Answer:
8 cm^2
Step-by-step explanation:
If the triangle is isosceles the sides are the same
Let the sides be x
We know that we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse
x^2+x^2 = (4 sqrt(2))^2
2x^2 =16(2)
2x^2 = 32
Divide by 2
2x^2/ 32/2
x^2 = 16
Taking the square root of each side
sqrt(x^2) = sqrt(16)
x = 4
The area of the triangle is
A =1/2 bh
A = 1/2 (4) (4)
A = 1/2(16)
A = 8
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
c = [tex]4\sqrt{2}[/tex]
[tex]c^{2} = 32[/tex]
a^2 + b^2 = 32
a=b (isosceles triangle)
a=b=4
base = 4
height = 4
area = 1/2 bh = 1/2(4)(4) = 8
Drag each equation to the correct location on the table.
Match the equations with the value of x that makes them true.
5x - 2x - 4 = 5
5x - (3x - 1) = 7
x + 2x + 3 = 9
2(2x - 3) = 6
4x - (2x + 1) = 3
5(x + 3) = 25
x = 2
X = 3
Answer:
The answer to your questions are given below.
Step-by-step explanation:
To answer the question given above, we shall determine the value of x in each equation. This can be obtained as follow:
5x - 2x - 4 = 5
3x - 4 = 5
Collect like terms
3x = 5 + 4
3x = 9
Divide both side by 3
x = 9/3
x = 3
5x - (3x - 1) = 7
Clear the bracket
5x - 3x + 1 = 7
2x + 1 = 7
Collect like terms
2x = 7 - 1
2x = 6
Divide both side by 2
x = 6/2
x = 3
x + 2x + 3 = 9
3x + 3 = 9
Collect like terms
3x = 9 - 3
3x = 6
Divide both side by 3
x = 6/3
x = 2
2(2x - 3) = 6
Clear the bracket
4x - 6 = 6
Collect like terms
4x = 6 + 6
4x = 12
Divide both side by 4
x = 12/4
x = 3
4x - (2x + 1) = 3
Clear the bracket
4x - 2x - 1 = 3
2x - 1 = 3
Collect like terms
2x = 3 + 1
2x = 4
Divide both side by 2
x = 4/2
x = 2
5(x + 3) = 25
Clear the bracket
5x + 15 = 25
Collect like terms
5x = 25 - 15
5x = 10
Divide both side by 5
x = 10/5
x = 2
SUMMARY:
x = 2
x + 2x + 3 = 9
4x - (2x + 1) = 3
5(x + 3) = 25
x = 3
5x - 2x - 4 = 5
5x - (3x - 1) = 7
2(2x - 3) = 6
Write the inequality shown in this graph.
Answer:
y > -1/2 x + 4
Step-by-step explanation:
Equation of a line : (y-y1)/(y2-y1) = (x-x1)/(x2-x1)
(y-4)/(2-4)= (x-0)/(4-0)
(y-4)/-2 = x/4
(-y+4)/2 = x/4
-y+4 = 1/2 x
-y = 1/2 x - 4
y = -1/2 x + 4
the solutions of the inequality are the points above this line, so
y > -1/2 x + 4
Rearrange to make P the subject, :)..
Answer: [tex]P = \frac{25}{E^2}-Q\\\\[/tex]
Work Shown:
[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]
A runner’s distribution of times for running 1,000 meters has a mean of 4.5 minutes with a standard deviation of 0.75 minutes. One of the runner’s times has a z-score of –1.08. Which of the following statements is the best interpretation of this z-score?
This runner’s time was faster than the mean time by 0.75 standard deviations.
This runner’s time was faster than the mean time by 1.08 standard deviations.
This runner’s time was slower than the mean time by 0.75 standard deviations.
This runner’s time was slower than the mean time by 1.08 standard deviations.
Answer:
I believe it is (C).
This runner’s time was slower than the mean time by 0.75 standard deviations.
ED2021
Answer:
B) This runner’s time was faster than the mean time by 1.08 standard deviations.
Step-by-step explanation:
The runner is FASTER because of the negative z score
Does the function f(x) = (0.68)^x represent exponential growth, decay, or neither?
Answer:
The function is always Decreasing
Step-by-step explanation:
By graphing the polyminal in order to determine the intervals over which it is increasing or decreasing we find that it always decreasing.
