Step-by-step explanation:
[tex] \frac{ {5}^{3} }{ {5}^{7} } \\ \\ = {5}^{3 - 7} \\ \\ = {5}^{ - 4} \\ \\ = \frac{1}{ {5}^{4} } [/tex]
The length of the hypotenuse of an isosceles right triangle is 14. What is the length of each leg of the triangle?
Answer:
leg = √7 units (approximately 2.65 units)
Step-by-step explanation:
Given a right isoceles triangle with a hypotenuse of 14 units, the two other legs must be congruent in length. Because this is a right triangle, the pythagorean theorem a^2 + b^2 = c^2, can be used.
Since the two legs are congruent, side a = side b. This means that
2leg^2 = hypotenuse.
_____________
2leg^2 = 14 units
÷ 2. ÷2
_____________
leg^2 = 7 units
√ √
____________
leg = √7 units
A square chunk of plastic has a length of 5 cm, width of 5 cm and height of 5 cm. It has a mass of 200 g. What is it’s density
Answer: isn’t it 1.6 because you multiply 5 x 5 x 5 = 125 and then you divide 200\125 =1.6
a football team ran two plays. on the first play, the quarterback was tackled for -8 yards. on the second play, the running back ran for 10 1/2 yards. on which play did the team gain more yards?
Answer:
both are 2cnd play
Step-by-step explanation:
Find the value of d. Show your work.
The value of the external part of the secant segment d is 3.
What is the numerical value of d?The secant-tangent power theorem states that "if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment."
It is expressed as:
( tangent segment )² = External part of the secant segment × Secant segment.
From the diagram:
Tangent segment = 6
External part of the secant segment = d
Secant segment = ( d + 9 )
Plug these values into the above formula:
( tangent segment )² = External part of the secant segment × Secant segment.
6² = d( d + 9 )
Solve for d
36 = d² + 9d
d² + 9d - 36 = 0
Factor usng method:
( d - 3 )( d + 12 ) = 0
d = 3 and d = -12
Since we are dealing with dimension, we take the positive value.
Therefore, the value of d is 3.
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In circle L with m∠KLM = 58∘ KL=14, find the area of sector KLM. Round to the nearest hundredth.
The area of sector KLM is approximately 24.0196 square units when rounded to two decimal places.
The area of sector KLM is to be found in circle L, which has a measure of 58 degrees and a length of 14.
The formula for determining the area of a sector is given below:Area of sector = (angle measure/360°) x πr²
The angle measure is 58°. The radius is half of the length of KL, which is 14 units. So, r = 14/2 = 7.Substituting the values in the formula,
Area of sector = (58/360) x π x 7²Area of sector = (0.1611) x (49π)Area of sector = 7.6379π
The final answer needs to be rounded off to two decimal places, which is achieved by multiplying it by 100, rounding to the nearest integer, and then dividing by 100.Area of sector ≈ 7.64 x π units²
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HELP ME PLEASE .find g(x+3) if g(v)=-5v-23
Answer:
g(x + 3) = -5x -38
Step-by-step explanation:
Given g(v) = -5v -23
We are to find g(x + 3)
What we shall simply do here is substitute (x + 3) for v in the g(v) equation
That would be;
g(x + 3) = -5(x + 3) -23
g(x + 3) = -5x -15 -23
g(x + 3) = -5x -38
a sauce recipe calls for 4 pounds of ground beef and you want to halve it how many ounces of ground beef do you need?
If you want to halve the recipe, you will need 32 ounces of ground beef. We can find it by multiplying.
To determine the amount of ground beef needed when halving the recipe, we need to convert pounds to ounces. There are 16 ounces in 1 pound.
Given that the original recipe calls for 4 pounds of ground beef, we can calculate the amount needed when halving the recipe by dividing it by 2.
Amount needed when halving = 4 pounds / 2 = 2 pounds.
To convert 2 pounds to ounces, we multiply it by 16:
2 pounds * 16 ounces/pound = 32 ounces.
Therefore, when you halve the recipe, you will need 32 ounces of ground beef.
In conclusion, to make half of the original recipe that calls for 4 pounds of ground beef, you will need 32 ounces of ground beef.
