Answer:
No Factors
Step-by-step explanation:
[tex]x^3-12x^2-19x+20 = 0\\Let \ p(x) = x^3-12x^2-19x+20[/tex]
Factors of 20 = ±1, ±2 , ±4 , ±5 , ±10 and ±20
±1, ±2 and ±3 are not the factors of given polynomial.
Putting x = 4 in the given polynomial
[tex]p(4) = (4)^3+12(4)^2-19(4)+20\\p(4) = 64+192-76+20\\p(4) = 200[/tex]
So, x = 4 is not a factor of p(x)
Putting x = -4 in the given equation
[tex]p(-4) = (-4)^3+12(-4)^2-19(4)+20\\p(-4) = -64+192-76+20\\p(-4) = 73[/tex]
So, x = -4 in the given equation
Putting x = 5 in the given equation
[tex]p(5) = (5)^3+12(5)^2-19(5)+20\\p(5) = 125+300-95+20\\p(5) = 350[/tex]
So, x = 5 is not a factor of p(x)
Putting x = -5 in the given equation
[tex]p(-5) = (-5)^3+12(-5)^2-19(-5)+20\\p(-5) = -125+300+95+20\\p(-5) = 290[/tex]
So, x = -5 is not a factor of p(x)
Putting x = 10 in the given equation
[tex]p(10) = (10)^3+12(10)^2-19(10)+20\\p(10) = 1000+1200-190+20\\p(10) = 2030[/tex]
So, x = 10 is not a factor of p(x)
Putting x = -10 in the given equation
[tex]p(-10) = (-10)^3+12(-10)^2-19(-10)+20\\p(-10) = -1000+1200+190+20\\p(-10) = 410[/tex]
So, x = -10 is not a factor of p(x)
Putting x = 20 in the given equation
[tex]p(20) = (20)^3+12(20)^2-19(20)+20\\p(20) = 8000+4800-380+20\\p(20) = 12440[/tex]
So, x = 20 is not a factor of p(x)
Putting x = -20 in the given equation
[tex]p(-20) = (-20)^3+12(-20)^2-19(-20)+20\\p(-20) = -8000+4800+380+20\\p(-20) = -2800[/tex]
So, x = -20 is not a factor of p(x)
From the above solution, we conclude that the given equation can not be factorized and thus, has no factors.
Answer:
[tex]\boxed{\mathrm{No \: factors}}[/tex]
Step-by-step explanation:
[tex]x^3 +12x^2 -19x= -20[/tex]
Add 20 on both sides.
[tex]x^3 +12x^2 -19x+20= 0[/tex]
Add 67x and 44 on both sides.
[tex]x^3 +12x^2 +48x+64= 67x + 44[/tex]
Factor left side of the equation.
[tex](x+4)(x+4)(x+4)= 67x + 44[/tex]
[tex](x+4)^3=67x+44[/tex]
Subtract 67x and 44 on both sides.
[tex](x+4)^3-67x-44=0[/tex]
Cannot be factored further.
This is a prime expression. A prime expression cannot be factored.
We cannot factor out x from the expression, there are no factors.
[tex]3x+5y=7\\9x+11y=13[/tex] Solve for the variables.
Answer:
x = -1
y =2
Step-by-step explanation:
3x+ 5y = 7
9x+ 11y = 13
Multiply the first equation by -3 so we can eliminate x
-3 (3x+ 5y = 7)
-9x -15y = -21
Add this to the second equation
-9x -15y = -21
9x+ 11y = 13
-------------------
- 4y = -8
Divide by -4
-4y/-4 = -8/-4
y=2
Now solve for x
3x+5y = 7
3x+5(2) = 7
3x+10 = 7
Subtract 10
3x = 7-10
3x = -3
Divide by 3
3x/3 = -3/3
x = -1
Answer:
-1, 2
Step-by-step explanation:
Although you already have the answer, here's another method of doing it that may or may not help you someday. First, we solve the top equation for x. We get:
[tex]x = \frac{7}{3} - \frac{5}{3}y\\9x + 11y = 13[/tex]
Now that we know what x is, we can plug it into the bottom equation to solve for y.
