Answer:
Step-by-step explanation:
The length of the ladder is the length of the hypotenuse of the right triangle formed. Since the height up the building is based on the distance the ladder is from the base of the building, and that distance is x, then the height up the building is x + 7. So what we have is a right triangle with one leg measuring x, the other leg measuring x + 7, and the hypotenuse measuring 13. Set up using Pythagorean's Theorem:
[tex]13^2=(x+7)^2+x^2[/tex] and do some simplifying. The left side is easy since 13-squared is 169; the right side not so much. We first have to expand that set of parenthesis by multiplying x + 7 by itself twice to get a second degree polynomial:
[tex](x+7)(x+7)=x^2+14x+49[/tex] and now we have:
[tex]169=x^2+14x+49+x^2[/tex] which simplifies down a bit to
[tex]169=2x^2+14x+49[/tex]
The only way to solve this for x, the height up the side of the building, is to factor. In order to do that, everything has to be on one side of the equals sign, setting the whole messy thing equal to 0:
[tex]2x^2+14x+49-169=0[/tex] and
[tex]2x^2+14x-120=0[/tex]. Begin by factoring out a 2:
[tex]2(x^2+7x-60)=0[/tex] and then factor the remaining quadratic using whatever method you are currently using in class to solve for x. Doing this will give that
x = -12 and 5. Since a side length will never be negative, we determine that x = 5 which is the distance between the bases of the buildings, and the height up the building where the ladder hits it is 12.
Complete the square for the function y = x2 + 6x +7. Which features are correctly stated?
A)
Axis of symmetry at x = -2
B)
Minimum = -2 at x = -3
Vertex form: (x + 3)2 - 2
D)
Zero at x = = √2-3
E)
Zero at x = 3-VE
Answer:
B and C
Step-by-step explanation:
The square for the function; [tex]y = x^2 + 6x +7[/tex] . Hence, the Vertex form of the function is [tex](x + 3)^2 - 2[/tex]. The function will be zero at x = 3- √E
What is a system of equations?A system of equations is two or more equations that can be solved to
get a unique solution. the power of the equation must be in one degree.
The square for the function;
[tex]y = x^2 + 6x +7[/tex]
Minimum = -2 at x = -3
Hence, the Vertex form of the function is [tex](x + 3)^2 - 2[/tex].
The function will be zero at x = 3- √E
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Jara quiere fabricar un cohete con cartulina. Para ello ha construido un cilindro de 0,25 metros de radio y medio metro de altura y un cono con el mismo radio y la mitad de la altura. ¿Que volumen ocupa su cohete? Ayudaaa
Respuesta:
0,114 m³
Explicación:
El volumen del cohete será igual a la suma de los volumenes del cilindro y del cono
Volumen del cilindro
El cilindro tiene un radio (r) de 0,25 m y una altura (h) de 0,5 m. Podemos encontrar su volumen usando la siguiente formula.
Vcil = π × r² × h
Vcil = π × (0,25 m)² × 0,5 m = 0,098 m³
Volumen del cono
El cono tiene un radio (r) de 0,25 m y una altura (h) de 0,25 m (la mitad de 0,5 m). Podemos encontrar su volumen usando la siguiente formula.
Vcono = 1/3 × π × r² × h
Vcono = 1/3 × π × (0,25 m)² × 0,25 m = 0,016 m³
Volumen del cohete
Vcohete = Vcil + Vcono = 0,098 m³ + 0,016 m³ = 0,114 m³
Lara charges $12 per hour for babysitting. If f represents Lara's total fee after babysitting for h hours, which answer choice shows two correct equations that could be used to model the problem?
A: f=112handh=12f
B: h=112fandf=12h
C: f=h+12andh=f−12
D: h=f+12andf=h−12
Answer:
Can't really read that but these would work
f = 12h
h = f/12
Step-by-step explanation:
3. At a manufacturing plant, it is known that 8% of the computer chips produced are defective. A random sample of 20 chips is taken.
What is the probability that 3 of those chips are defective?
.
Answer:
Probability of three chip being defective is 0.012
Step-by-step explanation:
Probability of a computer chip being defective is 0.08 or 8%
Total random sample = 20
Probability of three chip being defective = 3/20 * 0.08
= 0.012
Answer:
B) 0.14
Step-by-step explanation:
N=20
K=3
P=0.08
CoE= 1140
1140 x (0.08)^3 x (.92)^17
1140 x (0.000512) x (0.2423) = 0.141425 or B
10 A triangular prism and its dimensions are shown in the diagram.
5 cm
5 cm
8 cm
6 cm
What is the lateral surface area of this triangular prism in square centimeters?