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Exercises In Exercises 1-2, use Eq. (3) to find the length of the path over the given interval, and verify your answer using geometry. 1. (3t-1,2-21), 0≤t≤5 2. (1+5t, t-5), -3≤1≤3 In Exercises 3-8, use Eq. (3) to find the length of the path over the given interval. 3. (21², 312-1), 0≤t≤4 4. (31,413/2), 0≤t≤l 5. (31²,4t³), 1≤t≤4 6. (t³+1,t²-3), 0≤t≤1 7. (sin 3t, cos 3t), 0≤t≤π 8. (sin - cos, cos 0 + 0 sin 0), 0≤0 ≤2ib ((1)(0)2) = (12 In Exercises 9 and 10, find the length of the path. The following identity should be helpful: 010 dignatus = 1 - cost n²/1/2 2 = sin² 2:20 9. (2 cost - cos 2t, 2 sin t - sin 2t), 0≤t≤ 1/ 10. (5(0 sin 0), 5(1- cos 0)), 0≤0 ≤ 2π -
In the given exercises, the length of a path over a specific interval is to be found using Equation (3). The equation represents the distance between two points in a Cartesian coordinate system. In Exercises 1-2, the length is calculated using Equation (3) and then verified using geometry. In Exercises 3-8, the length is determined solely using Equation (3). Exercises 9 and 10 involve finding the length of the path using a relevant identity and the given coordinates.
Equation (3) represents the distance between two points (x₁, y₁) and (x₂, y₂) in a Cartesian coordinate system:
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)
In Exercises 1-2, the coordinates of the points are provided, along with the specified interval. The length of the path is found by substituting the coordinates into Equation (3) and evaluating the expression. To verify the answer geometrically, one can plot the points on a coordinate plane and measure the distance between them using a ruler or by applying geometric principles.
Exercises 3-8 involve using Equation (3) directly to find the length of the path over the given interval. The coordinates of the points are provided, and the interval specifies the range of t values to consider.
Exercises 9 and 10 require using a relevant identity to find the length of the path. The given coordinates are substituted into the identity, and the resulting expression is simplified to determine the length.
In summary, the exercises involve finding the length of paths using Equation (3) in various scenarios. The lengths are calculated by substituting the given coordinates into the equation, and in some cases, geometry or relevant identities are used to verify or simplify the expressions.
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What is the equation of the line that contains the
points (3, 5) and (7, 9)?
a. y = 2x - 1
b. y=x+2
c. y=x-2
d. y = 2x-5
Answer:
B
Step-by-step explanation:
y=kx+m
k=y2+y1 / x2+x1
(3,5) and (7,9)
k=(9-5)/(7-3)=4/4=1
Now we want to find out what m is. This is by inserting a point in the equation of the line y=kx+m.
so I'll pick (3,5)
5=1×3+m
m= 2
To check if it's correct we could try it with the other point, (7,9).
9=1×7+m
m=2
Therefor the equation would be. y=1x+2
What are the coefficients of the terms?
Consider the expression
x + 5x^(6) - x^(7)
Answer:
A term is a single mathematical expression.
It may be a single number (positive or negative), a single variable ( a letter ), several variables
multiplied but never added or subtracted. Some terms contain variables with a number in front
of them. The number in front of a term is called a coefficient.
Examples of single terms:
3x is a single term. The "3" is a coefficient. The "x" is the variable.
-5x2
y
3
z
4 is also a single term.
The "-5" is the coefficient. " x
2
y
3
z
4
" are the variables comprising the term.
12 is a single term.
It is simply a numerical term called a constant.
w is a single term too.
It is a single variable term and since there is only one "w" it has an implied coefficient of 1 .
We join terms together with addition to create expressions.
5x + 7y is a two termed expression.
The 5x is one term and the 7y is the second term. The two terms are separated by a plus sign.
7x2
y
3
- 2xy
4
+ 7 is a three termed expression.
7x2
y
3
is one term, - 2xy
4
is the second term, and 7 is the third term.
The coefficient of the first term is 7.
The coefficient of the second term is negative 2.
The third term is a constant, so it has no coefficient.
Like Terms
"Like terms" are terms which have variables which look EXACTLY alike.
