Answer:
- 7
Step-by-step explanation:
note that
+ (- ) = - ( adding a negative is equivalent to subtraction )
- (- ) = + ( subtracting a negative is equivalent to addition )
then
7 + (- 14) = 7 - 14 = - 7
Can someone help me out? :) The answer choices are:
A) 20.0
B) 21.2
C) 22.4
D) 23.6
Answer:
20.0
Step-by-step explanation:
We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of three sides separately.
AB = [tex]\sqrt{(-4+2) ^{2} +(1-3}) ^{2}}[/tex] = [tex]\sqrt{8}[/tex]
BC = [tex]\sqrt{(-2-3) ^{2} +(3+4) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
CA = [tex]\sqrt{(3+4) ^{2} +(-4-1) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
Perimeter = [tex]\sqrt{74}[/tex] + [tex]\sqrt{8}[/tex] + [tex]\sqrt{74}[/tex] = 20.0330776588 units
Answer:
Step-by-step explanation:
Write an equation for the nth term of the arithmetic sequence.
Step-by-step explanation:
Given [tex] \sf \: first \: term \: (a) = \dfrac{1}{4} \\ [/tex][tex] \small{\sf \: Common \: difference \: (d) = \dfrac{1}{2} - \dfrac{1}{4} = \bold{\dfrac{1}{4}}}[/tex]To findnth termSolution[tex] \sf \: T_n = a+(n-1)d[/tex]
[tex] \sf \: T_n = \frac{1}{4} +(n-1) \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{1}{4} + \frac{n}{4} - \frac{1}{4} [/tex]
[tex]\sf \: T_n = \frac{n}{4}[/tex]
an equation for the nth term of the arithmetic sequence. is n/4
Step-by-step explanation:
TN=n/4 is the nth term of arithmetic sequence.
Can anyone help me with this!
Answer:
The answer is B.
[tex] \frac{1025}{4} [/tex]
Step-by-step explanation:
Greetings ![tex] \frac{x {}^{6} - x}{4y} ...substitute \: x = - 4 \: and \: y = 4 \\ \frac{( - 4) {}^{6} - (- 4) }{4(4)} ...apply \: exponent \: rule \\ \frac{4096 + 4}{16} = \frac{4100}{16} = \frac{1025}{4} [/tex]
(-4)^6 - - 4 / 4 x 4
4096 + 4 / 16
4100/16
= 1025/4
So, answer is B. 1025/4
Hope this helps!
In the xy-plane, the line y = 2x + b intersects the parabola y = x² + bx + 5 at the point (3, k). If b is a
constant, what is the value of k?
By algebraic handling, the value of k of the system of equations is equal to 2.
What are the values of two constants such that a system of equations has a single solution?
Herein we find a system formed by two equations, a linear function and a quadratic equation with the following characteristics:
y = x² + b · x + 5 (1)
y = 2 · x + b (2)
If we eliminate y in (1) and (2), then we have this expression:
x² + b · 3 + 5 = 2 · x + b
3² + b · x + 5 = 2 · 3 + b
3 · b + 14 = 6 + b
14 = 6 - 2 · b
8 = - 2 · b
b = - 4
By (2), y = k, x = 3 and b = - 4, we find the value of k:
k = 2 · 3 - 4
k = 6 - 4
k = 2
By algebraic handling, the value of k of the system of equations is equal to 2.
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Which of the following is equivalent to the quotient below?
√135/√3
A. 5√3
B. √45/3
C. 3√5
D. 3√15
The answer is C. 3√5.
√135/√3√45√3² × 53√5 A ladder resting against a wall makes an
angle of 63° with the ground. The foot of
the ladder is 4.7 m from the wall.
Calculate the height of the top of the
ladder above the ground
Answer:
9.224
Step-by-step explanation:
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
For the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
Measures of a DataFrom the question, we are to determine the minimum, lower quartile, median, upper quartile, maximum, and interquartile range of the given data set
The given data set is
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Minimum = 48
Lower quartile = (54+56)/2
Lower quartile = 110/2
Lower quartile = 55
Median = (63+64)/2
Median = 127/2
Median = 63.5
Upper quartile = (74+74)/2
Upper quartile = 148/2
Upper quartile = 74
Maximum = 80
Interquartile range = Upper quartile - Lower quartile
Interquartile range = 74 - 55
Interquartile range = 19
Hence, for the given data set
Minimum = 48
Lower quartile = 55
Median = 63.5
Upper quartile = 74
Maximum = 80
Interquartile range = 19
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find the square roots of each of the following number
1: 81
2: 100
Multiply 9 with 9, and we get:
9 × 9 = 81
Multiply 10 with 10, and we get:
10 × 10 = 100
We get the final result as:
9²10²Hope this helps :)
What is the slope of the line that passes through the points (9, 2) and
(9,27)? Write your answer in simplest form.
