If you know the slope of the lines, you can also use these methods:
- see if the slopes multiplied by each other are -1 (should be if they're perpendicular)
- test if the slopes are opposite reciprocals (if they are, they are perpendicular)
Haley and tyler are on the cross country team. tyler can run 1 mile (ata constant speed) in 8 minutes and 20 seconds. haley's distances and times for a training run are given by the equation y=8x where x represent distanse and times in miles and y represents time in minutes. who ran farther in 10 minutes how much farther
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Tyler can run 1 mile in 8 minutes and 20 seconds.
Time taken = 8 mins + 20 sec (0.33 min) = 8.33 minutes
Speed = distance / time = 1 mile / 8.33 = 0.12 mile per min
In 10 minutes, distance = 0.12 mile per min * 10 min = 1.2 mile
Haler is given by:
y = 8x; where y is time and x is distance.
In 10 minutes, distance = y/8 = 10/8 = 1.25 miles
Haler ran farther than Tyler in 10 minutes. She covered an extra 0.05 miles compared to Tyler.
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help please!! show work if possible thank you!!
I don't get the minutes part
What is the exact value of cos (67.5°)?
OA.
OB.
OC. -√2+√2
√2+√2
2
-
√2-√2
2
OD. √2+ √2
4
first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so
[tex]cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\\\ cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}} \\\\[-0.35em] ~\dotfill\\\\ cos(135^o)\implies cos(90^o+45^o)\implies cos(90^o)cos(45^o)~~ - ~~sin(90^o)sin(45^o) \\\\\\ \left( 0 \right)\left( \cfrac{\sqrt{2}}{2} \right)~~ - ~~\left( 1\right)\left( \cfrac{\sqrt{2}}{2} \right)\implies -\cfrac{\sqrt{2}}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]cos(67.5^o)\implies cos\left( \frac{135^o}{2} \right)\implies \pm \sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}\implies \stackrel{I~Quadrant}{+\sqrt{\cfrac{ ~~ 1-\frac{\sqrt{2} ~~ }{2}}{2}}} \\\\\\ \sqrt{\cfrac{ ~~ \frac{2-\sqrt{2}}{2} ~~ }{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{\sqrt{4}}\implies \cfrac{\sqrt{2-\sqrt{2}}}{2}[/tex]
Round each fraction to help you estimate the solution for the following equation:
nine tenths minus eight tenths equals
0
one half
1
one and one half
Answer:
Step-by-step explanation:
answer is 1/2
How did doves view the conflict in Vietnam?
O As a vital Cold War battleground in the fight for democracy
O As a localized civil war that should not include the US
O As the first step in acquiring territory in Southeast Asia
O As a means to achieving Johnson's Great Society
The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).
What is the Vietnam War?The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.
Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:
VietnamCambodiaNorth VietnamSouth VietnamLaosSouth East AsiaIn conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.
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Im so confused please help!!
The factored form of the expression is (2x-1)(2x+5) and the x-intercept of the function is 1/4 and -5/2 respectively
Solving quadratic equationQuadratic equations are equations that has a leading degree of 2. Given the quadratic equation below;
y = 4x^2 + 8x -5
The x-intercept is the point where the value of y is zero.
Factorize the resulting expression
y = 4x^2 + 8x -5
y = 4x^2 - 2x + 10x -5
y = 2x(2x-1)+5(2x -1)
y = (2x-1)(2x+5)
The factored form of the expression is (2x-1)(2x+5)
Equate the given factors to zero
(2x-1)(2x+5) = 0
Equate the factors to zero
2x - 1 = 0
2x = 1
x = 1/4
Similarly
2x + 5 = 0
2x = -5
x = -5/2
Hence the x-intercept of the function is 1/4 and -5/2 respectively
C) For the end behavior, as the value of x tends to infinity, hence the y-values tends to infinity
D) In order to plot the graph, the x-intercepts of the will be plotted on the graph and then curve will be created.
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1.Name 4 other angles whose cosine is the same as cos pi/3 . Explain using mathematical language how you know this is true.
2.Is this statement true or false? Explain your answer.
All angles that have the same cosine will have the same sine.
The trigonometry illustrates that the four angles whose cosine is the same as cos pi/3 will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3
How to illustrate the information?From the information, given cos (x), the value that is similar to cos x will be the sum of the angle and multiple of 360.
Therefore, for the angle cos(∏/3), the angles that are similar to this angle will be expressed as Cos(2∏n + ∏/3) where n is any positive integer.