A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 8 feet per second, at what rate is the area of the triangle formed by the wall, the ground, and the ladder changing, in square feet per second, at the instant the bottom of the ladder is 12 feet from the wall?
Answer:
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
Step-by-step explanation:
From the question we are told that:
Slant height [tex]h=13ft[/tex]
Velocity [tex]v=\frac{dx}{dt}=8[/tex]
Distance [tex]d=12ft[/tex]
Generally the equation for area is mathematically given by
[tex]A=0.5*x*sqrt(169 - x^2)[/tex]
Differentiating
[tex]\frac{da}{dx}=\frac{169-2 x^2}{(2 sqrt(169-x^2))}[/tex]
Multiplying through by dx/dt
[tex]\frac{da}{dx}*\frac{dx}{dt}=\frac{169-2 x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-2x^2}{(2 \sqrt{169-x^2})}*\frac{dx}{dt}[/tex]
[tex]\frac{da}{dt}=\frac{169-(2*12^{2})}{2*\sqrt{(169-12^{2})}}*8[/tex]
[tex]\frac{da}{dt}=-95.2m/s^2[/tex]
the area of a triangular garden is 200 square feet. If the base is 30 feet more than its height, what is the base of the garden?
The base of the triangular garden is calculated as 40 ft
The given parameters include:
the area of the triangular garden, A₁ = 200 ft²let the height of the triangular garden = hthe base of the triangular garden, b = 30 ft + hThe area of a triangle is given as;
[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]
Now solve for 'b' = 30 ft + 10 ft = 40 ft
Therefore, the base of the garden is 40 ft
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!!I NEED THE ANSWER PLS!!
Which of the following represents the divisor and the dividend for the
synthetic division problem below?
- 3/ 2 4 -4 6
A. -3 and -2x2 - 4x2 + 4x-6
B. x+3 and -2x2 - 4x +47-6
C. X+3 and 2x + 4x2 - 4x+6
D. *-3 and 2x2 + 4x2 - 4x+6
Answer:
B
Step-by-step explanation:
B . x+3 and -2x2 - 4x +47-6
B . x+3 and -2x2 - 4x +47-6
The divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
What is synthetic division?"It is a way of dividing one polynomial by another polynomial of first degree."
What is dividend?"The value that is divided by another value to get the result. "
What is divisor?"The value that divides another number either completely or with a remainder."
For given question,
We have been given a synthetic division problem.
- 3/ 2 4 -4 6
We need to represent the divisor and the dividend for the given synthetic division problem.
We know that, to perform synthetic division, here are the steps:
- The leading coefficient of the divisor should also be 1.
- Express the dividend in standard form.
- Write the leading coefficient in the dividend.
- Place the product of the number you brought down and the number in the division box in the preceding column.
- Write the result at the bottom of the row.
So, the divisor of the given synthetic division form would be,
x - (-3) = x + 3
And the dividend of the given synthetic division form would be,
There are four leading coefficient.
This means the dividend polynomial must be of degree 3.
From the leading coefficients 2 4 -4 6
[tex]2x^3+4x^2-4x+6[/tex]
Therefore, the divisor and the dividend for the given synthetic division problem are : [tex]x+3[/tex] and [tex]2x^3+4x^2-4x+6[/tex]
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If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be? If a rope 36 feet long is cut into two pieces in such a way that one piece is twice as long as the other piece, how long must the long piece be
Answer:
24feet
Step-by-step explanation:
the first rope well give it letter X and the longer rope we'll give it 2x since it's twice then we add the two unknown numbers which must lead to a total of 36feet when we add the unknown digits we'll get 3x then simply the unknown digit with the total and u'll get 12 replace the X from the first letters with 12by multiplying
linear relation between c and n
Why is this? It's because each time x goes up by 2, y is also increasing by 2. The rate of change is constant. I'm treating n as x, and C as y.
Another way to see why we have a linear function is to pick any two points from that table, and apply the slope formula
m = (y2-y1)/(x2-x1)
You should find that no matter which two rows you pick, you should get a slope of 1.
Lastly, you can plot the three points from the table to find they all are on the same straight line as shown below. So there are at least 3 different ways to justify choice B as the answer.
Side note: The equation of the line is y = x-7, which then translates over to C = n-7.