3x2
and -7x2
are "like terms" because both terms have the variable x
2
5x2
y
6
z
5
, 13x2
y
6
z
5
, and -21x2
y
6
z
5
are "like terms" because all of the terms have the variables "
x
2
y
6
z
5
" in them.
Combining Like Terms
To combine "like terms", combine the coefficients of terms which look exactly alike.
If you start with several terms separated by addition and subtraction signs, your answer should
also contain addition and subtraction signs based on the signs obtained from doing the
arithmetic.
Combine like terms:
3x2
+ 2x + 9 - 2x
2
+ 5x - 3
3x2
+ 2x - 9 - 2x
2
+ 5x - 3
(3 - 2 )x
2
+ (2 + 5 )x + (-9 - 3 )
1x2
+ 7x + (-12)
1x2
+ 7x - 12
You may be required to perform some other algebraic operations before you are ready to
combine like terms.
Simplify. Combine like terms:
-5( 2x3
- 3x2
+ 1) + 2(-2x
3
+ 5x2
- 1)
Distribute the -5 into the first parentheses and multiply.
Do the same with the 2 in front of the second parentheses.
-5(2x
3
) -5(-3x
2
) -5(1) + 2(-2x
3
) + 2(5x2
) + 2(-1)
-10x
3
+ 15x
2
-5 -4x3
+10x2
-2
Now combine like terms,
(-10 - 4 )x
3
+ (15 + 10)x
2
+ (-5 - 2)
-14x3
+25x2
-7
Step-by-step explanation:
Annie can walk 1/2
of a mile in 1/4
of an hour. How many miles can she walk in 2 1/2hours if she walks at the same constant speed?
5 miles
2 1/2 hrs ÷ 1/4 hr = 10
1/2 mile × 10 = 5
Answer: The answer would be 5 miles
Step-by-step explanation:
There are 4 1/4 in a hour, 4 1/2 which would equal 2.
Then since you got 2 hours you would multiply 2 x 2 and get 4, and you got another half so that would equal 2/4 which would be plus 1 mile. =5
Find the equation of a hyperbola satisfying the given conditions. Asymptotes y = 3 X, Y = -3 x: one vertex (3.0) The equation of the hyperbola is. (Type an equation. Type your answer in standard form.
The equation of the hyperbola satisfying the given conditions with asymptotes y = 3x and y = -3x, and one vertex at (3, 0) is given by (x-3)²/9 - (y-0)²/3 = 1.
To find the equation of the hyperbola, we first note that the asymptotes of the hyperbola are given by y = mx and y = -mx, where m is the slope of the asymptotes. Here, the slopes of the asymptotes are 3 and -3, so the equations of the asymptotes are y = 3x and y = -3x.
The general equation for a hyperbola centered at the origin with asymptotes y = mx and y = -mx is given by x²/a² - y²/b² = 1, where a and b are the distances from the center to the vertices along the x-axis and y-axis, respectively.
Since the given vertex is (3, 0), we can determine that the distance from the center to the vertex along the x-axis is a = 3.
Substituting these values into the general equation, we have (x-3)²/9 - y²/b² = 1.
To determine the value of b, we consider that the distance from the center to the asymptote along the y-axis is b/3. Since the asymptotes have a slope of 3 and -3, the distance from the center to the asymptote along the y-axis is 1/3 times the distance from the center to the vertex along the x-axis. Therefore, b = 3a = 9.
Substituting the value of b into the equation, we get (x-3)²/9 - y²/9 = 1.
Simplifying, we obtain (x-3)²/9 - (y-0)²/3 = 1.
Thus, the equation of the hyperbola satisfying the given conditions is (x-3)²/9 - (y-0)²/3 = 1.
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The midpoint of AB is M(-1, -2). If the coordinates of A are (1,3), what are the
coordinates of B?
Answer: (-3,-7)
Step-by-step explanation: I had to get it wrong on delta to give u this answer, ur welcome.
Ashley needs a 4.6 yards of chain to hang some flower baskets the chain is sold by meter how many meters does Ashley need
If anyone knows algebra nation I need help on the section 2 test yourself at the end pls helppppp. I need all 10 answers. 10 answers for 20 points pls help. I will also give brainliest.
Answer:
you have to provide the questions
Step-by-step explanation:
What were some major changes that took place in the art world following the Reformation?