Then the other four angles will be 7∏/3, 13∏/3, 19∏/3, and 31∏/3. Also, the statement that all angles that have the same cosine will have the same sine is false. The sine of an angle is simply equal to the cosine of the complementary angle.
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A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?
44°
50°
64°
92°
The measure of Arc AU of the given Circle Geometry is; 50°
How to find the measure of arc angle?The circle theorem we will apply to solve for the arc measure states that “Measure of angles subtended to any point on the circumference of the circle from the same arc is equal to half of the angle subtended at the center by the same arc.”
We can express the above theorem as;
Angle at the center = 2 × Angle at the circumference
From the attached image below and from the given statement in the question, we are given that; ∠QUA = 111°
Therefore, applying the circle theorem earlier quoted, we can say that; m∠QDA = 2 × ∠QUA
m∠QDA = 2 × 111° = 222°
Which gives;
∠QOA = = 360° - 222° = 138°
∠QOA = ∠QOU + ∠UOA (by angle addition property)
Thus;
∠QOA = 138° = 88° + ∠UOA
∠UOA = 138° - 88° = 50°
Thus, the measure of Arc AU is;
Arc AU = ∠UOA = 50°
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Answer: b
Step-by-step explanation:
Using f(x), what is the equation that represents g(x)?
Og(x) = log5 (x) - 3
O
g(x) = log5 (x) +3
Og(x) = log5 (x-3)
Og(x) = logs(x + 3)
The equation that represents the function g(x) is g(x) = log₅(x - 3)
How to determine the equation that represents g(x)?The equation of the function f(x) is given as:
f(x) = log₅(x)
From the graph, we can see that the function g(x) is 3 units to the right of the function f(x)
This means that
g(x) = f(x - 3)
The function f(x - 3) is calculated as follows
f(x - 3) = log₅(x - 3)
Substitute f(x - 3) = log₅(x - 3) in g(x) = f(x - 3)
g(x) = log₅(x - 3)
Hence, the equation that represents the function g(x) is g(x) = log₅(x - 3)
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Find the term that must be added to the equation x2 6x=1 to make it into a perfect square.
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
What is a perfect square?
A perfect square exists as a number that can be described as the product of an integer by itself or as the second exponent of an integer.
The perfect square trinomial exists
[tex](a[/tex] ± [tex]b)^2[/tex] = [tex]a ^2[/tex] ± 2ab + [tex]b ^2[/tex]
[tex]$x^2-6x=1[/tex]
[tex]x^2-2*3x=1[/tex]
then [tex]$2ab = 2 * 3*x = 2 * x *3[/tex]
The value of a = x and b = 3
[tex]$b^2=3^2=9[/tex]
[tex]$x^2-6x+9=1+9[/tex]
[tex]$x^2-6x+9=10[/tex]
The value added to the equation [tex]$x^2-6x=1[/tex] exists [tex]$x^2-6x+9=10[/tex].
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the angle of depression from the top of the tower to a boulder on the ground is 38 degrees if the tower is 25 m high how far from the base of the tower is the boulder
Check the picture below.
Make sure your calculator is in Degree mode.
Match each quadratic function given in factored form with its equivalent standard form listed on the left. f(x) = (x 2)(x – 6) f(x) = (x – 4)(x 3) f(x) = (x – 12)(x 1) f(x) = (x – 3)(x 4)
standard form of the given equation are
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
What is quadratic function?A polynomial function with one or more variables in which the second-degree term is the highest degree is known as a quadratic function, quadratic polynomial, polynomial of degree 2, or simply a quadratic, in algebra.
What is standard form of a quadratic function?As long as an is not equal to zero, the quadratic function f(x) = a(x - h)2 + k is considered to be in standard form. The graph starts out in either an upward or a downward direction depending on the value of a. The point at the vertex of the symmetry is represented by the vertical line x = h. (h,k).
According to the given information:The standard form list.
1 . (x + 2)(x - 6)
= x² - 6x + 2x - 12
= x² - 4x -12
2. (x - 4)(x + 3)
= x² + 3x - 4x - 12
= x² - x - 12
3. (x - 12)(x + 1)
= x² + 1x - 12x - 12
= x² - 11x - 12
4. (x -3)(x + 4)
= x² + 4x - 3x - 12
= x² + x - 12
So the equivalent standard form of the give values are :
-f(*) = (x + 2)(x - 6) = x² - 4x - 12
f(x) = (x - 4)(x + 3) = x² - x - 12
f(x) = (x - 12)(x + 1) = x² - 11x - 12
f(x) = (x -3)(x + 4) = x² + x - 12
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I understand that the question you are looking for is:
Match each quadratic function given in factored form
with its equivalent standard form listed on the left.
f(x) = (x + 2)(x – 6)
f(x) = (x – 4)(x+3)
f(x) = (x – 12)(x+1)
f(x) = (x – 3)(x +4)
Find the missing side. Round your answer to the nearest tenth.
