Answer:
C.3
Step-by-step explanation:
SP and SR are tangent to circle Q.
-> SP = SR
-> 10x - 18 = 2x + 6
-> 10x - 2x = 18 + 6
-> 8x = 24
-> x = 24/8
-> x = 3
Answer:
C. 3
Step-by-step explanation:
A piece of twine 6 yards long costs $2.88. What is the price per foot?
Solution:
Note that:
1 yard = 3 foot6 yards = $2.88First, let's convert the yards into feet.
6 yards = 6 x 3 feet = $2.88=> 18 feet = $2.88Now, divide 18 both sides to find the cost of 1 foot.
=> 18 feet/18 = $2.88/18=> 1 foot = $0.16The price of the twine per foot is $0.16.
What is the cost of the twine per foot?The first step is to convert yards to foot: 1 yard = 3 foot
In order to convert yards to foot, multiply 6 by 3: 6 x 3 = 18 foot
The price per foot can be determined by dividing $2.88 by 18 foot
$2.88 / 18 = $0.16
To learn more about division, please check: https://brainly.com/question/194007
the 8th term of an arithmetic sequence is -42 and the 16th term is -74. Find and simplify an expression for the nth term
Answer:
[tex]a_{n}[/tex] = - 4n - 10
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₈ = - 42 and a₁₆ = - 74 , then
a₁ + 7d = - 42 → (1)
a₁ + 15d = - 74 → (2)
subtract (1) from (2) term by term to eliminate a₁
8d = - 74 - (- 42) = - 74 + 42 = - 32 ( divide both sides by 8 )
d = - 4
substitute d = - 4 into (1) and solve for a₁
a₁ + 7(- 4) = - 42
a₁ - 28 = - 42 ( add 28 to both sides )
a₁ = - 14
Then
[tex]a_{n}[/tex] = - 14 - 4(n - 1) = - 14 - 4n + 4 = - 4n - 10
Answer:
[tex]a_{n}=-10-4n[/tex]
Step-by-step explanation
[tex]a_{n}=a_{1}+(n-1)d\\Given:a_{8}=-42\\&a_{16}=-74\\Hence: \\a_{8}=a_{1}+7d=-42 (1)a_{16}=a_{1}+15d=-74 (2)\\ \left \{ {{a_{1}+7d=-42} \atop a_{1}+15=-74}} \right. \\(2)-(1):8d=-32\\ d=-32/8 =-4\\Substitute :d=-4 in equation (1)"\\-42=a_{1}+7(-4)\\-42=a_{1}-28\\a_{1}=-14\\Hence:\\a_{n}=-14-(n-1)4\\a_{n}=-14-4n+4\\a_{n}=-10-4n[/tex]
A pound of blueberries costs $3.50 and a pound of oranges cost $2.50. Whats the total cost of 0.6 pounds of blueberries and 1.8 pounds of oranges?
HELP PLEASE!!
Answer:
$6.60
Step-by-step explanation:
1 pound of blueberries = $3.50
if 0.6 pound = 3.50 × 0.6 = 2.10
1 pound of oranges = $2.50
if 1.8 pound = 2.50 × 1.8 = 4.50
Total = $4.60
how do you work this out
Answer:
gradient = 2
Step-by-step explanation:
calculate the gradient m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 0) and (x₂, y₂ ) = (5, 8) ← 2 points on the line
m = [tex]\frac{8-0}{5-1}[/tex] = [tex]\frac{8}{4}[/tex] = 2
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Please I really need help with this one! I have to do 38 questions before 11:38.
Answer:
B, between 3 and 4 miles
Step-by-step explanation:
We know that h is 9.
√1.5*9
1.5*9=13.5
This can be done without a calculator.
if we know that √13.5 is in between √9 and √16 and that √9=3 and that √16 is equal to √4, it can be concluded that the answer is in between 3 and 4.
The window shown is the shape of a semicircle with a radius of 6 feet. the distance from f to e is 3 feet and the measure of arc b c = 45°. find the area of the glass in region bcih, rounded to the nearest square foot. ft2
The area of the glass in the region BCIH, rounded to the nearest square foot is 11.