What is the intermediate step in the form
(�+�)2=�(x+a) 2=b as a result of completing the square for the following equation?
�2+32�+116=x 2 +32x+116=12�12x
The intermediate step in the form (a + b)2 = c (x + 4)2 = 8 as a result of completing the Square for the given equation.
The intermediate step in the form (a + b)2 = c (x + a)2 = b as a result of completing the square for the following equation is (x + 4)2 = 8.
The given quadratic equation is x2 + 32x + 116 = 12×12xTo solve this equation using the method of completing the square,
we need to express the quadratic equation in the form of (x + a)2 = b where a and b are real numbers. Hence, let's follow the steps given below:
Step 1: Rearrange the termsx2 + 32x + 116 = 12×12x becomes x2 + 32x + 116 - 144x = 0x2 - 112x + 116 = 0
Step 2: Find the value of a by dividing the coefficient of x by 2.a = (-112)/2 = -56
Step 3: Add and subtract the square of (a) to the left side of the equation.x2 - 112x + 116 = (x - 56)2 - 56(56) + 116x2 - 112x + 116 = (x - 56)2 - 3080
Step 4: Simplify(x - 56)2 - 3080 = 0(x - 56)2 = 3080
Now, comparing with (a + b)2 = c, we can say that the intermediate step in the form (a + b)2 = c (x + 4)2 = 8 as a result of completing the square for the given equation.
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Which group of numbers is ordered from least to greatest?
A. 45,−0.9,−3
B. −3,−0.9,45
C. −0.9,45,−3
D. 45,−3,−0.9
Answer: B.
Step-by-step explanation: Negatives are smaller than positive numbers
Answer:
That would be B
Step-by-step explanation:
because -3 is way behind 0 following by 0.9 being greater than -3 while 45 is greater and way ahead of the others
Given f(x)=-x+4 find x if f(x)=-5
Kyle can type 270 words in 4 minutes. How many words per minute can Kyle type?
(ratio form)
Answer:
67.5
Step-by-step explanation:
true or false: in large samples you do not have to worry about omitted variable bias. true false suppose you take a sample of student test scores and develop the following frequency distribution. the histogram has ten bins, with the height in each bin being the proportion of observations falling within the corresponding score interval. (note: in this case, the students who studied did well on the exam and those who didn't scored poorly.) 0 10 20 30 40 50 60 70 80 90 100 0.5 0.4 0.3 0.2 0.1 0 proportion in cell student scores (in percentage form) true or false: the data appear to be normally distributed. true false
Answer:
Step-by-step explanation:
false
Question 5
Read the question and type your response in the box provided. Your response will be saved automatically.
Two Grade 7 students, Layla and Camille, both solved the following math problem:
If the temperature drops from 8°F to -13°F by how much did the temperature decrease?
The students came up with different answers. Layla said the answer is 21°F, and Camille said the answer is 5°F. Who is correct? Explain y
B
X,
x?
©2020 Illuminate Education, Inc.
What would the answer be (: ASAP plsss
Answer:
t = -3
Step-by-step explanation:
8th grade math please help
Answer:
22.5 for both L and M
Step-by-step explanation:
Complete the following statement.
(-4) (?) = -20
(-4) (5)= -20
I hope it's helpful
write the exponential function f(x)=-4*2^(1-x) in the form f(x)=ab^x
The exponential function f(x) can be written in the form f(x) = -4×(2)⁻¹×2ˣ
The exponential function f(x) = -4×2¹⁻ˣ in the form f(x) = abˣ, we can simplify it as follows:
f(x) = -4×2¹⁻ˣ
Using the property of exponents that aᵇ⁻ⁿ = aᵇ / aⁿ, we can rewrite the function as:
f(x) = -4×(2¹ / 2ˣ)
Simplifying further:
f(x) = -4×(2 / 2ˣ)
Since 2 can be written as 2¹, we can rewrite the function as:
f(x) = -4×(2¹ / 2ˣ) = -4×(2¹×2⁻ˣ) = -4×2¹⁻ˣ
Now we can see that a = -4 and b = 2⁻¹. Therefore, the exponential function f(x) can be written in the form f(x) = abˣ as:
f(x) = -4×(2)⁻¹×2ˣ
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what is the answer for
-16+x=-15
Answer:
x=1
Step-by-step explanation:
-16+x=-15
-16+x+16=-15+16 Add the terms to both sides of the equation.