What are the steps to finding missing sides
Answer:
23.6
Step-by-step explanation:
→ Identify length not given
Opposite
→ Find a formula without opposite
Cos = Adjacent ÷ Hypotenuse
→ Rearrange
Adjacent = Cos × Hypotenuse
→ Substitute
cos 38 × 30 = 23.6
Answer:
[tex]x = 23.6[/tex]
Step-by-step explanation:
To find the missing side of a right-angled triangle, first look at the given angle, and notice its relationships with the given and required sides.
In this case:
• The side adjacent to the given 38° angle is [tex]x[/tex] (required).
• The hypotenuse is 30 units.
The trigonometric ratio that relates the adjacent side and hypotenuse of a triangle is cosine (cos), where:
[tex]\boxed{cos \space\ \theta = \frac{adjacent}{hypotenuse}}[/tex].
Substituting into the formula:
[tex]cos (38^{\circ}) = \frac{x}{30}[/tex]
⇒ [tex]x = cos(38^{\circ}) \times 30[/tex]
⇒ [tex]x = 23.6[/tex]
The student’s t distribution will approach the standard normal distribution as the number of the degrees of freedom goes up.
a. True
b. False
Answer:
True student distribution will approach the standard
For the same sample data and null hypothesis, how does the p-value for a two-tailed test of μ compare to that for a one-tailed test?.
A one-tailed test's p-value is half that of a two-tailed test.
What is the difference between the p-value for a two-tailed test and a one-tailed test?Whether it is positive or negative, when you find your test statistic, you also find a tail probability to the right or left of that test statistic. What is the likelihood that, if the null hypothesis is correct, you will obtain a value that is more extreme (far out in the tail) than the observed test statistic? If the test is two-tailed, the phrase "probability...more extreme" applies to both tails, beyond the positive and negative values of your test statistic. Your calculations will fall either on the right or left, but if the test is two-tailed, it will also apply to both tails.
What is null hypothesis ?Two possibilities sharing similarities is the null hypothesis. That the observed discrepancy is solely the result of chance is the null hypothesis. Calculating the probability that the null hypothesis is correct using statistical testing is achievable.
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PLEASE HELP ITS MATH PLEASE
Answer:
y=[4]x + [12]
Step-by-step explanation:
Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.
Familiarize yourself with point-slope form:
[tex]y-y1=m(x-x1)[/tex]
If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.
[tex]y-y1=4(x-x1)[/tex]
And we know the point it must pass through is (-2,4), so we can fill those values in too.
[tex]y-4=4(x+2)[/tex]
Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]
Answer:
[tex]y = 4x + 12[/tex]
Step-by-step explanation:
The solution is in the attached image
Consider a situation in which p(x) = and p(y) = . if p(x and y) is = , which best describes the events?
The correct option is (A) P(X) × P(Y) = P(X ∩ Y)
What is probability and example?
Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .We are given to consider a situation in which X and Y are two events such that
P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5
We are to select the statement that best describes the events X and Y
We know that
any two events A and B are said to be independent if
P(A) × P(B) = P (A ∩ B)
We have, for events X and Y,
P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)
P(X) × P(Y) = P(X ∩ Y)
Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)
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The complete question is -
Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?
They are independent because P(X) x P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) x P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).
Answer: a
Step-by-step explanation:
just took the test
Use the figure to the right to list all of the pairs of angles that fit each description.
The pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Angle DescriptionFrom the question, we are to list the angles that fit the given descriptions
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W;
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
Hence, the pairs of angles that fit the description are
1. alternate exterior angles S and Z; T and Y
2. alternate interior angles U and X; V and W
3. consecutive interior angles U and W; V and X
4. corresponding angles S and W; T and X; U and Y; V and Z
5. vertical angles S and V; U and T; W and Z; Y and X
6. adjacent angles S and T; Y and Z
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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)? f(x) = 2x2 x 4 x g(x) –2 1 –1 3 0 5 1 7 2 9 (-2, 10) (–1, 7) (0, 5) (1, 7)
The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:
g(x) = 5 + 2x.
The solution to the system of equations is found as follows:
f(x) = g(x)
2x² + x + 4 = 5 + 2x
2x² - x - 1 = 0
Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:
[tex]\Delta = b^2 - 4ac = (-1)^2 - 4(2)(-1) = 9[/tex][tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{9}}{4} = 1[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{9}}{4} = -0.5[/tex]When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).