The radius of the semicircle is 6 feet and the distance from F to E is 3 feet. The measure of an arc is 45°.
What is the area of the sector?
First, the sector is the part of the circle made of the arc of the circle along with its radii. The area of the sector of a circle is represented by
The angle of the sector is 360°
The area of the circle [tex]\rm \pi r^{2}[/tex] and the angle is ∅
The area of the sector, [tex]\rm A= \frac{\Theta}{360} \times\pi r^{2}[/tex]
Here, the area of the glass in region BCIHis the difference between the area of the sector of region BCIGH and the region HIG.
The area of the region BCIH
[tex]\rm = \frac{\ 45}{360} \times\pi (6^{2} -3^{2} )[/tex]
[tex]\rm = \frac{\ 1}{8} \times\pi (27 )[/tex]
[tex]\rm = 10.5\; ft^{2}[/tex]
Hence, The area of the glass in the region BCIH, rounded to the nearest square foot is 11.
Learn more about the area of the sector here;
https://brainly.com/question/15849991
Answer:
11 ft2
Step-by-step explanation:
hope this helps
which is equivalent to 1/2 sin 30
Answer:
1/2
Step-by-step explanation:
Sin 30 degree equals to the fractional value of 1/ 2. In the same way, we can derive other values of sin degrees like 0°, 30°, 45°, 60°, 90°,180°, 270° and 360°.
Answer:Sin 30=1/2
Step-by-step explanation:
A vendor buys x kg of peanuts and kg of cashew nuts.
(a) To get a good bargain, she must buy a minimum of 10 kg of peanuts and a minimum of 5 kg of cashew nuts.
(i)Write TWO inequalities which satisfy these conditions.
(ii) She buys no more than 60 kg of nuts. Peanuts cost $4.00 per kg and cashew nuts cost $8.00 per kg and she spends at least $200.
Write Two inequalities which satisfy these conditions.
The inequalities that satisfy this condition is 4x + 8y ≥ 200 and x + y ≤ 60
What is an inequality?
An inequality is an expression that shows the non equal comparison between two or more numbers and variables.
Let x represent the number of peanuts and y represent the number of cashew nuts.
She must buy a minimum of 10 kg of peanuts and a minimum of 5 kg of cashew nuts. Hence:
x ≥ 10, y ≥5
Also:
x + y ≤ 60
And:
4x + 8y ≥ 200
The inequalities that satisfy this condition is 4x + 8y ≥ 200 and x + y ≤ 60
Find out more on inequality at: https://brainly.com/question/24372553
Find the slope of the line in the image below.
Solution:
It should be noted:
Slope = Rise/RunUsing the formula:
Slope = Rise/Run=> Rise = 1; Run = 2=> Slope = 1/2Correct option is A.
y = m x + b for a trend line that passes through the points (2, 18) and (–3, 8). Which value should he use as b in his equation
Answer:
b = 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 18 ) and (x₂, y₂ ) = (- 3, 8 )
m = [tex]\frac{8-18}{-3-2}[/tex] = [tex]\frac{-10}{-5}[/tex] = 2 , then
y = 2x + b
to find b substitute either of the 2 points into the equation
using (2, 18 )
18 = 4 + b ⇒ b = 18 - 4 = 14
The magnitude, M, of an earthquake is defined to be M = log StartFraction I Over S EndFraction, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a "standard" earthquake, which is barely detectable. What is the magnitude of an earthquake that is 1,000 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth. 2 3 2004. 5 6. 9.
Answer:
9
Step-by-step explanation:
1 / sec^2x + 1 / csc^2x = 1
I need help verifying the trig function with steps.
Step-by-step explanation:
answer is provided in picture
For a standard normal distribution, find the approximate value of p (z greater-than-or-equal-to negative 1.25). use the portion of the standard normal table below to help answer the question. z probability 0.00 0.5000 0.25 0.5987 1.00 0.8413 1.25 0.8944 1.50 0.9332 1.75 0.9599 11% 39% 61% 89%
For a standard normal distribution, the approximate value of p
( z≥-1.25 ) is 0.8945.
What is a standard normal distribution?The standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation.