Answer:
Slope (m) = infinity
Step-by-step explanation:
Given points:
⇒ (9, 2) and (9, 27)
In order to find the slope of these points, we must use the slope formula.
So the formula is ⇒ y₂ - y₁ / x₂ - x₁
Plug in the given points:
⇒ 27 - 2 / 9 - 9
Solve both the top and bottom (numerator and denominator):
⇒ 25 / 0
Divide:
⇒ Undefined.
(Anything divided by zero is undefined).
Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
4
6
Answer:
144π or 452.16 units³
Step-by-step explanation:
The formula for volume of a cylinder is [tex]\pi r^2 h[/tex]. We can use the given values for radius and height to find the volume of the cylinder.
Finding the Volume[tex]V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16[/tex]
The volume of the cylinder is 144π or 452.16 units³.
Enter the correct answer in the box.
This graph represents a transformation of the parent square root function.
-10-8 -6
A
-2
10-
8
6-
2-
-2-
-4-
-6-
-8-
-10-
O
2
6 8 10
➜X
Replace the values of h and k to create the equation of the transformed function.
Answer:
Step-by-step explanation:
The most basic quadratic function is f(x) = x2, whose graph appears below. ... us to graph an entire family of quadratic functions using transformations.
Select the correct answer.
Consider this expression.
x-4
2(x+4)
For which product or quotient is this expression the simplest form?
O A.
B.
O C.
O D.
2x+8
x²16
x²16
2x+8
2x+8
x²16
x²16
2x+8
÷
÷
.
.
x² + 8x + 16
x +4
x +4
x² + 8x + 16
x² + 8x + 16
x + 4
x+4
x² + 8x + 16
The rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
Multiplying rational expressionsRational expressions are written in the form a/b where a and b are integers.
According to the question, we need to determine the expression that is equal to x-4/2(x+4)
From the fourth option;
x²-16/2x+8 * x+4/x²+8x+16
Factorize the quadratic part to have;
x²-16/2x+8 * x²+8x+16/x+4
(x+4)(x-4)/2(x+4) * x+4/(x+4)^2
Cancel out the common expression to have;
x-4 * 1/2(x+4)
x-4/2(x+4)
Hence the rational expression that results into x-4/2(x+4) is x²-16/2x+8 * x+4/x²+8x+16
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Find the Perimeter of the figure below, composed of a parallelogram and one
semicircle. Rounded to the nearest tenths place
4
14
The perimeter of the figure to the nearest tenth is 44.6 units
Perimeter of a figure?The perimeter of a figure is the sum of the whole sides.
Therefore,
A parallelogram has opposite sides equal to each other.
Therefore, the perimeter of the figure is as follows;
The figure combines a parallelogram and a semi circle.
Therefore,
perimeter of the figure = 4 + 14 + 14 + πr
perimeter of the figure = 32 + 3.14 × 4
perimeter of the figure = 32 + 12.56
perimeter of the figure = 44.56
perimeter of the figure ≈ 44.6 units
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Andre says that [tex]log_10(55)=1.5[/tex] because 55 is halfway between 10 and 100. Do you agree with Andre? Explain your reasoning.
I know that answer is false, but I don't know how to explain!!
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllllllll} \log_{\underline{10}}(10)=1&\implies &\underline{10}^1=10 ~~ \checkmark\\\\ \log_{10}(100)=2&\implies &10^2=100~~ \checkmark\\\\ \log_{10}(55)=1.5&\implies &10^{1.5}=55\implies 10^{\frac{3}{2}}=55\implies \sqrt[2]{10^3}=55\\\\ &&\sqrt{1000}\ne 55 ~~ \bigotimes \end{array}[/tex]
increments over the exponent, are not directly proportional to increments on the resulting values, namely the half-way from 10² and 10⁴ is not 10³, because 10⁴ is 100 times 10², and 10³ is simply 10 times 10².
sariah has just begun training for a half-marathon, which is 13.1 miles. since she was on vacation, she started the training program later than the rest of her running club. There are 6 weeks of training runs remaining before the race.
In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the train program for her to get up to half-marathon distance?