[tex]9(\frac{7}{3} - \frac{5}{3}y) + 11y = 13[/tex]
Simplify everything out, and you'll see that y = 2. We can now plug it into our equation to solve for x.
x = 7/3 - 5/3 x 2; x = -1
Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 − x2
Answer:
x = -1.964636
Step-by-step explanation:
Given equation;
eˣ = 4 - x²
This can be re-written as;
eˣ - 4 + x² = 0
Let
f(x) = eˣ - 4 + x² -----------(i)
To use Newton's method, we need to get the first derivative of the above equation as follows;
f¹(x) = eˣ - 0 + 2x
f¹(x) = eˣ + 2x -----------(ii)
The graph of f(x) has been attached to this response.
As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.
Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0
From Newton's method,
[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]
=> When n=0, the equation becomes;
[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]
[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]
Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;
f(-2) = e⁻² - 4 + (-2)²
f(-2) = e⁻² = 0.13533528323
And;
f¹(2) = e⁻² + 2(-2)
f¹(2) = e⁻² - 4 = -3.8646647167
Therefore
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - -0.03501863503[/tex]
[tex]x_{1} = -2 + 0.03501863503[/tex]
[tex]x_{1} = -1.9649813649[/tex]
[tex]x_{1} = -1.96498136[/tex] [to 8 decimal places]
=> When n=1, the equation becomes;
[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]
[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]
Following the same procedure as above we have
[tex]x_{2} = -1.96463563[/tex]
=> When n=2, the equation becomes;
[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]
[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]
Following the same procedure as above we have
[tex]x_{3} = -1.96463560[/tex]
From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately -1.964636 to 6 decimal places.
Newton's method of approximation is one of the several ways of estimating values.
The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
The equation is given as:
[tex]\mathbf{e^x = 4 - x^2}[/tex]
Equate to 0
[tex]\mathbf{4 - x^2 = 0}[/tex]
So, we have:
[tex]\mathbf{x^2 = 4}[/tex]
Take square roots of both sides
[tex]\mathbf{ x= \pm 2}[/tex]
So, the negative root is:
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]
Differentiate
[tex]\mathbf{f'(x) = e^x +2x }[/tex]
Using Newton's method of approximation, we have:
[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]
When x = -2, we have:
[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]
[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]
So, we have:
[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -1.96498136}[/tex]
Repeat the above process for repeated x values.
We have:
[tex]\mathbf{x_{2} = -1.96463563}[/tex]
[tex]\mathbf{x_{3} = -1.96463560}[/tex]
Up till the 6th decimal places,
[tex]\mathbf{x_2 = x_3}[/tex]
Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
Read more about Newton approximation at:
https://brainly.com/question/14279052
Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.
Answer:
The first statement is incorrect. They have to be complementary.
Step-by-step explanation:
You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.
You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.
The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
The first statement is incorrect. The angle B is not equal to theta θ. The two acute angles in the right triangle can be different, if the triangle was an isosceles right triangle then angle B would be equal to theta θ.
Question 15
1 pts
The cost of three avatars and three bats is $29.85. The cost of
three avatars and two bats is $23.90. How much will you pay
altogether if you purchase one of each.
O $5.95
O $8.92
$9.95
O $10.99
O $11.00
1 pts
Question 16
9
Answer:
$9.95.
Step-by-step explanation:
Let's say that you are buying a avatars and b bats.
3a + 3b = 29.85
Divide all terms by 3.
a + b = 9.95
You will pay $9.95 if you buy one of each.
Hope this helps!
Please help what’s the answer!!!
Answer:
-1
Step-by-step explanation:
Anything raised to 0 is 1
Multiply i 1 by 1
Simplify.
