Answer:
Y = 7x + 51
Step-by-step explanation:
Point-slope form is in this form: y = mx + b where b is the y-intercept and m is the slope. We have the slope, and we already have a point that must be on the line. The only thing we need is the y-intercept, so we can plug in the given point and the slope to solve for b.
Plug in (-7, 2) for x and y and the slope(7) for m. This gives: [tex]2 = 7*-7 + b[/tex], or [tex]2 = -49 + b[/tex]. Now add 49 to both sides to isolate x, and we get that [tex]b = 51[/tex]. We have everything we need for the equation now, so plug in the slope and y-intercept for m and b, giving us y = 7x + 51.\
Hope this helps!
the base of a right triangle is 6 and the perpendicular height is 8, what is the length of a hypotenuse
If the base of the right triangle is 6 and the perpendicular height is 8 , then the length of the hypotnuse is 10 .
In the question ,
it is given that ,
the base of the right triangle is 6 , and
the height of the perpendicular is 8 ,
let the length of the hypotnuse of the given triangle be = h
Since the triangle is a right triangle , So , it follows Pythagoras Theorem ,
that means ,
h² = 6² + 8²
h² = 36 + 64
h² = 100
Simplifying further ,
we get ,
h = 10
Therefore , the length of the hypotnuse is = 10 .
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PLEASE HELP WILL GIVE BRAINLIST ! , PLEASE MAKE IT FAST
Answer:
t >28= the temp is warmer than 28
t >29= the table is heavier than 29 kilos
t <29= tony is you get than 29 yrs old
t <28= tia ran the race in under 28 secs
Step-by-step explanation:
hope this helps
Graph each function and identify its domain, range, intercepts, asymptotes, and holes.
Thank you! :)
Answer:
Domain: real numbers except {-4, -3, 0}Range: real numbers except {2}Intercepts: (-1, 0); no y-intercept (see Holes)Asymptotes: horizontal, y = 2; vertical, x = -3Holes: (-4, 6), (0, 2/3)Step-by-step explanation:
You want the domain, range, intercepts, asymptotes, and holes of the rational function f(x) = (2x³ +10x² +8x)/(x³ +7x² +12).
SimplifiedThe given function can be simplified by cancelling common factors from numerator and denominator. These cancelled factors show where the holes are in the graph.
[tex]f(x)=\dfrac{2x^3+10x^2+8x}{x^3+7x^2+12}=\dfrac{2x(x+4)(x+1)}{(x(x+4)(x+3)}=2\left(\dfrac{x+1}{x+3}\right)\quad x\notin\{-4,-3,0\}[/tex]
DomainThe function is defined for all real numbers except those where the denominator is zero: {-4, -3, 0}.
RangeThe function can produce every output value except the value of the horizontal asymptote: y = 2. The range is all real numbers except 2.
InterceptsThe x-intercept is found where the numerator of the simplified function is zero: x = -1
The y-intercept is the function value at x=0. The function is undefined there, so the y-intercept does not exist. (The limit as x approaches zero is y = 2/3.)
AsymptotesThe function has a horizontal asymptote at the y-value corresponding to the ratio of the highest-degree terms of the numerator and denominator: y = 2.
The vertical asymptote is at the uncanceled denominator zero, x = -3.
HolesThe holes are where a numerator and denominator factor cancel. The y-value at the hole is the limit of the function value as x approaches the hole location. This is the value of the simplified function.
The holes are (-4, 6) and (0, 2/3).
the profit realized by the sales of a particular item follows a normal distribution with a mean of $0.5 million per quarter and a standard deviation of $0.1 million per quarter. what percent of the quarters can be expected to see a profit of at least $0.5 million?
98% of the quarters can be expected to see a profit of at least $0.5 million.
What is a standard deviation?
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Z score = 0.7-0.5 = 0.2
σ = 0.1
P-value from Z-Table:
P(x<0.5) = 0.97725
≈ 98%
Hence, 98% of the quarters can be expected to see a profit of at least $0.5 million.
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Find the angel between the two vectors (4,1) and (-8,3)
The angle between the two vectors (4,1) and (-8,3) will be 145.4°.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
It is possible to calculate the angle () between two vectors using the formula
[tex]\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
Calculate dot product:
=a · b
= ax · bx + ay · by
= 4 · (-8) + 1 · 3
= - 32 + 3
= -29
=|a|
= √ax² + ay²
= √4² + 1²
= √16 + 1
= √17
=|b|
=√ bx² + by²
= √(-8)² + 3²
= √64 + 9
= √73
[tex]\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}[/tex]
α = 145.40771131249005°
Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.