Describe how you would solve this problem using Polya’s four-step problem-solving method. Complete each task as part of your response. Be sure to number task 1-task 4 so that your instructor can tell which part you are answering.
1. understand the problem
task 1: read the problem and restate in your own words what the question asks.
2. formulate a plan
task 2: identify the model you would use to represent the problem and explain why you chose the model.
3. implement the plan
task 3: solve the problem and state your answer.
4. review the results
task 4: explain your problem-solving process and how you know your answer is correct.
There would not be enough time to reach the half marathon distance.
Would there be enough time to reach the half marathon distance?The distance run in a week can be represented with a linear equation. A linear equation is an equation that has a single variable raised to the power of 1.
The linear equation that would be used to represent the distance run would be in the form:
Miles run in a week = miles run the previous week - increase in miles
Increase in miles = 6 - 4.5 = 1.5 miles
Miles run in the fourth week = 1.5 + 6 = 7.5 miles
Miles run in the fifth week = 7.5 miles + 1.5 miles = 9 miles
Miles run in the sixth week = 9 + 1.5 = 10.5 miles
There would not be enough time to reach the half marathon distance because in the sixth week she would be able to run 10.50 miles
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The manager of spiffy lube auto lubrication shop is trying to revise his policy on ordering grease gun cartridges. currently he orders 110 cartridges per week, but he runs out of cartridges 1 out of 4 weeks. he knows that, on average, the shop uses 95 cartridges per week. he was also willing to assume that the demand for cartridges is normally distributed. a. compute the standard deviation of the distribution?
Using the normal distribution, it is found that the standard deviation is of 26.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, we have that the mean is of [tex]\mu = 95[/tex], while X = 110 has a p-value of 0.75, hence X = 110, Z = 0.575, and then we solve for [tex]\sigma[/tex] to find the standard deviation.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.575 = \frac{110 - 95}{\sigma}[/tex]
[tex]0.575\sigma = 15[/tex]
[tex]\sigma = \frac{15}{0.575}[/tex]
[tex]\sigma = 26[/tex]
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If you flipped two coins simultaneously, for a total of 24 times, how many times, on average, would you expect to get a head and a tail?
When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
For given question,
When two coins are tossed simultaneously, the sample space is as follows:
S = { HH, HT, TH, TT} where H denotes Head and T denotes tail.
Using the formula of probability,
P = Number of favorable outcomes/total number of outcomes,
we get,
P(HT) = 1/4
and
P(TH) = 1/4
We know that the occurrence of two mutually exclusive events is the sum of their individual probabilities.
So, P(Head on one and Tail on other)
= P(HT) + P(TH)
= 1/4 + 1/4
= 2/4
= 1/2
= 0.5
So, when two coins flipped simultaneously, the probability of flipping 2 coins and getting a head and a tail is 0.5
In this question, we need to find the number of times getting a head and a tail when two coins are flipped simultaneously 24 times
= 0.5 × 24
= 12
Therefore, When two coins are flipped simultaneously 24 times, on average 12 times we will get a head and a tail.
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[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
Ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0What is an equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. The word equation and its cognates in various languages may have somewhat different definitions; for example, in French, an équation is defined as including one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.To identify the ellipses:
For the standard-form equation of an ellipse: Ax^2+Bx+Cy^2+Dy+E=0
We can define:
p=min(A,C)q=max(A,C)Then the eccentricity can be shown to be:
e=(1-p/q)p/q=1-e^2For Eccentricity<0.5, we want:
p/q>3/4Checking the values of p/q for the given equations, we have p/q= equations (A), (B), and (F) are of ellipses with eccentricity < 0.5.
Therefore, ellipses that are represented by equations, whose eccentricities are less than 0.5 are:
(A) 49x2 -98x + 64yz +256y -2,831 = 0 (B) 81x2 -648x +100yz +200y -6,704 = 0 (F) 64x2 +512x +81y2 -324y -3,836 = 0Know more about equations here:
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The complete question is given below:
Identify the ellipses, represented by equations, whose eccentricities are less than 0.5.
(A) 49x2 -98x + 64yz +256y -2,831=0
(B) 81x2 -648x +100yz +200y -6,704 =0
(C) 6x2 -12x +54y2 +108y -426 =0
(D) 49x2 + 196x +36y2 +216y -1,244 =0
(E) 4x +32x +25y2 - 250y +589 =0
(F) 64x2 +512x +81y2 -324y -3,836 =0
Find the measure of x.
16
X
38°
x = [?]
Round to the nearest hundredth.