Rewrite i2 as −1
Move −1 to the left of i
Rewrite −1 i as −i
Factor out i2
Rewrite i2 as −1
Rewrite i2 as −1
Rewrite i4 as 1
Multiply −1 by 1
Draw a picture of the standard normal curve and shade the area that corresponds to the requested probabilities. Then use the standard normal table to find the following probabilities. Enter the probabilities as decimals. Enter the final answer only. 1.P(z>1.38)= 2.P(1.233 −2.43)= 7.P(z>−2.43)=
Answer:
a)P [ z > 1,38 ] = 0,08379
b) P [ 1,233 < z < 2,43 ] = 0,1012
c) P [ z > -2,43 ] = 0,99245
Step-by-step explanation:
a) P [ z > 1,38 ] = 1 - P [ z < 1,38 ]
From z-table P [ z < 1,38 ] = 0,91621
P [ z > 1,38 ] = 1 - 0,91621
P [ z > 1,38 ] = 0,08379
b) P [ 1,233 - 2,43 ] must be P [ 1,233 < z < 2,43 ]
P [ 1,233 < z < 2,43 ] = P [ z < 2,43 ] - P [ z > 1,233 ]
P [ z < 2,43 ] = 0,99245
P [ z > 1,233 ] = 0,89125 ( approximated value without interpolation)
Then
P [ 1,233 < z < 2,43 ] = 0,99245 - 0,89125
P [ 1,233 < z < 2,43 ] = 0,1012
c) P [ z > -2,43 ]
Fom z-table
P [ z > -2,43 ] = 1 - P [ z < -2,43 ]
P [ z > -2,43 ] = 1 - 0,00755
P [ z > -2,43 ] = 0,99245
Write the following Arithmetic Sequence using a Recursive Formula: a = -7 + 3(n - 1)
A : A1 = -7, an = an-1 + 3
B : A1= -7, a, = an+1 + 3
C : A1 = 3, an = an+1 - 7
D : A1 = 3, an = an-1 - 7
NEED ANSWER ASAP
Answer:
A : A1 = -7, an = an-1 + 3
Step-by-step explanation:
a1=-7, a2=-7+(1)3=-4
a3=-7+(2)3=-1
A study compared surgery and splinting for subjects suffering from carpal tunnel syndrome. It was found that among 73 patients treated with surgery,
there was a 92% success rate. Among 83 patients treated with splints, there was a 72% success rate. Calculations using those results showed that if
there really is no difference in success rates between surgery and splints, then there is about 1 chance in 1000 of getting success rates like the ones
obtained in this study. Which statement cannot be said?
The better treatment for carpal tunnel syndrome is surgery.
The result has practical significance.
The recommended treatment for carpal tunnel syndrome is splinting.
The result has statistical significance.
Answer:
the answer is c
Step-by-step explanation:
because if the surgery has a 92% success rate and the splints have a 72% success rate then surgery would be recommended because it has a higher success rate
Which expression is equivalent to the expression below? StartFraction 6 c squared + 3 c Over negative 4 c + 2 EndFraction divided by StartFraction 2 c + 1 Over 4 c minus 2 EndFraction StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction 3c –3c
Answer:
its D. -3c
Step-by-step explanation:
just took the test
The expression that is equivalent to the expression [(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)] is; -3c
The fraction we are given to work with is;[(6c² + 3c)/(-4c + 2)] ÷ [(2c + 1)/(4c - 2)]
Simplifying the fraction equation by factorization gives:[3c(2c + 1)/(-2(2c - 1))] ÷ [(2c + 1)/(2(2c - 1)]
Now, in division of fractions, we know that;3/2 ÷ 1/5 is the same as; 3/2 × 5/1
Applying this same method to our question gives;
[3c(2c + 1)/(-2(2c - 1))] × [(2(2c - 1)/(2c + 1)]
2(2c - 1) is common and will cancel out to get; 3c(2c + 1)/(-1/(2c + 1))2c + 1 is common and will cancel out to get; -3cRead more about simplification of fractions at;https://brainly.com/question/6109670
Need help with solving for x!