As we know that Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
It is given that z-score≥-1.25
From the standard normal table, the p-value corresponding to z≥-1.25 is
0.8945.
Therefore, For a standard normal distribution, the approximate value of p ( z≥-1.25 ) is 0.8945.
To get more about standard normal distribution visit:
https://brainly.com/question/6758792
Answer:
89%
Step-by-step explanation:
To make it easy. Hope this helps
Find the Total surface area of a cone if it's slant height is 21m and diameter of it's base is 24m.
Don't Spam
1244.57 cm²
Step-by-step explanation:
Given:
Slant height (l) is 21m Diameter (d) is 24mHence, radius will be :
➝ diameter/2
➝ 24/2
➝ 12m
[tex] \: [/tex]
To Find:
Total Surface Area (TSA) of the cone.Solution:
As, we know:
[tex] \star \quad{ \underline{ \green{ \boxed{TSA_{(cone)} = \pi r( l+r ) }}}} \quad\star \quad[/tex]
Here,
π = 22/7 r = 12m l = 21m[tex] \rightarrow \: \frac{22}{7} \times 12 \: (21 + 12)[/tex]
[tex] \rightarrow \: \frac{22}{7} \times 12 \: (33)[/tex]
[tex]\rightarrow \: \frac{8712}{7} {cm}^{2} [/tex]
Therefore, Total Surface Area of Cone is 8712/7 cm² or 1244.57cm².
_____________________Additional Information:[tex]\footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}[/tex]
PLEASE HELP ASAP ILL GIVE BRAINLIEST IF YOU SHOW THE STEPS!! You have to look at the picture for the questions!!
Answer:
3. f = gh
4. r = 1/s³
5. y = x[tex]\sqrt{z}[/tex]
6. m = n²/p
7. Inverse variation, s is constant
8. Direct Variation, x is constant
9. joint variation, q and r are both constants
10. Direct variation, r is constant
11. Joint variation, r and h are both constants
12. Inverse variation, x is constant
13. y = kx
17.5 = 21k
k = 21/17.5
y= (21/17.5)*39
y = 46.8
14.
m = kn
209 = 22k
k = 209/22
361 = (209/22)n
n = (361*22)/209
n = 38
Given the circle with the equation (X - 32 + y2 = 49, determine the location of each point with respect to the graph of the
circle. In your final answer, state whether each point is on the Interior, exterior, or circumference of the circle. Include
your calculations as proof of each point's location.
A. (-1,1)
B. (10,0)
C. (4, -8)
Answer:
To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
Step-by-step explanation:
What is the distance between (4, −3) and (9, −3) ? Enter your answer in the box.
Answer:
5 units
Step-by-step explanation:
Luckily, we don't need to use the distance formula as we just need to find the distance between the x-coordinates. Thus, |4-9| = |-5| = 5, which means that the distance between (4,-3) and (9,-3) is 5 units
Answer:
5
Step-by-step explanation:
Point (4, -3) and point (9, -3) have the same y-coordinate of -3. Therefore, both points are on the line y = -3.
Any line that is y = {number} is a horizontal line.
Therefore, to find the distance between the points, find the difference between the x-values:
9 - 4 = 5
Therefore, the distance between (4, −3) and (9, −3) is 5
what is 4 2/3 × 6 7/10
Answer:
[tex]31 \frac{4}{15}[/tex]
Step-by-step explanation:
(convert the mixed numbers into improper fractions = [tex]a\frac{b}{c} = \frac{a*c+b}{c}[/tex] )
[tex]\frac{4*3+2}{3}*\frac{6*10+7}{10}[/tex]
Steps if needed:
4*3 = 12+2 =14
6*10=60+7=67
[tex]\frac{14}{3} *\frac{67}{10}=\frac{14*67}{3*10}[/tex]
= [tex]\frac{938}{30}[/tex]
Simplify: Divide by 2
[tex]\frac{469}{15}[/tex] || 938/2 = 469 30/2 = 15
Convert your answer to a mixed fraction
[tex]31\frac{4}{15}[/tex]
469/15 = 31.26....