A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent. The class has suggested four different methods. Which describes the correct method? Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Answer:
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
its B
Option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The expressions are [tex]4x-x+5 , 8-3x-3[/tex]
If the expressions are equivalent then,
⇒ [tex]4x-x+5 = 8-3x-3[/tex]
⇒ [tex]3x+5=-3x+5[/tex]
In both the sides the x has different values.
So, Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Hence we can conclude that option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
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A certain positive integer has exactly 20 positive divisors.
What is the largest number of primes that could divide the integer?
thx for the help in advance
9514 1404 393
Answer:
3
Step-by-step explanation:
20 has at most 3 proper factors greater than 1: 2×2×5. Each of these can represent a prime factor of the number of interest, and is 1 more than that prime's power. That is, the number of interest (n) will have at most 3 prime factors p, q, r, and will be ...
n = p·q·r^4
_____
For some prime factorization ...
[tex]\displaystyle n=\prod_{k=1}^m{p_k^{q_k}}[/tex]
The total number of divisors of n is ...
[tex]\displaystyle\prod_{k=1}^m{(q_k+1)}[/tex]
a farmers field is 440 feet long and the length is 4 times the width of the field how wide is the field
Answer:
110 feet
Step-by-step explanation:
Take x as the width of the field.
4x = 440 feet
x = 440 feet ÷ 4
x = 110 feet
So, the field is 110 feet wide #
Which of these figures has rotational symmetry?
O A.
O B.
C.
O D.
The figure has rotational symmetry from the given options is shown in Figure B.
What is rotational symmetry?When a figure is rotated (by a certain amount) about a set point on its surface (often the center), and retains its original appearance, it is said to have rotational symmetry.
According to the given question,
We have the given options in this question:
Assuming that the problem in this instance does not require full rotation (because after full rotation, any figure appears to itself when it returns to its original location as it did before), the first figure that possesses rotational symmetry can be chosen.
It is because you obtain the same figure whether you rotate the first figure by a quarter, half, or quarter and a half rotation. For any of the other stated figures, it won't occur (you can imagine those figures rotating, and then will notice that only option B has rotation symmetry for other angles in addition to full rotation).
Therefore, the figure from the listed figures which has rotational symmetry is Figure B.
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Question
Alice drove her car 279 miles in 6 hours. Write this rate as a reduced fraction.
Answer:93/2 or 46.5 mph
Step-by-step explanation:
Answer:
93/2Step-by-step explanation:
•Form the given into a fraction using m/hrs format279/6•Reduced the fraction279 ÷ 3----------- 6 ÷ 3•Final answer93/2[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Sport Chek conducts customer satisfaction surveys by having its customers complete questionnaires regarding their customer service experience. Their computer system automatically sends surveys to customers who spend more than $100 at their store. What type of bias might result?
a) Response Bias
b) Sampling Bias
c) Both response bias and sampling bias
d) Neither response bias or sampling bias
Answer:
b
Step-by-step explanation:
Because only the customers who spend more than $100 get to complete the form. The other customers wont be able to complete it(people who spent less than $100). thats why the answer would be sampling bias.
Write a linear equation representing the information shown in the table.
A) y = 2x + 10
B) y = –2x + 10
C) y = 10x – 2
D) y = 10x + 2
Answer:
b
Step-by-step explanation:
y=-2x+10
y=-2×0+10 y=10
y=-2×1+10 y=8
y=-2×2+10 y=6
y=-2×3+10 y=4
Answer: B. y = –2x + 10
Step-by-step explanation:
Can someone please help me with part b ? It would be so appreciated you have no idea ;)
Answer:
absolutely yes, because pythagorean theorem is used in a right triangle
and when we match a line from the tee to the hole, we have a right triangle
Step-by-step explanation:
A researcher would like to investigate whether or not there is a difference in IQ between Psychology and History majors. She gathers 16 students (8 whose major is Psychology, and 8 whose major is history) and has them all take an IQ test to test this hypothesis using an alpha level of .01. Below are the data: Psych History
110 90 120 98 100 100 90110 124 100 102 120 110 110 123 120
a. What is the appropriate test?
b. State the null hypothesis:
c. State the alternative hypothesis:
d. Find the critical value:
e. Calculate the obtained statistic:
f. Make a decision:
g. What does your decision mean?
Answer:
Paired t test
H0 : μd = 0
H1 : μd > 0
Critical value = 3.499
Test statistic = 2.230
Reject H0 if test statistic > Critical value
Kindly check explanation.