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Matt and Jasmine are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Matt sold 7 packages of white chocolate chip cookie dough and 13 packages of gingerbread cookie dough for a total of $366. Jasmine sold 6 packages of white chocolate chip cookie dough and 15 packages of gingerbread cookie dough for a total of $387. Find the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough.
Answer:
i found something that might help you
Step-by-step explanation:
Find the values of x and y that make k || j and m || n. x = ° y = °
The values of x and y are x = 80° and y = 130°.
What is conservative interior angles?
When a line, referred to as the transversal line, crosses two other lines, two angles are created that are known as consecutive interior angles. Consecutive interior angles, or co-interior angles for short, are the angles formed on the inside of the two lines and on the same side of the transversal line.
Consecutive interior angle CONVERSE is another name for the same side interior angle CONVERSE.
Line line n || m
if (x - 30) + (x + 50) = 180.
x - 30 + x + 50 = 180
2x + 20 = 180
subtract 20 from both sides
2x = 160
divide both sides by 2
x = 80
IF (x - 30) + y = 180, then k || j.
(80 - 30) + y = 180
50 + y = 180
subtract 50 from both sides
y = 130
Hence, the values of x and y are x = 80° and y = 130°.
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Complete question:
Complete question is attached below,
if 11600 dollars is invested at an interest rate of 10 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
The compound interest after 5 years is $7,081.916.
Compound interest:
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Here we have to find the interest earned after 5 years.
Data given:
Principle (P) = $11600
rate(r) = 10%
time(t) = 5 years.
Formula to find compound interest:
CI = P( 1 + r/100[tex])^{t}[/tex] - P
Now put the values in the formula.
CI = 11600 ( 1 + 10/100[tex])^{5}[/tex] - 11600
= 18681.916 - 11600
= 7081.916
Therefore the compound interest is $7081.916.
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what is the rate of change in y = 2x + 4 and initial value?
Answer: rate of change is 2
Step-by-step explanation:
-3-6i divided by 3+2i please help
To divide complex numbers, you multiply by the conjugate of the denominator:
[tex]\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i}[/tex]
We do this to turn the denominator into a real number.
[tex]\begin{aligned}\dfrac{-3-6i}{3+2i}\cdot\dfrac{3-2i}{3-2i} &= \dfrac{-9+6i-18i+12i^2}{9-4i^2}\\[0.5em] &= \dfrac{-9-12i-12}{9+4}\\[0.5em] &= \dfrac{-21-12i}{13}\\[0.5em] &= -\dfrac{21}{13}-\dfrac{12}{13}i\end{aligned}[/tex]
Answer:
[tex]-\dfrac{21}{13}-\dfrac{12}{13}i[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{-3-6i}{3+2i}[/tex]
Multiply the numerator and denominator by the complex conjugate of the denominator:
[tex]\implies \dfrac{-3-6i}{3+2i} \cdot \dfrac{3-2i}{3-2i}[/tex]
Simplify:
[tex]\implies \dfrac{(-3-6i)(3-2i)}{(3+2i)(3-2i)}[/tex]
[tex]\implies \dfrac{-9+6i-18i+12i^2}{9-4i^2}[/tex]
[tex]\implies \dfrac{-9-12i+12i^2}{9-4i^2}[/tex]
Apply the imaginary number rule [tex]i^2=-1[/tex] :
[tex]\implies \dfrac{-9-12i+12(-1)}{9-4(-1)}[/tex]
[tex]\implies \dfrac{-9-12i-12}{9+4}[/tex]
[tex]\implies \dfrac{-21-12i}{13}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a-b}{c}=\dfrac{a}{c}-\dfrac{b}{c}:[/tex]
[tex]\implies -\dfrac{21}{13}-\dfrac{12}{13}i[/tex]
HELP
For the diagram below, calculate the value of x. Show your work
Answer: x = 6
Step-by-step explanation:
2x + 7 = 9x - 35
-7x + 7 = -35
-7x = -42
x=6
two brothers each purchased a new pair of hiking boots and two canteens the hiking boots cost $34.00 each and the total of their purchase was $98.00 what was the cost of each canteen
Answer:
Ok this is easy you got this!