Answer:
x = c × sin(α)
x = 15 x sin(38)
= 9.23492
= 9.2
Step-by-step explanation:
Find the length ofPR
Answer:
PR=8x+4
Step-by-step explanation:
Given:
PQ=3x-2
QR=5x+6
Required:
PR=?
Formula:
PR=PQ+QR
Solution:
PR=PQ+QR
PR=3x-2+5x+6
PR=3x+5x+6-2
PR=8x+4
Hope this helps ;)❤❤❤
Answer:
4(2x + 1)
Step-by-step explanation:
4(2x + 1)
CAN SOMEONE PLEASE HELP ME! To find x
ANSWERS
A-(11)
B-(14)
C-(7)
D-(3)
Answer:
C-(7)
Step-by-step explanation:
Given figure is a trapezoid and 21 - x is the mid segment.
Therefore by mid-segment formula of a trapezoid, we have:
21 - x = 1/2(17 + 11)
21 - x = 1/2 * 28
21 - x = 14
21 - 14 = x
7 = x
x = 7
what is the value of this expression when a = 2 and b = -3 ? a^3 - b^3 / 5
Answer:
13 2/5
Step-by-step explanation:
a = 2 and b = -3
so the question asks whats.... a^3 - b^3/5
First we plug in the values of a and b
(2)^3 - (-3)^3 /5
Now we solve the ones in paranthesis first
(2)^3 = 8 because 2×2×2 and
-(-3)^3 forget about the - outside the parenthesis so
(-3)^3 = (-27) because (-3)×(-3)×(-3)
now we put it back together
8 -(-27)/5
the two minus become plus so
8 + 27/5
Now we solve it like fractions
8 and 27/5
simplify
13 and 2/5
Hope that helps!
Mrs Tan has 2 daughters, Phoebe and Jody. The highest common factor and lowest common multiple of their ages are 3 and 168 respectively.If Phoebe is 3 years older than her sister, find her age.
Answer:
Phoebe's age = 24 years.
Step-by-step explanation:
Given:
Highest Common Factor and Lowest Common Multiple of the ages are 3 and 168 respectively.
Phoebe is 3 years older than Jody.
To find:
The age of Phoebe = ?
Solution:
Here, We have two numbers whose
HCF = 3 and
LCM = 168
Let the age of Phoebe = P years and
Let the age of Jody = J years
As per given statement:
[tex]P = J + 3 ...... (1)[/tex]
Let us learn about the property of LCM and HCF of two numbers.
The product of LCM and HCF of two numbers is equal to the product of the two numbers themselves.
LCM [tex]\times[/tex] HCF = P [tex]\times[/tex] J
[tex]\Rightarrow P\times J = 3 \times 168 \\\Rightarrow P\times J = 504[/tex]
Putting the value of P from equation (1):
[tex]\Rightarrow (J+3)\times J = 504\\\Rightarrow J^2+3J-504 = 0\\\Rightarrow J^2+24J-21J-504 = 0\\\Rightarrow J(J+24) - 21(J+24) = 0\\\Rightarrow (J - 21)(J+24) = 0\\\Rightarrow J = 21, -24[/tex]
Negative value for age is not possible So, Jody's age = 21 years
Using equation (1):
Phoebe's age = 21 + 3 = 24 years.
In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6970 subjects randomly selected from an online group involved with ears. There were 1334 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution.
Answer:
we will fail to reject the null hypothesis and conclude that the return rate is less than 20%.
Step-by-step explanation:
We are given;
Sample size;n = 6970
Success rate;X = 1334/6970 = 0.1914
Now, we want to test the claim that the return rate is less than p = 0.2, hence the null and alternative hypothesis are respectively;
H0: μ < 0.2
Ha: μ ≥ 0.2
The standard deviation formula is;
σ = √(x(1 - x)/n)
σ = √(0.1914(1 - 0.1914)/6970)
σ = 0.004712
Now for the test statistic, formula is;
z = (x - μ)/σ
z = (0.1914 - 0.2)/0.004712
z = -1.825
From the a-distribution table attached, we have a value of 0.03362.