Step-by-step explanation:
Given the data :
110 90 120 98 100 100 90 110
124 100 102 120 110 110 123 120
The hypothesis :
H0 : μd = 0
H1 : μd > 0
Tcritical value, df = n - 1 = 8 - 1 = 7
Tcritical(0.01, 7) = 3.499
The difference, d = (-14,-10,18,-22,-10,-10,-33,-10)
The test statistic :
Xdbar / Sd/√n
The mean difference, Xdbar = Σx / n = - 11.375
The standard deviation of difference, Sd = 14.431
The test statistic :
-11.375 / (14.431/√8) ;
-11.375 / 5.102
= 2.230
Decison :
Reject H0 if test statistic > Critical value
Since ; 2.230 <3.499 ;
We fail to reject the null
Express 8:28 in its simplest form
which of these figures has rotational symmetry
9514 1404 393
Answer:
A
Step-by-step explanation:
The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.
_____
Additional comment
When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.
how do you tell how many times greater is the 5 in 458,039 than the 5 in 271,145
Answer:
count the number of places it is. The 5 in 458,039 is in the 10,000 place and the 5 in 271,145 is in the ones place so the 5 in 458,039 is 10,000 times greater
What is the value of the expression below? (27^2/3)^1/2
A. 9
B. 81
C. 27
D. 3
Answer:it’s 3
Step-by-step explanation:
Source trust me bro
F(x) = x +3; G(x) = 2x^2 -4 Find (f*g)(x)
9514 1404 393
Answer:
(f·g)(x) = 2x^3 +6x^2 -4x -12
Step-by-step explanation:
The distributive property is used to find the expanded form of the product.
(f·g)(x) = f(x)·g(x) = (x +3)(2x^2 -4) = x(2x^2 -4) +3(2x^2 -4)
= 2x^3 -4x +6x^2 -12
(f·g)(x) = 2x^3 +6x^2 -4x -12
Hey good morning I need help ASAP thank you guys
Answer:
B. x = 2.77
Step-by-step explanation:
3^x = 21
You first look for a base for 21 that is 3 to the power of something.
21 = 3^2.77
So 3^x = 2^2.77
They have the same base so
x= 2.77
Solve for f(-7) plz thanks
Answer:
12
Step-by-step explanation:
If f(x) = 5 - x
Then f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September:
Answer:
Babies learn to crawl between age of 6 to 10 months.
Step-by-step explanation:
It may take longer for babies to crawl in winter season since the climate restricts the babies movement due to extra clothes. The babies who are born in summer will learn crawling earlier than those who are born in winter season.
Find the recursive formula for the geometric sequence. Then find a5,
2, 14, 98, 686,...
Answer:
the answer is C
Step-by-step explanation:
what’s the value of x? and what’s the measure of angel JHK?
Answer:
x = 14
JHK = 21
Step-by-step explanation:
The angles are vertical angles and vertical angles are equal
3x-21 = x+7
Subtract x from each side
3x-x -21 = x+7-x
2x-21 = 7
Add 21 to each side
2x-21+21 = 7+21
2x = 28
Divide by 2
2x/2 =28/2
x = 14
JHK = 3x-21 = 3(14) -21 = 42-21 = 21
Answer:
Because ∠GHI and ∠JHK are vertical angles, they're congruent. Therefore, set their angle measures equal to each other & solve for x.
[tex]x+7=3x-21\\x-3x=-7-21\\-2x=-28\\x=\frac{-28}{-2} =14\°[/tex]
Substitute in the value of x to find ∠JHK:
[tex]3x-21=3(14)-21=42-21=21\°[/tex]
write your answer in simplest radical form
Answer:
n = 8√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60°
Opposite = 4√6
Hypothenus = n =?
The value of n can be obtained by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 60 = 4√6 / n
√3/2 = 4√6 / n
Cross multiply
n × √3 = 2 × 4√6
n × √3 = 8√6
Divide both side by √3
n = 8√6 / √3
Rationalise
n = 8√6 / √3 × (√3/√3)
n = 8√(6×3) / 3
n = 8√18 / 3
Recall
√18 = √(9×2) = √9 × √2 = 3√2
Thus,
n = 8√18 / 3
n = 8 × 3√2 / 3
n = 8√2