After that you simplify.
which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital?
A representative sample based on the hospital scenario is option A
What is representative sample?A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.
Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.
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CAN SOMEONE HELP THIS IS DUE TODAY PLSS AND THANK YOU!!!
Answer:
YEA MAYBE STOP YELLING theres my advice like wht r u doing?
Step-by-step explanation:
How do you solve 3x+y=4 step by step?
Answer:
Step-by-step explanation:
3x+y=4
First this is not really have a soluction
So a list 2 soluction right here
solve for x
3x+y=4
-y -y
3x=4-y
x= -y+4/3
Or solve for y
3x+y=4
-3x
y=-3x+4
Or maby you want a another soluction...
Answer:
Slope Intercept form: y = -3x + 4
Slope: -3
Step-by-step explanation:
For slope intercept:
Subtract 3x from both sides:
3x + y - 3x = 4 - 3x
Simplify:
y = -3x + 4
For slope:
If the equation is y = -3x + 4 then using the formula y = mx + b:
Slope = -3
Simplified College Cost Worksheet
Calculate approximate monthly amount to invest at the beginning of the period. Round the final answer to two decimals. Please note that intermediate steps should be calculated to at least 4 decimals to get the answer correctly.
Assume the following information for your client
Step 1 Child's AGE 5
2 Years to college 18-(Step 1)
3 Annual College Costs (current dollars) $65,643
4 Assumed College Inflation rate 3.2%
5 College Inflation Factor. Calculate as (1+Step 4)^(Step 2) (1+Step 4)^(Step 2)
6 Estimate Future Annual Costs Calculate as (Step 3* Step 5) or use FV formula in Excel or financial calculator
7 Estimated Total Future Costs (Step 6*) years in college 4 Step 6*years in college
Funding requirements 8 Assumed after-tax return 10.3%
9 PV Factor 1/(1+Step 8)^Step 2
10 Total Lump-Sum Investment Currently Required Step 7*Step 9 or use PV formula in Excel or financial calculator
11 Amount already earmarked for education $27,231
12 Additional Limp-Sum funding required Step 10-Step 11
13 Years of funding 7
14 PVIFA Due Move to Step 15 to use Excel or financial calculator
15 Annual target amount to invest (Step 12*Step 14) or use formula PMT in Excel or financial calculator
16 Approximate monthly amount to invest (Step 15)/12 months
The client wants to fund the estimated cost of his child's education.The total future costs would be $97,621.34 x 4 = $390,485.36.The approximate monthly amount to invest is $42,798.40.
Given the age of the child, 5 years, and the years to college which is 18-5=13 years.The annual college cost of the child is $65,643, and the assumed college inflation rate is 3.2%.
Therefore the college inflation factor can be calculated as follows;(1+3.2%)^(13) = 1.48774963Estimate future annual costs (Step 6*):$65,643 x 1.48774963 = $97,621.34.
The total future costs (Step 7*) would be $97,621.34 x 4 = $390,485.36The client's assumed after-tax return is 10.3%.
Therefore the present value factor (PV Factor) can be calculated as follows;1/(1+10.3%)^13 = 0.28936396.
Total Lump-Sum Investment currently required (Step 10):$390,485.36 x 0.28936396 = $112,902.19The amount already earmarked for education is $27,231.
Therefore the additional Lump-Sum funding required would be; $112,902.19 - $27,231 = $85,671.19The client wants to fund the child's education for seven years.
Therefore the Present Value Interest Factor of Annuity Due (PVIFA Due) can be calculated as follows;PVIFA Due (Step 14) = ((1 - (1 + 10.3%)^(-7))) / (10.3% * (1 + 10.3%)^(-7))= 5.98297324.
Annual target amount to invest (Step 15):$85,671.19 x 5.98297324 = $513,580.78.
Approximate monthly amount to invest $513,580.78 / 12 = $42,798.40Rounding this to two decimal places will give $42,798.40.
The approximate monthly amount to invest is $42,798.40.
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