This p-value gotten from the z-table is more than the significance value of 0.01. Thus, we will fail to reject the null hypothesis and conclude that the return rate is less than 20%.
11 Is what percent of 20?
Answer:
55%
Step-by-step explanation:
Because 11/20= 0.55
0.55=55%
Write 21/7 as a whole number
Answer: 3
Step-by-step explanation:
7x=21 21/7=3
volume= (can someone explain please, im not really understanding this)
Not the greatest picture; I think it's trying to be a house, an A frame with a rectangular base.
This is a prism with a side 3 equilateral triangle at the end and a length of 6.
The area of the triangle is
[tex]\Delta = \dfrac{\sqrt{3}}{4} s^2[/tex]
The volume is area times length,
[tex]V = L \Delta = \dfrac{\sqrt{3}}{4} s^2 L[/tex]
[tex]V = \dfrac{\sqrt{3}}{4} (3^2) 6 = \dfrac{27}{2} \sqrt{3}[/tex]
Answer: (27/2) √3
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65
Answer:
50
Step-by-step explanation:
50 because of the 100 of 79 to 7
What is the average rate of change of f(x)=-2/x^2 when the interval is 1 to 2
Answer:
1.5
Step-by-step explanation:
average rate of change = (f(x2) - f(x1))/(x2 - x1)
f(x) = -2/x^2
f(x2) = f(2) = -2/(-2)^2 = -2/4 = -0.5
f(x1) = f(1) = -2/1^2 = -2
average rate of change = (-0.5 - (-2))/(2 - 1)
average rate of change = (-0.5 + 2)/1
average rate of change = 1.5
50 + 100n where n = 2
CAN ANYONE HELP ME THANKS FOR BRAINLIEST ANSWER? Find slope ( simplest form) parallel to the line 4x+2y=3
Answer:
Slope = -2
Step-by-step explanation:
You want to get it to the slope intercept form first.
2y = -4x + 3
Divide by 2
y = -2x + 3/2
Parallel means in the new slope intercept form there will still be -2x.
y = -2x + b (enter in points ( 0, 1.5 ) )
1.5 = 0 + b
b = 1.5
y = -2x + 1.5 ( just an example of a line parallel to 4x + 2y = 3 )
The graph of an exponential function has a y-intercept of 4 and contains the point (3,500). Construct the exponential function that describes the graph.
Answer:
The "formula" for an exponential function is f(x) = a * bˣ where a is the initial value / y-intercept. Therefore, a = 4 so f(x) = 4 * bˣ. To solve for b, we can plug in the values x = 3 and f(x) = 500 which becomes:
500 = 4 * b³
125 = b³
b = 5 so the answer is f(x) = 4 · 5ˣ.
Answer:
f(x)=4(5)x
Step-by-step explanation:
An exponential equation in the form y=a(b)x has initial value a and common ratio b. The initial value is the same as the y-intercept, 4, so the equation is in the form y=4(b)x. Substituting the point (3,500) gives 500=4(b)3. Solve for b to find that the common ratio is 5.
if you vertically stretch the expontial function f(x) = 2^2 by a factor of 5, what is the equation of the new function?
Answer:
g(x) = [tex]5(2^{2x} )[/tex]
Step-by-step explanation:
If a function f(x) is vertically stretched by a factor of k, the new function we get in the form of k.f(x).
Rule to be followed,
y = k.f(x)
Where k > 1
If the function is vertically compressed then 0 < k < 1
Following the same rule,
A function, f(x) = [tex]2^{2x}[/tex] when vertically stretched by a factor of 5,
Transformed function will be,
g(x) = [tex]5(2^{2x} )[/tex]
what is 4 1/3 x 4 1/5=
Answer:
18 1/5
Step-by-step explanation:
Hey there!
Well to multiply them let's make them improper.