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Answer:
D. (1,7)
Step-by-step explanation:
I took the exam
In a local shop some items are being sold at a third off. They now cost the following amounts. What was the original full price? 40 POINTS AND BRAINLIEST
1.£6.46
2.£58.24
3.£114.28
4.£12.50
5.£10.86
Answer:
1) 9.69
2) 87.36
3) 171.42
4) 18.75
5) 16.29
Step-by-step explanation:
Treat each value's full price as x. then, all of the values are (2/3)x. To get (2/3)x back to x, we must multiply (2/3)x*(3/2)=x. Multiply each of the questions given by 3/2 or 1.5
An unfair coin is flipped. if a head turns up you win $1. the probability of a head is. 54 and the probability of a tail is 0. 46. what is the expected value of the game?
Answer:
if you end up landing on a heads you should walk away with a $1.46
Using data from a study, we find a significant difference in the proportion of fruit flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using additional data from this study.1 In this case, we are testing
H0:po=pcHa:po>pc
where po and pc represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have n1=n2=500. Show all remaining details in the test, using a 5% significance level.
Effect of Organic Raisins After 15 Days
After 15 days, 320 of the 500 fruit flies eating organic raisins are still alive, while 300 of the 500 eating conventional raisins are still alive.
Give the test statistic and the p-value.
Round your answers to three decimal places.
What is the conclusion?
Do we have evidence that the proportion surviving after eating organic is higher?
The hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
How to illustrate the information?The following can be deduced from the information:
x1 = 275
x2 = 170
n1 = 500
n2 = 500
The sample proportion will be:
p1 = 275/500 = 0.55
p2 = 170/500 = 0.34
The pooled proportion will be:
= (275 + 170)/(500 + 500)
= 0.44
The test statistic is 6.681. It should be noted that the test statistics is a number that's calculated by a statistical test. It shows how the observed data are far from the null hypothesis.
The p value in this scenario is extremely small. The p value is a measurement used to validate a hypothesis against the observed data. Therefore, we have to reject the null hypothesis.
In this case, the hypothesis shows that we have evidence that the proportion surviving after eating organic is higher.
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Find the length of an arc of 40° in a circle with an 8 inch radius.
877
9inches
O 167
9inches
0
647
9inches
Answer:
16 pi/ 9 inches should be the right one.
Which of the following inequalities is graphed on the coordinate plane? A. y>-2x+1 B. y>-2x+1 C. y<-2x+1 D. y<-2x+1
The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Answer: The correct equation that has been shown by the graph is y<-2x+1. Option D
What is inequality?
The term inequality refers to a mathematical statement that contains the inequality sign rather than the equality sign. Looking at the inequality sign, we know that the sign ought to be less than.
Thus, the correct equation that has been shown by the graph is y<-2x+1. Option D
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Step-by-step explanation:
True or false? the patient should be given a receipt for payments on account even if the account is not paid in full.
Answer:
Step-by-step explanation:
true
Answer:
False because the account isn't full
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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find the maximum value of c=4x+2y subject to the fallowing constraints x≥0 y≥0 2x+2y≤10 3x+y≤9
The maximum value of c=4x+2y subject to the constraints is 14
How to determine the maximum value?The objective function is given as:
c = 4x+2y
The constraints are given as:
x≥0 y≥0
2x+2y≤10
3x+y≤9
Rewrite 2x+2y≤10 and 3x+y≤9 as equations
2x+2y = 10
3x+y = 9
Divide 2x+2y = 10 through by 2
x+y = 5
Subtract x+y = 5 from 3x+y = 9
3x - x + y - y = 9 - 5
Evaluate the difference
2x = 4
Divide by 2
x = 2
Substitute x = 2 in x+y = 5
2+y = 5
Solve for y
y = 3
So, we have
(x, y) = (2, 3)
Substitute (x, y) = (2, 3) in c = 4x+2y
c = 4 * 2 + 2 * 3
Evaluate
c = 14
Hence, the maximum value of c=4x+2y subject to the constraints is 14
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The area of a square is 400 square units. If the length of each side of the
square increased by one unit, would its area be a rational number? Explain.
yes it will be a rational number.
square having area 400 sq units will have a length of 20 on each side by increasing the length of each side by 1 we get 21 then the area will be
21 ^ 2=441
Then we will have a rational number.
Instead of recording the number 1.23 cm for the radius of 2 tube, a student recorded 1.32cm.find the percentage error, correct to 1.DP