Step-by-step explanation:
Ok so, we know their over total is 98.00, we also know that the boots cost $34 each
lets start with 34+34= 68
now we are going to take that from 98
98-68=30
now because they bought two canteens we will divide 30 by 2
30 divided by 2 is 15
the cost of each canteen is $15
the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km. what is the difference between these distances
The difference between these distances on the Earth is 3.32 × 10⁴.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression that shows the multiplication for the same number. Exponential expressions are just a way to write powers in short form. The exponent indicates the number of times the base is used as a factor. Exponents are used to show repeated multiplication of a number by itself
Given that the distance of earth's equator is 4.00x10^4 km. the distance around the moons equator is 6.8x10^3 km.
The difference will be:
= 4.00x10^4 km - 6.8x10^3 km.
= 3.32 × 10⁴
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What is the gradient of the graph shown? Give your answer in its simplest form.
Answer:
gradient = 2
Step-by-step explanation:
calculate the gradient m using the gradient formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = [tex]\frac{-1-(-5)}{2-0}[/tex] = [tex]\frac{-1+5}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
q4. a rt tomatometer score of 75% is considered fresh. is the mean mcu rt tomatometer score significantly above fresh?
From the given statement the mean mcr rt tomatometer score is significantly above fresh.
What is tomatometer score?
The Tomatometer score represents the percentage of professional critic reviews that are positive for a given film or television show.
To find answer we need to perform hypothesis.
The mean MCU Rotten Tomatoes score is equal to or less than 75%, which is the null hypothesis.
The mean MCU Rotten Tomatoes score is more than 75%, which is the alternative hypothesis. To test this theory, we can use a one-tailed t-test.
The null hypothesis can be rejected if the p-value is less than the significance level, which is typically 0.05, at which point it can be determined that the mean MCU Rotten Tomatoes score significantly exceeds fresh.
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Help me please please please please System of equations and inequalities aglebera 1
1.15 x240 not the answer the work I want.
Answer:
Step-by-step explanation:
Which should equal 92° to prove that r ∥ s? w x y z
w should be equal to 92° to prove that r || s.
To prove whether the two lines are parallel we should know whether
the pairs of corresponding angles are congruent if a transversal cuts two parallel lines (Corresponding Angles Theorem)the pairs of alternate interior angles are congruent if a transversal cuts two parallel lines (Alternate Interior Angles Theorem)the pairs of alternate exterior angles are congruent if a transversal cuts two parallel lines (Alternate Exterior Angles Theorem)the pairs of consecutive interior angles are supplementary if a transversal cuts two parallel lines (Consecutive Interior Angles Theorem)So for the given condition, the diagram is drawn. Mark the angles w, x, y, and z.
From the diagram, by the Corresponding Angles Theorem, ∠w=∠92°.
The answer is w. Therefore, option a is correct.
The complete question is -
Letters w, x, y, and z are angle measures. Lines r and s are intersected by line m. At the intersection of lines m and r, clockwise from the top, the angles are w, x, blank, blank. At the intersection of lines m and x, clockwise from the top, the angles are 92 degrees, y, z, blank. Which should equal 92° to prove that r ∥ s?
a)w
b)x
c)y
d)z
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Adam has 5 blue pencils. How many red pencils would he need to have so that the ratio of blue pencils to red pencils is 1:2?.
The number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
Explain the term ratio of the number?A ratio in mathematics demonstrates how several times one number is present in another. An set of points of numbers an as well as b, represented as a / b, is a ratio if b is not equal to 0. A proportion is indeed an equation that sets two ratios at the same value.Let the number of number of red pencils be 'x'.
Total blue pencils = 5.
Ratio = blue pencils/red pencils
5/x = 1/2
x = 5 x 2
x = 10
Thus, the number of red pencils is found to be 10 such that the ratio of blue pencils to red pencils is 1:2.
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a cell phone plan costs $200 to start. Then there is a $50 charge each mont. what is the total cost for x months
Answer$200+$50x
Step-by-step explanation:
Answer:
4 Months
Step-by-step explanation:
if X = total (not sure)
thats means you must do $200 / $50 = 4 Months
What is the polar form of negative 9 minus 9 i startroot 3 endroot ?
Using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.