The answer is.........
25.99
PLLLLLEASE T_T PLLLEASE
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
let's solve ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{4}{y - 6} + \cfrac{5}{y + 3} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4(y + 3) + 5(y - 6)}{(y - 6)(y + 3)} = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{4y + 12 + 5y - 30}{ {y}^{2} + 3y - 6y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{9y - 18}{ {y}^{2} - 3y - 18 } = \cfrac{7y - 4}{ {y}^{2} - 3y - 18} [/tex]
[tex]\qquad \sf \dashrightarrow \: 9y - 18 = 7y - 4[/tex]
[ denominator is same, so numerator must have same value to be equal ]
[tex]\qquad \sf \dashrightarrow \: 9y - 7y = - 4 + 18[/tex]
[tex]\qquad \sf \dashrightarrow \: 2y = 14[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 7[/tex]
Coplanar circles that have the same center, but not necessarily the congruent radii are called?
Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
How to complete the blank?From the question, we have the following statements:
The circles are coplanar i.e. they are on the same planeThey have the same circleThe radii of the circles are differentAs a general rule, circles that have the above features are referred to as concentric circles.
This is so because concentric circles have the same center, and they do not intersect
Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
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A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. the apothem of the hexagon is 2 centimeters. a cylinder is cut out of the middle of a hexagonal prism. the hexagon has an apothem with a length of 2 centimeters and base side lengths of 2.3 centimeters. the prism has a height of 2 centimeters. the cylinder has a diameter of 1.6 centimeters. the equation for the area of a regular hexagon = one-half (apothem) (perimeter). what is the volume of metal in the hex nut, to the nearest tenth? use 3.14 for π.
Subtracting the volume of the cylinder from the volume of the prism, the volume of metal in the hex nut to the nearest tenth exists [tex]$$23.6 cm^3[/tex]
How to estimate the volume of metal in the hex nut?Diameter of the cylinder be d = 1.6 cm
Apothem of the hexagon be a = 2 cm
Thickness of the steel hex nut be t = 2 cm
Volume of the prism be [tex]V_p[/tex]
Volume of the cylinder be [tex]V_c[/tex]
Volume of metal in the hex nut,
[tex]$$V = V_p - V_c[/tex]
To estimate the volume of a prism,
[tex]$$V_p = A_b h[/tex]
Ab = n L a / 2
Number of the sides, n = 6
The side of the hexagon be L
Height of the prism, h = t = 2 cm
Central angle in the hexagon, A = 360°/n
A = 360°/6 = 60°
[tex]$tan (\frac{A}{2} )=(\frac{L/2}{a})[/tex]
simplifying the value of L, we get
[tex]$tan (\frac{60}{2} )=(\frac{L/2}{2})[/tex]
[tex]$tan 30}=(\frac{L/2}{2})[/tex]
[tex]$tan (\frac{\sqrt{3}}{3} )=(\frac{L/2}{2})[/tex]
Solving for L/2:
[tex]$\frac{2 \sqrt{3}}{3} =\frac{L}{2}[/tex]
Solving the value of L, we get
[tex]$2\frac{2 \sqrt{3}}{3} =L[/tex]
[tex]$\frac{4 \sqrt{3}}{3} =L[/tex]
[tex]$L=4 \sqrt{3}/3 cm[/tex]
Ab = n L a / 2
Substitute the values in the above equation, we get
[tex]$A_b=\frac{6 (4 \sqrt{3}/3)(2)}{2}[/tex]
[tex]$$A_b=24 \sqrt{3}/3 $$cm^2[/tex]
[tex]$A_b=8 \sqrt{3} cm^2[/tex]
[tex]V_p = A_b h[/tex]
substitute the values in the above equation, we get
[tex]$V_p=(8 \sqrt{3})(2)[/tex]
[tex]$V_p=16 \sqrt{3} cm^3[/tex]
[tex]$$V_p=16 (1.732) cm^3[/tex]
[tex]$$V_p=27.712 cm^3[/tex]
To estimate the volume of cylinder,
[tex]$V_c[/tex] = (π[tex]d^2[/tex]/4) h
Here, π = 3.14 and d = 1.6 cm
Height of the cylinder, h = t = 2 cm
substitute the values in the above equation, we get
[tex]$V_c=[3.14 (1.6) / 4] (2)[/tex]
[tex]$V_c=[3.14 (2.56) / 4] (2)[/tex]
[tex]$V_c=(2.0096) (2)[/tex]
[tex]$$V_c=4.019 cm^3[/tex]
Substitute the values in the equation, we get
[tex]$$V=V_p-V_c[/tex]
[tex]$$V=27.712 - 4.019[/tex]
[tex]$$V=23.693 cm^3[/tex]
[tex]$$V=23.6 cm^3[/tex]
Therefore, the volume of metal in the hex nut, to the nearest tenth exists [tex]$$23.6 cm^3[/tex].
