence the reduced ratio form is 13/86.
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Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 timesExperiment result on previews question: The number 5 was rolled 9 times out of 20 on a previous question
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Explanation: To understand this problem we need to know that there are two different types of probability. The experimental probability and the theoretical probability.
- The experimental probability occurs once you conduct the experiment and after the experiment, you calculate the probability using the result of the experiment.
- The theoretical probability occurs before the experiment. Once you have information about the situation so you calculate the probability the get a specific result before trying.
Step 1: For this question, once we have a number cube with faces 1,2,3,4,5 and 6 and we want to know the experimental probability to get a 5 once you roll the cube 300 times you would need to get in real life a number cube and to roll it 300 times. After this experiment we would get all the results of each time we roll it and we would know how many times (from 300 times) we got a number 5. After that, we would use the following formula
[tex]Experimental_{probability}=\frac{number\text{ of times we got a number 5}}{300}[/tex]Once the get this result we finish the question.
do you think you'd be able to help me with this
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x = wz/y
Explanation:[tex]\frac{w}{x}=\frac{y}{z}[/tex]To solve for x, first we need to cross multiply:
[tex]w\times z\text{ = x }\times y[/tex]Now we make x the subject of the formula:
[tex]\begin{gathered} To\text{ make x stand alone, we n}ed\text{ to remove any other variable around x} \\ \text{divide both sides by y}\colon \\ \frac{w\times z}{y}\text{ =}\frac{\text{ x }\times y}{y} \end{gathered}[/tex][tex]x\text{ = }\frac{wz}{y}[/tex]12/13+-1/13 equals what ?
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Given:
[tex]\frac{12}{13}+(-\frac{1}{13})[/tex]Adding a negativen number is the same as subtracting that number, so:
[tex]\frac{12}{13}-\frac{1}{13}[/tex]Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)
[tex]\frac{(12-1)}{13}=\frac{11}{13}[/tex]Answer:
[tex]\frac{11}{13}[/tex]Josslyn placed $4,400 in a savings account which earns 3.2% interest, compounded annually. How much will she have in the account after 12 years?Round your answer to the nearest dollar.
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The equation for the total amount after compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}^{}[/tex]Where A is the final amount, P is the initial amount, r is the annual interest, n is how many times per year the interest is compounded and t is the time in years.
Since the interest is compounded annually, it is compounded only once per year, so
[tex]n=1[/tex]The other values are:
[tex]\begin{gathered} P=4400 \\ r=3.2\%=0.032 \\ t=12 \end{gathered}[/tex]So, substituteing these into the equation, we have:
[tex]\begin{gathered} A=4400(1+\frac{0.032}{1})^{1\cdot12} \\ A=4400(1+0.032)^{12} \\ A=4400(1.032)^{12} \\ A=4400\cdot1.4593\ldots \\ A=6421.0942\ldots\approx6421 \end{gathered}[/tex]So, she will have approximately $6421.
he two-way frequency table given shows the results from a survey of students who attend the afterschool program.
Takes Art Class Doesn't Take Art Class Total
Plays a Sport 45 120
Doesn't Play a Sport 45
Total 225
Does the data show an association between taking an art class and playing a sport?
There is a strong, positive association.
There is a strong, negative association.
There is a weak, positive association.
There is a weak, negative association.
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The association between the variables art class and playing a sport is classified as follows:
There is a strong, negative association.
What is the association between the two variables?The association between variables can be classified either as positive or as negative, as follows:
Positive: both variables behave similarly, either both increases or both decreasing.Negative: the variables behave in an inversely manner, with one increasing and the other decreasing, or vice-versa.In the context of this problem, it is found that of the students that take art class, the majority do not play a sport, while among those who do not take art class, the majority play a sport, hence there is a strong and negative association between the two variables.
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Question
Mrs. Hanson has a potato salad recipe that calls for 238 pounds of potatoes, but she wants to make 112 times as much as the recipe calls for.
The diagram represents the number of pounds of potatoes that Mrs. Hanson needs.
How many pounds of potatoes does Mrs. Hanson need?
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Answer:
3 9/16 lbs
Step-by-step explanation:
69=2g-24 I NEED TO FIND G
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Add 24 to 69 to get 93. Then divide 93 by 2 to get G
A house has increased in value by 35% since it was purchased. If the current value is S432,000, what was the value when it was purchased?
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The value of the house when it was purchased = $32000
Explanation:The original percentage value = 100%
The current percentage value = 100% + 35% = 135%
Current value = $432000
Original value = x
[tex]\begin{gathered} The\text{ current value =}\frac{135}{100}\times The\text{ original value} \\ \\ 432000=1.35\times x \\ \\ x=\frac{432000}{1.35} \\ \\ x=$ 320000 $ \end{gathered}[/tex]The value of the house when it was purchased = $32000
Which inequality is equivalent to this one?y-83-2O y-8+82-2-8O y 8+82-248o y 8+22-248o Y8+ 25-242
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Given the inequality:
[tex]y-8\le-2[/tex]If we add 2 on both sides, the inequality remains the same and we get:
[tex]y-8+2\le-2+2[/tex]2. What is the greatestcommon factor of12. 18, and 36?
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The Solution:
Given the numbers below:
12, 18 and 36.
We are asked to find the greatest common factor of the above numbers.
Note:
Greatest Common Factor means Highest Common Factor (HCF).
Recall:
The Greatest common factor of 12, 18 and 36 is the highest number that can divide 12, 18 and 36 without any remainder.
Thus, the correct answer is 6.
Can someone do it for me please
Answers
Step-by-step explanation:
13.
a/7 + 5/7 = 2/7
a/7 = 2/7 - 5/7 = -3/7
a = -3
14.
6v - 5/8 = 7/8
6v = 7/8 + 5/8 = 12/8
v = 12/8 / 6 = 2/8 = 1/4
15.
j/6 - 9 = 5/6
j - 54 = 5
j = 5 + 54 = 59
16.
0.52y + 2.5 = 5.1
0.52y = 5.1 - 2.5 = 2.6
y = 2.6/0.52 = 5
17.
4n + 0.24 = 15.76
4n = 15.76 - 0.24 = 15.52
n = 15.52/4 = 3.88
18.
2.45 - 3.1t = 21.05
-3.1t = 21.05 - 2.45 = 18.6
t = 18.6/-3.1 = -6
Write an expression to determine the surface area of a cube-shaped box, S A , in terms of its side length, s (in inches).
Answers
The cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
What is a cube?A three-dimensional object with six equal square faces is called a cube. The cube's six square faces all have the same dimensions.
A cube is become by joining 6 squares such that the angle between any two adjacent lines should be 90 degrees.
A cube is a symmetric 3 dimension figure in which all sides must be the same.
The cube has six equal squares.
It is known that the surface area of a square = side²
Therefore, the surface area of the given cube is 6 side².
Given cube has side length = s
So,
Surface area = 6s²
Hence the cube consists of 6 equal faces thus the surface area of the cube in terms of its side length s is 6s².
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