15*31 = 465
465+4 = 469
So your answer is 31 4/15
Ahmad drew a blueprint of a rectangular garden. The blueprint is 7 inches long, and the actual garden is 56 inches long. How many times longer is the actual garden than Ahmad's blueprint?
Answer:
8 times longer
Step-by-step explanation:
The actual garden is 8 times the blueprint.
Reasoning? 56/7=8
How to check:
Use inverse operations:
7*8=56
Giving right answer branleist
Answer:
Slope is -0.6, hope this helps
what is -12/5+|- 13/6| + (-3 2/3)
Answer: -39/10 alternative forms : -3 9/10, -3.9
Step-by-step explanation:
What is the LMC of 26 and 32
Answer:
The LCM of 26 and 32 is 416.
Please answer as soon as possible, and show all work. Thank you.
Answer:
[tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
Expanding/FactoringCalculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationThe definition of a derivative is the slope of the tangent line: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle f(x) = -4x^3 + 2x^2[/tex]
Step 2: Differentiate
[Function] Substitute in x: [tex]\displaystyle f(x + h) = -4(x + h)^3 + 2(x + h)^2[/tex]Substitute in functions [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-4(x + h)^3 + 2(x + h)^2 - \big( -4x^3 + 2x^2 \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{-12hx^2 - 12h^2x + 4hx - 4h^3 + 2h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h \big( -12x^2 - 12hx + 4x - 4h^2 + 2h \big)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} -12x^2 - 12hx + 4x - 4h^2 + 2h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = -12x^2 - 12(0)x + 4x - 4(0)^2 + 2(0)[/tex]Simplify: [tex]\displaystyle f'(x) = -12x^2 + 4x[/tex]∴ the derivative of the given function will be equal to -12x² + 4x.
---
Learn more about derivatives: https://brainly.com/question/25804880
Learn more about calculus: https://brainly.com/question/23558817
---
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What can you take away from 800 to make 500?
Answer:
it would be 800-300 =500.
Leslie is saving for a new $500 iPad. She currently has $125. If she saves $15 per week, how long must she wait to save at least $600 to cover tax and extras? Let x represent the number of weeks
Answer:
x=31.66
Step-by-step explanation:
1st i did 600-125=475
so now i have to do 475 divided by 15
that is 31.66
so she has to wait 31.66 weeks to get the $475 dollars she needs
7. Find the area of the figure.
Is it right??
Answer:
28.5 units²
Step-by-step explanation:
You are correct.
You divided the figure into a square, a rectangle and a triangle.
You can also just divide into a rectangle and a triangle as I did below, and there are other ways of dividing the figure to find the area.
Bottom rectangle: 8 units by 3 units
Top triangle: base = height = 3 units
total area = area of rectangle + area of triangle
total area = length × width + base × height / 2
total area = 8 units × 3 units + 3 units × 3 units / 2
total area = 24 units² + 4.5 units²
total area = 28.5 units²
5 3/7 x 3 1/2 pls help me bc iwill get trouble
Answer:
19
Step-by-step explanation:
What is half of a hundred?
Answer:
50
Step-by-step explanation:
What constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles? x2 8x
The constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.
What is a perfect square trinomial?A perfect square trinomial is an algebraic statement with three terms of the type ax²+bx+c. It is calculated by multiplying a binomial with itself.
For the given trinomial to be a perfect square trinomial, the value of the constant term should be such that the value of the term expression must be similar to (a+b)². Therefore,
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]=x^2+8x+16[/tex]
Now, if we compare the two equations we will understand that the first term of the perfect square trinomial is x, and thus, the last term should 16.
[tex](x+4)^2=x^2+8x+16[/tex]
Hence, the constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.
Learn more about Perfect Square Trinomial:
https://brainly.com/question/88561
16 is the constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles will be (x + 4).
What is a perfect square?
A perfect square is a number that may be written as the product of two integers or as the integer's second exponent.
The perfect square obtained from the given equation is (x + 4).;
On squaring we get;
[tex](x + 4)^2 = x^2 + 8x + 16.[/tex]
16 is the only constant term in the equation.
Hence 16 is the constant term that is necessary to complete the perfect square.
To learn more about the perfect square refer to the link;
https://brainly.com/question/385286