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A track coach is gathering data on the stride length of each of her 52 team members when running a distance of 500 meters. the population mean is 62.95 inches with a standard deviation of 5.65 inches. what is the standard error of the sample mean? round your answer to the nearest hundredth.
The standard error of the sample mean to the nearest hundredth is mathematically given as
S.E=0.784
What is the standard error?The amount by which the population means deviates from a sample mean is represented by the standard error of the mean, which is more often referred to as simply the standard error.
It informs you how much the sample means would change if you were to perform an experiment using fresh samples from the same population but this time uses different samples.
The standard error is obtained by calculating the standard deviation and then dividing that number by the square root of the sample size. It determines the accuracy of a sample mean by factoring in the variation in sample means that exists from one set of data to the next.
Generally, The population's mean height is 62.95 inches, so let's use that.
Taking into account that the population has a standard deviation of 5.65 inches
The sample mean is used to calculate the standard error of the mean.
[tex]SE=\frac{SD}{\sqrt{n}}[/tex]
Therefore
[tex]SE=\frac{5.65}{ \sqrt{52}}[/tex]
S.E=0.7835
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Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph?
The approximate solution to the given system of equation is (-2.71, 2.14)
Solving a system of linear equationsFrom the question, we are to determine the approximate solution to the given system of linear equations.
The given equations are
y = 0.5x + 3.5
y = -2/3 x+ 1/3
From the given information, we are to show the solutions on a graph
The graph that shows the solution to the given system of equation is shown below.
The solution to the given system is the point of intersection of the lines. The coordinate of the point of intersection of the lines is (-2.71, 2.14). That is, x = -2.71, y = 2.14.
Hence, the approximate solution to the given system of equation is (-2.71, 2.14)
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someone please help i will give brainliest
From the two functions function 2 has the highest maximum value.
Given two functions,one is y=-[tex]x^{2} -2x-2[/tex] and f(-2)=1,f(-1)=6,f(0)=9,f(1)=10,f(2)=9,f(3)=6.
We ae required to choose a function which is having highest maximum possible value.
Function is like a relationship between two or more variables expressed in equal to form. Each value of x of a function has some value of y.
The highest value in the second function is 10 which is at x=1. Put the value of x=1 in y=-[tex]x^{2} -2x-2[/tex].
y=-1-2-2
y=-5
So it might not be highest value of this function.So the second function has highest maximum value of 10 at x=1.
Hence the second function has highest value.
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Given MTS and SQP, find sq
From the given similar triangles we can conclude that the length of Side SQ is; 4
How to solve similar triangles?
We are given that;
PQ is parallel and congruent to MT.
Now, from the concept of similar triangles , we can say that;
PS/TS = QS/MS
From the given triangle we see that;
PS = 3 - 2x
QS = 6x - 1
MS = 30
TS = 10
Thus;
(3 - 2x)/10 = (6x - 1)/30
Cross multiply to get;
3(3 - 2x) = 6x - 1
9 - 6x = 6x - 1
Rearranging gives;
6x + 6x = 9 + 1
12x = 10
x = 10/12
x = 5/6
Thus;
SQ = 6(5/6) - 1
SQ = 4
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Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the function h(t) = −16t2 36t where t is the time in seconds. . how many seconds did the ball travel before returning the ground? t = 0.44 seconds t = 2.25 seconds t = 16 seconds t = 36 seconds
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
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please i need help FAST
Answers are needed urgently..ty
Angle <QAB is =15° because the opposite angles of an isosceles triangle are equal.
The length of the straight line AB = 80cm
Calculation of angle of a triangleThe angle at a point = 360°
Angle AQB= 360 - 210° = 150
But the angle that makes up a triangle= 180°
180-150= 30°
But <QAB = <QBA because triangle AQB is an isosceles triangle.
30/2 = 15°
To calculate the length of the straight line the following is carried out using the sine laws.
a/ sina, = b sinb
a= 8cm, sin a { sin 15)
b= ? , sin B = 150
make b the subject formula;
8/sin15= b/sin 150
b= 8 × sin 150/sin 15
b= 80cm
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