13/3 * 21/5
13*21 = 273
3*5 = 15
273/15
Simplified
18 1/5
Hope this helps :)
Answer:
[tex]\huge\boxed{4\dfrac{1}{3}\times4\dfrac{1}{5}=18\dfrac{1}{5}}[/tex]
Step-by-step explanation:
[tex]4\dfrac{1}{3}\times4\dfrac{1}{5}\\\\\bold{STEP\ 1}\\\text{convert the mixed numbers to the improper fractions}\\\\4\dfrac{1}{3}=\dfrac{4\times3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\4\dfrac{1}{5}=\dfrac{4\times5+1}{5}=\dfrac{20+1}{5}=\dfrac{21}{5}\\\\\bold{STEP\ 2}\\\text{simplify fractions}\\\\4\dfrac{1}{3}\times4\dfrac{1}{5}=\dfrac{13}{3}\times\dfrac{21}{5}=\dfrac{13}{1}\times\dfrac{7}{5}\\\\\bold{STEP\ 3}\\\text{multiply numerators and denominators}\\\\=\dfrac{13\times7}{1\times5}=\dfrac{91}{5}[/tex]
[tex]\bold{STEP 4}\\\text{convert the improper fraction to the mixed number}\\\\=\dfrac{91}{5}=\dfrac{90+1}{5}=\dfrac{90}{5}+\dfrac{1}{5}=18\dfrac{1}{5}[/tex]
Fake question: Should Wishing be a moderator? (If you could answer I'd appreciate it haha.)
Real question: Simplify [tex](z^3*z^2)-(y^4*y)[/tex]
Step-by-step explanation:
(z³*z²)-(y^4 *y) z^5 - y^5Answer:
[tex]z^5-y^5[/tex]
Step-by-step explanation:
=> [tex](z^3*z^2)-(y^4*y)[/tex]
When bases are same, powers are to be added
=> [tex](z^{3+2})-(y^{4+1})[/tex]
=> [tex]z^5-y^5[/tex]
P.s. Yessss, Wishing should be a moderator so that he can delete all the absurd or plagiarized answer!!!!!!!!
Syrus is buying a tent with the dimensions shown below. The volume inside the tent is 4.5 m34.5\text{ m}^34.5 m34, point, 5, start text, space, m, end text, cubed. Syrus isn't sure if the tent will be tall enough for him to stand inside. What is the height of the tent?
Answer:
2 meters
Step-by-step explanation:
The volume is 4.5
⋅1.5⋅h⋅3
=2.25h
=h
The height of the tent is 2 meters.
Hope this helps :)
Answer:
2 meters
Step-by-step explanation:
A gift package contains 6 wedges of cheese . If each wedges is 2/3 onuce what is the totel weight in pounds of cheese?
Answer:
4 ounces
Step-by-step explanation:
6x2/3= 4
A lease provides that the tenant pays $760 minimum rent per month plus 4% of the gross sales in excess of $150,000 per year. If the tenant paid a total rent of $20,520 last year, what was the gross sales volume?
Answer:
$435,000
Step-by-step explanation:
$760 per month * 12 months = $9,120
The minimum rent requires an annual rental cost of $9,120.
The annual rent was $20,520.
The excess was $20,520 - $9,120 = $11,400.
The amount of $11,400 of the rent was due to the gross sales in excess of $150,000.
$11,400 is 4% of the amount in excess of $150,000.
Let the amount in excess of $150,000 = x.
$11,400 = 4% of x
0.04x = 11,400
x = 285,000
$285,000 is the amount in excess of $150,000.
Total gross sales volume = $285,000 + $150,000 = $435,000
In the figure below, YZA and YZX are right angles, XYZ and AYZ are congruent, and XZ = 10. What is the length of ?
A.
25
B.
20
C.
10
D.
5
Answer:
C. 10
Step-by-step explanation:
The given information tells you that triangles YZX and YZA are congruent, so ZA = ZX = 10.