There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
So, we have -9 - 9√3i:
This quantity has a modulus.
|-9 - 9√3 i| = √((-9)² + (-9√3)²) = √324 = 18
And argument θ to the effect:
tan(θ) = (-9√3) / (-9) = √3
We anticipate that will be between -π and -π/2 radians since -9-9√3i lies in the third quadrant of the complex plane, so that:
θ = arctan(√3) - π = π/3 - π = -2π/3
The polar form is then:
18 (cos(-2π/3) + i sin(-2π/3))
And since -2π/3 is the same angle as 2π - 2π/3 = 4π/3, the right answer is: 18 (cos(4π/3) + i sin(4π/3))
Therefore, using trigonometry identities, we know that the polar form of -9-9√3i is (D) 18 (cos(4π/3) + isin(4π/3)).
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Complete question:
What is the polar form of Negative 9 minus 9 I StartRoot 3 EndRoot?
a. 9 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
b. 9 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
c. 18 (cosine (StartFraction pi over 3 EndFraction) + I sine (StartFraction pi Over 3 EndFraction) )
d. 18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Answer:
18 (cosine (StartFraction 4 pi over 3 EndFraction) + I sine (StartFraction 4 pi Over 3 EndFraction) )
Step-by-step explanation:
D
Please help!
Matrix Pre-calc
Answer:
M+N is defined
All others not defined
Step-by-step explanation:
Two matrices can be added or subtracted if and only if they have the same dimensions i.e. they must have the exact same number of rows and number of columns
Only M and N with dimensions (4 x 2) each can be added or subtracted.
(4 x 2 ) means 4 rows and 2 columns
So the only defined operation is
M + N
All the others are not defined
Answer:
[tex]\textsf{De\:\!fined}: \quad \boxed{M + N}[/tex]
[tex]\textsf{Not\:de\:\!fined}: \quad \boxed{N - Q} \quad \boxed{Q + L} \quad \boxed{M - P}[/tex]
Step-by-step explanation:
Generally, a matrix is referred to as [tex]n\times m[/tex] where n is the number of rows and m is the number of columns.
Therefore:
L is a 2 x 2 matrixM is a 4 x 2 matrixN is a 4 x 2 matrixP is a 2 x 2 matrixQ is a 2 x 1 matrixMatrices can be added or subtracted only when they are the same size.
[tex]\boxed{N - Q}[/tex]
Matrices N and Q are different sizes. Therefore, the operation is not defined.
[tex]\boxed{M + N}[/tex]
Matrices M and N are the same size. Therefore, the operation is defined.
[tex]\boxed{Q + L}[/tex]
Matrices Q and L are different sizes. Therefore, the operation is not defined.
[tex]\boxed{M - P}[/tex]
Matrices M and P are different sizes. Therefore, the operation is not defined.
Charolette earns 3,595 per month at her job. She will receive a 7% raise. How much more money will Charolette earn each year after her raise?
The increase in the salary for Charolette will be $251.65.
What is a percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Charolette earns 3,595 per month at her job. She will receive a 7% raise. The amount of raise will be calculated by simply multiplying the percentage that she was given for the raise in the salary by the initial salary that she was earning.
This will be illustrated thus:
= Percentage × Salary
= 7% × $3595
= $251.65
The value of $251.65 will the increase in the salary.
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design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The box's dimensions that reduce the overall cost of the materials are as follows:
L = W = 16 cm
H = 32 cm
Given,
What is the dimensions of the rectangle?
A rectangle has two dimensions: a length and a width that are both perpendicular to it. The interior of an oval or a triangle also has two dimensions.
Here,
We've got
Volume = 512 cm3 L* W * H
Sides of the box cost = 1 cent/cm²
Top and bottom cost 2 cent/cm²
Then,
Box dimensions that reduce the overall cost of materials used
We are aware of
L× W × H = 512 cm³
Where,
L stands for length, W for width, and H for height.
So, when we reduce the cost function
C(L, W, H) = (1) 1 H + (2) 1 (L + W)
Thus insert H.
Replacing H with 512/LW yields,
C(L, W) = 512(1/L, 1/W), plus 2LW
So
When both partial derivatives are 0, there will be a minimum cost.
512/L2 - 2W = dC/dL = 0
So
512/W2 - 2L = 0 for dC/dW.