Two searchlights on the shore of a lake are located 3020 yd apart. A ship in distress is spotted from each searchlight. The beam from the first searchlight makes an angle of 38 degrees with the baseline. The beam from the second light makes an angle of 57 degrees with the baseline. Find the ship's distance from each searchlight.
Answer:
x₁ = 1866.2 yd distance between ship and searchlight in C
x₂ = 2542.5 yd . distance between ship and searchlight in B
Step-by-step explanation:
The ship (point A) and the two searchlights points ( B and C) shape a triangle.
We have α = 38° ( opposite side x₁ or distance between ship and point C and β = 57 ° ( opposite side x₂ or distance between ship and point B then γ = 180 - ( α + β )
γ = 85°
Applying sin´slaw
x₁ / sin 38 = x₂/ sin57 = 3020 / sin 85
from sin table we find:
sin 38 = 0.6156
sin 57 = 0.8387
sin 85 = 0.9962
Then
x₁ / 0.6156 = 3020 / 0.9962
x₁ ( the opposite side to angle 38° ) / 0.6156 = 3031.5
x₁ = 3031.5*0.6156
x₁ = 1866.2 yd
x₂ = 3031.5 * 0.8387
x₂ = 2542.5 yd
40:√100 + √9.√36
????
Answer:
28
Step-by-step explanation:
[tex]\sqrt{100} + (\sqrt{9} \cdot \sqrt{36}) = 10 + (3 \cdot 6) = 10 + 18 = 28[/tex]
Help me with this below
Answer:
PlayStation = 175
Step-by-step explanation:
X box = x
PlayStation = x+15
X box + PlayStation = 335
x + x+15 = 335
Combine like terms
2x+15 = 335
Subtract 15
2x+15 -15 = 335-15
2x = 320
Divide by 2
2x/2=320/2
x =160
x box =160
PlayStation = x+15 = 160+15= 175
Answer:
Playstation costs 175 pounds
Step-by-step explanation:
335 = 15 + x + x
335 = 15 + 2x
335 - 15 = (15 - 15) + 2x
320 = 2x
320/2 = 2x/2
x = 160
CHECK WORK:
(15 + 160) + 160 = 335
(175) + 160 = 335
335 = 335
what is 5¹? and just what does ¹ mean? like whats the formula for the equation?
Answer:the answer is 5 it means you mutiply five that many times
Step-by-step explanation:
Answer:
5¹=5
5¹ means that you multiply 5 by itself 1 times
Maria put 18 crayons in 3 different baskets. She put the number of crayons in each basket.
How many crayons did Maria put in each basket?
Answer:
There are 18 crayons, and 3 baskets. Each basket has the same number of crayons. Therefore, we divide 18 into 3 different groups (each group = each basket). So, we have 18 ÷ 3, which is 6.
So, there are 6 crayons in each basket.
Answer:
6
Step-by-step explanation:
You have a cooking triangle at your camp. It makes great
hot dogs on a camp fire. The triangle has an area of 14
square feet. The height is four feet. What is the length of the
base?
Answer:
7 square feet
Step-by-step explanation:
We know that area is (h*b / 2)
Therefore, we find b:
(14 * 2) / 4 = 7
Please give brainliest
PLEASE HELP ASAP WILL GIVE POINTS AND BRAINLIEST! TY BESTIES! Factor using GCF 20x^2+10x please show work
Answer:
10x(2x+1)
Step-by-step explanation:
20x^2+10x
2*10*x*x + 10 *x
Factor out the common terms
10x(2x+1)
The cylinder is 40 feet tall and has a radius of 20 feet. The cone is 10 feet tall with the same radius. Approximately how many cubic feet of grain can fit in the silo?