L = 256/W²
Now
The answer to the aforementioned equation is
L = W = (256)⁻³ = 16cm
And
H = 512/16 = 32
H = 32 cm
Consequently, the box's measurements that reduce the overall cost of the materials utilized are:
L = W = 16 cm
H = 32 cm
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Find the product of 2x2(6x + 3)
Answer:
22x
Step-by-step explanation:
2x 2(6x+3)
2x 12x+6x
22x
an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 170 engines and the mean pressure was 6.7 lbs/square inch. assume the standard deviation is known to be 1. if the valve was designed to produce a mean pressure of 6.6 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
There is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
What is the Null hypothesis?In inferential statistics, the null hypothesis states that two possibilities are equal.
The observed difference is thought to be the sole product of chance, which is the underlying premise.
Statistical tests can be used to calculate the likelihood that the null hypothesis is true.
So,
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
As the population standard deviation is given when n > 30
So, we'll run the Z test.
Formula: [tex]z=\frac{x-\mu}{\frac{a}{\sqrt{n}}}[/tex]
Replace the values:
[tex]\begin{aligned}& z=\frac{7.7-7.6}{\frac{11.6}{\sqrt{160}}} \\& z=2.449\end{aligned}[/tex]
For the p-value, see the z table.
Consequently, p = 0.9927.
The two-tailed nature of the test So, p = 2(1- 0.9927) = 0.0146
α = 0.1
p value< α
Thus, we disregard the null hypothesis.
Hence, at the 0.1 level, there is enough evidence to conclude that the valve does not function as intended.
Therefore, there is sufficient data to infer that the valve does not operate as intended at the 0.1 level.
Null hypothesis: H₀ : μ = 7.6
Alternative hypothesis: Hₐ : μ ≠ 7.6
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which of the following statements are true for a frequentist definition for the probability of an event g
The frequentist probability is objective, based on observed data, need large sample or long term frequency, and doesn't have prior knowledge.
What is frequentist probability?Frequentist probability is a definition of probability that defines the probability of an event as the probability of an event being observed in a long-term or infinite experiment.
Frequentist probability is different from Bayesian probability in following points,
Frequentist is objective and Bayesian is subjectiveFrequentist based on observed data and Bayesian based on degree of beliefFrequentist need large sample and Bayesian not necessary need large sampleFrequentist reject the prior assumption or knowledge and Bayesian need prior assumption or knowledge for parameterThus, the statement are true for frequentist definition for the probability is doesn't have prior knowledge, need large sample, based on observed data, and objective.
Your question is incomplete, but it is general information about the frequentist definition of probability.
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It costs a craftsperson 110 to bring 150 picture frames to market and the picture frames sell for 2. The difference between the cost and the income from sales is the craftsperson’s profit?
(8x + 5)^3 find the product
Answer: [tex]512x^3+960x^2+600x+125[/tex]
Step-by-step explanation: Start by spreading the expression out so it turns into (8x + 5)*(8x + 5)*(8x + 5). (* means multiply). Then, foil (multiply the first numbers, outside numbers, inside numbers, and last numbers to form a new expression) the first two expressions to get 64x^2+80x+25*(8x + 5). Foil that again, going through and multiplying each number from both expressions by every number in the other expression to get 512x^3+960x^2+600x+125. Hope that helps.
Answer:
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Perfect Cube Formula}\\\\$\left(a+b\right)^3=a^3+3a^2b+3ab^2+b^3$\\\end{minipage}}[/tex]
To find the product of the given expression, use the perfect cube formula.
Given expression:
[tex](8x + 5)^3[/tex]
Therefore:
a = 8xb = 5Apply the perfect cube method:
[tex]\begin{aligned}(8x+5)^3&=(8x)^3+3(8x)^2(5)+3(8x)(5)^2+5^3\\&=8^3 \cdot x^3+3 \cdot 64x^2\cdot5+3\cdot 8x\cdot 25+125\\&=512x^3+960x^2+600x+125\end{aligned}[/tex]
A student believes she can prove the two triangles are congruent using SAS. Which pieces of
information does she need.
Chose ALL that apply. This question has multiple answers.
W
X
Y
Z
A.
B.
C. WZ-WZ by reflexive property
D. WY-WY by definition of rectangle
Answer:
<XWZ ≅ < XZW by alternate interior angles & WZ = WZ by reflexive property
Step-by-step explanation:
Because they're parallel lines cut by a transversal. So, <W is where one angle is, and <Z is where another angle is. They both share a side as well. Always look out for those types of triangles because those are types of hidden information