Answer:
54461.33 cubic feet
Step-by-step explanation:
Given data
Height of cylinder= 40 feet
Radius= 20feet
Height of cone= 10 feet
Radius of cone= 20feet
Volume of Cylinder= πr^2h
Volume of Cylinder= 3.142*20^2*40
Volume of Cylinder= 3.142*400*40
Volume of Cylinder= 50272 cubic feet
Volume of Cone= 1/3πr^2h
Volume of Cylinder= 1/3*3.142*20^2*10
Volume of Cylinder= 1/3*3.142*400*10
Volume of Cylinder= 1/3*12568
Volume of Cylinder=4189.33 cubic feet
Hence, the volume of the silo = volume of cylinder+ volume of cone
Volume of silo= 50272+4189.33
Volume of silo=54461.33 cubic feet
find the zeros the polynomial fx=2x^2 +9x-5
Answer:
The zeros the polynomial :
X=(1/2 , –5)
a sequence of transformation is applied to a polygon. Select all statements which indicate a sequence of transformations where the resulting a polygon has an area greater than the original polygon.
A. Translate even units left, rotate 90 degrees clockwise about the origin.
B. Reflect over the x-axis, dilate about the origin by a scale factor of 1/2 translate up 5 unit.
C. Rotate 90 degrees counterclockwise around the origin, dilate about the origin by a scale factor of 3/2
D. Dilate about the origin by a scale factor of 2/3. rotate 180 degrees clockwise around the origin, translate down 2 units.
E. Dilate about the origin by a scale factor of 2, reflect over the y-axis, dilate about the origin by a scale factor of 2/3
Answer:
than originally shared this meeting will
b) 6a and 6b are having a competition to see who can make the most money for Red Crescent. 6a make $2 for every $3 that 6b make. If 6a makes $30 AED profit how much will 6b make?
Answer:
45
Step-by-step explanation:
6a 6b
2 / 3
30 / x
30×3 / 2
90/2
=45
what is the sum of the first 6 odd numbers?
A. 26
B. 36
C. 32
D. 42
PLEASE HELP ( 10 PIONTS & FRIEND) :)
∠A and angle ∠B are vertical angles. If m∠ A=(2x-4) and ∠B = (x+1), then find the value of x
Answer:
x = 5
Step-by-step explanation:
vertical angles are equal so we can write this equation:
2x-4 = x+1
x - 4 = 1
x = 5
Greatest common factor of 8,56
Answer:
Propiedades del MCM de 8 y 56
Resumiendo, el mcm de 8 y 56 es 56. Se escribe como: mcm (8,56) = 56
Step-by-step explanation:
On selling an article for Rs 2300, a shopkeeper made a profit of 15 %. find the cost price of the article.
Answer:
Step-by-step explanation:
Sp of an article= Rs 2300
profit%=15%
let Cost Price of an article be X
SP=CP+PROFIT %*CP
2300=X+15/100*X
2300=100X+15X/100
2300*100=115X
230000/115=X
2000=X
Therefore cost price of an article is Rs 2000.
A teacher asked four students to estimate the length of a grain of rice. Jack answered 4.5 x 10^-3 kilometer, Lilly answered 4.5 x 10^-3meter, Diego answered 4.5 x 10^-3vcentimeter, and Willa answered 4.5 x 10^-3 millimeter. Who gave the best answer
Answer:
Lilly
Step-by-step explanation:
According to the literature, the length of a medium grain rice is between 5.3 and 5.9 mm. Let's take the average (5.6 mm) and convert it to meters to compare it with the estimations. We will use the conversion factor 1 m = 1000 mm.
5.6 mm × 1 m/1000 mm = 5.6 × 10⁻³ m
Jack answered 4.5 × 10⁻³ kilometers. We will convert it to meters using the conversion factor 1 km = 1000 m.
4.5 × 10⁻³ km × 1000 m/1 km = 4.5 m
Lilly answered 4.5 × 10⁻³ meters.
Diego answered 4.5 × 10⁻³ centimeters. We will convert it to meters using the conversion factor 1 m = 100 cm.
4.5 × 10⁻³ cm × 1 m/100 cm = 4.5 × 10⁻⁵ m
Willa answered 4.5 × 10⁻³ millimeters. We will convert it to meters using the conversion factor 1 m = 1000 mm.
4.5 × 10⁻³ mm × 1 m/1000 mm = 4.5 × 10⁻⁶ m
As we can see, Lilly gave the best answer (same order of magnitude).
PLS HELP
AND PLEASE EXPLAIN
Answer:
x=6, y=5 1/3 or 5.3333
Step-by-step explanation:
Austin is baking a pie in a pan that has a diameter of 8 inches. He wants to cover the top of the pie with a pie crust. What is the area of the crust that will cover the top of the pie?
The area of the crust that will cover the top of the pie is 50.24 square inches.
What is a circle?
A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.
For the given situation,
The baking pan is in the shape of a circle.
The diameter of a baking pan = 8 inches
So, the radius of a baking pan,r = [tex]\frac{diameter}{2}[/tex]
⇒ [tex]r=\frac{8}{2}[/tex]
⇒ [tex]r=4[/tex]
The area of the crust that will cover the top of the pie is
[tex]A=\pi r^{2}[/tex]
we know that the value of π is 3.14.
On substitute the above values,
⇒ [tex]A=(3.14)(4)^{2}[/tex]
⇒ [tex]A=(3.14)(16)[/tex]
⇒ [tex]A=50.24[/tex]
Hence we can conclude that the area of the crust that will cover the top of the pie is 50.24 square inches.
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An SRS of 100 flights by Nite-flite Airlines showed that 64 were on time. An SRS of 100 flights by Waxwing Airlines showed that 80 were on time. Let pN be the proportion of on-time flights for all Niteflite Airline flights, and let pW be the proportion of all on-time flights for all Waxwing Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines
Answer:
Step-by-step explanation:
pN = 64/100 = 0,64 = 64%
pW = 80/100 = 0,8 = 80%
The planes of Waxwing airlines are more punctual
Which number is greater than 555,621,000?
A. 5.0 x 10
B. 6.2 x 10
C. 5.55621 x 10
D. 9.99 x 10
Answer:
D
Step-by-step explanation:
im smart.
He sum of two numbers is negative twelve, and one number is five less than the other. Using the variables mm and nn to represent the two numbers, write a system of equations that describe the situation. Enter the equations below, separated by a comma.
Answer:
mm + nn = -12
mm - nn = 5
Step-by-step explanation:
two equations can be derived from the question
would it be B or C? help me please :(
Answer:
2x^2
Step-by-step explanation:
2x+x
3x
x(2+1)
2x+x
3x
2x^2(no equivalent to other option)
3x
i need help!! im struggling with this question
Answer:
1 gallon : 25.6 miles
Step-by-step explanation:
So, the way we can find the rate, or ratio between 2 units is to divide one unit by the other unit.
So basically, we see the first set of units is:
2 gallons - 51.2 miles
So basically, for every 2 gallons, there are 51.2 miles.
To find the ratio, or rate, we must find the miles per gallon.
We can do that by dividing both sides by 2:(g=gallons, m=miles)
2g/2=51.2/2m
=
g=25.6
So for every gallon, there is 25.6 miles.
We can write this as:
1 : 25.6
Hope this helps!
Answer:
25.6
Step-by-step explanation:
51.2/2=25.6
Please help me, this is like the easiest thing but I'm stuck
Answer: A. 384 sq. mm
Step-by-step explanation: The area for the square is 12x12 or 144. The area for a triangle is base x height x 1/2. Therefore, that would be 12 x 10 x 1/2 or 60. There are 4 sides to this pyramid, so 60 x 4 = 240. We then add 144 and 240 to get 384 sq. mm.
A researcher conducts an independent-measures, two-factor study with two levels of factor A and three levels of factor B, using a separate sample of n = 10 participants in each treatment condition. What are the df values for the F-ratio evaluating the main effect of factor A? (Hint: Enter in the degrees of freedom for the numerator first and the degrees of freedom for the denominator second.)
Answer:
(1, 36)
Step-by-step explanation:
Degrees of freedom for the F-test of the two way ANOVA
Here, we use a two factors, independent measures ANOVA, where, factor [tex]A[/tex] has 2 level and a factor [tex]B[/tex] also has 2 levels.
So, here,
[tex]$k_1$[/tex] = number of levels of A = 2
[tex]k_2[/tex] = number of levels of B = 2
And n = sample size in each treatment condition = 10
So we have,
[tex]d_1[/tex] = df of the main effect A = ([tex]$k_1$[/tex] - 1) = 2 - 1 = 1
[tex]d_2[/tex] = df of the main effect A = ([tex]$k_2$[/tex] - 1) = 2 - 1 = 1
[tex]d_3[/tex] = df of interaction effect (A x B) = ([tex]$k_1$[/tex] - 1)([tex]$k_2$[/tex] - 1)
= (2-1)(2-1)
= 1
And [tex]d_4[/tex] = df of within variation (i.e. error variation) = [tex]$k_1k_2(n-1)$[/tex]
= 2 x 2 x (10 - 1)
= 36
So, the df value for the F-ratio evaluating the main effect of factors-A is
= ([tex]d_1, d_4[/tex])
= (1, 36)